Please help me with the correct answer

A. If the radius of the sphere is r, what is the height of the cylinder H=4√r

B The volume of the sphere will be V=4πr³

Volume is defined as the space occupied by any object in the three-Dimenions. All three parameters are required for the volume like length, width and height of cube or cuboid.

Here for the part A If the radius of the sphere is r, what is the height of the cylinder the solution will be given as:-

The Volume of sphere = Volume of cylinder

4πr³=(π÷4) r²H

H=16r

H=4√r

Hence the height of the cylinder will be H=4√r

B. The volume of the shapes will be given as:-

(1) Volume of cylinder = (π÷4)r²H

Here r= radius of the cylinder

H = height of the cylinder

(2) The Volume of the Sphere=4πr³

Here r= radius of the cylinder

(3) The Volume of cone=(1÷3)πr³l

Here r = radius of the base

l=slant height of the cone

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Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

First, let's calculate the total amount he will need to finance:

Total amount to finance = R160,000 + 0.15 x R160,000 (VAT at 15%) = R184,000

Next, let's calculate the total interest he will need to pay over the 60 months:

Total interest = (principal x rate x time) / 100

where

Total interest = (R184,000 x 10% x 5) / 100 = R92,000

Therefore, the total amount Michael will need to pay over the 60 months is the sum of the total amount financed and the total interest:

Total amount to pay = Total amount to finance + Total interest = R184,000 + R92,000 = R276,000

So, Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

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Answer:

50% of the Basketball team is over 6 feet

Step-by-step explanation:

So half of 20 is 10 and if half is over 6 feet then it is 50% because 50% is half of 100% which equals the whole team. Sorry I'm really bad at explaining.

Option C, The greatest common factor of −20x³y − 8\(xy^4\) + 4xy³ is 4xy by simplifying expressions and solving equations.

To find the greatest common factor (GCF) of the given terms, we need to factor out any common terms that they share.

First, we can factor out 4xy from each term:

−20x³y − 8\(xy^4\) + 4xy³ = 4xy(-5x² - 2y³ + y)

Now we need to check if any further common factors can be factored out from the remaining expression (-5x² - 2y³ + y). However, there are no other factors that can be factored out from this expression.

As it enables us to factor out frequent terms and reduce the expression to its most basic form, the GCF is beneficial for simplifying expressions and solving equations.

Therefore, the GCF of the original terms is 4xy, option (c).

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Answer:

4xy

Step-by-step explanation:

I did the test and got it right !

It is the greatest common factor of 20, 8, and 4. And we add the “xy”.

The worker to be able to complete the operation in 9 minutes, in 13 cycles

We are given the projected learning curve equation as y = 15\(x^{(-0.074)}\), where y is the time to complete the operation in minutes, and x is the cumulative number of cycles. We want to find the value of x when the time y is 9 minutes (the standard time).

Setting y = 9 in the equation, we can solve for x:

9 = 15\(x^{(-0.074)}\)

Dividing both sides by 15:

0.6 = \(x^{(-0.074)}\)

Taking the reciprocal of both sides:

1/0.6 = x\(x^{(0.074)}\))

Simplifying:

1.6667 = \(x^{(0.074)}\)

To solve for x, we need to raise both sides to the power of 1/0.074:

x = \((1.6667)^{(1/0.074)}\)

Using a calculator, we find:

x ≈ 13.056

Therefore, it will take approximately 13 cycles for the worker to be able to complete the operation in 9 minutes, which is the standard time. Hence, the correct answer is option b: 13 cycles.

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The amount of the 90gram-sample that will remain after 290 years is 9.88 grams

We'll begin by obtaining the number of half lives that has elapsed. This can be obtained as follow:

Step1

n = t / t½

n = 290 / 91

n = 3.1868

Step 2

determine the amount remaining:

The amount remain can be obtained as follow:

N = N₀ / 2^n

N = 90 / 2^3.1868

=9.88

N=9.88 grams

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If we pick 23 fruits at random, then 7% of the time, their mean weight will be greater than 210.8 grams.

To solve this problem, we need to use the Central Limit Theorem, which states that the sampling distribution of the means of a random sample from any population will be approximately normally distributed if the sample size is large enough.

In this case, since we are picking 23 fruits at random, we can assume that the sampling distribution of the mean weight of the fruits will be approximately normal with a mean of 204 grams and a standard deviation of 16/sqrt(23) grams.

To find the weight of the fruits such that their mean weight will be greater than a certain amount 7% of the time, we need to find the z-score associated with that probability using a standard normal distribution table. The z-score can be calculated as:

z = invNorm(0.93) = 1.475

where invNorm is the inverse normal function. This means that the weight of the fruits such that their mean weight will be greater than this amount 7% of the time is:

x = 204 + 1.475*(16/sqrt(23)) = 210.8 grams (rounded to one decimal place)

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A dichotomous scale presents only two response options for participants to choose from.  A category scale provides multiple response options within a predefined set of categories.

a) The difference between a dichotomous and category scale lies in the number of response options provided.

Dichotomous Scale: A dichotomous scale presents only two response options for participants to choose from. It is a nominal scale with two categories, typically represented as "yes/no" or "true/false."

The responses are mutually exclusive and exhaustive, meaning participants must select one of the two options. Example: "Do you own a car?" (Response options: Yes/No)

Category Scale: A category scale provides multiple response options within a predefined set of categories. It allows participants to select from more than two options, providing a wider range of choices.

Category scales can be ordinal or nominal, depending on whether the categories have a specific order or not. Example: "What is your favorite color?" (Response options: Red, Blue, Green, Yellow, etc.)

b) Reliability of a measure is an indication of stability and consistency in the results obtained from the measure. It refers to the extent to which a measurement tool produces consistent and dependable results over time or across different conditions.

High reliability means that the measure is reliable and yields consistent results, while low reliability indicates inconsistency or measurement error.

To assess the reliability of a measure, various methods can be used, such as test-retest reliability, internal consistency reliability (e.g., Cronbach's alpha), inter-rater reliability, or split-half reliability.

These methods evaluate different aspects of reliability depending on the nature of the measurement and the specific research context.

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Answer:

Angle A: 30°

Angle B: 60°

Angle C: 90°

Step-by-step explanation:

Hopefully this helps! :)

The measure of the interior angles are Angle A: 30°, Angle B: 60° and Angle C: 90°

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

The given triangle has angle measurements of 30º and 90° which is given in the question.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

∵ The sum of the interior angles in the triangle = 180°

So the measure of the remaining angle would be x:

⇒ 30° + 90°  + x = 180°

⇒ x = 180 - 30° - 90°

⇒ x = 180 - 120°

⇒ x = 60°

Therefore, the required measure of the remaining angle x is 60°.

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Answer:

3. 15.02

4. 84.05

6. 4,301

Step-by-step explanation:

I'm not too sure how to explain this, but those are the answers.

Answer:

Candy canes are a classic Christmas treat, traditionally white with red stripes and flavored with peppermint. They have been popular since the 1600s and are thought to have originated in Germany. Today, 90 percent of all candy canes are sold between Thanksgiving and Christmas.

In a bag of Christmas treats, there are 3 red candy canes for every 5 gingerbread men. If there total is 40 treats, then the number of candy canes will be 24. This can be calculated by taking 40 divided by 8 (5+3) which equals 5, and then multiplying this by 3 which equals 15. Therefore, 24 candy canes are included in the bag of 40 Christmas treats.

Step-by-step explanation:

(B) 0

We have

\(p^2 = 2q^2 \implies \dfrac{p^2}{q^2} = \left(\dfrac pq\right)^2 = 2\)

but 2 is not a square number.

Answer:

a) The estimates for the solutions of \(4\cdot x^{2}-4\cdot x -1 = 0\) are \(x_{1}\approx -0.25\) and \(x_{2} \approx 1.25\).

b) The estimates for the solutions of \(4\cdot x^{2}-4\cdot x -1 = 2\) are \(x_{1}\approx -0.5\) and \(x_{2} \approx 1.5\)

Step-by-step explanation:

From image we get a graphical representation of the second-order polynomial \(y = 4\cdot x^{2}-4\cdot x -1\), where \(x\) is related to the horizontal axis of the Cartesian plane, whereas \(y\) is related to the vertical axis of this plane. Now we proceed to estimate the solutions for each case:

a) \(4\cdot x^{2}-4\cdot x -1 = 0\)

There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:

\(x_{1}\approx -0.25\), \(x_{2} \approx 1.25\)

b) \(4\cdot x^{2}-4\cdot x -1 = 2\)

There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:

\(x_{1}\approx -0.5\), \(x_{2} \approx 1.5\)

Answer:

x3

Step-by-step explanation:

There are 60 possible outcomes for this experiment.

The problem asks to determine the total number of outcomes for an experiment consisting of three steps with different numbers of possible outcomes at each step.

To solve this problem, we need to apply the multiplication principle, which states that the total number of outcomes for a sequence of events is equal to the product of the number of outcomes at each event.

In this case, there are two possible outcomes for the first step, six possible outcomes for the second step, and five possible outcomes for the third step.

Therefore, the total number of outcomes possible is:

2 * 6 * 5 = 60

Therefore, there are 60 possible sequences of events that can occur in this experiment.

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By using Chebyshev's Inequality with K=3, we can determine that at least 88.89% of the days had temperatures between "F and "F, where "F represents the mean temperature of 76.4°F.

Chebyshev's Inequality provides a lower bound on the proportion of data that falls within a certain number of standard deviations from the mean. In this case, K=3 means that we are considering a range of three standard deviations from the mean.

The inequality states that for any dataset, the proportion of data falling within K standard deviations of the mean is at least 1 - (1/K^2). So, for K=3, we have 1 - (1/3^2) = 1 - (1/9) = 8/9 ≈ 0.8889. Therefore, at least 88.89% of the data falls within three standard deviations of the mean.

In the context of the temperature data, we can conclude that at least 88.89% of the days had temperatures between the mean temperature of 76.4°F minus three standard deviations (76.4 - 3 * 7.3) and the mean temperature plus three standard deviations (76.4 + 3 * 7.3). This range represents a relatively high proportion of the dataset, indicating that the temperature observations are fairly concentrated around the mean with limited extreme values.

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Answer:

\(\sqrt{7}\)

Step-by-step explanation:

\(\sqrt{7}\) is the answer to almost anyway that you can solve this problem.

Multiply the numerator and denominator by the conjugate.

Answer:

46in²

Step-by-step explanation:

P = 5+1+5+1=12

H = 3

B = (5)(1) = 5

12(3)+2(5) = 46in²

Answer:

it is terminating

Step-by-step explanation:

Answer:

11/20 is a terminating decimal.

Step-by-step explanation:

1) Find the denominator of 11/20 in its lowest form.

The greatest common factor (GCF) of 11 and 20 is 1. Convert 11/20 to its simplest form by dividing the numerator and denominator by its GCF: The denominator of 11/20 in its lowest form is 20.

11 ÷ 1  / 20 ÷ 1  = 11 /  20

2) Find the prime factors of the answer in Step 1.

The prime factors of 20 are all the prime numbers that you multiply together to get 20. The prime factors of 20 are:

2 x 2 x 5

3) Determine if 11/20 is terminating.

A fraction is a terminating decimal if the prime factors of the denominator of the fraction in its lowest form only contain 2s and/or 5s or no prime factors at all. This is the case here, which means that our answer is as follows:

11/20  = terminating.

Hope this helps.

The equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is: (x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.

To find the equation of the sphere passing through the point (4, 3, -1) with a center at (3, 8, 1), we can use the general equation of a sphere:

(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2

where (h, k, l) represents the center of the sphere and r represents the radius.

First, we need to find the radius. The distance between the center and the given point can be calculated using the distance formula:

√[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]

Substituting the coordinates of the center (3, 8, 1) and the given point (4, 3, -1), we have:

√[(4 - 3)^2 + (3 - 8)^2 + (-1 - 1)^2]

Simplifying, we get:

√[1 + 25 + 4] = √30

Therefore, the radius of the sphere is √30.

Now we can substitute the center (3, 8, 1) and the radius √30 into the general equation:

(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30

So, the equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is:

(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.

This equation represents all the points on the sphere's surface.

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Answer:

B.  120°

Step-by-step explanation:

Sum of the measures of the interior angle of a polygon with n sides:

(n - 2)180

We have a pentagon, a 5-sided polygon, so n = 5.

We first find the sum of the measures of the angles of any pentagon.

(5 - 2)180 = 3(180) = 540

From the figure, we add the measures of the 5 angles and set the sum equal to 540°.

3x + 4x + 4x + 4x + 3x = 540°

18x = 540°

Divide both sides by 18.

x = 30°

The angle at vertex C measures 4x.

4x = 4 * 30° = 120°

Answer: B.  120°

The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

N is the number of observations in the data set.

It is given that:

The data set:

45, 76, 30, 22, 51, 40, 63, 66, 41

From the formula:

∑(x(i) - X)² = 2463.55

N = 9

SD = √(2463.55/9)

SD = 16.54

Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

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Answer:

a y=3/2× Pls help me do me one

a

Answer:

\(A)\ [-3+ (6-8)] - [40+ (5.3-7) +20.2] = -63.5\)

\(B)\ -4 + [- 2.6-1 - (- 3.4)] + (- 5) * (- 3) + (- 10) =0.8\)

\(C)\ -22 * \{- 5+ [8.3- (3.6-9)]\} - (- 2) * (3) =-185.4\)

\(D)\ -9 - (- 2 + 5) * [- 3 + (- 5) - (+ 2) +1] =18\)

\(E)\ 40 * \{- 12 * [4 + (- 6) * (- 5) -15.3 + 12]\} - 2 =-14738\)

\(F) -21 * \{- [- 6 * (7-3)] - (7.6-8.3)\} - 89 =-607.7\)

Step-by-step explanation:

\(A)\ [-3+ (6-8)] - [40+ (5.3-7) +20.2] =\)

Resuelve todas las expresiones en el paréntesis interior

\([-3-2] - [40 -1.7 + 20.2]\)

Resuelve cada paréntesis

\(-5 - 58.5\)

\(-63.5\)

\(B)\ -4 + [- 2.6-1 - (- 3.4)] + (- 5) * (- 3) + (- 10) =\)

Resuelve todas las expresiones en el paréntesis interior

\(-4 + [-0.2] + (- 5) * (- 3) + (- 10)\)

Resuelve todas las multiplicaciones y paréntesis.

\(-4 -0.2 + 15-10\)

\(=0.8\)

\(C)\ -22 * \{- 5+ [8.3- (3.6-9)]\} - (- 2) * (3) =\)

Resuelve todas las expresiones en el paréntesis interior

\(-22 * \{- 5+ [8.3 + 5.4]\} - (- 2). (3)\)

Resuelve todas las multiplicaciones y paréntesis.

\(-22 * 8.7 +6\)

\(-191.4 + 6\)

\(=-185.4\)

\(D)\ -9 - (- 2 + 5) * [- 3 + (- 5) - (+ 2) +1] =\)

Resuelve todas las expresiones entre paréntesis interiores

\(-9 - 3 * [- 3 - 5 - 2 +1]\)

\(-9-3 * -9\)

\(-9 + 27\)

\(= 18\)

\(E)\ 40 * \{- 12 * [4 + (- 6) * (- 5) -15.3 + 12]\} - 2 =\)

Resuelve todas las expresiones entre paréntesis interiores

\(40 * \{- 12 * [4 - 6 * - 5-15,3 + 12]\} - 2\)

Multiplicar -6 por -5

\(40 * \{- 12 * [4 + 30-15.3 + 12]\} - 2\)

Resuelve todas las expresiones en el paréntesis interior

\(40 *\{- 12 * 30.7\} - 2\)

Quitar todos los paréntesis

\(40 * -368.4 - 2\)

\(-14736 - 2 \\\)

\(=-14738\)

\(F) -21 * \{- [- 6 * (7-3)] - (7.6-8.3)\} - 89 =\)

Resuelve todas las expresiones entre paréntesis interiores

\(-21 * \{- [- 6 * 4] +0.7\} - 89\)

Multiplicar -6 por 4

\(-21 * \{24 +0.7\} - 89\)

Quitar todos los corchetes

\(-21 * 24.7 - 89\)

\(-518.7 - 89\)

\(=-607.7\)

The part in the steering column that allows for changes in the angle between the upper and lower shafts is the universal joint.

The universal joint, also known as a U-joint or Cardan joint, is a mechanical device that enables changes in the angle between two shafts that are not in a straight line. In the context of a steering column, the upper and lower shafts are connected by a universal joint.

As the steering wheel is turned, it exerts rotational force on the upper shaft of the steering column. The universal joint allows for the transmission of this rotational motion while accommodating changes in the angle between the upper and lower shafts. It provides flexibility and compensates for any misalignment between the two shafts, ensuring smooth and continuous rotation of the steering column.

The universal joint typically consists of two yokes connected by a cross-shaped component with needle bearings. These bearings allow for rotation in multiple axes, allowing the steering column to handle variations in the angle between the upper and lower shafts during steering movements.

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The correct option is option A , such that inequality is x - 3y < 5.

What are the inequalities ?

Inequalities are the expressions in which both sides are not equal and the equal sign in between is replaced by less than , greater than, etc.

We know that the slope intercept form of equation is given by y = mx + c , where m is the slope and c is the y - intercept.

In the graph , the upward sloping line has x and y intercepts of 5 and -3.

So its equation in slope intercept form is given by ,

- 3y = - x + 5

And the inequality with that boundary line is given by ,

- 3y < - x + 5

or

x - 3y < 5

Therefore , the inequality represented by graph is x - 3y < 5 or option A is correct.

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the formula for a linear regression line is y = ax + b

where a and b are:

Answer: 4.8x + 3

Step-by-step explanation:

Answer:

2x² - xy - 15y²

Step-by-step explanation:

(2x + 5y)(x - 3y)

Each term in the second factor is multiplied by each term in the first factor, that is

2x(x - 3y) + 5y(x - 3y) ← distribute parenthesis

= 2x² - 6xy + 5xy - 15y² ← collect like terms

= 2x² - xy - 15y²

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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The required interval of the given normal distribution using the empirical rule is [100, 140].

The empirical rule formula (also known as a 68 95 99 rule formula) uses data from a normal distribution to determine the first, second, and third standard deviations, which, respectively, differ from the mean value by 68%, 95%, and 99%. Additionally, it shows that 99.9% of the data fall inside the third standard deviation range (either above or below the mean value). The empirical rule formula is described below with cases that have been resolved.

In the question, we are given that IQ scores for adults aged 20 to 34 years are normally distributed according to N(120, 20), and are asked for the range in which the middle 68% of people in this group score on the test.

N(120, 20) signifies a normal distribution with mean, μ = 120, and the standard deviation, σ = 20.

By the empirical formula, 68% of the data lies within one standard deviation from the mean.

Thus, the required interval is [μ - σ, μ + σ] = [120 - 20, 120 + 20] = [100, 140].

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