Find the average for the set of numbers 7, 6, 12, 5, 7, 6, 13.

Answer:

The height of the desk is 8 cubic inches.

Hope this helps!

Step-by-step explanation:

The formula for the volume of a rectangular prism is Width × Length × Height or Base × Height.

Because the Base is already given ( 400 in² ), that means the height of the desk can be found by dividing 3200 by 400.

3200 ÷ 400 = 8

The height of the desk will be 8 cubic inches.

According to the information, the ball returns to the ground about 13.6 feet away.

To calculate how many feet away the ball returns to the ground we have to consider that the ball starts 0 feet above the ground (assuming the ground level is the reference point, where h(x) = 0).

To find the maximum height, we need to find the vertex of the parabola, which occurs at

x = -b/2a

where,

a = -0.25

b = 3.4.

x = -3.4 / (2 * (-0.25)) = 6.8

So, the ball reaches a max height of h(6.8) = -0.25(6.8)^2 + 3.4(6.8) = 8.2 feet at a horizontal distance of 6.8 feet away from the club it was hit with.

To find when the ball returns to the ground, we set h(x) = 0 and solve for x:

0 = -0.25x^2 + 3.4x

0.25x(13.6 - x) = 0

x = 0 or x = 13.6

Since x = 0 is the starting point, the ball returns to the ground at x = 13.6 feet away from the club it was hit with.

Therefore, the ball returns to the ground about 13.6 feet away.

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The coordinates of a vertex of the image of D are (3, 1)

From the question, we have the following parameters that can be used in our computation:

The coordinates of point D is

D = (1, 3)

The transformation rule is given as

y = x

Mathematically, this is represented as

(x, y) = (y, x)

Substitute the known values in the above equation, so, we have the following representation

D' = (3, 1)

Hence, the image of point D is D' = (3, 1)

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The probability that the point that is selected randomly would be in the semicircular region would be = 0.28.

To calculate the probability of a selected point, the formula for probability should be chosen. That is;

Probably = possible outcome/sample space

Possible outcome is the area of the semicircle = πr²/2

where r = 5 in

Area of semicircle = 3.14×5×5/2

=78.5/2 = 39.25 in²

The sample space = area of semicircle+area of square.

But Area of the square;

= length×width

= 10×10 = 100in²

sample space = 100+39.25 =139.25

Probability = 39.25/139.25 = 0.28

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Answer:

C -1

Step-by-step explanation:

in such a case the simplest way is to simply try the 4 numbers and see :

x² - 3x - 4 = |x + 3| - 2

x² - 3x - 2 = |x + 3|

A x = -4

(-4)² - 3×-4 - 2 = |-4 + 3|

16 + 12 - 2 = 1

26 = 1

wrong.

B x = -3

(-3)² - 3×-3 - 2 = |-3 + 3|

9 + 9 - 2 = 0

16 = 0

wrong.

C x = -1

(-1)² - 3×-1 - 2 = |-1 + 3|

1 + 3 - 2 = 2

2 = 2

correct.

D x = 4

4² - 3×4 - 2 = |4 + 3|

16 - 12 - 2 = 7

2 = 7

wrong.

The probability of passing the test by random guessing is 0.003%.

To estimate the probability of passing a true/false test of 70 questions, we can use the normal approximation to the binomial distribution. Since each question has only two possible outcomes (true or false), the binomial distribution can be used to calculate the probability of getting a certain number of correct answers out of 70.

The mean of the binomial distribution can be calculated as np, where n is the number of trials (70) and p is the probability of success (0.5, since the responses are random guesses). The standard deviation of the binomial distribution can be calculated as the square root of np*(1-p).

To find the probability of passing the test, we need to find the number of correct answers required to achieve a score of 80% or higher. Since 80% of 70 is 56, we need to get at least 56 questions correct.

Using the normal approximation, we can approximate the binomial distribution with a normal distribution with mean 35 and standard deviation 4.79. To find the probability of getting at least 56 questions correct, we can standardize the value (56-35)/4.79 = 4.02 and look up the probability in a standard normal table. The probability of getting at least 56 questions correct is approximately 0.00003.

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Based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.

The margin of error is a measure of the uncertainty in the survey results. It is based on the sample size and the level of confidence desired. In this case, the margin of error is 1.7%.

This means that the actual percentage of citizens in the town who would support a new coffee shop could be as much as 1.7% higher or lower than the survey result of 37%.

To calculate the range of possible values for the percentage of citizens who would support a new coffee shop, we add and subtract the margin of error from the survey result:

37% + 1.7% = 38.7%

37% - 1.7% = 35.3%

Therefore, based on the survey, we can say that between 35.3% and 38.7% of the citizens in the town would support a new coffee shop.

To determine the number of people who would support a new coffee shop, we need to multiply the percentage by the population of the town:

35.3% of 36,170 = 12,776

38.7% of 36,170 = 14,000

Therefore, based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.

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The calculated range of the amount of rainfall in mm is 20.5 mm

From the question, we have the following parameters that can be used in our computation:

Data values in mm

0.0, 12.2, 2.1, 0.0, 20.5, 5.5 and 1.0

The range of the rainfall  is the difference between the least and the highest amount of rainfalls

Using the above as a guide, we have the following:

Range = 20.5 - 0.00

Evaluate

Range = 20.5

Hence, the range of rainfall is 20.5 mm

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The time to take the money to triple is, 15.2 years

We have to given that;

It is invested $9000 in an account earning 7.5% interest compounded continuously.

Hence, We can formulate;

27,000 = 9000 (1 + 7.5/100)ⁿ

3 = (1 + 0.075)ⁿ

3 = (1.075)ⁿ

log 3 = n log (1.075)

0.477 = n x 0.0314

n = 0.477 / 0.0314

n = 15.2 years

Thus, The time to take the money to triple is, 15.2 years

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Answer:

Step-by-step explanation:

To divide 18 by 5.5, we can use long division method as follows:

       _________

   5.5 | 18.0000

       -16.5

       ------

        1.5

We first divide 5.5 into the first digit of 18, which is 1. This gives us 0 as the whole number part of the quotient. We then multiply 0 by 5.5 to get 0, and subtract it from 1, which gives us 1.

We then bring down the next digit 0 and get 10. We then divide 5.5 into 15, which gives us 2 as the whole number part of the quotient. We then multiply 2 by 5.5 to get 11, and subtract it from 15, which gives us 4.

We then bring down the next digit 0 and get 40. We then divide 5.5 into 40, which gives us 7 as the whole number part of the quotient. We then multiply 7 by 5.5 to get 38.5, and subtract it from 40, which gives us 1.5.

Since there are no more digits to bring down and the remainder is less than the divisor 5.5, we can stop here. Therefore, the result of 18 divided by 5.5 is approximately 3.27, which we get from the quotient of 0.327 rounded to two decimal places.

So 18 divided by 5.5 is approximately 3.27 or 3.27 to two decimal places.

Answer:

3.27 to 2dp

Step-by-step explanation:

18÷5.5

18/1×11/2

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"z" varies directly with }x^2}{z = k(x^2)}\hspace{5em}\textit{we also know that} \begin{cases} z=96\\ x=4 \end{cases} \\\\\\ 96=k(4^2)\implies \cfrac{96}{4^2}=k\implies 6=k\hspace{8em}\boxed{z=6x^2} \\\\\\ \textit{when x = 3, what's "z"?}\qquad z=6(3^2)\implies z=54[/tex]

Answer:

It’s 2.07 pounds/in 3

Step-by-step explanation:

1 kilogram = 2.2 × pounds, so,2.07 × 1 kilogram = 2.07 × 2.2 pounds (rounded), or2.07 kilograms = 4.554 pounds.Step 2: Convert the decimal part in pounds to ouncesAn answer like "4.554 pounds" might not mean much to you because you may want to express the decimal part, which is in pounds, in ounces which is a smaller unit.So, take everything after the decimal point (0.55), then multiply that by 16 to turn it into ounces. This works because one pound equals 16 ounces. Thus,4.55 pounds = 4 + 0.55 pounds = 4 pounds + 0.55 × 16 ounces = 4 pounds + 8.8 ounces. So, 4.55 pounds = 4 pounds and 8 ounces (when rounded). Obviously, this is equivalent to 2.07 kilograms. Step 3: Convert from decimal ounces to a usable fraction of ounceThe previous step gave you the answer in decimal ounces (8.8), but how to express it as a fraction? See below a procedure, which can also be made using a calculator, to convert the decimal ounces to the nearest usable fraction: a) Subtract 8, the number of whole ounces, from 8.8:8.8 - 8 = 0.8. This is the fractional part of the value in ounces.b) Multiply 0.8 times 16 (it could be 2, 4, 8, 16, 32, 64, ... depending on the exactness you want) to get the number of 16th's ounces:0.8 × 16 = 12.8.c) Take the integer part int(12.8) = 13. This is the number of 16th's of a pound and also the numerator of the fraction.Finalmente, 2.07 quilogramas = 4 pounds 8 3/4 ounces.A fração 12/16 não está simplificada, e ainda pode ser reduzida para 3/4 para que possamos expressar como a fração mais simples possível.In short:2.07 kg = 4 pounds 8 3/4 ounces

The area of the composite figure is equal to 89.5 square yards

The composite figure can be observed to be made up of a large rectangle at the center with a smaller rectangle and a triangle by the sides, so we shall calculate for the area of the three shape and sum the results to get the total area of the composite figure as follows:

area of the larger rectangle = 14 yd × 5 yd = 70yd²

area of the smaller rectangle = 5 yd × 3 yd = 15 yd²

area of the triangle = 1/2 × 3 yd × 3 yd= 4.5 yd²

total area of the composite figure = 70yd² + 15 yd² + 4.5 yd²

total area of the composite figure = 89.5 yd²

Therefore, the area of the composite figure is equal to 89.5 square yards

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The sides of the figure is solved to obtain

1. 3x - 8 = 2x - 3

2. x = 5

3. 5y = 3y + 2

4. y = 1

5. BE = 12

6. GH = 5

7. HF = 5

The equation to solve for x is written knowing that the tangents CH and BH are equal

1. CH = BH

3x - 8 = 2x - 3

2. solving for x

3x - 2x = -3 + 8

x = 5

3. HG = HF

5y = 3y + 2

4. solving for y

5y - 3y = 2

2y = 2

y = 1

5. BE = BH + HF

BE = 2x - 3 + 3y + 2

BF = 2 * 5  - 3 + 3 * 1 + 2

BE = 10 - 3 + 3 + 2

BE = 12

6. GH = 5y = 5 * 1 = 5

7. HF = 3y + 2

HF = 3 * 1 + 2

HF = 5

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Answer:

Figure A is greater.

Step-by-step explanation:

Figure A has 60 cubic units in volume, if you do length x width x height you get 60. And for figure B the volume is 40 because of again l x w x h.

Reflecting a point across the x-axis changes the sign of its y-coordinate while keeping the x-coordinate intact. As such, Z' can be rewritten in terms of (x, -y).

If a rectangle shifts downward by five units and rightward by three units, the transformation rule can be expressed as: (x, y) → (x + 3, y - 5).

Conversely, the given equation for this specified action is: (x, y) → (x - 3, y - 4).

Similar but reversed in reflection across the y-axis, where instead it is the x-coordinate that sees its sign changed, given the conditions that the y-coordinate stays constant. Hence, the transformation can be stated as: (x, y) → (-x, y).

The same applies for a mathematical exchange when it comes to reflecting about the x-axis; here the y-coordinate has its signs reversed with no transition in the x-coordinate – simply put, we have as follows: (x, y) → (x, -y).

Finally, observing what occurs when rototating clockwise 270° around the origin reveals each point experiencing an equal shift from said anchor point; permitting us to formalize the related rule accurately as: (x, y) → (y, -x).

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Answer:

Sure give me a sec

Step-by-step explanation:

1) A system of equations has no solution if the graphs of the equations do not intersect.  2) A system of equations has exactly one solution if the graphs of the equations intersect at exactly one point.  3) A system of equations has exactly two solutions if the graphs of the equations intersect at exactly two points.

Systems with no solution

A system of equations has no solution if the graphs of the equations do not intersect. This can happen if the graphs are parallel, or if one graph is completely contained within the other graph.

For example, the graph of a linear equation is a line, and the graph of a quadratic equation is a parabola. If the line and the parabola are parallel, then they will never intersect, and the system will have no solution.

Another way for a system to have no solution is if one graph is completely contained within the other graph. For example, the graph of the equation y = x is completely contained within the graph of the equation y = [tex]x^2[/tex]. This means that there are no points that satisfy both equations, and the system will have no solution.

Systems with exactly one solution

A system of equations has exactly one solution if the graphs of the equations intersect at exactly one point. This can happen if the graphs are intersecting lines, or if the graphs are intersecting parabolas.

For example, the graph of the equations y = x and y = [tex]x^2[/tex] intersect at exactly one point, which is the point (0,0). This is because the two graphs intersect when x = 0, and there is no other point where they intersect.

Systems with exactly two solutions

A system of equations has exactly two solutions if the graphs of the equations intersect at exactly two points. This can happen if the graphs are intersecting parabolas that have different slopes.

For example, the graph of the equations y = [tex]x^2[/tex] and y = 2[tex]x^2[/tex] intersect at exactly two points, which are the points (0,0) and (1,1). This is because the two graphs intersect when x = 0 and when x = 1, and there are no other points where they intersect.

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U.S. or federal income taxes became public policy in 1913 with the ratification of the 16th Amendment of the U.S. Constitution that gave the Congress the right to charge and collect taxes. Over 41 U.S. states also levy and collect state income taxes. Even local governments may collect local taxes.

The 16th Amendment to the much-vaulted United States Constitution was officially ratified in the year 1913. This momentous action has allowed Congress to successfully levy and accumulate income taxes from both individuals and businesses nationwide.

Not only does the federal government take part in the process of collecting taxation by means of earnings, but its 41 associated states have also implemented their own income taxes against citizens living within. Rates remain distinctive between each region; with additional brackets for those with higher incomes who must pay accordingly.

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The three consecutive even integers are 6, 8, and 10, which satisfy the Pythagorean Theorem.

We have,

The Pythagorean Theorem in a right-angled triangle,

a² + b² = c²

To find three consecutive even integers that satisfy this theorem, we can start by assuming that one of the even integers is x.

Then, the next two consecutive even integers would be x+2 and x+4.

We can then use the Pythagorean Theorem to set up an equation and solve for x:

x² + (x+2)² = (x+4)²

Expanding and simplifying:

x² + x² + 4x + 4 = x² + 8x + 16

Simplifying further:

x² - 4x - 12 = 0

Now we can use the quadratic formula to solve for x:

x = [4 ± √(4² - 4(1)(-12))] / (2 x 1)

x = [4 ± √64] / 2

x = [4 ± 8] / 2

x = 6 or x = -2

Since we are looking for three consecutive even integers, we can discard the negative solution and choose x = 6.

This gives us the three consecutive even integers: 6, 8, and 10, which satisfy the Pythagorean Theorem:

6² + 8 = 10²

36 + 64 = 100

100 = 100

Thus,

The three consecutive even integers are 6, 8, and 10, which satisfy the Pythagorean Theorem.

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The complete question.

Find three consecutive even integers that satisfy the Pythagorean Theorem.

Answer:

Step-by-step explanation:

Barbara read the first 100 pages from a 320-page in the last four days

Judy read the first 54 pages of a 260-page book in the previous three days.

Nancy read the first 160 pages from a 480-page book in the  previous  five days

Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book(Show all work)

The integral of 1/(2+4x²+25x²) using partial integration is (1/2) arctan(10x) + C, where C is the constant of integration.

To solve this integral, we will use the technique of partial integration. This technique is also known as integration by parts and is used to find the integral of a product of two functions. The formula for integration by parts is as follows:

∫u dv = uv - ∫v du

where u and v are functions, and du/dx is the derivative of u with respect to x, and dv/dx is the derivative of v with respect to x.

Let's apply this formula to our integral:

∫1/(2+4x²+25x²) dx

We need to choose two functions, u and dv, such that when we differentiate u, we get a simpler function, and when we integrate dv, we get a simpler function. In this case, we can choose:

u = 1, and dv = 1/(2+4x²+25x²) dx

Now, let's find du/dx and v:

du/dx = 0 (since u is a constant)

To find v, we need to integrate dv. We can use the substitution method to evaluate the integral:

Let u = 5x

du/dx = 5

dv = 1/(2+4x²+25x²) dx

Substituting u and dv:

v = ∫ dv/dx du = ∫1/(2+4u²) du

v = (1/2) arctan(2u)

v = (1/2) arctan(2(5x))

v = (1/2) arctan(10x)

Now, we can apply the formula for integration by parts:

∫1/(2+4x²+25x²) dx = uv - ∫vdu

∫1/(2+4x²+25x²) dx = (1) x (1/2) arctan(10x) - ∫(1/2) arctan(10x) x 0 dx

∫1/(2+4x²+25x²) dx = (1/2) arctan(10x) + C

where C is the constant of integration.

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Answer:

-506

Step-by-step explanation:

Answer:

-506

Step-by-step explanation:

2 - ([tex]2^{2}[/tex]) + [tex](-8)^{3}[/tex] + 8

2 - 4 -512 + 8

-2 - 512 + 8

-514 + 8

-506

Helping in the name of Jesus.

The two sets of possible dimensions for the rectangular plot of land are:

11 m x 22 m

8 m x 28 m

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be A

Now , the length of the rectangle be L

Let the width of the rectangle be W

Let's assume that the length of the rectangular plot of land is L meters and the width is W meters. Since Jamal has only 44 meters of fencing available, the perimeter of the enclosure will be 44 meters:

Perimeter = 2L + W = 44

W = 44 - 2L

The area of the rectangular plot of land is given as 192 square meters

Area = L x W = L x (44 - 2L) = 192

2L² - 44L + 192 = 0

Solving for L using the quadratic formula, we get:

L = (44 ± √(44² - 4 x 2 x 192)) / (2 x 2)

L = (44 ± √(1600)) / 4

L = (44 ± 40) / 4

So, the possible values of L are 11 and 8

If L = 11, then W = 44 - 2L = 22, and the dimensions of the rectangular plot of land are 11 m x 22 m

If L = 8, then W = 44 - 2L = 28, and the dimensions of the rectangular plot of land are 8 m x 28 m

Hence , the two sets of possible dimensions for the rectangular plot of land are 11 m x 22 m and 8 m x 28 m

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The angle in the rectangular coordinate system is 0 degrees, the compass bearing of the airplane is N (north).

The slope of the line can be found using the formula:

slope = (change in y-coordinate) / (change in x-coordinate)

In this case, the change in the y-coordinate is 0, and the change in the x-coordinate is 10. Therefore, the slope of the line is:

slope = (0 - 0) / (10 - 0) = 0

Since the slope of the line is 0, the line is horizontal, and the angle it makes with the x-axis is 0 degrees or 180 degrees. However, we need to determine which of these angles is the correct bearing of the airplane relative to the observer.

Since the airplane is in the positive x-axis, it lies in Quadrant I. In this quadrant, the angle that a line makes with the positive x-axis is measured counterclockwise from the positive x-axis.

Therefore, the angle that the line connecting the observer to the airplane makes with the positive x-axis is 0 degrees. This is the bearing of the airplane relative to the observer.

To express the bearing using the compass bearing method, we need to convert the angle from the rectangular coordinate system to the angle measured in degrees clockwise from the north direction.

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Answer:

1.

[tex]p(t) = 2000({2}^{ \frac{t}{4} }) [/tex]

2.

[tex]p(8) = 2000( {2}^{ \frac{8}{4} } ) = 2000( {2}^{2} ) = 2000(4) = 8000[/tex]

3. p'(t) = 2,000(1/4)(2^(t/4))(ln 2)

= (500 ln 2)(2^(t/4))

p'(t) = 2,000 ln 2 cells/hour

= about 1,386 cells/hour

Answer:

Y=1

Step-by-step explanation:

Answer:

Please give brainliest

Step-by-step explanation:

c

Answer:

Step-by-step explanation:

(4 – 5) – (13 – 18 + 2).

= -1-(13+2-18).

= -1-(15-18).

= -1-(-3).

= -1+3.

= 2.

Answer:

Step-by-step explanation:

To combine the terms 12a + 26b - 4b - 16a, you first simplify the like terms. Add the coefficients of a terms and add the coefficients of b terms separately. You get 12a - 16a + 26b - 4b which results in -4a + 22b. Therefore, the correct answer is (c) -4a + 22b.

The parallel lines are

a) y = ( 4/7 )x + 6/7

b) 7y = 4x - 18

The perpendicular lines are

a) y = - ( 7/4 )x - 7/4

b) y = - ( 7/4 )x + 2

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = ( 4/7 )x - 3

where the slope of the line is m = 4/7 and y-intercept is b = -3

The parallel lines have the same slope and the perpendicular lines have the negative reciprocal slope

So , the equation of lines are

The parallel lines are

a) y = ( 4/7 )x + 6/7

b) 7y = 4x - 18

And , the perpendicular lines are

a) y = - ( 7/4 )x - 7/4

b) y = - ( 7/4 )x + 2

The lines which are neither parallel not perpendicular are y = 2/3x - 3 and y = -4/7x + 7

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