a A population has a mean of 159.8 kg and a standard deviation of 12.6 kg. Under these circumstances, what z-score correspond to a mass of 148.3 kg? Oz = -1.06 z = -0.91 Oz = -0.85 Oz = 0.91

To use polar coordinates, we need to first express the equations of the surfaces in polar coordinates.

In polar coordinates, we have x = r cosθ and y = r sinθ. Therefore, the equation x^2 + y^2 = 1 becomes r^2 = 1.

To find the volume of the solid, we can integrate over the region in the xy-plane bounded by the circle r=1. For each point (r,θ) in this region, the corresponding point in 3D space has coordinates (r cosθ, r sinθ, r^2+3)

Thus, the volume of the solid can be expressed as the double integral:

V = ∬R (r^2+3) r dr dθ

where R is the region in the xy-plane bounded by the circle r=1.

We can evaluate this integral using the limits of integration 0 to 2π for θ, and 0 to 1 for r:

V = ∫₀^¹ ∫₀^(2π) (r^3 + 3r) dθ dr

= ∫₀^¹ [(r^3/3 + 3rθ)]₀^(2π) dr

= ∫₀^¹ (2πr^3/3 + 6πr) dr

= 2π[(1/12) + (1/2)]

= 2π(5/12)

= (5/6)π

Therefore, the volume of the solid is (5/6)π.

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The radius of a sphere with volume 288π cm³ is equal to 6 centimeter.

In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):

Volume of a sphere = 4/3 × πr³

Where:

r represents the radius.

By substituting the given parameters into the formula for the volume of a sphere, we have the following;

288π = 4/3 × π × r³

r³ = 864/4

Radius, r = ∛216

Radius, r = 6 centimeter.

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Answer:

The common difference is the difference between any two consecutive terms in an arithmetic sequence. 2, 8, 14, 20, 26 … = 2, (2 + 6), (8 + 6), (14 + 6), (20+ 6) … Therefore, the common difference is 6.

Step-by-step explanation:

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The required value of x is 15 for the given angles.

Since ∠KJN and ∠KJL form a linear pair, their sum is 180 degrees.

Therefore, we have:

2x - 10 + ∠KJL = 180

Simplifying, we get:

∠KJL = 190 - 2x

Similarly, angle MJN and angle MJL form a linear pair, so:

2x + 40 + ∠MJL = 180

∠MJL = 140 - 2x

Since ∠KJM is a right angle, we have:

∠KJN + ∠MJN = 90

Substituting the given values, we get:

2x - 10 + 2x + 40 = 90

4x = 60

x = 15

Hence, the value of x is 15.

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The estimated probability of getting at least 10 correct answers by random guessing is approximately 0.023, or about 2.3%.

To solve this problem, we need to use the binomial distribution. Let X be the number of correct answers out of 27, with each question having 4 possible choices, so the probability of guessing correctly is 1/4.

Let p = 1/4 be the probability of guessing a question correctly, and q = 1-p = 3/4 be the probability of guessing incorrectly.

The probability of getting at least 10 correct answers out of 27 is:

P(X >= 10) = 1 - P(X < 10)

We can use the binomial probability formula to calculate P(X < 10) as follows:

P(X < 10) = Σ_{k=0}^{9} (27 choose [tex]k) * p^k * q^(27-k)[/tex]

where (27 choose k) = 27! / (k! * (27-k)!) is the number of ways to choose k correct answers out of 27.

We can use a calculator or a computer program to evaluate this sum, or we can use a normal approximation to the binomial distribution.

Using the normal approximation, we can approximate the binomial distribution with a normal distribution with mean μ = np = 27*(1/4) = 6.75 and standard deviation σ = sqrt(npq) = sqrt(27*(1/4)*(3/4)) = 1.64.

Then, we can standardize the random variable X as follows:

Z = (X - μ) / σ

The probability of getting at least 10 correct answers is equivalent to the probability of Z being greater than or equal to:

Z' = (10 - 6.75) / 1.64 = 1.99

Using a standard normal distribution table or a calculator with a normal cumulative distribution function, we can find:

P(Z >= 1.99) = 0.023

Therefore, the estimated probability of getting at least 10 correct answers by random guessing is approximately 0.023, or about 2.3%.

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Answer:

$4853

Step-by-step explanation:

Since there are 12 months in 1 year, the monthly salary is 1/12 of the yearly salary. We divide the annual salary by 12 to calculate the monthly salary.

$58236/12 = $4853

The slope and y-intercept are 4.5 and 25 respectively.

A graph of the equation for the total shipping charges is shown below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about this freight company, the total shipping charges are given by;

C = 4.5n + 25

By comparison, we have the following:

Slope, m = 4.5.

y-intercept = 25.

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Answer:5/14

Step-by-step explanation:

you have 5 red and 14 total so your probability is 5/14 and 5/14 is the simplest terms

240 wooden cubes can fit in box.

We have,

Volume of wooden cube= 1/2 cubic foot

Dimension of box = 5ft x 8 ft x 3 ft

So, the Volume of Box

= l w h

= 5 x 8 x 3

= 120 ft³

Now, the number of wooden cubes fit in box

= 120/ 0.5

= 240

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The maximum total number of observations with a deviation of at least 5 would be 45.

To solve this problem, we can start by using the formula for the sum of deviations:

Sum of deviations = (number of observations) x (average deviation)

Since the average deviation in this case is 5, we can write:

Sum of deviations = (number of observations) x 5

We are given that the sum of deviations is 5 for 100 observations, so we can substitute these values into the formula and solve for the number of observations:

5 = 100 x 5

Number of observations = 100

This means that there are a total of 100 observations that have a deviation of at least 5 from the mean of 20. However, we are asked for the maximum total number of observations that meet this criteria. Since all 100 observations have a deviation of at least 5, there can be no additional observations that also have a deviation of at least 5. Therefore, the maximum total number of observations that meet this criteria is 100.

If the sum of deviations of 100 observations from 20 is 5, it means that the overall sum of differences between each observation and 20 is equal to 5. To find the maximum total number of observations that have a deviation of at least 5, we need to minimize the deviations of the other observations.

Let's say there are "x" observations with a deviation of at least 5. The remaining (100 - x) observations should have deviations that counterbalance the sum of deviations for the "x" observations so that the total sum of deviations is 5.

Assuming the minimum deviation for the (100 - x) observations is -4 (because the least deviation for the "x" observations is 5), we can create an equation:

5x - 4(100 - x) = 5

Solve for x:

5x - 400 + 4x = 5
9x = 405
x = 45

So, the maximum total number of observations with a deviation of at least 5 would be 45.

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The total number of five-digit odd numbers is 864 + 216 = 1080

The units digit must be one of 7 or 9 to make a five-digit odd number. The last four digits can be any of the six provided digits, and they can be repeated.

So we have two scenarios:

Case 1: The first digit of the units is 7.

In this scenario, we have four options for the initial digit (2, 4, 6, or 8) and six options for the following digits. As a result, the total number of five-digit odd numbers is:

4 x 6 x 6 x 6 = 864

Case 2: The unit digit is nine.

In this scenario, we only have one option for the initial digit (7) and six options for the other digits.

As a result, the total number of five-digit odd numbers is 864 + 216 = 1080

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The value of the fraction -5/7 and -4/7 added and subtracted from the fraction -21/2 added to 1/22 is 64/77.

The sum of 1/2 and -21/22 can be found by finding a common denominator,

1/2 = 11/22 (since 11 x 2 = 22)

-21/22 = -21/22

Therefore, the sum of 1/2 and -21/22 is,

= 11/22 - 21/22

= -10/22 = -5/11

The sum of -4/7 and -5/7 is,

-4/7 - 5/7 = -9/7

Now, subtracting as asked in the question.

= (-5/11)-(-9/7)

= (-5/11)+(9/7)

Finding common denominator to add the fractions,

7 x 11 = 77

(-5x7)/(11x7)+(9x11)/(7x11)

= -35/77 + 99/77

Now, we can combine the numerators,

-35/77 + 99/77 = 64/77

Therefore, the final answer is 64/77.

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Answer:

Step-by-step explanation:

1 plus 2 equals 3

3 plus 3 equals 6

6 plus 4 equals 10

10 plus 5 equals 15.       did this help?

We need a sample size of at least 62 to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

To answer this question, we need to use power analysis. Power is the probability of rejecting the null hypothesis when it is false. In this case, the null hypothesis is m = 0 and the alternative hypothesis is m > 0. We want to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

Assuming that s is 20 and we want to detect the alternative m > 4, we can use the following formula to calculate the sample size:

n = (Zα/2 + Zβ)² * σ² / δ²

where:
- Zα/2 is the critical value for the significance level α/2 (α = 0.05, so Zα/2 = 1.96)
- Zβ is the critical value for the power (power = 0.80, so Zβ = 0.84)
- σ is the standard deviation (σ = 20)
- δ is the difference between the null hypothesis and the alternative hypothesis (δ = 4)

Substituting these values into the formula, we get:

n = (1.96 + 0.84)² * 20² / 4²
n = 61.61

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Answer:its b

Step-by-step explanation:

There is a fraction of 0.525 liters of vinegar in the container for a container that holds 0.7 liters of oil and vinegar and 3/4 of the mixture is vinegar.

First, find out how much of the mixture is vinegar:

3/4 of the mixture = 3/4 × 0.7 = 0.525 liters

Therefore, there are 0.525 liters of vinegar in the container.

To express this as a fraction, we can write 0.525 as 525/1000 and simplify it to 21/40.

So, the answer in both fraction and decimal forms are:

0.525 liters = 21/40 liters

To check our answer in decimal form, we can add the amount of oil and vinegar to make sure it equals the total volume of the container:

0.525 + (1 - 0.75) × 0.7 = 0.525 + 0.175 = 0.7

As expected, the sum is equal to the total volume of the container, which is 0.7 liters.

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The question is -

A container holds 0.7 liters of oil and vinegar. 3/4 of the mixture is vinegar. how many liters of vinegar is in the container?

Cosx, -sinx, -cosx + C, sinx + C are the derivative answers to the question.

The derivative of sin x with respect to x is cos x.
The derivative of cos x with respect to x is -sin x.
The antiderivative of sin x with respect to x is -cos x + C, where C is the constant of integration.
The antiderivative of cos x with respect to x is sin x + C, where C is the constant of integration.

1. The derivative of sin(x) with respect to x is cos(x).
2. The derivative of cos(x) with respect to x is -sin(x).
3. The antiderivative of sin(x) with respect to x is -cos(x) + C, where C is the constant of integration.
4. The antiderivative of cos(x) with respect to x is sin(x) + C, where C is the constant of integration.

A derivative in mathematics is a measurement of how much a function alters as its input alters. It refers to how quickly a function alters in relation to its input variable. The slope of the tangent line to the function at a certain point is what it is, in other words.

The limit of the ratio of the change in the output to the change in the input, as the change in the input approaches zero, is known as the derivative of a function, indicated by the symbols f'(x) or [tex]dy/dx[/tex].

The opposite of differentiation is an antiderivative, usually referred to as an indeterminate integral. It is a function that yields the original function when differentiated. In other words, f(x) follows if [tex]f'(x) = g(x)[/tex].

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The number of white marbles in the bag is w = 7

Given data ,

Let's write "w" for the quantity of white marbles in the bag. Four of the twelve marbles in the bag are blue, as shown by the information provided. This indicates that "12 - 4 = 8" applies to the remaining white marbles.

Now , when a marble is randomly selected and returned to the bag, the probability of selecting a white marble is w/12, where "w" is the number of white marbles and 12 is the total number of marbles in the bag.

Similarly, when a second marble is randomly selected (with replacement), the probability of selecting a blue marble is 4/12, since there are 4 blue marbles out of 12 marbles in total.

So , the probability is given by

(w/12) x (4/12) = 7/36

On simplifying , we get

4w/144 = 7/36

Cross-multiplying:

144 x (4w/144) = 144 x (7/36)

4w = 28

Dividing both sides by 4:

w = 28/4

w = 7

Hence , the number of white marbles in the bag is 7

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Answer: f(2) = 18

Step-by-step explanation:

     To solve for f(2), we will substitute 2 for x in the equation.

Given:

     f(x) = 7x + 4

Substitute:

     f(2) = 7(2) + 4

Multiply:

     f(2) = 14 + 4

Add:

     f(2) = 18

Answer:

18

Step-by-step explanation:

Just replace x with 2 in the function

f(2) = 7(2) + 4

f(2) = 14 + 4

f(2) = 18

The probability that Kelsi will eat a custard filled donut and then a chocolate donut is approximately 0.1455.

To calculate the probability of Kelsi eating a custard filled donut and then a chocolate donut, we need to use the concept of conditional probability.

The probability of Kelsi eating a custard filled donut first is 4/12 (since there are 4 custard filled donuts out of a total of 12 donuts).

After Kelsi eats a custard filled donut, there are only 11 donuts left, and 6 of them are chocolate donuts. So the probability of Kelsi eating a chocolate donut second, given that she already ate a custard filled donut, is 6/11.

To find the probability of both events happening together (Kelsi eating a custard filled donut first and a chocolate donut second), we multiply the probabilities:

P(custard first and chocolate second) = P(custard first) * P(chocolate second | custard first)

P(custard first and chocolate second) = (4/12) * (6/11)

P(custard first and chocolate second) = 0.1455

Rounding to 4 decimal places, we get:

P(custard first and chocolate second) ≈ 0.1455

Therefore, the probability that Kelsi will eat a custard filled donut and then a chocolate donut is approximately 0.1455.

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The number of different towers with a height of 8 cubes can the child build with 2 red cubes, 3 blue cubes, and 4 green cubes is 312.

To solve this problem, we can use the formula for the number of ways to arrange n objects with k of one type, m of another type, etc. Specifically, the formula of combination  is:

(n-1)! / (k! * m! * ...)

In this case, we have 8 cubes total, with 2 red, 3 blue, and 4 green. So applying the formula, we get:

(8-1)! / (2! * 3! * 4!) = 7! / (2! * 3! * 4!)

= (7*6/2) * (5*4*3/6) * (4*3*2*1/24)

= 21 * 20 * 1

= 420

However, we have to remember that we are leaving out one cube. This means that for each tower we counted, there is actually a corresponding tower that is identical except for the color of the cube that was left out. So we need to divide by 3 (since there are 3 choices for which cube to leave out). This gives us:

420 / 3 = 140

So the answer is (c) 312.

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The probability of event B given event A has occurred is 0.5.

By using the conditional probability formula, we have:

P r(B | A) = P r(A ∩ B) / P r(A)

We are given that P r(A) = 0.4 and P r(A ∩ B) = 0.2.

Substituting these values, we get:

P r(B | A) = 0.2 / 0.4

By simplifying;

P r(B | A) = 0.5

Therefore, the probability of event B given event A has occurred is 0.5.

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Compared to the 1970s, there has been an increase in the proportion of middle-aged women in the 2010s who have opted not to have children.

This trend is often attributed to factors such as increased access to birth control, greater career opportunities for women, and a shift in societal attitudes towards motherhood. However, it's worth noting that there are still many women who do choose to have children in their middle age, and the decision to have children is a deeply personal one that varies from individual to individual.

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The probability that the cycle time exceeds 65 minutes given that it exceeds 55 minutes is 1/3.

To solve this problem, we can use conditional probability. We know that the cycle time for trucks hauling concrete is uniformly distributed between 50 to 70 minutes. Let X be the cycle time in minutes.

So, P(X > 65 | X > 55) = P(X > 65 and X > 55) / P(X > 55)

We can simplify the numerator as P(X > 65 and X > 55) = P(X > 65) since if X is greater than 65, it is also greater than 55. Using the formula for the uniform distribution, we get:

P(X > 65) = (70 - 65) / (70 - 50) = 1/4

Similarly, we can calculate the probability of X being greater than 55:

P(X > 55) = (70 - 55) / (70 - 50) = 3/4

Putting these values in the conditional probability formula, we get:

P(X > 65 | X > 55) = (1/4) / (3/4) = 1/3

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Based on the information, the most appropriate graph for this situation would be option A.

To identify the most appropriate graph for this situation we must analyze the data. In this case we have the relationship of the toppings with the number of customers who prefer each variety.

Now, We get;

Due to the above, we could affirm that the best option is A because it shows the number of people who prefer each topping in the order in which the table organizes them.

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Answer:

6

Step-by-step explanation:

With 5 elements, we have a total of 6 nodes. We need to obtain the temperature at each of these 6 nodes.

Increasing the number of elements is referred to as mesh refinement.

I hope this helped you:D

Answer: 512 feet^3

Step-by-step explanation:

The volume of a cube is x^3, where x is the sidelength.  8^3 is equal to 512 and since its in the 3rd dimension it's feet^3 or feet cubed.

Answer:

Approximately 243.917

Step-by-step explanation:

The cube has a volume of 8³ = 512.

The sphere has a volume of   [tex]\frac{4}{3}\pi r^3[/tex].

The volume inside the cube but outside the sphere is:

[tex]512-\frac{4}{3}\pi r^3[/tex] (1)

The radius of the sphere is equal to the sidelengths of the cube divided by 2 as seen by the picture.

So r = 8/2 = 4.

Substituting r into (1):

[tex]512-\frac{4}{3}\pi 4^3=512-\frac{256\pi }{3}=243.917[/tex]

Answer:

  AB is not tangent to the circle

Step-by-step explanation:

You want to know if segment AB of length 9 is tangent to the circle with diameter 12 at point B given that the third side of the triangle is 13 units long.

You know that the numbers {5, 12, 13} are a Pythagorean triple, so these lengths form a right triangle. The lengths (9, 12, 13) cannot form a right triangle, so AB will not be perpendicular to the diameter.

AB is not a tangent

The segments will form a right triangle if they satisfy the Pythagorean theorem, which requires the sum of the squares of the shorter sides equal the square of the longest side.

  9² +12² = 13²

  81 +144 = 169 . . . . . . false — not a right triangle

A "form factor" can be computed for the triangle to tell if the largest angle is acute, right, or obtuse. That is ...

  f = a² +b² -c²

  f = 81 +144 -169 = 56 . . . . . . . f > 0 means the triangle is acute

The measure of the largest angle can be found from ...

  C = arccos(f/(2ab)) = arccos(56/216) ≈ 74.97°

This is further confirmation that AB is not tangent to the circle.

__

Additional comment

The attached drawing is to scale. It shows AB has two points of intersection with the circle, so is not tangent.

The conclusion about p using an absolute value inequality would be that |p - 72| ≤ 4. This means that the difference between the true proportion p and the estimated proportion 72% is no more than 4%.

In other words, p is most likely to fall within the range of 68% to 76%, as determined by the margin of error in the statistical polling calculation. This emphasizes the importance of recognizing and accounting for the potential for error and uncertainty in estimating percentages and proportions in various fields, including politics and marketing.
To describe the conclusion about the percentage (p) in statistical polling using an absolute value inequality, you can use the margin of error (4% in this example) as a way to create the inequality.
In this case, we have a poll result of 72% and a margin of error of 4%. So, the absolute value inequality would be:
|p - 72%| ≤ 4%
This inequality shows that the difference between the true percentage (p) and the poll result (72%) should be less than or equal to the margin of error (4%). In other words, the true percentage (p) is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).

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