Mathematics College

## Answers

**Answer 1**

**EXPLANATION:**

We are given the linear equation;

[tex]y-4=3(x+1)[/tex]

To graph this equation, we would begin by re-writing the equation in the slope-intercept form, which is;

[tex]y=mx+b[/tex]

To do this, we first expand the parenthesis;

[tex]y-4=3x+3[/tex]

Next we add 4 to both sides;

[tex]y-4+4=3x+3+4[/tex][tex]y=3x+7[/tex]

We can now begin to plot the various points on the line. Starting from, x = -2 we would have;

[tex]\begin{gathered} x=-2: \\ y=3(-2)+7 \\ y=-6+7 \\ y=1 \end{gathered}[/tex]

We can now go on and plot other points depending on the limit imposed by the graph page.

However, what we have here shows the coordinates from which we may begin;

**ANSWER:**

[tex]\begin{gathered} (-2,1) \\ That\text{ is;} \\ x=-2,y=1 \end{gathered}[/tex]

## Related Questions

Write the following decimal numbers as a fraction: • One hundred and twenty four hundredths • Five tenths 5/10 Twenty seven thousandths Fifty two and nine hundredths

### Answers

**ANSWER:**

10024/100

5/10

27/1000

5209/100

**STEP-BY-STEP EXPLANATION:**

The first thing is to convert the writing into a decimal number and then convert it into a fraction, just like this:

One hundred and twenty four hundredths:

100.24 = 10024/100

Five tenths

0.5 = 5/10

Twenty seven thousandths

0.027 = 27/1000

Fifty two and nine hundredths

52.09 = 5209/100

What is the value of the expression below? If entering the value as fraction or mixed number, give the answer in lowest term.-0.2 + (-¾) + 2.15 - (-⅖)

### Answers

[tex]1\frac{3}{5}[/tex]

**Explanation:**

-0.2 + (-¾) + 2.15 - (-⅖)

let's convert the decimal to fractions:

-0.2 = -2/10 = -1/5

2.15 = 215/100 = 43/20

-0.2 + (-¾) + 2.15 - (-⅖) = -1/5 + (-¾) + 43/20 - (-⅖)

**Expanading the bracket:**

Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

= -1/5 -3/4 + 43/20 + 2/5

[tex]\begin{gathered} \text{The LCM = 20} \\ =\frac{-1(4)-3(5)+43+2(4)}{20} \\ \end{gathered}[/tex][tex]\begin{gathered} =\frac{-4-15+43+8}{20}=\frac{32}{20} \\ =\frac{8}{5} \\ =1\frac{3}{5} \end{gathered}[/tex]

Find the surface area of a sphere with a radius of 1 cm to the nearest tenth. (Do NOTtypeinany units in your answer.)

### Answers

**The area of the sphere is 12.6**

Here, we want to find the area of the sphere given the radius

Mathematically, we can calculate the area of the sphere using the formula below;

[tex]\begin{gathered} A\text{ = 4}\times\pi\times r^2 \\ r\text{ = 1 cm} \\ \pi\text{ = 3.142} \\ \text{Area of sphere = 4}\times3.142\times1^2=12.6cm^2 \end{gathered}[/tex]

At a fundraiser , a sorority is able to raise $5 less than four times the amount of money a fraternity raises

All together they raised $115

First question what is known is the situation?

Second question what is unknown in the situation

Third question how do I write an equation that represents the situation use at to represent the fraternity

NEED HELP ASAP I WILL MARK YOU BRAINLIEST NO LINKS PLEASE AND THANK YOU

### Answers

An **equation** that represents the situation used to represent the amount that the fraternity raises is; x + (4x - 5) = 115

How to solve Algebra Word Problems?

Let the **amount** of money **raised** by the fraternity be x.

Now, we are told that the sorority raises $5 less than four times the amount that a fraternity raises. Thus;

**Amount raised **by Sorority = $(4x - 5)

Together, we are told that they raised $115. Thus, the **equation** will be;

x + (4x - 5) = 115

5x - 5 = 115

5x = 115 + 5

5x = 120

x = 120/5

x = $24

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The value V of an item after t years is given by the following formula, assuming linear depreciation,V = C - Crt.where C is the original cost and r is the rate of depreciation expressed as a decimal.If you buy a car for $7191 and it depreciates linearly at a rate of 5% per year, what will be its value after 9 months? Round youranswer to the nearest cent.

### Answers

Here C=$7191

r=0.05

t=9 months=0.75 years

The value of the car will be

[tex]V=7191-7191\times0.05\times0.75\Rightarrow V=7191-269.6625\Rightarrow V=6921.34[/tex]

Hence the value of the car will be $6921.34.

Given the following expressions, you will identify the followingslope, y- intercept , x intercept, domain range , and is the function increasing or decreasing

### Answers

Given the following function:

[tex]\text{ 3x - 2y = 16}[/tex]

**A.) SLOPE**

Let's first transform the given equation into the standard slope-intercept form: **y = mx + b**

Because the **m** in the equation represents the value of the slope.

We get,

[tex]\begin{gathered} \text{ 3x - 2y = 16} \\ \text{ (3x - 2y = 16)( -}\frac{\text{ 1}}{\text{ 2}}) \\ \text{ -}\frac{3}{2}x\text{ + y = -}\frac{16}{2} \\ \text{ -}\frac{3}{2}x\text{ + y = -}8 \\ \text{ y = }\frac{3}{2}x\text{ - 8} \end{gathered}[/tex]

The slope-intercept form of 3x - 2y = 16 is y = (3/2)x - 8. Where m = 3/2.

Therefore, the slope of the function is **3/2**.

**B.) Y - INTERCEPT**

In the standard slope-intercept form : y = mx + b, b represents the y - intercept.

Therefore, in the converted form of the function y = (3/2)x - 8.** b** is equals to **-8**.

The y-intercept is** 0, -8**.

**C.) X - INTERCEPT**

The x - intercept is the point at y = 0.

We get,

[tex]\text{ 3x - 2y = 16}[/tex][tex]\text{ 3x - 2(0) = 16}[/tex][tex]\text{ 3x = 16}[/tex][tex]\text{ }\frac{\text{3x}}{3}\text{ = }\frac{\text{16}}{3}[/tex][tex]\text{ x = }\frac{\text{ 16}}{\text{ 3}}[/tex]

Therefore, the x - intercept is** 16/3, 0**

**D.) DOMAIN RANGE**

The function has no undefined points nor domain constraints. Therefore, the domain is

[tex]-\infty\: We usually encounter undefined points when a given value of x will make the denominator equal to zero (0).

Example: 2/(3 - x) at x = 3 is **undefined**.

**E.)** **INCREASING OR DECREASING**

The easiest way to determine if the function is decreasing or increasing is by looking at the **slope (m)**. If the slope is greater than 0 (m > 0) or a positive, **the function is increasing**. If the slope is less than 0 (m < 0) or a negative, **the function is decreasing**.

Here, the slope is 3/2 which we first solved. Since the slope is greater than zero or a positive, the function is, therefore**, increasing**.

The answer is **increasing**.

enter an equation that describes the propitiatial relationship between the number of days and the number of weeks in a giving length of time

### Answers

We need to find an equation that describes the relationship between days and week.

We know that one week has 7 days:

So, to find the number of days for a given number of weeks, what we need to do is multiply the number of weeks by 7.

If we call the number of weeks "w" and the number of days "d", the equation that describes the proportional relationship is:

[tex]d=7w[/tex]

The number of days is equal to the number of weeks multiplied by 7.

Now with this, we can complete the table of values. For 4 weeks, the number of days is:

[tex]\begin{gathered} d=7(4) \\ d=28 \end{gathered}[/tex]

For 5 weeks, the number of days is:

[tex]\begin{gathered} d=7(5) \\ d=35 \end{gathered}[/tex]

To complete the next row, we don't need the days, we need the number of weeks. For that, we take our equation and substitute the number of days:

[tex]\begin{gathered} d=7w \\ 42=7w \end{gathered}[/tex]

And we solve for "w" by dividing both sides by 7:

[tex]\begin{gathered} \frac{42}{7}=w \\ 6=w \end{gathered}[/tex]

Finally, for the last row, we find the number of days in 13 weeks using our equation:

[tex]\begin{gathered} d=7(13) \\ d=91 \end{gathered}[/tex]

i need help with math

### Answers

∠1 and ∠2 are on same side** exterior** angles. FALSE

∠3 and ∠12 are **alternate interior** angles. FALSE

∠2 and ∠10 are **corresponding angles**. TRUE

∠6 and ∠11 are** alternate exterior** angles. TRUE

What are the different types of angles?

**Corresponding angles** ; Angles that are present in similar locations are said to be in correspondence with one another. The dimensions of both angles are** equal**

**Alternate Interior Angle**: This term refers to the angles that are present on the opposing sides of the transversal. They can be found on the inside of the Z that the figure's Z has produced. The angles are both equal to one another.

**Alternative Exterior Angle**: The alternative exterior angles are those that are externally located and present on the opposing sides of the transversal. Both angles measure the same and they may be seen on the exterior.

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the square practice x² + 6x + 9 = 0

### Answers

**x = -3 twice **

Explanation:

x² + 6x + 9 = 0

Since the method for solving the question isn't specified, we will be using factorisation method to solve for x.

factors of 9 = 1, 3, 9

**The two numbers when multiplied gives 9 and when added gives 6 are +3 and + 3.**

**using factorisation method:**

x² + 3x + 3x + 9 = 0

x(x + 3) + 3(x + 3) = 0

(x + 3)(x + 3) = 0

(x+3) = 0 or (x+3) = 0

x = -3 or x = -3

**x = -3 twice **

**The second method is because of the square practice in the question.**

**Using complete the square:**

x² + 6x + 9 = 0

x² + 6x = -9

**we half the coefficient of x and the square the result**

coefficient of x = 6

1/2 of coefficient of x = 6/2

square of the result = (6/2)² = 3² = 9

**Add the above result from both sides of the equation:**

x² + 6x + 9 = -9 + 9

(x + 3)² = 0

**square root both sides:**

x + 3 = +/- √0

**subtract 3 from both sides:**

x +3 -3 = -3 +/-√0

x = -3 + 0 or -3 - 0

**x = -3 twice**

Answers : • center c and scale factor 2• center a and scale factor 5• center c and scale factor 1• center a and scale factor 2

### Answers

Scale factorInitial explanation

In order to find the scale factor of the dilation of ΔABC, we just need to divide any pair of the corresponding sides of both triangles. We have that the division of the corresponding sides will be always the same:

[tex]\frac{A^{\prime}C^{\prime}}{AC}=\frac{B^{\prime}C^{\prime}}{BC}=\frac{A^{\prime}B^{\prime}}{AB}=\text{scale factor}[/tex]

We are going to choose the first division:

[tex]\frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor}[/tex]Finding the scale factor

We have that AC = 5 and A'C' = 10:

Then:

[tex]\begin{gathered} \frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor} \\ \downarrow \\ \frac{10}{5}=2 \end{gathered}[/tex]

The scale factor is 2.

And since the point C and C' are the same, the center is C.

**Answer- A. center C and scale factor 2**

- Graph the function f (x) = x - 4. Use the line tool and select two points to graph. Line * Move Undo Redo x Reset 10 9 8 7 6 5 4 3 N 1 1 2. 3 4 6 7 8 9 10 10 9 8 7 6 5 4 3 2 -19 -2

### Answers

we have the function

f(x)=x-4

That is the equation of a line

to graph a line we need at least two points

so

Find out the intercepts

step 1

Find out the y-intercept (value of y when the value of x is zero)

For x=0

f(x)=0-4

f(x)=-4

the y-intercept is the point (0,-4)

step 2

Find out the x-intercept (value of x when the value of y is zero)

For y=0

0=x-4

x=4

the x-intercept is the point (4,0)

step 3

Plot the points (0,-4) and (4,0), join them, to graph the line

see the attached figure to better understand the problem

complete the square with the following equation of a circle so that you can convert the equation into standard form.

### Answers

**Equation of a Circle**

We are given the equation:

[tex]x^2+y^2+10x+12y+12=0[/tex]

The equation of a circle of radius r and center (h,k) is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

To convert the given equation into the standard form, we need to complete squares as follows.

First, rearrange terms:

[tex]x^2+10x+y^2+12y+12=0[/tex]

The term 10x is divided by 2x to find the correct number to complete:

10x/(2x) = 5

Similarly, dividing 12y/(2y) = 6

Now we complete both squares by adding (and subtracting) 25 and 36:

[tex]x^2+10x+25+y^2+12y+36+12-25-36=0[/tex]

Operating:

[tex](x+5)^2+(y+6)^2=49[/tex]

**Second choice**

Find the least-squares regression line y = bo + b₁x through the points

(-2,0), (0,7), (4, 15), (8, 18), (9,24),

and then use it to find point estimates y corresponding to x = 1 and x = 8.

For this problem and to give you practice for the test, use the shortcut method to find bo given that b₁ = 1.9051724137931.

For x = 1, y =

For x = 8, y^=

### Answers

The **values **for x = 1, then y = 38.23 **and **for x = 8, then y^ = 55.375.

**Given **that, [tex]y = b_{0}+ b_{1}x[/tex]

x y xy xx yy

-2 0 0 4 0

0 7 0 0 49

4 15 60 16 225

8 18 144 64 324

9 24 216 81 576

19 64 420 165 1174 - **Total**(T)

n = 5

**Given **line is [tex]y = b_{0}+ b_{1}x[/tex]

**Solve **for the **value **of [tex]b_{0}[/tex]

[tex]b_{0} = \frac{Ty*Txx-Tx*Txy}{nTx^{2} -(Tx)^{2} }[/tex]

[tex]= \frac{64*165-19*420}{5*165-(19)^{2} }\\ \\= \frac{10560-7980}{825-361}\\ \\= \frac{2580}{64} = 40.135[/tex]

**Solve **for the **value **of [tex]b_{1}[/tex]

[tex]b_{1} = \frac{nTxy-Tx*Ty}{nTx^{2} -(Tx)^{2} }\\ \\= \frac{5*420-19*64}{5*165 - (19)^{2} }\\ \\= \frac{2100-1216}{464}\\ \\= \frac{884}{464} = 1.905[/tex]

Therefore, y = 40.135 + 1.905x

To **solve **for x = 1

y = 40.135 + 1.905(1)

= 38.23

To **solve **for x = 8

y^ = 40.135 + 1.905(8)

= 55.375

Hence the **answer **is the **values **for x = 1, then y = 38.23 **and **for x = 8, then y^ = 55.375.

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how to solve the volume of sphere and the area of a cylinder.

### Answers

Consider a sphere of radius r, then the volume of the sphere is given by,

[tex]V=\frac{4}{3}\pi\times r^3[/tex]

Here

[tex]\pi=3.14[/tex]

Now let us consider a cylinder of with base radius r and height h, as in the figure,

The area is the total area of the base surface and the niddle surface.

This can be written as,

[tex]A=2\pi(h+r)[/tex]

Consider a sphere of radius 2 cm, the volume can be calculated as,

[tex]v=\frac{4}{3}\times3.14\times2^3=\frac{4}{3}\times3.14\times2\times2\times2=33.49cm^3[/tex]

Teresa is riding in a bike race that goes through a valley and a nearby mountain range.The table gives the altitude (in feet above sea level) for the five checkpoints in the race.Use the table to answer the questions.Checkpoint,Altitude(feet above sea level)1, -1152, 2,1663, 1,1854, -1685, -32(a)The top of a hill rises 530 feet above Checkpoint 4.What is the altitude of the top of the hill?(b)How much lower is Checkpoint 4 than Checkpoint 1?

### Answers

a)

Checkpoint 4 = -168 ft

Add 530

-168 + 530 = **362 ft**

b) Compare checkpoint 1 to checkpoint 4

1 = -115 ft

4 = -168

-168 -(-115) = -53

**Checkpoint 4 is 53ft lower than checkpoint 1 **

if you could please try to answer quickly my brainly keeps crashing

### Answers

The lateral area of a cylinder is given by:

[tex]L=2\pi rh[/tex]

where r represents the radius and h represents the height.

Then,

h=13m

In this case, we have the diameter. However, the radius is the half value of the diameter.

Then,

r=d/2=6m/2=3m

Replacing:

[tex]\begin{gathered} L=2\pi(3m)(13) \\ L=245m^2 \end{gathered}[/tex]

Hence, **the lateral area is 245m².**

11. The trigonometric ratio of cos B isPYTHAGOREAN TRIPLE PROBLEMB13590°A125/1212/135/1313/5

### Answers

From the given right-angled triangle, we have the following:

Hypothenuse side = 13

Opposite side = 12

Adjacent side = 5

**Solution**

The trigonometric ratio of cos B can be found using the relationship:

[tex]\cos \text{ B = }\frac{Adjacent}{Hypothenus}[/tex]

By substituting, we have:

[tex]cos\text{ B = }\frac{5}{13}[/tex]

**Hence, the answer is 5/13 (option C)**

4:58 PM 16 AA.18 Area of compound figures... < Surina Silva's prac... 38 What is the area of this figure? 3 mi 14 mi 5 mi 9 mi 10 mi 5 mi 4 mi 10 mi Write your answer using decimals, if necessary. square miles.

### Answers

**ANSWER**

230 square miles

**EXPLANATION**

We can divide this figure as shown in the picture: 2 rectangles and a right triangle. We find the area of each figure and then we add them up.

One of the rectangles's length is 5 mi and its width is 14 mi. Its area is:

[tex]A_{\text{rectangle}1}=5mi\times14mi=70mi^2[/tex]

The other rectangle's lenght is 10mi and its width is 5mi. Its area is:

[tex]A_{\text{rectangle}2}=10mi\times5mi=50mi^2[/tex]

The triangle height is:

[tex]3mi+5mi+10mi+4mi=22mi[/tex]

And its base is 10mi. Its area is:

[tex]A_{\text{triangle}}=\frac{22mi\times10mi}{2}=\frac{220mi^2}{2}=110mi^2[/tex]

The area of the figure is:

[tex]\begin{gathered} A=A_{\text{rectangle}1}+A_{\text{rectangle}2}+A_{\text{triangle}} \\ A=70mi^2+50mi^2+110mi^2 \\ A=230mi^2 \end{gathered}[/tex]

The 5 participants in a 200-meter dash had the following finishing times in seconds)24, 28, 26, 30, 32Send data to calculatorAssuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places,

### Answers

**Given:**

Data x: 24, 28, 26, 30, 32

n = 5

**Asked: **What is the standard deviation of the population?

**Formula: **

[tex]\text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}}[/tex]

**Solution:**

**Step 1: ***We will get the average of the data given. *

*NOTE: Bar x is also the mean or the average.*

[tex]\begin{gathered} \bar{x}\text{ = }\frac{24+28+26+30+32}{5}\text{ } \\ \bar{x}=\text{ 28} \end{gathered}[/tex]

**Step 2: ***We will subtract the mean from each number.*

**Step 3: ***We will square the differences and get the summation.*

**Step 4: ***We will substitute the acquired values to find the standard deviation using the formula above.*

[tex]\begin{gathered} \text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}} \\ \text{standard deviation = }\sqrt[]{\frac{40^{}}{5}}\text{ } \\ \text{standard deviation = 2}\sqrt[]{2}\text{ = }2.828427125 \end{gathered}[/tex]

**ANSWER: ****standard deviation = 2.83 ***(Rounded off to 2 decimal places)*

Question AA baseball is hit, following a path represented by x = 135t and y = 3.3 + 38t − 16t 2 for 0 ≤ t ≤ 3.Part A: Find the ordered pairs, (x, y) when t = 0.2, 1.2, and 2.2.Part B: The fence, which is 10 feet tall, lies 320 feet away from home plate. Does the baseball travel over the fence? Justify your answer mathematically.Part C: Write a rectangular equation to represent the plane curve.

### Answers

Explanation

For the given question, we have the following

[tex]\begin{gathered} x=135t \\ y=3.3+38t-16t^2 \end{gathered}[/tex]

Part A

find the ordered pairs (x,)

[tex]\begin{gathered} when \\ t=0.2 \\ \\ x=135(0.2)=27 \\ y=3.3+38(0.2)-16(0.2)^2=10.26 \\ \\ when\text{ t=0.2} \\ (x,y)=(27,10.26) \\ \end{gathered}[/tex]

[tex]\begin{gathered} when \\ t=1.2 \\ x=135(1.2)=162 \\ y=3.3+38(1.2)−16(1.2)^2=25.86 \\ \\ (x,y)=(162,25.86) \end{gathered}[/tex]

[tex]\begin{gathered} when \\ t=2.2 \\ x=135(2.2)=297 \\ y=3.3+38(2.2)−16(2.2)^2=9.46 \\ \\ (x,y)=(297,9.46) \end{gathered}[/tex]

Can help me:coin is flipped 6 times. What is the probability that heads and tails occur an equal number times?

### Answers

The **probability** that heads and tails occur an equal number times is 5/16.

From the question, we have

The **number** of permutations =HHHTTT

The total number of permutations = 6!=720.

Since, there are two groups comprising 3 identical objects, the number of **permutations** = 720/3!3!=20.

total number of **possibilities** in the event space= 2^6=64

the required **probability** = 20/64=5/16.

**Probability:**

**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 incorporated probability to forecast the **likelihood** of various 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.

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Use the Pythagorean Theorem to find the missi romanille 1 1 point a = 3 and b = 7. Round to two decimal places. Type your answer... 2. 1 point a = 3 and c = 23. Round to two decimal places. Type your answerExercise number 1

### Answers

The formula of the Pythagorean Theorem is

[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where c is the hypotenuse and} \\ a,b\text{ are the sides of the triangle} \end{gathered}[/tex]

Graphically,

So, in this case, you have

[tex]\begin{gathered} a=3 \\ b=7 \\ c=\text{?} \\ a^2+b^2=c^2 \\ \text{ Replacing} \\ (3)^2+(7)^2=c^2 \\ 9+49=c^2 \\ 58=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{58}=\sqrt[]{c^2} \\ 7.62=c \end{gathered}[/tex]

Therefore, **the missing side measurement is 7.62 units.**

Turn into an inequality A speed limit of 65 mph

### Answers

The question says we should turn into an inequality a speed limit of 65 miles per hour.

This means the speed should'nt be more than 65 miles per hour. In other words the speed shouldn't exceed 65 miles per hour.

Let represent the speed with a. Therefore,

a < 65 miles per hour

a < 65

Solve the following equation for X 5x+7y=19 X= ?

### Answers

[tex]x=\frac{19-7y}{5}[/tex]

**1) ** We can solve this equation for x, by doing the following algebraic manipulation:

[tex]\begin{gathered} 5x+7y=19 \\ \\ 5x+7y-7y=19-7y \\ \\ 5x=19-7y \\ \\ \frac{5x}{5}=\frac{19}{5}-\frac{7y}{5} \\ \\ x=-\frac{7}{5}y+\frac{19}{5} \\ \\ x=\frac{19-7y}{5} \end{gathered}[/tex]

**2) ** In this problem, we can't go any further than that. **So, that is the answer.**

At his job, Tomas earns a commission plus an hourly wage. The function below describes the total dollar amount Tomas earns, based on the number of hours he works,f(h) = 250 +8.5hWhat represents the hourly rate Tomas earns

### Answers

f(h) = 250 +8.5h

The function is on slope-intercept form:

y(x)= mx +b

Where m is the slope.

Rearranging the function given:

f(h) = 8.5h +250

Where:

250 is the fixed commission since it doesn't have a variable next to it.

8.5 is the hourly wage.

We can see that the hourly rate (8.5 per hour) is the slope of the function.

Us a tree diagram to find the sample space and the total number of possible outcomesSo which choice is the answer.

### Answers

In order to create the tree diagram, first, create the principal branches which is the type of item,

Then, divide the three colors for each of the items

.the, count the final branches to know the possible outcomes, meaning that the number of possible outcomes is 6.

I’m trying to figure out how to do this one ! It’s kind of got me stuck

### Answers

**ANSWER :**

The answer is **Option 3.**

**EXPLANATION :**

From the problem, we have the equation of the line :

[tex]y=x+3[/tex]

First thing to do is check the correctness of the table.

The given values in the table must satisfy the equation.

For Option 1.

Let's check the point (2, 3)

[tex]\begin{gathered} y=x+3 \\ 3=2+3 \\ 3=5 \\ \text{ False!} \end{gathered}[/tex]

For Option 2.

Let's check the point (-2, 1)

[tex]\begin{gathered} y=x+3 \\ 1=-2+3 \\ 1=1 \\ \text{ True!} \end{gathered}[/tex]

But the point (-2, 1) is not in the graph, so this is false!

For Option 3.

The points are the same with Option 2, so we need to check the graph.

(-2, 1) is on the graph.

(-1, 2) is on the graph.

(0, 3) is on the graph.

(1, 4) is on the graph.

(2, 5) is on the graph.

So this must be the correct table and graph.

Ahmad is choosing between two exercise routines.In Routine #1, he burns 20 calories walking. He then runs at a rate that burns 10.5 calories per minute.In Routine #2, he burns 46 calories walking. He then runs at a rate that burns 5.3 calories per minute.For what amounts of time spent running will Routine #1 burn fewer calories than Routine #2?Use t for the number of minutes spent running, and solve your inequality for t.0ロロロメロOSDDADxХ5?ExplanationCheck

### Answers

Solution:

Let t for the number of minutes spent running

In Routine #1, he burns 20 calories walking. He then runs at a rate that burns 10.5 calories per minute.

This can be represented as **20 + 10.5t**

In Routine #2, he burns 46 calories walking. He then runs at a rate that burns 5.3 calories per minute.

This can be represented as **46 + 5.3t**

The required inequality is

[tex]\begin{gathered} 20+10.5t<46+5.3t \\ 10.5t-5.3t+20<46+5.3t-5.3t \\ 5.2t+20<46 \\ 5.2t+20-20<46-20 \\ 5.2t<26 \\ \frac{5.2t}{5.2}<\frac{26}{5.2} \\ t<5 \end{gathered}[/tex]

**The answer is 5 minutes**

A sample of 26 customers was taken at a computer store. Each customer was asked the price of the computer she bought. Here is a summary Number of computers 7, 10,9 Price paid for each (in dollars) 900, 800, 1200 Find the mean price for this sample. Round your answer to the nearest dollar.

### Answers

formula for the mean

[tex]\bar{x}=\frac{\sum ^{\infty}_{n\mathop=0}x_i}{n}[/tex]

for this exercise n=26

replace data on the formula

[tex]\begin{gathered} \bar{x}=\frac{(7\cdot900)+(10\cdot800)+(9\cdot1200)}{26} \\ \bar{x}=965.385 \end{gathered}[/tex]

I'll send the question 2-x>8

### Answers

The given inequality is

[tex]2-x>8[/tex]

We subtract 2 from each side.

[tex]\begin{gathered} 2-2-x>8-2 \\ -x>6 \end{gathered}[/tex]

Then, we multiply the inequality by -1.

[tex]\begin{gathered} -x\cdot-1<6\cdot-1 \\ x<-6 \end{gathered}[/tex]Hence, the answer is b.