Find the midpoint of the line segment with end coordinates of: ( 0 , 2 ) and ( 8 , 8 )

Answer: Mean = 7.8

              Median = 9

             Mode = 2,9

Step-by-step explanation: Mean is the average value of a data set. Mean from a frequency table is calculated as:

\(E(X)=\frac{2(10)+3(9)+9(10)+11(7)+12(3)+15(4)+16(3)}{10+9+10+7+3+4+3}\)

E(X) = 7.8

Mean for the given frequency distribtuion is 7.8.

Median is the central term of a set of numbers. Median in a frequency table is calculated as:

1) Find total number, n:

n = 10 + 9 + 10 + 7 + 3 + 4 + 3 = 46

2) Find position, using: \(\frac{n+1}{2}\)

\(\frac{n+1}{2}=\frac{47}{2}\) = 23.5

Median is in the 23.5th position.

3) Find the position by adding frequencies: for this frequency distribution, 23.5th position is 9

Median for this frequency distribution is 9.

Mode  is the number or value associated with the highest frequency.

In this frequency distribution, 2 and 9 points happen 10 times. So, mode is 2 and 9.

Mode for this distribution is 2 and 9.

Following are the calculation of mean, median, and modes:

Given value:

\(\bold{x \ \ \ \ \ \ f} \\\\ 2\ \ \ \ \ 10 \\3\ \ \ \ \ 9\\9 \ \ \ \ \ 10\\11\ \ \ \ \ 7\\12 \ \ \ \ \ 3\\15 \ \ \ \ \ 4\\16 \ \ \ \ \ 3\\\)

To find:

mean, median, and modes=?

Solution:

\(\bold{x \ \ \ \ \ \ f \ \ \ \ \ \ cf \ \ \ \ \ \ fx} \\\\2\ \ \ \ \ 10 \ \ \ \ \ 10 \ \ \ \ \ 20 \\3\ \ \ \ \ 9 \ \ \ \ \ 19 \ \ \ \ \ 27 \\9 \ \ \ \ \ 10\ \ \ \ \ 29 \ \ \ \ \ 90 \\11\ \ \ \ \ 7\ \ \ \ \ 36 \ \ \ \ 77 \\12 \ \ \ \ \ 3\ \ \ \ \ 39 \ \ \ \ 36\\15 \ \ \ \ \ 4\ \ \ \ \ 43 \ \ \ \ 60\\16 \ \ \ \ \ 3\ \ \ \ \ 46 \ \ \ \ 48 \\\)

\(\Sigma f = 46 \ \ \ \ \ \ \ \ \ \ \Sigma fx= 358\)

Calculating the Mean:

\(Mean=\frac{\Sigma fx}{\Sigma f}\)

          \(=\frac{358}{46}\\\\= 7.78\)

Calculating the Median:

\(n= \Sigma f= 46\)

\(Median=\frac{ (\frac{n}{2})^{th} +(\frac{n}{2} +1)^{th}}{ 2}\)

             \(=\frac{ (\frac{46}{2})^{th} +(\frac{46}{2} +1)^{th}}{ 2}\\\\=\frac{ (23)^{th} +(24)^{th}}{ 2}\\\\=\frac{ 3 +3}{ 2}\\\\=\frac{ 6}{ 2}\\\\=3\)

Calculating the Mode:

Mode is the value of 'x' with the highest frequency is 10 for x= 2 and x=9 therefore, the mode is "2,9".

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Answer:

If the square end is under water: 312271.92  N

If the round end is under water:   262976.67 N

Step-by-step explanation:

We have to:

P = ρ·g·d

where:

P is hydrostatic pressure, g is gravitational acceleration, d is depth, ρ is fluid density

Force = hydrostatic pressure x submerged area

F = PA

You didn't specify the orientation

If the square end is under water:

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (2-y)√(64 - y²) dy .... from 0 to 2

F = 19620 ∫ (2-y)√(64 - y²) dy .... from 0 to 2

The result of the solution of the integral is 15.916

Thus:

F = 15.916*19620 = 312271.92  N

If the round end is under water:

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (y - 3) √(64- y²) dy .... from 3 to 5

F = 19620 ∫ (y - 3) √(25 - y²) dy .... from 3 to 5

The result of the solution of the integral is 13.403

Thus:

= 13.403*19620 = 262976.67 N

The hydrostatic force against one side of the plate:

If the square end is under water is 312271.92  N

If the round end is under water is 262976.67 N

This is the resultant force caused by the pressure loading of a liquid acting on submerged surfaces.

Hydrostatic pressure (P) = ρ·g·d where ρ is fluid density , g is gravitational acceleration, d is depth.

Force = hydrostatic pressure x submerged area

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (2-y)√(64 - y²) dy .. from 0 to 2

F = 19620 ∫ (2-y)√(64 - y²) dy .... from 0 to 2

 = 15.916

F = 15.916× 19620 = 312271.92  N

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (y - 3) √(64- y²) dy ... from 3 to 5

F = 19620 ∫ (y - 3) √(25 - y²) dy ...from 3 to 5

  = 13.403

F = 13.403*19620 = 262976.67 N.

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The plant's height after x months is 11.25 + 15x.

From the information illustrated, the plant is already 11.25 meters tall, and it will grow 15 centimeters every month.

In this case, let the plant's height be H (in meters)

Let the number of months be x.

The plant height will be:

= 11.25 + (15 × x)

= 11.25 + 15x

This is the height.

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Complete question

A plant is already 11.25 meters tall, and it will grow 15 centimeters every month. When is the plant's height, H (in meters), after x months?

Answer:

5.625 = 45/8 = 5 5/8

Step-by-step explanation:

The radius of the cylinder is approximately 6.75 inches.

We can use the formula for the volume of a cylinder to solve this problem:

\(V = \pi r^2h\)

We know that the volume V is 2,035.75 \(in^3\), and the height h is 3 times the radius r. So we can write:

\(V = \pi r^2(3r)\)

Simplifying this expression, we get:

V = 3π\(r^3\)

To solve for r, we can divide both sides of the equation by 3π\(r^2\):

V/(3π\(r^2\)) = r

Substituting the given value for V, we have:

2,035.75/(3π\(r^2\)) = r

Multiplying both sides by 3πr^2, we get:

2,035.75 = 3π\(r^3\)

Dividing both sides by 3π, we have:

\(r^3\) = 2,035.75 / (3π)

Taking the cube root of both sides, we get:

r = \((2,035.75 / (3\pi ))^{1/3\)

Using a calculator, we find that:

r ≈ 6.75 inches

Therefore, The cylinder has a radius of about 6.75 inches.

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Answer:

B. y - 0 = -⅓(x + 2)

Step-by-step explanation:

First, find the slope of the line using two points in the line, (-5, 1) and (-2, 0):

Slope (m) = ∆y/∆x = -⅓

To find the equation in point-slope form, substitute (a, b) = (-2 0), and m = -⅓ into y - b = m(x - a)

Thus:

y - 0 = -⅓(x -(-2))

y - 0 = -⅓(x + 2)

Answer:

Amanda's popcorn container holds more popcorn

Step-by-step explanation:

First we'll have to find the volume.

The Volume helps us determine which is bigger.

Step 1

We'll find Amanda's popcorn container

10cm*10cm*13.5cm=1350cm

Step 2

We'll find Mary's popcorn container

8cm*8cm*20cm=320cm

Step 3

Since Amanda's popcorn container has 1350cm (volume) and Mary's popcorn container has 320cm (volume) we'll have this. 1350cm>320cm. We can determine the Amanda's popcorn container has holds more,

Final Answer

Amanda's popcorn container holds more popcorn

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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Answer:

Step-by-step explanation:

Answer: The answer is log₅(p)¹/³(p+5).

Step-by-step explanation:

a2 is assigned the sum of \((1/2)^3 + (1/4)^3+ (1/6)^3 + ... +(1/128)^3\) using a for loop variable a2 = 0

for i in range(2, 129, 2):

a2 += 1/i**3  add 1/i^3 to a2 for each iteration

a2 contains the sum of

\((1/2)^3 + (1/4)^3+ (1/6)^3 + ... +(1/128)^3\)

The goal is to calculate

\((1/2)^3 + (1/4)^3+ (1/6)^3 + ... +(1/128)^3\),

and assign the result to the variable a2. To do this, we can use a for loop. First, we need to declare a2 and initialize it to 0. Then, we can use a for loop to iterate over all the numbers from 2 to 128, stepping in increments of 2. For each iteration, we can add the value of\(1/i^3\) to a2. When the loop is finished, the value stored in a2 will be the sum of \((1/2)^3 + (1/4)^3+ (1/6)^3 + ... +(1/128)^3\).

This value can then be used for further calculations or stored for later.

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The mistake that Katie made in the stem and leaf diagram, was that she D. Missed a length.

Looking at the stem and leaf diagram, we see that there are 14 leaves. This means that there are 14 lengths of caterpillars. However, there are 15 lengths shown on the table.

This means that there is a length missing that Katie failed to account for. Upon close inspection of the stem and leaf plot, we find that the missing length is a second value of 70 because there are two lengths that are 70 but this is shown only once on the stem and leaf plot.

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Answer:

⬇ Down Below is from Edge 2020 ⬇

The volume of a rectangular box= 1056 ft³

The surface area of a rectangular box= 632 square ft

Volume is a measure of three-dimensional space that is occupied. It is frequently quantified numerically using SI-derived units or different imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length (cubed) is related to volume. The volume of a container is commonly believed to be its capacity; that is, the amount of fluid (gas or liquid) that the container can hold, rather than the amount of space it occupies.

Volume was measured in ancient times using similar-shaped natural containers, and later, standardized vessels. Arithmetic formulas can quickly compute the volume of some simple three-dimensional shapes.

Given,

Length of the rectangular box= 11ft

Width of the rectangular box= 8 ft

Height of the rectangular box= 12 ft

Volume= Length× Width× Height

Volume= 11×8×12

=1056 ft³

Therefore, volume= 1056ft³

Surface area of a rectangular box is,

1 and 2 surfaces, 11 × 8 ===>

Surface area = 2× (11× 8) =  176 square ft

1 and 3 surfaces 11 × 12 ===>

Surface area = 2× (11×12) = 264 square inches

3• 2 surfaces 12 × 8 ===>

Surface area = 2× ( 12 × 8) = 192 square inches

Adding all the surface areas

176 +264 +192= 632  square ft.

The surface area of a rectangular box= 632 square ft

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<CAB= 56°

(DC= 78°

(DB= 78+56=134°

<DAB=134°

(BED=360-134= 226°

(BEC=226+78=304°

(CED= 360-78=282°

hey:) I hope this was correct and helpful

The value of f (x -1) is;

f (x - 1) = x + 4

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

Function f (x) = x + 5

Now,

Find the value of f (x - 1), we substitute the value x = x - 1;

f (x) = x + 5

f (x - 1) = (x - 1) + 5

f (x - 1) = x - 1 + 5

f (x - 1) = x + 4

Thus, The value of f (x -1) is;

f (x - 1) = x + 4

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Answer:

8)

  a) 6,320,000

  b) 230,000

  c) 10,000,000

8)

  a) 9,300,000

  b) 5,240

  c) 28,000

Answer:

54

Step-by-step explanation:

46+80=126 and every triangle adds up to 180 so subtract 180 from 126 (180-126=54)

Hope this helped!

Answer:

c)54 degrees

Step-by-step explanation:

A triangle has to be 180 degrees.

46+80=126

180-126=54

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Some things you can do to help you decide on a bank include:

When trying to locate a bank that offers competitive returns on savings and favorable borrowing costs, consider comparing interest rates.

To gather additional information about certain banks, why not solicit feedback from acquaintances? People who have personal experience with a particular bank can provide valuable insights into their satisfaction levels with regards to customer service, for example.

Finally, taking the time to visit branch offices can offer valuable clues regarding convenience level and overall atmosphere.

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We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...

The system of equations that can be used to find the number of medium coffees, x , and the number of large coffees, y , sold in the first hour after opening is x + y = 18 and 3x + 5y = 68.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given that;

Cost of medium coffee= $3

Cost of large coffee=$5

Price of 18 coffee= $68

Now, let x be the number of medium coffees sold and y be the number of large coffees sold in the first hour after opening.

We know that the total number of coffees sold is 18, so:

x + y = 18

We also know that the total sales from coffee is $68, and that the cost of a medium coffee is $3 and the cost of a large coffee is $5, so we can write:

3x + 5y = 68

Therefore, the equations will be x + y = 18 and 3x + 5y = 68.

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Derivative of 4x^2  is 8x .

Given function 4x^2

Let,

f(y) = 4x^2

Then dy/dx,

Using the derivative formula, x^n = nx^n-1

d(4x^2) / dx

d(4x^2) / dx = 8x

Hence dy/dx  is 8x.

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Kevin's error is that he incorrectly identified the vertex of the parabola as (3, 2) instead of (2, 3), which resulted to the parabola opens downward. The correct vertex is at (2, 3) and the parabola opens upward.

You are correct that the vertex of the parabola can be determined using the equation f(x) = a(x - h)² + k, where the vertex is at (h, k). In this case, we have f(x) = -(x-2)² + 3, so the vertex can be found by setting x - 2 = 0, which gives x = 2. Plugging this value into the equation,

we get f(2) = -(2-2)² + 3 = 3, so the vertex is at (2, 3).

However, your reasoning for why h is positive is not correct. The expression x - h represents the horizontal distance from the vertex to any point on the parabola. So if x is greater than h, then the expression x - h will be positive, and if x is less than h, then the expression x - h will be negative. In this case, the vertex is at (2, 3), so we have h = 2. This means that any point to the right of the vertex will have a positive value of x - h, while any point to the left of the vertex will have a negative value of x - h.

Therefore, the correct explanation of Kevin's error is that he incorrectly identified the vertex as (3, 2) instead of (2, 3), and as a result, he also incorrectly concluded that the parabola opens downward. In fact, the parabola opens upward because the coefficient of the x² term, -1, is negative.

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Answer:

Below in bold.

Step-by-step explanation:

Let the number of pistachios be x then the number of almonds = x-100.

The number of cashews = 1000 - x - (x - 100) = 1100-2x.

From the info given

3(1100-2x) + 4x + 5(x - 100) = 3700

3300 - 6x + 4x + 5x - 500 = 3700

3x = 3700 - 3300 + 500

3x = 900

x = 300

So there are 300 pistachios, 200 almonds and 500 cashews in the bag.

There are 300 pistachios, 200 almonds, and 500 cashews in the bag of mixed nuts.

To find the number of each type of nut in the bag, we can set up a system of equations based on the given information.

Let's assume there are x pistachios in the bag. According to the problem, there are 100 fewer almonds than pistachios, so the number of almonds will be (x - 100).

Now, the total number of nuts is 1,000:

x (pistachios) + (x - 100) (almonds) + cashews = 1000

The total weight of the nuts in the bag can be calculated as follows:

3g (cashews) * number of cashews + 4g (pistachios) * x + 5g (almonds) * (x - 100) = Total weight in grams.

Since we know that the bag weighs 3.7 kg, we need to convert the total weight to grams and set it equal to 3.7 kg * 1000g/kg = 3700g.

Now we have two equations:

x + (x - 100) + cashews = 1000

3g * cashews + 4g * x + 5g * (x - 100) = 3700

Let's simplify equation 1:

2x - 100 + cashews = 1000

2x + cashews = 1100

cashews = 1100 - 2x

Now, let's substitute the expression for cashews in equation 2:

3g * (1100 - 2x) + 4g * x + 5g * (x - 100) = 3700

Now, distribute the weights:

3300g - 6g * x + 4g * x + 5g * x - 500g = 3700

Combine like terms:

-6g * x + 4g * x + 5g * x = 3700 - 3300 + 500

3g * x = 900

x = 900 / 3

x = 300

Now that we have the value of x (number of pistachios), let's find the number of almonds:

almonds = x - 100

almonds = 300 - 100

almonds = 200

Now, let's find the number of cashews using the total nut count:

cashews = 1000 - (pistachios + almonds)

cashews = 1000 - (300 + 200)

cashews = 1000 - 500

cashews = 500

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Answer:

8p

Step-by-step explanation:

8 • p = 8p

The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment;

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively);

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%;

Given:

Hannah makes 5 out of 8 attempted free-throws.

Now,

The average waiting time of hannah to make her first basket is 5/8

The probability of hannah making basket at her last attempt is 1/8

The probability of hannah making basket before her last attempt is 2/8

Hence, the probabilty will be 1/8 and 2/8;

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Answer:

No, they are not equivalent

Step-by-step explanation:

Because

120/2 Can not be divided equally into 360/6

Answer:

Yes

Step-by-step explanation:

They are equivalent because if you write the ratio's out, you get 120:2 and 360:6. If you then simplify both, you get 60:1. To simplify these, you need to find a common factor. In 120:2, you can tell that both numbers can be divided by two because they are both even. After dividing, you get 60:1. In 360:6, you can tell that both numbers can be divided by 6 since they both are multiples of 6. After dividing, you get 60:1. Because these to ratio's are equal, they are equivalent.