a population of 1,000 students spends an average of $10.50 a day on dinner. the standard deviation of the expenditure is $3. a simple random sample of 64 students is taken. what is the shape of the sampling distribution of the sample mean?

False, Mathematically, an odds ratio equates to a risk ratio, therefore, odds ratios can be interpreted in an exactly same way as risk ratio.

What distinguishes risk from probability?

The fundamental distinction is that the relative risk is a ratio of two probabilities, but the odds ratio is a ratio of two odds (yes, it's that clear). (The risk ratio is another name for the relative risk.)

Used to approximate the relative risk in case-control studies, when the occurrence of diseases are KNOWN

odds of an event = the number of ways an event can occur to the numbers of ways an event cannot occur

odds ratio = P / (1-P)

where P = probability of occurrence

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Answer: The answer is 226.2 feet.

Step-by-step explanation: The formula to find the total surface area of a cylinder is 2\(\pi\) x radius squared x height. If you use the formula you will get 226.19 feet as your answer and I rounded that to 226.2 feet.

UR MOM

Answer:

y = -x + 2, B is the answer

Step-by-step explanation:

If slope is -1, the equation is y = -x+b

Plug in (3,-1) into that equation.

-1 = -3 + b

b = 2

The height of the building is estimated to be approximately 172.49 meters. Since sound travels at a speed of 340 m/s, the additional time for the sound wave to reach back to the observer should be taken into account to get an accurate estimation of the building's height.

Based on the given information that it took 5.9 seconds for the water to fall from the building to the pond, we can calculate the height of the building. Using the equation for free-fall motion, h = 0.5 * g *\(t^2\), where h is the height, g is the acceleration due to gravity, and t is the time, we can substitute the values and solve for h. The height of the building is estimated to be approximately 172.49 meters.

Regarding the second question, if the time for the sound to travel back to the observer is not considered, the height of the building would be underestimated. This is because the sound would take some time to travel back up, and not accounting for this additional time would result in a lower estimate of the building's height.

To find the height of the building, we can use the equation for free fall motion:

h = 0.5 * g * \(t^2\)

where h is the height of the building, g is the acceleration due to gravity (approximately 9.8 m/\(s^2\)), and t is the time it took for the water to fall (5.9 seconds).

Plugging in the values, we have:

h = 0.5 * 9.8 * \((5.9)^2\)

h ≈ 172.49 meters

Therefore, the height of the building is estimated to be approximately 172.49 meters.

For the second question, if the time for the sound to travel back to the observer is not considered, it would lead to underestimating the height of the building. This is because the sound wave needs time to travel from the observer to the top of the building and then back down to the observer.

By not accounting for the time taken for the sound wave to return, the estimated height would only be based on the time it took for the water to fall. Since sound travels at a speed of approximately 340 m/s, the additional time for the sound wave to reach back to the observer should be taken into account to get an accurate estimation of the building's height.

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Answer:

3

Step-by-step explanation:

(a) Position at t = 1 s: 0.32 meters (b) Position at t = 2 s: -0.06 meters (c) Position at t = 3 s: 1.16 meters (d) Position at t = 4 s: 16.28 meters (e) Displacement between t = 0 and t = 4 s: 16.34 meters (f) Average velocity from t = 2 s to t = 4 s: 8.17 meters per second

To find the position of the object at different values of t, we substitute the given values of t into the equation \(x = 3.27t - 4.00t^2 + 1.05t^3.\)

(a) When t = 1 s:

\(x = 3.27(1) - 4.00(1)^2 + 1.05(1)^3\)

x = 3.27 - 4.00 + 1.05

x = 0.32 meters

(b) When t = 2 s:

\(x = 3.27(2) - 4.00(2)^2 + 1.05(2)^3\)

x = 6.54 - 4.00(4) + 1.05(8)

x = 6.54 - 16.00 + 8.40

x = -0.06 meters

(c) When t = 3 s:

\(x = 3.27(3) - 4.00(3)^2 + 1.05(3)^3\)

x = 9.81 - 4.00(9) + 1.05(27)

x = 9.81 - 36.00 + 28.35

x = 1.16 meters

(d) When t = 4 s:

\(x = 3.27(4) - 4.00(4)^2 + 1.05(4)^3\)

x = 13.08 - 4.00(16) + 1.05(64)

x = 13.08 - 64.00 + 67.20

x = 16.28 meters

(e) The object's displacement between t = 0 and t = 4 s can be found by subtracting the initial position (t = 0) from the final position (t = 4 s):

Displacement = x_final - x_initial

Displacement = x(4) - x(0)

Displacement = 16.28 - 0

Displacement = 16.28 meters

(f) The average velocity from t = 2 s to t = 4 s can be found by calculating the change in position and dividing it by the change in time:

Average Velocity = (x_final - x_initial) / (t_final - t_initial)

Average Velocity = (x(4) - x(2)) / (4 - 2)

Average Velocity = (16.28 - (-0.06)) / 2

Average Velocity = 16.34 / 2

Average Velocity = 8.17 meters per second

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Answer:

10

Step-by-step explanation:

I mean if you need help then like you shouldn't be on here :/

i wasted 10 hours but i solved it is 10 because 1+1+1+1+1=5 and 1+1+1+1+1=5 add them you get 10 (づ｡ ◕‿‿◕｡) づ

100% is equal to the total earnings in a month which is $4000.So 33% is the rent so you say:

If 100%=4000

33%=?

[(33×4000)÷100]=$ 1320

f(x)>=-7

Functions:

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.

If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x

Given :

f(x) = -3|x+1|-4

using the table of values for g(x) = |x|

Solution :

f(x) = -3|x+1|-4

f(x) = -3|g(x)+1|-4

f(x) = -3||x|+1|-4

which means |x| is always positive |x|>0

f(x) = -3||x|+1|-4

f(x) = -3x-3-4

f(x) = -3x-7

f(x)>=-7

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The distance between the given points is 31.4 units.

Given are two points (-13, -8) and (6, 17) we need to find the distance between them,

We know that the distance between two points is given by =

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Here,

(x₁, y₁) and (x₂, y₂) are (-13, -8) and (6, 17),

So,

\(D = \sqrt{(6+13)^2+(17+8)^2}\\\\D = \sqrt{19^2+25^2}\\\\D = \sqrt{986}\)

D = 31.4

Hence the distance between the given points is 31.4 units.

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Answer:

(-4·3·2)^2 = 576

Step-by-step explanation:

Evaluate

Answer: (-4·3·2)^2 = 576

The value of 'x' for the given equation is found as: x = 14.

The given equation is-

- 3x = 4*7 - 5x

Simplifying:

- 3x = 28 - 5x

Collect variables on one side and constants on other side.

-3x + 5x = 28

Subtracting the variables:

2x = 28

Dividing both sides by 2.

x = 14

Thus, the value of 'x' for the given equation is found as: x = 14.

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The correct question is-

Find x.

- 3x = 4*7 - 5x

Answer: 5n^2 -19n^2-25

Step-by-step explanation: combine like terms / distribute

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Answer:

272

Concepts used:

Visual Reasoning/ Geometrical Properties of a Rectangle

Area of a Triangle = \(\frac{1}{2} b.h\)

(b: base, h: height)

Area of a Rectangle = \(l.b\)

(l:length, b: breadth)

Step-by-step explanation:

Height of triangle = 20-12

= 8 ft

Area of triangle = \(\frac{1}{2} b.h\)

= 1/2 of (8 · 8)

= 1/2 of 64

= 32 ft²

Area of rectangle = \(l.b\)

= 20 · 12

= 240 ft²

Aggregate Area = 240 + 32

= 272 ft²

Edit: Rectified Solution, Credits: 480443417713 (UserID-66721551)

Answer:

272 ft²

Step-by-step explanation:

In the attached picture, I did the work.

Triangle:

The formula for area of the triangle is (lxh)/2

So, the length is 8, and the height is 8, so:

(8x8)/2

64/2

=32

The area of the triangle is 32

Rectangle:

The formula for area of the rectangle is lxw

So, the length is 20 and the width is 12, so:

20x12

=240

The area of the rectangle is 240

Total Area:

The 2 areas added together:

240+32

=272

The total area is 272 ft²

Hope this helps :)

The correct hypothesis statement for this golfer to prove his claim would be:

\(H_{0} :u\geq 90\)

\(H_{1} :u < 90\)

The golfer claims that his average score is less than 90.

Therefore, the null hypothesis is the opposite of what he claims

Null hypothesis \(H_{0}\) is average score \(u\) is greater than or equal to 90:

\(u \geq 90\)

\(H_{0} :u\geq 90\)

Alternative hypothesis \(H_{1}\) is then the opposite of null hypothesis.

Hence alternate hypothesis \(H_{1}\) is u< 90

\(H_{1} :u < 90\)

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The equation to complete the square for x² + 3x = 6 is 3/2 (option a)

To complete the square for the equation x² + 3x = 6, we need to add a specific number to both sides of the equation. The number we need to add is half of the coefficient of x, squared. In other words, we need to find (b/2)², where b is the coefficient of x.

In this equation, b is 3, so (b/2)² is (3/2)², which simplifies to 9/4. Therefore, to complete the square, we need to add 9/4 to both sides of the equation:

x² + 3x + 9/4 = 6 + 9/4

Now, we can rewrite the left side of the equation as a perfect square:

(x + 3/2)² = 33/4

Finally, we can solve for x by taking the square root of both sides of the equation:

x + 3/2 = ± √(33/4)

x = -3/2 ± √(33/4)

Therefore, the answer to the question is a) 3/2.

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Answer:

number 3

Step-by-step explanation:

Answer:

M = 2 b= 10

Step-by-step explanation:

Turn it to mx + b form

By +2x to both sides

Y = 2x + 10

The formula for the uncertainty of x, where x = a/b, is δx = x * √[(bδa)^2 + (aδb)^2]/(a^2+b^2)^3/2. It is derived using partial derivatives of x with respect to a and b, and the formula for propagation of uncertainties.

Let's assume that a, b, and x are all measured quantities with uncertainties δa, δb, and δx, respectively. We want to derive the formula for the uncertainty of x in terms of δa and δb.

We start by taking the partial derivative of x with respect to a, holding b constant:

∂x/∂a = b/(a^2+b^2)

Similarly, we take the partial derivative of x with respect to b, holding a constant:

∂x/∂b = -a/(a^2+b^2)

The uncertainty of x, δx, can be estimated using the formula for propagation of uncertainties:

(δx/x)^2 = (δa/a)^2 * (∂x/∂a)^2 + (δb/b)^2 * (∂x/∂b)^2

Substituting the partial derivatives we calculated above, we get:

(δx/x)^2 = (δa/a)^2 * (b/(a^2+b^2))^2 + (δb/b)^2 * (-a/(a^2+b^2))^2

Simplifying the terms, we get:

(δx/x)^2 = [(bδa)^2 + (aδb)^2]/(a^2+b^2)^3

Taking the square root of both sides, we get:

δx = x * √[(bδa)^2 + (aδb)^2]/(a^2+b^2)^3/2

Therefore, the formula for the uncertainty of x in terms of δa and δb is:

δx = x * √[(bδa)^2 + (aδb)^2]/(a^2+b^2)^3/2

where x = a/b.

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The formula for the uncertainty of x in the equation x = ca/b is σ_x = x*sqrt((σ_a/a)^2 + (σ_b/b)^2), where x = ca/b and σ_a and σ_b are the uncertainties in a and b, respectively.

To derive the formula for the uncertainty of x, we can use the following equation for the propagation of uncertainties:

σ_x = sqrt((∂x/∂a)^2σ_a^2 + (∂x/∂b)^2σ_b^2)

where σ_x is the uncertainty in x, σ_a is the uncertainty in a, σ_b is the uncertainty in b, and ∂x/∂a and ∂x/∂b are the partial derivatives of x with respect to a and b, respectively.

Taking the natural logarithm of both sides of the given equation, we get:

ln(x) = ln(ca/b)

Using the properties of logarithms, we can rewrite this as:

ln(x) = ln(c) + ln(a) - ln(b)

Differentiating both sides with respect to a, we get:

(1/x)(∂x/∂a) = 1/a

Solving for ∂x/∂a, we get:

∂x/∂a = x/a

Differentiating both sides with respect to b, we get:

(1/x)(∂x/∂b) = -1/b

Solving for ∂x/∂b, we get:

∂x/∂b = -x/b

Substituting these partial derivatives and the given values into the equation for the uncertainty of x, we get:

σ_x = sqrt((x/a)^2σ_a^2 + (-x/b)^2σ_b^2)

Simplifying this equation, we get:

σ_x = x*sqrt((σ_a/a)^2 + (σ_b/b)^2)

Therefore, the formula for the uncertainty of x is σ_x = x*sqrt((σ_a/a)^2 + (σ_b/b)^2), where x = ca/b.

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Answer:

30%

Step-by-step explanation:

4320 - 288 = 4032

4032/12 =336 per copies

So, he sold them in 5760

5760 - 4032 = 1728

(1728/5760)*100 = 30%

The relationship between the number of weeks and cars are proportional since they are dependent on each other.

Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

In this question, Alfred, buy three car each week. As the number of weeks increase, so is the number of his car increasing at definite proportions.

This implies that we can set an equation to represent the number of cars Alfred will have after certain number of weeks.

Let;

y = 3x

At week 10, Alfred will have

y = 3(10) = 30 cars

After 10 weeks, Alfred will have 30 cars

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The probability of Pat finishing on or before the 18th house is approximately 0.9978. This problem can be modeled using a geometric distribution, where the probability of success (selling a candy bar) is 0.3 and we want to find the probability of reaching the 8th success.

(a) The probability that Pat sells his last candy bar on the 14th house is:

P(X=14) = (1-0.3)^{13} * 0.3 = 0.002678

(b) The probability of Pat finishing on or before the 18th house is:

P(X≤18) = 1 - P(X>18) = 1 - (1-0.3)^{18} = 0.997805

Therefore, the probability of Pat finishing on or before the 18th house is approximately 0.9978.

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Answer:

103.8

Step-by-step explanation:

Length of diagonal of a cube is given by the formula:

\(d = side \times \sqrt{3} \\ \\ \therefore \: d = 60 \times \sqrt{3} \\ \\ \therefore \: d = 60 \times 1.73 \\ \\ \therefore \: d = 103.8 \: units\)

The length of the diagonal of the cube is 103.9 units.

What is a cube?

A cube is a three dimensional figure or object which has all the side with equal length.

The length of each side of the cube = a = 60 units.

Therefore, the length of the diagonal of the cube = d = a\(\sqrt{3}\) = 60\(\sqrt{3}\) units = 103.9 units.

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The expression with its given values. 3x/y ; x = 4, y = 12 is 1

Given expression= 3x/y

x= 4 and y= 12

putting the values of x and y in the given expression,

3*4/12 = 1

The answer for the given expression is 1.

What is an Expression?

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Answer:

the bridge holds one ton. on Edgunuity

Step-by-step explanation:     <3

Answer: first one is 32000 the second one is 2000 and the third one Is  it will hold 1 ton

If two events, event A with probability P(A) and event b with probability P(B) are complementary events then the sum of the probability of events A and B will be one.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

When one event happens if and only if the other one doesn't, two occurrences are said to be complimentary. The odds of two complementary events equal one.

P(A) + P'(A) = 1

The chance of events A and B added together will equal one if events A with probability P(A) and event B with probability P(B) are complementary occurrences.

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the probability that the mean life of a random sample of 9 bread-making machines falls between 6.4 and 7.2 years is: 0.6106.

We can use the central limit theorem to approximate the sampling distribution of the sample mean of bread-making machines, which is also normally distributed with a mean of 7 years and a standard deviation of 1/√9 = 1/3 years.

Then, we need to standardize the values of 6.4 and 7.2 using the formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

For 6.4 years:

z1 = (6.4 - 7) / (1/3) = -1.2

For 7.2 years:

z2 = (7.2 - 7) / (1/3) = 0.6

We want to find the probability that the sample mean falls between 6.4 and 7.2 years, which is equivalent to finding the probability that the standardized sample mean falls between z1 and z2.

Using a standard normal distribution table or calculator, we can find the probabilities associated with each z-value:

P(z < -1.2) = 0.1151

P(z < 0.6) = 0.7257

Therefore, the probability that the mean life of a random sample of 9 bread-making machines falls between 6.4 and 7.2 years is:

P(-1.2 < z < 0.6) = P(z < 0.6) - P(z < -1.2) = 0.7257 - 0.1151 = 0.6106

The probability is approximately 0.6106 or 61.06%.

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