A right rectangular prism has a volume of 3.5 cubic inches. A second right rectangular prism is similar to the first one and has a volume of 756 cubic
inches.
What scale factor is used to go from the first prism to the second?

Answer:

a. 24

b. 864

Step-by-step explanation:

a. The demand function is:

P = 60 - 2Q

When P = 12:

12 = 60 - 2Q

2Q = 60 - 12

2Q = 48

Q = 48/2 = 24

b. Consumer surplus is given as the integral of Demand function:

\(CS = \int\limits {[P(Q) - (p)(Q)] \ dQ\\\)

This implies that:

\(CS = \int\limits {60 - 2Q} \, dQ\\\\CS = 60Q - Q^2\\\\CS = (60 * 24) - 24^2\\\\CS = 1440 - 576\\\\CS = 864\)

Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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Answer:

Current Bond price = $1155.5116

Step-by-step explanation:

We are given;

Face value; F = $1,000

Coupon payment;C = (7.3% x 1,000)/2 = 36.5 (divided by 2 because of semi annual payments)

Yield to maturity(YTM); r = 5.6%/2 = 2.8% = 0.028 (divided by 2 because of semi annual payments)

Time period;n = 13 x 2 = 26 years (multiplied by 2 because of semi annual payments)

Formula for bond price is;

Bond price = [C × [((1 + r)ⁿ - 1)/(r(r + 1)ⁿ)] + [F/(1 + r)ⁿ]

Plugging in the relevant values, we have;

Bond price = [36.5 × [((1 + 0.028)^(26) - 1)/(0.028(0.028 + 1)^(26))] + [1000/(1 + 0.028)^(26)]

Bond price = (36.5 × 18.2954) + (487.7295)

Bond price = $1155.5116

The coordinate point (x,y) = (3√2,0) represents the square root of 18 on the x-axis

The expression is given as:

x = √18

Express 18 as the product of 9 and 2

x = √9 * 2

Take the square root of 9

x = 3√2

This means that we plot the following coordinate point to represent the square root of 18 on the x-axis

(x,y) = (3√2,0)

See attachment for the plot

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Answer:

x − 9 x ^2 − 8

Step-by-step explanation:

The probability that the number of homicide deaths for a randomly selected day is:

a) 0: 0.18,

b) 1: 0.35,

c) 2: 0.27

The Poisson distribution is used to simulate the likelihood that a certain number of events will occur within a predetermined window of time or space.

In this instance, the Poisson distribution can be used to simulate the number of homicide deaths that occurred in Richmond, Virginia over the course of a year.

The Poisson distribution can be used to determine the likelihood of 0, 1, and 2 homicides happening on any given day.

One homicide occurs on a randomly chosen day with a 0.18 percent chance, one homicide occurs on a randomly chosen day with a 0.35 percent chance, and two homicides occur on a randomly selected day with a 0.27 percent chance.

Complete Question:

In one year, there were 116 homicide deaths in Richmond, Virginia. Using the Poisson distribution, find the probability that the number of homicide deaths for a randomly selected day is:

a) 0

b) 1

c) 2

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Therefore, we can estimate that the position of the particle at t = 4.2 is approximately 8.6 meters. It's important to note that this is only an estimate, and the actual position of the particle may differ slightly from this value.

To estimate the position of the particle at t = 4.2, we need to use linearization. Linearization is a method of approximating the behavior of a function by a linear equation near a particular point. In this case, we can use the linearization of the position function s(t) at t = 4.
The linearization of a function f(x) at a point x=a is given by:
L(x) = f(a) + f'(a)(x-a)
In our case, the position function is s(t), so the linearization is:
L(t) = s(4) + s'(4)(t-4)
We know that s(4) = 8 m and v(4) = s'(4) = 3 m/s, so we can substitute these values into the linearization equation:
L(t) = 8 + 3(t-4)
Simplifying this equation, we get:
L(t) = 3t - 4
Now we can use this linearization to estimate the position of the particle at t = 4.2:
L(4.2) = 3(4.2) - 4 = 8.6

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I'm confused but If you're asking what would be the length of the cube  I'll say your answer would be 5 srry

The depth of the water increasing when the water is 13 feet deep is approximately 1.68 feet per minutes.

We know that the conical water tank has a radius of 12 feet and is 26 feet high.

We also know that water is flowing into the tank at a rate of 30ft³/min. In other words, our derivative of the volume with respect to time t is:

                                   \(\frac{dV}{dt} = \frac{10 ft^3}{min}\)

We want to find how fast the depth of the water is increasing when the water is 13 feet deep. So, we want to find dh/ dt.

First, remember that the volume for a cone is given by the formula:

                V = 1/3 π r² h    

We want to find dh/dt. So, let's take the derivative of both sides with respect to the time t. However, first, let's put the equation in terms of h.

We can see that we have two similar triangles. So, we can write the following proportion:

         \(\frac{r}{h} = \frac{12}{36}\)

Multiply both sides by h:

    ⇒ \(r = \frac{12}{36} h\)

So, let's substitute this in r:

\(V = \frac{1}{3} \pi \frac{12}{36} h^{2} h\)

Square:

\(V = \frac{1}{3} \pi \frac{144}{3888} (h^{2} ) h\)

Simplify:

\(V = \frac{144}{3888} \pi h^{2}\)

Now, let's take the derivative of both sides with respect to t:

\(\frac{d}{dt} (V) = \frac{d}{dt} [\frac{144}{3888} ] \pi h^{3}\)

Simplify:

\(\frac{dV}{dt} =\frac{144}{3888} \pi (3h^{2} ) \frac{dh}{dt}\)

We want to find dh/dt when the water is 13 feet deep. So, let's substitute 13 for h. Also, let's substitute 10 for dV/dt. This yields:

\(10 = \frac{144}{3888} \pi (3(13^{2} ) \frac{dh}{dt}\)

\(10 = \frac{144}{3888} \pi (507) \frac{dh}{dt}\)

\(10 = \frac{73008}{3888} \pi \frac{dh}{dt}\)

\(38880 = 73008 \pi \frac{dh}{dt}\)

\(\frac{dh}{dt} = \frac{38880}{73008} \pi\)

\(\frac{dh}{dt} = \frac{38880}{73008} X\frac{22}{7}\)

≈ 1.6737109 feet / min

The water is rising at a rate of approximately 1.68 feet per minute.

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Answer:

comparing the means of three or more groups

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

119-59 = 60

Answer:

346

Step-by-step explanation:

i think

Answer:

32 cm

Step-by-step explanation:

The volume of the container is:

V= area of the base * the heigth

Since the container has a rectangular base the area of it is:

A = length * width

Let L be the missing length

A = L * 10

V = 10* 25 * L

The container can hold 8 Liters when it's completely full to its brim.

8 liters is 8000 cm^3 ( multiply by 1000)

8000 = 10*25*L

8000 = 250 *L

L = 8000/250

L = 32 cm

v=8litres which is 8 × 1000

l=?

b=10

h=25

since, v=lbh (volume of cuboid)

8000=l × 10 × 25

l=8000/250

l=32

therefore the length is 32cm

Answer:

A, 19:95

Step-by-step explanation:

there are 19 Spanish students and 95 total students

Answer:

A

Step-by-step explanation:

i got it right (: on edg

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

70% of the people attended the music concert also attended the drama play

Step-by-step explanation:

Drama:

50 x 350   = 175            

   100              

350 ÷ 2 (50%) = 175

50% (1/2) of 350 = 175

Music Concert:

175      x 100% = 70%

250

175 of 250 = 70%

70% of the people attended the music concert also attended the drama play

percentage, a relative value indicating hundredth parts of any quantity.

Given,

A school held several evening activities last month - a music concert, a basketball game, a drama play, and literacy night

The music concert was attended by 250 people

350 people attended the drama play.

50% of the people who attended the drama play also attended the music concert.

350/2=175

We need to find the percentage of the people who attended the music concert also attended the drama play.

175/250 x 100 = 70%

Hence 70% of the people attended the music concert also attended the drama play

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Answer:

7/12.

Step-by-step explanation:

There are 12 numbers totals.

The numbers 1, 7, 11, 8, 2, 4, and 10 are not in Set Q.

There are seven of those numbers which means that the probability of a number not being in Set Q is 7/12.

Answer:

7/12.

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

25x9 = 250+ tax

Answer:

0.53 is the right answer its not 0.28 because I did the work and I got 0.53 by dividing

Step-by-step explanation:

To determine the type of association between the time spent picking strawberries and the number of pounds of strawberries picked, more information and data would be needed, such as the results of experiments or observations conducted over a period of time.

What is the period of time?

The period of time is the duration or interval between two events or points in time. It refers to the amount of time that elapses between the beginning and the end of a specific event, process, or phenomenon. The period of time can be measured in various units such as seconds, minutes, hours, days, weeks, months, or years, depending on the context.

It is not possible to determine the type of association between the time spent picking strawberries and the number of pounds of strawberries picked without additional information or data.

Factors such as the location, weather, and the maturity of the strawberries can all influence the relationship between time spent picking and the amount of strawberries picked.

Additionally, there may be other variables that could influence the amount of strawberries picked, such as the worker's skill level or experience.

Therefore, to determine the type of association between the time spent picking strawberries and the number of pounds of strawberries picked, more information and data would be needed, such as the results of experiments or observations conducted over a period of time.

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Answer:

D, a quotient.

Step-by-step explanation:

The sign ÷ indicates a quotient.

Answer:

D.

Step-by-step explanation:

You are dividing the two numbers which gives you a quotient

Number of roots in the RHP of the complex plane: 31.2. Number of roots in the RHP of the complex plane: 0

The Routh-Hurwitz stability criterion is a technique for deciding the stability of linear time-invariant systems.

The Routh-Hurwitz criteria are a collection of necessary and sufficient conditions for the stability of a polynomial whose coefficients are real numbers.

It can be used to calculate the location of the roots of a polynomial's characteristic equation. Below are the solutions to the given polynomial equations:

Solution 1: Using Routh-Hurwitz criterion for s⁵ + 3s⁴ + 9s³ + 8s² + 65 + 4= 0:

Routh table is given below: s⁵ = 1 3 4 0 0

s⁴ = 3 8 65 0

s³ = 2.36 16.6 0

s² = 8.9 65 0

s¹ = 68 0

s⁰ = 4

There are three poles in the right half plane (RHP) of the complex plane for the given equation.

Hence, the system is unstable.

Solution 2: Using Routh-Hurwitz criterion for s⁵ + 6s³ + 5s² + 8s + 20=0:

Routh table is given below: 

s⁵ = 1 5

s⁴ = 6 8

s³ = 2 20

s² = 4 -20

s¹ = -10

s⁰ = 20

There are no poles in the RHP of the complex plane for the given equation.

Therefore, the system is stable.

Hence, the answer is:1.1

Note: When the roots of the characteristic equation are located on the imaginary axis, the Routh-Hurwitz criteria fail.

A little change in the equation coefficients leads to no information on stability.

Hence, we cannot conclude the stability of the system.

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Derek needs to make contributions of approximately $21,038.34 per year from his 26th birthday to his 65th birthday in order to accumulate $2,742,310.00 in his retirement account by the time he fully retires.

To determine the amount Derek needs in his retirement account on his 65th birthday, we can use the concept of present value. Since he plans to withdraw $184,036.00 per year, starting from his 66th birthday until his 90th, the cash flows can be treated as an annuity. The interest rate is 5.00%, and the time period is 25 years (from 66 to 90). Using the formula for the present value of an annuity, we can calculate the required amount. The formula is:

PV = PMT * (1 - \((1 + r)^(-n)\)) / r

where PV is the present value, PMT is the annual withdrawal amount, r is the interest rate per period, and n is the number of periods.

Plugging in the values, we get:

PV = $184,036.00 * (1 - \((1 + 0.05)^(-25)\)) / 0.05 ≈ $2,744,607.73

Therefore, Derek needs approximately $2,744,607.73 in his retirement account on his 65th birthday to cover his desired annual withdrawals.

Moving on to the second part, Derek plans to make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal of having $2,742,310.00 in his retirement account after fully retiring, we can calculate the necessary contributions using the formula for the future value of an ordinary annuity:

FV = PMT * \(((1 + r)^n\) - 1) / r

Rearranging the formula, we can solve for the required contributions (PMT):

PMT = FV * (r / (\(((1 + r)^n\) - 1))

Plugging in the values, we get:

PMT = $2,742,310.00 * (\(\frac{0.05} {((1+0.05)^{39}-1 )}\))≈ $21,038.34

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Answer:

NS=16

Step-by-step explanation:

In parallelogram, diagonals halves each other to 2 equal section

Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

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The perimeter of the regular hexagon is 42 inches.

Since a regular hexagon can be divided into six equilateral triangles, each triangle shares a side with the hexagon. Let's denote the perimeter of the hexagon as P.

Since the perimeter of one equilateral triangle is 21 inches, each side of the triangle has a length of 21/3 = 7 inches.

Since the hexagon consists of six equilateral triangles, it will have six sides, each of length 7 inches. Therefore, the perimeter of the hexagon is given by:

P = 6 * 7 = 42 inches.

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After d days, the number of lily pads in the pond can be calculated using the formula 2^d. So, if d is the number of days, then the number of lily pads after d days would be 2^d.

Each day, the number of lily pads doubles. So, on the first day, there is 1 lily pad. On the second day, the number doubles to 2. On the third day, it doubles again to 4, and so on. This doubling pattern continues for d days.

To calculate the number of lily pads after d days, we raise 2 to the power of d (2^d). This is because each day, the number of lily pads doubles, which can be represented as 2^1, 2^2, 2^3, and so on. By substituting the value of d into the equation, we can find the number of lily pads after d days.

For example, if d = 5, then the number of lily pads after 5 days would be 2^5 = 32. This means that there would be 32 lily pads in the pond after 5 days.

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