A 95% confidence interval for the population mean implies that if samples are drawn repeatedly and confidence intervals for μ are constructed, then 95% of the confidence intervals computed will contain the population mean (true or false)

The statement that apply is that the volume of the cone is One-third the volume of the cylinder

volume of a cone = 1 / 3 πr²h

where

Volume of a cylinder = πr²h

where

The cone and the cylinder has the same base and height. Therefore, the radius and height are the same .

volume of the cylinder = 84π

Therefore, the volume of the cone is One-third the volume of the cylinder.

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To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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Answer:

I believe the ans is (B) 40/9

Answer:

The answer is B. 40/9.

Step-by-step explanation:

We know, tan= opposite/adjacent

so, tan C = 40/9

To find out how long it will take for the two hoses to fill the pool working together, we need to determine their individual rates of filling the pool.

Let's assume the small hose fills the pool at a rate of 1 pool per x minutes, and the larger hose fills the pool at a rate of 1 pool per y minutes.

We can set up the following equation to represent the rates of filling the pool:

1/x + 1/y = 1/t

where t represents the time it takes for the two hoses to fill the pool together.

To simplify the equation, we can find a common denominator:

(y + x) / (xy) = 1/t

Cross-multiplying gives:

xy = t(y + x)

Now, we can solve for t:

t = xy / (y + x)

Using the given information that the small hose fills the pool in x minutes and the larger hose fills the pool in y minutes, we can substitute those values into the equation:

t = (x * y) / (y + x)

This formula gives us the time it takes for the two hoses to fill the pool together.

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Answer:

Based on the given information, it is not possible to definitively determine whether the number generator is fair or not. However, we can make some observations and inferences:

We know that 70% of the socks in the drawer are black, which means that in a random selection of 10 socks, we would expect to see around 7 black socks on average.

The dot plot shows the number of black socks in 10 trials of the number generator. We can see that the number of black socks varies from 0 to 10, with some frequencies being higher than others.

Without knowing the exact frequencies or probabilities, we can see that the dot plot does not appear to be centered around 7 black socks, which is what we would expect from a fair number generator. However, it is difficult to determine whether the deviations from 7 are statistically significant or not, without more information.

Therefore, based on the given information, the most accurate statement is:

The number generator's fairness cannot be determined with certainty from the given data, but there are indications that it may not be perfectly fair.

Step-by-step explanation:

The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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Given points are not the solution for the given System of equations.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given,  Two systems of equations,

a) (-10,-1) y= 1/2x+4, y=4x+30

b) (2, 3/2) y= 8-x/4, y= 5/4x-1

For the First system of equations:

y= 1/2x+4,

y =4x+30

Comparing both the equation:

4x + 30  = 1/2x + 4

3.5x = -26

x= -26/3.5

x = -7.428

Thus, the given point is not the solution to the equation.

For the second system of equations:

y= 8-x/4,

y= 5/4x-1

Comparing both the equation:

8-x/4 = 5/4x-1

6x/4 = 9

x = 6

Thus, the given point is not the solution to the equation

Therefore, Given points are not the solution for the given System of equations.

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The given problem is related to the revenue function of a machine parts company. The problem states that if the price of the product is set to $43, then the company can sell 1000 machine parts, whereas if the price is $29, then the company can sell 2000 machine parts.

We have to construct the revenue function as a function of items sold and find marginal revenue at 500 machine parts. Let the demand curve equation be y = mx + bwhere x represents the quantity, m is the slope of the demand curve, and b is the y-intercept.We can obtain the slope using two points on the curve. Thus, we can use the two data points to calculate the slope.The price is $43 when the company sells 1000 parts. Thus, the first point is (1000, 43).The price is $29 when the company sells 2000 parts.

Let's take the first point (1000, 43):43 = (-0.014) * 1000 + bSo, b = 57.R(x) represents the revenue function as a function of items sold. It is obtained by multiplying the price by the quantity, x. The price curve is linear, so the equation for R(x) will be a straight line.R(x) = price * quantity = (mx + b)x = mx² + bxThe equation becomes: R(x) = (-0.014x + 57)x = -0.014x² + 57xMR (500) represents the marginal revenue at 500 machine parts.

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Answer:

a couple different obes

Step-by-step explanation:

there are five

Answer:

S=32.5

W=97.5

Step-by-step explanation:

S=speed of plane in still air

W=speed of wind

-----------------------------------------

3(S+W)=130

6(S-W)=130

-----------------------------------------

S+W=43.33333...

S-W=21.66666...

2S=64.999...

S=32.5(simplified)

-----------------------------------------

32.5+W=130

W=97.5

-----------------------------------------

Answer:

d brainest plz

Step-by-step explanation:

Confidence interval = (y ± t∗s/√n)g1 = y - t*s/√ng2 = y + t*s/√n Substituting the values, g1 = 26.22 - 1.860*(0.11)/√9 = 25.84g2 = 26.22 + 1.860*(0.11)/√9 = 26.59Therefore, the statistics g1 and g2 that will satisfy the required inequality are 25.84 and 26.59 respectively.

The formula for finding the confidence interval is as follows: n − 1, where t is the value of the t-distribution corresponding to the specified confidence level and the sample size minus one.

As per the given exercise 7.11, suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample.

If a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p(g1 ≤ (y - u) ≤ g2) = 90

To find the statistics g1 and g2 that will satisfy the required inequality

the following formula can be used: Confidence interval = \((y ± t∗s/√n)\)

From the formula, we can see that the confidence interval depends on the values of y, s, t and n.

The value of y is the sample mean

the value of s is the sample standard deviation

And the value of n is the sample size.

The value of t depends on the confidence level desired and the degrees of freedom for the t-distribution. In this case, the confidence level is 90%, which means that we want to find the value of t that will give us a total area of 0.90 under the t-distribution curve with 8 degrees of freedom .Using the t-table, the value of t can be found to be 1.860, where the value for 90% and 8 degrees of freedom is 1.860.t = 1.860Now, we need to calculate the value of s, which is the sample standard deviation.

Since we do not have any information about the population standard deviation, we will use the sample standard deviation as an estimate of the population standard deviations = σ/√nσ = s*√nσ = 0.11*√9σ = 0.33Substituting the values in the confidence interval formula

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Answer:

He earns $58.5

Step-by-step explanation:

i did the math

It gradually decreases as alcohol is metabolized. The function C(t)=0.135 t e^{-2.802 t}models the mean BAC measured in g/mL.

The maximum average BAC during 3 hours is 0.0001358 g/mL.

f(t) = α t e−βt --(1)

Let's rewrite this in a simple form:

f(t)= α eˡⁿ ᵗ e⁻βt = αe^(ln t −βt)

Since e^x is strictly increasing and it will be maximized exactly when its argument is maximized, so we can maximize instead:

g(t)=ln t −βt

differentiating with respect to t , and g'(t) = 0

g′(t)=1/t − β = 0

=> t =1/β

we have given a function

C(t)=0.135 t e⁻²·⁸⁰²ᵗ

if we compare it with (1) we get

β = 2.802, 0.135 = α

For it's maximized we need to check the second order condition, and that of g will differentiate again , g′′(t)= −1/t² < 0

We have to compute the derivative of C(t):

C′(t) = 0.135 t⋅(−2.802)e⁻²·⁸⁰²ᵗ + 1.35e⁻²·⁸⁰²ᵗ

For optimum at t₀ if C′(t₀)=0 and C′′(t₀)≠0. Here, we have

C′(t₀) = 0.135t₀⋅(−2.802)e⁻²·⁸⁰²ᵗ₀+ 0.135e⁻²·⁸⁰²ᵗ₀ =e⁻²·⁸⁰²ᵗ₀(−0.135* 2.802t₀+ 0.135)=0

It is clear that e⁻²·⁸⁰²ᵗ₀ not equal to zero for all t₀∈R, so that

=> −0.135* 2.802t₀+0.135=0

=> t₀ = 1/2.802 ≈0.36

let us consider t is in hours, so that it makes t₀ =0.36h≈21.41min. This is the only optimum and one should verify it is indeed a maximum, i.e. C′′(t₀)<0.

Now, easily compute the maximum average BAC, which is C(t₀)=C(0.36) = 0.135 (0.36)e⁻²·⁸⁰²⁽⁰·³⁶⁾

= 0.0486(0.3678) = 0.01787508

Hence, the maximum average BAC, is 0.017 g/dL.

Maximum average BAC during the first 3 hours,

t = 3 , C(t)=C(3) = 0.135 (3)e⁻²·⁸⁰²⁽³⁾ = 0.0001358 g/mL

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Answer:

8

Step-by-step explanation:

(5 + 16) / 7 + 3^2 - (1 + 3)

21 / 7 + 3^2 - 4

21 / 7 + 9 - 4

3 + 9 - 4

12 - 4

8

Use PEMDAS.

P - Parenthesis

E - Exponents

M/D - Multiply/Divide

A/S - Add/subtract

So for this:

Start with parenthesis: (5+16) and (1+3), so 21 and 4

Then exponent: 3^2, which is 3*3 which is 9

Then divide: 21/7 is 3

And then the rest: 3 + 9 - 4. 3+9 is 12, 12-4 is 8, so you're answer is 8.

It would take a penguin approximately 4.5 hours to travel 112.5 miles at a speed of 25 miles per hour.

To find out how long it would take a penguin to travel 112.5 miles at a rate of 25 miles per hour, we can use the formula:

time = distance ÷ speed

Substituting the values given in the question, we get:

time = 112.5 miles ÷ 25 miles per hour

Simplifying this expression, we get:

time = 4.5 hours

Therefore, it would take a penguin approximately 4.5 hours to travel 112.5 miles at its maximum speed of 25 miles per hour. It's worth noting that this calculation assumes that the penguin would maintain a constant speed throughout its journey, which may not always be the case in reality. Factors such as weather conditions, terrain, and the penguin's energy levels could all affect its speed and travel time.

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The probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).

Given information:

five program systems are prepared so that they work independently of each other. Each system has a 0.3 chance of detecting an error.

Find the probability that at least one program system will detect an error. Use 4 decimal places.The probability of a system detecting an error is 0.3.

The probability of a system not detecting an error is 1 - 0.3 = 0.7.

Probability that none of the five systems detects an error is, P(error not detected in any of the five systems) = P(not detected in 1st) x P(not detected in 2nd) x ... x P(not detected in 5th) = 0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807.

The probability that at least one system detects an error is, P(at least one system detects an error) = 1 - P(error not detected in any of the five systems) = 1 - 0.16807 = 0.8319 (approx).

Therefore, the probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).

Hence, the correct option is 0.832.

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The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

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It takes 72 minutes for Nikki to paint the room working alone and 90 minutes for Greg to paint the room working alone given that Greg and Nikki takes a total of 40 minutes to paint a room if they work together and if Greg works alone, he takes 18 minutes longer to paint he room than Nikki takes if she works alone. This can be obtained by using suitable algebraic equation and quadratic formula.

Here in the question it is given that,

⇒  \(\frac{1}{time(Greg)} +\frac{1}{time(Nikki)} =\frac{1}{40}\)

⇒  time(Greg) = time(Nikki) + 18 ⇒ time(Greg) = x + 18

    ⇒    \(\frac{1}{x} +\frac{1}{x+18}= \frac{1}{40}\)

By simplifying the equation we get the quadratic equation,

⇒ \(\frac{x+18+x}{x(x+18)} =\frac{1}{40}\)

⇒ 40(2x + 18) = x(x + 18)

⇒ 80x + 720 = x² + 18x

⇒ x² - 62x - 720 = 0

By using quadratic formula we can find the value of x,

a = 1, b = - 62, c = - 720

⇒ b² - 4ac = (- 62)² - 4(1)(-720)

⇒ b² - 4ac = 3844 + 2880

⇒ b² - 4ac = 6724

√b² - 4ac = √6724

√b² - 4ac = 82

\(x = \frac{-b+\sqrt{b^{2}-4ac} }{2a}\) or \(x = \frac{-b-\sqrt{b^{2}-4ac} }{2a}\)

\(x = \frac{62+82}{2}\) or \(x = \frac{62-82}{2}\)

x = 144/2 or x = - 20/2

x = 72 or x = - 10

Since time taken cannot be negative we take the value of x as 72 min.

That is, time(Nikki) = x = 72 min

time(Greg) = x + 18

time(Greg) = 72 + 18

time(Greg) = 90 min

Hence it takes 72 minutes for Nikki to paint the room working alone and 90 minutes for Greg to paint the room working alone given that Greg and Nikki takes a total of 40 minutes to paint a room if they work together.

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Answer:

See photo #11

Step-by-step explanation:

Researchers try to gain insight into the characteristics of a sample population by examining a sample of the population.

A sample is a subset of individuals or units taken from a larger population. Researchers use sampling methods to select a representative group of individuals from the population they are interested in studying. By studying the sample, researchers can make inferences and draw conclusions about the characteristics, behaviors, or trends that may exist within the entire population.

The goal of sampling is to obtain a sample that accurately represents the population in terms of its relevant characteristics. Researchers carefully select their samples to ensure that they are representative and minimize bias. This allows them to generalize the findings from the sample to the larger population with a certain level of confidence.

By examining a sample, researchers can collect data, analyze patterns, and draw conclusions about the population as a whole. This approach is more feasible and practical than attempting to study the entire population, especially when the population is large or geographically dispersed.

Therefore, researchers use samples to gain insight into the characteristics of a population, making option d. "Sample" the correct answer.

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To find Andrew's total haircut payment, add the haircut cost to the tip amount, multiplying by 20%, and add the two amounts. The total amount is $18.

To find the total amount Andrew pays for the haircut, including the tip, we need to add the cost of the haircut to the amount of the tip.

First, let's calculate the amount of the tip. Andrew leaves a 20% tip, which means he pays 20% of the cost of the haircut as a tip. To find this amount, we multiply the cost of the haircut ($15) by 20% (0.20).

$15 * 0.20 = $3

So, the tip amount is $3.

To find the total amount Andrew pays, we need to add the cost of the haircut ($15) to the tip amount ($3).

$15 + $3 = $18

Therefore, the total amount Andrew pays for the haircut, including the tip, is $18.

I hope this helps! Let me know if you have any other questions.

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Answer:

Use " m-a-t-h-w-a-y " for this.

Step-by-step explanation:

Answer:

2/9 - 1/3 (If you want to solved: -1/9)

Step-by-step explanation:

2 over 9 is 2/9 minus is just -  and 1 over 3 is 1/3 so the equation looks like this: 2/9-1/3

To solve this you need to multiply the 1/3 by 3 on both the denominator and numerator: 2/9-3/9

simplify: -1/9

Hope this helps!

Step-by-step explanation:

point-slope firm is

y - y1 = m(x - x1)

m = slope of the line

(x1, y1) = coordinates of one point on the line.

the slope is the ratio y/x, which indicates how many units y is changing, when x changes a certain amount of units.

when we look at the 2 given points, we go from one point to the other - how much are x and y changing ?

let's just go in the direction of the original listing. so, we go from (0, -2) to (-1, 0).

x changes from 0 to -1, so, by -1.

y changes from -2 to 0, so, by +2

so, our slope is saying that when x changes by -1 unit, y changes 2 units.

=> m = y/x = 2/-1 = -2

so, as equation we get (by using the first point)

y - -2 = -2(x - 0) = -2x

y + 2 = -2x

or fully simplified leading to the slope-intercept form

y = -2x - 2

Answer:

a. Linear

A linear line is straight.

Answer:

$323.4

Step-by-step explanation:

I = Prt

I = (490)(0.11)(6)

I = 323.4

Answer:

$323.40

Step-by-step explanation:

False. A sample is a subset of all possible data values for a given subject under consideration, not the set of all possible data values.

What is sample space?

The set of all potential outcomes for an experiment is referred to as the sample space S in a random experiment. The results of a random experiment, also known as sample points, are incompatible (i.e., they cannot occur simultaneously).

A sample is a portion of a larger set of data that is selected for analysis or representation. It is not the entire set of all possible data values for a given subject, but rather a smaller subset chosen for the purpose of study.

Sampling is important because it allows researchers to study and make inferences about a larger population with a smaller, more manageable amount of data.

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