What is the range of g(x) = -2x+31 + 2?
A. (-0,2)
B. [3,00)
C.
[2,00)
D.
(-00,00)

Answer:

3 wooden plank he can saw

Answer:

he can saw 3 wooden planks

Step-by-step explanation:

Answer:

Option C is the correct option.

Solution,

Given that,

[tex]f(x) = (x - 8)(x + 3)[/tex]

put f(x)=y

[tex]y(x - 8)(x + 3) - - > equation \: (i)[/tex]

For finding y- intercept

put x=0

We get,

[tex]y = (0 - 8)(0 + 3) - - > from \: {eq}^{n} \: (i)[/tex]

[tex]y = ( - 8) \times 3 \\ y = - 24 \\ y - intercept = (0 ,- 24)[/tex]

hope this helps...

Good luck on your assignment..

Answer:

a) The probability that both adults dine out more than once per week = 0.0253

b) The probability that neither adult dines out more than once per week = 0.7069

c) The probability that at least one of the two adults dines out more than once per week = 0.2931

d) Of the three events described, the event that can be considered unusual because of its low probability of occurring, 0.0253 (2.53%), is the event that the two randomly selected adults both dine out more than once per week.

Step-by-step explanation:

In a sample of 1200 U.S. adults, 191 dine out at a restaurant more than once per week.

Assuming this sample.is a random sample and is representative of the proportion of all U.S. adults, the probability of a randomly picked U.S. adult dining out at a restaurant more than once per week = (191/1200) = 0.1591666667 = 0.1592

Now, assuming this probability per person is independent of each other.

Two adults are picked at random from the entire population of U.S. adults, with no replacement, thereby making sure these two are picked at absolute random.

a) The probability that both adults dine out more than once per week.

Probability that adult A dines out more than once per week = P(A) = 0.1592

Probability that adult B dines out more than once per week = P(B) = 0.1592

Probability that adult A and adult B dine out more than once per week = P(A n B)

= P(A) × P(B) (since the probability for each person is independent of the other person)

= 0.1592 × 0.1592

= 0.02534464 = 0.0253 to 4 d.p.

b) The probability that neither adult dines out more than once per week.

Probability that adult A dines out more than once per week = P(A) = 0.1592

Probability that adult A does NOT dine out more than once per week = P(A') = 1 - P(A) = 1 - 0.1592 = 0.8408

Probability that adult B dines out more than once per week = P(B) = 0.1592

Probability that adult B does NOT dine out more than once per week = P(B') = 1 - P(B) = 1 - 0.1592 = 0.8408

Probability that neither adult dines out more than once per week = P(A' n B')

= P(A') × P(B')

= 0.8408 × 0.8408

= 0.70694464 = 0.7069 to 4 d.p.

c) The probability that at least one of the two adults dines out more than once per week.

Probability that adult A dines out more than once per week = P(A) = 0.1592

Probability that adult A does NOT dine out more than once per week = P(A') = 1 - P(A) = 1 - 0.1592 = 0.8408

Probability that adult B dines out more than once per week = P(B) = 0.1592

Probability that adult B does NOT dine out more than once per week = P(B') = 1 - P(B) = 1 - 0.1592 = 0.8408

The probability that at least one of the two adults dines out more than once per week

= P(A n B') + P(A' n B) + P(A n B)

= [P(A) × P(B')] + [P(A') × P(B)] + [P(A) × P(B)]

= (0.1592 × 0.8408) + (0.8408 × 0.1592) + (0.1592 × 0.1592)

= 0.13385536 + 0.13385536 + 0.02534464

= 0.29305536 = 0.2931 to 4 d.p.

d) Which of the events can be considered unusual? Explain.

The event that can be considered as unusual is the event that has very low probabilities of occurring, probabilities of values less than 5% (0.05).

And of the three events described, the event that can be considered unusual because of its low probability of occurring, 0.0253 (2.53%), is the event that the two randomly selected adults both dine out more than once per week.

Hope this Helps!!!

Step-by-step explanation:

1. 180 - (36 +36)= 108

2. angle ABC = 108 angle DBC = 108-72=36

3. angle DCB=angle DBC. This is because the base angles are equal

4 therefore triangle BDC is isoscles

Answer:

Because ΔABD is isosceles, ∠ABD ≅ ∠ADB = 72° because of Base Angles Theorem which states that the base angles of an isosceles triangle are congruent. Then, ∠BDC = 180° - ∠ADB = 108° because they are supplementary angles. Because ΔABC is isosceles, ∠BAC ≅ ∠BCA = 36° because of Base Angles Theorem, which means ∠CBD = 180° - 108° - 36° = 36° because of the sum of angles in a triangle. Therefore, ΔBCD is isosceles because of the Converse of Base Angles Theorem.

Step-by-step explanation:

positive angle =300+180=480.

negative angle = 300 -180=120

Answer:

The total sales in dollars to make their pay equal is: $ 3800

Step-by-step explanation:

Since we need to find the number of sales that make both function equal in value, we equal both expressions, and solve for 'x":

[tex]180+0.05 \,x=104+0.07 \,x\\180-104=0.07\,x-0.05\,x\\76=0.02x\\x=\frac{76}{0.02} \\x=3800[/tex]

Answer: 10x^2 - 4x

Step-by-step explanation:

To expand, you are not simplifying, so multiplying out is the answer here. To do this, use the distributive property. The distributive property in this case means that if you are multiplying one number by a whole expression inside parenthesis, multiply the one number by each term in the expression:

2x(5x - 2)

= 2x(5x) + 2x(-2)

= 10x^2 - 4x

The product of the expression is equivalent to -

10x² - 4x.

Given is the expression as follows -

2x(5x - 2)

The given expression is -

2x(5x - 2)

10x² - 4x

Therefore, the product of the expression is equivalent to -

10x² - 4x.

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Answer:

1

Step-by-step explanation:

The mean is the average of the sum of all integers in a data set.

Caroline has 2 pieces of cheese, Samuel has 4 pieces of cheese, Abby has 4 pieces of cheese, and Jason has 2 pieces of cheese

2 + 4 + 4 + 2 = 12

12 divides by 4, since there are 4 people, to equal the mean

12 / 4 = 3

Now since we have the mean, find the distance from the mean to each number

3 - 2 = 1

4 - 3 = 1

4 - 3 = 1

3 - 2 = 1

1 + 1 + 1 + 1 = 4

4 / 4 = 1

Answer:

4/11

Step-by-step explanation:

Total number of marbles = 2(purple) + 4(white) + 3(blue) + 2(green)

                                          = 11

Number of white marbles = 4

Probability of selecting a white marble =

         number of white marbles/total number of marbles in the jar

         = 4/11

The probability of selecting a white marble from a jar of marbles is 4/11.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Purple Marbles = 2

White Marbles = 4

Blue Marbles = 3

Green Marbles = 2

Total marbles= 2+ 4+ 3+ 2= 11

So, the probability of selecting a white marble from a jar of marbles

= 4/11

Hence, the probability is 4/11.

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Answer:

2.17609

Step-by-step explanation:

Easiest and fastest way is to just directly plug log base 10 of 150 into the calc, as it is a nasty decimal.

Answer:

(A)30

(D)15

Step-by-step explanation:

Factors of 30 are 1,2,3,5,6,10,15 and 30

A composite number is any number that is not prime.

From the given options, the factors of 30 are 30, 5 and 15.

However, 5 is not a composite number.

Therefore, the number that Lacey could be thinking of will either be 30 or 15.

Answer/Step-by-step explanation:

When solving problems like this, remember the following:

1. + × + = +

2. + × - = -

3. - × + = -

4. - × - = +

Let's solve:

a. (-4) + (+10) + (+4) + (-2)

Open the bracket

- 4 + 10 + 4 - 2

= - 4 - 2 + 10 + 4

= - 6 + 14 = 8

b. (+5) + (-8) + (+3) + (-7)

= + 5 - 8 + 3 - 7

= 5 + 3 - 8 - 7

= 8 - 15

= - 7

c. (-19) + (+14) + (+21) + (-23)

= - 19 + 14 + 21 - 23

= - 19 - 23 + 14 + 21

= - 42 + 35

= - 7

d. (+5) - (-10) - (+4)

= + 5 + 10 - 4

= 15 - 4 = 11

e. (-3) - (-3) - (-3)

= - 3 + 3 + 3

= - 3 + 9

= 6

f. (+26) - (-32) - (+15) - (-8)

= 26 + 32 - 15 + 8

= 26 + 32 + 8 - 15

= 66 - 15

= 51

Answer:

its A, C, E on edg

Step-by-step explanation:

Answer:

a   c   e  

Step-by-step explanation:

Answer:

Just replace the variables with the number

d5

c4 (uh oh)

a2

b-3

f-7

d-c = 5 - 4 = 1

1/3 - 4(ab+f)

2 x -3 = -6

-6 + -7 = -13

-13 x 4 = -52

1/3 - -52 = 1/3 + 52 =

52 1/3

Hope this helps

Step-by-step explanation:

Answer:

The 75th percentile of this distribution is 11 .25 minutes.

Step-by-step explanation:

The random variable X is defined as the waiting time in line at an ice cream shop.

The random  variable X follows a Uniform distribution with parameters a = 3 minutes and b = 14 minutes.

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b;\ a<b[/tex]

The pth percentile is a data value such that at least p% of the data-set is less than or equal to this data value and at least (100-p)% of the data-set are more than or equal to this data value.

Then the 75th percentile of this distribution is:

[tex]P (X < x) = 0.75[/tex]

[tex]\int\limits^{x}_{3} {\frac{1}{14-3}} \, dx=0.75\\\\ \frac{1}{11}\ \cdot\ \int\limits^{x}_{3} {1} \, dx=0.75\\\\\frac{x-3}{11}=0.75\\\\x-3=8.25\\\\x=11.25[/tex]

Thus, the 75th percentile of this distribution is 11 .25 minutes.

[tex]answer \\ = (6.5 \: 8.5) \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

10 and 8

Step-by-step explanation:

10 and 8 are the factors in this equation because factors are the numbers that are mutiplied together to get the product (The answer to a mutiplication problem) Therefore the factors in this equation are 10 and 8 because those are the numbers that are mutiplied together to get the product.

Answer:

Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 100, \sigma = 15[/tex]

If you scored 130, your score would be higher than approximately what percent of adults?

To find the proportion of scores that are lower than, we find the pvalue of Z when X = 130. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{130 - 100}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

0.9772*100 = 97.72%.

Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.

Answer:

it should look like this

Answer:

The speed driven while returning is 88 mph.

Step-by-step explanation:

We are given that while traveling to and from a certain destination, you realized increasing your speed by 40 mph saved 4 hours on your return.

Also, the total distance of the roundtrip was 420 miles.

Let the speed driven while returning be 'x mph' which means that the speed driven while going was '(x - 40) mph' because it has been given that while returning we have increased the speed by 40 mph.

As we know that the Speed-Distance-Time formula is given by;

                         [tex]\text {Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]   or  [tex]\text {Time} = \frac{\text{Distance}}{\text{Speed}}[/tex]

So, according to the question;

[tex]\frac{420}{x-40} -\frac{420}{x} = 4 \text{ hours}[/tex]       where Distance = 420 miles

[tex]\frac{420x-420(x-40)}{x(x-40)} = 4[/tex]

[tex]\frac{420x-420x+16800}{x^{2} -40x} = 4[/tex]

[tex]\frac{16800}{x^{2} -40x} = 4[/tex]

[tex]4x^{2} -160x= 16800[/tex]

[tex]4x^{2} -160x- 16800=0[/tex]

[tex]x^{2} -40x- 4200=0[/tex]

Now finding the roots of the above equation;

Here a = 1, b = -40 and c = -4200

[tex]D = b^{2} -4ac[/tex]

   =  [tex](-40)^{2} -4(1)(-4200)[/tex] = 18400

Now, the roots of a quadratic equation is given by;

[tex]x = \frac{-b\pm \sqrt{D} }{2a}[/tex]

[tex]x = \frac{-(-40)\pm \sqrt{18400} }{2\times 1}[/tex]

So, the two roots of x are : [tex]x = \frac{40-\sqrt{18400} }{2}[/tex]  and  [tex]x = \frac{40+\sqrt{18400} }{2}[/tex]

Solving these two we get; [tex]x = -47.8[/tex]  and  [tex]x = 87.8[/tex]

Here we ignore the negative value of x, so the speed driven while returning is 87.8 ≈ 88 mph.

Answer:

(D)Equilateral Triangle

Step-by-step explanation:

Given a circle centre M; and

The measure of major arc JL = 300 degrees

The triangle formed by radii ML and MJ and chord JL is Triangle JLM.

Since ML=MJ (radii of a circle), the base angles are equal.

Therefore:

[tex]\angle MLJ= \angle MJL\\\angle LMJ =60^\circ\\$Therefore:\\\angle LMJ+2\angle MLJ=180^\circ\\60^\circ+2\angle MLJ=180^\circ\\2\angle MLJ=180^\circ-60^\circ\\2\angle MLJ=120^\circ\\\angle MLJ=60^\circ[/tex]

We can see that all the angles of triangle JLM are 60 degrees, therefore Triangle JLM is an Equilateral Triangle.

Answer:

X ~ Norm ( 13 , 25 )

P ( X > 17 ) = 0.2119

16.37 days

Step-by-step explanation:

Solution:-

- We are given a distribution for the amount of time for a kidney stone to pass.

- The distribution is parameterize by the mean time taken ( u ) and the standard deviation ( s ) as follows:

                                 u = 13 days

                                 s = 5 days

- Here, we will define a random variable X: The time taken by a kidney stone to pass to be normally distributed with parameters ( u ) and ( s ). We express the distribution in the notation form as follows:

                              X ~ Norm ( u , s^2 )

                              X ~ Norm ( 13 , 25 )

- We are to determine that a randomly selected individual takes more than 17 days for the stone to pass through.

- We will first standardize the limiting value for the required probability by computing the Z-score as follows:

                            [tex]Z-score = \frac{X - u}{s} \\\\Z-score = \frac{17 - 13}{5} \\\\Z-score = 0.8[/tex]

- We will use the standard normal table to determine the probability of kidney stone passing in less than 17 days ( Z = 0.8 ); hence, we have:

                           P ( X < 17 ) = P ( Z < 0.8 )

                           P ( X < 17 ) = 0.7881

- To compute the probability of an individual taking more than 17 days would be " total probability - P ( X < 17 )  as follows" . Where the total probability of any distribution is always equal to 1.

                        P ( X > 17 ) = 1 - P ( X < 17 )

                        P ( X > 17 ) = 1 - 0.7781

                        P ( X > 17 ) = 0.2119

- Nest we are to determine the amount of days it would take for an individual to lie in the upper quarter of the spectrum. We can interpret this by looking at the limiting value corresponding to the P ( X > x ) = 0.25.

- The upper quartile of any distribution amounts to probabilities: " > x = 0.25 " or " < x = 0.75 ".

- We will use the standard normal table for ( Z-score ) and look-up the Z-score value corresponding to P ( Z < a ) = 0.75 as follows:

                       P ( Z < a ) = 0.75

                       a = 0.674

- Now we will use the standardizing formula used in previous part and compute the value of "x" associated with the limiting Z-score value:

                       [tex]Z-score = \frac{x-u}{s} = 0.674\\\\x = 0.674*s + u\\\\x = 0.674*5 + 13\\\\x = 16.37[/tex]

Answer: It would should take more than 16.37 days for an individual if he is to lie in the upper quartile of the defined distribution.

Answer:

Exponents are simply repeated multiplication so the answer is 7 * 7 * 7 * 7.

Answer:

[tex]z=-\frac{20}{3}[/tex]

Step-by-step explanation:

[tex]\frac{3z}{10}-4=-6\\\\\frac{3z}{10}-4+4=-6+4\\\\\frac{3z}{10}=-2\\\\\frac{10\cdot \:3z}{10}=10\left(-2\right)\\\\3z=-20\\\\\frac{3z}{3}=\frac{-20}{3}\\\\z=-\frac{20}{3}[/tex]

Best Regards!

Answer:

A

Step-by-step explanation:

Her first error is,

C. She made a computational error when multiplying to find the unit price of the two cartons.

We have to given that,

Nikki used the calculations shown to determine whether a carton of 12 eggs or a carton of 18 eggs was the better buy.

Here, A carton of 12 eggs cost $2.39, and a carton of 18 eggs cost $3.39.

And, A carton of 12 eggs cost $2.39, and a carton of 18 eggs cost $3.39.

Unit price of the 12-egg carton = ($2.39)(12 eggs) = $28.68 per egg

Unit price of the 18-egg carton = ($3.39)(18 eggs) = $61.02 per egg

The 12-egg carton has the lower unit cost, so it is the better buy.

Here, It's first error is,

She made a computational error when multiplying to find the unit price of the two cartons.

Instead of dividing the cost of the 18-egg carton by the number of eggs, she multiplied the cost by 18, which resulted in an incorrect unit price.

Hence, It's first error is,

She made a computational error when multiplying to find the unit price of the two cartons.

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Answer:

[tex]2x+2=-50[/tex]

Step-by-step explanation:

[tex]x+2=y\\x+y=-50\\x+x+2=-50\\2x+2=-50[/tex]

The equation that can be used to find out [tex]x[/tex] and [tex]y[/tex] is [tex]2x+2=-50[/tex]

Answer:

[tex]\mathrm{A}[/tex]

Step-by-step explanation:

Two consecutive even integers.

The first integer is even and can be as [tex]x[/tex]

The second integer is also even and can be as [tex]x+2[/tex]

Their sum is [tex]-50[/tex]

[tex]x+x+2=-50[/tex]

[tex]2x+2=-50[/tex]

Answer:

$17.72 left

Step-by-step explanation:

144 inches = 4 yards

4(0.15) + 3.5(0.48) = 0.6 + 1.68 = $2.28 SPENT

20 - 2.28 = $17.72 left in change

Answer:

The probability that more than 2 of the sample deliveries arrive late = 0.0115

Step-by-step explanation:

This is a binomial distribution problem

A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.

It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.

The probability of each delivery arriving late = 5% = 0.05

- Each delivery is independent from the other.

- There is a fixed number of deliveries to investigate.

- Each delivery has only two possible outcomes, a success or a failure of arriving late.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of deliveries we're considering = 10

x = Number of successes required = number of deliveries that we expect to arrive late = more than 2 = > 2

p = probability of success = probability of a delivery arriving late = 0.05

q = probability of failure = probability of a delivery NOT arriving late = 0.95

P(X > 2) = 1 - P(X ≤ 2)

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.59873693924 + 0.31512470486 + 0.07463479852

= 0.98849644262

P(X > 2) = 1 - P(X ≤ 2)

= 1 - 0.98849644262

= 0.01150355738

= 0.0115

Hope this Helps!!!

Answer:

B. 0.835

Step-by-step explanation:

We can use the z-scores and the standard normal distribution to calculate this probability.

We have a normal distribution for the portfolio return, with mean 13.2 and standard deviation 18.9.

We have to calculate the probability that the portfolio's return in any given year is between -43.5 and 32.1.

Then, the z-scores for X=-43.5 and 32.1 are:

[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{(-43.5)-13.2}{18.9}=\dfrac{-56.7}{18.9}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{32.1-13.2}{18.9}=\dfrac{18.9}{18.9}=1\\\\\\[/tex]

Then, the probability that the portfolio's return in any given year is between -43.5 and 32.1 is:

[tex]P(-43.5<X<32.1)=P(z<1)-P(z<-3)\\\\P(-43.5<X<32.1)=0.841-0.001=0.840[/tex]

Answer:

[tex]b=\dfrac{1}{5}a[/tex].

Step-by-step explanation:

We need to write an  equation for the amount of chemical B as a function of the amount of chemical A.

[tex]b=f(a)[/tex]

[tex]b\propto a[/tex]

[tex]b=ka[/tex]     ...(1)

where, k is constant of proportionality.

It is given that fifteen grams of chemical A is used to produce 3 grams of chemical B. It means a=15 and b=3.

Substitute a=15 and b=3 in (1).

[tex]3=k(15)[/tex]

[tex]k=\dfrac{3}{15}=\dfrac{1}{5}[/tex]

Substitute [tex]k=\dfrac{1}{5}[/tex] in (1).

[tex]b=\dfrac{1}{5}a[/tex]

Therefore, the required function is [tex]b=\dfrac{1}{5}a[/tex].