The radius of a circle is increasing uniformly at the rate of 5cm/sec. Find the rate at which the area of the circle is increasing when the radius is 6 cm.

A) The total commission she earned is $475

B) Total sales for commission of $1375 is $20000

A) Total Commission = Commission 1+ Commission 2

Where:

Commission 1 = 5% of first $5000

Commission 2 = 7.5% of the amount left after $5000 is subtracted

thus

Commission 1 = $5000 * 0.05 = $250

Commission 2= $3000 * 0.075 = $225

Commission total = $250 + $225 = $475

The total commission she earned is $475

B) Total sales = Sales with 5% commission + Sales with 7.5% commission

Sales with 5% commission = $5000

Commission At 7.5% = Total commission -Commission with 5% =    $1375 - $250

Sales * 0.075 =  $1125

Sales with 7.5% commission = $15000

Total sales = $5000+$15000

Total sales = $20000

Total sales for commission of $1375 is $20000

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Complete question is:

A salesperson earns commission on the sales that she makes each month. The salesperson earns a 5% commission on the first $5,000 she has in sales.

The salesperson earns a 7.5% commission on the amount on her sales that are greater than $5,000.

Part A:

This month the salesperson had $8,000 in sales. What amount of commission, in dollars, did she earn?

Part B:

The salesperson earned $1,375 in commission, last month. How much money, in dollars, did she have in sales last month?

The derivative of (f∘g)(x) can be found using the chain rule, which states that the derivative of (f∘g)(x) is (f'(g(x)))(g'(x)).

In this case, (f∘g)(x) = f(g(x)) = 3(5^x) + 3cos(x), so we need to find f'(g(x)) and g'(x) and then multiply them together. The derivative of f(x) is f'(x) = 15^x * ln(5) + 1, so the derivative of f(g(x)) with respect to g(x) is f'(g(x)) = 15^(g(x)) * ln(5) + 1. The derivative of g(x) is g'(x) = -3sin(x). Therefore, using the chain rule, we have:(f∘g)'(x) = f'(g(x)) * g'(x) = (15^(g(x)) * ln(5) + 1) * (-3sin(x))Substituting g(x) = 3cos(x), we get:(f∘g)'(x) = (15^(3cos(x)) * ln(5) + 1) * (-3sin(x))So the correct answer is: (3(5^3cos(x)) ln(5) + 1) * (-3sin(x))

For more similar questions on topic a) The intervals for which f(x) = -5.5sin(x) + 5.5cos(x) is concave up and concave down on [0,2π] can be found by analyzing the second derivative of the function. Taking the second derivative of f(x), we get:

f''(x) = -5.5cos(x) - 5.5sin(x)

To find the intervals of concavity, we need to determine where f''(x) is positive and negative.

When f''(x) > 0, the function is concave up. When f''(x) < 0, the function is concave down.

Setting f''(x) = 0, we get:

-5.5cos(x) - 5.5sin(x) = 0

Simplifying, we get:

cos(x) + sin(x) = 0

Solving for x, we get:

x = 3π/4, 7π/4

These are the possible points of inflection for the function.

Using test intervals, we can determine the intervals of concavity:

When 0 ≤ x < 3π/4 or 7π/4 < x ≤ 2π, f''(x) < 0, so f(x) is concave down.

When 3π/4 < x < 7π/4, f''(x) > 0, so f(x) is concave up.

b) The possible points of inflection for f(x) on [0,2π] are x = 3π/4 and x = 7π/4. To find the coordinates of these points, we can substitute each value of x into the original function f(x):

f(3π/4) = -5.5sin(3π/4) + 5.5cos(3π/4) = 5.5√2 - 5.5√2/2 = 5.5√2/2

So the coordinates of the point of inflection at x = 3π/4 are (3π/4, 5.5√2/2).

Similarly, we can find the coordinates of the point of inflection at x = 7π/4:

f(7π/4) = -5.5sin(7π/4) + 5.5cos(7π/4) = -5.5√2 - 5.5√2/2 = -5.5(3/2)√2

So the coordinates of the point of inflection at x = 7π/4 are (7π/4, -5.5(3/2)√2).

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The measure of angle D is 25°

Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the opposite interior angles.

Angle D and angle C are the two opposite angles.

Therefore;

40+9x-2 = 20x +5

38+9x = 20x +5

38-5 = 20-9x

11x = 33

divide both sides by 11

x = 33/11

x = 3

Therefore since angle D = 9x-2

substitute 3 for x

D = 9(3) - 2

D = 27 -2

D = 25°

Therefore the measure of angle D is 25°

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1. The number of students choosing walking as their preferred method of transportation is 9. Therefore, the correct option is C.

2. The total students participated in the survey are 20. Therefore, the correct option is B.

3. The percentage of the total students choosing skateboarding is 10%. Therefore, the correct option is A.

4. The percentage of the boys choosing walking is 30%. Therefore, the correct option is A.

5. The percentage of the students who chose biking were girls is 37.5%. Therefore, the correct option is B.

1. The number of students who chose walking as their preferred method of transportation based on the information provided is 9. The total number of students who chose walking is given as 9 (3 boys + 6 girls). Hence the correct answer is option C.

2. The total students who participated in the survey based on the information provided are 20. The total number of students is given as 20 (10 boys + 10 girls). Hence the correct answer is option B.

3. The percentage of the total students who chose skateboarding based on the information provided is 10%. 3 students chose skateboarding out of 20 total students, so the percentage is (3/20) * 100% = 10%. Hence the correct answer is option A.

4. The percentage of the boys who chose walking based on the information provided is 30%. 3 boys chose walking out of 10 total boys, so the percentage is (3/10) * 100% = 30%. Hence the correct answer is option A.

5. The percentage of the students who chose biking were girls based on the information provided is 37.5%. 3 girls chose biking out of 8 total students who chose biking, so the percentage is (3/8) * 100% = 37.5%. Hence the correct answer is option B.

Note: The question is incomplete. The complete question probably is: Given the following data:

Activity Boys Girls Total

Walk 3 6 9

Bike 5 3 8

Skateboard 2 1 3

Total 10 10 20

1. How many students chose walking as their preferred method of transportation? A. 6 B. 3 C. 9 D. none of these. 2. How many total students participated in the survey? A. 10 B. 20 C. 15 D. none of these 3. What percentage of the total students chose skateboarding? A. 10% B. 20% C. 30% D. none of these. 4. What percentage of the boys chose walking? A. 30% B. 45% C. 25% D. none of these. 5. What percentage of the students who chose biking were girls? A. 30% B. 37. 5% C. 45% D. none of these.

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The correct comparison of the numbers is:

678,200 > 678,194 > 678,227

Therefore, the answer is the last option, "678,200 > 678,194 > 678,227".

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The divergence of the given vector field at all points where it's defined is div [tex]F = 4x - 2x × cos(x^2).[/tex]

To find the divergence of the given vector field at all points where it's defined, we will use the following terms:

divergence, vector field, and partial derivatives.

The given vector field is[tex]F = (2x^2 - sin(x^2)) i + 5j - sin(x^2) k.[/tex]

To find the divergence of F (div F), we need to take the partial derivatives of each component with respect to their

respective variables and then sum them up. So, div [tex]F = (∂(2x^2 - sin(x^2))/∂x) + (∂5/∂y) + (∂(-sin(x^2))/∂z)[/tex].

Find the partial derivative of the first component with respect to x:

[tex]∂(2x^2 - sin(x^2))/∂x = 4x - 2x × cos(x^2)[/tex] (applying chain rule).

Find the partial derivative of the second component with respect to y:

∂5/∂y = 0 (since 5 is a constant).

Find the partial derivative of the third component with respect to z:

[tex]∂(-sin(x^2))/∂z = 0[/tex] (since there is no z variable in the component).

Sum up the partial derivatives:

[tex]div F = (4x - 2x × cos(x^2)) + 0 + 0 = 4x - 2x × cos(x^2).[/tex]

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Answer:

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

The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n:

As per above mentioned definition we see that:

Hence the quotient of (n + 3)! and (n + 1)! is:

Answer:

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

Since CD is diameter, therefore the angle CAD opposite to it is a right angle.

We are given the lengths of two legs, AD = 16 and AC = 30.

Use Pythagorean theorem to find the length of the hypotenuse CD:

ANSWER:

(x+7)^2=16

Step-by-step explanation:

x^2-14x+49=16

x^2-14x+49-16=0

x^2-14x+33=0

subtract -33 on both sides

x^2-14x+33-33=-33

x^2-14x=-33

Add 49 on both sides

x^2-14x+49=-33+49

x^2-14x+49=16

x^2-7x-7x+49=16

x(x-7)-7(x-7)=16

(x-7)(x-7)=16

(x-7)^2=16

The solution is: 14 karat gold is 58.3333...% gold

We have given that;

75% gold and 50% gold and we need to make 200 grams of 58.3333...% gold.

Since, A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Here, we have,

A) x + y = 200

B) .75x + .50y = ( (14/24) * 200)

We multiply equation B) by -1.3333... and get

B) -x -.6666...y = -155.5555... then adding A)

A) x + y = 200  we get

.3333...y = 44.4444...

y = 133.3333... grams 12 karat gold

x = 66.6666... grams  18 karat gold

Double-Checking the answer

133.3333... * .5 = 66.6666...

66.6666 * .75 = 50.0000...

Hence, Concentration of final solution = (66.6666... + 50) / 200 = 58.3333...% which is 14 karat gold

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The equations to find the amount of red fabric Moses has are X = x + 2 and X + 222 = 1/3x + 223. These equations are obtained by using x as the amount of blue fabric and setting up equations based on the given information. So, the correct answer is A) and E).

There are two equations that can be used to find the amount of red fabric Moses has

X = x + 2, This equation represents the fact that Moses bought 2 more yards of red fabric than he originally had of blue fabric. So, the amount of red fabric (X) is equal to the amount of blue fabric (x) plus 2.

X + 222 = 1/3x + 223, This equation represents the fact that after buying 2 more yards of red fabric, Moses has equal amounts of red and blue fabric.

So, the amount of red fabric (X) plus 222 (the additional 2 yards he bought) is equal to one-third of the amount of blue fabric (1/3x) plus 223 (the original 2 yards of red fabric he had).

Therefore, the equations that could be used to find the amount of red fabric Moses has are A) and E).

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--The given question is incomplete, the complete question is given

" 6 Moses makes a school spirit flag. He has as many yards of red fabric as blue fabric. He buys 2 yards more red fabric. Now he has equal amounts of red and blue fabric. Use x to represent the amount of blue fabric. Which equations could you use to find the amount of red fabric Moses has? Select all that apply.

A X = x + 2

B x = 2

C 1/x + 273

D x= 1/3x - 223

E x + 2 2 2 = 1/3 x + 2 2 3

F x- 27 28 = 1/3 x

G = x+ {{22}*2}^3 "--

The top industries are agriculture, mining, tourism, and manufacturing.

The quadratic equations are as given.A manufacturing company in my fiefdom produces and sells ceramic pots.

The company has fixed costs of$ 10,000 per month and variable costs of$ 5 per pot. The company's profit is given by the quadratic function R( x) = -0.2 x2 50x, where x is the number of pots produced and vended in a month.

What's the maximum profit that the company can induce in a month: To break this problem, we can use the formula for chancing the maximum value of a quadratic function, which is given by x = - b/ 2a. In this case, the measure of the x2 term is-0.2, and the measure of the x term is 50. Plugging these values into the formula, we get x = -50/( 2 *(-0.2)) = 125 Hence we obtain the quadratic equation.

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The probability that during the next three months it has;

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 included probability to forecast the likelihood of certain events.

The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

The plant has on the average two breakdowns per month,

so the Poisson distribution is,

[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]

where,

X is the random variable representing the number of events

λ is the average rate at which the events occur

k is the number of events that occur

a)  at least five breakdowns

[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]

P(X =5) = [tex]\frac{e^{-2} 2^5}{5!}[/tex]

= 0.036

Thus, probability that at least five breakdowns in three months is 0.036.

b)  at most eight breakdowns

[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]

[tex]P(X=8) = \frac{e^{-2} 2^8}{8!}[/tex]

= 0.00085.

Therefore, probability of at most eight breakdowns is 0.00085.

c) more than five breakdowns.

[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]

P(X = 6) = [tex]\frac{e^{-2} 2^6}{6!}[/tex]

=0.012

Therefore, probability of more than five breakdowns is 0.012.

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The probability of choosing a red marble, then a white marble is 5/36

From the question, we have the following parameters that can be used in our computation:

A bag contains 4 white, 3 blue, and 5 red marbles

If the marbles were replaced, then we have

P(Red) = 5/12

P(White) = 4/12

So, we have

The probability of choosing a red marble, then a white marble  is

P = 5/12 * 4/12

Evaluate

P = 5/36

Hence, the probability of choosing a red marble, then a white marble is 5/36

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The probability that a senior drives to school is 0.3 or 30%.

To find the indicated probability using the two-way table, we need to locate the row for "senior" and the column for "drive to school" and then find the corresponding cell.

Let's assume that the two-way table shows the number of students who either drive or take the bus to school based on their grade level. We are interested in finding the probability that a student drives to school given that they are a senior.

So, we locate the row for "senior" and the column for "drive to school". Let's say that the cell in the intersection of these two is labeled "30". This means that there are 30 seniors who drive to school.

Next, we need to find the total number of seniors in the sample. Let's say that the total number of seniors in the sample is 100.

To find the probability that a senior drives to school, we divide the number of seniors who drive to school by the total number of seniors in the sample:

P(drive to school | senior) = 30/100 = 0.3 or 30%

Therefore, the probability that a senior drives to school is 0.3 or 30%.

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Answer:

38 degrees

Step-by-step explanation:

Vertical angles are congruent(equal measures), so mLA = mLB

STEP 1:

Let's use some simple substitution.

mLA = mLB

mLA = x+21, mLB = 4x-30

You plug these two in and get:

x+21 = 4x-30

This is your equation.

STEP 2:

Let's solve our equation!

x+21 = 4x-30

(add 30 to both sides)

x+51 = 4x

(subtract x from both sides)

51 = 3x

(switch order for comprehension)

3x = 51

(divide both sides by 3)

x = 17

Ta-da! You get the measure of x = 17 degrees.

STEP 3:

Let's plug in our value of x to get the value of LB.

mLB = 4x - 30

mLB = 4(17) - 30

mLB = 68 - 30

mLB = 38

This is your answer.

To solve the inequality -1/4a > 3a, we need to first multiply both sides by -4 to get rid of the fraction:
-1a > 12a
Next, we can subtract 12a from both sides to get:
-13a > 0
Dividing both sides by -13 gives us:
a < 0

To solve the inequality b – 12 > -3, we can add 12 to both sides:
b > 9

Now we need to find values of a and b that satisfy both inequalities. Since a < 0, we can try any negative value of a. Let's try a = -1:

-1/4(-1) > 3(-1)
1/4 > -3

This inequality is true, so we can move on to the next inequality. Let's plug in a = -1 and see if it satisfies b > 9:

b – 12 > -3
b > 9

Since -1 satisfies both inequalities, the values that make both inequalities true are: a = -1 and any value of b greater than 9.

The focus so far has been on similar triangles, but there are also theorems that deal with similar polygon

Theorems of similar triangles are important properties that hold true for any pair of similar triangles. Some of the most commonly used theorems are:

AA Similarity Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

SSS Similarity Theorem: If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar.

SAS Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.

These theorems are also applicable to similar polygons

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The focus so far has been on similar triangles, but there are also theorems that deal with similar polygons.

Hunter needs 3 ounces of seeds and 7 ounces of dried fruit, which will cost him $22 in total. The system of equations is 1.5x + 2.5y = 22 and x + y = 10. The solution is (x,y) = (3,7).

The total amount of snack mix required is 10 ounces. So, the sum of the amount of seeds and dried fruit should be 10.

x + y = 10 ---(Equation 1)

The cost of seeds is $1.50 per ounce and the cost of dried fruit is $2.50 per ounce. The total cost of snack mix should be $22.

1.50x + 2.50y = 22 ---(Equation 2)

To solve the system, we can use substitution method. Solving Equation 1 for y, we get

y = 10 - x

Substituting this value of y in Equation 2, we get

1.5x + 2.5(10 - x) = 22

Simplifying and solving for x, we get

1.5x + 25 - 2.5x = 22

-x = -3

x = 3

So, Hunter needs 3 ounces of seeds and 7 ounces of dried fruit to make 10 ounces of snack mix with a total cost of $22.

The ordered pair is (3, 7).

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The following are the updates for the given ordinary differential equation using Euler's method, the implicit Euler method, and the midpoint method.

To compute the update Ax for the given ordinary differential equation using Euler's method, we first need to discretize the time domain. Let t0 be the initial time and tn = t0 + nh be the time after n steps of size h. Then, using Euler's method, we have:

xn+1 = xn + hf(xn, tn)

where f(xn, tn) = 1 - ƛxn³/6. Therefore,

Ax = xn+1 - xn = h(1 - ƛxn³/6)

Using the implicit Euler method, we have:

xn+1 = xn + hf(xn+1, tn+1)

where f(xn+1, tn+1) = 1 - ƛxn+1³/6. Solving for xn+1, we get:

xn+1 = (xn + h)/[1 + ƛh/6(xn+1)²]

which is a nonlinear equation that needs to be solved iteratively at each step. Therefore, the update Ax becomes:

Ax = xn+1 - xn

Using the midpoint method, we have:

xn+1 = xn + hf(xn+½h, tn+½h)

where f(xn+½h, tn+½h) = 1 - ƛ(xn+½h)³/6. Therefore,

xn+1 = xn + h(1 - ƛxn³/6 + 3ƛx²n h/4)

and the update Ax becomes:

Ax = xn+1 - xn = h(1 - ƛxn³/6 + 3ƛx²n h/4)

These are the updates for the given ordinary differential equation using Euler's method, the implicit Euler method, and the midpoint method.

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The mean winnings for all of the show's contestants can be estimated with 92% certainty. 35014.48385 is the lower bound, while 40669.38281 is the upper bound.            

Lower Bound = [tex]X - t(\alpha/2) * s / \sqrt{(n)[/tex]            

Upper Bound = [tex]X + t(\alpha/2) * s / \sqrt{(n)[/tex]

where                

[tex]\alpha/2 = (1 - confidence\: level)/2 = 0.04 \\ X = sample\: mean = 37841.93333 \\ t(\alpha/2) = critical\: t \:for \:the\: confidence\: interval = 1.887496145 \\ s = sample\: standard\: deviation = 5801.688541 n = sample\: size = 15 \\ df = n - 1 = 14[/tex]          

Thus,          

Lower bound =     35014.48385            

Upper bound =     40669.38281            

A lower bound refers to the smallest possible value or limit that a given quantity or parameter can take. In various fields of mathematics and computer science, lower bounds are used to establish limits on the performance of algorithms, the complexity of computational problems, and the amount of resources required to solve a problem. This information can be useful in developing more efficient algorithms or determining the practicality of a given approach.

Lower bounds are useful for understanding the fundamental limits of a system or process. By establishing a lower bound, researchers and practitioners can better understand the potential of a given technology or approach, and can work to optimize it within the constraints imposed by the lower bound.

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Complete Question:-

How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 92% confidence the mean winning's for all the show's players.

30692 43231 48269 28592 28453

36309 45318 36362 42871  39592

35456 40775 36466 36287 38956

Lower confidence level (LCL) = ?

Upper confidence level (UCL) = ?

Sin(z) = 4/5, Cos(z) = 3/5, tan(z) = 4/3

We know that

sin(z) = perpendicular/hypotenuse

cos(z) = base/hypotenuse

tan(z) = perpendicular/base

Now putting we get,

Sin(z) = 4/5

Cos(z) = 3/5

tan(z) = 4/3

a. The two equations for the cost of buying groceries and meals are 13f + 4k = 487 and 65+2k = 232

b. The average costs of one fast food meal and of one trip to kroger is $77.33

To calculate the average cost, we divide the total cost by the number of meals or trips. For example, in the first month, the total cost of fast food meals and grocery trips was $487, and there were 13 fast food meals and 4 grocery trips. Therefore, the average cost of a fast food meal can be calculated by dividing the total cost of fast food meals ($487) by the number of fast food meals (13):

Average cost of a fast food meal = $487 / 13 = $37.46

Similarly, we can calculate the average cost of a grocery trip in the first month by dividing the total cost of grocery trips ($487 - total cost of fast food meals) by the number of grocery trips (4):

Average cost of a grocery trip = ($487 - $37.46 x 13) / 4 = $89.38

Using the same method, we can calculate the average cost of a fast food meal and a grocery trip in the second month. In the second month, the total cost of fast food meals and grocery trips was $232, and there were 6 fast food meals and 2 grocery trips. Therefore, the average cost of a fast food meal is:

Average cost of a fast food meal = $232 / 6 = $38.67

And the average cost of a grocery trip is:

Average cost of a grocery trip = ($232 - $38.67 x 6) / 2 = $77.33

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The coordinate of the image point is (9,1).

There are eight types of rules for the transformation of a point. When the  takes place across a line, then the point (x,y) is changed to the point (y,x).

Given that the rule for the transformation of a point P(1,1) is [tex]R_{x=5} (P)[/tex], which defines the reflection of a point about a line, that is parallel to the y-axis. The line [tex]x=5[/tex] is like a mirror. So, the distance between the line and the image point is equal to the distance between the line and the original point.

Using the point-line distance formula, the distance between the line [tex]x=5[/tex] and a point (1,1) is given by [tex]|5-1|=4[/tex].

Similarly, by the above statement, the distance between the line [tex]x=5[/tex] and the image point will also be 4.

Therefore, the coordinate of the image point is (9,1).

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The complete question is -

If P = (1,1), then find the reflection [tex]R_{x=5} (P)[/tex].

Answer:

we 1st can get the weight of rat by

1 rat and 1 cat + 1 dog and rat = 30

2 rat + 1 cat + 1 dog = 30

Then 1 rat and cat measure 24 so

2 rat + 24 =30

2 rat + 24 =30 1 rat = 3 kg

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 10

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 10

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg 1 dog = 17kg

so we get the weight of each now we r going to sum them 1 rat + 1 cat + 1 dog = x

1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x

1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x 27 kg = x ..... is the mass of 3 of them

Answer:

Nicole has 9 dimes and 19 nickels.

Triangle FGH is a right triangle because (HG)²= (FG)²+ (FH)²

Similar triangles are triangles that have the same shape, but their sizes may vary. The ratio of corresponding sides of similar triangles are equal.

Therefore;

6/5 = 3.6/FH

represent FH by x

6/5 = 3.6/x

6x = 5 × 3.6

6x = 18

divide both sides by 6

x = 18/6 = 3

Since FH is 3, this means that the sides of triangle FGH are Pythagorean triple, hence FGH is a right triangle.

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Rylee did approximately 58.6 sit-ups.

We are given that the mean number of sit-ups is 46 and the standard deviation is 7. We are also given that Rylee's Z-score was 1.8, we can use the formula for Z-score to find how many sit-ups she did.

The formula for Z-score is [tex]Z = \frac{X-\mu}{\sigma}[/tex]

Z = Z-score

μ = mean

σ = standard deviation

X = ?

Substituting these values into the formula

1.8 = (X - 46)/7

1.8 × 7 = X - 46

X - 46 = 12.6

X = 12.6 + 46

X = 58.6

Therefore, Rylee did approximately 58.6 sit-ups.

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