1. The population growth of a small town is modeled by the function P(t) = 6545.52e^0.149t where is the populationand is the number of years since 1980. A. What is the growth rate for P(t)? B. What was the population in 1980? C. Find P(11) and explain what it means in the context of the problem. D. What is the projected population in 2019?

Answer:

P(X < 80) = 0.89435.

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 = 60, \sigma = 16[/tex]

P(X < 80)

This is the pvalue of Z when X = 80. So

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

[tex]Z = \frac{80 - 60}{16}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.89435.

So

P(X < 80) = 0.89435.

Answer:

A) [tex]a_{1}[/tex] = 1, [tex]a_{2}[/tex] = 4

B) [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] + 2

C)    [tex]a_{n} = 2^{n-1} + 2^n -2\\a_{n} = 2^n + 2^{n-1} -2[/tex]

Step-by-step explanation:

For n ≥ 1 ,

S is a set containing 2^n distinct real numbers

an = no of comparisons to be made between pairs of elements of s

A)

[tex]a_{1}[/tex] = no of comparisons in set (s)

that contains 2 elements = 1

[tex]a_{2}[/tex] = no of comparisons in set (s) containing 4 = 4

B)  an = 2a[tex]_{n-1}[/tex] + 2

C) using the recurrence relation

a[tex]_{n}[/tex] = 2a[tex]_{n-1}[/tex] + 2

substitute the following values  2,3,4  .......... for n

a[tex]_{2}[/tex] = 2a[tex]_{1}[/tex] + 2

a[tex]_{3}[/tex] = 2a[tex]_{2}[/tex] + 2 = [tex]2^{2} a_{1} + 2^{2} + 2[/tex]

a[tex]_{4}[/tex] = [tex]2a_{3} + 2 = 2(2^{2}a + 2^{2} + 2 ) + 2[/tex]

    = [tex]2^{n-1} a_{1} + \frac{2(2^{n-1}-1) }{2-1}[/tex]   ---------------- (x)

since  2^1 + 2^2 + 2^3 + ...... + 2^n-1 =  [tex]\frac{2(2^{n-1 }-1) }{2-1}[/tex]

applying the sum formula for G.P

[tex]\frac{a(r^n -1)}{r-1}[/tex]

Note ; a = 2, r =2 , n = n-1

a1 = 1

so equation x becomes

[tex]a_{n} = 2^{n-1} + 2^n - 2\\a_{n} = 2^n + 2^{n-1} - 2[/tex]

Answer:

Step-by-step explanation:

The complete statement would be "if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other".

The reason for this is because parallel lines have the same slope, that's the condition. On the other hand, parallel lines have opposite and reciprocal slopes.

So, if you think this through, if a line is perpendicular to another, then it's going to be perpendicular to all different lines which are parallel to the first one, because all their slopes are equivalent, and they will fulfill the perpendicularity condition.

Answer:

Parallel line

Step-by-step explanation:

Hope It Helps

Hey there! :)

Answer:

Choice C: x + 8 = 3x.

Step-by-step explanation:

Solve this question by simplifying each answer choice:

a) 4x = 20

Divide both sides by 4:

4x/4 = 20/4

x = 5. This is incorrect.

b) x/2 = 8

Multiply both sides by 2:

x = 16. This is incorrect.

c) x + 8 = 3x

Subtract x from both sides:

8 = 2x

Divide 2 from both sides:

x = 4. This is correct.

d) x = x+5 /2

Multiply both sides by 2:

2x = x + 5

Subtract x from both sides:

x = 5. This is incorrect.

Therefore, choice C is the correct answer.

Answer:

C . x+8=3x

Step-by-step explanation:

[tex]x +8 = 3x\\Collect-like-terms\\8=3x-x\\8=2x\\\frac{2x}{2} =\frac{8}{2} \\x =4[/tex]

Answer:

SOLUTION SET={x/x>-1} and SOLUTION SET={x/x<-1}

Step-by-step explanation:

1)4x-39>-43

evaluating the inequality

adding 39 on both sides

4x-39+39>-43+39

4x>-4

dividing 4 on both sides

4x/4>-4/4

x>-1

SOLUTION SET={x/x>-1}

2)8x+31<23

evaluating the inequality

subtracting 31 on both sides

8x+31-31<23-31

8x<-8

dividing 8 on both sides

8x/8<-8/8

x<-1

SOLUTION SET={x/x<-1}

i hope this will help you :)

Answer: There are no solutions

Step-by-step explanation:Khan Academy

Answer:

A

Step-by-step explanation:

9-2x≤3x+24

-15≤5x

-3≤x

so it's:

[-3,∞)

Answer:

Options (D), (E) and (F) are the correct options.

Step-by-step explanation:

From the figure attached,

1). Angle 4 is the exterior angle of the given triangle having interior angles 1, 2 and 3.

Therefore, by the property of exterior angle,

∠4 = ∠1 + ∠2

2). Since ∠4 = ∠1 + ∠2,

Therefore, ∠4 will be greater than ∠1

 Similarly, ∠4 will be greater than ∠2

Therefore, Options (D), (E) and (F) are the correct options.

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

Explanation:

Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.

Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.

Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.

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

Another approach

Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is

1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute

x = number of minutes

(combined rate)*(time) = number of jobs done

(1/24)*x = 1

x = 1*24

x = 24 is the time it takes if they worked together without getting in each other's way.

Effectively, we are solving the equation

1/A + 1/B = 1/C

with

A = time it takes Wilma to do the job on her own

B = time it takes Rocky to do the job on his own

C = time it takes the two working together to get the job done

The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.

So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.

Together they can mow the lawn in 24 minutes.

Time and efficiency are inversely proportional to each other.

Time and work are directly proportional to each other.

Given, Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes.

Assuming total work to be 120 as it is the LCM of 40 and 60.

So, The efficiency of Wilma is (120/60) = 2 and the efficiency of Rocky is

(120/40) = 3.

Now together their efficiency is (2 + 3) = 5.

∴ Together they can complete the work in (120/5) = 24 minutes.

learn more about time and work here :

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Answer:

Lower Quartile: 62

Upper Quartile: 81

Interquartile Range: 19

Step-by-step explanation:

To find the lower quartile, you want to find the median from the minimum to the median.

49, 55, 62, 64, 67

The median of this is 62. Therefore, 62 is the lower quartile.

To find the upper quartile, you want to find the median from the median to the maximum.

76, 79, 81, 82, 83

The median of this is 81. Therefore, 81 is the upper quartile.

To find the interquartile range, you subtract the upper and lower quartile.

81-62=19

The difference is 19. Therefore, the interquartile range is 19.

Answer:

0.49

Step-by-step explanation:

From the Venn diagram:

The number of students that study biology and physics = 2

The number of students that study biology and chemistry = 6

The number of students that study chemistry and physics = 4

The number of students that study only physics = 5

The number of students that study only biology = 7

The number of students that study only chemistry = 8

The number of students that study all 3 subjects = 3

The number of students that study none = 6

Therefore the total number of students = 2 + 6 + 4 + 5 + 7 + 8 + 3 + 6 = 41 students

The number of students that study chemistry = 8 + 6 + 3 + 4 = 21 students

The number of student that does not study chemistry = 41 - 21 = 20 students

the probability chosen at random that that child does not study chemistry =  number of student that does not study chemistry / total number of students  = 20/41 = 0.49

Answer:

56% shaded

Step-by-step explanation:

if there are 100 boxes, then every box it 1%

5 rows (50%) + 6 extra boxes (6%) = 56%

Answer:

-189

Step-by-step explanation:

(63) -3

Calculate the product

-3(63)

Multiply both numbers

-3 × 63

= -189

Answer:

[tex]\overrightarrow{AB}=\frac{-9}{-4}[/tex]

[tex]\overrightarrow{CD}=\frac{-5}{4}[/tex]

Step-by-step explanation:

A vector quantity is represented by [tex](\frac{y}{x})[/tex]

where y = y-coordinate and x = x-coordinate

Since vector AB represents a vector in 3rd quadrant,

It starts from point A and ends at B,

Therefore, coordinates of B are (-9, -4)

[tex]\overrightarrow{AB}[/tex] = [tex](\frac{-9}{-4})[/tex]

Similarly vector CD starts with C and ends at D in the 2nd quadrant,

Therefore coordinates of D will be (-5, 4)

[tex]\overrightarrow{CD}=\frac{-5}{4}[/tex]

Answer:

P10 = 27.4

P90 = 22.0

It helps the producer to know the higher (P10) and lower estimates (P90) for the amount of chocolate chips per cookie.

Step-by-step explanation:

In P10 and P90 the P stands for "percentile".

In the case of P10, indicates the value X of the random variable for which 10% of the observed values will be above this value X.

In the case of P90, this percentage is 90%.

In this case, we can calculate from the z-values for each of the percentiles in the standard normal distribution.

For P10 we have:

[tex]P(z>z_{P10})=0.1\\\\z_{P10}=1.2816[/tex]

For P90 we have:

[tex]P(z>z_{P90})=0.9\\\\z_{P90}=-1.2816[/tex]

Then, we can convert this values to our normal distribution as:

[tex]P10=\mu+z\cdot\sigma=24.7+1.2816\cdot 2.1=24.7+2.7=27.4 \\\\P90=\mu+z\cdot\sigma=24.7-1.2816\cdot 2.1=24.7-2.7=22.0[/tex]

Answer:

unit rate of lemonade to cranberry juice

= 5:1

Step-by-step explanation:

A recipe for fruit punch calls for 1/2 liter of lemonada and 1/10 liter of cranberry juice

1/2 liter of lemonada= 0.5

1/10 liter of cranberry juice = 0.1

unit rate of lemonade to cranberry juice

= 0.5/0.1

unit rate of lemonade to cranberry juice

= (5*10^-1)/(1*10^-1)

unit rate of lemonade to cranberry juice

= 5/1 *(10^-1)/10^-1)

unit rate of lemonade to cranberry juice

= 5/1

unit rate of lemonade to cranberry juice

= 5:1

The unit rate of lemonade to cranberry juice is 5 : 1.

1/2 liters of lemonada are to be mixed with 1/10 litres of cranberry juice.

In ratio form this is:

1/2 : 1/10

To make it a unit rate of lamonada, you should divide both sides by the ratio of lamonada to cranberry juice in order to take lomonada's ratio to 1.

= 1/2 ÷ 1/2 :  1/10 ÷1/2

= 1 : 0.2

You then need to make the decimal a whole number by dividing both sides by the decimal:

= 1 ÷ 0.2 : 0.2 ÷0.2

= 5 : 1

The unit rate of lamonada to cranberry juice is therefore 5 : 1.

Find out more at https://brainly.com/question/18314944.

Answer:

Correct option: C.

Step-by-step explanation:

(Assuming the correct function is R(x) = 2x^2 + 3x + 5)

To find the input value that gives the value of R(x) = 19, we just need to use this output value (R(x) = 19) in the equation and then find the value of x:

[tex]R(x) = 2x^2 + 3x + 5[/tex]

[tex]19 = 2x^2 + 3x + 5[/tex]

[tex]2x^2 + 3x -14 = 0[/tex]

Solving this quadratic function using the Bhaskara's formula (a = 2, b = 3 and c = -14), we have:

[tex]\Delta = b^2 - 4ac = 9 + 112 = 121[/tex]

[tex]x_1 = (-b + \sqrt{\Delta})/2a = (-3 + 11)/4 = 2[/tex]

[tex]x_2 = (-b - \sqrt{\Delta})/2a = (-3 - 11)/4 = -3.5[/tex]

So looking at the options, the input to the function is x = 2

Correct option: C.

Answer:

m^4+(1/m^4)= 123.4641 or 118.6

Step-by-step explanation:

m-(1/m)=3

m² - 1= 3m

m² -3m -1= 0

m = (3-√13)/2 = -0.3

Or

m =( 3+√13)/2= 3.3

m^4+(1/m^4) for m = -0.3

= (-0.3)^4 + (1/(0.3)^4)

= 0.0081 + 123.456

= 123.4641

m^4+(1/m^4) for m = 3.3

= (3.3)^4 + (1/(3.3)^4)

= 118.5921 + 0.008432

= 118.6

Answer:

x is 64 and y is 16 but if you can't comprehend thats 64/16 = 4

Step-by-step explanation:the power is the number multiplied by it self so 8 to the power if 2 is 8 x 8 and 2 to the power of four is 2 x 2 x 2 x 2= 16

Answer:

100%

Step-by-step explanation:

Total = 7

Odd or less than 7 = 6+1

=> 7

P(odd or less than 7) = 7/7

In %age:

100%

Answer:

100%

Step-by-step explanation:

Number of cards= 7

Odd or less than 7= 7

P= 7/7=1=100%

Answer:

To construct a confidence interval, Normal distribution should be used since the sample size is quite large (n > 30)

From the z-table, at α = 0.025 the critical value is

[tex]z_{\alpha/2} = 1.96[/tex]

Step-by-step explanation:

We are given the following information:

The sample size is

[tex]n = 235[/tex]

The mean weight is

[tex]\bar{x}= 33.7 \: hg[/tex]

The standard deviation is

[tex]s = 7.3 \: hg[/tex]

Since the sample size is quite large (n > 30) then according to the central limit theorem the sampling distribution of the sample mean will be approximately normal, therefore, we can use the Normal distribution for this problem.

The correct option is (b)

The critical value corresponding to 95% confidence level is given by

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

From the z-table, at α = 0.025 the critical value is

[tex]z_{\alpha/2} = 1.96[/tex]

What is Normal Distribution?

A Normal Distribution is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

Answer:

The 97% upper confidence limit for the proportion of green items is 0.502.

Step-by-step explanation:

We have to calculate a 97% upper confidence limit for the proportion.

The sample proportion is p=0.294.

[tex]p=X/n=5/17=0.294\\[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.294*0.706}{17}}\\\\\\ \sigma_p=\sqrt{0.01221}=0.11[/tex]

The critical z-value for a 97% upper confidence limit is z=1.881.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.881 \cdot 0.11=0.208[/tex]

Then, the upper bound is:

[tex]UL=p+z \cdot \sigma_p = 0.294+0.208=0.502[/tex]

The 97% upper confidence limit for the proportion of green items is 0.502.

Answer:

16x^2 + 8x.

Step-by-step explanation:

To find the area of the walkway, you need to do the area of the whole thing minus the area of the pool.

The area of the whole thing is (8x - 3)(2x + 7) = 16x^2 - 6x + 56x - 21 = 16x^2 + 50x - 21.

The area of the pool is (8x - 3 - x - x)(2x + 7 - x - x) = (6x - 3)(7) = 42x - 21.

So, the area of the walkway is 16x^2 + 50x - 21 - (42x - 21) = 16x^2 + 50x - 21 - 42x + 21 = 16x^2 + 8x.

If you want, you can factor that and make it 8x(2x + 1).

Hope this helps!

Answer:

Step-by-step explanation:

No, it is not an even function.  The graph is not symmetric about the y-axis.

Answer:

(a) The probability you pass the exam is 0.0000501.

(b) The expected number of correct guesses is 7.5.

(c) The standard deviation is 2.372.

Step-by-step explanation:

We are given that you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. And you randomly guess on all 30 questions.

Since there is an assumption of only 1 correct choice out of 4 which means the above situation can be represented through binomial distribution;

[tex]P(X =x) = \binom{n}{r}\times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,3,......[/tex]

where, n = number of trials (samples) taken = 30

           r = number of success = at least 60%

           p = probbaility of success which in our question is the probability

                 of a correct answer, i.e; p = [tex]\frac{1}{4}[/tex] = 0.25

Let X = Number of questions that are correct

So, X ~ Binom(n = 30 , p = 0.25)

(a) The probability you pass the exam is given by = P(X [tex]\geq[/tex] 18)

Because 60% of 30 = 18

P(X [tex]\geq[/tex] 18) = P(X = 18) + P(X = 19) +...........+ P(X = 29) + P(X = 30)

= [tex]\binom{30}{18}\times 0.25^{18}\times (1-0.25)^{30-18} + \binom{30}{19}\times 0.25^{19}\times (1-0.25)^{30-19} +.......+ \binom{30}{29}\times 0.25^{29}\times (1-0.25)^{30-29} + \binom{30}{30}\times 0.25^{30}\times (1-0.25)^{30-30}[/tex]

= 0.0000501

(b) The expected number of correct guesses is given by;

  Mean of the binomial distribution, E(X) =  [tex]n \times p[/tex]

                                                                =  [tex]30 \times 0.25[/tex] = 7.5

(c) The standard deviation of the binomial distribution is given by;

      S.D.(X)  =  [tex]\sqrt{n \times p \times (1-p)}[/tex]

                    =  [tex]\sqrt{30 \times 0.25 \times (1-0.25)}[/tex]

                    =  [tex]\sqrt{5.625}[/tex]  =  2.372                

Answer:

1) 2/9

2)3/9

Step-by-step explanation:

sorry,thats what i know so far

Answer:

The breadth is 16m because a square is a quadrilateral (four sided shape) that has all its side to be of equal measure.

Answer:

[tex]P(40<X<55)[/tex]

And since we need to use excel the code in order to find the answer would be:

=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)

And the answer would be:

[tex]P(40<X<55)=0.819[/tex]

Step-by-step explanation:

Let X the random variable that represent the respiratory rate of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(50,5)[/tex]  

Where [tex]\mu=50[/tex] and [tex]\sigma=5[/tex]

We are interested on this probability

[tex]P(40<X<55)[/tex]

And since we need to use excel the code in order to find the answer would be:

=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)

And the answer would be:

[tex]P(40<X<55)=0.819[/tex]

Answer:

The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 100, p = 0.42[/tex]

92% confidence level

So [tex]\alpha = 0.08[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.08}{2} = 0.96[/tex], so [tex]Z = 1.75[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.3336[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.5064[/tex]

The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).

Answer:

The equation is:

[tex]L=3\,\,d^2\\[/tex]

and a beam with 10 in diagonal will support 300 lb

Step-by-step explanation:

The mathematical expression that represents the statement:

"The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. "

can be written as:

[tex]L=k\,\,d^2[/tex]

where k is the constant of proportionality

To find the constant we use the data they provide: "A beam with diagonal 6 in will support a maximum load of 108 lb.":

[tex]L=k\,\,d^2\\108 = k\,\,(6)^2\\k=\frac{108}{36} \,\,\frac{lb}{in^2}\\ k = 3\,\,\frac{lb}{in^2}[/tex]

Now we can use the proportionality found above to find the maximum load for a 10 in diagonal beam:

[tex]L=3\,\,d^2\\L=3\,\,(10)^2\\L=300 \,\,lb[/tex]

Answer:

L=3d^2 the beam will support 300 pounds

Step-by-step explanation:

108=k x 6^2

Dividing by 6^2=36 gives k=3, so an equation that relates L and d is

L=3d^2 d=10 yields

3(10)^2=300

So a beam with a 10in diagonal will support a 300lb load.

Hey there! :)

Answer:

To graph y = -3x - 2, we can start by solving for some points. Plug in x values for x in the equation to solve for the y value:

X                   Y

-2                  4

-1                    1

0                   -2

1                     -5

2                    -8

Use these points to graph the line (Graphed below)