Select the best answer for the question.
16. Phil Smith is a car salesman. Last
week his total sales amounted to
$27,650.00, and he received $1,382.50 in
commission. What is his rate of
commission?
O

Step-by-step explanation:

[tex](x + 3)(x - 3) \\ = {x}^{2} - 3x + 3x - 9 \\ = {x}^{2} - 9[/tex]

Answer:

I don't know how to do it the subject

Answer:

Both students scored in the top 10% of their classes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Top 10% = Above the 100 - 10 = 90th percentile.

The 90th percentile of scores is X when Z has a pvalue of 0.9, that is, Z = 1.28.

So, the student who had a z-score above 1.28 scored in the 90th percentile of their class.

In student A's class the mean was 78 and the standard deviation of 5. He scored 87.

We have that [tex]\mu = 78, \sigma = 5, X = 87[/tex]

Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{87 - 78}{5}[/tex]

[tex]Z = 1.8[/tex]

1.8 > 1.28, so student A scored in the top 10% of his/her class.

Student B's class the mean was 76 with a standard deviation of 4. Scored 87.

We have that [tex]\mu = 76, \sigma = 4, X = 87[/tex]

Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{87 - 76}{4}[/tex]

[tex]Z = 2.75[/tex]

2.75 > 1.28, so student B also scored in the top 10% of his/her class.

Both students scored in the top 10% of their classes.

Answer:

12

Step-by-step explanation:

Answer:

203 more minutes

We know she swam 154 min in first week.

And in two weeks she swam 357 minutes.

We need to figure out x (total of minutes swam in week two)

So do 357=x+154

Subtract 154 from both sides

x=203

Hope this helps

Answer:

55

Step-by-step explanation:

Remark

This is a really good question to know the answer to. <PRQ = 1/2 POQ (the central angle. )

The central angle for this question is 110o. So any angle that has its vertex on the circumference is 1/2 110 = 55. The central angle and the angle on the circumference must be related as they are as this question is. (Both are on the same side of PQ which is not drawn but you can draw it).

Answer:

C x= 85°

Step-by-step explanation:

x+ 60° + 35° =180°

x= 180° - 60° - 35°

x= 85°

Answer:

0.0195 = 1.95% probability that on any given day only John gets homework

Step-by-step explanation:

What is the probability that on any given day only John gets homework?

John has a 65% probability of getting homework.

Paul has a 100 - 80 = 20% probability of not getting homework.

Sonia has a 100 - 85 = 15% probability of not getting homework.

Since these events are independent, the probability is the multiplication.

0.65*0.2*0.15 = 0.0195

0.0195 = 1.95% probability that on any given day only John gets homework

Answer: 2 places to the right

Step-by-step explanation:

If i'm wrong sorry hope it helps

Answer:

116+34+x=180

150+x=180

x=180-150

x=30

Answer:

6 inches

Step-by-step explanation:

area = l x w

area = 60

6 x 10 = 60

lenght: 10

width: 6

The width is 6 inches.

Answer:

JONATHAN WILL NEED 14 PAGES.

Explanation:

33 + 67 = 100

100 - 12 = 88

88 ÷ 6 = 14.6666667

14.6666667 ⇒ 14

(Round 14.6666667 down to 14 because Johnathan does not have .6666667 of a page.)

Answer:

b = 9cm is the answer.

Step-by-step explanation:

a = 12cm

b = ?

c = 15cm

By using the Pythagoras theorem,

a² + b² = c²

12² + b² = 15²

144 + b² = 225

b² = 225 - 144

b² = 81

b = 9cm.

∴ b = 9cm is the length of the missing leg.

Answer:

50

Step-by-step explanation:

30 + 100 = 130

130 + 50 = 180

all triangles are 180 degrees, so add it up and subtract.

Answer:

50 degrees will be your answer

Step-by-step explanation:

180-(30+100)=50

180 degrees is the whole angle of a triangle. so we subtract the two sides.

Answer:

(a)

[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]

(b) Rate = 5

(c) Rate = 5

Step-by-step explanation:

Given

The attached graph

Solving (a): The piece-wise function

For the first line

Calculate the slope of the first line

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (0,0)[/tex]

[tex](x_2,y_2) = (5,25)[/tex]

So, the slope is:

[tex]m = \frac{25 - 0}{5 - 0}[/tex]

[tex]m = \frac{25}{5}[/tex]

[tex]m = 5[/tex]

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (0,0)[/tex]

[tex]y = 5(x - 0) + 0[/tex]

[tex]y = 5(x) + 0[/tex]

[tex]y = 5x[/tex]

So, the function of the first line is:

[tex]f(x) = 5x;\ 0 < x \le 5[/tex]

For the second line

Calculate the slope of the second line

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (5,20)[/tex]

[tex](x_2,y_2) = (9,40)[/tex]

So, the slope is:

[tex]m = \frac{40 - 20}{9 - 5}[/tex]

[tex]m = \frac{20}{4}[/tex]

[tex]m = 5[/tex]

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (5,20)[/tex]

[tex]y = 5(x - 5) + 20[/tex]

[tex]y = 5x - 25 + 20[/tex]

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

So, the function of the second line is:

[tex]f(x) = 5x -5;\ x>5[/tex]

Hence, the piece-wise function is:

[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]

Solving (b): The rate at which customers that buy up to 5lb buy.

[tex]x = 5[/tex]

This question implies that, we determine the rate at which this customer buys.

For [tex]x = 5[/tex]

[tex]f(x) = 5x;\ 0 < x \le 5[/tex]

The slope of the above function is 5.

So, this customer buys at the rate of $5 per lb

Solving (b): The rate at which customers that buy more than 5lb buy the extra pounds above 5lb.

For [tex]x > 5[/tex]

[tex]f(x) = 5x -5;\ x>5[/tex]

Assume x = 6

[tex]f(6) = 5 * 6 - 5[/tex]

[tex]f(6) = 30 - 5[/tex]

[tex]f(6) = 25[/tex]

Express as 20 + 5

[tex]f(6) = 20 + 5 * 1[/tex]

Assume x = 7

[tex]f(7) = 5 * 7 - 5[/tex]

[tex]f(7) = 35 - 5[/tex]

[tex]f(7) = 30[/tex]

[tex]f(7) = 20 + 10[/tex]

Express 10 as 5 * 2

[tex]f(7) = 20 + 5 * 2[/tex]

So, we have:

[tex]f(6) = 20 + 5 * 1[/tex]

[tex]f(7) = 20 + 5 * 2[/tex]

This can be generalized as:

[tex]f(x) = 20 + 5(x - 5)[/tex]

For the above functions;

20 represents the amount they buy the first 5

5 represents the rate at which they buy extra pounds above 5

Hence, they buy the extra pounds at the rate of $5 per pound

Answer:

4050 cubic feet.

Step-by-step explanation:

Let's first find the volume of the green cube. It is the edge length cubed, or 15^3 which equals 3375.

Now, let's find the volume of the brown pyramid on the cube. To find the volume, multiply the  base of the pyramid by the height, then divide by 3.

Using the edge length of 15, we can find that the square is 15^2 which equals 225.

Multiply 225 by the height 9,

225*9=2025

Then divide by 3.

2025/3=675.

Knowing the volume of the green cube, 3375, and the volume of the brown pyramid, 675, we can find that the volume of the entire figure is

3375 +675=4050 cubic feet.

Answer:

39 glasses

Step-by-step explanation:

use proportion:

g = # glasses punch

4/6 = g/26

cross-multiply

4g = 26(6)

4g = 156

g = 39

Answer:

7.8 mi is the answer.

Step-by-step explanation:

a = 6 mi

b = 5 mi

c = ?

According to the Pythagorean theorem,

a² + b² = c²

6² + 5² = c²

36 + 25 = c²

c² = 61

c = 7.810

Round to the nearest tenth,

c = 7.8 mi

Answer: 0.62

Step-by-step explanation: I got the answer

The probability that the next customer will pay with cash is 0.62

"It is finding out the possibilities of the occurrence of an event."

"P(A) = n(A) / n(S)

where, n(A) is the number of favorable outcomes of an event A

n(S) is the total number of outcomes for an experiment"

For given example,

in the last week 80 customers paid cash, 45 customers used a debit card, and 4 customers used a credit card.

So, the total number of customers:

⇒ n(S) = 80 + 45 + 4

⇒ n(S) = 129

Let event A: the next customer will pay with cash

n(A) = 80

So, the probability that the next customer will pay with cash would be,

⇒ P(A) = n(A)/n(S)

⇒ P(A) = 80/129

⇒ P(A) = 0.62

Therefore, the probability that the next customer will pay with cash is 0.62

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

Answer:

Physical is the answer

Answer:

The median is 6.5

Step-by-step explanation:

To find the median, first organize the numbers from least to greatest:

1, 4, 6, 6, 7, 8, 9, 10

The median is always the number in the middle, but since there are eight numbers here, there will be two numbers in the middle: 6 and 7.

To solve for this, we have to find the average of the numbers.

Add the two numbers together and then divide by 2 (we divide by 2 because we are averaging two numbers).

(6 + 7)/2

13/2

6.5

Answer:

answer is A

Step-by-step explanation:

slope goes up positive 4 and it crosses the y intercept at 3 so yeg there ya go ig

This question is incomplete, the complete question is;

he Eco Pulse survey from the marketing communications firm Shelton Group asked individuals to indicate things they do that make them feel guilty (Los Angeles Times, August 15, 2012).

Based on the survey results, there is a 0.39 probability that a randomly selected person will feel guilty about wasting food and a 0.27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room.

Moreover, there is a 0.12 probability that a randomly selected person will feel guilty for both of these reasons.

Required:

a. What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both (to 2 decimals)?

b. What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?

Answer:

a)

the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both is 0.54

b)

the probability that a randomly selected person will not feel guilty for either of these reasons is 0.46

Step-by-step explanation:

Given the data in the question;

lets A represent person feels guilty about wasting food and B represent leaving the light on when not in room;

probability; feel  guilty about wasting food P(A) = 0.39

probability; feel guilty about leaving light on P(B) = 0.27

probability; feel guilty for both P(A ∩ B ) = 0.12

a)

probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both

p( A ∪ B ) = P(A) + P(B) - P(A ∩ B )

we substitute

p( A ∪ B ) = 0.39 + 0.27 - 0.12

p( A ∪ B ) = 0.54

Therefore, the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both is 0.54

b)

probability that a randomly selected person will not feel guilty for either of these reasons;

p( A ∪ B )' = 1 - p( A ∪ B )

p( A ∪ B )' = 1 - 0.54

p( A ∪ B )' = 0.46

Therefore, the probability that a randomly selected person will not feel guilty for either of these reasons is 0.46

Answer:

B. 5(2x+5)

Step-by-step explanation:

Factor 5 out of 10x+25. and you get 5(2x+5)

Answer:

B. 5(2x + 5

Step-by-step explanation:

If you have any questions feel free to ask in the comments

Answer:

6/8

Step-by-step explanation:

3/4 is equal to 6/8

Answer:

92.091

Step-by-step explanation:

81+10=91

.296

+

.795

_____

1.091

So: 91+1.095=92.091

Answer:

It can't be simplified or added together because one is multiplied by x and the other is not

Step-by-step explanation: