Find the sample variance and standard deviation. 4,53,12,50,33,27,33,30,34,29 만 Choose the correct answer below. Fill in the answer box to complete your choice. (Round to two decimal places as needed.) A. σ 2
= B. s 2
=

Answer:

first one

Step-by-step explanation:

if y=-5x-3

y=kx+b

k<0 and b<0

Answer:

Step-by-step explanation:

pc ma chu so online theye na no mobile so cant reply sorry

To maximize the enclosed area, we need to determine the dimensions of the rectangular field that will allow for the largest possible area.

Let's denote the width of the rectangular field as x and the length as y.

The total length of fencing used will be the sum of the four sides of the field, which is equal to 2x + y.

According to the problem, we have 400 feet of fencing available, so we can write the equation:

2x + y = 400

To subdivide the field into 33 identical smaller plots, we need to place two fences parallel to one of the shorter sides. This means that the width of each smaller plot will be x/33, and the length will be y.

The area of each smaller plot is given by A = (x/33) * y.

To maximize the area, we can express the area in terms of a single variable. Let's substitute y = 400 - 2x into the area equation:

A = (x/33) * (400 - 2x)

To find the maximum area, we can take the derivative of A with respect to x and set it equal to zero:

dA/dx = (400 - 4x)/33 = 0

Simplifying the equation, we get:

400 - 4x = 0

Solving for x, we find:

x = 100

Substituting this value back into the equation 2x + y = 400, we can solve for y:

2(100) + y = 400

200 + y = 400

y = 200

Therefore, the dimensions that maximize the enclosed area are x = 100 feet and y = 200 feet.

The area of the rectangular field is A = x * y = 100 * 200 = 20,000 square feet.

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Answer:

$42.12

Step-by-step explanation:

Calculation for How much will Gretta pay in total for this transaction

First step is to calculate the new price

New price=$65- ($65*40%)

New price=$65-26

New price=$39

Second step is to calculate the sales tax amount

Sales tax=8%*39

Sales tax=$3.12

Last step is to calculate How much will Gretta pay in total for this transaction using this formula

Total Amount to be paid=New price+Sales tax

Let plug in the formula

Total Amount to be paid=$39+$3.12

Total Amount to be paid=$42.12

Therefore the amount that Gretta will pay in total for this transaction will be $42.12

The value of sec(-3π/2) is undefined.

We know that,

sec x = \(\frac{1}{cos x}\).

By the concept of unit circle, we can say,

cos (x) is an X-coordinate of a point on a unit circle, where the radii make an angle "x" with a positive direction of the X-axis if we count from the positive direction of the X-axis counter-clockwise.

Now given,

sec(-3π/2) = \(\frac{1}{cos(\frac{-3\pi}{2} )}\).

∴Angle \(\frac{-3\pi}{2}\) represents the point (0,-1)

Therefore, \(cos(\frac{-3\pi}{2} )\) = 0.

And sec(-3π/2) = \(\frac{1}{cos(\frac{-3\pi}{2} )}\)

Hence, the value of sec(-3π/2) is undefined.

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Answer:

7.6 cm²

Step-by-step explanation:

Area of rectangle= l x w

3 x 4 = 12 cm

Area of circle= πr²

π x 2.5²= 19.625

Area of shaded= Area of circle - area of rec

19.625- 12= 7.625 cm²

≈7.6

I HOPE THIS HELPED

In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force

Percentages are fundamentally fractions with 100 as the denominator. To show that a number is a percentage, the percent symbol (%) is placed next to it. For instance, if you answered 45 out of 100 questions on a test accurately (45/100), you would have gotten a 45% mark.

According to the given information

In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force compared with 75.5 percent of mothers whose youngest child was age 6 to 17.

In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force

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George made 75 percent of the shots.

First, let us understand the percentage:

A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.

To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.

We are given the following:

George shot the basketball 20 times in his game on Saturday.

Of those 20 shots, he made 15.

We need to find the percentage of the shots George made.

The percentage of shots George made is given by:

Percentage = 15 / 20 * 100 = 15 * 5 = 75 %

So, 75 % of the shots did George make.

Thus, George made 75 percent of the shots.

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Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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The maximum area of the rectangular patio is 1800 square feet.

To determine the dimensions that would create the patio of maximum area, let the length of the fence parallel to the rock wall be x, and the lengths of the other two fences be y. We know that the fencing available is 120 feet, so the equation is x + 2y = 120. We need to express y in terms of x, so y = (120 - x)/2.

The area of the patio is A = xy. Substitute the expression for y: A = x((120 - x)/2). To find the maximum area, we can use calculus by taking the derivative of A with respect to x, and then setting it equal to zero to find the critical points.

dA/dx = (120 - 2x)/2. Setting dA/dx = 0, we have 120 - 2x = 0, so x = 60. Substituting this value back into y = (120 - x)/2, we get y = (120 - 60)/2 = 30. Therefore, the dimensions of the patio are 60 feet by 30 feet, and the maximum area is A = (60)(30) = 1800 square feet.

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Among the given options for input statements involving int variables X and y, the valid option is b) cin >> x >> y.

This statement uses the extraction operator (>>) to read input values and assign them to the variables x and y consecutively. The extraction operator allows for multiple inputs in a single line, separated by spaces or other delimiters.

This statement ensures that two integer values can be entered and stored correctly in the variables x and y. The extraction operator (>>) is commonly used with the cin object in C++ for input operations. It facilitates convenient and efficient input handling for multiple variables in a single statement.

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Answer:

Step-by-step explanation:

It is the volume of a cone plus half the volume of a sphere.

Volume of a cone = 1/3 π r² h

Volume = 1/3(3.14)(4²)(10)

Volume = 167.55 cu ft³

Then the sphere:

Volume = 4/3 π r³

Volume = 4/3 (3.14) (4³)

Volume = 4/3(3.14)(64)

Volume = 268.1 cu ft³

You add the volume of the cone and half the volume of the sphere:

167.55 + 134.05 = 301.6 cu ft³ - round to 302 cu ft³

Answer:

6n

Step-by-step explanation:

The marginal probability mass functions of X and Y are:

In the given scenario, X and Y are two random variables that are uncorrelated but not independent. The joint probability mass function of X and Y is provided as follows:

P(X = 0, Y = 0) = 0.2

P(X = 0, Y = 1) = 0.1

P(X = 0, Y = 2) = 0.1

P(X = 1, Y = 0) = 0.1

P(X = 1, Y = 1) = 0.2

P(X = 1, Y = 2) = 0.1

To obtain the marginal probability mass functions, we sum the probabilities for each value of X and Y.

For X:

P(X = 0) = 0.2 + 0.1 + 0.1 + 0.1 = 0.5

P(X = 1) = 0.1 + 0.2 + 0.1 + 0.1 = 0.5

Therefore, the marginal probability mass function of X is P(X = 0) = 0.5 and P(X = 1) = 0.5.

For Y:

P(Y = 0) = 0.2 + 0.1 = 0.3

P(Y = 1) = 0.1 + 0.2 + 0.1 = 0.4

P(Y = 2) = 0.1 + 0.1 = 0.2

Hence, the marginal probability mass function of Y is P(Y = 0) = 0.3, P(Y = 1) = 0.4, and P(Y = 2) = 0.2.

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The height of the screen will be;

⇒ h = 28 inches

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A flat screen television is a rectangle with a 53-invh diagonal and a width of 45 inches.

Here,

The diagonal of the screen television = 53 inches

And, The width of the screen television = 45 inches

Let the height of the television = h

So, By the Pythagoras theorem, we get;

⇒ AC² = AD² + DC²

Where, AC = Diagonal of television.

AD = Height of the television

DC = Width of the television.

Substitute all the values, we get;

⇒ 53² = h² + 45²

⇒ 2809 = h² + 2025

⇒ 2809 -2025 = h²

⇒ h² = 784

⇒ h = √784

⇒ h = 28 inches

Thus, The height of the screen = 28 inches

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Answer:

20°

Step-by-step explanation:

i just did it. got it correct

Answer:

His total will be $15.99, so the sales tax is $0.99

Step-by-step explanation:

15 increase 6.6% =

15 × (1 + 6.6%) = 15 × (1 + 0.066) = 15.99

1) 6/108= 1/18

8/200= 1/25

6 calculators for $108 is better

2) 35/490 = 1/14

21/210 = 1/10

21 ipads for $210 is better

-7.763 will be the total to the answer.

The Laplace transform of the given function f(t) is (5 - 5e^(-4s))/s.

We can write the given function f(t) in terms of unit step functions as follows:

f(t) = 5u(t) - 5u(t-4)

This expression gives us the value of f(t) as 5 for 0 ≤ t < 4, and as -5 for t ≥ 4.

To find the Laplace transform of f(t), we use the linearity property of Laplace transforms and the fact that the Laplace transform of a unit step function u(t-a) is given by e^(-as)/s. Therefore, we have:

L{f(t)} = L{5u(t)} - L{5u(t-4)}

= 5L{u(t)} - 5L{u(t-4)}

= 5 * [1/s] - 5 * [e^(-4s)/s]

Simplifying this expression, we get:

L{f(t)} = (5 - 5e^(-4s))/s

Therefore, the Laplace transform of the given function f(t) is (5 - 5e^(-4s))/s.

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Answer:

the population grew by approximately 11,200 people from 2010 to 2015.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this inequality, we have to find x (or make x the subject of the inequality:

since     ⁻ˣ/₃  ≤ 6       [multiply both sides by 3]

               - x ≤ 18      [multiply both sides by -1; this flips the inequality sign]

To graph the inequality, draw the line x = - 18 with a solid line, and then shade the region that is x > -18.

We use a solid line because the point x = -18 is included. However, hypothetically,  if the inequality was x > -18 only, a broken line would be used to show that the line x = -18 is not included.

Answer: 125

Step-by-step explanation:

simplify 5 to the power of 3

Answer:

125

Step-by-step explanation:

5^3 = 5*5*5

= 125

The future value of depositing $1,000 every year for 20 years, with payments made at the beginning of each period, at an interest rate of 7% compounded yearly, is approximately $43,865.18.

To calculate the future value of a series of deposits, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value

P is the periodic payment

r is the interest rate per period

n is the number of periods

In this case, the periodic payment is $1,000, the interest rate is 7% (or 0.07), and the number of periods is 20.

Plugging these values into the formula, we get:

FV = 1000 * [(1 + 0.07)^20 - 1] / 0.07

  = 1000 * [1.07^20 - 1] / 0.07

  ≈ 1000 * [2.6532976 - 1] / 0.07

  ≈ 1000 * 1.6532976 / 0.07

  ≈ 43,865.18

Therefore, the future value of this series after 20 years would be approximately $43,865.18.

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Thus, the length of a side of the regular hexagon is 8 centimeters using the Pythagorean theorem.

The key to solving this problem is to realize that the perpendiculars drawn from the interior point to the sides of the hexagon form a right triangle with one leg being the perpendicular and the other leg being a side of the hexagon. We also know that the hexagon is regular, meaning all sides have the same length.

Let's label the length of the side of the hexagon as "x". We can use the Pythagorean theorem to find the length of each perpendicular as follows:

- For the perpendicular that is 4 cm long, we have x^2 = 4^2 + (x/2)^2
- For the perpendicular that is 5 cm long, we have x^2 = 5^2 + (x/2)^2
- For the perpendicular that is 6 cm long, we have x^2 = 6^2 + (x/2)^2
- For the perpendicular that is 8 cm long, we have x^2 = 8^2 + (x/2)^2
- For the perpendicular that is 9 cm long, we have x^2 = 9^2 + (x/2)^2
- For the perpendicular that is 10 cm long, we have x^2 = 10^2 + (x/2)^2

Simplifying each equation and using a bit of algebra, we get:

- 3x^2 = 16^2
- 7x^2 = 25^2
- 12x^2 = 36^2
- 24x^2 = 64^2
- 33x^2 = 81^2
- 40x^2 = 100^2

Solving for x in each equation, we find that x = 8 cm. Therefore, the length of a side of the regular hexagon is 8 centimeters.

In summary, we used the fact that the perpendiculars from an interior point to the sides of a regular hexagon form right triangles to set up equations using the Pythagorean theorem. Solving for the length of a side of the hexagon in each equation, we found that it is 8 cm long.

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The probability that more than 70 of them germinate is 0.

The manufacturer of a fertilizer guarantees that, with the aid of the fertilizer, 90% of planted seeds will germinate. Suppose the manufacturer is correct. If 100 seeds planted with the fertilizer are randomly selected, the probability that more than 70 of them germinate is required to be determined.

In order to find out the probability that more than 70 of them germinate, let us first find the mean and the standard deviation of the binomial distribution.

Formula to find mean and standard deviation of binomial distribution :μ = np and σ = √np(1−p)Where n = 100 (sample size)p = 0.90 (probability of germination)Substituting the given values in the above formulas,μ = 100 × 0.90 = 90σ = √100 × 0.90 × 0.10 ≈ 3.0We are required to find the probability that more than 70 seeds germinate.

This can be expressed in terms of z-score as follows:z = (70−90)/3.0 = −6.67The z-score is very low which makes the area in the z-table close to zero. Thus, the probability that more than 70 of them germinate is approximately 0. Therefore, the probability that more than 70 of them germinate is 0.

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a)The linear equation is C=25n + 2500 to produce n 3000 toys, b) The total cost to produce 3000 toys is $77,500, c) With $32500, a total of 1200 toys can be produced in Pinwheel Industries.

An equation is a mathematical statement with an equal symbol (=) between the algebraic expression. Equations with a degree of one are called linear equations. It is the straight line's equation. Whenever values are substituted for the unknown values in linear equations, the solutions produce values that make the equation true. Since there is only one variable, there is only one solution. For instance, the equation x + 2 = 0 has just one solution, which is x = -2. In the case of the two-variable linear equation, however, the solutions are determined as the Cartesian coordinates of a point on the Euclidean plane.

The three different types of linear equations are: 1) Standard Form

2) The slope intercept form

3)Point Slope Form

How to solve?

A) Linear equation y=mx+b,

C (total cost) = y and n (number of toys) =x.

C=25n + 2500

B) Put n=1750

C= 25(3000) + 2500

C= $77,500

C)

32500= 25n +2500

30000=25n

n = 1200

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The constant a should be chosen in such a way that cov(θˆ1, θˆ2) is minimized to reduce the variance of θˆ3.

In statistics, the variance of a linear combination of random variables can be affected by the covariance between those variables. In this case, we have θˆ1 and θˆ2, which are not independent but are related by their covariance, cov(θˆ1, θˆ2).

To minimize the variance of θˆ3, we need to minimize the covariance term cov(θˆ1, θˆ2). The covariance measures the extent to which θˆ1 and θˆ2 vary together, and it can be positive, negative, or zero.

To minimize cov(θˆ1, θˆ2), we should choose the constant a in a way that reduces the dependence or relationship between θˆ1 and θˆ2. This can be achieved by selecting a value of a that makes the covariance as close to zero as possible. By doing so, the contribution of the covariance term to the variance of θˆ3 will be minimized.

Therefore, the constant a should be chosen to minimize the covariance between θˆ1 and θˆ2, thus reducing the variance of θˆ3.

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Answer:

See below.

Step-by-step explanation:

So we have the parent function:

\(f(x)=x^2\)

And it was transformed into:

\(g(x)=(3x)^2+6\)

First, the +6 at the very end simply tells us that the graph was shifted upwards by 6 units.

For the (3x), this is essentially saying that:

\(f(x)=x^2\)

If we use 3x for x:

\(f(3x)=(3x)^2\)

Therefore, we essentially multiplied the x variable by 3.

In other words, this is a horizontal compression by a factor of 3.

So, our transformations are:

1) 6 units upwards

2) Horizontal compression by 3