Triangular prism B is the image of triangular prism A after dilation by a scale factor of 4. If the volume of triangular prism B is 4352 km^3 , find the volume of triangular prism A, the preimage

a. The control limits for the 3-sigma x-bar chart are: UCL x-bar = 61.744 lb. and LCL x-bar = 59.756 lb.

b. The control limit for the 3-sigma R-chart is UCL R = 4.051 lb., rounded to three decimal places.

(a) To determine the control limits for the 3-sigma x-bar chart, we need to use the given information of the sample size, overall mean, and average range.

For the x-bar chart, the control limits are calculated using the formula:

Upper Control Limit (UCL x-bar) = overall mean + (A2 * average range)

Lower Control Limit (LCL x-bar) = overall mean - (A2 * average range)

Where A2 is a constant depending on the sample size. For a sample size of 7, the value of A2 is 0.577.

Substituting the values into the formula, we get:

Upper Control Limit (UCL x-bar) = 60.75 + (0.577 * 1.78) = 61.744

Lower Control Limit (LCL x-bar) = 60.75 - (0.577 * 1.78) = 59.756

Therefore, the control limits for the 3-sigma x-bar chart are: UCL x-bar = 61.744 lb. and LCL x-bar = 59.756 lb.

(b) To calculate the control limits for the 3-sigma R-chart, we only need the value of the average range.

The control limits for the R-chart are calculated as follows:

Upper Control Limit (UCL R) = D4 * average range

Lower Control Limit (LCL R) = D3 * average range

For a sample size of 7, the values of D3 and D4 are 0 and 2.282, respectively.

Substituting the values into the formula, we get:

Upper Control Limit (UCL R) = 2.282 * 1.78 = 4.051 lb.

Therefore, the control limit for the 3-sigma R-chart is UCL R = 4.051 lb., rounded to three decimal places.

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Answer: Step 2 : Additive

              Step 4 : Multiplicative

Step-by-step explanation:

Also, if you could hook me up into Passione, that'd be cool

It is false that  the graph of y = sinx is increasing on the interval [pi / 2, 3pi   / 2].

Cos x is the derivative of sin x. Cos x appears to have negative values between pi / 2 (exclusive) and 3 pi / 2 (exclusive). That indicates that the original function, sin x, is getting smaller over time.

Sin value typically increases from 0 to 90 degrees.

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Answer:

Area = 50

Step-by-step explanation:

x2 = 36

x = 6

36 + 6 + 6 + 1 + 1 =50

the small squares = 1

Answer:

Step-by-step explanation:

The actual change in f is 0.06917. The error in the Linear Approximation is 0.

To use the linear approximation, we need to find the equation of the tangent line to the function f(x) = \(x^{1/4}\) at x = 9. The slope of the tangent line is f'(9) = (1/4) * \(9^{-3/4}\) = 1/12. The y-intercept is f(9) = 3.

So the equation of the tangent line is y = (1/12)(x-9) + 3.

Using this line, we can estimate the value of f(9.8) as follows:

f(9.8) ≈ (1/12)(9.8 - 9) + 3 = 3.0691666667

Similarly, we can estimate the value of f(9) as follows:

f(9) ≈ (1/12)(9 - 9) + 3 = 3

Therefore, the actual change in f is:

Δf = f(9.8) - f(9) = 0.0691666667

The error in the linear approximation is the absolute difference between the actual change and the estimated change:

Error = |Δf - Δf_approx| = |0.0691666667 - 0.0691666667| = 0

So the estimate is exact, with no error. Therefore:

Δf ≈ 0.06917
Δf = 0.06917
Error = 0

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Answer:

\(\large\boxed{\tt x = 2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for x in the given equation.}\)

\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)

\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{How is this possible?}}\)

\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)

\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)

\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)

\(\textsf{of once.}\)

\(\large\underline{\textsf{For our problem;}}\)

\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)

\(\textsf{Property of Equality;}/tex]

\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)

\(\tt - x^{3} = 8\)

\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)

\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)

\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)

\(\underline{\textsf{Evaluate;}}\)

\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)

\(\textsf{*Note;}\)

\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)

\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)

\(\underline{\textsf{We should have;}}\)

\(\tt -x=2\)

\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)

\(\large\boxed{\tt x = 2}\)

Answer:

sorry but I can understand

The cheaper drink between the drink is the 12 ounces drink.

The cheaper drink between the 8 ounce drink and the 12 ounces drink, would be the one that cost less per ounce.

To find the cheaper drink, the formula is:

= Cost of drink / Number of ounces

The cost of the 8 ounce drink is:

= 1. 28 / 8

= $ 0. 16 per ounce

The cost of the 12 ounces drink is:

= 1. 68 / 12

= $ 0.14 per ounce

The 12 ounces drink is therefore cheaper.

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The question is:

Which drink is cheaper per ounce ?

Answer:

1

Step-by-step explanation:

rise/run = 1/1 = 1

Answer:

The equation that can be used to find the number of pencils Andrew bought is:

x=(c-3.50)/0.99

Step-by-step explanation:

With the information provided, you can say that the total amount paid would be equal to the price of the pack of erasers plus the price per pencil for the number of pencils purchased, which can be expressed as:

c=3.50+0.99x, where:

c is the total cost

x is he number of pencils purchased

Now, you can solve for x in order to find the equation to calculate the number of pencils Andrew bought:

c-3.50=0.99x

x=(c-3.50)/0.99

According to this, the answer is that the equation that can be used to find the number of pencils Andrew bought is:

x=(c-3.50)/0.99

Answer:

18%

Step-by-step explanation:

540$ is 18% of what he put towards the loan :))

Answer:

ITS A

Step-by-step explanation:

Took DA TEST

Answer:

a

Step-by-step explanation:

The average value of S$ (if all possible orders of these 20 people are considered)  to 91/10

Average value is a statistical measure that is used to describe the central tendency of a set of data points, or the average of a group of numbers. It is calculated by taking the sum of all values in a dataset and dividing by the number of values in the dataset. Average value can also be used to compare different datasets to find out which one has the highest or lowest value. It is an important tool used in mathematics and statistics to measure the center of a data set.

Assume that the class attempted each setup.boy i and young girl j would remain close to one another in 2 various orders, in 19 various positions, 18! times each.

Adding more than all i,j gives

\($7\cdot13\cdot2\cdot19\cdot18!=\tfrac{91}{10}\cdot20!$\)

so the normal worth of 91/10

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The expected value of the winnings from the game is $0.02.

To find the expected value of the winnings from the game, we need to multiply each possible payout by its corresponding probability, and then sum these products.

The expected value, denoted by E(X), can be calculated using the formula:

E(X) = ∑(xi × pi)

where:

xi is the possible payout

pi is the probability of receiving that payout

E(X) = (-1) × 0.70 + 1 × 0.15 + 3 × 0.10 + 5 × 0.04 + 7 × 0.01

= -0.70 + 0.15 + 0.30 + 0.20 + 0.07

= 0.02

Therefore, the expected value of the winnings from the game is $0.02.

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The indefinite integral of ∫(5 + 9t)t^2 dt is (5/3)t^3 + (9/4)t^4 + C.

To explain the process of finding the indefinite integral of ∫(5 + 9t)t^2 dt, we use the power rule for integration, which states that the integral of x^n with respect to x is (1/(n+1))x^(n+1), where n is any real number except -1.

In this case, we have the function (5 + 9t)t^2. To integrate this function, we apply the power rule and distribute the t^2 term:

∫(5 + 9t)t^2 dt = ∫(5t^2 + 9t^3) dt

Now, we can integrate each term separately:

∫(5t^2 + 9t^3) dt = (5/3)t^3 + (9/4)t^4 + C

In the first term, we apply the power rule with n = 2, which gives us (1/(2+1))t^(2+1) = (1/3)t^3. Then, we multiply by the coefficient 5, resulting in (5/3)t^3.

In the second term, we apply the power rule with n = 3, which gives us (1/(3+1))t^(3+1) = (1/4)t^4. Then, we multiply by the coefficient 9, resulting in (9/4)t^4.

Finally, we add the constant of integration C, which represents an arbitrary constant that can be added to the result since the derivative of a constant is zero.

Therefore, the indefinite integral of ∫(5 + 9t)t^2 dt is (5/3)t^3 + (9/4)t^4 + C.

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The 5-point DFT of the sequence Y(k) is [15 -2.5 + 3.4j -2.5 + 0.81j -2.5 - 0.81j -2.5 - 3.4j]. So, the correct answer is 1).

We can find the 5-point DFT of y(n) using the formula

Y(k) = sum_{n=0}^{4} y(n) exp(-2piikn/5), k = 0,1,2,3,4

Substituting the values of y(n) = {1, 2, 3, 4, 5}, we get

Y(0) = 1 + 2 + 3 + 4 + 5 = 15

Y(1) = 1 + 2exp(-2pii/5) + 3exp(-4pii/5) + 4exp(-6pii/5) + 5exp(-8pii/5) = -2.5 + 3.4j

Y(2) = 1 + 2exp(-4pii/5) + 3exp(-8pii/5) + 4exp(-12pii/5) + 5exp(-16pii/5) = -2.5 + 0.81j

Y(3) = 1 + 2exp(-6pii/5) + 3exp(-12pii/5) + 4exp(-18pii/5) + 5exp(-24pii/5) = -2.5 - 0.81j

Y(4) = 1 + 2exp(-8pii/5) + 3exp(-16pii/5) + 4exp(-24pii/5) + 5exp(-32pii/5) = -2.5 - 3.4j

Therefore, the 5-point DFT of the sequence Y(k) is [15, -2.5 + 3.4j, -2.5 + 0.81j, -2.5 - 0.81j, -2.5 - 3.4j], which is option 1.

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Emmett will have $99.225 in 2 years.

A compound is the interest calculated on the principal amount and the interest accumulated over the various time period.

Emmett deposited the initial amount, p=$90

Rate of interest, r=5%

Time period ,t = 2 years.

Interest compounded annually i.e., n=1

\(A=P(1+\frac{r}{n}) ^{(n*t)}\)

\(A=99(1+\frac{0.05}{1}) ^{(1*2)}\)

A=99*1.5625

A=$99.225

Hence, Emmett will have $99.225 in years.

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Answer: $99.225

Step-by-step explanation:

Answer:

Answer on a graph

Answer:

No solution

Step-by-step explanation:

-8l2x -5l =16  When I divide both sides by -8

l2x - 5l = -2

The absolute value cannot equal a negative number.

Answer:

19%

Step-by-step explanation:

create the formula :

P(A+B) / P(B)

meaning :

probability of getting a large cold drink / getting a large drink

= 5/(5+22)

= 5/27

=5/27 * 100

=18.518

to the nearest percentage  = 19 %

nots : GIVEN THAT --- indicates a criteria - this is put as a denominator

Answer:

No solution

Step-by-step explanation:

Solving inequalities is similar to solving equations. First let's distribute the 3 with (k-9)

\(3(k - 9) > 3k + 6\)

\(3k - 27 > 3k + 6\)

(Subtract 3k from both sides)

\( - 27 > 6\)

\( - 33 > 0\)

(Subtract 6 from both sides. You can also add 27 to both sides. You will get the same answer.)

This inequality is invalid. There are no values of k that make the inequality true.

Answer:

No solution

Step-by-step explanation:

=================================================

Explanation:

Multiply the two values to get 4*15 = 60

Then divide by the GCF 1 to get 60/1 = 60. The GCF being 1 means the result hasn't changed.

------

Another example would be: "Find the LCM of 6 and 8". We would first do 6*8 = 48, then divide by the GCF 2 to get 48/2 = 24. The LCM of 6 and 8 is 24.

Answer:

60

Step-by-step explanation:

When a clay ball is flattened into a pancake-shaped piece, its volume spreads out, resulting in a larger surface area.

However, the amount of clay remains the same, so the total mass or weight of the flattened clay ball does not change.

Therefore, the correct statement is that both the original clay ball and the flattened clay ball will weigh the same.

When clay is flattened, its thickness decreases while its width and length increase. This change in shape affects the distribution of mass, but it does not alter the amount of clay present. As a result, the weight of both clay balls remains equal.

In summary, when a clay ball is flattened into a pancake shape, its weight remains the same.

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Answer:

588.75m³

Step-by-step explanation:

I found out the area of the circle on the bottom and it was 78. 5 which I then times by the height to make 785. 75% of 785 is 588.75

Answer:

Step-by-step explanation:

From the options presented, driver B has the fastest typical race time because he recorded the smallest time taken to complete an individual race.

Also from the standard deviation given (3.96) for driver B, it shows that the individual time spread from the standard deviation is minimal and that the driver maintained a fairly consistent time of race throughout the racing period.

Answer:

77

Step-by-step explanation:

I am right for sure

Answer:

A. 4%

Step-by-step explanation:

We can find out the total weight in the beginning by adding 240+10 which is 250

Then we divide 10/250 or we can multiply both sides by 4 to move the denominator to the 1000th which is 40/1000 and remove a 0 from both sides which makes 4/ 100 or 0.04 which is 4%

Answer:

100 = 2*2*5*5

2 and 5 are the prime factors of 100