3. James has a box shaped as a rectangular prism. The container is 8 inches long, 4 inches wide, and 5 inches high. (a) Here is a model of the box. It is filled with unit cubes. Find the volume of the box using the unit cubes. Explain your answer. Answer: 160 cubic inches (b) Find the volume of the box using the formula. Answer: (c) Find the volume of the box using the formula. Answer: (d) How does using the volume formulas to find the volume of a rectangular prism compare to counting unit cubes? Compare your answers in parts (b) and (c) your answer in part (a) to answer the question. Answer:

The value of the coordinates of point D is, (3, - 1)

We have to given that;

All the coordinates of rectangles are,

A(-2,1), B(-6, -9), C(-1, -11)

Now, Let the fourth coordinate of rectangle is,

D (x, y)

Hence, Midpoint of AC and BD are same.

So., Midpoint of AC is,

⇒ AC = (- 2 + (- 1))/ 2, (1 + (- 11))/2

          = (- 3/2 , - 5)

And, Midpoint of BD,

⇒ BD = (- 6 + x)/2, (- 9 + y)/2

By comparing;

⇒ (- 6 + x)/2 = - 3/2

⇒ - 6 + x = - 3

⇒ x = - 3 + 6

⇒ x = 3

⇒ (- 9 + y)/2 = - 5

⇒ - 9 + y = - 10

⇒ y = -10 + 9

⇒ y = - 1

Thus, The value of the coordinates of point D is, (3, - 1)

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ1

The absolute maximum value of the function on the interval (-5, 11) is 670, which occurs at x = -5, and the absolute minimum value is approximately 400.847, which occurs at x ≈ 1.154.

To find the absolute maximum and minimum values of the function f(x) = -2x^3 + 8x + 400 on the interval (-5, 11), we need to consider the critical points and the endpoints of the interval.

First, we find the derivative of the function:

f'(x) = -6x^2 + 8

Setting f'(x) = 0 to find the critical points, we get:

-6x^2 + 8 = 0

x^2 = 4/3

x = ±√(4/3)

Since only √(4/3) is within the interval (-5, 11), this is the only critical point we need to consider.

Next, we evaluate the function at the endpoints of the interval:

f(-5) = -2(-5)^3 + 8(-5) + 400 = 670

f(11) = -2(11)^3 + 8(11) + 400 = -1666

Finally, we evaluate the function at the critical point:

f(√(4/3)) = -2(√(4/3))^3 + 8(√(4/3)) + 400 ≈ 400.847

Therefore, the absolute maximum value of the function on the interval (-5, 11) is 670, which occurs at x = -5, and the absolute minimum value is approximately 400.847, which occurs at x ≈ 1.154.

To learn more about derivative visit: https://brainly.com/question/25324584

#SPJ11

To find the average rate of change of a function in a given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the length of the interval.

In this case, the interval is (0,2) and the function is f(x) = x^2 - 3x.

At the left endpoint, x=0, we have f(0) = 0^2 - 3(0) = 0.

At the right endpoint, x=2, we have f(2) = 2^2 - 3(2) = -2.

Therefore, the difference in the function values is f(2) - f(0) = -2 - 0 = -2.

The length of the interval is 2 - 0 = 2.

So the average rate of change of f(x) over the interval (0,2) is:

(-2)/2 = -1

Therefore, the average rate of change of f(x) over the interval (0,2) is -1.
Hi! To find the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x, you can use the following formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)

In this case, a = 0 and b = 2. First, calculate the function values at these points:

f(0) = (0)^2 - 3(0) = 0
f(2) = (2)^2 - 3(2) = 4 - 6 = -2

Now, apply the formula:

Average Rate of Change = (f(2) - f(0)) / (2 - 0) = (-2 - 0) / (2) = -2 / 2 = -1

So, the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x is -1.

To learn more about average rate visit;

brainly.com/question/12395856

#SPJ11

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

To know more about equation, refer to the link below:

https://brainly.com/question/30137119#

#SPJ1

To express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4), we need to find the values of r and s such that:

u = rv + sw

Substituting the given values, we get:

(7, -10) = r(2, 1) + s(1,4)

Using the symbolic notation, we can write this as a system of equations:

7 = 2r + s
-10 = r + 4s

We can solve this system of equations by using the elimination method:

Multiply the second equation by 2:

7 = 2r + s
-20 = 2r + 8s

Subtracting the first equation from the second, we get:

-27 = 7s

Dividing both sides by 7, we get:

s = -27/7

Substituting this value of s into the first equation, we get:

7 = 2r - 27/7

Multiplying both sides by 7, we get:

49 = 14r - 27

Adding 27 to both sides, we get:

76 = 14r

Dividing both sides by 14, we get:

r = 38/7

Therefore, u = (7, -10) can be expressed as the linear combination:

u = (38/7)(2,1) + (-27/7)(1,4)

Using fractions where needed, the answer is:

u = (76/7, 38/7) + (-27/7, -108/7)
Visit here to learn more about the coordinates of vertices

brainly.com/question/28852734

#SPJ11

The original price of the product was approximately $98.00.

To determine the original price before the 15.5% decrease, we can use the following equation:

Original price - (15.5% of original price) = $82.81

Let's solve for the original price:

Original price - (0.155 * Original price) = $82.81

Simplifying the equation:

0.845 * Original price = $82.81

Dividing both sides by 0.845:

Original price = $82.81 / 0.845

Calculating the original price:

Original price ≈ $98.00

Therefore, the original price of the product was approximately $98.00.

Learn more about determining the original price.

brainly.com/question/29069013

#SPJ11

The crate can hold 175 bricks.

First, we need to convert the volume of the crate from cubic meters to cubic centimeters because the volume of each brick is given in cubic centimeters.

1 m = 100 cm

Volume of crate = 2.8 m3 = 2.8 x (100 cm)3 = 2,800,000 cm3

Now we can find the number of bricks that can be packed into the crate by dividing the volume of the crate by the volume of each brick:

Number of bricks = Volume of crate / Volume of each brick

= 2,800,000 cm3 / 16,000 cm3

= 175 bricks

Learn more about volume,

brainly.com/question/1578538?

#SPJ11

Sam increase the amount of protein she eats by a percentage of 30%.

To find the percentage increase, we can use the formula: (change in amount / original amount) x 100%.

Percentage is a way to express a number as a fraction of 100. It is a convenient method for comparing ratios or proportions because it standardizes them to a common denominator of 100. In this case, we want to find the percentage increase in Sam's daily protein consumption.

First, we need to determine the change in amount. This can be found by subtracting the original amount from the new amount: 58.5g - 45g = 13.5g.

Next, we'll divide the change in amount by the original amount: 13.5g / 45g = 0.3. To express this as a percentage, we'll multiply by 100: 0.3 x 100% = 30%.

Therefore, Sam increased her daily protein intake by 30%. This percentage helps us understand the relative change in her protein consumption compared to her initial intake.

Learn more about percentage here: https://brainly.com/question/24877689

#SPJ11

Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.

Probability is the ratio of favourable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.

Positive Outcomes/Total Results = x/n = Probability(Event)

Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.

Here in the question,

Total region = 8.

Shaded region = 5

So, probability of falling in the shaded region = 5/8

To know more about probability, visit:

https://brainly.com/question/29251004

#SPJ1

Answer:

m = 6/5

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (3, 9) and (8, 15)

We see the y increase by 6 and the x increase by 5, so he slope is

m = 6/5

Answer:

The slope of the points is 6/5.

Step-by-step explanation:

SOLUTION :

Using slope of a line formula to find the slope of the points :

[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]

Substituting all the given values in the formula to find the slope of the points :

[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]

[tex]\quad\dashrightarrow{\sf{m = \dfrac{15 - 9}{8 -3}}}[/tex]

[tex]\quad\dashrightarrow{\sf{m = \dfrac{6}{5}}}[/tex]

[tex]\quad{\star\underline{\boxed{\sf{\red{m = \dfrac{6}{5}}}}}}[/tex]

Hence, the slope of the points is 6/5.

Answer: 7x=30.5

Step-by-step explanation: If you were to answer this equation with the given information it would not be correct. 7(4.25)=29.75.  You need to go through BEDMAS to answer this.

You what you need to do is divide 30.5 by 7 to get the amount she needs to jog for a week, if you do that you get 4.37 miles each day to get to 30.5 in a week.

Therefore , the solution of the given problem of unitary method comes out to be (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period).

The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.

Here,

You must be aware of an account's daily balance over a specific time period in order to determine the average daily amount. how to get an average daily balance:

The time frame for which you wish to compute the average daily balance should be chosen. This could, for instance, be a month, a quarter, or a year.

Find the account balance at the end of each day during the specified period.

Sum up each day's balance for the duration.

By the number of days in the time frame, divide the sum. You are then given the daily average balance.

The formula for determining the typical daily balance is as follows:

=> (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period)

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1  

The derivative of the function y = 2(2^x)-2 is 12 * 2^x ln(2) or 12ln(2)x(2^x-1).

To find the derivative of the function y = 2(2^x)-2, we will use the power rule and the chain rule of differentiation.

Apply the power rule to the function y = 2(2^x)-2. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1).

y' = [2(2^x)-2]'

= 2[(2^x)-2]'

= 2ln(2^x)'

Apply the chain rule to (2^x)'. The chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x))h'(x). In this case, g(x) = 2^x, so g'(x) = ln(2)*2^x.

y' = 2ln(2^x)'

= 2ln(2^x)

= 2ln(2)x(2^x-1)

Therefore, the derivative of the function y = 2(2^x)-2 is 12 * 2^x ln(2) or 12ln(2)x(2^x-1).

For more questions like Derivative click the link below:

https://brainly.com/question/25324584

#SPJ11

To satisfy the conditions that the mode is larger than the median, and the median is larger than the mean, one possible set of frequencies is 1 person chooses 1, 3 people choose 2, 4 people choose 3, 1 person chooses 4 and 11 people choose 5 This results in a mode of 5, a median of 4, and a mean of approximately 3.75.

Since we are given that the mode is larger than the median, that means that at least 11 people must choose the same number. Let's assume that 11 people choose the number 5.

Now, since the median is larger than the mean, we want to make sure that the remaining 9 people choose numbers that are smaller than 5. If they all choose 1, 2, or 3, then the median will be 3, which is larger than the mean. Therefore, we need to make sure that at least one person chooses 4.

So one possible set of frequencies could be

1 person chooses 1

3 people choose 2

4 people choose 3

1 person chooses 4

11 people choose 5

This set of frequencies gives us a mode of 5 (since 11 people choose 5), a median of 4 (since the middle value is 4), and a mean of

(11 + 32 + 43 + 14 + 11*5) / 20 = 3.7

Since the median is larger than the mean, this set of frequencies satisfies all the given conditions.

To know more about mode:

https://brainly.com/question/30891252

#SPJ4

The new measurement based on the given scale factor of 4 is 36. The scale factor is the ratio of the new size of an object to its original size. In this case, the scale factor is 4, which means the new size is 4 times larger than the original size.

If the original measurement is 9, then the new measurement can be calculated by multiplying the original measurement by the scale factor.
New measurement = Original measurement x Scale factor
New measurement = 9 x 4
New measurement = 36
Therefore, the new measurement based on the given scale factor of 4 is 36.

To explain it further, imagine you have a drawing that is 9 inches wide. If you were to increase the scale factor to 4, the new drawing would be 4 times larger, which means it would be 36 inches wide. This concept is commonly used in architecture, engineering, and other fields where scaling drawings or models is necessary to represent them accurately. Understanding scale factors is important in order to make accurate and proportional changes to objects and designs.

To know more about scale factor click here

brainly.com/question/29464385

#SPJ11

The value of the scale factor for the similar figures is 1/3

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

The similar figures

The corresponsing sides of the similar figures are

Original = 12

New = 4

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

Scale factor = New /Original

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

Scale factor = 4/12

Evaluate

Scale factor = 1/3

Hence, the scale factor for the similar figures is 1/3

Read mroe about scale factor at

https://brainly.com/question/29229124

#SPJ1

Answer:

  (x, y) = (5, 3)

Step-by-step explanation:

You want the solution to the system of equations ...

It is convenient to subtract the second equation from 3 times the first:

  3(4x -3y) -(5x -9y) = 3(11) -(-2)

  12x -9y -5x +9y = 33 +2

  7x = 35 . . . . . . . simplify

  x = 5 . . . . . . . . . . divide by 7

  4(5) -3y = 11 . . . . . substitute into the first equation

  9 = 3y . . . . . . . . add 3y-11 to both sides

  y = 3 . . . . . . . . divide by 3

The solution is (x, y) = (5, 3).

__

Additional comment

We find using a graphing calculator to be the easiest way to solve a pair of simultaneous equations. The attachment shows the solution is the one we found above.

The approach of "substitution" is straightforward, if error-prone. Basically, you solve one equation for either variable, then use that expression in the other equation. Here, for example, you can solve the first for x:

  x = (11 +3y)/4

Then use that in the second equation:

  5(11 +3y)/4 -9y = -2

  5(11 +3y) -36y = -8 . . . . eliminate the denominator

  55 +15y -36y = -8 . . . . . eliminate the parentheses

  -21y = -63 . . . . . . . . . . . simplify, subtract 55

  y = 3 . . . . . . . . . . . . divide by -21

  x = (11 +3(3))/4 = 20/4 = 5 . . . . find x

In the above, we used "elimination." We took advantage of the fact that the y-coefficients were related by a factor of 3. To cancel y-terms, we need to have the equations we "add" have opposite signs for the y-terms. Here, we do that by multiplying the first by 3 (to make -9y), then subtracting the second equation (which has -9y, so will cancel). We could have subtracted 3 times the first from the second, but that would make all the resulting coefficients be negative, which we like to avoid.

Or, we could have multiplied the first equation by -3 to make the y-coefficients opposite, then added the results. (Again, that would give negative coefficients in the sum.) Planning ahead can help avoid mistakes due to minus signs.

In 2002, the average price of a two-bedroom apartment in the uptown area was approximately $0.316 million, and it was increasing at a rate of about $0.0328 million per year.

To find the average price of a two-bedroom apartment in 2002 (t=8), you need to evaluate the given function p(t) = 0.17e^(0.10t) at t=8:

p(8) = 0.17e^(0.10 * 8)

p(8) = 0.17e^0.8 ≈ 0.316 million dollars

To find the rate at which the price was increasing in 2002, you need to find the derivative of the function p(t) with respect to t, and then evaluate it at t=8:

p'(t) = d/dt (0.17e^(0.10t))
p'(t) = 0.17 * 0.10 * e^(0.10t)

Now, evaluate p'(t) at t=8:

p'(8) = 0.17 * 0.10 * e^(0.10 * 8)
p'(8) ≈ 0.0328 million dollars per year

So, in 2002, the average price of a two-bedroom apartment in the uptown area was approximately $0.316 million, and it was increasing at a rate of about $0.0328 million per year.

To learn more about average price, refer below:

https://brainly.com/question/23754986

#SPJ11

For March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.

To determine the equivalent units of production for conversion costs in March 2020 for Dorchester Company, we need to follow these steps:
Calculate the equivalent units for the beginning work in process inventory:
Beginning WIP units = 6,000
Completion percentage for conversion costs = 50%
Equivalent units for beginning WIP = 6,000 * 50% = 3,000
Calculate the equivalent units for the units started and completed during March:
Units started and completed = 24,500
Completion percentage for conversion costs = 100%
Equivalent units for started and completed units = 24,500 * 100% = 24,500
Calculate the equivalent units for the ending work in process inventory:                                                                         Ending WIP units = 6,500
Completion percentage for conversion costs = 50%
Equivalent units for ending WIP = 6,500 * 50% = 3,250
Sum up the equivalent units from steps 1, 2, and 3:
Total equivalent units for conversion costs = 3,000 (beginning WIP) + 24,500 (started and completed units) + 3,250 (ending WIP) = 30,750
So, for March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.

Learn more about equivalent units here, https://brainly.com/question/29754038

#SPJ11

The lateral area of the rectangular prism with base square with the side 2 cm and height 125 mm is 10,000 mm².

To calculate the lateral area of a rectangular prism, we need to add up the areas of all its lateral faces.

In this case, the base of the prism is a square with side length 2 cm. Since there are four lateral faces on a rectangular prism, and each lateral face of the rectangular prism is a rectangle, we know that the length and width of each lateral face is equal to the height of the prism, which is 125 mm.

First, let's convert the side length of the base to millimeters to match the unit of the height:

2 cm = 20 mm

Now, we can calculate the lateral area of the rectangular prism as follows:

Lateral area = 4 x (length x height)

= 4 x (20 mm x 125 mm)

= 10,000 mm²

Therefore, the lateral area of the rectangular prism with base square with the side 2 cm and height 125 mm is 10,000 mm².

Learn more about rectangular prism

brainly.com/question/13162015

#SPJ11

The type of triangle formed from the side lengths of a triangle 2, 10, 11 is a scalene triangle.

Based on the given side lengths of a triangle (2, 10, 11), we can determine the type of triangle formed by examining their relationships. First, let's check if these side lengths can form a valid triangle using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. In this case, 2 + 10 > 11, 2 + 11 > 10, and 10 + 11 > 2, so a triangle can be formed.

Now let's identify the type of triangle. There are three main categories to consider: equilateral, isosceles, and scalene. An equilateral triangle has all three sides equal in length, which doesn't apply here. An isosceles triangle has two sides with equal lengths, but in this case, all three sides have distinct lengths. Therefore, the triangle is a scalene triangle, meaning it has no sides of equal length.

In summary, the triangle formed by side lengths 2, 10, and 11 is a scalene triangle because all three sides have different lengths and satisfy the Triangle Inequality Theorem.

Learn more about Triangle Inequality Theorem here: https://brainly.com/question/1163433

#SPJ11

Points lie on the graph of the inverse of f(x)=5x−2.

Hence, the correct option is C,E,F.

To find the points on the graph of the inverse of f(x), we need to switch the x and y coordinates of each point on the graph of f(x). Then, we can simplify the equation to isolate y and get the inverse function.

f(x) = 5x - 2

y = 5x - 2 (replace f(x) with y)

x = 5y - 2 (switch x and y)

x + 2 = 5y (add 2 to both sides)

y = (x + 2)/5 (divide both sides by 5)

So, the inverse function of f(x) is

[tex]f^{-1}[/tex](x) = (x + 2)/5

Now, we can substitute each point from the given options into the inverse function to see if it lies on the graph of the inverse of f(x).

1. (0, -2)

[tex]f^{-1}[/tex](0) = (0 + 2)/5 = 2/5

No, this point does not lie on the graph of the inverse of f(x).

2. (1, 3)

[tex]f^{-1}[/tex](1) = (1 + 2)/5 = 3/5

No, this point does not lie on the graph of the inverse of f(x).

3. (-2, 0)

[tex]f^{-1}[/tex](-2) = (-2 + 2)/5 = 0

Yes, this point lies on the graph of the inverse of f(x).

4. (2/5, 1)

[tex]f^{-1}[/tex](2/5) = (2/5 + 2)/5 = 6/25

No, this point does not lie on the graph of the inverse of f(x).

5. (0, 2/5)

[tex]f^{-1}[/tex](0) = (0 + 2)/5 = 2/5

Yes, this point lies on the graph of the inverse of f(x).

6. (3, 1)

[tex]f^{-1}[/tex](3) = (3 + 2)/5 = 1

Yes, this point lies on the graph of the inverse of f(x).

Therefore, the points that lie on the graph of the inverse of f(x) are (-2, 0),  (0, 2/5) and (3, 1),

Hence, the correct option is C,E,F.

To know more about graph here

https://brainly.com/question/24660980

#SPJ1

The balance of the CD after 6 years will be $678.35.

To calculate the balance of the CD after 6 years, we need to use the formula:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:
A = the balance after 6 years
P = the initial deposit of $500
r = the annual interest rate of 2.25%
n = the number of times the interest is compounded per year (biweekly = 26 times per year)
t = the number of years (6)

Plugging in the values, we get:

A = [tex]500(1 + 0.0225/26)^{(26*6)[/tex]
A = 500(1.001727)¹⁵⁶
A = 500(1.3567)
A = $678.35

Therefore, the balance of the CD after 6 years will be $678.35.

To know more about balance, refer to the link below:

https://brainly.com/question/23634236#

#SPJ11

If the mean time for problem 1 is 10 minutes, and the mean time for problem 2 is 15 minutes, The dot plots show the amount of time it takes each person in a random sample to complete two similar problems.

To find the mean time for each problem, we need to add up all the times and divide by the total number of people in the sample. Let's assume that the first dot plot represents problem 1 and the second dot plot represents problem 2.

After calculating the mean times for each problem, we can make a comparative inference based on the mean values. For instance, if the mean time for problem 1 is 10 minutes, and the mean time for problem 2 is 15 minutes, we can infer that problem 2 takes longer to complete on average than problem 1.

Comparative inference refers to the process of comparing two or more sets of data to draw conclusions about their similarities or differences. In this case, we are comparing the mean times for two similar problems to see which one takes longer on average.

To know more about  mean time refer here:

https://brainly.com/question/7303654#

#SPJ11

Answer: 50

Step-by-step explanation:

37 is 74 percent of what number

We already have our first value 37 and the second value 74. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1   37 = 74% × Y

STEP 2   37 = 74/100× Y

Multiplying both sides by 100 and dividing both sides of the equation by 74 we will arrive at:

STEP 3     Y = 37 × 10074

STEP 4     Y = 37 × 100 ÷ 74

STEP 5     Y = 50

Finally, we have found the value of Y which is 50 and that is our answer.

The effect of the student presenting such a monologue would be B. The mean will decrease.

Order the data points:

1. 5, 1. 5, 2, 2. 5, 2. 5, 2. 5, 3, 3. 5, 3. 5, 4

Find the mean ;

= (1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 10

= 27 / 10

= 2. 7

Then find the new mean after the student presents the monologue:

= ( 0. 5 + 1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 11

= 2. 5

The mean therefore reduced.

Find out more on median at https://brainly.com/question/13221365

#SPJ1

Answer:

b

Step-by-step explanation:

When we look at [tex]f(t)=1/7 t^3-4t-12[/tex], this is a cubic equation, and solving it analytically is not straightforward.

To find the value of r such that f(r) = 0, we need to solve the equation:

[tex]1/7 r^3 - 4r - 12 = 0[/tex]

This is a cubic equation, and solving it analytically is not straightforward.

Yet, it is possible to obtain the value of r that meets the equation using numerical schemes such as Newton-Raphson or bisection. Additionally, one can take advantage of calculation tools and graphical software to calculate an estimation of r.

Read more about equations here:

https://brainly.com/question/25678139

#SPJ1

Answer:

The answer to your problem is, F = 15N

Step-by-step explanation:

You have: F = ka

Where F is the force acting on the object, A is the object's acceleration and is the constant of proportionality.

Which will be our letters that we will NEED to use for today.

You can calculate the constant of proportionality by substituting F = 18 and a = 6 into the equation and solving for k: Then we can now figure out the “ formula of expression “

18 = k6

k = [tex]\frac{18}{6}[/tex]

K = 3

We would need to calculate the force when the acceleration of the object becomes 5 m/s², as following: F = 3 x 5 ( Basic math )

= F = 15

Thus the answer to your problem is, F = 15N

The probability of choosing exactly 13 students who dressed up as the 40s out of the 16 selected students is approx. 0.4334.

We can model this situation as a hypergeometric distribution, where we have a population of 19 students, 15 of whom dressed up as the 40s.

We want to choose a sample of 16 students and find the probability that exactly 13 of them dressed up as the '40s.

The probability of choosing exactly 13 students who dressed up as the 40s can be calculated:

(number of ways to choose 13 students who dressed up as the 40s) * (number of ways to choose 3 students who dressed up as other decades) / (total number of ways to choose 16 students)

The number of ways to choose 13 students who dressed up as the '40s is the number of combinations of 15 choose 13:

(15 choose 13) = 105

The number of ways to choose 3 students who dressed up as other decades is the number of combinations of 4 choose 3, which is:

(4 choose 3) = 4

The total number of ways to choose 16 students from 19 is the number of combinations of 19 choose 16, which is:

(19 choose 16) = 969

105 * 4 / 969 = 0.4334

Therefore, the probability of choosing exactly 13 students who dressed up as the 40s = 0.4334 (rounded to four decimal places)

Learn more about probability at brainly.com/question/13604758

#SPJ1