The 40-ft-long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. The cross-sectional area of each rail is 6.00 in2.

Part B: Using this gap, what would be the axial force in the rails if the temperature were to rise to T3 = 110 ∘F?

Answer is 24

Step-by-step explanation:

If line LN is equal to 12 and since rhombuses are morrored triangles then LN would be congruent or equal to line JN. Then you would add LN 12

Answer:

box 6 inputs:

2

6

10

box 7 inputs:

3

5

6

8

11

Step-by-step explanation:

The area of region R2 is (sqrt(13)-1)/8 square units. To find the area of region R1, we need to integrate the difference between the two curves with respect to x. The curves intersect when 2x2 = 3 - x, which simplifies to 2x2 + x - 3 = 0. Solving for x, we get x = \((sqrt(13)-1)/4\)or x = (-sqrt(13)-1)/4. Since we only care about the positive value, the intersection point is x =\((sqrt(13)-1)/4.\)

So, the area of region R1 is given by:

∫[0,(sqrt(13)-1)/4] (3-x - \(2x^2\)) dx

Using the power rule and evaluating at the limits of integration, we get:

(3(sqrt(13)-1)/4) - (2(sqrt(13)-\(1)^3\)/48) = (3sqrt(13)-11)/12

Therefore, the area of region R1 is (3sqrt(13)-11)/12 square units.

B) To find the area of region R2, we can see that it is a triangle with height equal to the y-coordinate of the intersection point between y=\(2x^2\) and y=3-x (which we found in part A) and base equal to the x-coordinate of the intersection point. So, the area of region R2 is:

(1/2) [(sqrt(13)-1)/4] [2(sqrt(13)-1)/4] = (sqrt(13)-1)/8

Therefore, the area of region R2 is (sqrt(13)-1)/8 square units.

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The value of vector A is approximately 17.08.

To find the magnitude of a vector with components = 4.43 and = -16.5, you can use the Pythagorean theorem.

The formula for the magnitude of a vector (|A|) is:

|A| = √(x² + y²)

In this case, x = 4.43 and y = -16.5.

Plugging these values into the formula, you get:

|A| = √((4.43)² + (-16.5)²)

|A| = √(19.5849 + 272.25)

|A| = √(291.835)

Calculating the square root, you find that the magnitude of vector A is approximately 17.08.

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Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Both equal 2/3

The simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

To simplify the given expression, let's evaluate the square roots individually and then perform the addition.

√900 = 30, since the square root of 900 is 30.

√0.09 = 0.3, as the square root of 0.09 is 0.3.

√0.000009 = 0.003, since the square root of 0.000009 is 0.003.

Now, we can add these simplified values together

√900 + √0.09 + √0.000009 = 30 + 0.3 + 0.003 = 30.303

Therefore, the simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

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The pharmaceutical company uses the quantitative variable to conducts an experiment.

Variables:

A variable is a characteristic of an object. Their values may occur more than once for a set of data. We consider just two main types of variables in this course.

Quantitative Variables - Variables whose values result from counting or measuring something.

Qualitative Variables - Variables that are not measurement variables. Their values do not result from measuring or counting.

Given,

A pharmaceutical company conducts an experiment in which a subject takes 75 mg of a substance orally.

And  the researchers measure how many seconds it takes for one quarter of the substance to exit the bloodstream.

Here we need to find the kind of variable is the company​ studying.

Here the company uses the Qualitative Variable because here they measure the effects of the medicine not the measurement.

So, the experiment uses the Qualitative Variable.

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Answer:

Hello

Step-by-step explanation

3 3/4 goes first on the left side then 3 1/4, 2 3/4,

2 1/2 ,1 3/4, 1 1/4, 1, 2, 3

Hope this helps

Answer:

Step-by-step explanation:

What's the line plot about, so we can find an appropriate label for it?  

Answer:

(60-x)(35-x)

Step-by-step explanation:

Answer:

(60-x)(35-x)

i think it is a right answer

The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The p-value is 0.024.

The null and alternative hypotheses for the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level are:

H0: p = 0.7 (null hypothesis

)H1: p ≠ 0.7 (alternative hypothesis)

The test is a two-tailed test because the alternative hypothesis includes not equal to (<>) which means either p is less than 0.7 or greater than 0.7

Based on a sample of 500 people, 62% owned cats.

This means that the sample proportion, p = 0.62.

To calculate the p-value, we will use the z-test statistic.

The formula for calculating the z-test statistic is given as:

z = (p - P) / √(PQ/n) where P is the hypothesized proportion (P = 0.7), Q is the complement of P (Q = 1 - P), and n is the sample size.

Using the given values in the formula, we have; z = (0.62 - 0.7) / √(0.7 × 0.3 / 500) = -2.52

The p-value for a two-tailed test at 0.02 level of significance is obtained from the standard normal table.

The area in both tails beyond the z-score of 2.52 is 0.012.

Therefore, the p-value is:

p-value = 2 × 0.012 = 0.024

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Answer:

Your answer is D or $112 + 0.40($112)

Explanation:

I got it right on edge 2021

Answer:

B.17 °

Step-by-step explanation:

note : can uh be more specific to the question it seems incomplete

Answer:

What value of x is in the solution set of 3(x - 4) = 5x + 2?

Solution:

3(x - 4) = 5x + 2 [Given]

Using the distributive law of multiplication on LHS

3x - 12 = 5x + 2

By grouping the similar terms on either sides and solving for x, we get

3x - 5x = 2 + 12

- 2x = 14

Divide both sides by -2 (by division property of equality)

(- 2x/2 )= 14/2

-x = 7

Therefore, the value of x is -7.

Let's create a vector F(x, y, z) with at least two variables in its components:

F(x, y, z) = (xy + 2z)i + (yz + 3x)j + (xz + y)k

Now, let's find the gradient, divergence, and curl of this vector:

1. Gradient (∇F):

The gradient of a vector is given by the partial derivatives of its components with respect to each variable. For our vector F(x, y, z), the gradient is:

∇F = (∂F/∂x)i + (∂F/∂y)j + (∂F/∂z)k

Calculating the partial derivatives:

∂F/∂x = yj + zk

∂F/∂y = xi + zk

∂F/∂z = 2i + xj

Therefore, the gradient ∇F is:

∇F = (yj + zk)i + (xi + zk)j + (2i + xj)k

2. Divergence (div F):

The divergence of a vector is the dot product of the gradient with the del operator (∇). For our vector F(x, y, z), the divergence is:

div F = ∇ · F

Calculating the dot product:

div F = (∂F/∂x) + (∂F/∂y) + (∂F/∂z)

Substituting the partial derivatives:

div F = y + x + 2

Therefore, the divergence of F is:

div F = y + x + 2

3. Curl (curl F):

The curl of a vector is given by the cross product of the gradient with the del operator (∇). For our vector F(x, y, z), the curl is:

curl F = ∇ × F

Calculating the cross product:

curl F = (∂F/∂y - ∂F/∂z)i - (∂F/∂x - ∂F/∂z)j + (∂F/∂x - ∂F/∂y)k

Substituting the partial derivatives:

curl F = (z - 3x) i - (z - 2y) j + (y - x) k

Therefore, the curl of F is:

curl F = (z - 3x)i - (z - 2y)j + (y - x)k

That's it! We have calculated the gradient (∇F), divergence (div F), and curl (curl F) of the given vector F(x, y, z) by finding the partial derivatives, performing dot and cross products, and simplifying the results.

Answer. I think is A

Step-by-step explanation:

The average rate of change tell you in this context the volume of water in the base as the volume changes from 2.5 cups to 4.25 cups.

The average rate of change is a mathematical concept used to describe how a change in one quantity affects another quantity.

To calculate the average rate of change, we need to know the height of water in the vase at two different volumes. Let's call the height of water at a volume of 2.5 cups "h1" and the height of water at a volume of 3.25 cups "h2". Then, the average rate of change over the interval from 2.5 cups to 3.25 cups is calculated as:

=> (h2 - h1) / (3.25 - 2.5) = (h2 - h1) / 0.75

This average rate of change tells us how much the height of water changes, on average, for every one cup increase in the volume of water in the vase.

In other words, the average rate of change provides us with a measure of the "slope" of the relationship between the height of water and the volume of water in the vase over the interval from 2.5 cups to 3.25 cups.

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Answer:

127.3 feet

Step-by-step explanation:

Use Pythagorean Theorem which says

leg^2+leg^2=hyp^2

90^2+90^2= c^2

8100 +8100=c^2

16200 = c^2

sqrt16200 = c

c ~= 127.27922

Round to one decimal place.

c ~= 127.3 feet

OR, use the shortcut of Special Right Triangles, 45°-45°-90° where, the long side (hypotenuse) is the leg•sqrt2

The legs are 90.

So, the long side is 90•sqrt2

~= 127.27922

~= 127.3 feet

see image.

Answer:

X = 1

Step-by-step explanation:

To solve the system of equation by susbtitution:

3x + y = 9

y = –4x + 10

We can follow the steps thus:

Substitute the value of y in the first equation:

As in the second equation y = -4x + 10 we can substitute in the first equation as follows:

3x + y = 9

3x + -4x + 10 = 9

Combine like terms:

3x + -4x + 10 = 9

Like therms are the therms with X (3x - 4x = -1x):

-1x + 10 = 9

Apply the subtraction property of equality:

-1x + 10 = 9

As 10 is suming, it passes to subtracting the 9:

-1x  = 9 - 10

-1x = -1

Apply the division property of equality:

-1x = -1

Dividing in -1:

x = -1 / -1

Answer:

b

Step-by-step explanation:

The value of x in this system of equations is 1.

3x + y = 9

y = –4x + 10

Substitute the value of y in the first equation:

Combine like terms:

Apply the subtraction property of equality:

Apply the division property of equality:

3x + (–4x + 10) = 9

–x + 10 = 9

–x = –1

x = 1

What is the value of y?

y =  

The probability that exactly 5 of the next 7 patients survive the operation is approximately 0.123, or 12.3%.

To find the probability that exactly 5 out of the next 7 patients survive the operation, we can use the binomial probability formula, which is:
\(P(X=k) = C(n, k) * p^k * (1-p)^(n-k)\)
where:
- P(X=k) represents the probability of exactly k successes (survivals) in n trials (operations)
- C(n, k) is the number of combinations of n items taken k at a time
- n is the number of trials (in this case, 7 patients)
- k is the number of successful outcomes (5 patients surviving)
- p is the probability of a successful outcome (0.9 for a patient surviving the operation)
Applying the formula, we have:
\(P(X=5) = C(7, 5) * 0.9^5 * (1-0.9)^(7-5)\)
First, let's calculate the number of combinations C(7, 5):
C(7, 5) = 7! / (5! * (7-5)!)
C(7, 5) = 7! / (5! * 2!)
C(7, 5) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1 * 2 * 1)
C(7, 5) = 21
Now, we can plug this into the binomial probability formula:
\(P(X=5) = 21 * 0.9^5 * 0.1^2\)
P(X=5) = 21 * 0.59049 * 0.01
P(X=5) ≈ 0.1232019.

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The bearing of how far east of point G is point H is 51.68 m

Bearing is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass. It is used to describe a particular direction in which an object is traveling.

How to determine this

When point G and point H are 58 m apart

Point H is at a bearing of 63 degrees

i.e At point H = 63°

To calculate how far east of point G is to point H

When North to East is 90°

So, 90° - 63°

= 27°

x meter away from point H to the East

= cos 27° * 58 m

= 0.9114 * 58 m

= 52.86 m

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the new coordinates of the rhombus W'X'Y'Z' after a dilation with scale factor k=3 are: \(W'(3,0), X'(12,-3), Y'(15,-12), Z'(6,-9)\)

To find the new coordinates of the image after dilation, we need to multiply the coordinates of each vertex by the scale factor k = 3.

Let's start with vertex W(1,0):

Multiply the x-coordinate by  \(3: 1 *\times 3 = 3\)

Multiply the y-coordinate by \(3: 0 \times 3 = 0\)

So the new coordinates of W' are \((3,0).\)

Next, let's look at vertex X(4,-1):

Multiply the x-coordinate by \(3: 4 \times 3 = 12\)

Multiply the y-coordinate by \(3: -1 \times 3 = -3\)

So the new coordinates of X' are \((12,-3).\)

Now for vertex Y(5,-4):

Multiply the x-coordinate by \(3: 5 \times 3 = 15\)

Multiply the y-coordinate by \(3: -4 \times3 = -12\)

So the new coordinates of Y' are  \((15,-12).\)

Finally, let's consider vertex Z(2,-3):

Multiply the x-coordinate by  \(3: 2 \times 3 = 6\)

Multiply the y-coordinate by  \(3: -3 \times3 = -9\)

So the new coordinates of Z' are \((6,-9)\)  .

Therefore, the new coordinates of the rhombus  \(W'X'Y'Z'\) after a dilation with scale factor k=3 are:

\(W'(3,0)\)

\(X'(12,-3)\)

\(Y'(15,-12)\)

\(Z'(6,-9)\)

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Answer:

Step-by-step explanation:

you didn’t post the given line.

if it’s parallel, that means they have the same slope.

Answer:

12

Step-by-step explanation:

let x = number of 3 wheel stollers

let y = number of 4 wheel strollers

x + y = 28

y = 28 - x

3x + 4y = 100

3x + 4(28 - x) = 100

3x + 112 - 4x = 100

-x = -12

x = 12

And there you go, your answer is 12.

Answer:

B

Step-by-step explanation:

12

(a) We can represent Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel as f(24.9).

(b) We can represent Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel as f(49.71).

(a) We have to determine how can we represent Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel.

We can create the a table and function to describe that statement but F(24.9) is the best representation of Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel.

(b) We have to determine how can we represent Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel.

We can create the a table and function to describe that statement but F(49.71) is the best representation of Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel.

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The complete question is:

In the previous modules we developed formulas, tables, and graphs to represent how two varying quantities change together. For example, we considered how Kristin's height above the ground changed as her total distance traveled increased while riding a Ferris wheel.

We even assigned letters to represent the possible varying values each quantity can assume.

• Let d represent the distance Kristin has traveled (in meters) around the Ferris wheel starting at the bottom.

• Let h represent Kristin's height above the ground (in meters).

Note that the way we are thinking about this relationship is that we vary Kristin's distance traveled and observe what happens to her height above the ground.

What if you want to communicate information about her position after she traveled some number of feet? You could write it out in words, like "Kristin was 16.3 meters above the ground when she had traveled 23.7 meters around the Ferris wheel". However, that's a lot to have to write out, especially if you want to talk about multiple values. You could also draw a table or create a graph, but mathematicians developed a tool called function notation to help them represent values in a covarying relationship.

[Note: We will define the exact meaning of "function" later in this investigation. For now, just think of "function" as meaning the same thing as "relationship".]

First, we pick a letter to represent the name of the relationship. Let's call this relationship "f". Now, instead of saying "the relationship between Kristin's height above the ground (in meters) and her total distance traveled (in meters)" we can simply say "relationship f".

Also, we can use f(d) to represent values of Kristin's height above the ground (values of h). We read this as "f of d", and the parentheses here are just part of the notation. They do NOT indicate multiplication.

For example, f(13) represents Kristin's height above the ground (in meters) when she has traveled 13 meters around the Ferris wheel.

a. How can we represent Kristin's height above the ground (in meters) when she has traveled 24.9 meters around the Ferris wheel?

(Hint: you should use function notation.) Preview syntax error Enter an algebraic expression (more..]

b. How can we represent Kristin's height above the ground (in meters) when she has traveled 49.71 meters around the Ferris wheel? x Preview

Answer:

Reduce 9/4 to lowest terms

94 is already in the simplest form. It can be written as 2.25 in decimal form (rounded to 6 decimal places).

Step-by-step explanation:

Answer:

63 degrees

Step-by-step explanation:

m<FGH is asking for the measure of angle fgh.

when there are 3 letters, the middle one represents the point of the angle

m<FGH=63

I'm not sure about the second part because it's a drop down menu, but hope my explanation helps.