Solve the system of equations using any method. 2X – Y + Z = – 2, 6X + 3Y – 4Z = 8, – 3X + 2Y +3Z = – 6

Answer: the radius of a cylinder is 4 cm

Step-by-step explanation:

\(S_{ts}=352\ cm\ \ \ \ H=10\ cm\ \ \ \ \ r=?\)

The total surface area:

\(\displaystyle\\ S_{ts}= 2\pi r^2+2\pi rH\\\\S_{ts}=2\pi (r^2+rH)\\\\352=2\pi (r^2+10r)\\\\\)

Divide both parts of the equation by 2π:

\(\displaystyle\\56=r^2+10r\\\\56-56=r^2+10r-56\\\\0=r^2+10r-56\\\\Thus,\\\\ r^2+10r-56=0\\\\D=(-10)^2-4(1)(-56)\\\\D=100+224\\\\D=324\\\\\sqrt{D}=\sqrt{324} \\\\\sqrt{D}=18\\\\ r=\frac{-10б18}{2(1)} \\\\r=-14\notin\ (r > 0)\\\\r=4\ cm\)

Answer:

r ≈ 4 cm

Step-by-step explanation:

Total Surface Area of a cylinder

A = Base Area x 2 + Lateral Surface Area

A = 2(πr²) + 2πrh

where r = radius of base and h = height of cylinder

Solving for r we get

\(\displaystyle r = \dfrac{1}{2} \sqrt{h^2 + 2 \dfrac{A}{\pi} }-\dfrac{h}{2}\\\\\)

Given h = 10 cm and A = 325 we get

\(\displaystyle r = \dfrac{1}{2} \sqrt{10^2 + 2 \dfrac{352}{\pi} }-\dfrac{10}{2}\\\\\\\)

\(\sqrt{10^2 + 2 \dfrac{352}{\pi} } =\sqrt{100+\dfrac{704}{\pi }}\\\\= \sqrt{100 + 224.09}\\\\\\\)

= \(\sqrt{324.09}\)

= 18.0025

1/2 x 18.0025 ≈ 9

So r ≈  9 - 10/2 = 9 -5 = 4

r ≈ 4 cm

The statement is true.True or false: The population mean will always be the same as the mean of all possible x-bars that can be computed from samples of size 200.

False. The population mean is a fixed value that represents the average of the entire population. The mean of all possible x-bars (sample means) that can be computed from samples of size 200 is expected to be very close to the population mean due to the central limit theorem. However, it is not guaranteed to be exactly the same. Sampling variability can cause slight differences between the sample means and the population mean. If x represents a random variable with mean 40 and standard deviation 12, then the standard deviation of the sampling distribution with sample size 36 is 2.

False. The standard deviation of the sampling distribution is not a fixed value. It depends on the sample size (n) and the population standard deviation (σ). The standard deviation of the sampling distribution is given by σ / √n, where σ is the population standard deviation and n is the sample size. In this case, if the population standard deviation is 12 and the sample size is 36, the standard deviation of the sampling distribution would be 12 / √36 = 12 / 6 = 2. Therefore, the statement is true.

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Answer:

4075 squares centimeters

Step-by-step explanation:

V=4/3pi(r^3)

V=4/3pi(9^3)

V=3,054 inches^3

airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. then In this situation of statistics , individual is the cases are the bags or each piece of baggage.

What is a case?

In statistics, the word case is used to refer to the individual from which data is collected. For example, in a study about students' performance, the cases are each of the students.

What is the case in this situation?

Considering the administrators will need to weight and record each bag, the cases are each piece of baggage.

A. Number of bags weighing more than 75 pounds.

B. Average weight of the bags.

C. Each piece of baggage.

D. The airport administrators.

Hence airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. then In this situation of statistics , individual is the cases are the bags or each piece of baggage.

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Therefore, the expression is undefined when the value of x = 7 or x = -3.

An equation is a mathematical statement that asserts the equality of two expressions. It typically involves one or more variables and can be written using mathematical symbols such as addition, subtraction, multiplication, division, exponents, and roots. The goal of solving an equation is to find the values of the variables that satisfy the equation.

Here,

To simplify the expression, we first factor the denominator:

x² - 4x - 21 = (x - 7)(x + 3)

Now, we can rewrite the expression as:

(12x + 36) / (x - 7)(x + 3)

We can simplify the numerator by factoring out 12:

12(x + 3) / (x - 7)(x + 3)

The (x + 3) terms cancel out, leaving:

12 / (x - 7)

So the simplified expression is 12 / (x - 7).

The restrictions on the variable come from the fact that the denominator cannot be equal to zero. So we set the denominator equal to zero and solve for x:

(x - 7)(x + 3) = 0

x = 7 or x = -3

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Answer:

  (a)  x=−20 1/2

Step-by-step explanation:

Multiply by the product of the denominators and solve the resulting linear equation in the usual way.

  \(\dfrac{2}{7}=\dfrac{-5}{x+3}\\\\2(x+3)=-5(7)\qquad\text{multiply by $7(x+3)$}\\\\2x+6=-35\qquad\text{simplify}\\\\2x=-41\qquad\text{subtract 6}\\\\\boxed{x=-20\dfrac{1}{2}}\qquad\text{divide by 2}\)

Answer:

it the second one

Step-by-step explanation:

the pizza is 10 bucks. The 3 drinks all together cost 9 dollars. 3 times 3 is nine.

The correct representation is (b)

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Total cost of a pizza and 3 drinks is 19$.

If pizza cost 10.

Then, remaining drinks costs = 19-10

                                                 = 9$

If each drinks carry equal price, so

= 9/3

= 3$

Each drinks cost $3.

Hence, the correct representation is (b): 10, d, d, d.

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The estimated minimum monthly cost of natural gas for 1 year is represented by the function C(a) = 3 - 42a + 187.

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According to the information, we can infer that A. 1: Real, Rational, Integer, Whole, Natural, B. 5.1: Real, Rational, C. √(-142): Non-real, D. \(\pi\) (Pi): Irrational, Real, E. 2/3: Rational, Real, F. ∛(-27): Non-real, G. 0.671: Real, Rational, H. 3√7: Irrational, Real, I. 0: Real, Rational, Integer, Whole, Natural, J. -√16: Real, Rational.

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Answer:

a: 00:45

b: 7:30 PM

Step-by-step explanation:

Hope this is right

The number of ways in which you can answer the questions is: 6561 ways

Permutations and combinations are simply defined as  the various ways whereby objects from a peculiar set may be selected, generally without any replacement, to form subsets. This selection of subsets is referred to as a permutation when the order of selection is a factor, but then referred to as a combination when order is not a factor.

The formula for permutation is:

nPr = n!/(n - r)!

The formula for combination is:

nCr = n!/(r!(n - r)!

Thus, the solution here is calculated as:

3⁸ = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3

= 6561 ways

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Answer:

a) The differential equation for the velocity is given by

(dv/dt) = k(250 - v)

b) v(t) = 250 - e⁽⁵•⁵² ⁻ ᵏᵗ⁾

With units of km/h

Step-by-step explanation:

Acceleration, a ∝ (250 - v)

But acceleration is widely given as dv/dt

(dv/dt) ∝ (250 - v)

(dv/dt) = k(250 - v)

where k = constant of proportionality

(dv/dt) = k(250 - v)

b) (dv/dt) = k(250 - v)

dv/(250 - v) = k dt

∫ dv/(250 - v) = ∫ k dt

- In (250 - v) = kt + c (where c is the constant of integration)

v(0) = 0; meaning, at t = 0, v = 0

- In 250 = 0 + C

c = - In 250 = - 5.52

- In (250 - v) = kt - 5.52

In (250 - v) = 5.52 - kt

250 - v = e⁽⁵•⁵² ⁻ ᵏᵗ⁾

v = 250 - e⁽⁵•⁵² ⁻ ᵏᵗ⁾

With units of km/h

i hope this work for you

and sory if im wrang

Given:

defective units = 29.1

total production = 9,700

Hence:

substituting values in the formula:

ANSWER

0.3 percent of the production is defective.

According to the given statement , the value of "b" in the equation cos(22.6°) = b/13 is approximately 12.

To solve for "b" in the equation cos(22.6°) = b/13, we can use trigonometric functions.

Step 1:

Rewrite the equation as cos(22.6°) = b/13.

Step 2:

Multiply both sides of the equation by 13 to isolate "b". This gives us:

b = 13 * cos(22.6°).

Step 3:

Use a calculator to find the cosine of 22.6°. The value of cos(22.6°) is approximately 0.9239.

Step 4:

Substitute this value back into the equation to find "b". b = 13 * 0.9239.

Step 5:

Calculate the value of "b" by multiplying 13 by 0.9239. The result is approximately 11.999.

Step 6:

Round the value of "b" to the nearest whole number. Since 11.999 is closer to 12, we round up to 12.

Therefore, the value of "b" in the equation cos(22.6°) = b/13 is approximately 12.

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Answer:

No, Dale Isn't correct because 3:5 is greater than 2:10

Step-by-step explanation:

3:5 and 2:10 is the same as in \(\frac{3}{5}\)  and \(\frac{2}{10}\)

First Find the least common denominator or LCM of the two denominators:

LCM of 5 and 10 is 10

Next, find the equivalent fraction of both fractional numbers with denominator 10

For the 1st fraction, since 5 × 2 = 10,

\(\frac{3}{5} =\frac{3*2}{5*2} =\frac{6}{10}\)

Likewise, for the 2nd fraction, since 10 × 1 = 10,

\(\frac{2}{10} =\frac{2*1}{10*1} =\frac{2}{10}\)

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

\(\frac{6}{10} >\frac{2}{10} Or\frac{3}{5} >\frac{2}{10}\)

Hence, \(\frac{3}{5}\) is Greater than \(\frac{2}{10}\)

Hence, 3:5 is Greater than 2:10

Perimetrul paralelogramului este 14 cm, iar aria este 12 cm².

Pentru a găsi perimetrul unui paralelogram, trebuie să adunăm lungimea tuturor laturilor sale. În acest caz, avem două perechi de laturi egale: AB = DC = 7 cm și AD = BC = 3 cm + 4 cm = 7 cm. Astfel, perimetrul paralelogramului este 2 x (AB + AD) = 14 cm.

Pentru a găsi aria unui paralelogram, trebuie să înmulțim lungimea unei laturi cu înălțimea corespunzătoare. În acest caz, înălțimea este linia AD, care este perpendiculară pe BD. Prin urmare, aria paralelogramului este AD x BD = 3 cm x 4 cm = 12 cm².

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The probability that the volume of soda in a randomly selected bottle will be less than 64.0 oz will be 0.4013

Given,

The volumes of soda in tested soda bottles are normally distributed.

The mean of the distribution, μ = 64.6 oz

Standard deviation, σ = 2.40 oz

We have to find the probability that the volume of soda in a randomly selected bottle will be less than 64.0 oz;

Let x be the volume of randomly selected quart soda bottle.

z score = (x - μ) / σ = (64 - 64.6) / 2.4 = -0.25

Then,

The probability that the volume of soda in a randomly selected bottle will be less than 64​ oz

P(x < 64) = P(z < -0.25) = 0.4013

That is,

The probability that the volume of soda in a randomly selected bottle will be less than 64.0 oz will be 0.4013

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If you calculate SLE to be $25,000 and that there will be one occurrence every four years (ARO), then the ALE is $40,000.

A expected monetary decline each moment an asset is at risk is referred to as single-loss expectancy (SLE). It is a term that is most frequently used during risk analysis and attempts to assign a monetary value to each individual threat.

Quantitative risk analysis predicts the likelihood of certain risk outcomes as well as their approximate monetary cost using relevant, verifiable data.

IT professionals must consider a wide range of risks, including the following:

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The joint distribution is Pr(Y1=y1, Y2=y2, ..., Y100=y100|θ) = θ^∑yi(1-θ)^(100-∑yi), and the form of Pr(∑Yi=y|θ) is a binomial distribution.

The joint distribution:

We are given that Y1, Y2, ..., Y100 are independent and identically distributed (i.i.d.) binary random variables with an expectation of θ. The joint distribution of Pr(Y1=y1, Y2=y2, ..., Y100=y100|θ) can be written as the product of individual probabilities. Since each Yi can take on values of 0 or 1, the joint distribution can be expressed as:

Pr(Y1=y1, Y2=y2, ..., Y100=y100|θ)

= θ^∑yi(1-θ)^(100-∑yi)

Pr(∑Yi=y|θ):

The form of Pr(∑Yi=y|θ) follows a binomial distribution. It represents the probability of obtaining a specific sum of successes (∑Yi=y) out of the total number of trials (100) given the parameter θ.

Computing Pr(∑Yi=57) for each value of θ:

To compute Pr(∑Yi=57) for each value of θ ∈ {0.0, 0.1, ..., 0.9, 1.0}, you substitute ∑Yi with 57 in the binomial distribution formula and calculate the probability for each θ value.

Computing p(θ|∑Yi=57) using Bayes' rule:

Given that the prior probabilities for each θ-value are equal, you can use Bayes' rule to compute the posterior distribution p(θ|∑Yi=57) for each θ-value. Bayes' rule involves multiplying the prior probability by the likelihood and normalizing the result.

Plotting the distributions:

After obtaining the probabilities for each value of θ, you can plot the probabilities as a function of θ to visualize the distributions. You will have plots for the probabilities Pr(∑Yi=57) and the posterior distribution p(θ|∑Yi=57) for different scenarios.

These steps involve probability calculations and plotting, allowing us to analyze the distributions and relationships among the different scenarios.

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The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.

To understand this ratio, let's break it down using different units:

A. 1/3 part bleach and 2/3 part water:

If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.

B. 2 cups of bleach and 3 cups of water:

If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.

C. 3 cups of bleach and 2 cups of water:

If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.

Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

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The given statement "As the level of confidence increases the number of item to be included in a sample will decrease when the error and the standard deviation are held constant." is False because error increases.

As the level of confidence increases, the required sample size will increase when the error and standard deviation are held constant.

This is because as the level of confidence increases, the range of the confidence interval also increases, which requires a larger sample size to ensure that the estimate is precise enough to capture the true population parameter with the desired level of confidence.

For example, if we want to estimate the mean height of a population with a 95% confidence interval and a margin of error of 1 inch, we would need a larger sample size than if we were estimating the same mean height with a 90% confidence interval and the same margin of error.

The larger sample size ensures that the estimate is more precise and that we have a higher level of confidence that it captures the true population parameter.

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Answer:

Mean = 48.5, Median = 53, Mode = nothing, Outlier = 17

Step-by-step explanation:

Mean: Add all the numbers (388) then divide by how many numbers (8) are there. (= 48.5)

Median: Is the middle number () so you have to order them from least to greatest (17, 42, 45, 52, 54, 57, 58, 63) and then just keep marking them off left, right, left, right... until you get to the middle. But since there are two numbers (52, 54) you have to add them (106) then you divide by 2 (53).

Mode: Is the number that shows up the most. In this case none of them do.

Outlier: The number that is farthest from the other numbers (17).

Answer:

answer: 1.6 is not valid probability because 1.6 is 160% so thats not valid cause its over 100 percent

The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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Based on the figure provided, it is clear that each man has a preference for a certain woman. Specifically, man 1 prefers woman 3, man 2 prefers woman 5, man 3 prefers woman 2, man 4 prefers woman 4, and man 5 prefers woman 1.

Using this information, we can determine the number of matchings by considering each man and his preferred woman.

Starting with man 1, he must be matched with woman 3. There is only one possible match for him.

Moving on to man 2, he must be matched with woman 5. Again, there is only one possible match for him.

For man 3, his preferred woman is already matched with man 1. Therefore, he must be matched with woman 4.

For man 4, his preferred woman is already matched with man 2. Therefore, he must be matched with woman 2.

Finally, for man 5, his preferred woman is already matched with man 3. Therefore, he must be matched with woman 1.

Putting all of these matches together, we have:

Man 1 -> Woman 3
Man 2 -> Woman 5
Man 3 -> Woman 4
Man 4 -> Woman 2
Man 5 -> Woman 1

Therefore, there is only one possible matching of the five men with the five women given the constraints in the figure above.

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