A salesperson makes a base salary of $2100 per month. Once he reaches $42,000 in total sales, he earns an additional 5% commission on the amount in sales over $42,000.
(1) Graph the function.
(2) If the salesperson had $80,000 in sales, how much was his salary?
(3) If the salesperson's total salary for a month was $4500, how much were his total sales for that month?
(4) Compute S(25000) and interpret what this means in the context of the problem.

Answer:

[tex]x=\frac{2}{5}[/tex] or [tex]x=1[/tex]

Step-by-step explanation:

The given quadratic equation is

[tex]5x^2-7x+2=0[/tex]

Group the constant terms on the right hand side.

[tex]5x^2-7x=0-2[/tex]

[tex]5x^2-7x=-2[/tex]

Divide through by 5.

[tex]x^2-\frac{7}{5}x=-\frac{2}{5}[/tex]

Add the square of half the coefficient of x., which is [tex](\frac{1}{2}\times- \frac{7}{5})^2=\frac{49}{100}[/tex] to both sides of the equation.

[tex]x^2-\frac{7}{5}x+\frac{49}{100}=-\frac{2}{5}+\frac{49}{100}[/tex]

The left hand side is now a perfect square.

[tex](x-\frac{7}{10})^2=\frac{9}{100}[/tex]

Take the square root of both sides;

[tex](x-\frac{7}{10})=\pm \sqrt{\frac{9}{100}}[/tex]

[tex]x-\frac{7}{10}=\pm \frac{3}{10}[/tex]

[tex]x=\frac{7}{10}\pm \frac{3}{10}[/tex]

[tex]x=\frac{7-3}{10}[/tex] or [tex]x=\frac{7+3}{10}[/tex]

[tex]x=\frac{4}{10}[/tex] or [tex]x=\frac{10}{10}[/tex]

[tex]x=1[/tex] or [tex]x=\frac{2}{5}[/tex]

Answer:

[tex]x_1=1\\\\x_2=\frac{2}{5}[/tex]

Step-by-step explanation:

- You must divide the equation by 5:

[tex]x^{2}-\frac{7}{5}x+\frac{2}{5}=0[/tex]

- Add and subtract [tex](\frac{\frac{7}{5}}{2})^2[/tex]:

 [tex]x^{2}-\frac{7}{5}x+(\frac{7}{10})^2+\frac{2}{5}-(\frac{7}{10})^2=0[/tex]

Therefore, you obtain:

[tex](x-\frac{7}{10})^2-0.09=0[/tex]

-add 0.09} to both sides:

[tex](x-\frac{7}{10})^2=0.09[/tex]

- Apply square root to both sides and solve for x:

[tex]\sqrt{(x-\frac{7}{10})^2}=\sqrt{\0.09}\\x-\frac{7}{10}=\sqrt{0.09}\\\\x_1=\frac{7}{10}+\sqrt{0.09}=1\\\\x_2=-\frac{7}{10}-\sqrt{0.09}=\frac{2}{5}[/tex]

Answer:

There is a 7/10 chance that it is not white

Step-by-step explanation:

To find this, start by finding the number of total shirts.

9 + 6 + 5 = 20

Now find the number that are not white.

9 + 5 = 14

Now divide the number of non-white by the number in total.

14/20

And simplify the fraction.

7/10

Final answer:

The probability of choosing a shirt that is not white from the drawer is 7/10, since there are 14 non-white shirts out of a total of 20 shirts.

Explanation:

The question asks to find the probability that a shirt chosen at random from a drawer is not white, given that there are 9 black shirts, 6 white shirts, and 5 gray shirts. To tackle this, we'll look at the total number of shirts and then subtract the number of white shirts from this total to find how many shirts are not white. The total number of shirts is 9 (black) + 6 (white) + 5 (gray) = 20 shirts. The number of shirts that are not white would be 20 (total) - 6 (white) = 14 shirts. Therefore, the probability of choosing a non-white shirt is 14 (non-white shirts) divided by 20 (total shirts), which simplifies to 7/10. This fraction is already in its simplest form.

Answer:

Step-by-step explanation:

One unit up:  y = x + 1

One unit down:  y = x - 1

One unit to the left:  y = x + 1

One unit to the right:  y = x - 1

Final answer:

To translate the graph of y = x, add or subtract from either x or y in the equation; for example, translating one unit up is expressed as y = x + 1.

Explanation:

To translate the graph of the function y = x in various directions, we apply different transformations to the equation. For each translation, there's a specific algebraic manipulation:

Shifting a graph vertically involves adding or subtracting from the y-value, while shifting horizontally involves adding or subtracting from the x-value before it is plugged into the function.

Answer:

1. Option A

2. Option B

3. Option D

4. Option C

Step-by-step explanation:

The given vertices of triangle ABC are A(-3, 6), B(2,1), C(9, 5).

We have to fine the distance AB, BC and AC.

To calculate the distance between two vertices we will use the formula

[tex]d=\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]

For the length of side AB

AB=[tex]\sqrt{(2+3)^{2}+(1-6)^{2}}=\sqrt{5^{2}+5^{2}}=\sqrt{50}[/tex]

Option A. is the correct option

For the length of side BC

[tex]BC=\sqrt{(9-2)^{2}+(5-1)^{2}}=\sqrt{7^{2}+4^{2}}=\sqrt{65}[/tex]

Option B is the answer.

For the length of side AC

[tex]AC=\sqrt{(9+3)^{2}+(5-6)^{2}}=\sqrt{12^{2}+(-1)^{2}}=\sqrt{145}[/tex]

Option D is the answer.

For ∠ABC we will use the formula [tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]

Since angle ABC is formed by two sides AB and BC

So we will find the slopes of these two lines and find the angle

Now slope of AB, [tex]m_{1}=\frac{y-y'}{x-x'}=\frac{1-6}{2+3}=\frac{-5}{5}=-1[/tex]

Slope of BC, [tex]m_{2}=\frac{5-1}{9-2}=\frac{4}{7}[/tex]

[tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]

[tex]tan\theta =\frac{(-1)-(\frac{4}{7})}{1+(-1)(\frac{4}{7})}=\frac{\frac{-11}{7}}{1-\frac{4}{7}}=\frac{\frac{-11}{7}}{\frac{3}{7}}=\frac{-11}{7}\times \frac{7}{3}=-\frac{11}{3}=-3.67[/tex]

[tex]\theta =tan^{-1}(-3.67)=74.75[/tex]

Since angle between them [tex]tan\theta[/tex] is negative that means angle theta will be obtuse angle.

So the angle between AB and BC = (180 - 74.75) = 105.26°

Therefore Option C. 105.26° is the answer.

Answer: The mean is 2.

Step-by-step explanation:

The mean number is a group of numbers is the average. In this group, the numbers are 1, 3, 2, 4 and 0. The total of all of the numbers is 10. In order to calculate the average/mean you need to divide the total by the number of values, which is 10/5 = 2. The mean is 2.

Answer:

D.  [tex]f^{-1}(x)=\frac{x-5}{2}[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)=2x+5[/tex]

Let [tex]y=2x+5[/tex]

Interchange  x and y.

[tex]x=2y+5[/tex]

Solve for y.

[tex]x-5=2y[/tex]

Divide both sides by 2

[tex]\frac{x-5}{2} =y[/tex]

Hence [tex]f^{-1}(x)=\frac{x-5}{2}[/tex]

Answer: OPTION D

Step-by-step explanation:

To find the inverse of the function given in the problem, you must apply the proccedure shown below:

1- Rewrite the function:

[tex]y=2x+5[/tex]

2- You must solve for x from the functionn, as following:

[tex]y-5=2x\\\\x=\frac{y-5}{2}[/tex]

[tex]f^{-1}(x)=\frac{x-5}{2}[/tex]

ANSWER

See graph in attachment.

EXPLANATION

The given function is

[tex]y = \sqrt[3]{x + 1} - 2[/tex]

The parent function is

[tex]y = \sqrt[3]{x} [/tex]

The transformation applied to this parent function is

[tex]f(x+1)-2[/tex]

That, is a shift to the left by 1 unit, and a downward shift by 2 units.

See attachment for correct choice.

[tex]x - 79 = 147[/tex]

147+79=226 Amy started with 226 donuts.

Final answer:

Amy started with 226 donuts. The equation x - 79 = 147 was solved by adding 79 to both sides to find x, representing the total amount of donuts she had originally.

Explanation:

The question involves solving a basic algebra problem to find the total number of donuts Amy started with. If Amy handed out 79 donuts and still has 147 left, we can set up the following equation where x represents the total number of donuts she originally had:

x - 79 = 147

To solve for x, we add 79 to both sides of the equation:

x - 79 + 79 = 147 + 79

x = 226

Therefore, Amy started with 226 donuts.

Answer:

c

Step-by-step explanation:

thats the answer

room=400

Ppl=25p

Total cost=775

775=25p+400 ⟨—— equation

775-400=25p

375/25=p

15=p

15 people attended his party

Answer:

C

Step-by-step explanation:

Simply plug in x for all the questions to see if the x is the solution

A.) 3(20-14) = 44

3(16)=48

so A is incorrect

B.) 3(12-14) = 6

3(-2) = -6

so B is incorrect

C.) 2(14-3) =22

2(11) =22

C is correct

D.) 2(14)-3=22

28-3 = 25

so D is incorrect

Answer:

the answer would be 2(x - 3) = 22  (C)

Step-by-step explanation:

step 1:

2(x - 3) = 22

step 2: divide both sides by the equation 2

x - 3 = 11

step 3: move constant (3) to the right and change its sign

x = 11 + 3

step 4: add the numbers (11 and 3)

x = 14

Answer:

Step-by-step explanation:

Look at the picture.

The edge of the cube is equal to the diagonal of the sphere.

Therefore, the length of the cube's edge is 3 inches.

The formula of a surface area of a cube:

[tex]S.A.=6a^2[/tex]

Substitute a = 3 in:

[tex]S.A.=6(3^2)=6(9)=54\ in^2[/tex]

Answer:

- 4 > n and Notion form : [ -4 , -∞).

Step-by-step explanation:

Given : (n-7)>2n-3.

To find : Solve the inequality.

Solution : We have given

(n - 7) > 2 n - 3.

On adding both sides by 3

n - 7+ 3 > 2n .

n - 4 > 2n .

On subtracting b both sides by n

-4 > 2n -n.

- 4 > n.

So, we can say value of n is less  than - 4 like -5,-6, -7 ........-∞

Notion form : [ -4 , -∞).

Therefore, - 4 > n and Notion form : [ -4 , -∞).

n  = {n | n ∈ R,  n < -4}

The given inequality is:

n  -  7   >  2n  -  3

Collect like terms

n  -  2n  >   -3  +  7

-n    >   4

Multiply both sides by -1 and change the sign to <

-1(-n)  <  -1(4)

n    <   -4

In set notation:

n  = {n | n ∈ R,  n < -4}

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Answer:  4h - 3

Step-by-step explanation:

replace "x" with "h - 1" and simplify

f(x) = 3x + h

f(h - 1) = 3(h - 1) + h

          = 3h - 3 + h

          = 4h - 3

the value of x = the answer is D 11/2

Answer:

1. Minimum Value  = 14

2. First Quartile (Q₁)  = 28

3. Median  = 32

4. Third Quartile (Q₃) = 48

5. Maximum Value  = 65

Step-by-step explanation:

The five-number summary includes five things that are:

1. Minimum Value

2. First Quartile (Q₁)

3. Median

4. Third Quartile (Q₃)

5. Maximum Value

So, Firstly arrange given data in ascending order:14, 18, 28, 29, 32, 44, 48, 50, 65

1. Minimum Value = 14

It can be found by arranging the data in ascending order, the first value we will get is the minimum value.

2. First Quartile is the middle value between Minimum value and Median of data after arranging data in ascending order.

First Quartile (Q₁) = 28

3. Median is the middle value of the data after arranging them in ascending order.  

Median = 32

4. The third Quartile is the middle value between Median and Maximum Value of data after arranging data in ascending order.

Third Quartile (Q₃) = 48

5. Maximum Value is the largest value of the data or is the last value after arranging the data in ascending order.

Maximum Value = 65.

Answer:

7.5 ft²/student

Step-by-step explanation:

This is a "unit rate" problem.

30 ft²

------------------ = 7.5 ft²/student

 4 students

Each student will  paint 7.5 ft² of the wall.

Answer:

A) A

Step-by-step explanation:

The equation of a line is given by

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

where

m is the slope of the curve

q is the y-intercept of the curve

The two lines given in the problem are:

[tex]y=\frac{4}{3}x+2[/tex] --> slope of 4/3 and y-intercept of +2

[tex]y=5x[/tex] --> slope of 5 and y-intercept of 0

By exclusion, we see that the correct answer is A. In fact:

- Option B is wrong, because one of the two lines has negative slope, while the two lines given in the problem have both positive slope

- Option C is wrong, because one of the two lines is flat (slope=0), while none of the two lines given in the problem has a slope of zero

- Option D is wrong, because again one of the two lines has negative slope

Option A is the correct one: in fact, we see that the black line has an y-intercept of +2 and a slope of 4/3, while the green line has a slope of 5 and an y-intercept of zero.

Answer:

The answer

D) D

Step-by-step explanation:

I knew this because one, i just did the test and two the previous answer that was given was incorrect

Answer:

Help with this please

Step-by-step explanation:

i have the attachment down there

Answer:

The least balance is your own because -50$ is the farthest from 0 on the number line

Step-by-step explanation:

Answer:

24.2%

Step-by-step explanation:

The total regular price was:

$10.99 + $11.90 + $10.08 = $32.97

She paid:

$25

She saved: $32.97 - $25 = $7.97

Now we need to calculate what percent of $32.97 is $7.97.

To find what percent a number is of another number, divide the first number by the second number and multiply by 100.

percent saved = $7.97/$32.97 * 100 = 24.2%

Part (b)

Harry, Julie's best friend, also paid $25 for 3 t-shirts at a sale at another store. The sale price saved Harry 30% of the original price of the 3 t-shirts. What is the original price of Harry's 3 t-shirts? Who got the better deal?

Harry paid $25 and saved 30% over his original price. Let his original price be x. The original price was 100% of the original price since 100% means the whole amount. Since he saved 30%, that means he paid 70% of the original price.

70% of the original price = $25

70% of x = 25

70%x = 25

0.70x = 25

0.70x/0.70 = 25/0.70

x = 35.71

The t-shirts Harry bought had an original price of $35.71.

Harry got the better deal because he bought t-shirts with an original higher price for the same $25.

Answer:

$604.80

Step-by-step explanation:

With 8% tax rate, multiply the cost of the item (560) by 8% (0.08)

    560*.08 = 44.80 (sales tax)

Add the cost of item (560) and the sales tax (44.80)

    560 + 44.80 = 604.80

Answer:

8327.800

-     12.034

___________

  8315.766

Step-by-step explanation:

The answer would be:

8,315.766

To solve this you do:

8,327.8 subtracted by 12.034

Once you do you end up with your results.

Hope this helps! :3

75% × X =531.75

X =531.75/75

X = 7.09

Answers

7.09

Check! Proof!

75% × 7.09

=531.75

Answer:

2/3 is the correct answer so C. Hope this helps you. :)

Step-by-step explanation:

In this experiment, the ratio of heads to tails comes out to be 2/1.

Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.

Probability is the ratio of the number of favourable outcomes to the total number of outcomes of an event.

The number of favourable outcomes for an experiment with 'x' and the total outcomes is represented by the symbol 's'. The following formula can be used to determine how likely an event is to occur.

Probability = Favourable Outcomes/Total Outcomes = x/s

The total number of the outcomes are 36.

The total outcome for head is 24 times.

So, the total outcome for tail will be 36 - 24 = 12

The ratio of head to tail is = favourable outcome for heads/ favourable outcomes for tails.

Thus,

heads/ tails = 24/12

heads/tails = 2/1

Therefore, the ratio of heads to tails in the experiment is 2/1.

To know more about binomial distribution in probability and its example, here

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The median is 52 you can put this in a stat line in a graphing calculatior

Given the even number of data set, the median which is the average of the middle two numbers in the arranged data set is 52.

Median is simply the middle value in a set of variables arranged in a descending or ascending order.

Given the data set; 40 49 62 56 68 39 50 61 54 44.
First, we arrange is ascending order.

39 40 44 49 50 54 56 61 62 68

Since it is an even number set ( 10 )

We find the average of the middle two numbers

Median = ( 50 + 54 ) / 2

Median = 104 / 2

Median = 52

Therefore, the given the even number of data set, the median which is the average of the middle two numbers is 52.

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Answer:x=10

Step-by-step explanation:

5/2 × 2/5 = 4/1 × 5/2

Multiply and simplify and x=10

The solution to the equation 2/5x = 4 is x = 10. You can find the solution by multiplying both sides of the equation by 5/2, which cancelled out the 2/5 on the left side, and then performing the operation on the right side.

To solve the equation 2/5x = 4, you'll first want to isolate the variable 'x' on one side of the equation. You can do this by dividing both sides of the equation by the coefficient of 'x', which is 2/5. However, instead of dividing by a fraction, it's easier to multiply by the reciprocal of the fraction.

So, we multiply both sides of the equation by 5/2. The 5/2 multiplied by 2/5 on the left side of the equation equals 1, leaving us with just 'x' on the left side of the equation.

So, you would have x = 4 * 5/2.

Now, we just perform the operation on the right side to find the value of 'x', and we get x = 20/2 = 10.

So, the solution to the equation 2/5x = 4 is x = 10.

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Answer:

TRUE, because you are adding a unit more to a, then by logic laws, the quantity grow.

Best regards

Answer:

b > a - True

Step-by-step explanation:

We are given the following expression and we are to determine whether [tex] b > a [/tex] is true or not:

[tex] a + 1 = b [/tex]

Considering the given equation, if we take both the variables on one side so we will get:

[tex] 1 = b - a [/tex]

Sign of the variable [tex]a[/tex] will change to negative while [tex]b[/tex] remains positive.

It means that [tex][/tex] is greater than [tex]a[/tex] (b > a) so it is true.