Determine if the
following equation
represents a function:
y = 1/3x – 4

Determine If Thefollowing Equationrepresents A Function:y = 1/3x 4

Answers

Answer 1

Answer:

Function

Step-by-step explanation:

y = 1/3 x - 4

Is a function because for every x, we will get only one value of y.

Answer 2

Answer:

Yes,is a function

We can obtain the points (0,-4)(6,-2)

I hope this help you :)......  


Related Questions

hey guys, can you help me please​

Answers

Answer: 93.382 square cm

=========================================================

Work Shown:

The green triangle in the back has height 2.6 and an unknown base x. Half of this is x/2, which I'll call y. So y = x/2.

The green triangle in the back is split along the vertical dotted line to get two right triangles. The base of each right triangle is y = x/2.

Use the Pythagorean theorem to find y. Use that to find x

a^2+b^2 = c^2

y^2+(2.6)^2 = (3.2)^2

y^2 + 6.76 = 10.24

y^2 = 10.24 - 6.76

y^2 = 3.48

y = sqrt(3.48) .... apply square root

y = 1.8654758 approximately

x/2 = 1.8654758

x = 2*1.8654758

x = 3.7309516 also approximate

The base of the triangle is roughly 3.7309516 meters

We can now find the area of one green triangle

area of triangle = base*height/2 = 3.7309516*2.6/2 = 4.85023708

two triangles have approximate area 2*(4.85023708) = 9.70047416

----------------------------------

So far we've only considered the triangular faces. There are 3 more faces which are the rectangular sides. These are known as the lateral sides.

One way to get the lateral surface area is to multiply the perimeter of the triangle by the depth of the prism

perimeter of triangle = (side1)+(side2)+(side3)

perimeter = 3.7309516 + 3.2 + 3.2

perimeter = 10.1309516

lateral surface area = (depth)*(perimeter)

lateral surface area = (8.26)*(10.1309516)

lateral surface area = 83.681660216

----------------------------------

The last step is to add this lateral surface area onto the area of the two triangles to get the full surface area

surface area = (triangular area) + (lateral surface area)

surface area = (9.70047416) + (83.681660216)

surface area = 93.382134376

surface area = 93.382 square cm

ANswer
93.382 square mtrs

Importance of Index Number ​

Answers

Answer:

Index numbers are intended to measure the degree of economic changes over time. These numbers are values stated as a percentage of a single base figure. Index numbers are important in economic statistics. ... Index numbers are intended to study the change in the effects of such factors which cannot be measured directly.

Answer:Index numbers are important in economic statistics. In simple terms, an index (or index number) is a number displaying the level of a variable relative to its level (set equal to 100) in a given base period. Index numbers are intended to study the change in the effects of such factors which cannot be measured directly.

Step-by-step explanation:

Connecticut families were asked how much they spent weekly on groceries. Using the following data, construct and interpret a 95% confidence interval for the population mean amount spent on groceries (in dollars) by Connecticut families. Assume the data come from a normal distribution
210 23 350 112 27 175 275 50 95 450

Answers

Answer:

The 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

Step-by-step explanation:

The data for the amount of money spent weekly on groceries is as follows:

S = {210, 23, 350, 112, 27, 175, 275, 50, 95, 450}

n = 10

Compute the sample mean and sample standard deviation:

[tex]\bar x =\frac{1}{n}\cdot\sum X=\frac{ 1767 }{ 10 }= 176.7[/tex]

[tex]s= \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} } = \sqrt{ \frac{ 188448.1 }{ 10 - 1} } \approx 144.702[/tex]

It is assumed that the data come from a normal distribution.

Since the population standard deviation is not known, use a t confidence interval.

The critical value of t for 95% confidence level and degrees of freedom = n - 1 = 10 - 1 = 9 is:

[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, (10-1)}=t_{0.025, 9}=2.262[/tex]

*Use a t-table.

Compute the 95% confidence interval for the population mean amount spent on groceries by Connecticut families as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}[/tex]

     [tex]=176.7\pm 2.262\cdot\ \frac{144.702}{\sqrt{10}}\\\\=176.7\pm 103.5064\\\\=(73.1936, 280.2064)\\\\\approx (73.20, 280.21)[/tex]

Thus, the 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

A circular swimming pool has a diameter of 20 ft, the sides are 6 ft high, and the depth of the water is 5 ft. How much work (in ft-lb) is required to pump all of the water out over the side

Answers

Answer:

19467649.76 lb-ft^2/s^2

Step-by-step explanation:

diameter of the pool d = 20 ft

radius = d/2 = 20/2 = 10 ft

height of pool side h = 6 ft

depth of water d = 5 ft

the force on the bottom of the pool due to the water in the pool is

F = pgdA

where p = density of water = 62.4 lb/ft^3

g = acceleration due to gravity = 32.17 ft/s^2

Area A = [tex]\pi r^{2}[/tex] = [tex]3.142 * 10^{2}[/tex] = 314.2 ft^2

Force on pool bottom = 64.2 x 32.17 x 5 x 314.2 = 3244608.29 lb-ft/s^2

work done = force times the height the water will be pumped

work = F x h = 3244608.29 x 6 = 19467649.76 lb-ft^2/s^2

The work (in ft-lb) is required to pump all of the water out over the side is :

Given :Diameter of the pool d = 20 ftRadius = d/2 = 20/2 = 10 ftHeight of pool side h = 6 ftDepth of water d = 5 ft

Formula:

F = pgdA

p = density of water = 62.4 lb/ft^3

g = acceleration due to gravity = 32.17 ft/s^2

Area A = [tex]\pi r2\\[/tex] = 314.2 ft^2

Force on pool bottom = 64.2 x 32.17 x 5 x 314.2 = 3244608.29 lb-ft/s^2work done = force times the height the water will be pumpedwork = F x h = 3244608.29 x 6 = 19467649.76 lb-ft^2/s^2

The work (in ft-lb) is required to pump all of the water out over the side is 19467649.76 lb-ft^2/s^2.

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What type of error is present in the underlined


sentence?


Which is the best revision to fix the error?

Answers

Answer:

Type of error: Run-on(comma splice).

Best revision to fix it: Adding a semicolon after beginners .

Explanation:

A run-on sentence is described as a sentence in which two independent clauses are joined inappropriately. It could be either comma splice where the two independent clauses are incorrectly linked using a comma or fused sentence when the two clauses run-on without employing appropriate coordinating conjunction or punctuation marks to separate the two ideas.

In the given sentence, it exemplifies a comma splice type of run-on sentence error. To fix this error, a semicolon after 'beginners' can be employed instead of a comma. This will help in connecting the two ideas appropriately where the first idea leads the second. Thus, the final sentence reads as:

'The guitar is another excellent instrument for beginners; however, it takes more practice than a recorder.'

Answer:

Many people play a musical instrument music can be soothing. A lot of schools teach the recorder; it is inexpensive and easy to play. The guitar is another excellent instrument for beginners, it takes more practice than a recorder.

What type of error is present in the underlined sentence?

✔ run-on

Which is the best revision to fix the error?

✔ adding a semicolon after instrument

Step-by-step explanation:

P(AB) can be read as "the probability that A occurs given that Bhas
occurred."
A. True
B. False

Answers

Answer:

False

Step-by-step explanation:

from *millermoldwarp*

"Events are called dependent when the probability of an event depends on the occurrence of another. When event A depends on event B, the probability that A occurs, given that B has occurred, is different from the probability that A occurs only ."

hopes this helps

Answer:false

Step-by-step explanation:

In the figure, if the measure of 28 = 72°, what's the measure of 214?

Answers

Answer:

72°

Step-by-step explanation:

Angle 8 and angle 14 are corresponding angles.

∠8=∠14

72=∠14

Tyler drew a figure that has two pairs of equal sides, four angles formed by perpendicular lines, and two pairs of parallel sides. What geometric term best describes the figure Tyler drew? What geometric term best describes the figure Tyler drew?

Answers

Answer:

A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.

A cooler has a temperature of 32 degrees Fahrenheit. A bottled drink is placed in the cooler with an initial temperature of
70 degrees Fahrenheit. The function
[tex]f(t) = {ce}^{ (- kt)} + 32[/tex]
,represents the situation, where t is time in minutes, C is a
constant, and k is a constant.
After 3 minutes the bottle has a temperature of 42 degrees. What is the approximate value of k?​

Answers

Answer:

[tex]k \approx 0.44[/tex]

Step-by-step explanation:

Given function:

[tex]f(t) = (ce)^{-kt}+32[/tex]

As per question statement:

Initial temperature of bottle is 70 [tex]^\circ F[/tex].

i.e. when time = 0 minutes, f(t) = 70 [tex]^\circ F[/tex]

[tex]70 = ce^{-k\times 0}+32\\\Rightarrow 38 = ce^{0}\\\Rightarrow c = 38[/tex]

After t = 3, f(t) = 42[tex]^\circ F[/tex]

[tex]42 = 38 \times e^{-k\times 3}+32\\\Rightarrow 42-32 = 38 \times e^{-3k} \\\Rightarrow 10 = 38 \times e^{-3k} \\\Rightarrow e^{3k} = \dfrac{38}{10}\\\Rightarrow e^{3k} = 3.8\\\\\text{Taking } log_e \text{both the sides:}\\\\\Rightarrow log_e {e^3k} = log_e {3.8}\\\Rightarrow 3k \times log_ee=log_e {3.8} (\because log_pq^r=r \times log_pq)\\\Rightarrow 3k \times 1=log_e {3.8}\\\Rightarrow 3k = 1.34\\\Rightarrow k = \dfrac{1.34}{3}\\\Rightarrow k \approx 0.44[/tex]

Hence, the value is:

[tex]k \approx 0.44[/tex]

If the denominator of 5/9 is increased by a number and the numerator is doubled, the result is 1. Find the number.

Answers

Answer: 1

Explanation:

The numerator is doubled, so the fractions looks like 10/9. To make it one, it must be 10/10 and 9+1=10

◇Given :-

The denominator of a fraction is increased by a number and numerator will be doubled

To find

We have to find the required number or fraction

[tex]\underline{\bigstar{\sf\ \ Solution:-}}[/tex]

Now let us consided as the number be a

Then

[tex]\underline{\bigstar{\textit\ According\ to \ Question:-}}[/tex]

The given fraction is 5/9

[tex]:\implies\sf \dfrac{5\times 2}{9+a}= 1\\ \\ \\ :\implies\sf \dfrac{10}{9+a}=1\\ \\ \\ :\implies\sf 10= 1(9+a)\\ \\ \\ :\implies\sf 10-9=a\\ \\ \\ :\implies\sf 1=a [/tex]

[tex]\underline{\therefore{\textit{\textbf { The \ required \ number \ is \ 1}}}}[/tex]

An article discussed how anger intensity in children's tantrums could be related to tantrum duration as well as behavioral indicators such as shouting, stamping, and pushing or pulling. The following frequency distribution was given:0-<2: 136 2- <4: 92 4-<11: 7211-<20 26 20-<30 7 30-<40: 3Required:Draw the histogram and then comment on any interesting features.

Answers

Answer:

Increase in age is indirectly proportional to anger intensity in children's tantrums

Step-by-step explanation:

Let's begin by reproducing the given information into a frequency distribution table (shown below):

Age Group   Frequency

   0 - <2              136

   2 - <4              92

   4 - <11              72

   11 - <20           26

   20 - <30          7

   30 - <40          3

Observing the dataset above, we will see a trend; increase in age is inversely proportional to anger intensity. Kindly note that the histogram is attached as a picture.

Analysis of Histogram

Age group 1 (infants) have the highest indices of anger intensity in tantrums. This is expected because they do not know much yet and have an entitlement mentality.

Age group 2 (infants) also have a pretty high amount of anger intensity in children tantrums. They have transitioned from infancy but are yet immature & can easily flare up when disgruntled.

Age group 3 (children) are not far off from the previous age bracket, also having a significantly fairly high anger intensity. They are advancing in years & as they do, their emotional rage to tantrums is reducing.

Age group 4 (pre-teens/teens) experience a significant and drastic drop in emotional rage due to children's tantrums. They are maturing and are learning to communicate in less fitful ways. They now know better than to express their displeasure like infants.

Age group 5 (youths) also see a drastic drop in such anger intensity. The reason is not far-fetched; they are more mature and can express their displeasure in more mature ways.

Age group 6 (Adults) almost have almost a zero or non-existent such attitude among them. At this point, they have come to understand & know that they can get much more done with words than such outlandish methods.

In conclusion, as a child advances in years (changing from one age group to another → from infant to adult), their anger intensity takes a nosedive. We rightly interpret the histogram when we say that physical maturity is inversely proportional to anger intensity in children's tantrums.

How many pairs are shown ?????????

Answers

Answer:8 i ithink

Step-by-step explanation:

Answer:

12, go for 24.

Step-by-step explanation:

There are 6 sides of a cube.

There are 2 pairs of parallel line segments for each side.

6 x 2 = 12

Although that answer is not there, you should go for 24. Since there are 2 variables for each line segment, 12 x 2 = 24. Not sure, hope this helps.

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Which leader was a member of the Kikuyu tribe?

A. Kwame Nkrumah

B. Marcus Garvey

C. Mohandas Gandhi

D. Jomo Kenyatta

Answers

Answer:

Jomo Kenyatta

Step-by-step explanation:

Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.

Answer:

Jomo Kenyatta

Step-by-step explanation:

took the test

The manager of a warehouse would like to know how many errors are made when a product’s serial number is read by a bar-code reader. Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.


Just to be sure, the manager has six more samples taken:


33, 45, 34, 17, 1, and 29 errors, per 1,000 scans each


How do the mean and standard deviation change, based on all 12 samples?

Answers

Answer:

The mean and standard deviation changed to 23.5 and 14.62 respectively, based on all 12 samples.

Step-by-step explanation:

We are given that the Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.

Representing the data in tabular form;

           X                            [tex]X - \bar X[/tex]                            [tex](X - \bar X)^{2}[/tex]

          36                     36 - 20.5 = 15.5                   240.25

          14                      14 - 20.5 = -6.5                     42.25  

          21                       21 - 20.5 = 0.5                      0.25

          39                      39 - 20.5 = 18.5                   342.25

           11                        11 - 20.5 = -9.5                     90.25

           2                         2 - 20.5 = -18.5                  342.25    

        Total                                                                 1057.5      

Now, the mean of these value is given by;

        Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                         =  [tex]\frac{36+14+21+39+11+2}{6}[/tex]

                         =  [tex]\frac{123}{6}[/tex]  =  20.5

Standard deviation formula for discrete distribution is given by;

           Standard deviation, [tex]\sigma[/tex]  =  [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]

                                                 =  [tex]\sqrt{\frac{1057.5 }{6-1} }[/tex] = 14.54

Now, the manager has six more samples taken:

33, 45, 34, 17, 1, and 29 errors, per 1,000 scans each

So, the modified table would be;

           X                            [tex]X - \bar X[/tex]                            [tex](X - \bar X)^{2}[/tex]

          36                     36 - 23.5 = 12.5                   156.25

          14                      14 - 23.5 = -9.5                     90.25  

          21                       21 - 23.5 = -2.5                     6.25

          39                      39 - 23.5 = 15.5                   240.25

           11                        11 - 23.5 = -12.5                   156.25

           2                         2 - 23.5 = -21.5                   462.25    

          33                       33 - 23.5 = 9.5                     90.25

         45                        45 - 23.5 = 21.5                   462.25

         34                        34 - 23.5 = 10.5                   110.25

          17                         17 - 23.5 = -6.5                    42.25

           1                           1 - 23.5 = -22.5                   506.25

          29                        29 - 23.5 = 5.5                   30.25      

        Total                                                                    2353      

Now, the mean of these value is given by;

        Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                         =  [tex]\frac{36+14+21+39+11+2+33+45+34+17+1+29}{12}[/tex]

                         =  [tex]\frac{282}{12}[/tex]  =  23.5

Standard deviation formula for discrete distribution is given by;

           Standard deviation, [tex]\sigma[/tex]  =  [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]

                                                 =  [tex]\sqrt{\frac{2353 }{12-1} }[/tex] = 14.62

Adult male heights are a normal random variable with mean 69 inches and a standard deviation of 3 inches. Find the height, to the nearest inch, for which only 8 percent of adult males are taller (i. find the 92nd percentile)

Answers

Answer:

The height (corresponding to the [tex] \\ 92^{nd}[/tex] percentile) is (to the nearest inch) 73 inches (and, approximately, only 8% of adult males are taller than this height.)

Step-by-step explanation:

Roughly speaking, the [tex] \\ 92^{nd}[/tex] percentile is the x value (in the distribution) for which 92% of the observations in the [normal] distribution are below this x value, and 8% of the observations are above this x value.

To answer this question, we already know that:

Heights are a normal random variable, i.e, it follows a normal distribution.The mean for this distribution is [tex] \\ \mu = 69[/tex] inches.The standard deviation is [tex] \\ \sigma = 3[/tex] inches.

Strategy for solving the question

For solving this, we have to use here the following key concepts: z-scores, the cumulative standard normal distribution, and the cumulative standard normal table.

Z-scores

To find the [tex] \\ 92^{nd}[/tex] percentile, we can use z-scores or standardized values. A z-score is a value that tells us the distance in standard deviations units from the mean. When the z-score is positive, it means that the value is above the mean. A negative indicates that the z-score is below the mean. The formula to obtain a z-score is as follows:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where

z is the z-score.x is the raw score.[tex] \\ \mu[/tex] is the mean.[tex] \\ \sigma[/tex] is the standard deviation.

Cumulative standard normal distribution and corresponding table

We still need to know the corresponding z-score, z, for the cumulative probability of 92%. For this, we have to consult the standard normal table, available on the Internet or in any Statistics books.

In this case, we look in the different columns of the standard normal table a probability value (exact or approximate) to 0.92 and then find the value for z that corresponds to this probability. The value for z is between 1.40 (0.91924) and 1.41 (0.92073).

Using z = 1.40 in [1], we have:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ 1.40 = \frac{x - 69}{3}[/tex]

Then, solving for x:

Multiplying by 3 at each side of the equation:

[tex] \\ 1.40 * 3 = x - 69[/tex]

Adding 69 at both sides of the equation:

[tex] \\ (1.40 * 3) + 69 = x[/tex]

[tex] \\ x = (1.40 * 3) + 69[/tex]

[tex] \\ x = 4.20 + 69[/tex]

[tex] \\ x = 73.20[/tex]

That is, the [tex] \\ 92^{nd}[/tex] percentile is 73.20 inches, and to the nearest inch, this percentile is 73 inches.

This result indicates that, approximately, 92% of the heights are below 73 inches, and only 8% of heights are taller than this height.  

The shaded area in the graph below shows an area of 0.08076 (8.076%) for 73.20 inches.  

Five pulse rates are randomly selected from a set of measurements. The five pulse rates have a mean of 65.4 beats per minute. Four of the pulse rates are 57​, 55​, 62​, and 83. a. Find the missing value. b. Suppose that you need to create a list of n values that have a specific known mean. Some of the n values can be freely selected. How many of the n values can be freely assigned before the remaining values are​ determined? (The result is referred to as the number of degrees of​ freedom.)

Answers

Answer:

a) 70b) n-1

Step-by-step explanation:

Mean is defined as the sum total of data divided by the total number of data.

[tex]\overline x = \frac{\sum Xi}{N}[/tex]

Xi are individual data

N is the total number of data = 5

Given the mean of the pulse rate = 65.4

a) Let the 5pulse rates be our data as shown: 57​, 55​, 62​, 83 and y where y is the missing value. According to the formula:

[tex]65.4 = \frac{57+55+62+83+y}{5}[/tex]

[tex]65.4 = \frac{257+y}{5}\\ 257+y = 65.4*5\\257+y = 327\\y = 327-257\\y = 70[/tex]

The missing value is 70

b) Since the total list of numbers is n values with a specific known mean, if some of this values can be freely selected, the number of n values that can be freely assigned before the remaining values are​ determined is any values less than n i.e n-1 values.

From the formula for calculating mean:

[tex]\overline x = \frac{\sum Xi}{N}\\{\sum Xi} = N\overline x[/tex]

This shows that the sum of all the values is equal to the product of the total values and the mean value. Since we can freely choose n-1 values, then sum of the set of data can be written as [tex]\sum \sumx^{n-1} _i__=_1 Xi[/tex]

[tex]\sum \sumx^{n-1} _i__=_1 Xi \ =\ N \overline x[/tex]

The number of n values which is referred to the degree of freedom is n-1

∠A and ∠B are supplementary, and ∠A and ∠C are supplementary. Which conclusion is valid? Select one: A. ∠B and ∠C are supplementary. B. ∠B and ∠C are acute. C. ∠B and ∠C are complementary. D. ∠B and ∠C are congruent.

Answers

Option D is the correct answer.

Answer:

D. ∠B and ∠C are congruent.

Step-by-step explanation:

Since, ∠A and ∠B are supplementary.

Therefore,

∠A + ∠B = 180°.....(1)

Since, ∠A and ∠C are supplementary.

Therefore,

∠A + ∠C = 180°.....(2)

From equations (1) & (2)

∠A + ∠B = ∠A + ∠C

=> ∠B = ∠C

Hence, ∠B and ∠C are congruent.

The management of a chain of frozen yogurt stores believes that t days after the end of an advertising campaign, the rate at which the volume V (in dollars) of sales is changing is approximated by V ' ( t ) = − 26400 e − 0.49 t . On the day the advertising campaign ends ( t = 0 ), the sales volume is $ 170 , 000 . Find both V ' ( 6 ) and its integral V ( 6 ) . Round your answers to the nearest cent.

Answers

Answer:

Step-by-step explanation:

Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation

V ' ( t ) = − 26400 e^− 0.49 t .

t = time (in days)

.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:

V'(6) = − 26400 e− 0.49 (6)

V'(6) = -26400e-2.94

V'(6) = -26400×-0.2217

V'(6) = $5852.88

V'(6) = $5,853 to nearest dollars

V'(6) = 585300cents to nearest cent

To get v(6), we need to get v(t) first by integrating the given function as shown:

V(t) = ∫−26400 e− 0.49 t dt

V(t) = -26,400e-0.49t/-0.49

V(t) = 53,877.55e-0.49t + C.

When t = 0, V(t) = $170,000

170,000 = 53,877.55e-0 +C

170000 = 53,877.55(2.7183)+C

170,000 = 146,454.37+C

C = 170,000-146,454.37

C = 23545.64

V(6) = 53,877.55e-0.49(6)+ 23545.64

V(6) = -11,945.63+23545.64

V(6) = $11,600 (to the nearest dollars)

Since $1 = 100cents

$11,600 = 1,160,000cents

A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.a. P(A ∩ B).b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.

Answers

Complete question is;

A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.

a. P(A ∩ B).

b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.

Answer:

A) 0.4

B) 0.4

Step-by-step explanation:

We are given;

P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8

A) To solve this question, we will use the the general probability addition rule for the union of two events which is;

P(A∪B) = P(A) + P(B) − P(A∩B)

Making P(A∩B) the subject of the equation, we have;

P(A∩B) = P(A) + P(B) − P(A∪B)

Thus, plugging in the relevant values, we have;

P(A∩B) = 0.7 + 0.5 - 0.8

P(A∩B) = 0.4

B)The probability that the lifeline usage amount is exceeded in exactly one of the two months can be described in terms of A and B as:

P(A but not B) + P(B but not A) = P(A∩B') + P(B∩A')

where;

A' is compliment of set A

B' is compliment of set B

Now,

P(A∩B') = 0.7 − 0.4 = 0.3

P(B∩A') = 0.5 − 0.4 = 0.1

Thus;

P(A but not B) + P(B but not A) = 0.1 + 0.3 = 0.4

Which statements are true of the function f(x) = 3(2.5)x? Check all that apply

Answers

Answer:

The function is exponential.

The function increases by a factor of 2.5 for each unit increase in x.

The domain of the function is all real numbers

The true statements are:

[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential functionThe function represents an exponential growthThe domain of the function is the set of all real numbers

The function is given as:

[tex]\mathbf{y = 3(2.5)^x}[/tex]

An exponential function is represented as:

[tex]\mathbf{y = ab^x}[/tex]

Where: a represents the initial value, and b represents the rate

This means that:

[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential function

By comparison:

[tex]\mathbf{b = 2.5}[/tex]

When b > 0, then the function represents an exponential growth

2.5 is greater than 0.

So, the function represents an exponential growth

Lastly, there is no restriction to the values of x.

So, the domain of the function is the set of all real numbers

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Consider the differential equation4y'' − 4y' + y = 0; ex/2, xex/2.Verify that the functions ex/2 and xex/2 form a fundamental set of solutions of the differential equation on the interval (−[infinity], [infinity]).The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) =

Answers

Step-by-step explanation:

Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.

The Wronskian of them functions be

W = (y1y2' - y1'y2)

y1 = (e^x)/2 = y1'

y2 = (xe^x)/2

y2' = (1/2)(x + 1)e^x

W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)

= (1/4)(x + 1 - x)e^(2x)

W = (1/4)e^(2x)

Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.

Answer:

W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)

= (1/4)(x + 1 - x)e^(2x)

W = (1/4)e^(2x)

Step-by-step explanation:

Joni wants to measure the degree to which male college students belong to the political left (liberal). She decides simply to measure the length of male college students hair using a ruler. Her hypothesis is that longer hair will mean more left-wing (liberal) beliefs.

Required:
a. Is this method likely to be reliable? Why?
b. This measurement appears to be invalid. Why?
c. Nevertheless, it is possible that measuring politics by hair length might have some predictive validity. Explain how this could happen.

Answers

Answer:

It is explained below

Step-by-step explanation:

Taking into account the required points we can say the following:

In this case measuring the duration of hair is reliable. The purpose for my opinion is that regardless of how often Joni will degree a persons hair the effects will always be more or less the same. There fore, we are able to rely on the fact that the outcomes may be similar this method is reliable. On the other hand, this technique isn't valid, due to the fact the length of a persons' hair has nothing to do with political opinion. The prediction theory that occurs to me with respect to the model is that the longer the person's hair is, the more they tend to be liberal, due to the rebellious thinking of the left-wing.

What number should go in the space? Multiplying by 0.65 is the same as decreasing by _____%

Answers

Answer: 35%

Step-by-step explanation:

If no is 10, 10 x 0.65 = 6.5. OR

10 - 35% of 10 = 6.5

  Multiplying by 0.65 is the same as decreasing by 35%

Conversion of statements into algebraic expression:To convert the statement into algebraic expression choose the variables first.Then form the expression or equation as per given statements.

Let the number is 'a' and percentage decrease is 'b',

Expression for the given statement will be,

a × 0.65 = a - (b% of a)

[tex]0.65a=a(1-\frac{b}{100})[/tex]

[tex]0.65=1-\frac{b}{100}[/tex]

[tex]\frac{b}{100}=1-0.65[/tex]

[tex]b=100(0.35)[/tex]

[tex]b=35[/tex]

    Therefore, Multiplying by 0.65 is the same as decreasing by 35%.

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⅝ of a school's population are girls. There are 129 boys. If each classroom can hold 25 students. How many classroom does the school have ?​

Answers

Answer:

AT least 14 classrooms to hold the total number of students

Step-by-step explanation:

Since  we don't know the numer of girls in the school, let's call it "x".

What we know is that the number of girls plus the number of boys gives the total number of students. This is:

x + 129 = Total number of students

Now, since 5/8 of the total number of students are girls, and understanding that 5/8 = 0.625 in decimal form, then we write the equation that states:

"5/8 of the school's population are girls" as:

0.625 (x + 129) = x

then we solve for "x":

0.625 x + 0.625 * 129 = x

0.625 * 129 = x - 0.625 x

80.625 = x (1 - 0.625)

80.625 = 0.375 x

x = 80.625/0.375

x = 215

So now we know that the total number of students is: 215 + 129 = 344

and if each classroom can hold 25 students, the number of classroom needed for 344 students is:

344/25 = 13.76

so at least 14 classrooms to hold all those students

Approximately 10% of all people are left-handed. If 200 people are randomly selected, what is the expected number of left-handed people? Round to the whole number. Do not use decimals. Answer:

Answers

Answer:

N(L) = 20

The expected number of left handed people is 20.

Step-by-step explanation:

Given;

Percentage of left handed people P(L) = 10%

Total number of selected people N(T) = 200

The Expected number of left handed people N(L) is;

N(L) = Total number of selected people × Percentage of left handed people/100%

N(L) = N(T) × P(L)/100%

Substituting the given values;

N(L) = 200 × 10%/100%

N(L) = 200 × 0.1

N(L) = 20

The expected number of left handed people is 20.

A large toiletry distributor claims that 35% of all individuals who purchase toilet paper from the stores that carry its product choose original toilet paper, 28% choose sensitive toilet paper, 20% choose ultra-strong toilet paper, and 17% choose ultra-soft toilet paper. To investigate this claim, researchers collected data from a random sample of customers in a large city. The results were 170 packages of original, 105 sensitive, 80 ultra-strong, and 45 ultra-soft toilet paper purchases. Are the data from the sample consistent with the distributor's claim

Answers

p-value < 0.05, reject null hypothesis and we can conclude that data is not consistent with distributor's claim.

Given, data of toiletry distributors.

Total number of observations

= 170 + 105 + 80 + 45

= 400

Expected count = [tex]p_i \times 400[/tex]

Calculation table is attached below.

Test statistic:

Chi square score

= 6.429 + 0.438 + 0.000 + 7.779

= 14.645

Degree of freedom:

df = 4-1

=3

p-value = CHIDIST(14.645,3)

= 0.00215

Therefore , p-value < 0.05

Reject null hypothesis and we can conclude that data is not consistent with distributor's claim.

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) Let an denote number of n-digit ternary sequences (sequences of 0,1 and 2) which have no consecutive 0’s in them. Find a recurrence relation for an. (Do not solve the recurrence. However, depending on the order of the recurrence, provide a sufficient number of initial conditions. )

Answers

Answer:

The recurrence relation for aₙ is  aₙ = 2aₙ - 1 + 2aₙ -2 ; is n≥ 3 with the initial conditions as a₁ =3; a₂ = 8

Step-by-step explanation:

Solution

Recurrence relation for n - digit ternary sequence with no occurrence of consecutive 0's in them.

Ternary sequence is sequence with each of digits either 0, 1 or 2.

Now

Let aₙ = denote the number of n - digit ternary sequence with no occurrence of consecutive 0's in them.

Let us first find few initial values of aₙ

For n = 1

a₁ represent the number of 1- digit ternary sequence with no occurrence of consecutive 0's in them.  

This 1-digit sequence can be either 0 or 1 or 2.

Thus,

a₁ = 3

For n =2

a₂ represent the number of 2- digit ternary sequence with no occurrence of consecutive 0's in them.

This 2-digit sequence can have either 0 or 1 or 2 as each of its two digit, but making sure that there are no two consecutive 0 in the sequence.

here are " 9 " 2-digit ternary sequence ........... (three choices for 1st digit and three choices for 2nd digit)  

But one of these 9 sequence there are consecutive 0's .... (00)  

So we eliminate this one sequence.

So, a₂ = 8

Now

let us find the recurrence relation

Fir n ≥ 3

aₙ s the number of n - digit ternary sequence with no occurrence of the consecutive 0's in them.

For the first case: if 1st digit of this n - digit ternary sequence is 1 or 2

Let assume the 1st digit of this n - digit ternary sequence is 1.  

Then for remaining n - 1 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them.

For example, we have to form a n-1-digit ternary sequence with no occurrence of consecutive 0's in them which is by definition aₙ -1

So,

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 1 is aₙ -1.

Likewise, the number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 2 is aₙ -1.

So  

If 1st digit of this n - digit ternary sequence is 1 or 2, then the number of n - digit ternary sequence with no occurrence of consecutive 0's in them is shown as:

aₙ-1 + aₙ -1 = 2aₙ -1

For the second case: if 1st digit of this n - digit ternary sequence is 0

If 1st digit of this n - digit ternary sequence is 0, then the next digit cannot be 0 as well because that would make two consecutive 0's in the sequence Thus,

If 1st digit of this n - digit ternary sequence is 0, the next term can be either 1 or 2.

So there are 2 choices for 2nd digit.  

After this there are more n-2 digits.  

Then

For remaining n - 2 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them  

For example, we have to form a n-2-digit ternary sequence with no occurrence of consecutive 0's in them. which is by definition aₙ - 2.

Now,

The total number of sequence in this case is given as:

2aₙ -2........... (2 choices for 2nd digit and aₙ - 2 choices for remaining n-2 digit)

Hence  

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 0 is aₙ = 2aₙ - 1 + 2aₙ -2 which is n≥ 3

Now,

The recurrence relation for aₙ is shown below:

aₙ = 2aₙ - 1 + 2aₙ -2; is n≥ 3

With the initial conditions as a₁ =3; a₂ = 8

Suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward along the z-axis a distance of 9 units. What are the coordinates of your position

Answers

Answer:

The coordinates of the new position are

(x, y, z) = (7, 0, -9)

Step-by-step explanation:

So assuming a 3D plane x, y, z

The starting point is the origin that is

(x, y, z) = (0, 0, 0)

Move a distance of 7 units along the positive x-axis

(x, y, z) = (7, 0, 0)

Then move a distance of 9 units downwards along the z-axis

downward = negative and upward = positive

(x, y, z) = (7, 0, -9)

Therefore, the coordinates of the new position are

(x, y, z) = (7, 0, -9)

Refer to the attached plot where the above coordinates are plotted on a 3D surface using an online 3D plotter.

Each small box corresponds to 1 unit.

Let U be the 3 2 matrix [0.45 0.42, 0.25 0.35, 0.15 0.15]. The first column of U lists the costs per dollar of output for manufacturing product​ B, and the second column lists the costs per dollar of output for manufacturing product C. The first row is the cost of​ materials, the second row is the cost of​ labor, and the third row is the cost of overhead. Let q1 be a vector in set of real numbers R2 that lists the output​ (measured in​ dollars) of products B and C manufactured during the first quarter of the​ year, and let q2, q3 ​, and q4 be the analogous vectors that list the amounts of products B and C manufactured in the​ second, third, and fourth​ quarters, respectively. Give an economic desciption of the data in the matrix​ UQ, where Upper Q = [q1 q2 q3 q4].A. The 4 columns of UQ list the profit made from selling products B and C during the 4 quarters of the year. B. The 3 rows of UQ list the costs for materials, labor, and overhead used to manufacture products B and C for the year. C. The 4 columns of UQ list the total costs for materials, labor, and overhead used to manufacture products B and C during the 4 quarters of the year. D. The 4 columns of UQ list the total number of each product manufactured during the 4 quarters of the year.

Answers

Answer:

C. The 4 columns of UQ list the total costs for materials, labor, and overhead used to manufacture products B and C during the 4 quarters of the year.

Step-by-step explanation:

[tex]U=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)[/tex]

[tex]q_1[/tex] is a vector in the set of real numbers [tex]R^2[/tex] that lists the output​ (measured in​ dollars) of products B and C manufactured during the first quarter of the​ year.

Therefore:

[tex]UQ=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)\left(\begin{array}{ccc}q_{1B}\\q_{1C}\end{array}\right)\left(\begin{array}{ccc}q_{2B}\\q_{2C}\end{array}\right)\left(\begin{array}{ccc}q_{3B}\\q_{3C}\end{array}\right)\left(\begin{array}{ccc}q_{4B}\\q_{4C}\end{array}\right)[/tex]

[tex]=\left(\begin{array}{c|c|c|c}q_1&q_2&q_3&q_4\\0.45q_{1B}+0.42q_{1C}&0.45q_{2B}+0.42q_{2C}&0.45q_{3B}+0.42q_{3C}&0.45q_{4B}+0.42q_{4C}\\0.25q_{1B}+0.35q_{1C}&0.25q_{2B}+0.35q_{2C}&0.25q_{3B}+0.35q_{3C}&0.25q_{4B}+0.35q_{4C}\\0.15q_{1B}+0.15q_{1C}&0.15q_{2B}+0.15q_{2C}&0.15q_{3B}+0.15q_{3C}&0.15q_{4B}+0.15q_{4C}\end{array}\right)[/tex]Therefore, UQ has 4 columns and 3 rows.

The 4 columns of UQ list the total costs for materials(Row 1), labor(Row 2), and overhead(Row 3) used to manufacture products B and C during the 4 quarters of the year.

deandre saves rare coins. he starts his collection with 14 coins and plans to save 3 coins each month. write an equation to represent the number of coins saved, y, in terms of the number of months, x. if deandre saved for 30 months, how many coins will he have?

Answers

Answer:

equation: y = 3x + 14

number of coins after 30 months: 104 coins

Hope this helps :)

An equation is formed of two equal expressions. The number of coins that will be with Deandre after a period of 30 months is 104 coins.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

As it is given that in the initial phase Deandre saves 14 coins. While he adds 3 coins each month. Therefore, the equation that will represent the number of coins that Deandre will have after a period of x months can be written as,

y = 14 + 3x

where y is the number of coins and x is the number of months.

After a period of x=30 months, the number of coins that will be with Deandre can be written as,

[tex]y = 14 + 3x\\\\y = 14 + 3(30)\\\\y = 104[/tex]

Thus, the number of coins that will be with Deandre after a period of 30 months is 104 coins.

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