Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
0 , x<0
f(x) = ((x^2)/4) , 0 <= x <= 2
1 , 2<= x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) P(X %u2264 1)
(b) P(0.5 %u2264 X %u2264 1)
(c) P(X > 1.5)(d) The median checkout duration [solve 0.5 = F(mew)](e) Use F'(x) to obtain the density function f(x)
(f) Calculate E(X)
(g) Calculate V(X) and %u03C3x
(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

The angle that is vertical to angle 3 is angle 1

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

This means that angles that are vertical are angle s that are opposite to each other. In the diagram above, angle 2 is opposite to angle 4 and angle 1 and angle 3.

Therefore all the angles will make a point. This means the sum of the angles is 360°.

angle 2 and angle 3 are adjascent to each other and angle 1 and 4 are adjascent to each other

Therefore the angle that is vertical to the angle 3 is angle 1

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What describes the literature during the Goryeo dynasty is: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.

Literature during the Goryeo dynasty (918-1392 CE) in Korea was characterized by a flourishing of literature in both Confucianism and Buddhism, which were the two dominant religions at the time.

The literature of this period included works on history, sacred texts, legends, and biographies written by scholars from both traditions. Poetry and drama also became popular during this time.

Therefore, we can state that: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.

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Answer: 490.87 is the answer, rounded to a whole number is 491.

Step-by-step explanation: A≈490.87m²

Solving for A

A=1

4πd2=1

4·π·252≈490.87385m²

Not sure that's really an explanation but... Hope that makes since :)

Answer: To find the percentage of customers who chose the same meal, we need to divide the number of people who chose the same meal by the total number of customers, and then multiply by 100 to convert to a percentage:

percentage = (34 / 85) x 100

percentage = 40

Therefore, 40% of the customers chose the same meal.

Step-by-step explanation:

Answer:

Its 40%

Step-by-step explanation: you divide 85 by 34 to get your answer

As a result, the answer to the following question, Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches.

An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.

Rectangle area = length x breadth = 12 x 7 = 84 square inches

The size of the rectangle that makes up the space inside the letter E must then be subtracted:

5 × 6 = 30 square inches is the area of the inner rectangle.

A tiny rectangle's area 5 x 1 = 5 square inches = 1 = length x width

A tiny rectangle's area 5 x 1 = 5 square inches = 2 = length x width

A tiny rectangle's area 2 x 3 = 6 square inches = 3 = length x width

5 + 5 + 6 = 16 square inches is the total area of little rectangles.

Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches

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The Curved surface area of the frustum is 60π.

In geometry, a frustum, is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid.

The Curved surface area of the frustum is equal to the curved surface area of the large cone minus the curved surface area of the small cone.

The height of the large cone=√[tex]10^{2}[/tex]-[tex]8^{2}[/tex]

=√[tex]100-64[/tex]

=6cm

The height of small cone=6×(1/2)=3cm

(The little cone's height is equal to half that of the giant cone's height.)

The arc length of the small cone=10×1/2=5cm

The curved surface area of the frustum=π×8×10-π×r×5

=80π-5rπ

r=√[tex]5^{2}[/tex]-[tex]3^{2}[/tex]

=√25-9

=4cm

Hence, Curved surface area of the frustum is

= 80π-5×4×π

=80π-20π

=60π

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The two sets of data are

Set 1: 5, 6, 7, 8, 9, 10, 20

Set 2: 1, 2, 3, 4, 5, 15, 16

The median is a measure of central tendency in a data set that represents the middle value of the data when arranged in order.

To find the median of a data set, we need to arrange the values in ascending or descending order and then find the middle value.

The IQR (Interquartile Range) is a measure of variability in a data set that represents the difference between the 75th percentile (third quartile) and the 25th percentile (first quartile).

To calculate the IQR of a data set, we need to find the values of the first quartile (Q1), and third quartile (Q3), and then subtract Q1 from Q3.

Here we have

Each data set has 7 values, -

The median of set 1 is greater than the median of set 2, -

The IQRs of the data sets are the same.

To create the sets assume a positive value as the median of the data and make sure that the value is in the middle of the data.

Similarly, take another positive value that is greater than the previous value and make sure that the value is also in the middle.

Now arrange the remaining values such that both sets of data have the same IQRs.  

Here are two sets of data that meet the given characteristics:

Set 1: 5, 6, 7, 8, 9, 10, 20

Median: 8

IQR: 4 (Q3 = 9, Q1 = 5)

Set 2: 1, 2, 3, 4, 5, 15, 16

Median: 4

IQR: 4 (Q3 = 5, Q1 = 1)

Therefore,

The two sets of data are

Set 1: 5, 6, 7, 8, 9, 10, 20

Set 2: 1, 2, 3, 4, 5, 15, 16

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A) Rounding to the nearest whole number, Anthony needs to scoop out 13 cups of water with this cup.

B) Rounding to the nearest whole number, Anthony needs to scoop out 3 cups of water with this cup.

The volume of the sink is given as 660 Pi inch cubed, which means the radius of the half-sphere sink is:

[tex]r = (3 \times 660 Pi / 4Pi)^{(1/3)} = 9 inches[/tex]

A) For the first cup with a diameter of 5 inches and a height of 8 inches, the volume of the cup is:

[tex]V = Pi \times r^2 \times h = Pi \times (2.5)^2 \times 8 = 50[/tex]Pi inch cubed

The number of scoops required to empty the sink can be found by dividing the volume of the sink by the volume of one scoop:

Number of scoops = 660 Pi / 50 Pi = 13.2

Rounding to the nearest whole number, Anthony needs to scoop out 13 cups of water with this cup.

B) For the second cup with a diameter of 10 inches and a height of 8 inches, the volume of the cup is:

[tex]V = Pi \times r^2 \times h = Pi \times (5)^2 \times 8 = 200[/tex] Pi inch cubed

The number of scoops required to empty the sink can be found by dividing the volume of the sink by the volume of one scoop:

Number of scoops = 660 Pi / 200 Pi = 3.3

Rounding to the nearest whole number, Anthony needs to scoop out 3 cups of water with this cup.

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Answer:

144 in^3

Step-by-step explanation:

You need to separate the figure into the top and bottom rectangles

For the top, the volume = 12 x 4 x 1 = 48

For the bottom, the length is 12, the height is 5 - 1 = 4, the width is 2

so the volume is 12 x 4 x 2 = 96

The volume of the figure is 48 + 96 = 144 in^3

Answer:

1440 ft²

Step-by-step explanation:

The roof is made up of 4 congruent triangles.

We first solve for the area of one of the triangles using the formula:

A = (1/2) · b · h

↓ plugging in given values

A = (1/2) · 40 ft · 18 ft

A = 20 ft · 18 ft

A = 360 ft²

Now, we can solve for the surface area of the entire roof by multiplying the area of one of the triangles by 4 (because there are 4 congruent triangles).

SA = 360 ft² · 4 = 1440 ft²

—

Note that we can solve for the area of the triangles using the formula {A = (1/2) · b · h} because the slant height of a pyramid is perpendicular to the side of the pyramid's base that it connects to, thereby making it the height of the triangle that is the pyramid's side.

—

he volume of the drum can be calculated as follows:

Volume of drum = πr²h

= π(4.2m)²(3.5m)

≈ 246.33 m³

To find out how many full bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the volume of one wheat bag:

Number of full bags of wheat = Volume of drum ÷ Volume of one bag

= 246.33 m³ ÷ 5.39 m³

≈ 45.72

Therefore, the circular drum can hold approximately 45 full bags of wheat.

Answer: 45 Full of bags.

Step-by-step explanation:

The volume of the drum can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.

V = π(4.2m)^2(3.5m)

V ≈ 246.73 m³

To find out how many bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the space required for one bag:

246.73 m³ ÷ 5.39 m³/bag ≈ 45.81 bags

Since we can't have a fraction of a bag, we need to round down to the nearest whole number:

Number of bags = 45

Therefore, 45 full bags of wheat can be emptied into the drum.

To calculate the z-score for the new case count in Orange County, we use the formula:
z = (x - μ) / σ
where x is the value we are calculating the z-score for, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Plugging in the values given in the question, we get:
z = (178 - 7.29) / 110.87
z = 170.71 / 110.87
z = 1.54
So the z-score for the new case count in Orange County is 1.54. This means that the new case count in Orange County is 1.54 standard deviations above the mean of the distribution.

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According to the algebraic expression 1.50x + 0.75y:

An algebraic expression is a combination of variables, values, numbers, and constants.

An algebraic expression is short of an equation, which consists of two or more algebraic expressions that are equated to each other.

The cost of hot dogs per unit = $1.50

The cost of cans of soda per unit = $0.75

Let the number of hot dogs bought = x

Let the number of cans of soda bought = y

1.50x + 0.75y = Customer's total expenses

Thus, the variables x and y in the algebraic expression represent the number of units of each type of item sold during the BBQ fundraiser.

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Answer: Part A:

If Isabella's mother has a garden with an area of 10 2/3 square feet, and she plants peas in 1/4 of the garden, we can calculate the area used for planting peas by multiplying the garden area by 1/4:

Area used for planting peas = (10 2/3 square feet) x (1/4) = (32/3) x (1/4) = 8/3 square feet

Therefore, the area used for planting peas is 8/3 square feet.

Part B:

If Isabella's mother sells the peas and gets 3 dollars for each square foot, we can calculate how much money she made by multiplying the area used for planting peas by 3:

Money made = (8/3 square feet) x (3 dollars/square foot) = 8 dollars

Therefore, Isabella's mother made 8 dollars by selling the peas she planted in her garden.

Answer:

x=16.3

Step-by-step explanation:

sine: opposite side ÷ hypotenuse

sine(x)= 7 ÷ 25 = 0.28

sine^-1(0.28) = 16.3

x = 16.3

Answer:

16.3 rounded to the nearest tenth

Step-by-step explanation:

The formula for the sine rule is Sin A / a= Sin B / b = Sin C / c which is as, Sin V / v = Sin X / x = Sin S / s

Sin 90 / 25 = Sin X / 7, that is,

1 / 25 = Sin X / 7 (cross multiply)

Make Sin X the subject of the formula;

Sin X = 7 / 25

X = Sin^-1(7 / 25)

X = 16.26 = 16.3 rounded to the nearest tenth

Answer:

Step-by-step explanation:

The total amount paid at the end of sixth month is S/78,000. So, the correct answer is (b).  Total amount paid at the end of the nth month is 24,000n + 9,000. So, the correct answer is (b). If the cooperative has already paid 50% of the price of the land by the end of the tenth month, the payment option did they choose is 20% down payment and fixed monthly payments of S/5,000. So, the correct option is (a).

For the first payment option, the down payment is 20% of S/240,000, which is S/48,000. The remaining balance is S/192,000, which is paid in fixed monthly payments of S/5,000. Therefore, at the end of the sixth month, the total amount paid is:

S/48,000 + 6 x S/5,000 = S/78,000

So, the answer is (b) S/78,000.

The amount of money paid at the end of the nth month for the second payment option is the sum of the down payment and the total monthly payments up to that month. The down payment is 10% of S/240,000, which is S/24,000. The total monthly payments up to the nth month is S/9,000 x n. Therefore, the expression for the total amount paid at the end of the nth month is:

S/24,000 + S/9,000 x n = (3S + 8n)/72

So, the answer is (b) 24,000n + 9,000.

We can find out which payment option they chose by comparing the total amount paid up to the tenth month for each option to half of the price of the land.

For the first payment option, the down payment is S/48,000 and the total monthly payments up to the tenth month is

10 x S/5,000 = S/50,000.

Therefore, the total amount paid up to the tenth month is:

S/48,000 + S/50,000 x 10 = S/480,000/25

For the second payment option, the down payment is S/24,000 and the total monthly payments up to the tenth month is

10 x S/9,000 = S/9,000.

Therefore, the total amount paid up to the tenth month is:

S/24,000 + S/9,000 x 10 = S/24,000 + S/900

For the third payment option, there is no down payment, and the total monthly payments up to the tenth month is

10 x S/12,000 = S/1,200.

Therefore, the total amount paid up to the tenth month is:

S/1,200 x 10 = S/12,000

Comparing each total amount paid up to the tenth month to half of the price of the land (S/240,000 x 0.5 = S/120,000), we see that only the first payment option meets the condition, since:

S/480,000/25 < S/120,000

Therefore, the answer is (a) First.

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Answer:

one apple: 75 cents

one orange: 60 cents

Step-by-step explanation:

let x be price of one apple

let y be price of one orange

3x + 4y = 4.65

5x + 8y = 8.55

we can do elimination, substitution, or graphing.

this is elimination: (we're eliminating the x in this case to find y, and then use y to find x)

ORIGINAL EQUATIONS: (we're multiplying by 5 so we can eliminate x)

3x + 4y = 4.65

5x + 8y = 8.55

5(3x + 4y = 4.65) = 15x + 20y = 23.25

3(5x + 8y) = 8.55 = 15x + 24y = 25.65

(distribute, and then subtract to get one equation and eliminate x)

  15x + 20y = 23.25

-  15x + 24y = 25.65

------------------------------

  0    -    4y = - 2.4

so we got that, now we make it this:    -4y = -2.4

divide both sides by -4.

-4y = -2.4

-----    -----

-4          -4

y (orange variable) = 0.60

therefore, one orange cost 60 cents.

plug y (the 60 cents) back into one of the original equations (either works) and solve for x.

3x + 4y = 4.65

5x + 8y = 8.55

let's use this equation:  5x + 8y = 8.55

5x + 8(0.6) = 8.55

5x + 4.8 = 8.55

     -4.8      -4.8

5x = 3.75

----    ------

5        5

x = 0.75

therefore, one apple cost 75 cents.

(also, there was an easier number to multiple the equations by)

3x + 4y = 4.65

5x + 8y = 8.55

We could have multiplied (3x + 4y = 4.65) with 2, distributing and bringing it to 6x + 8y = 9.30

Then subtract 6x + 8y = 9.30 from 5x + 8y = 8.55, and you would have solved and gotten x just fine, then plugged x back in to find y)

sorry this answer is so long...good luck :))

Answer:

62.85 units

Step-by-step explanation:

s= rΘ

s= 4*5π/3= 20π/3

the perimeter= 20π/3*3

= 20π

= 20*22/7

= 440/7=62.85

Answer:

Red I think maybe we should try hi friends I am new to this app

The area of the actual gym in the middle school is 20,400 square feet.

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

If the scale is 1 inch : 5 feet, then we can use this ratio to convert the dimensions of the gym in the drawing to their actual size.

The length of the gym in the actual middle school is:

34 inches x 5 feet/inch = 170 feet

The width of the gym in the actual middle school is:

24 inches x 5 feet/inch = 120 feet

The area of the gym in square feet is:

Area = length x width

Area = 170 feet x 120 feet

Area = 20,400 square feet

Therefore, the area of the actual gym in the middle school is 20,400 square feet.

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The missing cοmpοnent in this study is  cοntrοl grοup

A methοd used in a cοntrοlled envirοnment tο find an unknοwn effect οr law, test οr establish a hypοthesis, οr prοvide an example οf an established law

In the scenariο described, individuals are chοsen at randοm tο participate in a new interventiοn, which appears tο be an example οf an experiment.

A cοntrοl grοup is a grοup οf participants whο are used fοr cοmparing anοther grοup tο in a test οr experiment. It is cοmpοsed οf participants whο dο nοt receive the experimental treatment.

In the given situatiοn an energy drink cοmpany claims that its prοduct increases students' memοry levels.

Tο suppοrt its claims, the cοmpany issues advertisements claiming that 8 οut οf 10 peοple (chοsen randοmly frοm acrοss the cοuntry) whο tried their prοduct repοrted imprοved memοry.

But they haven't cοmpοse a cοntrοl grοup tο cοmpare the results fοr test.

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Answer:

A. Control Group

Plato

If babies weight increases by 8% over a month from birth to 4. 5 kg, the baby's weight at birth was approximately 4.17 kg.

To find out the weight at birth, we need to use the given information that the baby's weight increased by 8% over a month to reach 4.5 kg.

Let's start by setting up an equation. We can let x be the baby's weight at birth in kg. Then, we know that the baby's weight increased by 8% over a month, so the weight after one month would be:

x + 0.08x = 4.5 kg

Simplifying this equation by combining like terms, we get:

1.08x = 4.5 kg

To solve for x, we can divide both sides of the equation by 1.08:

x = 4.17 kg

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Step-by-step explanation:

Her interest earned will be   p r t    

p = principal = amount of deposit = 1100 dollars

r = decimal  interest rate = .09

t = time in years = 3

$ 1100 * .09 * 3 = $ 297 .

Answer: is there a Pic it would help

Step-by-step explanation:

Atul's father is wrong. The average amount is greater than Atul's allowance.

In order to determine if Atul is justified to ask for a raise in allowance, the mean of the data collected by Atul has to be determined.

Mean is the average of a set of numbers. It can be determined by adding the numbers together and dividing it by the total numbers in the dataset. Mean is a measure of central tendency.

Mean = sum of numbers / total numbers

(120 + 180 + 100 + 50 + 250 + 200 + 200 + 220 + 150 + 100 + 100 + 150 + 130 + 200 + 180 + 100 + 150 + 100 + 180 + 150+ 120 + 150+ 100 + 150 + 100 + 120 + 180 + 200 + 50) / 30 = 139.33

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Answer:

Step-by-step explanation:

First we sould factor out the function:

y=x^2+5x-6

y=(x+6)(x-1)

Note: if you multiply out the factored equation, you will get your original equation.

Now, find what we need to plug in to make it equal 0.

If we plug in -6, then the (x+6) part equals 0. Since we are multiplying by 0, the whole thing equals 0.

If we plug in 1, then the (x-1) part equals 0. Since we are alo multiplying by 0 here, the function comes out to 0.

This means that at x=-6 and x=1 the function comes out to 0.

The sοlutiοn οf the given prοblem οf interest cοmes οut tο be Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.

Tο calculate the simple interest rate, divide the amοunt by the cοst οf financing, the amοunt οf time left, and οther variables. The simple return strategy in marketing is principal student lοans hrs. This methοd is the mοst basic methοd fοr figuring οut invοlvement. The mοst typical methοd fοr calculating incοme is as a share οf the principal amοunt. Tο put this intο perspective, if he wants tο bοrrοw $100 frοm a single οf these friends .

Here,

a. The fοllοwing methοd can be used tο determine the mοnthly payment fοr a lοan:

=> The mοnthly payοut =  (P*r) / (1 - (1+r)(-n)).

We must first determine the entire lοan amοunt, including interest, that Reh must pay back. After 4.5 years οf interest accrual, the lοan sum is:

=>  [tex]9900 \times (1 + 0.0429/12)^{(12 \times 4.5)[/tex] = 12,723.97

The οverall debt balance is $12,723.97.

The numbers can then be entered intο the fοrmula as fοllοws:

=>  (12723.97*(0.0429/12)) / (1 - (1+(0.0429/12))(-12*10))

is the fοrmula fοr the mοnthly payοut.

Payment due each mοnth: $131.19 (rοunded tο the nearest dοllar)

Reh's mοnthly payment is therefοre $131, rοunded tο the clοsest dοllar.

b. The fοllοwing fοrmula can be used tο determine the tοtal interest charged οver the lοan's term:

=> tοtal interest = (mοnthly payment X n) - P .

There have been a tοtal οf:

=> 120 is equal tο ten years times οne year.

The entire interest paid is thus:

=> ($3,943.80) (tοtal mοnthly installments * n) - P

=> (131.19 * 120) - 9900 (rοunded tο the nearest dοllar)

Sο, rοunded tο the clοsest dοllar, Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.

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We can say that after answering the offered question As a result, the equation for the circle with centre (7, -7) and point (11, -3) i[tex](x - 7)2 + (y + 7)2 = 32.[/tex]

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

Determine the radius:

The radius of the circle is the distance between the circle's centre (7, -7) and any point on it (11, -3).

We may calculate the distance using the distance formula:

[tex]r = \sqrt((11 - 7)^2 + (-3 - (-7))\\v^2)\\r = \sqrt(4^2 + 4^2)\\r = \sqrt(32) (32)[/tex]

In the standard form equation of a circle, substitute the centre and radius:

A circle with centre (h, k) and radius r has the following standard form equation:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

With h = 7, k = -7, and r = sqrt(32), we get:

[tex](x - 7)^2 + (y + 7)^2 = 32[/tex]

As a result, the equation for the circle with centre (7, -7) and point (11, -3) is[tex](x - 7)2 + (y + 7)2 = 32.[/tex]

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The critical value for a 0.05 level of significance is 1.96, so the calculated t-test statistic (-1.166) is lower than the critical value and therefore does not reject the null hypothesis.

The related samples t-test is used to determine if there is a statistically significant difference between the two sets of data. In this case, the t-test is used to determine if the students' grades have improved after receiving tutoring.

To calculate the t-test statistic, we need to first calculate the mean and standard deviation of the before and after data sets.

For the before data set, the mean is 2.56 and the standard deviation is 0.8. For the after data set, the mean is 3.22 and the standard deviation is 0.5.

We can then calculate the t-test statistic using the following formula:

t = (mean before - mean after) / (standard deviation before + standard deviation after / √n)

where n is the number of samples.

In this case, n = 5, so the t-test statistic is:

t = (2.56 - 3.22) / (0.8 + 0.5 / √5) = -1.166

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Answer:

6

Step-by-step explanation:

To find the hours of labor it took to repair the car, we need to subtract the cost of parts from the total cost and then divide the result by the cost per hour of labor.

So, $340 - $100 = $240 was spent on labor.

$240 ÷ $40 per hour = 6 hours of labor.

Therefore, the answer is OB. 6 hours.