Anthony sells cars. Each month, he is paid $2,000, plus a 15% commission on monthly sales above $20,000. Which function calculates his monthly earnings (E) as a function of m, his monthly sales?

Answer:

192 m^2.

Step-by-step explanation:

We can split this up into 3 rectangles:

Area of the bottom rectangle = 27 * (9-3)

= 27 * 6 = 162 m^2.

Area of rectangle on the left = (18-6)*2

= 24 m^2

Area of small rectangle on the right = 3*2

= 6 m^2

Total area = 162+24+6

192 m^2.

Complete Question

Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets. Could they take 9 children and 4 adults to both shows? Show your work. A yes or no answer is not sufficient for credit.

Answer:

Yes it is  possible to take the  9 children and 4 adults to both shows

Step-by-step explanation:

From the question we are told that

    The  cost of the Matinee tickets for a child is  z =  $4

    The  cost of the Matinee tickets for an adult is  a  = $ 4

     The cost of the Evening tickets for  a child is  k =  $6

      The cost of the Evening tickets for an adult is  b =  $8    

      The  maximum amount to be spent on Matinee tickets is  m = $80

       The maximum amount to be spent on Evening tickets is  e =  $100

       The  number of child to be taken to the movies is  n  = 9

        The number of adults to be taken to the movies is  j  =  4

Now the total amount of money that would be spent on Matinee tickets is  mathematically evaluated as      

           [tex]t = 4 n + 4 j[/tex]

substituting values

           [tex]t = 4 * 9 + 4* 4[/tex]

           [tex]t = 52[/tex]

Now the total amount of money that would be spent on  Evening ticket is mathematically evaluated as      

      [tex]T = 6n + 8j[/tex]

substituting values

     [tex]T = 6(9) + 8(4)[/tex]

    [tex]T = 86[/tex]

This implies that it is possible to take 9 children and 4 adults to both shows

given that

      [tex]t \le m[/tex]

i.e  $56  [tex]\le[/tex]$ 80

and  

      [tex]T \le e[/tex]

i.e   $ 86 [tex]\le[/tex] $ 100

Answer:

1

Step-by-step explanation:

We will use polynomial remainder theorem or little Bézout's theorem. It states that reminder p(x) divided by (x - a) is p(a). In our case (a = 3) it is p(3) = 1

Answer:

[tex]f^{-1}(x)= - \frac{1}{8} x+\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]f(x) = -8x + 2[/tex]

[tex]y = -8x + 2[/tex]

[tex]y-2=-8x[/tex]

[tex]- \frac{1}{8} y+\frac{1}{4} =x[/tex]

[tex]- \frac{1}{8} x+\frac{1}{4} =y[/tex]

[tex]f^{-1}(x)= - \frac{1}{8} x+\frac{1}{4}[/tex]

Answer:

Step-by-step explanation:

[tex]A=\begin{bmatrix}0 &0 &5 \\ 0 &0 &-3 \\ 0 &0 &3 \end{bmatrix}[/tex]

[tex]B=\begin{bmatrix}8 &-12 &5 \\ 7 &19 &5 \\ 0 &0 &0 \end{bmatrix}[/tex]

A.B = A × B

[tex]A.B=\begin{bmatrix}0 &0 &0 \\ 0 &0 &0 \\ 0 &0 &0 \end{bmatrix}[/tex]

Dimension of the resultant matrix is (3 × 3)

Answer:

x=-1

Step-by-step explanation:

8/x+2=2/x-4

8/x=2/x-6

8=2-6x

6=-6x

-1=x

Answer:

x=6

Step-by-step explanation:

8/x+2=2/x-4

Using cross products

8*(x-4) = 2 (x+2)

Distribute

8x - 32 = 2x+4

Subtract 2x

8x-2x -32 = 2x-2x+4

6x-32 = 4

Add 32

6x-32+32 = 4+32

6x = 36

Divide by 6

6x/6 = 36/6

x = 6

Answer:

Step-by-step explanation:

The second is correct

f(x) <0 on ( _ infinit, -2.7) and ( -1, 0.8)

hope it helps uh.......

Answer:

3lbs

Step-by-step explanation:

Answer:

a) P(male=blue or female=blue) = 0.71

b) P(female=blue | male=blue) = 0.68

c) P(female=blue | male=brown) = 0.35

d) P(female=blue | male=green) = 0.31

e) We can conclude that the eye colors of male respondents and their partners are not independent.

Step-by-step explanation:

We are given following information about eye colors of 204 Scandinavian men and their female partners.

              Blue    Brown     Green    Total

Blue        78         23            13          114

Brown     19         23            12          54

Green     11           9             16          36

Total      108       55            41          204

a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?

Using the addition rule of probability,

∵ P(A or B) = P(A) + P(B) - P(A and B)

For the given case,

P(male=blue or female=blue) = P(male=blue) + P(female=blue) - P(male=blue and female=blue)

P(male=blue or female=blue) = 114/204 + 108/204 − 78/204

P(male=blue or female=blue) = 0.71

b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=blue) = 78/114

P(female=blue | male=blue) = 0.68

c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=brown) = 19/54

P(female=blue | male=brown) = 0.35

d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=green) = 11/36

P(female=blue | male=green) = 0.31

e) Does it appear that the eye colors of male respondents and their partners are independent? Explain

If the following relation holds true then we can conclude that the eye colors of male respondents and their partners are independent.

∵ P(B | A) = P(B)

P(female=blue | male=brown) = P(female=blue)

or alternatively, you can also test

P(female=blue | male=green) = P(female=blue)

P(female=blue | male=blue) = P(female=blue)

But

P(female=blue | male=brown) ≠ P(female=blue)

19/54 ≠ 108/204

0.35 ≠ 0.53

Therefore, we can conclude that the eye colors of male respondents and their partners are not independent.

Answer:

1. JG (Jim gets first prize, George gets second prize)

2. JH (Jim gets first prize, Helen gets second prize)

3. JM (Jim gets first prize, Maggie gets second prize)

4. GH (George gets first prize, Helen gets second prize)

5. GJ (George gets first prize, Jim gets second prize)

6. GM (George gets first prize, Maggie gets second prize)

7. MJ (Maggie gets first prize, Jim gets second prize)

8. MG (Maggie gets first prize, George gets second prize)

9. MH (Maggie gets first prize, Helen gets second prize)

Step-by-step explanation:

The question asks for the list of outcomes in the event "Not A". We are looking for the reverse or negative of Event A.

The above given list is the list of outcomes in the event where Helen DOES NOT get first prize.

Answer:

x=30

Step-by-step explanation:

Find the value of x that will make A and B parallel

For A & B to be parallel, the interior angles must be supplementary, i.e.

4x+2x = 180

6x=180

x=30

When x=30, the interior angles are 120 and 60 which are supplementary.

Answer:

c. dividing is the inverse of multiplying because it doesn't really relate the equation like the others do.

Answer:

hope u get it.......!!

Hello! :)

____________ ☆ ☆____________________

Answer:

(7a+4)⋅(a+7)

Step-by-step explanation:

First you have to multiply... 7x28=196

Now find the factors of 196

Factor: 53

Add the first two terms

Add up the four terms and you get your answer

ANSWER: (7a + 4) • (a + 7)

_____________ ☆ ☆___________________

Hope this helps! :)

By BrainlyMember ^-^

Good luck!

Answer:

The LCM of 5, 4, and 10 is 20 so we can rewrite this expression as:

8/20 + 5/20 + 14/20 = (8 + 5 + 14) / 20 = 27 / 20 = [tex]1\frac{7}{20}[/tex]

Adding all the three fractions ,

Simplest form is

[tex]1\frac{7}{20}[/tex]

Given :

[tex]\frac{2}{5}+\frac{1}{4} +\frac{7}{10}[/tex]

Step-by-step explanation:

To add all the fractions , the denominators should be same

Lets find out LCD of 5,4  and 10

[tex]5= 1,5\\4=2,2\\10=5,2\\LCD=5\cdot 2\cdot 2=20[/tex]

Least common denominator = 20

Multiply the first fraction by 4  and second fraction by5  and third fraction by 2 to get same LCD 20

[tex]\frac{2}{5}+\frac{1}{4}+\frac{7}{10}\\\frac{8}{20}+\frac{5}{20}+\frac{14}{20}\\\\\frac{8+5+14}{20}\\\frac{27}{20}[/tex]

We cannot simplify the fraction further . So we write it in mixed form

[tex]1\frac{7}{20}[/tex]

Learn more :  brainly.com/question/22881654

Answer:

{1,5}

Step-by-step explanation:

The intersection of the sets are all of the numbers that appear in both sets. In this case, the only numbers that appear in both are 1 and 5.

Answer:

{ 1,5}

Step-by-step explanation:

The intersection is what the two sets have in common

{1, 5, 10, 15}∩ {1, 3, 5, 7}

= { 1,5}

Answer:

C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.

Step-by-step explanation:

Duran uses cost accounting technique to identify cost per unit for its products. The costing techniques allows us to identify the cost of unit that are not completely finished. It is not necessary that all unit must be completed in order to find out the cost per unit of the product. The process costing is the best method to identify cost per unit for products that are in process.

The required length of the line is given as 14.4 feet, as of the given conditions.

As given in the question, A kite is flying 12 ft off the ground. Its line is pulled taut and casts an 8 -ft shadow, to determine the length of the line.

In a right-angled triangle, its side, such as the hypotenuse, is perpendicular, and the base is Pythagorean triplets.

Here,
let the length of the line be x,
The scenario formed is right angle triangle,
Apply Pythagoras' theorem,
x² = 12² + 8²
x = √208
x = 14.4

Thus, the required length of the line is given as 14.4 feet, as of the given conditions.

Learn  more about Pythagorean triplets here:

brainly.com/question/22160915

#SPJ2

Answer:

Step-by-step explanation:

Hello!

The variable of interest is X: time it takes a customer from Andrew's computer store to pay his invoices.

You have the information of a sample of n= 17 customers

19, 15, 43, 39, 35, 31, 27, 34, 34, 30, 30, 26, 26, 26, 21, 21, 17

To determine the class width of the intervals for the divide the difference between the ending and initial class boundaries by the number of intervals that you want to determine:

Class width: (49.5-14.5)/5= 7

Then, starting from the initial class boundary, you have to add the class width to determine the next boundary, and so on until the ending class boundary:

Initial class boundary: 14.5

14.5 + 5.6= 20.1

1st interval: [14.5; 21.5]

and so on:

[21.5; 28.5]

[28.5; 35.5]

[35.5; 42.5]

[42.5; 49.5]

Once you determined all class intervals, you have to order the values of the data set from least to greatest and then count how many observations correspond to each interval and arrange it in a frequency table.

15, 17, 19, 21, 21, 26, 26, 26, 27, 30, 30, 31, 34, 34, 35, 39, 43

[14.5; 21.5] ⇒ 5

[21.5; 28.5] ⇒ 4

[28.5; 35.5] ⇒ 6

[35.5; 42.5] ⇒ 1

[42.5; 49.5] ⇒ 1

Once you have the data set organized in the table, you can proceed to draw the histogram.

(See attachment)

I hope this helps!

Answer:

1 1/8

Step-by-step explanation:

1/4 + 7/8

Make denominators equal.

2/8 + 7/8

Add the fractions.

9/8

Convert to a mixed fraction.

1 1/8

Answer:

1  1/8

Step-by-step explanation:

1/4 + 7/8

Get a common denominator

1/4 * 2/2 + 7/8

2/8 + 7/8

9/8

Change to a mixed number

8/8+ 1/8

1  1/8

Answer:

a) The domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex]  [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex], b) The range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex], c) The ball is 73 meters off of the ground at x = 3 seconds.

Step-by-step explanation:

The complete statement is: A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function [tex]f(x) = -5\cdot x^{2} + 6\cdot x + 100[/tex] represents this situation where x is time and y is the distance off of the ground.

a) What domain does the function make sense?

b) What range does the function make sense ?

c) How far off the ground is the ball at time x = 3 seconds?

a) Let [tex]x[/tex] and [tex]f(x)[/tex] be the time, measured in seconds, and the distance of the ground, measured in meters, respectively. Time is a positive variable, so domain corresponds to the interval when [tex]f(x) \geq 0[/tex] and [tex]t \geq 0[/tex]. That is:

[tex]-5\cdot x^{2} + 6\cdot x + 100 \geq 0[/tex]

[tex]-(x-5.112\,s)\cdot (x+3.912\,s) \geq 0[/tex]

Therefore, the domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex]  [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex]

b) The distance off of the ground is also a positive variable, where ball is thrown upward at a height of 100 meters and hits the ground at a height of 0 meters. Hence, the range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex]

c) The distance of the ball off of the ground at x = 3 seconds is found by evaluating the function:

[tex]f(3\,s) = -5\cdot (3\,s)^{2} + 6\cdot (3\,s) + 100[/tex]

[tex]f(3\,s) = 73\,m[/tex]

The ball is 73 meters off of the ground at x = 3 seconds.

Answer:

Radius = 6.5cm

Diameter = 13cm

Step-by-step explanation:

The diameter is given (13)

Radius is half the diameter (13/2=6.5)

Answer:

Explanation

The straight line is drawn from the centre of a circle to a point on its circumference is called radius of the circle. The radius of a circle is half of its diameter.

The chord that passes through the centre of a circle is called diameter of circle. Diameter is also called the largest chord of any circle. The length of diameter of a circle is two times it's radius.

Hope this helps...

Good luck on your assignment...

Answer:

7.8 DAYS

Step-by-step explanation:

The time taken for the substance to reach 12g is 7.8 days

The half-life of a substance is the time taken for it to reach half it's initial value.

I will list some formula and concepts which are of importance to this topic but not necessarily this question.

In solving this problem, we may need the formula to calculate half life of a substance which is given as.

[tex]T_\frac{1}{2}= In2/[/tex]λ

where λ = Disintegration constant.

But to find this constant, we need to use another formula

[tex]N=N_oe^-yt\\\frac{N}{N_o}= e^-yt\\[/tex]

where the values are

However,

[tex]n=\frac{Log_e\frac{No}{N} }{Log_e2}[/tex]

Everything remains the same as above but only a slight change now

Substituting the values,

[tex]n = \frac{Log_e(\frac{30}{12}) }{log_e2}\\n = 1.32[/tex]

Since n stands for the half life passed within time (t)

The time taken would be

[tex]t = 1.32 * 5.9\\t =7.8[/tex]

The time taken for the substance to reach 12g is 7.8 days.

Learn more about half-life here;

https://brainly.com/question/2320811

Answer:

11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet

Step-by-step explanation:

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

Permutations of four letters from a set of 12 letters. So

[tex]P_{(12,4)} = \frac{12!}{(12-4)!} = 11800[/tex]

11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet

Answer: it’s 11,880

not 11800

Answer:

32.5861

Step-by-step explanation:

I interpreted it this way:

20 - stop at n = 20 (inclusive)

1 - start at n = 1

4(8/9)^(n - 1) - geometric expression

Answer:

  B. II

Step-by-step explanation:

G is in quadrant IV. The quadrant that is across the origin from that is quadrant II.

  G' will lie in quadrant II

Answer:

B. 11

Step-by-step explanation:

Answer:

Critical value: b. 2.33

As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]

The significance level is 0.01.

The sample 1 (women), of size n1=150 has a proportion of p1=0.62.

The sample 2 (men), of size n2=200 has a proportion of p2=0.24.

The difference between proportions is (p1-p2)=0.38.

[tex]p_d=p_1-p_2=0.62-0.24=0.38[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{93+48}{150+200}=\dfrac{141}{350}=0.403[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.403*0.597}{150}+\dfrac{0.403*0.597}{200}}\\\\\\s_{p1-p2}=\sqrt{0.001604+0.001203}=\sqrt{0.002807}=0.053[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.38-0}{0.053}=\dfrac{0.38}{0.053}=7.17[/tex]

The critical value for a right-tailed test with a signficance level of 0.01 is zc=2.33 (see picture attached).

As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Answer:

a. AEB

b. BEC

c. CED

d. AED

Step-by-step explanation:

Each angle is made up of three points. All three points in order is the name of the angle.

Answer:

a. ∠1 = ∠AEB or ∠BEA

b. ∠2 = ∠BEC or ∠CEB

c. ∠3 = ∠CED or ∠DEC

d. ∠4 = ∠DEA or ∠AED

Step-by-step explanation: Penn <3