Please find the variance and standard deviation
Coffee with Meals A researcher wishes to determine the number of cups of coffee a customer drinks with an evening meal at a restaurant. X 01 2 3 4 P(X) 0.22 0.31 0.42 0.04 0.01 Send data to Excel Part

The height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

The volume of the cylinder can = 1000 cubic cm

Consider the height of the cylinder as h and the radius of the base is r

Volume of the cylinder = π\(r^2\)h = 1000

h = 1000 / π\(r^2\)

The surface area of the cylinder

A = 2π\(r^2\) + 2πrh

A = 2π\(r^2\) + 2πr(1000 / π\(r^2\) )

A = 2π ( \(r^2\) + 1000 / π\(r^2\))

Differentiate the terms

A' =  2π (2r + 1000 / π\(r^3\))

When the minimum surface area

2π (2r + 1000 / π\(r^3\)) = 0

r = \((1000/2\pi )^\frac{1}{3}\)

r = 5.41 cm

Then,

h =  1000 / π\(r^2\)

= 1000 / (π × 5.41 × 5.41)

= 1000 / 91.94

= 10.87 cm

Hence, the height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

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Answer:

y = -3x + 6

Step-by-step explanation:

Any line perpendicular to

y = (1/3)x + 4

has a slope of -1/(1/3) = -3

and equation

y = -3x + b  .................(1)

If the line has an x intercept of 2 at (0,2), then

0 = -3(2) + b

solving

b = 6

By substituting b=6 into (1), the line required

y = -3x + 6

Answer:

y = -3x + 2

Step-by-step explanation:

y= \(\frac{1}{3}x +4\)

Slope \(m_{1}=\frac{1}{3}\)

slope of the perpendicular line \(m_{2}\) = \(\frac{-1}{m_{1}}\) = \(\frac{-1}{\frac{1}{3}}=-1*\frac{3}{1}=-3\\\)

b= 2

Slope intercept form of required line: y = mx + b

y = -3x + 2

Answer:

A = 148 cm^2

Step-by-step explanation:

To calculate the surface area of the cuboid we use the following equation

A = 2 x (lh + lw+ hw) (l: length, w: width, h: height)

A = 2 x (6*5 + 6*4 + 5*4)

A = 2 x (30 + 24 + 20)

A = 2 x 74

A = 148 cm^2

Las funciones trigonométricas se utilizan fundamentalmente en la solución de triángulos

rectángulos, recordando que todo triángulo rectángulo tiene un ángulo de 90° y sus ángulos

interiores suman 180°. La notación que se acostumbra es la siguiente.

Answer:

the slant height cone a is..... 5 yd

Step-by-step explanation:

Answer:

10.77

Step-by-step explanation:

 Plzzzz mark me brainliest

The value of x from the given set of values is 5

A rectangle is a 2 dimensional shape with 4 sides and angle. The formula for calculating the area and perimeter is given as:

Area = length * width

Perimeter = 2(length + width)

If the length of a rectangle is 2 inches more than its width and the perimeter of the rectangle is 24 inches, the resulting equation will be:

2x + 2(x + 2) = 24,

Expand and determine the value of "x"

2x+ 2x + 4 = 24

4x + 4 = 24

Subtract 4 from both sides

4x = 24 - 4

4x = 20

Divide both sides by 4

4x/4 = 20/4

x = 5

Hence the value of x from the given set of values is 5

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Complete question

The length of a rectangle is 2 inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x + 2) = 24, where x is the width in inches, represents this situation. The value of x from the set {1, 3, 5, 7} that holds true for the equation is . So, the width of the rectangle is inches and its length is inches.

The probability of picking a black ball and then another black ball is; Due to conditional probability and is equal to 1/15.

Now, the total balls in the bag are:

The probability of first picking a black ball is:

Now, when a black ball is picked, there will be 9 balls left in the bag of which only 2 are black.

Thus, the probability of picking another black ball is:

Thus; the probability of picking a black ball and then another black ball is;

Therefore, the probability of picking a black ball and then another black ball is; Due to conditional probability and is equal to 1/15.

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The third approximation is x3 = 19.6

The Newton's method allow to approximate the root of a function as:

Newton's method, commonly referred to as the Newton-Raphson method after Isaac Newton and Joseph Raphson, is a root-finding algorithm that generates progressively improved approximations to the roots (or zeroes) of a real-valued function. The most fundamental form begins with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial point x0 for the root of f.

xₙ = xₙ₊₁ + f(xₙ)/f'(xₙ)

For this function, it is:

f(x) = 1/3x³+1/2x²+8

f'(x) = 2/3x²+x

For x1=-3,

f(x1) = 1/3x³+1/2x²+8 = -9 + 4.5 + 8 =3.5

f'(x1) = 2/3x²+x = 3

x2 = x1 + f(x1)/f'(x1) = -1.8

Therefore, x2 = -1.8

Then, the third approximation is x_3 is

x3 = x2 + f(x2)/f'(x2) = -1.8+ (7.72/0.36)

x3 = 19.6

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Answer:

No.

Step-by-step explanation:

If these sides come out true in the Pythagorean Theorem, then it is a right triangle.

a² + b² = c²

56² + 80² = 100²

3136 + 6400 = 10000

9536 ≠ 10000

Since these values do not come out true in the Pythagorean Theorem, it is not a right triangle.

Answer:

Possibly, A right triangle has a really long side that is "c" in the picture. If the 100 length is c then the 80 one could be "b" while the 56 is "a"

I know it doesnt make much sense but I hope it helps

I see people looking at mine because its simple but you should look at the other guys awnser. He has information and details that explain their awnser. I didn't really do much to get the awnser. Look at theirs Please.

The type of standard score that has a mean (m) of 0 and a standard deviation (sd) of 1 is known as the Z-score.

The Z-score, also referred to as the standard score, is a statistical measure that standardizes a given value in a distribution. It indicates how many standard deviations a particular value is away from the mean of the distribution. When the mean (m) is 0 and the standard deviation (sd) is 1, the resulting Z-score is based on this standardization. The formula for calculating the Z-score is (x - m) / sd, where x represents the value being standardized. By using this formula with m = 0 and sd = 1, the Z-score provides a standardized value that allows for comparisons and analysis across different datasets with varying means and standard deviations.

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The amount of ascent, or vertical distance, divided by the run, or horizontal distance, is how slope is commonly expressed as a percentage.

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Answer:

x = 4

Step-by-step explanation:

(2x + 3) + (2x + 3) + (2x + 3) = 33

Combine 2x and 2x to get 4x.

4x + 3 + 3 + 2x + 3 = 33

Add 3 and 3 to get 6.

4x + 6 + 2x + 3 = 33

Combine 4x and 2x to get 6x.

6x + 6 + 3 = 33

Add 6 and 3 to get 9.

6x + 9 = 33

Subtract 9 from both sides.

6x = 33 − 9

Subtract 9 from 33 to get 24.

6x = 24

Divide both sides by 6.

\(x = \frac{24}{6} \)

Divide 24 by 6 to get 4.

\(x = 4\)

Answer:

Morgan (17.06 secs)

Step-by-step explanation:

Jackie, morgan, Kylie and chung ran the 100 meter dash race

Jackie finished the race in 17.6 secs

Morgan finished the race in 17.06 secs

Kylie finished the race in 17.66 secs

Chung finished the race in 17.066 secs

Hence Morgan finished the race in the least amount of time in 17.06 seconds

Based on the given options, the errors Amy made in simplifying the complex fraction problem include not using the reciprocal of the divisor and not simplifying the resulting fraction.

To analyze the errors made by Amy in simplifying the complex fraction problem, let's go through each option:

1. She converted the mixed number to the wrong improper fraction: This error is related to the specific problem at hand and cannot be determined without the actual problem statement. Please provide the specific complex fraction problem so that I can assess this error.

2. She did not use the reciprocal of the divisor: This error suggests that Amy did not take the reciprocal of the divisor (denominator) when dividing by a fraction. This error would be applicable if the problem involved dividing by a fraction. However, without the specific problem, it is difficult to confirm this error.

3. She added the numerators: This error indicates that Amy added the numerators of the complex fraction instead of performing the appropriate operations on them. This error can occur if the problem required multiplication, subtraction, or other operations instead of addition.

4. She added the denominators: This error implies that Amy added the denominators of the complex fraction instead of performing the necessary operations. This error can occur if the problem involved addition or if the denominators needed to be combined differently.

5. She did not simplify: This error suggests that Amy did not simplify the resulting fraction to its simplest form after performing the operations. This error can occur if the fraction can be further reduced or simplified.

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Answer:

x = -4, 2

Step-by-step explanation:

(2x + 2)² = 36

Remember that the square root of 36 has a positive and a negative root.

(2x + 2) = ±6

2x + 2 = -6                                       2x + 2 = 6

     2x = -8                                              2x = 4

       x = -4                                                 x = 2

Therefore, the solution(s) of the equation are x = -4, 2

Answer:

\(cos\theta = -\frac{12}{37}\)

Step-by-step explanation:

Given

\(tan\theta = \frac{35}{12}\)

Quadrant: 3rd

Required

Determine \(cos\theta\)

This question will be solved using the Pythagoras theorem

\(Hyp^2 = Adj^2 + Opp^2\)

The tangent of an angle is calculated as thus;

\(tan\theta = \frac{Opp}{Adj}\)

Comparing

\(tan\theta = \frac{35}{12}\) to \(tan\theta = \frac{Opp}{Adj}\)

We can conclude that

\(Opp = 35\)    \(Adj = 12\)

Substitute these values in the Pythagoras formula

\(Hyp^2 = 35^2 + 12^2\)

\(Hyp^2 = 1225 + 144\)

\(Hyp^2 = 1369\)

Square root of both sides

\(Hyp = \sqrt{1369}\)

\(Hyp = 37\)

SInce \(\theta\) is in the 3rd quadrant, then

\(cos\theta = -\frac{Adj}{Hyp}\)

Where \(Adj = 12\) and \(Hyp = 37\)

\(cos\theta = -\frac{12}{37}\)

Answer:

WYM

Step-by-step explanation:

Answer:

108°

Step-by-step explanation:

The total number of apple pies is 22 and the total number of blueberry pies is 17.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that baker sold apples pies for $10 and blueberry pies for$14. One Saturday they sold a total of 39 pies and collected a total of $458.

Asumme the total number of apple pies be 'x' and the total number of blueberry pies be 'y'.

The linear equation that represents the total number of pies is:

x + y = 39

x = 39- y   --- (1)

The linear equation that represents the total amount collected is:

10x + 14y = 458--- (2)

Substitute the value of 'x' in equation (2).

10(39- y) + 14y = 458

y = 17

Then Substitute the value of 'y' in the equation (1).

x = 39 - 17

x = 22

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The function f(x) is defined as f(x) = 4x/8x-6.

This can be simplified to f(x) = 1/2x-3. The horizontal asymptote for this function is y = 0, as its denominator approaches 0 as x approaches infinity or negative infinity.The function f(x) is defined as f(x) = 4x/8x-6.  To find the vertical asymptote, we need to set the denominator to 0. We can solve this equation to find that the vertical asymptote of f(x) is x = 6. This means that as x approaches the value of 6, the function approaches infinity. Therefore, the horizontal asymptote of this function is y = 0 and the vertical asymptote is x = 6.

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\( \huge\underline\mathcal{Answer \: - }\)

Pythagoras theorem states that the square of hypotenuse equals the sum of square of other two sides.

therefore ,

\((25) {}^{2} = (x + 3) {}^{2} + 4 { }^{2} (x + 2) {}^{2} \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16(x {}^{2} + 4 + 4x) \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16x {}^{2} + 64x + 64 \\ \\ \longrightarrow \: 625 = 17x {}^{2} + 70x + 73 \\ \\ \longrightarrow \: 17x {}^{2} + 70x + 73 - 625 = 0 \\ \\ \longrightarrow \: 17x {}^{2} + 70x - 552 = 0\)

now using quadratic formula ,

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

here , a = 17 , b = 70 , c = -552

substituting the values in the equation above ,

\(x = \frac{70 \: \pm \: \sqrt{70 {}^{2} - 4(17)( - 552)} }{2 \times 17} \\ \)

after simplifying we get ,

\(\boxed{x = 4} \: \: or \:\boxed{ x = \frac{ - 138}{7} } \\ \)

since length can't be negative , therefore the other value will be neglected and hence ,

\(\boxed{value \: of \: x \: = \: 4 \: cm}\)

hope helpful ;-;

======================================================

Work Shown:

As you mentioned, we'll use Pythagoras' Theorem aka Pythagorean Theorem.

\(a^2+b^2 = c^2\\\\(x+3)^2+(4(x+2))^2 = 25^2\\\\(x+3)^2+16(x+2)^2 = 625\\\\(x^2+6x+9)+16(x^2+4x+4) = 625\\\\x^2+6x+9+16x^2+64x+64 = 625\\\\17x^2+70x+73 = 625\\\\17x^2+70x+73-625 = 0\\\\17x^2+70x-552 = 0\\\\\)

Next, we'll use the quadratic formula with a = 17, b = 70, c = -552.

\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-70\pm\sqrt{(70)^2-4(17)(-552)}}{2(17)}\\\\x = \frac{-70\pm\sqrt{42436}}{34}\\\\x = \frac{-70\pm206}{34}\\\\x = \frac{-70+206}{34} \ \text{ or } \ x = \frac{-70-206}{34}\\\\x = \frac{136}{34} \ \text{ or } \ x = \frac{-276}{34}\\\\x = 4 \ \text{ or } \ x \approx -8.1176\\\\\)

Ignore the negative x value solution. The sides (x+3) and 4(x+2) will be negative values if we plugged in x = -8.1176, but negative side lengths do not make sense.

This makes x = 4 the only possible solution.

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

If x = 4, then,

This is a 7-24-25 right triangle.

We can confirm this using the pythagorean theorem

\(a^2+b^2 = c^2\\\\7^2+24^2 = 25^2\\\\49+576 = 625\\\\625 = 625 \ \ \ \checkmark\)

Correlation coefficients examine the relationship between variables.

They help in determining the strength and direction of the association between two continuous variables, making it easier to understand and interpret their connection.

Correlation coefficients are statistical measures used to examine the relationship between two or more variables. The correlation coefficient quantifies the degree to which the variables are related or associated with each other.

A positive correlation coefficient indicates that when one variable increases, the other variable also tends to increase, while a negative correlation coefficient indicates that when one variable increases, the other variable tends to decrease.

A correlation coefficient of zero indicates no relationship between the variables.

Correlation coefficients are often used in research studies to examine the strength and direction of the relationship between two variables.

For example, in a study examining the relationship between exercise and weight loss, a correlation coefficient could be calculated to determine how strongly exercise and weight loss are related.

It is important to note that correlation does not imply causation, and a strong correlation between two variables does not necessarily mean that one variable causes the other.

Correlation coefficients are simply used to describe the relationship between two variables and to identify patterns in the data.

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nCr(20, 2) = 190 ways of selecting 2 from 20

nCr(10, 1)    =   10 ways of selecting 1 from 10

To find the over all probability of winning,

Calculate the Harmonic Mean (19) and divide by 2

Equivalent to

1/ (1//190 + 1/10) =9.5

So the probability is 1/9.5 = 2/19.

The length of the protein molecule, in meters, is 208 × 10⁻⁹m.

To find the length of the protein molecule:

Diameter of hydrogen atom = 104 × 10⁻¹⁰m

We are given that A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom.

Therefore, the length of the protein molecule, in meters, is 208 × 10⁻⁹m.

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The correct question is given below:

The diameter of a hydrogen atom is about 1.04 cross times 10 to the power of negative 10 end exponent meters. A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom. What is the length of the protein molecule, in meters, if it were written in scientific notation?

The sustainable growth rate for Premier Corporation is 10.575 percent.

Here, we have,

The sustainable growth rate (SGR) is a measure of how much a company can grow its earnings without relying on external financing.

It can be calculated using the following formula:

SGR = ROE × (1 - Payout Ratio)

In this case, the ROE (Return on Equity) is 14.1 percent, and the payout ratio is 25 percent.

Let's substitute these values into the formula:

SGR = 14.1% × (1 - 25%)

To calculate the sustainable growth rate, we need to convert the percentages to decimal form:

SGR = 0.141 × (1 - 0.25)

Simplifying the equation:

SGR = 0.141 × 0.75

SGR = 0.10575

The sustainable growth rate for Premier Corporation is 10.575 percent.

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The smallest positive integer x for which the expression \($\log\left(\sin^2{x}-\frac{1}{2}\right)$\) is not defined is x = π/4

We have,

The expression \($\log\left(\sin^2{x}-\frac{1}{2}\right)$\) is defined only when the argument is positive.

Therefore, we must solve the inequality  sin²x - 1/2 > 0

Using the identity sin²x + cos²x =1,

We have,

cos²x = 1/2 and sin²x = 1/2

Therefore,

sin²x - 1/2 = 1/2 - 1/2 = 0

when sin²x = 1/2

So the smallest positive integer x for which the expression \($\log\left(\sin^2{x}-\frac{1}{2}\right)$\)is not defined is the smallest positive integer x for which sin²x = 1/2.

Since sin π/4 = √2/2 and (√2/2)² = 1/2,

We have x = π/4

Therefore,

The smallest positive integer x for which the expression \($\log\left(\sin^2{x}-\frac{1}{2}\right)$\) is not defined is x = π/4

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Answer:

B

Step-by-step explanation:

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Answer:

B) y-intercept: 1; x-intercepts -3.414 and -0.586

Step-by-step explanation:

see attached graph

y-intercept: 1; x-intercepts -3.414 and -0.586

Answer: 8

Step-by-step explanation:  You can see each time on the graph it goes up by 8. So your answer will be   I hope this helps.

A.

(or c)

Answer: You need to count how many squares are shaded (at least half of it), therefore the area is 32 square units.