A gallon of gasoline costs $2.96 your car has a 25- gallon gas tank and can travel 28.8 miles one each gallon of gasoline find the cost of filling your gas tank if it’s already 3/8 full

The height of the air balloon is 63.4 yards.

Trigonometry is a branch of mathematics that uses variables to determine heights and distances. It is the study of the properties of right angled triangles and trigonometric functions and of their applications.

For the given situation,

The diagram below shows the situation described above.

The distance between Caleb and Emily = 100 yards

Let the distance from Caleb to the air balloon be 'x'

Let the distance from Emily to the air balloon be 'y'

Let height of the air balloon be 'h'

⇒ [tex]x+y=100[/tex]

⇒ [tex]x=100-y[/tex]

We know that, [tex]tan[/tex] θ = [tex]\frac{perpendicular }{base}[/tex]

Now consider the triangle with angle 45°,

[tex]tan 45[/tex]° = [tex]\frac{h}{x}[/tex]

We know that tan 45° = 1 and substitute x = 100-y,

⇒ [tex]1 = \frac{h}{100-y}[/tex]

⇒ [tex]h=100-y[/tex]

This is equation 1.

Now consider the triangle with angle 60°,

[tex]tan60[/tex]° = [tex]\frac{h}{y}[/tex]

We know that, tan 60° = √3

⇒ [tex]\sqrt{3} = \frac{h}{y}\\[/tex]

⇒ [tex]h=y\sqrt{3}[/tex]

This is the equation 2.

On equating equation 1 and 2,

⇒ [tex]100-y=y\sqrt{3}[/tex]

⇒ [tex]y+y\sqrt{3}=100[/tex]

⇒ [tex]y(\sqrt{3}+1 )=100[/tex]

⇒ [tex]y=\frac{100}{\sqrt{3}+1 }[/tex]

Thus height, [tex]h=y\sqrt{3}[/tex]

Substitute the value of y in h,

⇒ [tex]h=\sqrt{3}(\frac{100}{\sqrt{3} +1} )[/tex]

⇒ [tex]h=\frac{100\sqrt{3} }{\sqrt{3}+1 }[/tex]

⇒ [tex]h=\frac{173.205}{2.732}[/tex]

⇒ [tex]h=63.397[/tex]

⇒ [tex]h=63.4[/tex]

Hence we can conclude that the height of the air balloon is 63.4 yards.

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Casey earned $780.25 in tips last week. This was calculated by first finding out her earnings from her hourly wage, and then subtracting this from her total earnings.

First, we need to calculate how much Casey earns from the hourly rate alone. Given that Casey's hourly rate is $4.55 per hour and she worked for 26 hours last week, we multiply the two to get her earnings from the hourly wage, which is $4.55 * 26 = $118.30.

Then we need to find out how much Casey made in tips. Casey's total earnings last week were $898.55. We subtract the earnings from her hourly rate from her total earnings to find out how much she made in tips. So, $898.55 - $118.30 = $780.25.

Therefore, Casey earned $780.25 in tips last week, which corresponds to option D.

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The odds against selecting a person who commutes by bicycle from a town where 10% of people commute that way would be 9 to 1. This is based on the percentage of people who do not commute by bicycle versus those who do.

In statistical terms, the question is asking us to calculate the odds against selecting someone who commutes by bicycle. With 10% of people in this town commuting by bicycle, it means that 90% of them do not. Therefore, the odds against selecting someone who commutes by bicycle are 90 to 10 or 9 to 1.

This is calculated by dividing the number of unsuccessful outcomes (people not commuting by bicycle - 90%) by the number of successful outcomes (people commuting by bicycle - 10%). This gives us the odds against selecting someone who commutes by bicycle.

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To find the absolute minimum and absolute maximum values of the function f(x) = x - ln 8x on the interval [1/2, 2], we find the critical points and evaluate the function at the endpoints and critical points. The absolute minimum value is f(1/2) = 1/2 - ln 4 and the absolute maximum value is f(2) = 2 - ln 16.

To find the absolute minimum and absolute maximum values of the function f(x) = x - ln 8x on the given interval [1/2, 2], we need to find the critical points and the endpoints of the interval. First, we find the derivative of the function: f'(x) = 1 - 1/x. Then, we solve the equation f'(x) = 1 - 1/x = 0 to find the critical points. The critical point is x = 1. Next, we evaluate the function at the critical point and the endpoints of the interval to determine the absolute minimum and absolute maximum values.

1. Evaluating the function at the critical point: f(1) = 1 - ln 8
2. Evaluating the function at the endpoint x = 1/2: f(1/2) = 1/2 - ln 4
3. Evaluating the function at the endpoint x = 2: f(2) = 2 - ln 16

The absolute minimum and absolute maximum values of the function on the given interval are:

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The formula for finding the slope of a line is expressed as:

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

Given the coordinate points (2, 1) and (2, 0). Get the slope of the line passing through the coordinate points

[tex]m=\frac{0-1}{2-2}\\m=\frac{-1}{0}\\m=\infty[/tex]

The equation of the line in point-slope form is [tex]y-y_0=m(x-x_0)[/tex]

Since the slope of a vertical line does not exist, hence the equation of the line cannot be written in point-slope form

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Answer:

slope of the line will be [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

We have to find the slope of a given line whose equation is 4y - 3x + 6 = 0

If a line is in the form of y = mx + c

Then m represents slope of the line

4y - 3x + 6 = 0     [ Given equation ]

4y = 3x - 6

y = [tex]\frac{1}{4}[/tex] ( 3x-6 )

y = [tex]\frac{3}{4}x[/tex] - [tex]\frac{3}{2}[/tex]

Therefore, slope of the line will be [tex]\frac{3}{4}[/tex]

perimeter = 2W+2L

Length = 4W

160 = 2W +2(4W)

160 = 10W

w = 160/10 = 16 yards

length = 16*4 = 64 yards

Check:

64*2 = 128, 16*2 = 32

128+32 = 160

Length = 64 yards, Width = 16 yards

Answer: No

Step-by-step explanation: It does not go through the origin (0,0) in a straight line. Also, it has a y-intercept, meaning it doesn't go through the origin (0,0) and goes through the line that is up and down; vertically.

The total number of grandchildren of Kamiko and her 4 sisters is 72.

Kamiko and her 4 sisters each have 18 grandchildren. To calculate the total number of grandchildren, we will multiply the number of grandchildren per person by the total number of sisters.

Number of grandchildren per person: 18

Total number of sisters: 4

Therefore, the total number of grandchildren of Kamiko and her 4 sisters is 72.

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The unit rate at which Belmond cuts bricks is 28 bricks per hour, which is calculated by dividing the total number of bricks (84) by the total hours worked (3).

To find the unit rate of bricks cut per hour by Belmond, we simply divide the total number of bricks by the total time in hours. Belmond cuts 84 bricks in 3 hours, so the unit rate is:

Unit rate = Total bricks \/ Total time in hours
Unit rate = 84 bricks \/ 3 hours = 28 bricks per hour

This means that Belmond cuts 28 bricks every hour. When you need to find a unit rate, it is a matter of dividing the total quantity by the time it takes to accomplish that quantity, thus yielding the rate per single time unit (in this case, per hour).

A binary search in a set of 64 sorted items will, in the worst-case scenario, require 6 comparisons. This is calculated as log2(64) = 6. The binary search method works by repeatedly halving the search interval until it finds the desired item.

In order to find out how many comparisons are needed for a binary search in a set of 64 elements, we need to understand how a binary search works. It's an efficient algorithm that finds an item from a sorted list by repeatedly dividing the search interval in half. Every time it analyzes the middle element, it either discards the half that it is sure does not contain the desired item, or determines that the middle element is the desired item.

With a set of 64 elements, a binary search would perform log2(64) or 6 comparisons, as the base-2 logarithm of 64 is 6. Therefore, the maximum number of comparisons necessary using a binary search to locate a particular item in a set of 64 elements is 6 comparisons.

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In a binary search of a 64 element set, the worst-case scenario requires 6 comparisons. This is determined by the base 2 logarithm of the number of elements.

The number of comparisons in a binary search is governed by the logarithm base 2 of the number of elements in the set. With a set of 64 elements, the worst case scenario for the number of comparisons needed would be log2(64) which equals 6. This is because a binary search works by repeatedly dividing the searchable set in two until it finds the desired element, making it a very efficient search algorithm.

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Answer:

The rate of change of the volume of the cylinder when the radius is 10 ft is

[tex]\frac{dV}{dt}=400\pi \:{\frac{ft^3}{min} }[/tex]

Step-by-step explanation:

This is a related rates problem. A related rates problem is a problem in which we know the rate of change of one of the quantities (the height of a grain) and want to find the rate of change of the other quantity (the volume of grain in the cylinder).

The volume of a cylinder is given by

[tex]V=\pi r^2 h[/tex]

V and h both vary with time so you can differentiate both sides with respect to time, t, to get

[tex]\frac{dV}{dt}=\pi r^2 \frac{dh}{dt}[/tex]

Now use the fact that [tex]\frac{dh}{dt} = 4 \:{\frac{ft}{min} }[/tex] and [tex]r = 10 \:ft[/tex]

[tex]\frac{dV}{dt}=\pi (10)^2 \cdot 4\\\\\frac{dV}{dt}=100\cdot \:4\pi \\\\\frac{dV}{dt}=400\pi[/tex]

The point slope form of the line has the following form:

y – y1 = m (x – x1)

The slope m can be calculated using the formula:

m = (y2 – y1) / (x2 – x1)

m = (1 - -3) / (4 – 0) = 1

So the whole equation is:

y – -3 = 1 (x – 0)

y + 3 = x

The number of people George can feed is 6.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, George bought 4 submarine sandwiches for a birthday party.

Each person will eat 2/3 of a sandwich

Number of people George can feed

= 4÷2/3

= 4×3/2

= 6

Therefore, the number of people George can feed is 6.

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The solution to the system of equations is x = 1, y = 2, and z = -1.

The given system of equations is:

1. x + y - 2z = 5

2. -x + 2y + z = 2

3. 2x + 3y - z = 9

We can solve this system using various methods such as substitution, elimination, or matrices. Let's use the elimination method to solve this system:

1. Add equations (1) and (2):

(x + y - 2z) + (-x + 2y + z) = 5 + 2

x - x + y + 2y - 2z + z = 7

3y - z = 7   (Equation 4)

2. Multiply equation (2) by 2 and add it to equation (3):

2(-x + 2y + z) + (2x + 3y - z) = 2 × 2 + 9

-2x + 4y + 2z + 2x + 3y - z = 4 + 9

7y + z = 13  (Equation 5)

Now we have equations (4) and (5):

4. 3y - z = 7

5. 7y + z = 13

Let's solve this system by adding equations (4) and (5):

(3y - z) + (7y + z) = 7 + 13

3y + 7y = 20

10y = 20

y = 2

Now that we have found y = 2, we can substitute this value into either equation (4) or equation (5) to solve for z.

Let's use equation (4):

3(2) - z = 7

6 - z = 7

-z = 7 - 6

-z = 1

z = -1

Now that we have found y = 2 and z = -1, we can substitute these values into any of the original equations to solve for x.

Let's use equation (1):

x + 2 - 2(-1) = 5

x + 2 + 2 = 5

x + 4 = 5

x = 5 - 4

x = 1

Complete Question may be:

Solve the system of equations:

x + y - 2z = 5

-x + 2y + z = 2

2x + 3y - z = 9