Find the surface area of the solid shown or described. If necessary, round to the nearest tenth. 348m^2 484m^2 180.7m^2 262m^2

Answer:

a) 294

b) 180

c) 75

d) 174

e) 105

Step-by-step explanation:

I assume that for each problem, the first digit can't be 0.

a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.

6×7×7 = 294

b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.

6×6×5 = 180

c) Again, each digit can only be used once, but this time, the last digit must be odd.

If only the last digit is odd, there are 3×3×3 = 27 possible numbers.

If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.

If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.

If all three digits are odd, there are 3×2×1 = 6 possible numbers.

The total is 27 + 24 + 18 + 6 = 75.

d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.

If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.

If the first digit is greater than 3, there are 3×7×7 = 147 numbers.

The total is 6 + 21 + 147 = 174.

e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.

If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.

The total is 15 + 90 = 105.

Answer:

a. 45/1024

b. 1/4

c. 15/128

d. 193/512

e. 9/256

Step-by-step explanation:

Here, each position can be either a 0 or a 1.

So, total number of strings possible = 2^10 = 1024

a) For strings that have exactly two 1's, it means there must also be exactly eight 0's.

Thus, total number of such strings possible

10!/2!8!=45

Thus, probability

45/1024

b) Here, we have fixed the 1st and the last positions, and eight positions are available.

Each of these 8 positions can take either a 0 or a 1.

Thus, total number of such strings possible

=2^8=256

Thus, probability

256/1024 = 1/4

c) For sum of bits to be equal to seven, we must have exactly seven 1's in the string. Also, it means there must also be exactly three 0's

Thus, total number of such strings possible

10!/7!3!=120

Thus, probability

120/1024 = 15/128

d) Following are the possibilities :

There are six 0's, four 1's :

So, number of strings

10!/6!4!=210

There are seven 0's, three 1's :

So, number of strings

10!/7!3!=120

There are eight 0's, two 1's :

So, number of strings

10!/8!2!=45

There are nine 0's, one 1's :

So, number of strings

10!/9!1!=10

There are ten 0's, zero 1's :

So, number of strings

10!/10!0!=1

Thus, total number of string possible

= 210 + 120 + 45 + 10 + 1

= 386

Thus, probability

386/1024 = 193/512

e) Here, we have fixed the starting position, so 9 positions remain.

In these 9 positions, there must be exactly two 1's, which means there must also be exactly seven 0's.

Thus, total number of such strings possible

9!/2!7!=36

Thus, probability

36/1024 = 9/256

Answer:

When an outline exists.

Step-by-step explanation:

As compared to the range, the interquatile range is somewhat resistant to the outliers. This is because the interquartile range itself is not always affected by the outliers if they lie at both ends of the data sets.

The IQR only describes the range of the middle 50% of the values in a data set, which is calculated as the difference between the 75th and 25th percentile values.

It also helps in the identification of these outliers using mild outliers being those values lower than the 25th quartile minus 1.5×IQR, or those values greater than the 75th quartile plus 1.5×IQR.

Answer:

here,

a=b+12

b=a-12----> equation (i)

b= c+4

putting the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

hope this helps...

Good luck on your assignment...

The value of a + c is 16.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

a=b+12

So, b=a-12 ---- equation (i)

and, b= c+4

Substitute the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

Hence, the value of a+ c is 16.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ2

Answer:

  A.  y > x+1; y≤10; x≥0

Step-by-step explanation:

Other things being equal, which they are, you're looking for an inequality that has "y >". You know this because shading is above (>) the dashed line (not ≥). Only choice A matches.

__

If the boundary line were solid, you would be looking for "y ≥", since y=(boundary line) is included in the solution set in that case.

Answer:

The answer is option C

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the line first find the slope

The line has a y intercept of 2 which is

(0 , 2)

Slope of the line using points

( 1 ,1) and (0,2) is

[tex]m = \frac{2 - 1}{0 - 1} = \frac{1}{ - 1} = - 1[/tex]

So the equation of the line using point (1,1) is

y - 1 = - 1(x - 1)

y - 1 = - x + 1

x + y - 1 - 1 = 0

We have the final answer as

Hope this helps you

Answer:

A,B,E

Step-by-step explanation:

Just took the quiz

Answer:

A,B,E

Step-by-step explanation:

Give me brainliest.

Answer:

Step-by-step explanation:

For private Institutions,

n = 20

Mean, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (43120 - 34623.05)^2+ (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95

Standard deviation = √(1527829234.95/20

s1 = 8740.22

For public Institutions,

n = 20

Mean, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15

Summation(x - mean)² = (25469 - 25063.15)^2+ (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95

Standard deviation = √(283738188.55/20

s2 = 3766.55

This is a test of 2 independent groups. Let μ1 be the mean out-of-state tuition for private institutions and μ2 be the mean out-of-state tuition for public institutions.

The random variable is μ1 - μ2 = difference in the mean out-of-state tuition for private institutions and the mean out-of-state tuition for public institutions.

We would set up the hypothesis. The correct option is

-B. H0: μ1 = μ2 ; H1: μ1 > μ2

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)

t = 9559.9/2128.12528473889

t = 4.49

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114

df = 26

We would determine the probability value from the t test calculator. It becomes

p value = 0.000065

Since alpha, 0.01 > than the p value, 0.000065, then we would reject the null hypothesis. Therefore, at 1% significance level, the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions.

Answer:  

y = x - 3

y = -5x +2

Step-by-step explanation:  for The "missing" coefficient of x (m in the y=mx+b format) is an implied +1. So the slope is "up-one & over one." y-intercept is -3

y = -5x +2   The slope is -5 so "down 5 & over 1" on the graph, The y-intercept is +2

Answer:

Option B

Step-by-step explanation:

Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -

[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]

Convert this to slope - intercept form -

[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]

Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -

( 0, 10 ),

( 15, 9 ),

( 17, 0 )

When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -

Option B

Answer:

V =972 pi mm ^3

Step-by-step explanation:

The diameter is 18 so the radius is 1/2 of the diameter

18/2 = 9

r=9

The volume of a cylinder is

V = pi r^2 h

V = pi (9)^2 12

V =972 pi mm ^3

Answer:

972pi mm^3

Step-by-step explanation:

What is the volume of the cylinder below? A cylinder with a height of 12 millimeters and diameter of 18 millimeters. 108 pi mm3 216 pi mm3 648 pi mm3 972 pi mm3

V = (pi)r^2h

r = d/2 = 18 mm/2 = 9 mm

V = (pi)(9 mm)^2(12 mm)

V = 972pi mm^3

Answer:

C = 56.6

Step-by-step explanation:

Circumference Formula: C = 2πr

Simply plug in r into your formula

C = 2π(9)

C = 18π or 56.556

Answer:

D. Find the x- and y-intercepts and then graph

Step-by-step explanation:

Answer:

1. The 99% confidence interval is from 941.527 to 958.473

2. The 99% confidence interval is from 933.054 to 966.946

3. The 99% confidence interval is from 916.108 to 983.892

Step-by-step explanation:

The confidence interval is given by

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by

[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]

Where n is the sample size,

s is the sample standard deviation,

[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level

The t-score corresponding to 99% confidence level is

Significance level = α = 1 - 0.99 = 0.01/2 = 0.005

Degree of freedom = n - 1 = 13 - 1 = 12

From the t-table at α = 0.005 and DoF = 12

t-score = 3.055

1. 99% Confidence Interval when s = 10

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]

The 99% confidence interval is from 941.527 to 958.473

2. 99% Confidence Interval when s = 20

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]

The 99% confidence interval is from 933.054 to 966.946

3. 99% Confidence Interval when s = 40

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]

The 99% confidence interval is from 916.108 to 983.892

As the sample standard deviation increases, the range of confidence interval also increases.

Answer:

The time period is 13 years.

Step-by-step explanation:

Interest rate (r )= 5% or 5%/12 = 0.42% per months

The investment amount (Present value) = $10500

Final expected amount (future value) = $20000

Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.

Use the below formula to find the time period.

Future value = present value (1 + r )^n

20000 = 10500(1+0.0042)^n

1.9047619 = (1+0.0042)^n

1.9047619 = 1.0042^n

n = 153.74 months.

Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)

Answer:

7

Step-by-step explanation:

Rs 150- Rs 75=Rs 75 remaining

Rs 75/10= 7 as whole

Step-by-step explanation:

given,

total amnt =rs.150

cost of pen= rs.75

now,

left money =150_75

=rs.75

now,cost of 1 copy=10

then , no. of copies=75/10

=7.5

so he can buy 7 copies.

Answer:

5

Step-by-step explanation:

(14 × 5 × 4) ÷ (28 × 2)

Solve brackets.

280 ÷ 56

Divide.

= 5

Answer:. x = 18

Step-by-step explanation:

Solve by substitution. Given: y= 12x. Rewrite the original equation y= 180 + 2x to 12x = 180 +2x. Subtract 2x from both sides. 10x = 180. Then divide both sides by 10.

x=18

So once she has sold 18 necklaces, she has covered her costs (180 + 36) and she begins to make a profit.

Answer:

$-4.90.

Step-by-step explanation:

Fathi has $1.10. Each sheet costs him $0.25. He wants to print 47 pages.

If he prints double sided, then he will use 47 / 2 = 23.5 sheets of paper. But he can't print a half-sheet, so he will use 24 sheets of paper.

Each sheet costs $0.25. 0.25 * 24 = 6. The printing will cost him $6.

Since he only has $1.10, his remaining balance will be 1.1 - 6 = -4.9. The balance on his printing account will be $-4.90.

Hope this helps!

Answer:

-1.90

Step-by-step explanation:

Khan Academy

I got it right for sure

Answer:

Step-by-step explanation:

Let's solve this by eliminating z, then we'll go from there.

Add 6 times the second equation to the first.

  (3x -3y +6z) +6(x +2y -z) = (3) +6(4)

  9x +9y = 27 . . . simplify

  x + y = 3 . . . . . . divide by 9 [eq4]

Add 13 times the second equation to the third.

  (5x -8y +13z) +13(x +2y -z) = (2) +13(4)

  18x +18y = 54

  x + y = 3 . . . . . . divide by 18 [eq5]

Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:

  y = 3 -x . . . . solve eq5 for y

  x +2(3 -x) -z = 4 . . . . substitute into the second equation

  -x +6 -z = 4

  x = 2 - z . . . . . . add x-4

  y = 3 -(2 -z)

  y = z +1

So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...

  x = 2 -a

  y = 1 +a

  z = a

_____

Check

First equation:

  3(2-a) -3(a+1) +6a = 3

  6 -3a -3a -3 +6a = 3 . . . true

Second equation:

  (2-a) +2(a+1) -a = 4

  2 -a +2a +2 -a = 4 . . . true

Third equation:

  5(2-a) -8(a+1) +13a = 2

  10 -5a -8a -8 +13a = 2 . . . true

Our solution checks algebraically.

Answer:

Step-by-step explanation:

A) The constant of proportionality in terms of minutes per bracelet is

15/3 = 5 minutes per bracelet

B) The constant of proportionality represents man hour rate

C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

t = kb

D) the constant of proportionality in terms of number of bracelets per minute is

3/15 = 1/5

E) The constant of proportionality represents production rate

F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

b = kt

G) The constants of proportionality are reciprocals

H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.

Answer:the sample answers, change them up so you dont get in trouble

A To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:

constant of proportionality=15 MINUTES/3 BRACELETS=5  minutes per bracelet.

B The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.

C Here’s one way to set up the equation:

time = constant of proportionality × number of bracelets

Let m be time in minutes and let b be the number of bracelets. Substitute the variables (m and b) and the value of the proportionality constant (5 minutes per bracelet) into the equation: m = 5b.

thats all ik srry

Step-by-step explanation:

Answer:

Vertex:  ( -1 , − 9 )

X intercepts (0,-4)(0,2)

Step-by-step explanation:

Answer:

( -1, -9)

And

x-intercepts: (-4, 0), (2,0)

Step-by-step explanation:

Sacrificed my grade

Answer:

[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]    

[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]    

Step-by-step explanation:

Data given

20 13 21 18 19 22 19 15 12 12 18 21

We can calculate the sample mean and deviation with the following formulas:

[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And we got:

[tex]\bar X = 17.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=3.61 represent the sample standard deviation

n=12 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=12-1=11[/tex]

Since the Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be given by [tex]t_{\alpha/2}=[/tex]

Now we have everything in order to replace into formula (1):

[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]    

[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]    

Answer:

The probability that he requires 18 shots is 0.04785

Step-by-step explanation:

To answer this, we shall be using the negative binomial distribution

From the question;

P = 0.25 , r = 6

q will be 1-p = 1-0.25 = 0.75 Which is the probability of missing a target on any trial

P(X = 18) = (18-1)C(6-1) (0.25)^6 (0.75)^(18-6)

P(X = 28) = 17C5 (0.25)^6 (0.75)^12) = 0.04785

Answer:

y=x-1

Step-by-step explanation:

since the slope is just one up and one over and it's positive it would just be x

and since the intercept is just -1 it would be y=x-1

Answer:

- How does their confidence level compare to the confidence level of the interval stated above?

Provided all the other parameters involved in the determination of margin of error remains constant, the confidence level of the interval obtained by the second set of researchers (with a larger margin of error) is definitely greater than the confidence of the first stated interval.

- How will the margin of error of the 95% confidence interval constructed based on data from the new survey compare to the margin of error of the interval stated above?

Provided all the other parameters involved in the determination of margin of error remains constant, the margin of error of the confidence interval of data from the new survey will be less than the margin of error of the initially stated interval because the margin of error is inversely proportional to the sample size and the sample size of the new survey (2500) is more than the sample size of the old survey (1155).

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Since the sample sizes are so large, the critical value for this would be obtained from the z-distribution tables.

And critical value increases with higher confidence level.

Which directly translates to margin of error increasing with higher confidence level.

A) Hence, if all other parameters stay the same, the margin of error can only be larger if the confidence level of the second researchers is more than than the confidence level at which the initial research was carried out.

B) In the determination of the margin of error

Margin of Error = (Critical value) × (standard Error of the mean)

Standard error of the mean = σₓ = (σ/√n)

where σ = population standard deviation or sample standard deviation for a sample size that's very large

n = sample size

If the critical value stays the same (the tests in the two years being considered are performed at the same level) and the standard deviation too remain almost the same (the question asks us to assume that the population characteristics, with respect to how much time people spend relaxing after work, have not changed much within a year), the margin of error is obviously inversely proportional to the sample size.

Margin of error = (zσ/√n)

zσ = constant = k

Margin of error = (k/√n)

So, if the sample size increases, the new margin of error that will be obtained will be lesser.

Hope this Helps!!!

Answer:

a

Step-by-step explanation:

Answer:

[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]    

[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X=32.9[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s=4.9 represent the sample standard deviation

n=8 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

the degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this cae would be [tex]t_{\alpha/2}=2.365[/tex]

Now we have everything in order to replace into formula (1):

[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]    

[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]    

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

a

 [tex]z = 6.25 \ cm/yr[/tex]

b

   [tex]k = -0.25 \ cm /yr[/tex]

Step-by-step explanation:

From the first image  the rate of  rate of change of the height from age 8 to 16  

  is  mathematically evaluated from the graph as  

             [tex]z = \frac{175 - 125}{16-8}[/tex]

            [tex]z = 6.25 \ cm/yr[/tex]

From the first image  the rate of  rate of change of the height from age 60 to 80.

  is  mathematically evaluated from the graph as

             [tex]k = \frac{175 - 170}{60-80}[/tex]

            [tex]k = -0.25 \ cm /yr[/tex]

Answer:

Step-by-step explanation:

Using Secant-Secant theorem we can find the value of x.

The product of one segment and its external segment is equal to the product of the other segment and its external segment.

5 × 3 = x × 4

15 = 4x

15/4 = x

3.75 = x