A moving truck claims to hold 300 cubic feet of boxes. The truck is 25 feet in length and 8 feet in height. What is the width of the moving truck?

Answer:

Step-by-step explanation:

Statements 1, 2, 5 are all true

Assuming that the clock is circular, the length of the minute hand is the radius.

The distance that the tip of the minute hand moves in a given time is the length of an arc along the circle.  

If s is the length of arc, then s = rθ, where r is the radius and θ is the measure (in radians) of the central angle formed by the initial position and the final position of the minute hand (measured clockwise).  

(a)

r = 2.5"

20 minutes is 1/3 of an hour.

Since there are 2π radians in 1 rotation of the minute hand (1 hour),

θ = (1/3)(2π) = 2π/3.

So, s = rθ = (2.5")(2π/3) = 10π/3 inches ≈ 5.24"

(b)

A = π x ^ 2 x 2

3.14 x 15 x 15 = 706.5

The area of the watch face is covered by the minute hand in 30 minutes is 706.5

hope you understood this question

Answer:

  y = -1/500x² +2/5x

Step-by-step explanation:

You want the equation for the path of a football that is thrown 200 m downfield and reaches a maximum height of 20 m.

The initial height is not given. The equation is much more easily written if we assume it is zero, or we assume the launch height is the same height at which the ball is caught.

We know the maximum height is reached halfway between the launch point and the final point of interest. Then we're required to write the equation of a parabola that passes through the points (0, 0), (100, 20), and (200, 0).

Since we know the x-intercepts, we can write the equation as ...

  y = ax(x -200)

Then all we have to do is find the value of 'a' so the equation has (100,20) as a solution.

  20 = a(100)(100 -200) = -10000a

  a = -1/500 . . . . . divide by -10000

The equation of the path of the football is ...

  y = (-1/500)(x)(x -200)

  y = -1/500x² +2/5x

__

Additional comment

When x=185, y = -1/500(185)(185 -200) = 15/500(185) = 5.55 . . . meters

The domain is [0, 200]; the range is [0, 20].

To achieve that distance and height, the football would need to be thrown at a speed in excess of 119 miles per hour. For comparison, the fastest baseball pitch ever thrown was 108.1 miles per hour.

Answer:

0

Step-by-step explanation:

Answer: To compute the volume of a prism, we need to know the area of the base and the height of the prism. Assuming that the prism has a rectangular base, the formula for the volume of the prism is:

Volume = Area of Base × Height

Let's assume that the length and width of the rectangular base are both equal to 2d (since we don't have specific dimensions). The height of the prism is also equal to d, as given.

When d = 1:

The area of the base is 2d × 2d = 4 square units

The height is d = 1 unit

Therefore, the volume is:

Volume = Area of Base × Height = 4 × 1 = 4 cubic units

When d = 2:

The area of the base is 2d × 2d = 8 square units

The height is d = 2 units

Therefore, the volume is:

Volume = Area of Base × Height = 8 × 2 = 16 cubic units

When d = 1/2:

The area of the base is 2d × 2d = 1 square unit

The height is d = 1/2 unit

Therefore, the volume is:

Volume = Area of Base × Height = 1 × (1/2) = 1/2 cubic units

So, the volume of the prism is 4 cubic units when d=1, 16 cubic units when d=2, and 1/2 cubic units when d=1/2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given : O is the centre of the circle with radius r. AB, CD and EF are the diameters of the circle. ∠OAF = ∠OCB = 60°.

To Find : What is the area of the shaded region?​

Solution:

∠OAF =   60°

OA = OF  = Radius

=> ΔOAF is Equilateral Triangle

∠OCB = 60°

OC = OB Radius

Hence ΔOCB  is Equilateral Triangle

∠AOF = 60° , ∠BOC = 60°

=> ∠COF = 180° - 60° - 60° = 60°   as  AC is straight Line

∠DOE  = ∠COF ( vertically opposite angle )

∠DOE  =   60°

ΔODE is also an equilateral Triangle

Each sector has 60 ° angle

Area of shaded region  =  (60/360)πr² - (√3/4) r²

= r² (π/6 - √3/4)

= (r²/6) (π  - 3√3/2)

Area of 3 shaded regions

= 3  (r²/6) (π  - 3√3/2)

= (r²/2) (π  - 3√3/2)

(r²/2) (π  - 3√3/2)  is the correct answer

Answer: W=10pi

Step-by-step explanation:

Answer:

To draw a line graph, you need to plot your data on the graph. For example, if you have the data for the number of cars produced in a year, you would plot the number of cars on the Y-axis and the year on the X-axis. Then, you would trace both lines to the point where they intersect and place a dot on the intersection. You would repeat this process for each year and then connect the dots with a line.

Answer:

u ≤ 9

Step-by-step explanation:

5u ≤ 45 ( divide both sides by 5 )

u ≤ 9

The equation that correctly compares the number of marbles used, x, to the number of blue marbles, y, is y = 3/8x.

To calculate the number of marbles used, x, and the number of blue marbles, y, Molly is making, the following equation can be used: y = 3/8x. This equation states that for every 8 marbles used, 3 of them will be blue. For example, if Molly uses 24 marbles, then 3/8x = 3/8(24) = 9. Therefore, 9 of the 24 marbles will be blue. To calculate the number of blue marbles for a different number of marbles used, x, the equation can be rearranged to solve for y. For example, if Molly uses 48 marbles, then the equation can be rearranged to y = 8/3x, and then 8/3(48) = 16. Therefore, 16 of the 48 marbles will be blue.

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Answer: 210

Step-by-step explanation:

The value of 14x15 is 210.

If an art teacher ordered 26 sets for class and there are 100 markers in each set, then the total number of markers is:

26 x 100 = 2600

Therefore, there would be 2600 markers in 26 sets.

Answer:

tan(sin^-1(-1)) is undefined.

The inverse sine function returns a value between -pi/2 and pi/2, and since sin(-pi/2) = -1, sin^-1(-1) = -pi/2. However, at -pi/2, the tangent function is undefined since it results in a vertical asymptote.

Decimal form of number 39.76% is,

= 0.3976

We have to write,

A number 39.76% into a decimal form.

Now, We can write the number in decimal form as,

= 39.76%

= 39.76 / 100

= 0.3976

Therefore, Decimal form of number 39.76% is,

= 0.3976

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Answer:

(1, -4)

Step-by-step explanation:

if you rotate from quadrant 3 to 4, x=-y and y=x

After the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).

Given is the coordinate of point as (-4, - 1). It is rotated by 90° clockwise about the origin.

When we rotate a figure 90 degrees clockwise about the origin, then the new coordinates will be -

A(x, y) → A(y, - x)

Then, we can write the new coordinates according to the rule as -

P(-4, - 1) → P'(- 1, - 4)

Therefore, after the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).

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Answer: { (-1/2)x - 1, -2 ≤ x ≤ 4

Step-by-step explanation:

Let's start with the first line:

The line passes through two points: (-5, 8) and (-2, 2). The hollow circle at (-5, 8) indicates that this point is not included in the graph, while the closed circle at (-2, 2) indicates that this point is included.

We can find the slope of the line using the two points:

slope = (change in y) / (change in x) = (2 - 8) / (-2 - (-5)) = -6 / 3 = -2

Using point-slope form, we can write the equation of the line as:

y - 2 = -2(x - (-2))

Simplifying:

y - 2 = -2x - 4

y = -2x - 2

Next, let's consider the second line:

The line passes through two points: (-2, -2) and (4, -5). The hollow circle at (-2, -2) indicates that this point is not included in the graph, while the closed circle at (4, -5) indicates that this point is included.

We can find the slope of the line using the two points:

slope = (change in y) / (change in x) = (-5 - (-2)) / (4 - (-2)) = -3 / 6 = -1/2

Using point-slope form, we can write the equation of the line as:

y - (-2) = (-1/2)(x - (-2))

Simplifying:

y + 2 = (-1/2)x + 1

y = (-1/2)x - 1

Now we can write the piecewise function:

f(x) = { -2x - 2, -5 ≤ x < -2

{ (-1/2)x - 1, -2 ≤ x ≤ 4

This piecewise function represents the two lines graphed on the given axes, where the first line is defined for x values between -5 and -2 (inclusive on -2 but not on -5), and the second line is defined for x values between -2 and 4 (inclusive on both).

Answer:

the gradient of the line is 7.

Step-by-step explanation:

To find the gradient of the straight line that passes through the points (3,1) and (8,36), we use the formula:

Gradient = (change in y) / (change in x)

The change in y is the difference between the y-coordinates of the two points, which is:

36 - 1 = 35

The change in x is the difference between the x-coordinates of the two points, which is:

8 - 3 = 5

Therefore, the gradient of the straight line is:

Gradient = (change in y) / (change in x) = 35 / 5 = 7

So the gradient of the line is 7.

Answer:

Column 1:

[tex]\pi/3[/tex] (given)

[tex]5\pi/4[/tex]

[tex]11\pi/6[/tex]

Column 2:

[tex]\sqrt{3}/2[/tex]

[tex]-\sqrt{2}/2[/tex] (given)

[tex]-1/2[/tex]

Column 3:

all given

Column 4:

[tex]\sqrt{3}[/tex]

[tex]1[/tex]

[tex]-\sqrt{3}/3[/tex] (given)

Step-by-step explanation:

Solved by using unit circle and inverse trig functions

The only significant variation between the red and black graphs is the scales used for the x and y axes. The two graphs both display the same quadratic function.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-degree polynomial problem in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given :

The quadratic function f(x) = -16x2 + 120x + 10 is depicted in both the red and black graphs, however, they are plotted at various scales. In comparison to the black graph, the red graph has a narrower range on both the x and y axes.

On both graphs, the parabola's vertex, or lowest point on the curve, is situated at x = 3.75 and y = 412.5.

This indicates that the cannonball's maximum height is 412.5 feet, and it does so at a horizontal distance of 3.75 feet from the cannon.

The only significant variation between the red and black graphs is the scales used for the x and y axes. The two graphs both display the same quadratic function.

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Answer:

area=192.6yards^2

Step-by-step explanation:

9×2.2=19.8÷2= 9.9 for area of one of the triangles

19.2×9=172.8 for area of the rectangle

21.4-19.2=2.2

2.2×9=19.8÷2=9.9

19.8+172.8=192.6

Answer: its a

Step-by-step explanation:

Answer:

1,45

Step-by-step explanation:

[tex] \frac{29 \times 5\%}{100\%} = 1.45[/tex]

The standard error of the sampling distribution of sample proportions for samples size

1) n = 35 ⇒ SE = 0.07

2) n = 100 ⇒ SE = 0.04

3) n = 250 ⇒ SE = 0.03

We know that the formula for thr standard error(SE) of the sample Proportion is:

SE = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

as the sample size increases, the standard error decreases.

Here, the percentage of people who prefer dogs to cats is 78%

so, p = 0.78

For samples of size n = 35,

SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{35} }[/tex]

SE = [tex]\sqrt{\frac{0.1716}{35} }[/tex]

SE = 0.07

For sample size n = 100,

SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{100} }[/tex]

SE = [tex]\sqrt{\frac{0.1716}{100} }[/tex]

SE = 0.041

For samples of size n = 250,

SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{250} }[/tex]

SE = [tex]\sqrt{\frac{0.1716}{250} }[/tex]

SE = 0.03

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The complete question is:

The percentage of people who prefer dogs to cats is 78% for a given population. What is the standard error of the sampling distribution of sample proportions for samples of size n=35, n=100, and n=250?

The probability that a randomly selected adult does not meet the "US-military"  standards is 16%.

The "IQ-scores" follow a normal distribution having mean = 100 and  standard deviation = 15.

In order to find the probability that a randomly selected adult does not meet US-military enlistment standards (which is an IQ score of less than 85),

We need to find the area under the normal-distribution curve to the left of 85,

Using the z-score formula, we can convert the IQ score of 85 to a standard score (z-score):

⇒ z = (x - μ)/σ,

Where x = IQ score, μ = mean, and σ = standard deviation.

Substituting the values,

We get,

⇒ z = (85 - 100)/15 = -1,

The area to left of -1 in a standard normal distribution table, we get approximately 0.1587 = 15.87% ≈ 16%.

Therefore, the required probability is 16%.

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Lynne can buy 5 apples and 6 oranges with her $8.00.

The first thing to do is determine how much money Lynne spends on the apples. Since she is buying 5 apples,

we can multiply the price of each apple ($0.65) by 5: $5 * 0.65 = $3.25

Therefore, Lynne has $8 - $3.25 = $4.75 to spend on oranges.

Now we need to determine the maximum number of whole oranges that she can buy with $4.75. We can do this by dividing $4.75 by the price of each orange ($0.75): $4.75 ÷ $0.75 = 6.33.

Since we can't buy a fraction of an orange, the maximum number of whole oranges Lynne can buy is 6. Therefore, Lynne can buy 5 apples and 6 oranges with her $8.00.

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The overall DPMO for the boards would be 4750.

Boardwalk Electronics manufactures 200,000 circuit boards per month. A random sample of 4,000 boards is inspected every week for seven characteristics. During a recent week, seven defects were found for one characteristic, and two defects each were found for the other six characteristics. If these inspections produced defect counts that were representative of the population, the dpmo's for the individual characteristics and what is the overall dpmo for the boards would be as follows:To calculate the DPMO, the formula used is:DPMO = (Number of defects / Number of Opportunities) × 1,000,000For Characteristic

1:Number of defects = 7Number of opportunities = 4000DPMO = (7/4000) × 1,000,000= 1750For Characteristic 2:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 3:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 4:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 5:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 6:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 7:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500The overall DPMO for the boards would be the sum of the DPMO of all characteristics which would be 1750 + 500 + 500 + 500 + 500 + 500 + 500 = 4750.

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The height of the can is approximately 9.74 centimeter.

The surface area of a cylinder is the total area of the curved and flat surfaces that make up the cylinder. It can be calculated using the formula:

SA = 2πr² + 2πrh

where r is the radius of the cylinder and h is its height.

In this case, we are given that the diameter of the can is 4 cm, which means the radius is 2 cm.

We are also given that the surface area is 130 square centimeters. Substituting these values into the formula, we get:

130 = 2π(2)² + 2π(2)h

Simplifying this equation, we get:

130 = 8π + 4πh

Subtracting 8π from both sides, we get:

122 = 4πh

Dividing both sides by 4π, we get:

h = 122/(4π) ≈ 9.74 cm (rounded to the nearest hundredth using 3.14 for π)

Therefore, the height of the can is approximately 9.74 cm.

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Answer:

america

Step-by-step explanation:america!!

The statement " a shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint" is true because  shadow prices provide valuable information about the marginal value of resources and constraints in linear programming problems

A shadow price represents the marginal value of a resource or constraint in a linear programming problem. It indicates how much the optimal value of the objective function will increase if the right-hand side of a constraint is increased by one unit, while keeping all other constraints and variables fixed. The shadow price of a constraint is calculated by adding one unit to the right-hand side of the constraint and re-solving the linear programming problem.

The resulting increase in the objective function value is the shadow price of that constraint. Shadow prices are useful in making decisions about resource allocation, pricing, and capacity planning in a variety of industries such as manufacturing, transportation, and energy.

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The equation y = a√x² is equal to y = 0.1√x² given that y = 0.4 when

x = 4. We also found that when x = 100, y = 10 and when y = 1.4, x = 14.

Given y = a√x² and y = 0.4 when x = 4.

a. To find y in terms of x, we substitute the given values into the equation y = a√x² as follows:

0.4 = a√4²

0.4 = 4a

Dividing both sides by 4, we get:

a = 0.1

Therefore, the equation becomes:

y = 0.1√x²

b. To find y when x = 100, we substitute x = 100 in the equation y = 0.1√x² as follows:

y = 0.1√10000

y = 10

Therefore, when x = 100, y = 10.

c. To find x when y = 1.4, we substitute y = 1.4 in the equation y = 0.1√x² as follows:

1.4 = 0.1√x²

Squaring both sides, we get:

1.96 = 0.01x²

Dividing both sides by 0.01, we get:

x² = 196

Taking the square root of both sides, we get:

x = ±14

Since x represents a distance, it cannot be negative. Therefore, x = 14.

Therefore, when y = 1.4, x = 14.

In conclusion, we found that the equation y = a√x² is equal to y = 0.1√x² given that y = 0.4 when x = 4. We also found that when x = 100, y = 10 and when y = 1.4, x = 14.

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If the rate of decay is proportional to the amount of the substance present at time t, then the amount remaining after 24 hours is 57.7 milligrams

Now we need to find the value of k. We know that the mass decreased by 5% after 6 hours, which means that the amount remaining is 95% of the initial amount. We can substitute these values into our formula and solve for k:

0.95 initial amount = initial amount x (1 - k x initial amount)⁶

Simplifying this equation, we get:

1 - [tex](0.95)^{(1/6)})[/tex] = k x initial amount

Solving for k, we get:

k = (1 - [tex](0.95)^{(1/6)})[/tex]) / initial amount

Now we can use this value of k to find the amount remaining after 24 hours:

Amount remaining = 100 x (1 - k x 100)²⁴

Plugging in the value of k, we get:

Amount remaining = 100 x (1 - (1 - [tex](0.95)^{(1/6)})[/tex] * 100)²⁴

Evaluating this expression, we get:

Amount remaining = 57.7 milligrams

Therefore, after 24 hours, there will be approximately 57.7 milligrams of the radioactive substance remaining.

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