A supermarket has three options for purchasing a brand of cereal:
Standard $2. 49 for 220g
Economy $5. 00 for 725g
Supersize $11. 50 for 2kg
Compare the cost of each for 100g, and order the brands from cheapest to most expensive

The congruent triangles is solved and the triangles are congruent by AAS postulate

Given data ,

Let the two triangles be represented as ΔRQT and ΔTQS

And , the side TQ is the common side of both the triangles

Now , the measure of ∠TQR ≅ measure of ∠TQS ( given )

And , the measure of ∠TRQ ≅ measure of ∠TSQ ( given )

So , Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Hence , the triangles are congruent by ASA postulate

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The amount made by Caroline is $593.75 and 200 + 0.25x when she made $1574 and $x in sales respectively.

The total amount will be given by the formula using percentage -

Total amount = Base salary + 25% × her total sales

Keep the value in equation when she made $1575

Total amount = 200 + 25% × 1575

Total amount = 200 + 393.75

Total amount = $593.75

Keep the value in equation when she made $x

Total amount = 200 + 25% × x

Total amount = 200 + 0.25x

Hence, the earned amount is $593.75 and 200 + 0.25x.

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The complete question is -

Caroline works in a department store selling clothing. She makes a guaranteed salary of $200 per week, but is paid a commision on top of her base salary equal to 25% ofher total sales for the week. How much would Caroline make in a week in which she made $1575 in sales? How much would Caroline make in a week if she made x dollars in sales?

The palm tree is 21 feet tall.

To find the height of the palm tree, we can use the concept of similar triangles, where the ratio of corresponding sides is equal. In this case, the terms we need are Katie's height, her shadow length, the palm tree's shadow length, and the palm tree's height.

Step 1: Set up the proportion using the given information.
(Katie's Height / Katie's Shadow Length) = (Palm Tree Height / Palm Tree Shadow Length)

Step 2: Plug in the given values.
(6 ft / 2.5 ft) = (Palm Tree Height / 8.75 ft)

Step 3: Solve for Palm Tree Height.
(6 ft / 2.5 ft) * 8.75 ft = Palm Tree Height
2.4 * 8.75 ft = Palm Tree Height

Step 4: Calculate the height.
21 ft = Palm Tree Height

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The series of transformations correctly shows that △ABC≅△XYZ is D

a translation 2 units left and a reflection over the x-axis.

if a translation happens to each point of △ABC horizontally to the left by 2 units, which means  subtracting 2 from the x-coordinate of each vertex, we notice that a transformation of ABC to coordinates that are almost identical to XYZ but let it be called it A'B'C'

A(3, 0) ⇒ A'(1, 0)

B(2, -3) ⇒ B'(0, -3)

C(0, 3) ⇒ C'(-2, 3)

Secondly, if a reflection happens to A'B'C' at the x axis the transformation becomes identical to △XYZ

A'(1, 0) ⇒ X(1, 0)

B'(0, -3) ⇒ Y(0, 3)

C'(-2, 3) ⇒ Z(-2, -3)

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Answer:To find the value of x, bring the all the variable to the left side and bring all of the remaining values to the right side. You then simplify the values to find the answer.

Step-by-step explanation:

Answer:

im not sure bud because i don't know  what is the full question?

Step-by-step explanation:

The horizontal distance between the solutions is -12/5.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function is y = [tex]-5x^2+12x[/tex].

Now take y=0 then,

=>  [tex]-5x^2+12x[/tex] = 0

=> x(-5x+12) = 0

=> x = 0 and -5x = 12

=> [tex]x_1[/tex] = 0 and [tex]x_2[/tex] = -12/5

Then horizontal distance = [tex]x_2-x_1[/tex]

=> [tex]\frac{-12}{5}-0[/tex] = -12/5

Hence the horizontal distance between the solutions is -12/5.

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The prices of the four movies that Sally has already seen will not change after she sees the next movie.

The ticket prices of the four movies that Sally has already seen are fixed and do not depend on whether she sees another movie or not. Therefore, these prices will remain the same even after she sees the next movie. The price of the next movie that Sally plans to see is $34, which is independent of the ticket prices of the previous movies.

Thus, the cost of the previous movies that Sally has seen will not change after she sees the next movie. In other words, the previous expenses are sunk costs and are irrelevant to future decisions.

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The value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

GH² = IH × JI {secant tangent segments}

JI = 12 - IH, we shall represent IH with x so that;

8² = x(12 - x)

64 = 12x - x²

x² - 12x + 64 = 0 {rearrange to get a quadratic equation}

with the quadratic formula;

x = [12 + √(-112)]/2 or x = = [12 - √(-112)]/2

√(-112) = 4i√7 {where i = √(-1)}

so;

x = (6 + 2i√7) or x = (6 - 2i√7)

Therefore, the value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)

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in the given triangle, using SOH CAH TOA, the value of x is 16.48

From the question, we are to determine the value of x in the given diagram

In the given diagram,

We are given a right triangle.

70° is the included angle

6 is the adjacent

and x is the opposite

Using SOH CAH TOA,

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

Then, we can write that

tan (angle) = Opposite / Adjacent

Then,

tan (70°) = x/6

x = 6 × tan(70°)

x = 16.48

Hence, the value of x is 16.48

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The number of years apart between Eratosthenes was born in 276 BC (Before Christ) Abraham Lincoln died in 1865 is 2140 years.

Eratosthenes was born in 276 BC

Abraham Lincoln died in 1865 AD

BC = Before Christ

AD = anno dominie

The difference between the born date of Eratosthenes and the death date of Abraham Lincoln is to be calculated by

Year difference = BC year + AD year - 1

Year difference = 276 + 1865 - 1

Year difference = 2140

hence the  difference between the born date of Eratosthenes and the death date of Abraham Lincoln is 2140

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The average x-coordinate of the points in the prism is 3.

A prism is a polyhedron that has two parallel and congruent polygonal bases that are linked by parallelogram faces that are lateral. The height of the prism is the perpendicular distance between the bases.

The formula for calculating the average x-coordinate of the points in the prism D = {(x,y,z):0 ≤ x ≤ 6,0 ≤ y ≤ 18-3x, 0 ≤ z ≤ 4} is$$\frac{\text{sum of all x-coordinates}}{\text{number of vertices}}$$

The vertices of a prism are the points where two adjacent edges meet. There are eight vertices in a rectangular prism, and the x-coordinate of each vertex is either 0 or 6. The x-coordinates of the vertices are $$0,0,0,0,6,6,6,6.

$$The sum of all the x-coordinates is 24. Thus, the average x-coordinate of the points in the prism is$$\frac{24}{8}=\boxed{3}.

$$Hence, the average x-coordinate of the points in the prism is 3.

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Answer:

divide by 100

Step-by-step explanation:

hope it helps

Convert 1 Kilograms to Meters (kg to m) with our conversion calculator and conversion tables. To convert 1 kg to m use direct conversion formula below.

Convert 1 Kilograms to Meters (kg to m) with our conversion calculator and conversion tables. To convert 1 kg to m use direct conversion formula below.1 kg = 1 m.

Convert 1 Kilograms to Meters (kg to m) with our conversion calculator and conversion tables. To convert 1 kg to m use direct conversion formula below.1 kg = 1 m.You also can convert 1 Kilograms to other Weight (popular) units.

[tex]Direct \: \: conversion \: \: formula: 1 Kilograms * 1 = 1 Meters[/tex]

The value of (7 4/9 -8)*3.6-1.6*(1/3-3/4)+ 1 2/5 ÷(0.35) is given as 241/54.

(7 4/9 -8) = -5/9.

3.6-1.6 = 2.0

1/3-3/4 = 1/3 - 3/4

= 4/12 - 9/12

= -5/12

we will have -5/9 *  2 = -10/9.

-10/9 *  -5/12

10/9 * -5/12 = (10 * 5) / (9 * 12) = 50/108

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

50/108 = 25/54

we will have

25/54 + 1 2/5 ÷(0.35)

1 2/5 ÷ 0.35 = (7/5) ÷ (35/100) = (7/5) * (100/35) = 4

Now, we can substitute this value into the expression:

25/54 + 4 = (25/54) + (216/54) = 241/54

Therefore, the value of the expression 25/54 + 1 2/5 ÷(0.35) is 241/54.

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a. The limit does not exist.
b. The limit is equal to 4.

a. To find the limit as x approaches 2, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
Left-hand limit: lim f(x) as x approaches 2 from the left
We have f(x) = x - 1 for x < 2. So, as x approaches 2 from the left, f(x) approaches 1.
Right-hand limit: lim f(x) as x approaches 2 from the right
We have f(x) = 1 for 2 ≤ x ≤ 6 and f(x) = x + 4 for x > 6. So, as x approaches 2 from the right, f(x) approaches 6.
Since the left-hand and right-hand limits are not equal, the limit as x approaches 2 does not exist.
b. To find the limit as x approaches 6, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
Left-hand limit: lim f(x) as x approaches 6 from the left
We have f(x) = 1 for 2 ≤ x ≤ 6 and f(x) = x + 4 for x > 6. So, as x approaches 6 from the left, f(x) approaches 1.
Right-hand limit: lim f(x) as x approaches 6 from the right
We have f(x) = x + 4 for x > 6. So, as x approaches 6 from the right, f(x) approaches 10.
Since the left-hand and right-hand limits are not equal, the limit as x approaches 6 does not exist.
Therefore, the correct choices are:
a. The limit is not -oo or co and does not exist.
b. lim = 4.

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If 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards, the possible outcome is (10, 10, 5). So, correct option is B.

One possible method to approach this problem is to first find the total number of trading cards Royce has in his collection, which is the sum of baseball cards, football cards, and basketball cards:

Total number of cards = 16 + 21 + 13 = 50

Then, we can find half of the total number of cards, which is the number of cards Royce gives to his friend:

Half of total number of cards = 1/2 x 50 = 25

To find possible outcomes of this selection, we can start by considering how many baseball cards Royce can give to his friend. Since he has 16 baseball cards in total, he can give any number of them from 0 to 16, but he cannot give more than 25 cards in total.

Similarly, he can give any number of football cards from 0 to 21 and any number of basketball cards from 0 to 13.

Therefore, possible outcomes of this selection can be represented by the set of triples (x, y, z) where x is the number of baseball cards, y is the number of football cards, and z is the number of basketball cards, such that x + y + z = 25 and 0 ≤ x ≤ 16, 0 ≤ y ≤ 21, and 0 ≤ z ≤ 13.

The possible outcome is (10, 10, 5), which means Royce gives 10 baseball cards, 10 football cards, and 5 basketball cards to his friend.

So, correct option is B.

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Complete question is:

Royce has a collection of trading cards. 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards. He chooses half of this collection and gives them to his friend. Which of the following represent possible outcomes of this selection?

A) (10.20,20)

B) (10, 10, 5)

C) (20, 10, 5)

D) (10, 10, 25)

There were 490 walkers at the 10k fund-raiser.

The ratio of runners to walkers is 5:7, that means that the every five runners, there are 7 walkers so therefore we will use ratio formula.

If there have been 350 runners, we can use this ratio to discover what number of walkers there were:

5/7 = 350/x

Where x is the number of walkers.

To solve for x, we will cross-multiply:

5x = 7 * 350

5x = 2450

x = 490

Consequently, there were 490 walkers at the 10k fund-raiser.

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Answer:

Step-by-step explanation:

The solution to the differential equation is:

[tex]y = e^{(2\sqrt{y} - 0.6137)}[/tex]

To solve this differential equation, we can use the method of separation

of variables. This involves isolating the variables x and y on different

sides of the equation and then integrating both sides with respect to

their respective variables.

Starting with the given equation:

[tex]dy/dx = e^{(\sqrt{(x/y)} )}[/tex]

We can begin by multiplying both sides by dx:

[tex]dy = e^{(\sqrt{(x/y)} ) dx}[/tex]

Now we can separate the variables and integrate both sides:

[tex]\int(1/y)dy = ∫e^{(\sqrt{(x/y))dx} }[/tex]

ln|y| = 2√y + C1 ...where C1 is a constant of integration

To solve for y, we can exponentiate both sides:

[tex]|y| = e^{(2\sqrt{y} + C1)}[/tex]

Since y(1) = 4, we can use this initial condition to determine the sign of y and the value of C1:

[tex]4 = e^{(2\sqrt{4} + C1)} \\4 = e^{(4 + C1)}[/tex]

ln(4) = 4 + C1

C1 = ln(4) - 4 = -0.6137

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Answer:

the answer is 14,986 centimetres

The estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.

Let V = (1/3)πr²h be the volume of the cone, where r and h are the base radius and height of the cone, respectively.

Let dr and dh be the possible errors in the measurements of r and h, respectively.

Then, the actual dimensions of the cone are (r+dr) cm and (h+dh) cm, respectively.

The differential of V is given by:

dV = (∂V/∂r)dr + (∂V/∂h)dh

We have:

∂V/∂r = (2/3)πrh and ∂V/∂h = (1/3)πr²

Substituting the given values, we get:

∂V/∂r = (2/3)π(10 cm)(25 cm) = 500π/3

∂V/∂h = (1/3)π(10 cm)² = 100π/3

Substituting into the differential equation, we get:

dV = (500π/3)dr + (100π/3)dh

Using the given maximum error of 0.1 cm for both r and h, we have:

|dr| ≤ 0.1 cm and |dh| ≤ 0.1 cm

Therefore, the maximum possible error in V is given by:

|dV| = |(500π/3)(0.1 cm) + (100π/3)(0.1 cm)|

|dV| = 50π/3 + 10π/3

|dV| = 60π/3

|dV| = 20π cm³

Therefore, the estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.

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Step-by-step explanation:

The coordinates of point B: (0,6)

Coordinates of point C: (3,8)

A kite has 4 sides, of which we have 2 equal pairs, thus the coordinates of point D must be (6,6)

Answer:

(6,6)

Step-by-step explanation:

The question is asking us to complete the half figure, and make it a kite.  We can see that the 2 lines AB and BC are half of the shape.  In the attachment, I drew a line of symmetry down the middle of the shape.  

I also created a point, Y, down the red line, AC, to represent the perpendicular bisector of the 2 diagonals.  We can see that line segment BY is the radius of the entire line BD.  

This radius is 3 units, so we now know that the diameter horizontally is 6 units.  We can draw this on the other side to create point D.  

This means that point D is at (6,6).

See attachment for more information, hope this helps!

The best estimate of the charge Zachary will later find on his credit card statement is $20

The formula to be used is -

Amount in USD = Amount of MYR/Value of one MYR

As, 3.04 MYR is 1 USD performing money conversion of 58 MYR

So, 58 MYR will be = 58/3.04

Divide the values in Right Hand Side of the equation to find the value of MYR in USD

Value in USD = $19.07

Hence, the credit card statement will reflect usage of $20 (since it is the closes correct option and we have been asked the best estimate).

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The critical numbers are 4, -4.

To find the critical numbers of the function g(v) = v³ - 48v + 6, follow these steps:

1. Find the derivative of the function, g'(v).
2. Set g'(v) equal to 0 and solve for v.
3. List the critical numbers as a comma-separated list.

Step 1: Find the derivative of the function.
g(v) = v³ - 48v + 6
Using the power rule, the derivative is:
g'(v) = 3v² - 48

Step 2: Set g'(v) equal to 0 and solve for v.
3v² - 48 = 0
Divide both sides by 3:
v² - 16 = 0
Factor the equation:
(v - 4)(v + 4) = 0
Solve for v:
v = 4, -4

Step 3: List the critical numbers.
The critical numbers of the function g(v) = v³ - 48v + 6 are v = 4, -4.

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Thus, approximately 33.33% of the data values are between 25 and 45.

A box-and-whisker plot, also known as a box plot, is a graphical representation of a set of data that shows the distribution of the data along a number line. The plot is composed of a box that represents the middle 50% of the data, along with two "whiskers" that represent the lowest and highest values in the data set. The box is drawn between the first and third quartiles of the data, with a line inside the box representing the median value. The distance between the first and third quartiles is known as the interquartile range (IQR), which can be used to identify outliers in the data. Box-and-whisker plots are useful for comparing the distribution of data between different groups or data sets.

Here,

To find the percentage of the data values that are between 25 and 45 on the given box-and-whisker plot, we need to find the area of the box that is between the lower quartile (Q1) and the median (Q2). From the plot, we can see that the lower quartile (Q1) is at 30, and the median (Q2) is at 40. The interquartile range (IQR), which is the distance between Q1 and Q3, is 20.

Therefore, the box extends from 30 to 40, which is a distance of 10. The total length of the plot is 30 (from 25 to 55), so the percentage of data values between 25 and 45 is:

10/30 * 100% = 33.33%

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Complete question:

The box-and-whisker plot below represents some data set. What percentage of the data values are between 25 and 45?

If a time capsule has been buried 98m away from the cave at a bearing of 312. the time capsule is buried about 82.2 meters west of the cave.

To find how far west the time capsule is buried, we need to find the horizontal component of the displacement vector that points from the cave to the location of the time capsule. We can use trigonometry to do this:

cos(312°) = adjacent/hypotenuse

The hypotenuse is the distance between the cave and the time capsule, which is 98m. The adjacent side represents the horizontal distance between the two points, which is what we want to find. Rearranging the equation, we get:

adjacent = cos(312°) x hypotenuse

adjacent = cos(312°) x 98

adjacent ≈ 82.2

Therefore, the time capsule is buried about 82.2 meters west of the cave.

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The most reasonable estimate for the number of Auto Wheel Magazine subscribers who own fewer than 2 vehicles is 102.

To estimate the number of Auto Wheel Magazine subscribers who own fewer than 2 vehicles, we can use the proportion of subscribers in the sample who reported owning fewer than 2 vehicles. We can assume that this proportion is representative of the proportion of all subscribers who own fewer than 2 vehicles.

The proportion of subscribers in the sample who own fewer than 2 vehicles is:

15/50 = 0.3

This means that 30% of the sample subscribers own fewer than 2 vehicles. To estimate the number of all subscribers who own fewer than 2 vehicles, we can multiply this proportion by the total number of subscribers:

0.3 x 340 = 102

Hence, the most reasonable estimate = 102.

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The final value is f'(-1) = 16,777,2160.

We can use the chain rule and the power rule of differentiation to find f'(-1).

Recall that the chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) h'(x). Applying this rule to f(x) = (h(x))^10, we get:

f'(x) = 10(h(x))^9 h'(x)

Now, we can substitute x = -1 into the above equation, since we are asked to find f'(-1). Thus, we have:

f'(-1) = 10(h(-1))^9 h'(-1)

We are given that h(-1) = 3 and h'(-1) = 6, so we can substitute these values to get:

f'(-1) = 10(3)^9 (6)

Simplifying, we get:

f'(-1) = 16,777,2160

Therefore, f'(-1) = 16,777,2160

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According to the 68-95-99.7 rule, approximately 68% of the distribution falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, the mean is 7.06 minutes and the standard deviation is 0.75 minutes. Therefore, the range of times that covers the middle 95% of the distribution would be from the mean minus two standard deviations (7.06 - 2 x 0.75 = 5.56 minutes) to the mean plus two standard deviations (7.06 + 2 x 0.75 = 8.56 minutes).

In other words, 95% of the male college students' mile run times are expected to fall between 5.56 and 8.56 minutes. This means that most of the students' mile run times will be within this range, and only a small percentage will be outside of it.

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The drive-thru is able to estimate their wait time more consistently will be A. Burger Quick, because it has a smaller IQR.

The interquartile range (IQR) is a measure of variability that represents the range of values in the middle 50% of scores in a distribution. It is used when the data is skewed and the median is a better measure of central tendency than the mean.

In this scenario, Burger Quick has an IQR of 14.5, while Fast Chicken has an IQR of 4.5.

The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

For Burger Quick, Q1 is 9.5 and Q3 is 24, so the IQR is 24 - 9.5 = 14.5. For

Fast Chicken, Q1 is 10 and Q3 is 14.5, so the IQR is 14.5 - 10 = 4.5.

Therefore, Burger Quick has a larger IQR than Fast Chicken, indicating that its data is more consistent and less spread out. This means that Burger Quick is better able to estimate its wait time consistently.

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The p-value of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.

We are told that:

Time spent by U.S. drivers on average each day = 51 minutes behind the wheel

Thus, the null hypothesis is:

H₀: μ = 51

The alternate hypothesis is:

Hₐ: μ < 51

The formula for the test statistic is:

z = (x' - μ)/(σ/√n)

where:

x' is sample mean

n is sample size

μ is population mean

σ is standard deviation

Thus:

z = (46.4 - 51)/(18.8/√75)

z = -2.12

From online p-value from z-score calculator, we have:

The p-value of the test is referred to as the probability of finding a sample mean that is less than 46.4, which is the p-value of z when X = 46.4.

Looking at the z-table, z = -2.12 has a p-value of 0.017.

Decision:

The p-value of the hypotheses test is seen to be0.017 > 0.01.

Thus, this tells us that we don't have convincing evidence that the mean time spent behind the wheel for all U.S drivers is less than 51 minutes.

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