Mathematics College

## Answers

**Answer 1**

we have the equation

y= 4.983 −.010x

where

x ----> the salary

y ----> number of viewers

so

For x=$3 million

substitute

in the given equation

y=4.983-0.010(3)

y=4.953 millions

therefore

The answer is 5.0 million (one decimal place)

## Related Questions

I need geometry help.

### Answers

**Answer:**

**YES**

**Step-by-step explanation:**

What's the question?

-16(4/5)/(4/5)Solve as a fraction and decimal

### Answers

The expression -16(4/5)/(4/5), ther is only multiplication and divisions, so we can do them in any order.

So, we can rewrite it as:

[tex]-16\cdot\frac{\frac{4}{5}}{\frac{4}{5}}[/tex]

The division of fractions can be turned into a multiplication of fractions:

[tex]-16\cdot\frac{4}{5}\cdot\frac{5}{4}=-16\cdot\frac{4\cdot5}{5\cdot4}=-16\cdot1=-16[/tex]

So, this expression is the same as **-16**. There is no decimals and there is no need for fractions, because the denominator is 1 so **-16** is already in a decimal and fractionform.

The answer is **-16**

I need Help with this problem please show steps so i can understand it

### Answers

**ANSWER**

93 degrees

**EXPLANATION**

We have the two angles on that line, x and x - 6.

**Angles on a line sum up to 180 degrees**. So, we have that:

x + x - 6 = 180

**Collect like terms**:

=> 2x = 180 + 6 = 186

x = 186 / 2

**x = 93 degrees**

That is the value of x

Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable isyour estimate when compared to the actual answer?A full-time employee who works 40 hours per week earns $8.50 per hour. Estimate that person's annual income. Round 52 weeks to 50 weeks per year, and round the hourly wage to the nearest dollar for the estimate. The estimate of annual income is $(Round to the nearest thousand as needed.

### Answers

The annual income of the employee can be calculated as:

[tex]\text{income}=(\text{price per hour)}\cdot\text{ (hours per week)}\cdot(\text{ weeks per year)}[/tex]

To estimate the income, we are going to round the price per hour to $9 per hour and the total weeks to 50 weeks. So, the estimated income is:

[tex]E\text{stimate Income = \$9}\cdot40\cdot50=\text{ \$18,000}[/tex]

On the other hand, the actual income is:

[tex]\text{Actual Income= \$ 8.50}\cdot40\cdot52=\text{ \$17,680}[/tex]

So, the difference between them is $320

**Answer: Estimate: $18,000**

** Actual: $ 17,680**

** Difference: $320**

Is my answer correct?

### Answers

**Answer:**

No, your answer is not correct. The correct answer is x = 2 and y = 152.

**Step-by-step explanation:**

(15x-2) = (9x+10), so x = 2. When you put x into 9x+10, you get 28, and 28 + 152 = 180. This works because adjacent angles on a straight line always add up to 180.

Hope this helps.

Mark as brainliest please

Sarah takes home $33,000 per year from her job as a computer repair person. Her only debt obligations are a car loan payment of $395 and a credit card payment of $110 every month Help Sarah go through the steps to see if she is in danger of credit overload. Part I: How much money does Sarah take home per month?Part II: What is 20% of Sarah's monthly take home pay? Part III: How much does Sarah spend in total every month towards paying off her debt? Part IV: Which is greater, 20% of Sarah's monthly take home pay or the amount Sarah spends in total every month towards paying off her debt?

### Answers

To find out how much money sarah takes per month we divided her total income by 12.

[tex]\frac{33000}{12}=2750[/tex]

**Therefore, Sarah takes home $2750 per month.**

To find out Sarah monthly for her home we multiply his total salary per month by .20:

[tex]2750\cdot0.20=550[/tex]

**Therefore, he pays $550 for her gome.**

**The total amount he pays of debt is $505.**

**The monthly take home pay is greater than the total amount she pays per month.**

I need to know how to do this number 13 and the question

### Answers

**ANSWER:**

By 4

[tex]-8x-20y=-4[/tex]

**STEP-BY-STEP EXPLANATION:**

We have the following system of equations:

[tex]\begin{gathered} -2x-5y=-1 \\ 8x+4y=16 \end{gathered}[/tex]

If we want to solve the system by means of the elimination method, the coefficients of one of the unknowns must be the same with the opposite sign, in such a way that when added, they are eliminated.

Since we must multiply is the first equation, we look at the unknown x, they already have an opposite sign, therefore we must multiply by a number that multiplied by 2, is equal to 8.

This number is 4, since 2 multiplied by 4 equals 8.

After multiplying by 4, the equation would look like this:

[tex]\begin{gathered} 4\cdot(-2x-5y=-1) \\ -8x-20y=-4 \end{gathered}[/tex]

Dexter has 56 tiles left from tiling his bathroom floor, and he would like to use them to tile the front entrance of his house. Each tile has an area of 36in?. The function A(C) = 36t represents the area, A(t), in square inches that t tiles cover. Select the domain and range that are reasonable for the function.

### Answers

we have the function

[tex]A(t)=36t[/tex]

this is a linear equation (equation of the line)

the domain is all the possible values of t

Remember that the number of tiles are 56

so

the domain is the interval {0,56}

so

the answer for domain is the option B

The range is the set of all possible values of A(t)

Remember that

For t=0

A(t)=0

For t=56

A(t)=36(56)=2,016 in^2

so

the range is the interval {0, 2,016}

answer for range is the option F

a. List all transformations on the equation y = -2x +31 + 2 by graphing the parent function and using transformations. ( points) b. Identify the domain and range of the graph. 2 points)

### Answers

we know that

the parent function of this problem is

[tex]y=\mleft|x\mright|[/tex]

so the transformations are

First

A dilation of the y component with a scale factor of -2

the rule is

(x,y) -----> (x,ay)

a=-2

[tex]y=\mleft|x\mright|\text{ ---}\longrightarrow\text{ y=-2}\mleft|x\mright|[/tex]

Second

A translation of 3 units at left and 2 units up

the rule is

(x,y) ------> (x-3,y+2)

therefore

[tex]\text{y=-2}|x|\text{ ----}\longrightarrow\text{ y=-2}\mleft|x+3\mright|+2[/tex]

using a graphing tool

see the attached image

please wait a minute

the domain is all real numbers

the range is the interval (-infinite, 2}

What is the solution to the system of equations shown below?S 3x + y = 61ly= -4x + 5)

### Answers

Let us write out the equation,

[tex]\begin{gathered} 3x+y=6\ldots\ldots\text{.}.1 \\ y=-4x+5\ldots\ldots2 \end{gathered}[/tex]

We will apply the method of substitution to resolve the equations.

Let us make y the subject of the formula in equation 1,

[tex]\begin{gathered} 3x+y=6 \\ y=6-3x\ldots\ldots\ldots.3 \end{gathered}[/tex]

Let us substitute the value of y=6-3x into equation 2, and solve for x

[tex]\begin{gathered} 6-3x=-4x+5 \\ \text{collect like terms} \\ -3x+4x=5-6 \\ x=-1 \end{gathered}[/tex]

Let us solve for y by substituting the value of x= -1 into equation 3.

[tex]\begin{gathered} y=6-3x \\ y=6-3(-1) \\ y=6+3 \\ y=9 \end{gathered}[/tex]

**Hence, the solution of the equation is**** (x,y)= (-1,9)****.**

**The correct option is option 1.**

=Given P(A) = 0.74, P(B) = 0.45 and P(B|A) = 0.55, findthe value of P(A and B), rounding to the nearest thousandth, ifnecessary.

### Answers

Given P(A) = 0.74, P(B) = 0.45 and P(B|A) = 0.55, find

the value of P(A and B), rounding to the nearest thousandth, if

necessary

Remember that

P(A and B)=P(B/A)*P(A)

so

we have

P(A) = 0.74

P(B) = 0.45

P(B|A) = 0.55

substitute

P(A and B)=0.55*0.74

P(A and B)=0.407

I need help on this please

### Answers

The expression we have is:

[tex]2xy\cdot xy^2[/tex]

And we are given some values for x and y:

[tex]\begin{gathered} x=2 \\ y=4 \end{gathered}[/tex]

The first step will be to **substitute the given values into the expression:**

[tex]2(2)(4)\cdot(2)(4)^2[/tex]

The next step is to solve 4^2 which is equal to 16:

[tex]2(2)(4)\cdot(2)(16)[/tex]

And then we solve the multiplications, 2(2)(4) is equal to 16 and (2)(16) is equal to 32:

[tex]16\cdot32[/tex]

Solving this final multiplication we get the result:

[tex]512[/tex]

**Answer: 512**

Can you help with a geometry problem? Perimeter of a rectangle is 64 and the width is 6 centimeters less than the length, so what’s the width

### Answers

For this problem, we are given the perimeter of a rectangle and a relation between the width and the length. We need to determine the width.

The perimeter of a rectangle is given by:

[tex]P=2(\text{ width + length\rparen}[/tex]

Therefore, we have:

[tex]2\text{ width}+2\text{ length}=64[/tex]

We know that the width is 6 centimeters less than the length, therefore we can write the expression below:

[tex]\text{ width}=\text{ length}-6[/tex]

If we replace the expression above on the second one, we have:

[tex]\begin{gathered} 2(\text{ length}-6)+2\text{ length}=64\\ \\ 2\text{ length}-12+2\text{ length}=64\\ \\ 4\text{ length}=64+12\\ \\ 4\text{ length}=76\\ \\ \text{ length}=\frac{76}{4}=19 \end{gathered}[/tex]

We can use this value to find the width, which is:

[tex]\text{ width}=19-6=13[/tex]

**The width is equal to 13 cm.**

Which of the following graphs shows a positive linear relationship with acorrelation coefficient, r, close A. Graph AB. Graph BC. Graph CD. Graph D

### Answers

Answer:

Graph C (option C)

Explanation:

**Given:**

Four different graphs

**To find:**

the graph that shows a positive linear relationship with a correlation coefficient, r, close to 1

A negative correlation is a graph where an increase in one quantity leads to a decrease in the other quantity. The graph declines

A positive correlation is a graph where an increase in one quantity leads to an increase in the other quantity. The movement is from left to right (rises)

For the correlation coefficient to be close to 1, the points will be close to the slant straight line.

The graph which satisfies the above is Graph C (option C)

the spinner has 8 congruent sides. What is the probability of spinning a number divisible by 3 two times in a rowoptions:3/41/165/161/4

### Answers

**1/16**

Explanation:

Spinner is divided into 8

The total possibilities when you spin once = 8

Numbers divisible by 3 = 3, 6

**There are 2 numbers divisible by 3**

Probability of getting number divisible by 3 = numbers divisible by 3/total possibility

Probability of getting number divisible by 3 = 2/8

**Probability of getting number divisible by 3 two times in a row:**

The two events are independent of one another. The probability of spinnig the first one will not affect the probability of spinning the 2nd one

Probability of getting number divisible by 3 two times in a row = Probability of getting number divisible by 3 × Probability of getting number divisible by 3

= 2/8 × 2/8 = 4/64

simplify = 1/16

**Probability of getting number divisible by 3 two times in a row = 1/16**

Hans drained an aquarium. He took 15 minutes. The graph shows the amount of water (In liters) in the aquarium versus time (in minutes)Find the domain and the range of the function shown.

### Answers

The domain is all the possible values that x can in our case

[tex]0\le x\le15[/tex]

the range is all the possible values for y

[tex]0\le y\le75[/tex]

Write the equation of the quadratic function in standard form given the roots are 6 and -2 and a point on the graph is (10,24)

### Answers

**EXPLANATION**

Since we have that the roots are (6,0) and (-2,0) and a point on the graph, the canonical quadratic equation is as follows:

[tex]y=a(x-6)(x-(-2))[/tex]

Subtracting:

[tex]y=a(x-6)(x+2)[/tex]

Applying the distributive property:

[tex]y=a(x^2+2x-6x-12)[/tex]

Adding like terms:

[tex]y=a(x^2-4x-12)[/tex]

Now, in order to compute the value of a, we must plug the point (10,24):

[tex]24=a(10^2-4\cdot10-12)[/tex]

Multiplying numbers:

[tex]24=a(100-40-12)[/tex]

Adding numbers:

[tex]24=a(48)[/tex]

Dividing both sides by 48:

[tex]\frac{24}{48}=a[/tex]

Simplifying:

[tex]\frac{1}{2}=a[/tex]

Switching sides:

[tex]a=\frac{1}{2}[/tex]

Plugging in a into the equation:

[tex]y=\frac{1}{2}(x^2-4x-12)[/tex]

Applying the distributive property:

[tex]y=\frac{1}{2}x^2-2x-6[/tex]

In conclusion, the expression of the quadratic equation is as follows:

[tex]y=\frac{1}{2}x^2-2x-6[/tex]

if they had 300 patches of a pet shop and you were to divide that by 1 what would be the answer because it's very confusing

### Answers

if they had 300 patches of a pet shop and you were to divide that by 1, the right answer would be 300 because you were to divide that by 1., the right answer would be 300 be, the right answer would be 300 be

Solve the system of equations-5x + 4y =3x = 2y -15x= y=

### Answers

Equation 1: -5x + 4y = 3

Equation 2: x = 2y - 15

Since Equation 2 is already solved for x, we will use this value of x in the firs equation:

-5x + 4y = 3

-5(2y - 15) + 4y = 3

-10y + 75 + 4y = 3

-6y = 3 - 75 = -72

y = -72/-6 = 12

y = 12

Using this value of y in equation 2:

x = 2y -15

x = 2(12) - 15

x = 24 -15

x = 9

**Answer:**

**x = 9**

**y = 12**

17. The scores for a math test are shown below, ordered from smallest to largest.606162636364646566666669727272747580828486868787898990939498Fill out the stem and leaf plot below for this data. Enter the leaves separated by commas (ex: 1,1,2,3).StemsLeaves

### Answers

The stem and leaf plot is used to organize data. To construct it you have to "break" the data into steam and leaf. For the given data set, you have to separate both digits, the first digit will represent the steam and the second digit will represent the leaf.

First step, group the data acording to the first digit of the number:

Group 1:

60, 61, 62, 63, 63, 64, 64, 65, 66, 66, 66, 69

Group 2:

72, 72, 72, 74, 75

Group 3:

80, 82, 84, 86, 86, 87, 87, 89, 89

Group 4:

90, 93, 94, 98

The plot will have 4 stems 6, 7, 8, and 9, and the leaves will be the second digit of each observation that belongs to the group. They can be repeated as many times as the number itself is:

Martha manages a home improvement store and uses this function to model the number of customers that visit the store each hour on aSaturday afternoon.n(t) = -2.82t^2 + 25.74t + 60.87Which graph would most likely be associated with this model?

### Answers

Consider the equation:

[tex]n(t)-2.82t^2+25.74t+60.87[/tex]

The graph is given as:

6. Solve and graph on a number line the solution to the inequality - 4x + 6 < 10

### Answers

[tex]\begin{gathered} -4x+6<10 \\ \end{gathered}[/tex]

subtract 6 from both sides:

[tex]\begin{gathered} -4x+6-6<10-6 \\ -4x<4 \end{gathered}[/tex]

divide both sides by -4:

[tex]\begin{gathered} \frac{-4x}{-4}<\frac{4}{-4} \\ x>-1 \end{gathered}[/tex]

The graph off (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of g (in red).The function fis defined by f(x) = Vx.Write down the expression for g(x).

### Answers

Given the function below,

[tex]f(x)=\sqrt[]{x}[/tex]

To find the g(x) by translating f(x),

The function f(x) is translated 4 units horizontally to the right and 3 units vertcally upward to give the function g(x),

**Hence, the expression for ****g(x)**** will be**,

[tex]g(x)=\sqrt[]{x-4}+3[/tex]

A 25 foot tall flagpole casts a 42 foot shadow. What is the angle that the sun hits the flagpole?

### Answers

In the given figure :

AB is height of the flagpole : **AB = 25 feet**

BC is the length of shadoe : **BC = 42 foot**

and angle FAE is the angle that the sun hits the flagpolem : **FAE = θ**

Since, line AE and line BC are the staright horizontal line, so they are parallel

and the line FC act as a transversal

So, Angle ACB = Angle FAE by corresponding angle properties

Now for angle ACB : line AB is opposite to the angle and the line BC is adjacent

Apply the trignometri ratio of Opposite side to adjacent side i.e. tangent of the angle

[tex]\tan \theta=\frac{Opposite\text{ side}}{Adjacent\text{ Side}}[/tex]

Substitute the value and simplify :

[tex]\begin{gathered} \tan \theta=\frac{Opposite\text{ side}}{Adjacent\text{ Side}} \\ \tan \text{ }\theta=\frac{AB}{BC} \\ \tan \theta=\frac{25}{42} \\ \tan \theta=0.5952 \\ \theta=\tan ^{-1}(0.5951) \\ \theta=30.76^o \end{gathered}[/tex]

So, angle is 30. 76 degree

Angle FAE = θ = 30.76 degree

Angle FAE = 30.76 degree

The angle that the sun hits the flagpole is 30.76 degree

**Answer : The angle that the sun hits the flagpole is 30.76 degree **

a. 5x+y=-310x +2y=-6QUESTIONS•M=SLOPE YINT•NUMBER OF SOLUTIONS

### Answers

**ANSWERS**

• m =, -5

,

• y-intercept = ,-3

,

• Number of solutions: ,infinite solutions ,(many solutions)

**EXPLANATION**

Note that the second equation of this system is the first equation multiplied by 2:

[tex]\begin{gathered} 2\cdot(5x+y=-3) \\ 2\cdot5x+2y=-2\cdot3 \\ 10x+2y=-6 \end{gathered}[/tex]

This means that these two equations represent the same line. If they are both the same line, then they intersect in infinite points, so the system has infinite solutions.

On the other hand, both equations have the same slope and y-intercept. If we rewrite the first equation in slope-intercept form, by clearing y, we can see them more easily:

[tex]\begin{gathered} 5x+y=-3 \\ y=-5x-3 \end{gathered}[/tex]

The slope is -5 and the y-intercept is -3

What is the equation of the directrixfor the following parabola:(x - 1)2 = 12(y + 2)

### Answers

Given an equation of a parabola;

[tex]\begin{gathered} (x-h)^2=4p(y-k)\text{ } \\ \text{Directrix is y=k-p} \end{gathered}[/tex][tex]\begin{gathered} From\text{ the equation of a parabola;} \\ h=1,k=-2\text{ and p=3} \\ \text{Directrix is} \\ y=-2-3 \\ y=-5 \end{gathered}[/tex]

Determine the radius and height of the rectangle so as to maximize the area

### Answers

**SOLUTION **

The perimeter of the shape becomes

[tex]\begin{gathered} P=2h+2r+\text{length of arc } \\ P=2h+2r+\frac{180}{360}\times2\times\pi r \\ P=2h+2r+\frac{1}{2}\times2\times\pi r \\ P=2h+2r+\pi r \\ 2h+2r+\pi r=920 \\ \text{making h the subject, we have } \\ 2h=920-2r-\pi r \\ \text{dividing both sides by 2} \\ \frac{2h}{2}=\frac{920}{2}-\frac{2r}{2}-\frac{\pi r}{2} \\ h=460-r-\frac{\pi r}{2} \end{gathered}[/tex]

So from the perimeter, we now have an equation to find the height.

Now, let us find the area, A of the figure

[tex]\begin{gathered} A=(2r\times h)+\frac{1}{2}\pi r^2 \\ A=2rh+\frac{1}{2}\pi r^2 \\ \text{substituting the equation we got for h } \\ A=2r(460-r-\frac{\pi r}{2})+\frac{\pi r^2}{2} \\ A=920r-2r^2-\pi r^2+\frac{\pi r^2}{2} \\ A=920r-2r^2-\frac{\pi r^2}{2} \\ A=920r-(2+\frac{\pi}{2})r^2 \end{gathered}[/tex]

Now, we have the equation for the area

To maximize the area, the derivative of the equation for the area must be equal to zero, so we have

[tex]\begin{gathered} A=920r-(2+\frac{\pi}{2})r^2 \\ \frac{dA}{dr}=920-2(2+\frac{\pi}{2})r=0 \\ 920=2(2+\frac{\pi}{2})r \\ 460=(2+\frac{\pi}{2})r \\ r=\frac{460}{(2+\frac{\pi}{2})} \end{gathered}[/tex]

So, from here, we can get r, then substitute the value to get h

Hence from the equation, r becomes

[tex]\begin{gathered} r=\frac{460}{(2+\frac{\pi}{2})} \\ r=\frac{460}{3.5707963} \\ r=128.822805 \\ r=128.82\text{ to the nearest hundredth } \end{gathered}[/tex]

Hence** the radius is 128.82 to the nearest hundredth **

For the height we have

[tex]\begin{gathered} h=460-r-\frac{\pi r}{2} \\ h=460-128.822805-\frac{\pi\times128.822805}{2} \\ h=460-128.822805-202.354389 \\ h=128.822806 \end{gathered}[/tex]

Hence** the height is 128.82 to the nearest hundredth **

Solve the system of equations by multiplying first. Enter the solution as an ordered pair.S x + 3y = -134x + 5y =-17The solution is

### Answers

In order to solve this system by multiplying first, let's multiply the first equation by -4. This way, we can add both equations and cancel the variable x:

[tex]\begin{gathered} \begin{cases}x+3y=-13 \\ 4x+5y=-17\end{cases} \\ \begin{cases}-4x-12y=52 \\ 4x+5y=-17\end{cases} \\ -4x-12y+4x+5y=52-17 \\ -7y=35 \\ y=-5 \\ \\ x-3\cdot5=-13 \\ x-15=-13 \\ x=2 \end{gathered}[/tex]

So the value of x is 2 and y is -5, therefore **the ordered pair is (2, -5).**

06Question 21 of 40What is the solution to √6x-3 = 2√x?O A. -3/2OB.c.O C.3122314O D. 1/314

### Answers

**Solution:**

[tex]\sqrt{6x-3}=2\sqrt{x}[/tex]

**Square both sides;**

[tex]\begin{gathered} (\sqrt{6x-3})^2=(2\sqrt{x})^2 \\ \\ 6x-3=4x \end{gathered}[/tex]

**Collect like terms;**

[tex]\begin{gathered} 6x-4x=3 \\ \\ 2x=3 \end{gathered}[/tex]

**Divide both sides by 2;**

[tex]\begin{gathered} \frac{2x}{2}=\frac{3}{2} \\ \\ x=\frac{3}{2} \end{gathered}[/tex]

**CORRECT OPTION: ****C**

How do I solve this problem? Directions: Factor each expression completely.

### Answers

Given:

[tex]2n^2+4n-48[/tex]

To factor the given expression, we first factor out the common term 2:

[tex]2n^2+4n-48=2(n^2+2n-24)[/tex]

Next, we note that -4 and 6 are the two numbers that add up to 2 and multiply -24. Hence, we rewrite the expression:

[tex]n^2+2n-24=(n-4)(n+6)[/tex]

**Therefore, the answer is:**

[tex]2(n-4)(n+6)[/tex]