Find the missing length. Can someone explain it to me, I would be deeply grateful.

Answer:  b) they ARE similar because BRAD:KELY is 1:2

Step-by-step explanation:

In order for the shapes to be similar they must have congruent angles and proportional sides.

With the options a through d given, we can assume that their sides are proportional.  Since BRAD is smaller than KELY, BRAD would have the smaller number in the ratio.

Answer:

They are similar because Brad and Kelly are 1:2

Step-by-step explanation:

Answer:

As the P-value (0.0107) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that listening to music while solving math problems will make a particular brain area more active.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that listening to music while solving math problems will make a particular brain area more active.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=35\\\\H_a:\mu> 35[/tex]

The significance level is 0.01.

The sample has a size n=1.

The sample mean is M=58.

The standard deviation of the population is known and has a value of σ=10.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{1}}=10[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{58-35}{10}=\dfrac{23}{10}=2.3[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>2.3)=0.0107[/tex]

As the P-value (0.0107) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that listening to music while solving math problems will make a particular brain area more active.

Answer:

a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data

b) [tex] P(191.5<X<319.5)[/tex]

We can find the number of deviations from the mean for the limits using the z score formula given by:

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

And replacing we got:

[tex] z=\frac{191.5-255.4}{63.9}= -1[/tex]

[tex] z=\frac{319.3-255.4}{63.9}= 1[/tex]

So we have values within 1 deviation from the mean and using the empirical rule we know that we have 68% of the values for this case

Step-by-step explanation:

For this case we have the following properties for the random variable of interest "blood platelet counts"

[tex]\mu = 255.4[/tex] represent the mean

[tex]\sigma = 63.9[/tex] represent the population deviation

Part a

From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data

Part b

We want this probability:

[tex] P(191.5<X<319.5)[/tex]

We can find the number of deviations from the mean for the limits using the z score formula given by:

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

And replacing we got:

[tex] z=\frac{191.5-255.4}{63.9}= -1[/tex]

[tex] z=\frac{319.3-255.4}{63.9}= 1[/tex]

So we have values within 1 deviation from the mean and using the empirical rule we know that we have 68% of the values for this case

Answer:

4,500 x 5 = 22,500

4,500 divided by 5 = 900

4,500 plus 5 = 4,505

4,500 minus 5 = 4,495

Step-by-step explanation:

it is either one of those that u have to choose from good luck

Answer:

122 in2

Step-by-step explanation:

area = (2*tri area) + (3*rec area)

area = (2*0.5*4*3.5) + (3*4*9)

area = 14 + 108 = 122 Squared in

Answer:

We have to multiply P(A) and P(B) which is 0.0045 * 0.01 * 100 (to make it a percentage) = 0.0045%.

Answer:

Step-by-step explanation:

Using the compound interest formula

[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]

A = final amount after t years

P = amount borrowed = Principal = 6709R

r = rate (in %) = 12 1/3%

n = number of times the interest is applied = 2 months

t = time the period elapsed = 2 1/2 years

[tex]A = 6709(1+\frac{\frac{37}{300} }{\frac{2}{12} } )^{\frac{2}{12} *\frac{5}{2} } \\A = 6709(1+0.1233/0.1667)^{2\0.41667} \\A = 6709(1+0.7397)^{2\0.41667} \\A = 6709(1.7397)^{2\0.41667} \\A = 6709(3.81195)\\A = 25,574.373[/tex]

She will have to pay 25,574.373R after 2 and a half years

interest paid by her = Amount - Principal

Interest paid by her = 25,574.373 - 6709

Interest paid by her = 18,865.373R

Answer:

  340 square feet

Step-by-step explanation:

If we "unwrap" the painted surface from the shed, it will have the shape shown in the attachment. It is essentially a 40' by 8' rectangle with two 10' wide by 2' high triangles added.

The rectangle area is ...

  A = LW = (40 ft)(8 ft) = 320 ft²

The total area of the two triangles is ...

  A = 2(1/2)bh = (10 ft)(2 ft) = 20 ft²

Then the painted area is ...

  total area = 320 ft² +20 ft²

  total area = 340 ft²

Given Information:

Population proportion = p =  0.55

Sample size 1 = n₁ = 30

Sample size 2 = n₂ = 100

Sample size 3 = n₃ = 1000

Required Information:

Standard error = σ = ?

Answer:

[tex]$ \sigma_1 = 0.091 $[/tex]

[tex]$ \sigma_2 = 0.050 $[/tex]

[tex]$ \sigma_3 = 0.016 $[/tex]

Step-by-step explanation:

The standard error for sample proportions from a population is given by

[tex]$ \sigma = \sqrt{\frac{p(1-p)}{n} } $[/tex]  

Where p is the population proportion and n is the sample size.

For sample size n₁ = 30

[tex]$ \sigma_1 = \sqrt{\frac{p(1-p)}{n_1} } $[/tex]

[tex]$ \sigma_1 = \sqrt{\frac{0.55(1-0.55)}{30} } $[/tex]

[tex]$ \sigma_1 = 0.091 $[/tex]

For sample size n₂ = 100

[tex]$ \sigma_2 = \sqrt{\frac{p(1-p)}{n_2} } $[/tex]

[tex]$ \sigma_2 = \sqrt{\frac{0.55(1-0.55)}{100} } $[/tex]

[tex]$ \sigma_2 = 0.050 $[/tex]

For sample size n₃ = 1000

[tex]$ \sigma_3 = \sqrt{\frac{p(1-p)}{n_3} } $[/tex]

[tex]$ \sigma_3 = \sqrt{\frac{0.55(1-0.55)}{1000} } $[/tex]

[tex]$ \sigma_3 = 0.016 $[/tex]

As you can notice, the standard error decreases as the sample size increases.

Therefore, the greater the sample size lesser will be the standard error.

Answer:

is that the question because I'm not sure

Answer:

whats the full question

Step-by-step explanation:

Answer:

The probability that all three have type B​+ blood is 0.001728

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have type B+ blood, or they do not. The probability of a person having type B+ blood is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that a person in the United States has type B​+ blood is 12​%.

This means that [tex]p = 0.12[/tex]

Three unrelated people in the United States are selected at random.

This means that [tex]n = 3[/tex]

Find the probability that all three have type B​+ blood.

This is P(X = 3).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.12)^{3}.(0.88)^{0} = 0.001728[/tex]

The probability that all three have type B​+ blood is 0.001728

Answer:

a) May be used to predict a value of y if the corresponding x value is given

Step-by-step explanation:

In regression analysis, the vertical distance from the regression line to the data points can be minimized using the least square regression line.

Given the example of a least square regression equation:

y = ax + b

Where

a = slope

b = Y-intercept

If the value of x is known, the value of y may be predicted.

Option A is correct.

A least squares regression line may be used to predict a value of y if the corresponding x value is given

The least square regression line implies a mathematical equation which models the relationship between the dependent and independent variables. Hence, it may be used to predict a value of y if the corresponding x value is given.

Hence, the most appropriate option is "

may be used to predict a value of y if the corresponding x value is given."

Learn more : https://brainly.com/question/16975425

Answer:

1. Clockwise rotation by π/2 radians

: D

2. Reflection about the x-axis

: E

3. Counterclockwise rotation by π/2 radians

: F

4. The projection onto the x-axis given by T(x,y) = (x,0)

: C

5. Reflection about the y-axis : A

6. Reflection about the line y = x : B

Step-by-step explanation:

Given a linear transformation [tex]T:\mathbb{R}^2\to\mathbb{R}^2[/tex], one matrix representation of T is obtained by stacking the vectors T(1,0) and T(0,1) in columns.

a) A counter clockwise rotation of [tex]\pi/2[/tex] radians sends (1,0) to (0,-1) and it sends (0,1) to (1,0), so the matrix representation is

[tex]\left[\begin{matrix} 0& 1 \\ -1 & 0 \end{matrix}\right][/tex] which corresponds to matrix D.

From now on, I will provide the values of T(1,0) and T(0,1)

b) Reflection about the x-axis T(1,0) = (1,0) and T(0,1) = (0,-1), which corresponds to matrix E.

c) Counterclockwise rotation by π/2 radians T(1,0) = (0,1), T(0,1) = (-1,0). Matrix   F

d) The projection onto the x-axis given by T(x,y) = (x,0). T(1,0) = (1,0) T(0,1) = (0,0). Matrix C

e) Reflection about the y-axis T(1,0) = (-1,0) T(0,1) = (0,1). Matrix A

f) Reflection about the line y = x. This transformation corresponds to interchanging the values of x and y. That is, send (x,y) to (y,x). So, in this case

T(1,0) = (0,1) T(0,1) = (1,0). Matrix B

Answer:

g(-5) = 2

g(0) = -2

g(1) = 2

Step-by-step explanation:

g(-5) satisfies x <-2, since -5 is less than -2.

g(0) satisfies -2≤x≤1 since 0 is greater than 2 but less than 1. When we plug in 0 into (x+1)^2 -2, we get -2.

g(1) satisfies -2≤x≤1 since it says that x is less than OR EQUAL TO 1. We then plug in 1 into (x+1)^2 -2 and get 2.

Answer:

Option c

Step-by-step explanation:

Systematic sampling is a probability type of samplng method in which elements are picked from a large population at a random start point and then the others are picked by constant periodic intervals which is usually done by dividing the population size by the chosen sample size. Then do a random start between 1 and the sampling interval, then repeatedly add the sampling interval to select subsequent elements.

Answer:

Step-by-step explanation:

Area of rectangular menu

Length × breadth

3×2=6sq feet

Answer:

6 ft^2

Step-by-step explanation:

area of rectangle = length * width

area = 3 ft * 2 ft

area = 6 ft^2

Answer:

Please the read the answer below

Step-by-step explanation:

In order to find the 95% confidence interval for the difference of the two populations, you use the following formula (which is available when the population size is greater than 30):

CI = [tex](p_1-p_2)\pm Z_{\alpha/2}(\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}})[/tex]     (1)

where:

p1: proportion of one population = 52/9853 = 0.0052

p2: proportion of the other population = 41/11541 = 0.0035

α: tail area = 1 - 0.95 = 0.05

Z_α/2: Z factor of normal distribution = Z_0.025 = 1.96

n1: sample of the first population = 52

n2: sample of the second population = 41

You replace the values of all parameters in the equation (1) :

[tex]CI =(0.0052-0.0035)\pm (1.96)(\sqrt{\frac{0.0052(1-0.0052)}{52}+\frac{0.0035(1-0.0035)}{41}})\\\\CI=0.0017\pm0.026[/tex]

By the result obtained in the solution, you can conclude that the sample is not enough, because the margin error is greater that the difference of proportion of each sample population.

Answer:

D. e - 35

Step-by-step explanation:

We have that:

George earned e extra points.

Kate earned k extra points.

Kate earned 35 fewer extra credit points than George.

This means that k is e subtracted by 35, that is:

k = e - 35

So the correct answer is:

D. e - 35

Answer:

a) 64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

b) The hardness distribution is not given. But you would have to find s when n = 39, then the probability would be 1 subtracted by the pvalue of Z when X = 51.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n trials, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]

In this question:

[tex]n = 48, \mu = 48*5 = 240, s = 4\sqrt{48} = 27.71[/tex]

These values are in minutes.

(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?

From 6:50 PM to 11 PM there are 4 hours and 10 minutes, so 4*60 + 10 = 250 minutes. This probability is the pvalue of Z when X = 250. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{250 - 240}{27.71}[/tex]

[tex]Z = 0.36[/tex]

[tex]Z = 0.36[/tex] has a pvalue of 0.6406

64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51?

The hardness distribution is not given. But you would have to find s when n = 39(using the standard deviation of the population divided by the square root of 39, since it is not a sum here), then the probability would be 1 subtracted by the pvalue of Z when X = 51.

Answer:

Step 1

Step-by-step explanation:

Deepak given problem is: [tex]\dfrac52-3x-5+4x=-\dfrac74[/tex]

[tex]\left|\begin{array}{c|cc}$Steps&$Resulting Equation\\$1, Use the distributive property to simplify.&\dfrac52-5+4x-3x=-\dfrac74\\$2, Simplify by combining like terms&-\dfrac52+x=-\dfrac74\end{array}\right|[/tex]

[tex]\left|\begin{array}{c|cc}$3, Use the addition property of equality&-\dfrac52+\dfrac52+x=-\dfrac74+\dfrac{10}{4}\\$4, Simplify by combining like terms&x=\dfrac34\end{array}\right|[/tex]

In Step 1, he simply rearranged like terms. He did not use the distributive property. Therefore, the instruction in Step 1 was incorrect.

Answer:

step 1

Step-by-step explanation:

Answer:

The probability that a basketball will weigh between 21.4 and 23.8 ounces is 0.62465.

Step-by-step explanation:

We have all this information from the question:

To answer this question:

Important concepts to remember:

For this, it is crucial three concepts: the standard normal distribution, the standard normal table, and z-scores:

Roughly speaking, the standard normal distribution is a normal distribution for standardized values. We can obtain standardized values using the formula for z-scores:

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

And these values represent the distance from the population mean in standard deviation units. When they are positive, these values are above the population mean, [tex] \\ \mu[/tex]. In case they are negative, they are below [tex] \\ \mu[/tex].

We can obtain probabilities for any normally distributed data using the standard normal distribution. These values are tabulated into the standard normal table, available in Statistics books or on the Internet.

In general, these values are cumulative probabilities, that is, probabilities from [tex] \\ -\infty[/tex] to the value x in question (a raw value).

At this stage, we have enough information to solve the question.

Solving the question

Cumulative probability for [tex] \\ P(X<21.4)[/tex] ounces.

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

[tex] \\ z = \frac{21.4 - 22}{1.2}[/tex]

[tex] \\ z = \frac{-0.6}{1.2}[/tex]

[tex] \\ z = -0.5[/tex]

That is, the raw score [tex] \\ x = 21.4[/tex] is 0.5 standard deviations below, [tex] \\ z = -0.5[/tex], the population mean.

Since [tex] \\ P(X<21.4) = P(Z<-0.5)[/tex], we can consult the standard normal table, using [tex] \\ z = -0.5[/tex] as an entry (using its first column).

The first row of this table has a second digit in the decimal part for the value of z. In this case, this second digit is zero (or to be more precise, -0.00), because [tex] \\ z = -0.50[/tex]. With the intersection of these two values in the table, namely, -0.5 and -0.00, we finally obtain the cumulative probability, [tex] \\ P(Z<-0.50) = 0.30854[/tex].

Thus, [tex] \\ P(X<21.4) = P(Z<-0.50) = 0.30854[/tex]

Cumulative probability for [tex] \\ P(X<23.8)[/tex] ounces.

We can follow the same steps as before:

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

[tex] \\ z = \frac{23.8 - 22.0}{1.2}[/tex]

[tex] \\ z = \frac{1.8}{1.2}[/tex]

[tex] \\ z = 1.5[/tex]

[tex] \\ P(X<23.8) = P(Z<1.5) = 0.93319[/tex] using the standard normal table (z =1.5, +0.00).

Therefore, [tex] \\ P(X<23.8) = P(Z<1.5) = 0.93319[/tex]

Then, to answer the probability that a basketball will weigh between 21.4 and 23.8 ounces, we subtract (as we mentioned before) both cumulative probabilities:

[tex] \\ P(21.4 < X < 23.8) = P(-0.5 < Z < 1.5) = P(X<23.8) - P(X<21.4) = P(Z<1.5) - P(Z<-0.5) = 0.93319 - 0.30854 = 0.62465[/tex]

Then, the probability that a basketball will weigh between 21.4 and 23.8 ounces is 0.62465.

We can see this probability represented by the shaded area in the below graph.  

Answer:

C. 44

Step-by-step explanation:

[tex] \frac{1}{2} m - \frac{3}{4} n = 16 \\ \\ \frac{1}{2} m - \frac{3}{4} \times 8 = 16..( plug \: n = 8) \\ \\ \frac{1}{2} m - 3 \times 2 = 16 \\ \\ \frac{1}{2} m - 6 = 16 \\ \\ \frac{1}{2} m = 16 + 6 \\ \\ \frac{1}{2} m = 22 \\ \\ m = 22 \times 2 \\ \\ m = 44[/tex]

The value of m in the given equation is equal to 3.

Given the following data:

To find the value of m in the given equation:

In this exercise, you're required to determine the value of m in the given equation. Thus, we would translate the word problem into an algebraic equation.

[tex]\frac{1}{2m} -\frac{3}{4n} =16[/tex]

Substituting the value of n in the equation, we have;

[tex]\frac{1}{2m} -\frac{3}{4(8)} =16\\\\\frac{1}{2m} -\frac{3}{32} =16\\\\16m-32=16\\\\16m=16+32\\\\16m=48\\\\m=\frac{48}{16}[/tex]

m = 3.

Read more on word problems here: brainly.com/question/13170908

Answer:

57.1428571429 miles per hour Round off the answer to what your teacher asked.

Step-by-step explanation:

Since we want final answer in miles per hour, lets change the 30 mins to 0.5 hours

Phase 1 =25miles per 0.5 hours

Phase 2 = (200miles-25miles) per 3 hours

Speed = distance/time

Average speed = total distance/ time

Total distance is 200miles because both phases say from new york that means it travels 25 miles away from new york then 3 hours later it is 200 miles away from new york

total time =3 hours+0.5 hours = 3.5 hours

Average speed = 200/3.5

Average speed = 57.1428571429 miles per hour

Rate brainliest please

We want to get the average speed between the 30 minute and 3-hour time frame.

The average speed in that time frame is 70 miles per hour.

We will define average speed as the quotient between the distance travelled and the time it takes to travel that distance.

We know that at 30 minutes, the car is 25 miles away from NY

At 3 hours, the car is 200 miles away from NY.

So the distance travelled in that time frame is:

200 miles - 25 miles = 175 miles.

And the time between 30 minutes and 3 hours is just:

3 h - 0.5h = 2.5 h

So the average speed is:

S = (175 mi)/(2.5 h) = 70 mi/h

The average speed is 70 miles per hour.

If you want to learn more, you can read:

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Answer:

The factorized form will be {(2x^3)-1}×{(8x^3)+9}=0

The simplified form will be (16x^6)+(10x^3)-9=0

Answer:

8p + 2s <= 150

Step-by-step explanation:

Let p = number of a pizza.

Let s = price of a bottle of soda.

The inequality is

8p + 2s <= 150

Answer:

At  α= 0.05, there is enough evidence to support the claim that the average rent has increased from $2800.

P-value = 0.001.

Step-by-step explanation:

The question is incomplete:

The average monthly rent for a one bedroom apartment in NYC was $2,800 in 2013. A random sample of 16 apartments in NYC showed that the average rent is $2,850 with standard deviation of $50. . Test the claim that the average rent has increased at α= 0.05.

This is a hypothesis test for the population mean.

The claim is that the average rent has increased from $2800.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=2800\\\\H_a:\mu> 2800[/tex]

The significance level is 0.05.

The sample has a size n=16.

The sample mean is M=2850.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=50.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{50}{\sqrt{16}}=12.5[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2850-2800}{12.5}=\dfrac{50}{12.5}=4[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=16-1=15[/tex]

This test is a right-tailed test, with 15 degrees of freedom and t=4, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>4)=0.001[/tex]

As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average rent has increased from $2800.

Answer:

Step-by-step explanation:

Plotting a point A and tracing a point B at 4 units from A results in a circle.

▪The locus of a point at equal distance from a fixed point is a circle.

▪Point A is (5,5) and length of AB is 4 units

This implies that the radius of circle is 4 units.

▪The point B can be swirled around A keeping the distance AB constant.

▪The resulting figure is a circle.

▪This circle is plotted and attached below.

I hope this helped. I am sorry if you get it wrong

Answer:

This is the right answer for Edementum and Plato users

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Answer: 90 minutes

Step-by-step explanation:

Area of the side = 15 x 18 = 270 sq. ft.

3 sq. ft take a minute to paint

270 sq. ft. will take 270 / 3

= 90 minutes

Answer:

  15

Step-by-step explanation:

The general form of an exponential equation is ...

  f(x) = (initial value)(growth factor)^x

That is, the "growth factor" is the base of the exponent. In your equation ...

  f(x) = (1/5)(15^x)

the growth factor is 15.

Answer:

D

Step-by-step explanation:

because you put the one and the five and BOOM the inter carol makes the wheel go round and round.