Solve for j in the proportion.

keeping in mind that a centroid cuts all medians at a 2 : 1 ratio, meaning that the median AE gets cut on a 2 : 1 ratio, meaning AG : GE = 2 : 1, Check the picture below.

Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

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Answer:

\( \frac{k}{2} + \frac{1}{2} = 3 \\ \frac{k}{2} = 3 - \frac{1}{2} \\ \frac{k}{2} = \frac{(6 - 1)}{2} \\ \frac{k}{2} = \frac{5}{2} \\ \boxed{k = 5}✓\)

The Z-value represents the number of standard deviations away from the mean a particular value is. To find the Z-value when x is 10, given the population mean and standard deviation of 7 and 3, respectively, we use the following formula:

Z = (X - μ) / σ

Where:

X = 10 (the value of x)

μ = 7 (the population mean)

σ = 3 (the population standard deviation)

Plugging in the values, we get:

Z = (10 - 7) / 3 = 3 / 3 = 1

So the Z-value when x is 10 is 1, which means that x is 1 standard deviation above the mean.

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Answer:

C) 98

Step-by-step explanation:

Hope this helps! sry  if I'm wrong

The value of x in the given equation 15x + 120 = 5x + 1100 is 98. Option C is correct.

An equation is a combination of numbers, variables, mathematical operations, and functions. It is basically a statement emphasising that the two or more expressions are equal to each other.

The given equation is

15x + 120 = 5x + 1100

Take the like terms together,

15x - 5x = 1100 - 120

10x = 980

x = \(\frac{980}{10}\)

x = 98.

Thus, the option C is correct stating that the value of x in the given equation is 98.

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The complete question is as follows:

Find the value of x in the equation:

15x + 120 = 5x + 1100.

A. 66

B. 122

C. 98

D. 76

SUBMIT.

Answer:

1/4xy(x^2+3y)

Step-by-step explanation:

oh ok last one was missing that y thx for reposting

The model used by Victor in the linear equation is incorrect,

The parameters are that;

Victor saved: $89.25

Cost of the bicycle = $129.85

Thus, to find the amount extra that he will need to purchase the bicycle, the equation model should be;

$89.25 + x = $129.85

This can be expressed in words as;

The amount of money he already has saved + the amount of money he still requires = the total price of the bike.

An equation that correctly represents this problem can show the sum of the amount of money he already has and the amount of money he needs equals the total cost of the bicycle

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Complete question is;

Victor has saved $89.25 for the bicycle that he wants. The bicycle costs $129.85. Victor writes the equation below to help him determine the additional amount that he needs to solve to have enough to buy the bicycle.

89.25 + 129.85 = x

Does Victor's equation correctly model the problem?

The possible number of ways of selection by using combination formula is 3060.

What is combination?

A grouping of items where the order in which they were chosen is irrelevant is known as combination.

Given that the number of people in the group is 18. Only 4 people will be member of the council.

The formula of combination is \(^{n}C_{r}=\frac{n!}{r!(n-r)!}\) , where r number of objects are selected from n objects.

In the given question the value of n is 18 and the value of r is 2.

Substitute the value of n and r in \(^{n}C_{r}=\frac{n!}{r!(n-r)!}\).

\(^{18}C_{4}=\frac{18!}{4!(18-4)!}\)

Solve the above expression:

18^C_4 = 18x17x16x15x14/4x14

18^C_4 = 18x17x16x15/4x3x2x1

3060 18^C_4 = 3060

The number of ways such selection is 3060.

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Answer:

Please check explanations

Step-by-step explanation:

Mathematically, the area of a triangle

A = 1/2 * b * h

b is base, h is height

For 12 square units, we can have a base of 6 and a height of 4

By tripling the dimensions for the second triangle, we will have a triangle of 18 by 12

So the new area is;

A = 1/2 * 12 * 18

That was how we got 108 square units

Answer: X= - or + square root of 10

Step-by-step explanation: both negative or positive roots would multiply to be 10

Answer: Your welcome the answer is in the attached Image.

Step-by-step explanation: mark me brainliest.

Answer:

Step-by-step explanation:

1) 2.094  <  2.702

2) 10.09 < 10.9

5) 24.552 = 24.522

6) 21.337 > 21.31

At least 36.05 games should be played for the owner to make at least $75.

Let the number of games played = g

According to question,

Cost of each game = $7

Cost of g games = 7g

Prizes awarded to the winner costs the owner = $177.35

To make at least $75, the equation is

7g - 177.35 ≥ 75

7g ≥ 75 + 177.35

7g ≥ 252.35

 g ≥ 252.35 / 7

 g ≥ 36.05

Hence, at least 36.05 games should be played.

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Answer:

6

Step-by-step explanation:

Let x = amount of her pocket money.

Let b = price of 1 blouse.

Let j = price of 1 pair of jeans.

j = 3b

3/8 x was used for blouses

5/8 x was left after the blouses

3/5 of 5/8 x was used for 2 pairs of jeans

3/8 x was used for 2 pairs of jeans

1 pair of jeans costs 3/16 x

3 blouses cost 3/16 x

1 blouse costs 1/16 x

3/8 x was used for blouses

1 blouse costs 1/16 x

(3/8) / (1/16) = 3/8 × 16/1 = 6

Answer: 6

Answer:(12,-7)

Step-by-step explanation:

Answer:

c = 36

Step-by-step explanation:

If the coefficient of \(x^{2}\) is one, then c = \((\frac{12}{2}) ^{2} = 6^{2} = 36\)

Answer: A. 85.5 square feet

Step-by-step explanation: Hope this help :D

The distance of the hiker of a linear function.

The true statement is (d) The y-intercept is (0, 2), and the 2 represents the number of miles  from the car at the start of this time period.

From the graph, we can see that the graph crosses the y-axis at: (0,2)

This means that, the y-intercept is (0,2), and 2 represents the number of miles, he started with.

Hence, the correct statement is (d)

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Answer: 59.5

Step-by-step explanation:

took the test

The dimensions are 156m and 65m

The perimeter is 442m.

The formulae that can be used to determine the dimensions when the ratio of the dimensions are given and the diagonal is given are:

h = \(\frac{H}{\sqrt{ 1 + r^{2} } }\)

w = \(\frac{Hh}{\sqrt{ 1 + r^{2} } }\)

Where:

h = \(\frac{169}{\sqrt{ 1 + 0.41667^{2} } }\) = 156m

w = \(\frac{(169 x 156)}{\sqrt{ 1 + 0.41667^{2} } }\) = 65m

The perimeter of a rectangle = 2(length + width)

2(156 + 65)

2(221) = 442m

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(7x8)+10

I’m pretty sure, so sorry if I’m wrong

7+8=15

15<25

this is probs the wrong answer but my sister made me put it i said

7+8=15

15+10=25

i dont know which one you are looking for but i think mine is correct

The correct alternative hypothesis in this case would be Ha: u not equal to 8, option a. This is because the null hypothesis in this scenario would be that the mean of the bottles of cream being filled is equal to 8 ounces.

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Answer: c

Step-by-step explanation: i took the test and got it right sorry if it is wrong hope it helps

Answer:

7/9= 0.77(repeating) and 3/8=0.375

Step-by-step explanation:

The survival time of a 60kg deer without food at -20 degrees Celsius depends on various factors, including its age, sex, and physical condition. However, assuming the deer is healthy and has 5kg of fat, it could potentially survive for around 30 to 50 days without food.

The exact survival time can vary depending on several factors, such as the deer's level of physical activity, environmental conditions, and how much energy it is expending to stay warm in the cold temperature. Additionally, if the deer is able to find sources of water, this can also increase its chances of survival.

It's important to note that this is just an estimate and that the actual survival time may vary. If the deer is injured or sick, its chances of survival may be reduced, and it may not be able to survive as long without food.

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Complete Question

How many days could a 60kg deer survive without food at -20 degrees Celsius if it has 5kg of fat?

The  p-value is approximately 0.027 (rounded off to two decimal places).

To determine whether there is strong evidence that more than 15% of college students in America have at least one sibling, we can use a hypothesis test with a significance level of 0.05.

Let p be the proportion of college students in America who have at least one sibling. The null hypothesis is that p ≤ 0.15, and the alternative hypothesis is that p > 0.15.

Under the null hypothesis, the number of students in a sample of 100 who have at least one sibling follows a binomial distribution with parameters n = 100 and p = 0.15. We can use this distribution to calculate the probability of observing 20 or more students with at least one sibling in a sample of 100 if the null hypothesis is true.

The p-value is the probability of observing a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. In this case, the test statistic is the number of students with at least one sibling in a sample of 100.

Using a binomial distribution calculator or software, we find that the probability of observing 20 or more students with at least one sibling in a sample of 100 if p = 0.15 is approximately 0.027.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is strong evidence that more than 15% of college students in America have at least one sibling.

Therefore, the p-value is approximately 0.027 (rounded off to two decimal places).

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A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable.

In experimental research, an independent variable is a variable that the researcher manipulates or systematically varies in order to study its effect on the dependent variable. It is called "independent" because it is not influenced by any other variables in the experiment, and its effects on the dependent variable can be observed and measured independently of any other factors.

Only when a possible design confound fluctuates systematically with the independent variable does internal validity come under threat. In other words, it might be challenging to distinguish between the effects seen on the dependent variable and the independent variable if there is a component that fluctuates consistently or predictably with changes in the independent variable. Internal validity is less likely to be threatened by random or unplanned variation.

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A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable. This means that if the confound varies randomly or haphazardly, it is less likely to affect the results of the study.

This means that the confound is consistently related to the independent variable, making it difficult to determine if the observed effects are due to the independent variable or the confound. If the confound varies spontaneously or haphazardly, it is less likely to pose a threat to internal validity, as it would not be consistently associated with the independent variable.

However, if the confound is related to the independent variable in a consistent and predictable way, it can introduce bias and undermine the internal validity of the study. It is important for researchers to carefully control for potential confounds and ensure that any observed effects are truly due to the independent variable and not some other factor.

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The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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The values of a,b,c,d for \(2x^3-6x^2-36x=2x(ax+b)(cx+d)\) are given by 1, -6, 1, 3 respectively.

Given the equation is,

\(2x^3-6x^2-36x=2x(ax+b)(cx+d)\)

factorizing the left hand expression we get,

\(2x^3-6x^2-36x\\=2x(x^2-3x-18)\\=2x(x^2-6x+3x-18)\\=2x[x(x-6)+3(x-6)]\\=2x(x+3)(x-6)\)

So, 2x(x-6)(x+3) = 2x(ax+b)(cx+d)

So, a=1, c=1, b= - 6, d=3

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Answer: .018 and .02

Step-by-step explanation:

X=.9Y

X+Y=.038

X=.9Y

X=-Y+.038

-Y+.038=.9Y

-1.9Y=-.038

Y=.02

X+.02=.038

X=.018