For problems 8 and 9, find the length of the missing side of each right triangle. Round your
answers to the nearest tenth, if necessary. (2 points each)

The height of the basketball hoop is 13.32'.

What is law of similarity?

The Law of Similarity in mathematics states that if two geometric figures have the same shape but different sizes, then they are considered similar. This means that the corresponding angles of the two figures are congruent, and the corresponding sides are proportional in length.

Formally, if we have two geometric figures A and B, and if every angle of figure A is congruent to the corresponding angle of figure B, and if the ratio of the length of any pair of corresponding sides of A and B is constant, then we can say that A and B are similar figures.

Here we can see two triangle and base of two triangle is given.

Here base of small triangle is 12' and the base of big triangle is [tex](12'+25') = 37[/tex]

It is also given that height of small triangle is 4'3.84".

Now we want to find the height of the basketball hoop which is equal to height of big triangle.

Let the height of the basketball hoop be x.

So, by law of similarity ratios,[tex] \frac{12'}{37'} = \frac {4'3.84''}{x}[/tex]

Now, [tex]4'3.84''= 4.32'[/tex]

So, 12'/37' = 4.32'/x

Therefore, [tex]x = 13.32'[/tex]

Therefore, the height of the basketball hoop is 13.32'.

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According to the information, the approximation and exact values are V = 65.45 cubic cm (approximation to the nearest hundredth), Exact value: V = (4/3)π(2.5)^3 = 65.44984695 cubic cm (exact).

The formula for the volume of a sphere is:

V = (4/3)πr^3

Since the diameter of the sphere is given as 5 cm, the radius is half of that, which is:

Substituting this value into the formula, we get:

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Answer: C (61°)

Step-by-step explanation:

∠KIH = 180 - 128

∠KIH = 52

∠GHF = 180 - 86 - 27

∠GHF = 67

∠GHF = ∠KHI

∠K OR ∠IKH = 180 - ∠KIH - ∠KHI

∠K OR ∠IKH = 180 - 52 - 67

∠K OR ∠IKH = 61°

Check the picture below.

The model P = at + b, which can interpret the period of its graph.

What is an arithmetic progression?

An arithmetic progression is a sequence of numbers where each term is obtained by adding a fixed number to the previous term. In other words, if we have a sequence a1, a2, a3, that is arithmetic, then a2 - a1 = a3 - a2 = d, where d is a common difference.

To write a model that gives P as a function of t, we can use the general form of an arithmetic sequence:

P= at + b

where a is the common difference and b is the initial value of the sequence. To find a and b, we can use the information given in the table. For example, we can use the first two data points to get:

P1 = a(1)+b

P2 = a(2)+b

Subtracting the first equation from the second gives:

P2 - P1 = a(2-1)

​or

a = P2 - P1

​

Once we have a, we can use either of the equations above to solve for b. For example, using the first equation, we get:

b = P1 − a(1)

Now that we have the model P = at + b, we can interpret the period of its graph.

The period of an arithmetic function is the smallest positive value of k such that f(x) = f(x + k) for all x. In this case, the function is linear, so it has no periodic behavior.

hence, the model P = at + b, which can interpret the period of its graph.

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The length of the ladder is 14.36 feet. To the nearest tenth of a foot, the length of the ladder is 14.4 feet.

Trigonometric functions such as sine, cosine, and tangent are used to model and describe physical phenomena like waves, sound, and light.

The given problem can be solved using the trigonometric concept. The basic trigonometric equation used is:

Opposite Side (S) = Adjacent Side (L) x Tan(θ)

Where θ is the angle in degrees and L is the length of the ladder.

In this problem,

θ = 62°

S = 27 ft

Using the equation, we can find the length of the ladder (L).

L = S/Tan(θ)

L = 27/Tan(62°)

L = 27/1.88

L = 14.36 ft

The length of the ladder is 14.36 feet. To the nearest tenth of a foot, the length of the ladder is 14.4 feet.

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The relationship is non-existent and positive about the plot in terms of the relationships between the two variables.

A scatter plot is a graph that compares two different sets of data by plotting them as points on a graph. A scatter plot is utilized to investigate the degree of correlation between two different data sets. The points' placement on a scatter plot implies a correlation between the two data sets that can be classified as positive, negative, or non-existent.

The following statements are true about the plot in terms of the relationships between the two variables:There is no association between music and living spaces.Therefore, the answer is: non-existent.The majority of students who play an instrument live off-campus.Therefore, the answer is: Positive.There is no association between the Northside and playing an instrument.Therefore, the answer is: Non-existent.

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Answer: 94.25yd = 94.25 yards

Step-by-step explanation:

Please brainliest if the helped you! :D

Out of  [tex]5000[/tex] middle school pupils, [tex]3100[/tex]  are predicted to purchase lunches in the upcoming school year.

We can predict that 37 kids out of every 100 students—or 37% of students—expect to buy lunch one or two days per week.

Likewise, 25% of students claim to buy lunch three to four days each week. This shows that on average, 25 pupils out of every 100 say they'll follow suit.

13% of students said they won't buy lunch every day of the week, or roughly 13 students out of every 100, don't plan to buy lunch at all.

[tex]5000 \times 0.37 = 1850[/tex]

Students who intend to purchase lunch three to four days each week include:

[tex]5000 \times 0.25 = 1250[/tex]

Students who don't have any plans to purchase lunch include:

[tex]5000 \times 0.13 = 650[/tex]

In light of this, the total number of students planning to buy lunch (either 1-2 or [tex]3–4[/tex]  days a week) is:

[tex]1850 + 1250 = 3100[/tex]

Therefore, out of  [tex]5000[/tex] middle school pupils, [tex]3100[/tex]  are predicted to purchase lunches in the upcoming school year.

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Answer: To solve the equation Three-fifths (30 x - 15) = 72, we can start by simplifying the left side of the equation by distributing the coefficient 3/5 to the terms inside the parenthesis:

Three-fifths (30 x - 15) = 72

18x - 9 = 72 (dividing both sides by 3/5)

Multiplying both sides of the equation by 5/3, we get:

10x - 5 = 24

10x = 29

x = 2.9

So the value of x for the original equation is x = 2.9.

Now we can test each option to see which equations have the same value of x:

18x - 15 = 72

18(2.9) - 15 = 40.2

This equation does not have the same value of x as the original equation.

50x - 25 = 72

50(2.9) - 25 = 125

This equation does not have the same value of x as the original equation.

18x - 9 = 72

18(2.9) - 9 = 40.2

This equation does not have the same value of x as the original equation.

3(6x - 3) = 72

3(6(2.9) - 3) = 72

This equation has the same value of x as the original equation.

x = 4.5

This equation does not have the same value of x as the original equation.

Therefore, the equations that have the same value of x as the original equation are:

3(6x - 3) = 72

x = 2.9

Step-by-step explanation:

Answer: Let's first determine the number of hours SCVCS will be renting the Koger Center from 10:00 am to 3:00 pm. There are 5 hours between 10:00 am and 3:00 pm, so the rental time is:

Rental time = 5 hours

Using this information, we can write an equation to model the total cost of renting the Koger Center, y, as a function of the rental time, x, in hours:

y = 425x + 500

Here, the slope of the line represents the rental cost per hour, and the y-intercept represents the setup/cleanup fee.

Substituting x = 5 into the equation, we get:

y = 425(5) + 500

y = 2125 + 500

y = $2,625

Therefore, it will cost $2,625 to rent the Koger Center from 10:00 am to 3:00 pm.

So, the completed expression is:

y = 425x + 500

Substitute x = 5 into the equation.

It will cost $2625 to rent the Koger Center.

Step-by-step explanation:

We need a sample size of 35 to reduce the margin of error to $25 for a 95% confidence interval, given that we have reason to believe that the population standard deviation of credit card debts for this group is $150.

To determine the sample size needed to reduce the margin of error to $25 for a 95% confidence interval, we can use the following formula:
n = (z * σ / E)²
Where:
n = sample size
z = z-score corresponding to the desired confidence level (1.96 for 95% confidence)
σ = population standard deviation
E = desired margin of error
Substituting in the given values:
n = (1.96 * 150 / 25)²
n = 34.57
Rounding up to the nearest whole number, we get a sample size of 35. Therefore, we need a sample size of 35 to reduce the margin of error to $25 for a 95% confidence interval, given that we have reason to believe that the population standard deviation of credit card debts for this group is $150.

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Answer:

30 degrees

Step-by-step explanation:

Sascha receives 3.65% more percentage yield from the corporate bond than from dividends.

What is percentage yield?

To find out how much more percentage yield Sascha receives from the corporate bond than from dividends, we need to calculate the yield for each investment and compare them.

For the corporate bond:

Annual interest = 8.07% of $8,706 = $703.24

Yield = Annual interest / Bond value = $703.24 / $8,706 = 0.0809 or 8.09%

For the stock:

Dividend yield = Annual dividend / Stock value = $2 / $45 = 0.0444 or 4.44%

To find out the difference in percentage yield, we subtract the dividend yield from the bond yield:

8.09% - 4.44% = 3.65%

Therefore, Sascha receives 3.65% more percentage yield from the corporate bond than from dividends.

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Answer:

[tex]x∈[4; + ∞)[/tex]

Step-by-step explanation:

[tex]x + 10 \geqslant 14[/tex]

Make x the subject (also, when moving terms to the other side, make sure to change their signs into the opposite of the previous one):

[tex]x \geqslant 14 - 10[/tex]

[tex]x \geqslant 4[/tex]

[tex]x∈[4; + ∞)[/tex]

I also added a photo of my graph

Answer:x ≥+4

Step-by-step explanation:

Remember in an earlier lesson, you learned about taking x by it's self.

You're doing the same thing here.  

(-10)  x+14 ≥ 14    (-10)

x≥ +4

Then you a dot on the +4 spot your line. and since this is an equal greater sign, you fill in the dot. Lastly you draw the arrow as it's been shown.

The maximum volume of the silo is V = SA/8(4-π), where SA is the surface area of the cylinder formed by the 2000 square feet of material.

We are given that 2000 square feet of material will be used to form a cylinder-shaped silo. We need to find the maximum volume of the silo.

Let's use the formula for the cylindrical surface area:

SA = πr^2 + 2πrh

We can solve for h in terms of r as follows:

SA = πr^2 + 2πrh

2πrh = SA - πr^2

h = (SA - πr^2) / (2πr)

Now, let's substitute this expression for h into the formula for the volume of a cylinder:

V = πr^2h

V = πr^2[(SA - πr^2) / (2πr)]

V = (SA - πr^2) / 2

We want to find the maximum volume, so we need to find the value of r that maximizes V. To do this, we can take the derivative of V with respect to r and set it equal to zero:

dV/dr = -πr/2 + SA/4π = 0

Solving for r, we get:

r = √(SA/(2π))

Substituting this value of r back into the expression for V, we get:

V = (SA - π(SA/(2π))^2) / 2

V = (SA - SA^2/(4π)) / 2

V = SA/8(4-π)

Therefore, the maximum volume of the silo is V = SA/8(4-π), where SA is the surface area of the cylinder formed by the 2000 square feet of material.

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The measure of ∠AOB is 80°.

In geometry, an angle is a figure formed by two rays, or half-lines, that originate from a common endpoint, which is called the vertex. The rays can be thought of as emanating from the vertex and extending infinitely in opposite directions.

The measure of an angle is typically given in degrees, where a full circle is 360 degrees. Angles can be classified according to their size:

An acute angle is less than 90 degrees.

A right angle measures exactly 90 degrees.

An obtuse angle is greater than 90 degrees but less than 180 degrees.

A straight angle measures exactly 180 degrees.

A reflex angle is greater than 180 degrees but less than 360 degrees.

A full angle measures exactly 360 degrees.

In a parallelogram, opposite angles are equal, so we have:

∠OAD = ∠OCB = a2 + b2 (1)

∠OAB = ∠ODC = a1 + d1 (2)

∠OAB + ∠OAD = ∠BOC = 180° (3)

∠OAD + ∠BOC = ∠AOB + ∠ODC = 180° (4)

From (1), (2), and (3), we have:

∠AOB = 180° - (a1 + b2 + a2 + d1)

= 180° - (a1 + a2 + b1 + b2 + c1 + d1 + d2)

= 180° - ∠ABD - ∠BCD

Since ABCD is a parallelogram, we have ∠ABD = ∠BCD. Therefore,

∠AOB = 180° - 2∠ABD

Let x be the measure of angle ABD. Then we have:

∠ABD + ∠BCD = 180°

x + (d1 + d2) = 180° (5)

In triangle ADO, we have:

∠ADO + ∠ODA + ∠OAD = 180°

d2 + x + a2 = 180° (6)

From (5) and (6), we get:

d1 + d2 + a2 + x = 180°

Substituting this expression into (3), we obtain:

∠AOB = 180° - 2(d1 + d2 + a2 + x)

= 80°

Therefore, the answer is (d) 80°.

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The measure of ∠AOB is 80°. The required answer for the given question is option (d). 80°.

An angle is a figure in geometry made up of two rays, or half-lines, that start from a single endpoint known as the vertex. You can imagine the

rays coming from the vertex and continuing in opposing directions indefinitely.

A whole circle has 360 degrees, hence an angle is commonly measured in degrees. Angles can be grouped based on their size:

Acute angle is one that is less than 90 degrees.

A right angle has a 90 degree angle.

Obtuse angles are those that are greater than 90 degrees and less than 180 degrees.

A straight angle has a 180 degree length.

Greater than 180 degrees and less than 360 degrees is a reflex angle.

360 degrees makes up a whole angle.

Since opposite angles in a parallelogram are equal, we have:

∠OAD = ∠OCB = [tex]a_2+b_2[/tex] (1)

∠OAB = ∠ODC = [tex]a_1+d_1[/tex] (2)

∠OAB + ∠OAD = ∠BOC = 180° (3)

∠OAD + ∠BOC = ∠AOB + ∠ODC = 180° (4)

From (1), (2), and (3), we have:

∠AOB = 180° - [tex](a_1 + b_2 + a_2 + d_1)[/tex]

= 180° - [tex](a_1 + a_2 + b_1 + b_2 + c_1 + d_1 + d_2)[/tex]

= 180° - ∠ABD - ∠BCD

Due to the parallelogram that is ABCD, we have ∠ABD = ∠BCD.

∠AOB = 180° - 2∠ABD

Let x be the measure of angle ABD. Then we have:

∠ABD + ∠BCD = 180°

x + [tex](d_1 + d_2)[/tex] = 180° (5)

In triangle ADO, we have:

∠ADO + ∠ODA + ∠OAD = 180°

[tex]d_2[/tex] + x + [tex]a_2[/tex] = 180° (6)

From (5) and (6), we get:

[tex]d_1 + d_2 + a_2[/tex] + x = 180°

Substituting this expression into (3), we obtain:

∠AOB = 180° - 2[tex](d_1 + d_2 + a_2 + x)[/tex]

= 80°

Therefore, the answer is (d) 80°.

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Maple Farms needs to pay $10,944 in taxes for a land measuring

15,200 m².

Here we are given that Maple Farms owns an area of 15,200 m²

Now for every 2500 m² area of farm land, the tax needed to be paid in the city of London is $1,800. We are required to find tax to be paid for 15,200 m² of farmland.

First, we need to find the tax to be paid for every 1 m² of farmland.

This will be

$ 1800/ 2500

= $ 0.72

Hence for a land of area 15,200 m²

The amount to be paid is

$ 15,200 X 0.72

= $10,944

Hence Maple Farms needs to pay $10,944 in taxes

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Answer:

(v - 6)(-5v + 1)

Step-by-step explanation:

[tex] - 5 {v}^{2} + 31v - 6[/tex]

[tex] - 5 {v}^{2} + 30v +v - 6[/tex]

[tex] - 5v(v - 6) +(v - 6)[/tex]

[tex] (v - 6)( - 5v + 1)[/tex]

Answer:48%

Step-by-step explanation:

have a good day

Answer: 627.9

Step-by-step explanation: Im pretty sure you just multiply all the numbers.

V= w*h*l=8.4·6.5·11.5=627.9

Answer:

627.9

Step-by-step explanation:

Required equation of graphed function is y=x³.

What is equation?

An equation is a statement that shows the equality between two expressions, which may contain one or more variables. Equations are typically written using mathematical symbols, such as "equals" (=), plus (+), minus (-), multiplication (*), division (/), exponentiation (^), and parentheses ().

For example, the equation "2x + 5 = 11" shows that the expression "2x + 5" is equal to the expression "11" when the value of the variable x is 3.

Equations are fundamental in mathematics and have numerous applications in various fields, including physics, engineering, economics, and computer science. They are used to model real-world phenomena, make predictions, solve problems, and develop theories.

The graph of the function f(x) = x³ is a curve that passes through the origin and has a shape similar to that of a "S" curve. The equation of the graphed function is y = x³, where y represents the value of the function at any given x. This means that for any value of x, the corresponding value of y on the graph is given by y = x³.

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the expression 1.01 represents the interest rate applied to the initial amount of 1.005 thousand dollars

In the given expression 1.01 × [tex]1.005^{t}[/tex], the value 1.01 represents the annual interest rate on Carter's savings account. To understand this, let's break down the expression: "1.005" represents the initial amount of money in Carter's savings account, in thousands of dollars. "t" represents the number of years that have passed since he opened the account, and t is the variable that represents this time. "1.01" represents the interest rate on Carter's savings account. The interest rate of 1.01 means that for every 1 dollar in Carter's savings account, he earns an additional 1.01 cents of interest after one year.  Therefore, the expression 1.01 ×[tex]1.005^{t}[/tex]represents the amount of money in thousands of dollars that Carter has in his savings account after t years, with 1.01 being the interest rate applied to the initial amount of 1.005 thousand dollars

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Complete Question

The expression 1.01*1.005(^t) gives the amount of money, in thousands of dollars, in Carter's savings account (t) years after he opens it. What does 1.01 represent in this expression?

The margin of error would have been much smaller if Dr. Si Sanchez had increased his sample size to 1,000.

A margin of error quantifies the amount of random sampling error in survey results. The smaller the margin of error, the larger the sample size. This is due to the fact that a larger sample size reduces the amount of random variation in the data, allowing the estimate to be more precise.

Dr. Sanchez's margin of error decreases as he increases his sample size from 500 to 1000, because sample size is proportional to margin of error.

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The answer for BLANK 1 is 575,000. This is because the exponential function given is f(x) = 575(1+0.40)ˣ.

The answer for BLANK 2 is 805,000.

The correct answer for BLANK 3 is 230,000.

An exponential function contains an exponent. It is written as f(x)=b^x where b is the base and x is the exponent. Exponential functions can represent growth or decay, and the graph of an exponential function is an exponential curve.

The correct answer for BLANK 1 is 575,000.

This is because the exponential function given is f(x) = 575(1+0.40)ˣ. This means that the initial population at x=0 is 575,000.

The correct answer for BLANK 2 is 805,000. This is because the exponential function given is f(x) = 575(1+0.40)ˣ.

This means that the population at x=7 hours is 805,000.

The correct answer for BLANK 3 is 230,000. This is because the exponential function given is f(x) = 575(1+0.40)ˣ.

This means that the population increases by 230,000 per hour. This can be calculated by taking the difference between the population at x=7 hours (805,000) and the population at x=0 (575,000) and dividing it by 7 hours.

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The tennis ball will hit the ground [tex]5[/tex] seconds after being dropped from an initial height of  [tex]400[/tex]feet.

To determine when the tennis ball hits the ground, we need to find the value of t when h becomes 0, since at that time the height of the ball is zero, which means it has hit the ground.

So, we can set  [tex]h = 0[/tex] and solve for t:

[tex]0 = -16t^2 + 400[/tex]

Adding 16t^2 to both sides:

[tex]16t^2 = 400[/tex]

Dividing both sides by 16:

[tex]t^2 = 25[/tex]

Taking the square root of both sides:

[tex]t = \pm5[/tex]

Since we cannot have a negative time, we can disregard the negative solution.

Therefore, the tennis ball will hit the ground  [tex]5[/tex] seconds after being dropped from an initial height of  [tex]400[/tex] feet.

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The area of the rectangle is:

length x width

We need to first convert the length and width to the same units. We can convert them to twelfths of a meter, since both 6 and 4 are factors of 12.

Length = 3 and 2/6 meters = 3 x 12/6 + 2/6 = 18/6 + 2/6 = 20/6 = 10/3 twelfths of a meter

Width = 2 and 3/4 meters = 2 x 12/4 + 3/4 = 24/4 + 3/4 = 27/4 twelfths of a meter

Now we can find the area:

Area = length x width = (10/3) x (27/4) = 90/12 = 15/2 = 7.5 square meters

Therefore, the answer is option C) six and five-tenths m² (rounded to one decimal place).

the standard form of the equation is: [tex](x - 2)^2 + (y - 7)^2 = 4^2.[/tex]

The center of the circle is (2, 7) and the radius is 4.

What is meant by radius?

Radius is a straight line segment that joins the center of a circle or sphere to any point on its circumference.

To rewrite the equation in standard form, we need to complete the square for both x and y terms:

[tex]y^2 - 14y + x^2 - 4x + 37 = 0[/tex]

[tex]y^2 - 14y + 49 + x^2 - 4x + 4 = -37 + 49 + 4[/tex] (adding and subtracting appropriate constants to complete the square for y and x terms)

[tex](y - 7)^2 + (x - 2)^2 = 16[/tex]

Therefore, the standard form of the equation is:

[tex](x - 2)^2 + (y - 7)^2 = 4^2[/tex]

The center of the circle is (2, 7) and the radius is 4.

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The area of the shaded region is 170.88 sq. cm.

A circle with a radius of 6 cm is inside a circle with a radius of 9.5 cm.

The area of a circle is given by the formula:

A = πr²Where,A = Areaπ = 3.14r = radius

For the shaded area, we need to subtract the area of the smaller circle from the larger circle.

the radius of the larger circle is 9.5 cm and the radius of the smaller circle is 6 cm.

So, the area of the shaded area can be given as:

Area of the shaded region = Area of larger circle - Area of smaller circle

Area of larger circle = πr²= π(9.5)²= π(90.25) sq. cm.= 283.92 sq. cm.

Area of smaller circle = πr²= π(6)²= π(36) sq. cm.= 113.04 sq. cm.

So, the area of the shaded region is:

Area of the shaded region = 283.92 - 113.04= 170.88 sq. cm.

Therefore, the area of the shaded region is 170.88 sq. cm.

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Question

A circle with radius of 6 cm sits inside a circle with radius of 9 cm.

What is the area of the shaded region?

Round your final answer to the nearest hundredth.

A circle with radius of 6 cm sits inside a - 1

Answer:

The height of the statue is 152ft.

Step-by-step explanation:

305 = 153 + h

152 = h

Answer:

If y varies directly as x, then we can express this relationship using a proportionality constant k, such that:

y = kx

To solve for k, we can use the initial condition given:

y = 21 when x = 3

Substituting these values into the equation above, we get:

21 = k * 3

Solving for k, we get:

k = 7

Now that we have k, we can use the equation to find y when x = 2:

y = kx

y = 7 * 2

y = 14

Therefore, when x = 2, y = 14.

Step-by-step explanation: