A right rectangular prism is sliced in a way such that the plane passes through the prism at a slant. what is the resulting cross section?

Answer:

(15×7)×29/€549×898×68

An writing format called R Markdown (. Rmd) makes it simple to create dynamic documents, presentations, and reports with R.

It mixes R code chunks that are embedded and run so that their result can be included in the final document with the basic grammar of R markdown, a simple plain text format. The following are some benefits of utilizing R markdown: explicitly connects your data, R code, and output to produce a workflow that is completely reproducible. You can include ALL of the R code that was used to explore, summarize, and analyze your data in a single, simple-to-read document.

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A valid study is one that portrays the population being studied and measures what it is supposed to. It must use random sampling and produce expected results to be deemed a reliable source. However, such studies do not necessarily result in a causal relationship between the independent and dependent variables.

The primary goal of any study is to depict the population being investigated in an accurate and unbiased manner. This involves selecting an appropriate sample of the population to study. This is why a study must use random sampling, which means every member of the population has an equal chance of being selected. This helps avoid sample bias, which is when a sample is chosen in a way that it is not representative of the population, leading to incorrect or inaccurate conclusions.

A valid study must measure what it is supposed to, which means that the study should be designed to measure what it claims to measure. For instance, a study on the effects of sleep on memory should use measures that accurately assess memory and sleep. If the study is designed to assess memory but fails to do so, the results will be unreliable. Finally, a valid study verifies expected results.

This means that the study should produce results that are consistent with what is expected based on prior research or theory. However, this does not mean that a study necessarily results in a causal relationship between the independent and dependent variables. Rather, such a relationship can only be inferred if the study is well-designed and the results are properly analyzed and interpreted.

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The correct answer is A) \(5^10\). The expression \(5^3 × 5^7\) is equal to 5 raised to the power of 10.

To simplify the expression \(5^3 × 5^7,\) we can use the property of exponents that states:\(a^m × a^n = a^(m+n).\)

In this case, we have\(5^3 × 5^7.\) According to the exponent property, when we multiply two numbers with the same base, we add their exponents. Therefore, we add the exponents 3 and 7:

\(5^3 × 5^7 = 5^(3+7) = 5^10.\)

So, the correct answer is A) \(5^10\). The expression\(5^3 × 5^7\) is equal to 5 raised to the power of 10.

It's important to understand the exponent properties and the rules of arithmetic when dealing with exponents. When multiplying powers of the same base, we add the exponents. In this case,\(5^3 × 5^7\) simplifies to 5^10.

Therefore, the correct answer is A) \(5^10.\)

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Select the correct answer from the options below. Complete 5^3×5^7=5^2 A)5^10 B)5^15 (C) 5^25 D 5^21

We accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

We have given: μ = 14, x bar = 16, n = 40, s = 6,  α = 5%, = 0.05

To test μ0 : μ = 14   Vs  H1: μ > 14

Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081

So, P value = 0.021

Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

P value for the hypothesis test

n = 50, x bar = 420, sx = 81, μ = 400,

To test:  H0: μ 400    Vs   H1:  μ > 400

It is right tail test

Test statistics =  (X bar - μx)√n / sx = (420 - 400) √50 / 81 =

z = 1.7459

P value = 0.04093

Declsion: We reject H0 is p value < α

Here α = 0.05

Hence P value < α

Conclusion: We accert H1 alternative that is result is population mean greater than 400.

Hence, we accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

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The triangular parcel of land has a total area of 299,294.07 square feet.

To find the area of the triangular parcel of land, we can use Heron's formula, which is based on the lengths of the three sides:

Area = √(s(s-a)(s-b)(s-c))

where a, b, and c are the lengths of the sides, and s is the semiperimeter (half of the perimeter):

s = (a + b + c) / 2

Substituting the given values, we get:

s = (860 + 820 + 1038) / 2

s = 1759

Area = √(1759(1759-860)(1759-820)(1759-1038))

Area = √(1759*899*939*721)

Area = 299294.07

Rounding to two decimal places, the area of the triangular parcel of land is approximately 299,294.07 square feet.

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Answer:

$848

20% of 1000 = 200

1000 - 200 = 800

6% of 800 = 48

800 + 48 = 848

The slope of the line given the information in the table is 1.

The slope is found in linear functions. The slope measures the rate of change of the dependent variable with respect to the independent variable. In this question, the independent variable is x and the dependent variable is y.

Slope = change in the value of y / change in the value of x

Slope = (0 - - 1) / (1 - 0) = 1

Slope =  (1 - 0) / (2 - 1) = 1

Slope = (2 -1 ) / (3 - 2) = 1

Based on the value of the slope, it means that for every one percent change in the value of x, the value of y changes by 1%.

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Answer:

Step-by-step explanation:

look at the x and axis and the irrational fractions and you should find your slope

In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.

The correct answer is Option D.

The key concept here is that a plane is defined by having at least three non-collinear points.

When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.

Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.

Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.

The correct answer is Option D.

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Answer:

Graph A

Step-by-step explanation:

The slope and the intercept represents the week after loan

The amount is not proportional to the number of weeks

What do the slope and the intercept represent?

y = 90 - 10x

y = -10x + 90

The slope = -10

The intercept is given as 90

The y coordinate would be given as 50 dollars while the x coordinate is 4 dollars

2. The slope and the x coordinates are there to tell us of the amount of weeks that are after the loan

3. From the graph, a week is given as 80 dollars

and 4 weeks is given as 50 dollars

This is not proportional

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Answer:

Go to the bottom of that problem and click save for later

Step-by-step explanation:

1 business = 736800 ÷ 9 = 81866.66

Each business associates 81866.66

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

1.  The simultaneous solution of the given equations is X=12/5 and Y=4/5

2.1)The combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.

2)The combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.

To find the simultaneous solution of the given equations 4X+3Y=12 and 2X+4Y=8, we can use the method of elimination, also known as the addition method. Multiplying the second equation by 2, we get 4X+8Y=16.

Now, we can subtract the first equation from the second equation: 4X+8Y - (4X+3Y) = 8Y - 3Y = 5Y and 16 - 12 = 4. Thus, 5Y=4 or Y = 4/5.

Substituting this value of Y in any of the two equations, we can find the value of X. Let's substitute this value of Y in the first equation: 4X+3(4/5)=12 or 4X

= 12 - (12/5)

= (60-12)/5

= 48/5.

Thus, X = 12/5. Hence, the simultaneous solution of the given equations is X=12/5 and Y=4/5.2. To find the optimal values of X and Y that will maximize the objective function Z=$10X+$50Y, we need to use the method of linear programming.

First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 3X+4Y=12, 2X+5Y=10, X=0, and Y=0.

To find the optimal solution, we need to evaluate the objective function at each of the corner points of the feasible region, and choose the one that gives the maximum value.

Let's denote the corner points as A, B, C, and D, as shown above. The coordinates of these points are: A=(0,3), B=(2,1), C=(5/2,0), and D=(0,0). Now, let's evaluate the objective function Z=$10X+$50Y at each of these points:

Z(A)=$10(0)+$50(3)

=$150, Z(B)

=$10(2)+$50(1)

=$70, Z(C)

=$10(5/2)+$50(0)

=$25, Z(D)

=$10(0)+$50(0)=0.

Thus, we can see that the maximum value of Z is obtained at point A, where X=0 and Y=3. Therefore, the combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.

To find the combination of X and Y that will provide a minimum for the problem Minimize Z=X+5Y subject to: 4X+3Y≥12 and 2X+5Y≥10, we need to use the same method of linear programming as above.

First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 4X+3Y=12, 2X+5Y=10, X=0, and Y=0.

To find the optimal solution, we need to evaluate the objective function Z=X+5Y at each of the corner points of the feasible region, and choose the one that gives the minimum value.

Let's denote the corner points as A, B, C, and D, as shown above.

The coordinates of these points are: A=(3,0), B=(5,1), C=(0,4), and D=(0,0).

Now, let's evaluate the objective function Z=X+5Y at each of these points:

Z(A)=3+5(0)=3,

Z(B)=5+5(1)=10,

Z(C)=0+5(4)=20,

Z(D)=0+5(0)=0.

Thus, we can see that the minimum value of Z is obtained at point A, where X=3 and Y=0. Therefore, the combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.

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If two angles are on a straight line, that means the sum of the two angles is 180 degrees, so we get the equation:

   \(5x +13x = 180\)

Hope that helps!

Answer:

(a) False

(b) False

(c) True

Step-by-step explanation:

(a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger.

No, since changing the units of measurement does not change the correlation coefficient

(b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date.

Negative association means that as one variable increases, the other decreases, Here, we see that as the heights of the men increase, the height of the women do not reliably decrease, hence there is no strong negative asscoiation

(c) There is a positive association between the heights of men and women.

We see from the values given that as the heights of men increase, so do the heights of women and vise versa, so there is a positive association between the heights of men and women

The capacity of the process would remain the same even if all workers do all three tasks. This is because the capacity of a process is determined by the slowest step, or the bottleneck, in the process.

In this case, the bottleneck is still the same, so the capacity of the process will not change. However, integrating the work so that all workers do all three tasks can increase the efficiency and flexibility of the process, as workers can switch between tasks as needed.

It is important to note that the capacity of the process is not determined by the number of workers or stations, but by the slowest step in the process. Therefore, even if all workers do all three tasks, the capacity of the process will remain the same.

In conclusion, the capacity of the process will remain the same if all workers do all three tasks, as the bottleneck in the process remains the same. However, integrating the work can increase the efficiency and flexibility of the process.

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Answer:

Step-by-step explanation:

top one : surface area of a cone

middle one : surface area of a cylinder

last one: surface area of a pyramid

Answer:

70.01.

Step-by-step explanation:

159 - 88.99

= 159 - 90 + 1.01

= 69 + 1.01

= 70.01.

The phase margin of the system is approximately 7.38 degrees.

To find the phase margin, we first need to find the closed-loop transfer function of the system. For a unity feedback system, the closed-loop transfer function is given by:

T(s) = G(s) / (1 + G(s))

where G(s) is the forward path transfer function.

Substituting G(s) into the equation above, we get:

T(s) = 100 (s + 2) s(s + 1)(s + 4) / [s(s + 1)(s + 4) + 100 (s + 2)]

Simplifying the expression above, we get:

T(s) = 100 (s + 2) / [s(s + 1)(s + 4) + 100 (s + 2)]

To find the phase margin, we need to find the frequency at which the phase of the closed-loop transfer function is -180 degrees. We can do this by setting the denominator of the closed-loop transfer function equal to zero and solving for the frequency. This frequency is known as the phase crossover frequency.

Setting the denominator of the closed-loop transfer function equal to zero, we get:

s(s + 1)(s + 4) + 100 (s + 2) = 0

Expanding the equation above, we get:

s^3 + 5s^2 + 4s + 200 = 0

Using a numerical method or a graphical method, we can find that the phase crossover frequency is approximately 2.02 rad/s.

To find the phase margin, we need to evaluate the phase of the closed-loop transfer function at the frequency of 2.02 rad/s. We can do this by substituting s = j2.02 into the closed-loop transfer function and computing the phase angle.

Substituting s = j2.02 into the closed-loop transfer function, we get:

T(j2.02) = 100 (j2.02 + 2) / [j2.02(j2.02 + 1)(j2.02 + 4) + 100 (j2.02 + 2)]

Taking the complex conjugate of the denominator and multiplying the numerator and denominator by the complex conjugate of the denominator, we get:

T(j2.02) = [100 (j2.02 + 2)] / [|j2.02|^2 (j2.02 + 1)(j2.02 + 4) + 100 (j2.02 + 2)] × e^jθ

where θ is the phase angle.

Computing the magnitude and phase angle of the closed-loop transfer function at the frequency of 2.02 rad/s using a calculator or software, we get:

|T(j2.02)| = 0.2806

θ = -172.62 degrees

The phase margin is then given by:

PM = 180 degrees + θ

PM = 180 degrees - 172.62 degrees

PM = 7.38 degrees

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The given question is incomplete, the complete question is:

For the unity feedback system, the forward path transfer function is: G(s) = 100 (s + 2) s(s + 1)(s + 4) . find the phase margin.

Answer: 0.75 cups in each serving

Step-by-step explanation:

13 and 1/2 cups of cereal in a box, and evenly distributed would be 13.5/18

There are 3/4 cups of cereal in each serving.

Given that there are 18 servings in a box of cereal, the box contains 13 1/2 cups of cereal,

We need to find the number of cups in each serving.

To find out how many cups are in each serving, you need to divide the total number of cups in the box (13 1/2 cups) by the number of servings (18).

To perform the calculation, let's first convert the mixed number 13 1/2 into an improper fraction:

13 1/2 = (2 x 13) + 1 = 27/2

Now, divide the total cups by the number of servings:

Cups per serving = Total cups / Number of servings

Cups per serving = 27/2 / 18

To divide a fraction by a whole number, you multiply the fraction by the reciprocal of the whole number:

Cups per serving = (27/2) x (1/18)

Now, simplify the fraction:

Cups per serving = 27/36

Cups per serving = 3/4

So, there are 3/4 cups in each serving of cereal.

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In order to make it simpler to recognize the values in the chart, a gridline is a line that extends from the chart's horizontal or vertical axis into the plot area.

Therefore, in order to make it simpler to recognize the values in the chart, a gridline is a line that extends from the chart's horizontal or vertical axis into the plot area.

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Correct question:
a(n) ____ is a line that extends from the chart's horizontal or vertical axis into the plot area, making it easier to identify the values in the chart.

Answer:

51 seats

Step-by-step explanation:

96 = 2 buses minus six seats

96 = 2x -6

102 = 2x

102/2 = x

51 seats

To show that the Bessel equation of order one-half, x^2y'' + xy' + (x^2 - 1/4)y = 0, x > 0, can be reduced to the equation v'' + v = 0, we will use the change of dependent variable y = x^(-1/2)v(x).

First, we will find the derivatives of y in terms of v:
y' = -1/2x^(-3/2)v + x^(-1/2)v'
y'' = 3/4x^(-5/2)v - x^(-3/2)v' + x^(-3/2)v'

Next, we will substitute these derivatives into the original Bessel equation:
x^2(3/4x^(-5/2)v - x^(-3/2)v' + x^(-3/2)v') + x(-1/2x^(-3/2)v + x^(-1/2)v') + (x^2 - 1/4)x^(-1/2)v = 0

Simplifying the equation gives us:
(3/4)v - x^(-1/2)v' + x^(-1/2)v' - (1/2)x^(-1/2)v + x^(1/2)v' + x^(3/2)v - (1/4)x^(-1/2)v = 0

Combining like terms gives us:
v'' + v = 0

Therefore, the Bessel equation of order one-half can be reduced to the equation v'' + v = 0 by the change of dependent variable y = x^(-1/2)v(x).

From this, we can conclude that y1(x) = x^(-1/2)cosx and y2(x) = x^(-1/2)sinx are solutions of the Bessel equation of order one-half, since they satisfy the equation v'' + v = 0.

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Answer:

∠ W = 30°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos W = \(\frac{adjacent}{hypotenuse}\) = \(\frac{WY}{WX}\) = \(\frac{2\sqrt{21} }{4\sqrt{7} }\) = \(\frac{1}{2}\) \(\sqrt{\frac{21}{7} }\) = \(\frac{\sqrt{3} }{2}\) , then

∠ W = \(cos^{-1}\) ( \(\frac{\sqrt{3} }{2}\) ) = 30°

Answer:

ITs C One solution

Step-by-step explanation:

Two sides are not equal.

Answer:

what are the options?

Step-by-step explanation:

The proof of similar triangles are;

1)  Triangles ABC and EFG are not similar triangles.

2) Both triangles are similar triangles by AA Similarity Postulate

Similar triangles are defined as triangles that have the same shape, but then their sizes may vary. Now, all equilateral triangles, squares of any side lengths are examples of similar objects. This means that, if two triangles are similar, then we can say that their corresponding angles are congruent and corresponding sides are in equal proportion.

1) Triangles ABC and EFG are not similar because none of the corresponding angles nor corresponding sides are congruent to themselves.

2) Looking at both triangles formed, we can say that;

∠JLK ≅ ∠JMN by alternate angles postulate

∠JNM ≅ ∠JKL by alternate angles postulate

Similarly ∠J is congruent to itself by Reflexive property and as such both triangles are similar by AA Similarity postulate.

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