(Multiplying Rational Numbers MC)
ft.
Lorie ordered a shed to hold her gardening supplies. The shed had a length of 14.25 ft, a width of 13 ft, and a height of 4
Determine the volume, V, using the formula V = wh.
O 778.05 ft
O728.05 ft
O 59.85 ft³
O 31.45 ft

The normal distribution have an importance in statistics of whether or not out appears in nature, because it fits several natural phenomena.

For exa. measurement error, heights, IQ scores, and physical activity measures all follow the normal distribution.

In this question we need to describe why does the normal distribution have an importance in statistics of whether or not out appears in nature.

We know that if we plot the probability distribution and it forms a bell-shaped curve. If the mean, mode, and median of the sample are equal then the variable has normal distribution.

A normal distribution is dependent on two parameters of the data set: mean and the standard deviation of the sample.

This characteristic of the normal distribution makes it extremely simple.

Also, the normal distribution is important because of the Central limit theorem.

It makes math easy - like calculating moments, correlations between variables, and other calculations that are domain specific.

So, the normal distribution have an importance in statistics of whether or not out appears in nature.

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Answer:

c. 4^3 * 5^2 (1600)

d. 9^4 * 7^2 (321489)

Step-by-step explanation:

Hi!

Remember that exponents are the number times itself (2*2 = 2^2).

So, in c, we have 4 times 4 times 4. We have 4 multiplied by 4 3 times. We can also write this as 4^3.

We also have 5 times 5. We can also write this as 5^2.

However, we need to multiply 5^2 by 4^3. So:

4^3 times 5^2 or 1600.

d.

Let's group the similar numbers together.

9 x 9 x 9 x 9 and 7 x 7

There are 4 9's, so 9^4.

There are 2 7's, so 7^2

Multiply the 2.

9^4 * 7^2

Answer:

30 days.

Step-by-step explanation:

Hope it helps! =D

Answer:

ummmm

Step-by-step explanation:

The 715 cm² area of the disc and the ±5 cm² error tolerance, gives;

a) x = √(715/π) cm

b) The range for the radius is; [√(710/π) cm, √(720/π) cm]

c)

f(x) = π•x²

L = 715 cm²

E = 5 cm

d = √(5/π) cm

Area of the circular metal disk = 715 cm²

a) Required; The disk radius

Let A represent the area of the disk and let x represent the radius, we have;

A = π•x²

Therefore;

x = √(A/π)

Which gives;

x = √(715/π) cm

b) Allowed area error tolerance = ± 5 cm²

The allowed range of values for the area is therefore;

Which gives;

√(710/π) ≤ x ≤ √(720/π)

c) From the \( \epsilon / \delta \) definition of limits, we have;

\( \lim\limits_{x → √(715/π)} f(x) = 715 \)

Which gives;

f(x) = A = π•x²

L = 715

|f(x) - L| < E = 5 cm

|x - √(715/π)| < d = √(5/π)

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Answer:

This statement is true.

In the simplex method, choosing the pivot row involves selecting a row with a negative value in the right-hand column and dividing the elements in the last column by the corresponding elements in the selected row to obtain the ratios. The row with the smallest non-negative ratio is then chosen as the pivot row.

By choosing the pivot row in this way, we ensure that the new solution will still be feasible, meaning that all the constraints will still be satisfied. This is because choosing the smallest non-negative ratio ensures that the new solution will not violate any of the non-negativity constraints.

Therefore, requiring that the ratio associated with the pivot row be the smallest non-negative number is an important step in the simplex method to ensure that the iteration will not take us from a feasible point to a non-feasible point.

Step-by-step explanation:

This statement is true when using the simplex method to solve a linear programming problem.

In the simplex method, we start with a feasible solution and iteratively improve it until we reach an optimal solution. At each iteration, we choose a pivot row and a pivot column to pivot around. The pivot row is chosen based on the ratio of the right-hand side value to the coefficient of the entering variable in that row. This ratio is called the pivot ratio.

Choosing the pivot row with the smallest non-negative pivot ratio ensures that we pivot to a new feasible solution. This is because the pivot row represents a constraint in the linear programming problem, and the pivot ratio represents how much we can increase the value of the entering variable while still satisfying that constraint. If the pivot ratio is negative, it means that increasing the entering variable would violate the corresponding constraint, and so we cannot pivot in that direction.

Therefore, by choosing the pivot row with the smallest non-negative pivot ratio, we ensure that we pivot in a direction that preserves feasibility and does not take us to a non-feasible point.

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The question is incomplete. Here is the complete question.

Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. find the probability that a call takes

a) 3 minutes or less

b) 4 minutes of less

c) 5 minutes of less

d) Longer than 5 minutes

e) Longer than 7 minutes

Answer: a) P(X<3) = 0.882

              b) P(X<4) = 0.908

              c) P(X<5) = 0.928

              d) P(X>5) = 0.286

              e) P(X>7) = 0.174

Step-by-step explanation: Exponential distribution is related with teh amount of time until some specific event happens.

If X is a continuous random variable, probability is calculated as:

\(P(X<x) = 1-me^{-mx}\)

in which:

m is decay parameter, given by: \(m=\frac{1}{mean}\)

For the Nite Time Inn calls:

\(m=\frac{1}{4}\)

m = 0.25

(a) P(X<3)

\(P(X<3) = 1-0.25e^{-0.25.3}\)

\(P(X<3) = 1-0.25e^{-0.75}\)

\(P(X<3) = 1-0.25*0.472\)

P(X < 3) = 0.882

The probability the call takes less than 3 minutes is 0.882.

(b) P(X<4)

\(P(X<4) = 1-0.25e^{-0.25.4}\)

\(P(X<4) = 1-0.25e^{-1}\)

P(X < 4) = 0.908

The probability the call takes less tahn 4 minutes is 0.908.

(c) P(X<5)

\(P(X<5) = 1-0.25e^{-0.25.5}\)

\(P(X<5) = 1-0.25e^{-1.25}\)

P(X < 5) = 0.928

The probability of calls taking less than 5 minutes is 0.928.

(d) P(X>5)

Knowing that the sum of probabilities of less than and more than has to equal 1:

P(X<x) + P(X>x) = 1

P(X>x) = 1 - P(PX<x)

\(P(X>x) = 1-(1-me^{-m*x})\)

\(P(X>x)=me^{-mx}\)

For P(X>5):

\(P(X>5) = 0.25e^{-1.25}\)

P(X > 5) = 0.286

The probability of calls taking more than 5 minutes is 0.286.

(e) P(X>7)

\(P(X>7)=0.25e^{-0.25.7}\)

\(P(X>7)=0.25e^{-1.75}\)

P(X > 7) = 0.174

The probability of calls taking more than 7 minutes is 0.174.

Based on the analysis, discuss any differences observed between the two training methods. Discuss the analysis and findings. Reflect on the results of the analysis.

However, I can guide you on how to approach the analysis and provide you with a general outline of the steps you can follow:

Read the case problem

Review the case problem from Chapter 11 of the ebook related to the Air Force training program.

Perform the analysis

a) Run the F-test two-sample for variances:

Using Excel's Data Analysis ToolPak, follow the instructions from the provided video to perform an F-test two-sample for variances on the training data file.

b) Summarize the training time data:

Calculate appropriate descriptive statistics (e.g., mean, standard deviation) for each training method. Compare the summary statistics to identify similarities or differences between the two methods.

c) Conduct a hypothesis test on the difference between population means:

Perform a hypothesis test (e.g., independent t-test) to assess whether there is a statistically significant difference between the population means of the two training methods. Interpret and discuss the findings.

d) Calculate standard deviation and variance:

Compute the standard deviation and variance for each training method. Compare the values to gain insights into the variability within each method.

e) Conduct a hypothesis test on the equality of population variances:

Perform a hypothesis test (e.g., F-test) to determine if there is a significant difference in population variances between the two training methods. Analyze the results and discuss the findings.

f) Draw conclusions and provide recommendations:

Based on the analysis, discuss any differences observed between the two training methods. Provide a conclusion and recommendation on which training method appears to be more effective. Justify your recommendation with supporting evidence from the analysis.

Discuss the analysis and findings

Reflect on the results of the analysis. Identify any surprising or noteworthy findings. Formulate recommendations based on the findings and include specific details from the managerial report to support your recommendations.

Please note that without access to the actual data or case problem, the guidance provided is general in nature. It's important to adapt the steps to the specific case problem and data provided in the ebook.

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none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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Answer:

£65

Step-by-step explanation:

1235 / 19 = 65

(Meeting character limit)

The general expression is 130 x - 600 and total points scored by the player is 1220

A) Let the number of correctly answered questions be x.

∴ Number of incorrectly answered questions will be 20 - x.

+ 100 points is awarded for each question answered correctly while -30 points is awarded for each question answered incorrectly.

Thus, the general equation becomes

= 100x - (20 - x)(-30)

= 100x +30x - 600

= 130x - 600

Thus the general expression becomes 130 x - 600

B)  The player answers 14 questions correctly, thus x = 14

Substituting the value of x =14 in the general equation we get,

= 130(14) - 600

= 1820 - 600

= 1220.

Thus the total points scored by the player will be 1220

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Answer:

7y2 + 8xy - 3

Step-by-step explanation:

7y2 + 6xy + 2xy -3  You distribute the - sign through the second binomial.  You are distributing or multiplying (-2xy -3) by -1  Combine like terms

7y2 + 8xy -3

Answer:

What is the difference of the two polynomials?

(7y2 + 6xy) – (–2xy + 3)

7y2 + 4xy – 3

7y2 + 8xy – 3 Correct

7y2 + 4xy + 3

7y2 + 8xy + 3

Step-by-step explanation:

Answer:

b =0

Step-by-step explanation:

The only value where  |b| = -b  is when b=0

|0| = -0

0 = 0

Absolute value means non- negative

non-negative = negative

This is only true when we equal zero

Answer: b = 0 or anything negative (like b = -2)

So any value of b such that \(b \le 0\)

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

Explanation:

|b| is the distance from b on the number line to 0

The distance is never negative as negative distance does not make sense.

If b was some positive number, then |b| = b. For instance, |7| = 7. This shows 7 is seven units away from 0 on the number line.

----------

If b is negative or zero, then |b| = -b. Why? Because the result of |b| is the opposite of whatever negative b value you put in. For example, b = -2 leads to

|b| = |-2| = 2

while

-b = -(b) = -(-2) = 2

The two negatives cancel each other out to get a positive result.

This shows, |-2| = -(-2) = 2

Meaning that the location -2 is two units away from 0 on the number line.

Answer:8000

Step-by-step explanation:

The Volume of the box will be 8000 in.³

What is volume ?

Volume is a three dimensional space occupy by the body of particular shape such as here :

It should be noted that a box has six sides that are equal. In this case, we've been given the side of one of the lengths to be 20 inches.

The volume of a cube is :

V = a³

Therefore, the Volume of the box will be :

V = 20³

V = 8000 in.³

Therefore, the Volume of the box will be 8000 in.³

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If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;

P = l+l+w+w

P= 2(l+w)

60 = 2( 17+w)

60 = 2( 17+w)

17+w= 60/2

17+ w = 30

w = 30-17

w = 13cm

Therefore the height of the train ticket is 13cm

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Answer:

−x5 + 7x4 + 8x2 − 9x − 5

Step-by-step explanation:

I do not have one so sorry :/

The subsequent hypothesis tests has to be run the alternative hypothesis Hₐ: μ < 1200, it is a left tail test.

Given that,

If the typical round-trip cost between Philadelphia and Dublin is less than $1,200, Expedia would want to investigate.

We have to find which of the subsequence hypothesis tests has to be run.

We know that,

The claim : If the average round-trip between Philedelphia and

Dublin is less than $1200.

So, claim is the alternate hypothesis.

Hₐ: μ < 1200

H₀: μ = 1200

Since the Hₐ: μ < 1200, it is a left tail test.

Therefore, the subsequent hypothesis tests has to be run the alternative hypothesis Hₐ: μ < 1200, it is a left tail test.

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The individuals in this set are C) Basketball players

This is because it's listing all the player names with their associated stats.

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

The data contains B) 3 variables, 2 of which are quantitative

The variables are

The first two variables are quantitative as they deal with numeric values, and it makes sense to do things like find the average. The last variable is qualitative. It is also an ordinal variable because we can order the labels from freshman to senior.

This data on the statistics from the basketball game contains 3 variables, 2 of which is quantitative.

A quantitative variable is a variable that can be used to show the degree of magnitude. This means that quantitative variables can be represented with numbers.

The quantitative variables are free throw percentage and the number of assists.

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\( \frac{4}{6} \times \frac{2}{5} \\ = \frac{4 \times 2}{6 \times 5} \\ = \frac{8}{30} \\ = \frac{4}{15} \)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Her grade on a fourth test is 75.

The average of e for the four tests is 84.

By substituting the given data in the equation, we get

Let the fourth test marks be x

83 + 90 + 88 + x / 4 = 84

261 + x / 4 = 84

261 + x = 336

x = 336 - 261

x = 75

An average may be described as the sum of all numbers divided by means of the whole quantity of values.

A mean can be defined as an average of the set of values in a sample of data. In different words, a median is also called the mathematics mean.

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When the population standard deviation is unknown and the population is not skewed or has outliers, we can use the t-distribution for inference about a mean.

If the population standard deviation, σ, is unknown, and the shape of the original population is not skewed and does not possess outliers, we may use the t-distribution for inference about a mean.

The t-distribution is a probability distribution that is similar to the normal distribution but with slightly thicker tails. It is used when the population standard deviation is unknown and the sample size is small (typically less than 30). The t-distribution allows us to calculate confidence intervals and perform hypothesis tests for the population mean.

To use the t-distribution, we need to know the sample mean, sample size, and the critical value from the t-table or t-distribution calculator. The critical value depends on the desired level of confidence and degrees of freedom, which is determined by the sample size minus one.

To calculate a confidence interval, we use the formula:

Confidence interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

To perform a hypothesis test, we compare the test statistic (calculated using the t-distribution) to the critical value from the t-table.

In summary, when the population standard deviation is unknown and the population is not skewed or has outliers, we can use the t-distribution for inference about a mean.

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The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.

To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.

The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).

To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.

Comparing the two equations, we get:

4a = 16

a = 4

Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.

Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.

Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.

Substituting x = 8 into the equation of the parabola, we get:

\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)

Therefore, the width of the rectangle is approximately 11.31 units.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(length + width)

Plugging in the values, we have:

Perimeter = 2(16 + 11.31)

Perimeter ≈ 2(27.31)

Perimeter ≈ 54.62

Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.

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The value of the function r′(8) to the nearest tenth when r(x)=90x⁵/2ˣ term is given is -785.1

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealisation of how a variable quantity depended on another quantity.

r(x) = \(\frac{90x^5}{2^x}\)

r'(x) = 450x⁴/2ˣ + 90x⁵ [-log2/2ˣ]

= 450x⁴ - 90x⁵.log2/2ˣ

= 90x⁴{5 - xlog2}/2ˣ

So, the value of 1 ate x = 8

90x 8⁴{5-8log2}

= -785.1 ( rounding off to the nearest decimal )

\(\int\limits^a_b {7x(2x^2+1)^6} \, dx = 7/4\int\limits^a_b {4x(2x^2+1)^6} \, dx\)

Let, 2x² +1 = y

4xdx = dy

\(\int\ {7x(2x^2+1)^6 } \, dx \\\\=7/4\int {y^6} \, dy\\\\=1/4.y^7\\\\=y^7/4\\\\=(2x^2+1)^7/4\)

So the value of ∫7x(2x²+1)⁶ is (2x²+1)⁷/4

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Answer:

To find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8), we can use the formula:

P = (1 - t)A + tB

where t is a scalar value that represents the position of P on the segment AB, and A and B are the coordinates of the two endpoints of the segment.

In this case, we know that the part-to-whole ratio is 1:5, so t = 1/6.

So we substitute the values for A, B and t into the formula:

P = (1 - 1/6)A + (1/6)B

P = (5/6)A + (1/6)B

P = (-95/6, 35/6) + (1/6, 8/6)

P = (-15/2, 5/2) + (1/6, 4/3)

P = (-15/2 + 1/6, 5/2 + 4/3)

P = (-30/3, 23/6)

The coordinates of P are (-10,3.83)

For the second problem,

To find the coordinates of P so that P partitions the segment AB in the ratio 3 to 1 if A(7, -4) and B(-5, 4), we can use the same formula as above:

P = (1 - t)A + tB

In this case, we know that the part-to-whole ratio is 3:1, so t = 3/4.

So we substitute the values for A, B and t into the formula:

P = (1 - 3/4)A + (3/4)B

P = (1/4)A + (3/4)B

P = (7/4, -4/4) + (-53/4, 43/4)

P = (7/4 + -15/4, -4/4 + 3)

P = (-8/4, -1/4)

The coordinates of P are (-2,-0.25)

So in the first problem point P is (-10,3.83) and in the second problem point P is (-2,-0.25)

AnswerAnswerAnswerAnswerAnswerAnswerdeciAnswerAnswer:17/20

Step-by-step explanation:

.85 converts to 85/100 because you move the decimal over two placesplacesplaces. Then you devide both the top and bottom numbers by 5 which would equal 17/20.

The maximum-flow problem is set up by representing the package types as source nodes, the trucks as sink nodes, and introducing intermediate nodes for individual packages.

We can represent the types of packages as source nodes, the trucks as sink nodes, and the edges between them as the possible flow of packages. Each edge will have a capacity equal to the number of available packages of that type. For example, if there are three packages of type A, there will be an edge from the source node of type A to each truck node, with a capacity of 3.

Additionally, to ensure that no truck carries two packages of the same type, we can introduce intermediate nodes representing the individual packages. Each package node will be connected to the corresponding type node and truck nodes. This will create a one-to-one mapping between package nodes and truck nodes for each package type.

To represent the constraints on truck capacities, we assign the capacities of the edges between the package nodes and truck nodes as the capacities of the trucks. For instance, if Truck 1 has a capacity of 6 packages, the corresponding edge capacity will be 6.

By finding a maximum flow in this graph using algorithms like Ford-Fulkerson or Edmonds-Karp, we can determine whether it is possible to load the packages onto the trucks without any truck carrying two packages of the same type. If the maximum flow is equal to the total number of packages, it indicates a feasible solution.

In summary, the maximum-flow problem is set up by representing the package types as source nodes, the trucks as sink nodes, and introducing intermediate nodes for individual packages. The capacities of the edges are determined by the package counts and truck capacities. The objective is to find a maximum flow that satisfies the constraints, indicating whether the packages can be loaded onto the trucks without violating the given conditions.

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Answer:

$240

Step-by-step explanation:

30 (the weeks in 7 months) times 8 (his weekly savings) = 240

Answer:

\(\frac{8}{5}\)  or 1.6

Step-by-step explanation:

If this is the equation then the answer should be correct.

\(2^{3x}\) x \(2^{2x}\) = \(2^{8}\)