Mathematics College

## Answers

**Answer 1**

We have to graph the line y = -2/5*x-5.

To do that, we need two points that belong to the line.

We can give two arbitrary values to x and calculate y using the equation of the line.

For example, for x=0, we get:

[tex]x=0\Rightarrow y(0)=-\frac{2}{5}\cdot0-5=-5[/tex]

Then, the point is (0,-5).

Now, if we make x = 5, we can calculate y as:

[tex]x=5\Rightarrow y(5)=-\frac{2}{5}\cdot5-5=-2-5=-7[/tex]

Then, we get the point (5, -7).

Using this two points we can graph the line as:

*NOTE: In the case that the graph is limited to certain intervals in x or y, we have to try with different values of x until we find two points within the range shown by the graph.*

*In this case, (0,-5) and (5,-7) will be located within the range shown.*

## Related Questions

If you receive 360 promotional emails per month and only 2.5% percent of those emails are of interest to you, what is the expected number of promotional emails that will be of interest to you each month?

### Answers

Given

Total email 360

percentage email of interest 2.5%

Solution[tex]\begin{gathered} \frac{2.5}{100}\times360=9 \\ \end{gathered}[/tex]The final answer9 promotional emails that will be of interest to you each month

Identify the graphs that represent a linear function. Check all that apply.On a coordinate plane, a line has a positive slope.On a coordinate plane, a curve opens down.On a coordinate plane, a graph decreases, increases, and then decreases again.On a coordinate plane, a line has a negative slope.

### Answers

A **linear function** is represented by a straight line, that means the right answers are those graph with straight lines.

Therefore, the right graphs are the first and the last one.

• The first graph represents a linear function with a positive slope.

,

• The last graph represents a linear function with a negative slope.

First and last one.

uhh yeah its right i jus tried it

I have no clue how to graph inequalities and find the solution

### Answers

In the graph we can see two line y=2 and y=x.

Also, we know that there is a system of inequalities and the blue area in the graph represent the solutions for the system.

We can see that the blue area is above the line y=2, thats mean one inequality is:

[tex]y\ge2[/tex]

So, any points that y-coordinate is greater than or equal than 2 satisfy the inequality.

Also we can see that the blue area is bellow the line y=x and the line is a dotted line, this last means the inequality do not take take value in the line. So, the second inequation is:

[tex]ySo, the points that satisfy the system of inequalities are above the line y=2 and bellow the line y=x and not touch the line y=x.

Stats To quality for a police academy, applicants are given a lest of physical Itness. Ihe scores are normallyDistributed with a mean of 64 and a standard deviation of 9. If only the top 20% of the applicants are selected,Find the cutoff score.

### Answers

Since we want just the top 20% applicants and the data is normally distributed, we can use a z-score table to check the z-score that gives this percentage.

The z-score table usually shows the percentage for the values below a certain z-score, but since the whole distribution accounts to 100%, we can do the following.

We want a z* such that:

[tex]P(z>z^*)=0.20[/tex]

But, to use a value that is in a z-score table, we do the following:

[tex]\begin{gathered} P(zz^*)=1 \\ P(zz^*)=1-0.20=0.80 \end{gathered}[/tex]

So, we want a z-score that give a percentage of 80% for the value below it.

Using the z-score table or a z-score calculator, we can see that:

[tex]\begin{gathered} P(zNow that we have the z-score cutoff, we can convert it to the score cutoff by using:[tex]z=\frac{x-\mu}{\sigma}\Longrightarrow x=z\sigma+\mu[/tex]

Where z is the z-score we have, μ is the mean and σ is the standard deviation, so:

[tex]\begin{gathered} x=0.8416\cdot9+64 \\ x=7.5744.64 \\ x=71.5744\cong72 \end{gathered}[/tex]

so, the cutoff score is **approximately 72**.

Solve the following linear equation using equivalent equations to isolate the variable. Express youranswer as an integer, as a simplified fraction, or as a decimal number rounded to two places.2345 2----U43НЕ KeyAnswerHow to enter your answer (Opens in new window)Keyboard ShoU=

### Answers

Given the equation

[tex]\frac{-3}{4}-\frac{2}{3}=\frac{5}{4}u-\frac{2}{3}u[/tex]

We add and subtract similar terms:

[tex]-\frac{17}{12}=\frac{7}{12}u[/tex]

Multiply both sides by 12:

[tex]\begin{gathered} -\frac{17}{12}\cdot12=12\cdot\frac{7}{12}u \\ -17=7u \end{gathered}[/tex]

Divide both sides by 7:

[tex]\begin{gathered} -\frac{17}{7}=\frac{7u}{7} \\ u=-\frac{17}{7} \end{gathered}[/tex]

**Answer:**

[tex]u=-\frac{17}{7}[/tex]

A sales person is given a choice of two salary plants plan one is a weekly salary of 800 plus 3% commission of sales. plan 2 is a straight commission of 11% of sales. how much in sales must she make in a week for both plans to result in the same salary

### Answers

SOLUTION:

Let us represent the amount in sales that we are to calculate with "x".

For both plans to result in the same salary, we have;

Plan 1 = Plan 2

[tex]800\text{ + 3 \% of x = 11 \% of x}[/tex][tex]\begin{gathered} 800\text{ + 0.03x = 0.11x} \\ 800\text{ = 0.11x - 0.03x} \\ 800\text{ = 0.08x} \\ \\ \frac{0.08x}{0.08}\text{ = }\frac{800}{0.08} \\ \\ x\text{ = 10,000} \end{gathered}[/tex]

The amount in sales she must make in a week for both plans to result in the same salary is 10,000

Four different stores have the same digital camera on sale. The original price and discounts offered by each store are listed below. Rank the stores from the cheapest to most expensive sale price of the camera.

Store A: price $99.99 and discount of 15%

Store B: price $95.99 and discount of 12%

Store C: price $90.99 and discount of 10%

Store D: price $89.99 and successive discounts of 5% and 5%

### Answers

**Answer:**

**Step-by-step explanation:**

store A $99.99 x 0.15= 14.9985

99.99-14.9985 = 84.99

store B $95.99 X 0.12= 11.5188

95.99 - 11.5188= 84.47

store C $90.99 x 0.10= 9.099

90.99-9.099= 81.891

store D = $89.99 x 0.05=4.4995

89.99- 4.4995= 85.4905 x 0.05= 4.27

85.4905- 4.27= 81.22

STORE D

STORE C

STORE B

STORE A

15. Graph the rational function ya*-*Both branches of the rational function pass through which quadrant?Quadrant 2Quadrant 3Quadrant 1Quadrant 4

### Answers

SOLUTION:

**CONCLUSION:**

**Both branches of the rational function pass through Quadrant 1.**

Parallelogram ABCD is below. m

### Answers

The consecutive angles of a parallelogram are supplementary. therefore:

[tex]\begin{gathered} m\angle A+m\angle B=180 \\ 41+x+8.5=180 \\ x+49.5=180 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=180-49.5 \\ x=130.5 \\ x\approx131 \end{gathered}[/tex]

What is the length of the side of an equilateral triangle if the height is 9√3

### Answers

An equilateral triangle is a triangle were all the sides have the same measurement, and all the angles are the same**(60º)**.

The height of an equilateral triangle divides the triangle into two equal right triangles. The height represents the oposite side of the angle of 60º, and the hypotenuse has the length of the side of the equilateral triangle, if we find the hypotenuse we have our answer.

Using trigonometric relations on the right triangle, we can find the value for the hypotenuse. The ratio between the opposite side to an angle and the hypotenuse is equal to the sine of this angle. If we call the hypotenuse as **h,** we have the following relation

[tex]\sin (60^o)=\frac{9\sqrt[]{3}}{h}[/tex]

The sine of 60º is a known value

[tex]\sin (60^o)=\frac{\sqrt[]{3}}{2}[/tex]

Then, combining both expressions, we have

[tex]\frac{9\sqrt[]{3}}{h}=\frac{\sqrt[]{3}}{2}[/tex]

Solving for **h**

[tex]\begin{gathered} \frac{9\sqrt[]{3}}{h}=\frac{\sqrt[]{3}}{2} \\ \frac{9}{h}=\frac{1}{2} \\ \frac{h}{9}=2 \\ h=18 \end{gathered}[/tex]

The length of the side of an equilateral triangle if the height is 9√3 is equal to **18**.

AMAn art teacher has 9 3/5 gallons of paint to pour into containers. If each container holds3/5 gallon, how many containers can they fill?Answer type: Mixed numberSubmit Answerattempt 1 out of

### Answers

**So they can fill 16 containers.**

1) If an art Teacher has

9 3/5 gallons

Each container holds

3/5 gallons

2) Firstly, let's turn that mixed number into an improper fraction

9 3/5 = (5 x 9+3) /5 = 48/5

Given that each container holds 3/5, then let's divide

48/5 ÷ 3/5 = 48/5 x 5/3 =16

If we hadn't turned

9 3/5 ÷ 3/5 = 16

3) **So they can fill 16 containers.**

÷

the line on the coordinate plane makes an angle of depression 32 degrees

### Answers

From the given figure

The angle is in the third quadrant

This means we must add 180 degrees to the given angle to get the true angle

Since 32 + 180 = 212,

Then look at the third row on the table to find the sine of the angle

sine the true angle is the number in the 3rd-row 1st column is **-0.5299**

**The answer is B**

b.

The slope of the line is

[tex]\begin{gathered} m=\tan (212) \\ m=0.6249 \end{gathered}[/tex]

**The slope of the line is 0.6249**

A chemistry student needs 80.0 mL of ethanolamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers thatthe density of ethanolamine is 1.02 g.cm. Calculate the mass of ethanolamine the student should welgh out.Be sure your answer has the correct number of significant digits.

### Answers

STEP 1: Identify and Set Up

We are given a question that requires us to find mass when given volume and density.

It is common knowledge that these parameters are related by the formulae:

[tex]\begin{gathered} \text{density = }\frac{\text{mass}}{\text{volume}} \\ \text{This gives mass = volume }\times\text{ density} \end{gathered}[/tex]

We use this relation to find mass

STEP 2: Execute

Density = 1.02 g/cc

Volume = 80ml = 80 cc

Mass is therefore:

[tex]\text{mass = 1.02}\times80=81.6g[/tex]

**Mass = 81.6g**

Focus (1,4)Directrix=x-7,What is the vertex (h,k)?what is p?what is the equation?

### Answers

Let's begin by listing out the information given to us:

[tex]undefined[/tex]

Convert the Cartesian equation x^2 + y^2 + 3y = 0 to a polar equation.r^2 = -3 sin θr = √3 sin θr = -3 sin θ

### Answers

**SOLUTION**

From the question

[tex]x^2+y^2+3y=0[/tex]

This becomes

[tex](x^2+y^2)+3y=0[/tex]

In polar,

[tex]\begin{gathered} x^2+y^2=r^2 \\ \\ \text{and } \\ \\ y=r\sin \theta \end{gathered}[/tex]

So, this becomes

[tex]\begin{gathered} r^2+3r\sin \theta=0 \\ \\ \frac{r^2}{r}=\frac{-3r\sin \theta}{r} \\ \\ r=-3\sin \theta \end{gathered}[/tex]

Write the equation to solve and then find the measure of each acute angle(3x + 8° (2x + 12)°

### Answers

We have here a right triangle, and that is why we have two acute angles (that is, the measure of each of them is less than 90 degrees).

We also know that the sum of the inner angles of a triangle is 180 degrees.

Having this information at hand, we can proceed as follows:

[tex](3x+8)+(2x+12)+90=180[/tex]

This is the equation. Now, we need to solve this equation to find x, and then we need to use the algebraical equations to find each of the acute angles.

**Solving the equation**

**1. Sum the like terms (like terms have the same variable or they are constants.)**

[tex]3x+2x+8+12+90=180[/tex]

Then, we have:

[tex]5x+110=180\Rightarrow5x=180-110\Rightarrow5x=70[/tex]

2. We need to divide each side of the equation by 5 to isolate x:

[tex]\frac{5x}{5}=\frac{70}{5}\Rightarrow x=14[/tex]

Now, we have** x = 14**. Therefore, the values for each of the acute angles are (we need to substitute the value of x in each equation):

a. 3x + 8 ---> 3 * (**14**) +8 = 42 + 8 =50. Hence, **one acute angle measures 50 degrees.**

b. 2x + 12 ---> 2 * **(14**) + 12 = 28 + 12 = 40 degrees. Therefore,** the other acute angle measures 40 degrees.**

In summary, the equation to solve is:

[tex](3x+8)+(2x+12)+90=180[/tex]

**And the values for each of the acute angles are 50 and 40 degrees.**

use the given graph to find the mean, median and mode of the following distribution: the mean is _______the median is _______the mode(s) is/are: __________Note: when the data is presented in a frequency table, the formula to find the mean is:

### Answers

**Solution:**

**Given:**

From the graph above, a frequency table can be made as shown below;

**To calculate the mean;**

[tex]\begin{gathered} \text{Mean}=\frac{\Sigma fx}{\Sigma f} \\ \text{Mean}=\frac{189}{20} \\ \text{Mean}=9.45 \end{gathered}[/tex]

**Therefore, the mean is 9.45**

**To calculate the median;**

**Median is the middle term when the data is arranged in rank order.**

Since we have 20 terms, then the middle terms will be the 10th and 11th terms.

The median will be the mean of these two numbers.

[tex]\begin{gathered} 10th\text{ term=9} \\ 11th\text{ term=10} \\ \text{Median}=\frac{9+10}{2} \\ \text{Median}=\frac{19}{2} \\ \text{Median}=9.5 \end{gathered}[/tex]

**Therefore, the median is 9.5**

**To calculate the mode;**

**The mode is the data that appears most in the set. It is the data with the highest frequency.**

From the graph

From the graph

Question 7 of 10Use the properties of logarithms to expand the following expression.(√log(x+4)5x³Your answer should not have radicals or exponents.You may assume that all variables are positive.

### Answers

We have:

[tex]\begin{gathered} log(\sqrt{\frac{(x+4)^5}{x^3}}) \\ =log(\frac{(x+4)^2\sqrt{x+4}}{x\sqrt{x}} \end{gathered}[/tex]

Applying properties of logarithms:

[tex]\begin{gathered} =log((x+4)^2\sqrt{x+4})-log(x\sqrt{x}) \\ =2log(x+4)+log(\sqrt{x+4})-logx-log\sqrt{x} \end{gathered}[/tex]

Ost< and cost is given. Use the Pythagorean identity sin2 t + cos2 t = 1 to find sin t.18) cos i =316I need help with #18

### Answers

sin^2t + cos^2t = 1

sint = 1/4

(1/4)^2 + cos^2 t = 1

1/16 + cos^2 t = 1

cos^2 t = 1 - 1/16

cos^2 t = (16 - 1)/16

cos^2 t = 15/16

take root both side,

[tex]\begin{gathered} cost=\sqrt[]{\frac{15}{16}} \\ \cos t=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]

**so the answer is option D**

solve for theta. Enter answer only round to the tenth

### Answers

**ANSWER:**

[tex]\theta=62.73\text{\degree}[/tex]

**STEP-BY-STEP EXPLANATION:**

We can calculate the value of the angle by means of the trigonometric ratio sine which is the following

[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{ hypotenuse}} \\ \text{opposite = 24} \\ \text{hypotenuse = 27} \end{gathered}[/tex]

Replacing and solving for the angle:

[tex]\begin{gathered} \sin \theta=\frac{24}{27} \\ \theta=\arcsin (\frac{24}{27}) \\ \theta=62.73\text{\degree} \end{gathered}[/tex]

Find a quadratic function of the form y=ax^2 that passes through the point (-2,-8)

### Answers

Solution

[tex]\begin{gathered} \text{ since }y=ax^2 \\ \\ \text{ at }(-2,-8) \\ \\ \Rightarrow-8=a(-2)^2 \\ \\ \Rightarrow-8=a(4) \\ \\ \Rightarrow a=-\frac{8}{4}=-2 \\ \\ \Rightarrow y=-2x^2 \end{gathered}[/tex]

The quadratic equation is

[tex]y=-2x^2[/tex]

4.

The value of a truck decreases exponentially since its purchase. The two points on the

graph shows the truck's initial

value and its value a decade afterward.

[6040,000)

a) Express the car's value, in dollars, as a function of time

d, in decades, since purchase.

(1 24,000)

b) Write an expression to represent the car's value 4 years

after purchase.

c) By what factor is the value of the car changing each year? Show your reasoning.

### Answers

**Answer**:

a. v = 40 000 (3/ 5)^d

b. v = 40 000 (3/5)^(4/10)

c. 0.95

**Explanation**:

The exponential growth is modelled by

[tex]v=A(b)^d[/tex]

We know that points (0, 40 000) and (1, 24 000) lie on the curve. This means, the above equation must be satsifed for v = 40 000 and d = 0. Putting v = 40 000 and d = 0 into the above equation gives

[tex]40\; 000=Ab^0[/tex]

[tex]40\; 000=A[/tex]

Therefore, we have

[tex]v=40\; 000b^d[/tex]

Similarly, from the second point (1, 24 000) we put v = 24 000 and d = 1 to get

[tex]24\; 000=40\; 000b^1[/tex][tex]24\; 000=40\; 000b^{}[/tex]

dividing both sides by 40 000 gives

[tex]b=\frac{24\; 000}{40\; 000}[/tex][tex]b=\frac{3}{5}[/tex]

Hence, our equation that models the situation is

[tex]\boxed{v=40\; 000(\frac{3}{5})^d\text{.}}[/tex]

Part B.

Remember that the d in the equation we found in part A is decades. Since there are 10 years in a decade, we can write

**t = 10d**

or

**d = t/10 **

Where t = number of years

Making the above substitution into our equation gives

[tex]v=40\; 000(\frac{3}{5})^{\frac{t}{10}}[/tex]

Therefore, the car's value at t = 4 is

[tex]\boxed{v=40\; 000(\frac{3}{5})^{\frac{4}{10}}}[/tex]

**Part C:**

**The equation that gives the car's value after t years is **

[tex]v=40\; 000(\frac{3}{5})^{\frac{t}{10}}[/tex]

which using the exponent property that x^ab = (x^a)^b we can rewrite as

[tex]v=40\; 000\lbrack(\frac{3}{5})^{\frac{1}{10}}\rbrack^t[/tex]

Since

[tex](\frac{3}{5})^{\frac{1}{10}}=0.95[/tex]

Therefore, our equation becomes

[tex]v=40\; 000\lbrack0.95\rbrack^t[/tex]

This tells us that** the car's value is changing by a factor of 0.95 each year. **

Which expression has the fewest number of significant figures?A. 5,280B. 360C. 296.54D. 18.3

### Answers

Concept

To determine the number of significant figures in a number use the following 3 rules:

1. Non-zero digits are always significant.

2. Any zeros between two significant digits are significant.

3. A final zero or trailing zeros in the decimal portion ONLY are significant.

Let's check through the options:

5,280

This has 3 significant figures

360

This has 2 significant figures

296.54

This has 5 significant figures

18.3

This has 3 significant figures

Cuál es el MCD de 42 y 30 ?. Opción única. (3 puntos) 5 6 7 15

### Answers

**Greatest Common Factor:**

*The greatest common factor, or GCF, is the greatest factor that divides two numbers.*

Given Numbers : 42 & 30

Factors of 42 : 7x3x2x1, 7x6x1,

Factors of 30=5x3x2x1, 5x6,1

Here the common factors of 42 & 30 are : 6,3, 2, 1

The greatest number in 6, 3, 2, 1 is **6**

So, the greatest common factor is 6

**The greatest common factor of 42 & 30 is 6**

**Answer: B) 6**

Omor is preparing the soil in his garden for planting squash. The directions say to use 4 poundsof fertilizer for 160 square feet of soil The area of Omar's garden is 200 square feet.How much fertilizer is needed for a 200 square-foot garden?1

### Answers

So the formula say 4 pounds of fertilizer for 160 square feet and he has to made for 200 square feet so we can made a rule of 3 so:

[tex]\begin{gathered} 4\to160 \\ x\to200 \end{gathered}[/tex]

and the equation will be:

[tex]\begin{gathered} x=\frac{200\cdot4}{160} \\ x=5 \end{gathered}[/tex]

So he need 5 pounds of fertilizer

Divide 22 stars to represent the ratio 4:7.

### Answers

**Answer**

Dividing **22 stars **into the ratio **4:7 **will give

**8 stars : 14 stars**

**Explanation**

We need to divide **22 stars **into the ratio **4:7**

Divide the ratio through by **11 **(the sum of the two numbers in the ratio)

**4:7 = (4/11) : (7/11)**

Multiplying through by **22**

**(4/11) : (7/11) **

**= (4 × 22/11) : (7 × 22/11)**

**= 8 : 14**

**Hope this Helps!!!**

What is the y-intercept in this equation: -1.5= y-12/0-4

### Answers

The y-**intercept **in this **equation**: -1.5= y-12/0-4 is 18.

What is equation?

Equation: A statement stating the equality of two **expressions** with variables or **integers**. Essentially, **equations **are questions, and attempt to systematically find the answers to these questions have been the inspiration for the development of **mathematics**.

**Given **Equation:

-1.5 = y - 12 / 0-4

Solve the above equation, and we get,

-1.5 = y - 12 / (-4)

y -12 = 6.0

y = 18

Therefore, the y-intercept in this equation: -1.5= y-12/0-4 is 18.

To know more about **equation**:

https://brainly.com/question/12788590

#SPJ1

In a coordinate plane, quadlateral PQRS has vertices P(0,7), Q(4,6), R(2,3), S(-1,3). Find the coordinates of the vertices of the image after each reflection.Reflection across the line y = x

### Answers

First we need to draw the graph

Then reflect with respect to the X axis

which is basically changing the sign of the Y values for each point

So, we can calculate the new points

[tex]\begin{gathered} P^{\prime}(0,-7) \\ Q^{\prime}(4,-6) \\ R^{\prime}(2,-3) \\ S^{\prime}(-1,-3) \end{gathered}[/tex]

Pleasr help fast it's due today 1. Consider the surface area of the following pyramid.224 am4 am4 am2.24 cm4 cm3 cm4 cm4 cm3 cm13 cm4 cm4 cm3 cm4 cm4 cm3 cm(a) Calculate the total surface area of the pyramid. Show your work.

### Answers

Given data:

The given figure of square pyramid.

The expresssion for the total surface area is,

[tex]\begin{gathered} \text{TSA}=(3\text{ cm)(3 cm)+4}\times\frac{1}{2}(3\text{ cm)(}2.24\text{ cm)} \\ =9cm^2+2(3\text{ cm)(2.24 cm)} \\ =22.44cm^2 \end{gathered}[/tex]

Thus, the total surface area of the given pyramid is **22.44 sq-cm.**

The scatterplot shows the average number of hours each of 13 people spends at work every week and the average number of hours each of them spends recreational activities every week.Based on the scatterplot,what is the best prediction of the average number of hours a person spends at work every week if that person spends an average of 10 hours on recreational activities every week?A.33 hB.95 hC.50 hD.65 h

### Answers

We want to find the best prediction of the average number of hours a person spends at work every week if that person spends an average of 10 hours on recreational activities every week.

We will **construct a line that adapts to the system by simple linear regression**, and then we will find the x-value that makes the line take y=10.

First, we have the data:

We remember that in a *simple regression model, *we want to write an equation of the form:

[tex]y=\hat{\alpha}+\hat{\beta}x[/tex]

where:

[tex]\begin{gathered} \hat{\alpha}=\bar{y}-\hat{\beta}\bar{x} \\ \hat{\beta}=\frac{nS_{xy}-S_xS_y}{nS_{xx}-S^2_x}_{} \end{gathered}[/tex]

And the Sx, Sy and Sxx are the sums over all the x-values, the y-values and the multiplication of the x-values and y-values (respectively).

We will find those values:

[tex]\begin{gathered} S_x=\sum ^{13}_{i=1}x_i=370 \\ S_y=\sum ^{13}_{i=1}y_i=336.5 \end{gathered}[/tex]

Also, we have:

[tex]\begin{gathered} S_{xx}=\sum ^{13}_{i=1}x^2_i=12600 \\ S_{xy}=\sum ^{13}_{i=1}x_iy_i=8680_{}_{} \end{gathered}[/tex]

And **applying the formula, having in mind that n=13**, we get:

[tex]\begin{gathered} \hat{\beta}=\frac{nS_{xy}-S_xS_y}{nS_{xx}-S^2_x}_{} \\ =\frac{13(8680)-(370)(336.5)}{13(12600)-(370^2)} \\ =\frac{-11665}{26900} \\ \approx-0.4336 \end{gathered}[/tex]

And, for alpha:

[tex]\begin{gathered} \hat{\alpha}=\frac{1}{n}S_y-\hat{\beta}\frac{1}{n}S_x \\ =\frac{1}{13}(336.5)-(-0.4336)\frac{1}{13}(370) \\ \approx38.2255 \end{gathered}[/tex]

This means** that the linear regression equation will be:**

[tex]y=38.2255-0.4336x[/tex]

For finding the x-value that will have 10 hours of recreational activities, **we replace the 10 value on y, and clear out the variable x:**

[tex]10=38.2255-0.4336x[/tex]

And thus,

[tex]\begin{gathered} 10-38.2255=-0.4336x \\ \frac{-28.2255}{-0.4336}=x \\ 65.09=x \end{gathered}[/tex]

This means that **when a person works 65 hours approximately, he will have 10 hours of recreational activities every week. **