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Question the formula (equation) for finding the VOLUME of a rectangular prism is?
A= 1/2 bh

A= lw

V= lwh

V= x + 3

A. A table of values and graph of the function is shown below.

B. The object would hit the ground at approximately 8.963 seconds.

Based on the information provided, we can logically deduce that the height (s) in meters, of this object above the​ ground is related to time by the following quadratic function:

s(t) = -4.9t² +39.2t + 42.3

When t = 0, s(t) is given by;

s(0) = -4.9(0)² +39.2(0) + 42.3

s(0) = 42.3

When t = 1, s(t) is given by;

s(1) = -4.9(1)² +39.2(1) + 42.3

s(1) = 76.6

When t = 2, s(t) is given by;

s(2) = -4.9(2)² +39.2(2) + 42.3

s(2) = 101.1

Therefore, the table can be created as follows;

Time (t)     Height s(t)

0                  43.3

1                   76.6

2                  101.1

3                  115.8

4                  120.7

5                  115.8

Part B.

Generally speaking, the height of this object would be equal to zero (0) when it hits the ground. By critically observing the graph (see attachment), we can logically deduce that the object would hit the ground at approximately 8.963 seconds.

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Step-by-step explanation:

Let's start by using the formula for the volume of a cylinder:

V = πr^2h

where V is the volume of the cylinder, r is the radius of the cylinder, h is the height of the cylinder, and π is a mathematical constant (approximately equal to 3.14).

Since we are dealing with a drain pipe, we can assume that the height of the cylinder is fixed and does not change. Therefore, we can rewrite the formula as:

V = πr^2h = Ah

where A is the cross-sectional area of the cylinder.

Now, let's use the given information that the drain pipe can carry 36 litres per second. We know that the volume of water that passes through the pipe in one second is equal to 36 litres. We can therefore write:

36 = Ahv

where v is the velocity of the water flowing through the pipe. Since we are assuming that the height of the cylinder is fixed, we can simplify this equation to:

36 = Av

Now we need to determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second. Let's call the new diameter d2 and the old diameter d1. We can set up a proportion to solve for d2:

A1/A2 = d1^2/d2^2

We know that A1 and A2 are proportional to the volumes of water the pipe can carry, so we can write:

A1/A2 = 36/60

Simplifying this equation, we get:

A1/A2 = 3/5

Substituting in the formula for the cross-sectional area of a cylinder, we get:

πd1^2/4 / πd2^2/4 = 3/5

Simplifying further, we get:

d1^2/d2^2 = 3/5

Taking the square root of both sides, we get:

d1/d2 = sqrt(3/5)

Now we can solve for d2:

d2 = d1 / sqrt(3/5)

We want to know the percentage increase in the diameter, which we can find using the formula:

% Increase = (New Value - Old Value) / Old Value x 100%

Substituting in our values, we get:

% Increase = (d1 / sqrt(3/5) - d1) / d1 x 100%

Simplifying, we get:

% Increase = (1 / sqrt(3/5) - 1) x 100%

Using a calculator, we get:

% Increase ≈ 34.64%

Therefore, the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is approximately 34.64%.

The solution is:

The average speed of bicyclist is 120 miles per hours

The speed of wind is 30 miles per hours .

Here, we have,

Given as :

The distance that bicyclist cover = d = 30 miles

The time taken by bicyclist to cover 30 miles = t = 5 hours

Let the average speed of bicyclist = x miles per hours

Let The speed of wind = y miles per hours

Now, biking into wind

The time taken in return by bicyclist = 5 hours

∵ Speed = Distance × time

i.e  x + y = d × t

∴  x + y = 30 miles × 5 hours

Or, x + y = 150 mi/h          ...........A

Again

Now, biking against wind

The time taken in return by bicyclist = 3 hours

∵ Speed = Distance × time

i.e  x - y = d × t

∴  x - y = 30 miles × 3 hours

Or, x - y = 90 mi/h                  ......B

Solving equation A and B

(x + y) + (x - y) = 150 mi/h + 90 mi/h

Or, (x + x) + (y - y) = 240 mi/h

Or, 2 x + 0 = 240 mi/h

∴   x = 240/2

i.e. x = 120 mi/h

So, The average speed of bicyclist = x = 120 miles per hours

Now, Put the value of x into eq B

∵ x - y = 90 mi/h

Or,  120 mi/h  - y = 90 mi/h

∴ y = 120 mi/h - 90 mi/h  

I.e.  y = 30 mi/h

So, The  speed of wind = y = 30 miles per hours

Hence, The average speed of bicyclist is 120 miles per hours

And The speed of wind is 30 miles per hours .

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complete question:

Biking into the wind on a flat path, a bicyclist takes 5 hours to travel 30 miles. The return bike takes 3 hours. The wind speed remains constant during the trip. What is the bicyclist's average speed in the air? What is the speed of the wind?

Answer:

x = 71

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

then

[tex]log_{4}[/tex] (x - 7) = 3 , then

x - 7 = 4³ = 64 ( add 7 to both sides )

x = 71

Answer:

Hope this helps :)

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{2}{3}[/tex]

When dividing by a fraction, we just have to multiply by the reciprocal, making the equation:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{2}[/tex]

Then we multiply and end up with:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{2}[/tex] [tex]=\frac{3}{4}[/tex]

The choice of measure depends on the characteristics of the data and the purpose of the analysis.

The measure commonly used to describe the center of the data is the arithmetic mean or average. The arithmetic mean is calculated by summing all the data points and dividing the sum by the total number of data points. It provides a representative value that balances the contributions of all the data points.

Another measure of center is the median, which represents the middle value when the data is arranged in ascending or descending order. Unlike the mean, the median is not affected by extreme values or outliers, making it a robust measure of central tendency.

Additionally, there is the mode, which represents the most frequently occurring value in the dataset. It can be useful in cases where identifying the most common observation is important.

Each measure has its strengths and limitations, and researchers need to consider the nature of the data and the research question at hand to determine the most appropriate measure of center

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Answer:

undefined

Step-by-step explanation:

To find the slope of the line passing through the points (4, 7) and (4, -6), we can use the slope formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates of the points (4, 7) and (4, -6) into the formula:

m = (-6 - 7) / (4 - 4)

m = (-13) / (0)

The denominator is zero, which means the line is vertical and parallel to the y-axis. When the denominator is zero, the slope is undefined.

Therefore, the line passing through the points (4, 7) and (4, -6) has an undefined slope.

Answer:

Step-by-step explanation:

median is 37 mode is 20

Vector v can be written as the sum of two vector components, [tex]v_x = -5i[/tex]  and [tex]v_y = 6j[/tex]

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as [tex]v_x[/tex] and the component along the y-axis as [tex]v_y.[/tex]

The x-component, [tex]v_x,[/tex] represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

[tex]v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5[/tex]

Similarly, the y-component, [tex]v_y,[/tex] represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

[tex]v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6[/tex]

Now, we can write vector v as the sum of its components:

[tex]v = v_x + v_y = -5i + 6j[/tex]

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

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The correct comparison symbol from the drop-down box is,

⇒ 0.67 = 0.670

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

To compare between 0.67 and 0.670

Now, We know that;

The value of zero after any number in decimal expression has neglect.

So, By definition of decimal numbers, we get;

The correct comparison symbol from the drop-down box is,

⇒ 0.67 = 0.670

Hence, The correct comparison symbol from the drop-down box is,

⇒ 0.67 = 0.670

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Answer:

D

Step-by-step explanation:

To reach this, you would divide both by half.

8.5 ÷ 2= 4.25

11 ÷ 2= 5.5

therefore, D

Answer:

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

There are 12 months in a year.

Multiply 25 by the number of months to get the number of e-mails per year:

Answer:

300

Step-by-step explanation:

To calculate the number of emails sent in a year based on an average of 25 emails per month, you simply multiply the average monthly emails by the number of months in a year.

Average emails per month: 25

Number of months in a year: 12

Therefore,

Emails per month × Months per year

25 × 12 = 300 emails per year

So, on average, a person would send about 300 emails in a year.

Answer:

There are 47.2242 miles in 76 kilometers.

1.6 km = 1 mile

76 km = 76/1.6 = 47.5 mile

There are 47.5 miles in 76 kilometers.

The value of x, applying the trigonometric ratios, is given by the following option:

B) 8.0.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For this problem, we have that side x is opposite to the angle of 28º, while the hypotenuse has a length of 17.

Hence the length x is obtained as follows:

sin(28º) = x/17

x = 17 x sine of 28 degrees

x = 8.

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Angle EFG is an angle with a measure of 42 degrees is drawn below.

Given that, angle EFG= 42 degrees.

Angle EFG is an angle with a measure of 42 degrees. To draw angle EFG, first draw a line segment and mark two points on the line segment. Label the two points E and F. Then, using a protractor, measure out an angle with a measure of 42 degrees from the line segment EF, starting from point E. Finally, mark the end of the angle as point G.

Therefore, angle EFG is an angle with a measure of 42 degrees is drawn below.

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Answer:

  C.  1000/x + 5000/(2x -10)

Step-by-step explanation:

You want the total time a climber spent when he climbed 1000 feet at x feet per hour, and 5000 more feet at (2x -10) feet per hour.

The relation between time, speed, and distance is ...

  time = distance / speed

The total time is the sum of the times for the two distances.

The time for 1000 ft at x feet per hour is ...

  time 1 = 1000/x

The rate for the second part of the climb was 10 ft per hour less than twice the first rate, so was ...

  2x -10

Then the time for 5000 ft at this rate is ...

  time 2 = 5000/(2x -10)

The total time spent climbing was ...

  total = time 1 + time 2

  total = 1000/x + 5000/(2x -10) . . . . . . matches choice C

__

Additional comment

The relation between speed, time, and distance is usually seen as ...

  speed = miles per hour

As a fraction, this is ...

  speed = distance / time

Above, we rearranged this to ...

  time = distance / speed

It's just another form of the relationship ...

  distance = speed × time

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To reduce his entertainment percentage to 12.5% of his total spending and allocate the savings to his grocery budget, he needs to decrease his entertainment spending and increase his grocery budget accordingly.

To reduce the entertainment percentage to 12.5% of his total spending, the individual needs to make adjustments to his budget.

Calculate the current entertainment percentage:

Let's assume the individual's total spending is $X, and the current entertainment spending is $Y.

The current entertainment percentage can be calculated by dividing Y by X and multiplying by 100.

Current entertainment percentage [tex]= (Y / X) \times 100[/tex]

Determine the desired entertainment spending:

To reduce the entertainment percentage to 12.5%, we need to find the new entertainment spending amount.

Let's call it Z.

Desired entertainment spending [tex]= 0.125 \times X[/tex]

Calculate the amount to be saved:

The amount to be saved is the difference between the current entertainment spending (Y) and the desired entertainment spending (Z).

Amount to be saved = Y - Z

Add the saved amount to the grocery budget:

The individual wants to add the money saved from the entertainment budget to the grocery budget.

Let's call the current grocery budget G.

The new grocery budget (G') will be:

New grocery budget = G + Amount to be saved

By following these steps, the individual can reduce his entertainment percentage to 12.5% of his total spending and allocate the saved money to the grocery budget.

It's important to note that the specific dollar amounts will depend on the individual's current spending and budget.

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The margin of error is given as follows:

D) +- 6.7%.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The parameters are given as follows:

[tex]n = 220, \pi = 0.38[/tex]

Hence the margin of error is given as follows:

[tex]M = 1.96\sqrt{\frac{0.38(0.62)}{220}}[/tex]

M = 0.067.

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y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

The measure of LA is . B'C'= 1, mLA' = 37"

A dilation is a mathematical operation that involves multiplying the distance between each point in an object and a fixed point, referred to as the center of dilation, by a constant factor known as the scale factor.

In the given scenario, the scale factor is specified as follows:

k = 1/3.

Consequently, the length of B'C' is obtained by multiplying the length of BC by 1/3, which can be understood as dividing the length by 3 after the dilation.

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The meaning of "ϕ(x, y, p)" depends on the context in which it is used. Without further information, it is difficult to determine the specific meaning of this expression. However, in mathematics and physics, the symbol "ϕ" often represents a function or a potential.

Symbol "ϕ": The symbol "ϕ" is a Greek letter called "phi" and is commonly used to represent various concepts in mathematics and physics. It is often used to denote a scalar function or a potential.

(x, y, p): The variables x, y, and p represent the independent variables or parameters of the function or potential ϕ. The specific interpretation of these variables depends on the context of the problem.

Function or Potential: In mathematics, a function ϕ(x, y, p) maps elements from the domain (x, y, p) to corresponding values in the range. The function can represent various mathematical relationships or operations.

In physics, the symbol "ϕ" often represents a potential, such as the electric potential or gravitational potential. In this case, ϕ(x, y, p) would represent the potential function that depends on the variables x, y, and p.

Further Context: To fully understand the meaning of "ϕ(x, y, p)", additional information about the specific field of study or problem is necessary. Different disciplines may assign different meanings to this expression.

In conclusion, without additional context, "ϕ(x, y, p)" represents a function or potential with variables x, y, and p. The specific interpretation and meaning of this expression depend on the field of study or problem at hand.

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Answer:

B: 2/9

Step-by-step explanation:

There are a total of 9 bills in Scott's pocket, and he has 2 five dollar bills.

This means that the probability of pulling out a 5 dollar bill is 2/9.

The solution for the given expression is  7 + 5/12

First we need to write the expression, using fractions, we will get:

(5 + 6/8) + (4 + 4/15) - (2 + 6/10)

We can group like terms, and we will get:

(5 + 6/8) + (4 + 4/15) - (2 + 6/10) = (5 + 4 -2) + (6/8 + 4/15 - 6/10)

Now just simplify that to get.

(5 + 4 -2) + (6/8 + 4/15 - 6/10) =  7 + 3/4 + 4/15 - 3/5

                                                =  7 + 3/4 + 4/15 - 9/15

                                                = 7 + 3/4 - 5/15

                                                = 7 + 9/12 - 4/12

                                                 = 7 + 5/12

That is the answer.

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The total number of shirts in the dresser is 4y + ×. The correct option is A

We need to add up the number of shirts on each shelf.

The first shelf's shirt count is indicated with the number x.

y indicates how many shirts are present on each of the four remaining shelves.

We may add up the shirts on each rack to determine the overall number of shirts:

Total = x + y + y + y + y

Simplifying the expression, we have:

Total = x + 4y

Therefore, The total number of shirts in the dresser is 4y + ×.

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Answer:

50 students will pass

Step-by-step explanation:

100÷40=2.5

20×2.5=50

or another way is 20 is half of 40 so half of 100 is 50

Answer:

The area of a leaf is obtained by using a graph paper. A graph paper has small squares of area 1 mm 2 each. The area of the leaf will be equal to the number of squares it covers on the graph paper.

Step-by-step explanation:

The value of angle C is calculated by applying cosine rule as  50.67 ⁰.

The value of angle C is calculated by applying cosine rule as shown below;

c² = a² + b² - 2ab cosC

The given parameters in the diagram;

length a = 22

length b = 18

c = 20

The value of angle C is calculated as;

20² = 22² + 18² - (2 x 22 x 18) cos C

792 cos C = 502

cos C = 502/792

cos C = 0.6334

C = arc cos (0.6334)

C = 50.67 ⁰

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Answer:

hello

the answer is:

total mass = 3.94 + 14.81 + 11.27 + 7.65 = 37.65 kg