An auto repair shop charged a customer $496 to repair a car. The bill listed $96 for parts and the remainder for labor. If the cost of labor is $40 per hour, how many hours of labor did it take to repair the car?

Answer:

a)

b. Joel

c. Juan

d. Linda

b)

b. Joel

c)

a. Jan

f.Susan

d)

a. Jan: 140

b. Joel: 156

c. Juan: 196

d. Linda: 191

e. Robert: 183

f. Susan: 110

Step-by-step explanation:

Z-score:

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, positive z-scores are above the mean, negative are below the mean and 0 is 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.

Question a:

Robert, Juan and Linda had positive z-scores, so they scored above the mean, and the correct options are c,d,e.

(b) Which of these students scored on the mean?

Joel, which had a z-score of 0, so the correct option is b.

(c) Which of these students scored below the mean?

Jan and Susan had negative z-scores, so them, options a and f.

Question d:

We have that [tex]\mu = 156, \sigma = 24[/tex], so we have to find X for each student.

Jan:

Z = -0.65. So

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

[tex]-0.65 = \frac{X - 156}{24}[/tex]

[tex]X - 156 = -0.65*24[/tex]

[tex]X = 140[/tex]

b. Joel

Z = 0, so:

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

[tex]0 = \frac{X - 156}{24}[/tex]

[tex]X - 156 = 0*24[/tex]

[tex]X = 156[/tex]

c. Juan

Z = 1.66, so:

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

[tex]1.66 = \frac{X - 156}{24}[/tex]

[tex]X - 156 = 1.66*24[/tex]

[tex]X = 196[/tex]

d. Linda

Z = 1.46. So

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

[tex]1.46 = \frac{X - 156}{24}[/tex]

[tex]X - 156 = 1.46*24[/tex]

[tex]X = 191[/tex]

e. Robert

Z = 1.11. So

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

[tex]1.11 = \frac{X - 156}{24}[/tex]

[tex]X - 156 = 1.11*24[/tex]

[tex]X = 183[/tex]

f. Susan

Z = -1.9. So

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

[tex]-1.9 = \frac{X - 156}{24}[/tex]

[tex]X - 156 = -1.9*24[/tex]

[tex]X = 110[/tex]

Answer:

18 GIRLS

Step-by-step explanation:

1. Lets write a fraction (4 boys/12 girls)

[tex]\frac{4 \\boys}{12 \\ \\girls}[/tex]

2. Now lets plug the value in

[tex]\frac{6 \\boys}{x girls}[/tex]

3. In the original equation, the amount of girls is 3 times the amount of boys

4. multiply 6 and 3 = 18

5. 18 girls

Answer:

18 <3

Step-by-step explanation:

Answer:

Step-by-step explanation:

a)

The mean for ground floor is 20.67

The mean for balcony is 15.8

b)

the difference between the means is ground floor - balcony

20.67 - 15.8 = 4.87

You can talk about it yourself for part c

Answer:

See image below:) :)

Step-by-step explanation:

Answer:

$5900

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Simple Interest Rate Formula: A = P(1 + rt)

Step-by-step explanation:

Step 1: Define

Identify variables

P = 5000

r = 3% = 0.03

t = 6

Step 2: Find Interest

Answer:

[tex]\text{1) }\frac{1}{2}(8)(5)[/tex]

Step-by-step explanation:

The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is equal to [tex]A=\frac{1}{2}bh[/tex]. Since we're given a base of 5 and a height of 8, the area is given by [tex]\boxed{\text{1) }\frac{1}{2}(8)(5)}[/tex].

Answer:

x=28

y=v7vub8b9nf7v6v

Answer:

-5 is the answer

Step-by-step explanation:

Answer:

-5 corresponds to the coldest temperature here.

Step-by-step explanation:

-5 is to the left of -1 on a number line and is therefore smaller than -1.

Answer:

y ≤ 5

Step-by-step explanation:

5 is the highest y value in this graph. All other y values are below 5.

Answer:

Timmy's tubes = 11.25$

Fred's floats = 11.375$

Step-by-step explanation:

For Timmy's tubes

We use unitary method to solve

For 2 1/2 hours, it charges $18.75

So, for 1 1/2 hours it charges $11.25

Similarly for Fred's floats

Base fee = $2

Fee per hour = $6.25

So, for 1 1/2 hour fee = 2 + 6.25 + 3.125 = $11.375

So, Terry should choose Timmy's tubes

well, let's see, what do we know about Timmy's Tubes, is a direct variation equation, since he's charging depending on the hours it's rented, thus

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\stackrel{\textit{\underline{c}ost varying with \underline{h}ours}}{c = kh}\qquad \textit{we know that } \begin{cases} c=18.75\to \frac{75}{4}\\ h=1\frac{1}{2}\to ~\hfill \frac{5}{2} \end{cases} \\\\\\ \stackrel{cost}{\cfrac{75}{4}}=\stackrel{hours}{\cfrac{5}{2}h}\implies 2\cdot 75=4\cdot 5h\implies 150=20h\implies \cfrac{150}{20}=h\implies \cfrac{15}{2}=h \\\\\\ therefore\qquad c=\cfrac{15}{2}h\impliedby \textit{Timmy's rate}[/tex]

now, Fred charges $2 flat right off, plus $6.25 for every added hour, so Fred's equation will more or less be

1 hour 2 + 6.25(1)

2 hours 2 + 6.25(2)

3 hours 2 + 6.25(3)

1)

how much will Timmy charge for 1 1/2 hour?

[tex]c = \cfrac{15}{2}\cdot \stackrel{h}{1\frac{1}{2}}\implies c = \cfrac{15}{2}\cdot \stackrel{h}{\cfrac{3}{2}}\implies c = \cfrac{15}{4}[/tex]   or just 3.75

how much will Fred charge for the same time?

[tex]c=2+6.25\left( \frac{3}{2} \right)\implies c=9.375[/tex]

2)

using only $12 for each, who is the better bargain?

[tex]\stackrel{\textit{Timmy's}}{c = \cfrac{15}{2}h}\implies 12=\cfrac{15h}{2}\implies 24=15h\implies \cfrac{24}{15}=h\implies \boxed{1.6=h} \\\\\\ \stackrel{\textit{Fred's}}{c = 2 + 6.25h}\implies 12=2+6.25h\implies 10=6.25h \\\\\\ \cfrac{10}{6.25}=h\implies \boxed{ 1.6=h}[/tex]

well, let's notice, Terri is going to get the same amount of hours with either, so, it really doesn't matter, both will only give 1.6 hours, or 1 hour and 36 minutes.

Answer:

0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.

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.

N(489,6)

This means that [tex]\mu = 489, \sigma = 6[/tex]

What is the probability that the box will contain less than the advertised weight of 466 g?

This is the p-value of Z when X = 466. So

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

[tex]Z = \frac{466 - 489}{6}[/tex]

[tex]Z = -3.83[/tex]

[tex]Z = -3.83[/tex] has a p-value of 0.000064

0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.

Answer:

B or graph 2

Step-by-step explanation:

when y = 0 then x = 6

when x = 0 then y = -3

find those points

Answer: b

question

hich is the graph of the linear equation x – 2y = 6?

On a coordinate plane, a line goes through points (negative 6, 0) and (0, 3).

On a coordinate plane, a line goes through points (0, negative 3) and (6, 0).

On a coordinate plane, a line goes through points (negative 6, 0) and (0, negative 3).

On a coordinate plane, a line goes through points (0, 3) and (6, 0).

Answer:

m<F = 95°

Step-by-step explanation:

We'll begin by calculating the value of x. This can be obtained as follow:

m<C = 50

m<A = (10x – 5)

m<B = m<G = (2x + 15)

m<C + m<A + m<B = 180 (Sum of angles in a triangle)

50 + (10x – 5) + (2x + 15) = 180

50 + 10x – 5 + 2x + 15 = 180

50 – 5 + 15 + 10x + 2x = 180

60 + 12x = 180

Collect like terms

12x = 180 – 60

12x = 120

Divide both side by 12

x = 120 / 12

x = 10

Finally, we shall determine the value of m<F. This can be obtained as follow:

m<F = m<A

But

m<A = 10x – 5

x = 10

Therefore,

m<F = 10x – 5

m<F = 10(10) – 5

m<F = 100 – 5

m<F = 95°

Given:

The coordinates of point P are (-5,4).

Point P is reflected over the x-axis.

To find:

The new coordinates after the reflection.

Solution:

If a point is reflected across the x-axis, then the rule of reflection is:

[tex](x,y)\to (x,-y)[/tex]

Using this rule, we get

[tex]P(-5,4)\to P'(-5,-4)[/tex]

The new coordinates of point P after the reflection over the x-axis are (-5,-4).

Therefore, the correct option is B.

Answer:

.101501615

.84982392

.901244701

Step-by-step explanation:

For this question use a binomial distribtuion

a.

12C3*.44³*(1-.44)⁹= .101501615

b.

to find at least 4 find the probability of less than 4 and take its compliment

12C0*(1-.44)¹²+12C1*.44*(1-.44)¹¹+12C2*.44²*(1-.44)¹⁰+12C3*.44³*(1-.44)⁹= .15017608

1-.15017608=.84982392

c.

To find less than eight's probability find the proability of at least 8 and take its compliment

12C8*.44⁸(1-.44)⁴+12C9*.44⁹(1-.44)³+12C10*.44¹⁰(1-.44)²+12C11*.44¹¹*(1-.44)+12C12*.44¹²= .098755299

1-.098755299= .901244701

Answer:

well,

it's more than (20ft)²

bc 20*20 =400

21² = 21 * 21 = 441

getting closer...

22² = 22 * 22 = 484

[tex] \sqrt{484} = {22}^{2} [/tex]

yet, we arrived, short trip tough, pls leave the bus in an orderly manner

Answer:

A plane figure with 4 sides is called a quadrilateral.

Step-by-step explanation:

A plane figure bounded by more than four straight lines is generally referred to as a polygon. A polygon is a closed two-dimensional shape formed by connecting multiple line segments. The line segments, also known as sides, should intersect only at their endpoints, forming vertices of the polygon.

Polygons can have various numbers of sides, and their names are typically based on the number of sides they possess. Some common examples include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), and so on.

However, when the statement specifies that the plane figure is bounded by "more than four" straight lines, it suggests that the figure in question is a polygon with more than four sides. The exact name or classification of the polygon would depend on the specific number of sides it possesses.

To know more about plane figure . here

https://brainly.com/question/29797834

#SPJ2

Answer:

ED = 31

DT = 20

Step-by-step explanation:

m< ESD = 90-52=38°

the distance ED = 40×tan 38° = 31.25 = 31

ET = 40 x tan (90-38) = 40×tan 52°

= 51.19= 51

the distance DT = 51-31 = 20

Answer:

this is a linear equation. whatever value you set for x, you substitute and make a table that would probably look like this.

      x      |     y

-------------|-----------

5            | 17/3       <------- what would y be if x is 5?

3             | 5                     lets substitute x with 5

               |                          y=1/3*5+4

               |                         y=5/3+4

               |                        y=17/3

Answer:

8 hours

Step-by-step explanation:

simple, divide 536 miles by 804 miles and multiply the fraction with 12 hours

fraction = 0.6666666 or 536/804 OR two thirds or 2/3

multiply 2/3 by 12 hours

it would take approximately 8 hours to arrive at 536 miles

Answer:

The relationship between the above two triangles is SAS and they are congruent

Answer:

Larger angle= 73, smaller angle= 17

Step-by-step explanation:

I wrote an equation, and x is the measure of one of the angles

90=2x-56

90+56=2x-56+56

146=2x

73=x

One of the angles is 73, so subtract 53 from 73 to find the second angle. 73+56=17

You can make sure it adds up to a complementary angle by seeing if 17+73=90

Answer:

if you assume one box as 1 m^2

then area of the shape is 54 m^2

but i am not sure if this is correct answer

Answer:

24x+2

Step-by-step explanation:

Answer:

The amount of money one may spend in a month may be greater than that of ones monthly payment especially when the payment is at a lower rate.

Answer: 135 minutes or 2 hours and 15 minutes  

Step-by-step explanation:

4/18 = 30/ x

Solve for duh 'x'

Answer:

[tex]2x^2y\sqrt[3]{7xy^2}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{56x^7y^5}[/tex]

Required

Solve

Expand

[tex]\sqrt[3]{8*7*x^6*x*y^3*y^2}[/tex]

Rewrite as:

[tex]\sqrt[3]{8*x^6*y^3*7*x*y^2}[/tex]

Split

[tex]\sqrt[3]{8*x^6*y^3} *\sqrt[3]{7*x*y^2}[/tex]

Express 8 as 2^3

[tex]\sqrt[3]{2^3*x^6*y^3} *\sqrt[3]{7*x*y^2}[/tex]

Apply law of indices

[tex]2^{(3/3)}*x^{(6/3)}*y^{(3/3)} *\sqrt[3]{7*x*y^2}[/tex]

[tex]2*x^2*y *\sqrt[3]{7*x*y^2}[/tex]

[tex]2x^2y *\sqrt[3]{7xy^2}[/tex]

[tex]2x^2y\sqrt[3]{7xy^2}[/tex]

9514 1404 393

Answer:

  B.  (-∞, 1) ∪ (1, 2]

Step-by-step explanation:

When you are looking for answers to domain questions, you are looking for values of the variable(s) that make the function undefined. Here, there is a square root involved, and the rational function has a denominator that might be zero.

The function is only defined for square roots of non-negative numbers. That is ...

  2-x ≥ 0   ⇒   x ≤ 2

The rational function is only defined for non-zero denominators, so ...

  x-1 ≠ 0

  x ≠ 1

__

So, you're looking for a domain description that includes all numbers less than or equal to 2, and excludes x=1. The attached number line shows a graph of this.

The domain divides into two parts: all numbers less than 1, and those numbers between 1 and 2 (including 2). This will be the union ...

  (-∞, 1) ∪ (1, 2]

Answer: domain: ARN

Range: y less than or equal to 0

Step-by-step explanation:

The arrows indicate that the lines continue forever, so the domain is all real numbers.

The lines only travel under the x-axis, so the range is y less than or equal to zero.