A) Express the confidence interval (0.013, 0.089) in the form of ^p-E < p < ^p+E

? < p < ?

Answer:

The mean of C is 170 households

The standard deviation of C, is approximately 5 households

Step-by-step explanation:

The given parameters are;

The percentage of households in the United States that had a computer in 2014 = 85%

The size of the randomly selected sample in 2014, n = 200

The random variable representing the number of households that had a computer = C

Therefore, we have;

The probability of a household having a computer P = 85/100 = 0.85

Let

Therefore;

The mean (expected) number in the sample, μₓ, = E(x) = n × P is given as follows;

μₓ = 200 × 0.85 = 170

The mean of C = μₓ = 170

The variance, σ² = n × P × (1 - P) = 200 × 0.85 × (1 - 0.85) = 25.5

Therefore;

The standard deviation, σ = √(σ²) = √(25.5) ≈ 5.05

The standard deviation of C, σ ≈ 5 households (we round (down) to the nearest whole number)

The mean and the standard deviation of C are 170 and 5.05 respectively

The given parameters are:

\(\mathbf{n = 200}\) -- the sample size

\(\mathbf{p = 85\%}\) -- the proportion of household that had a computer

(a) The mean

This is calculated as:

\(\mathbf{\bar x = np}\)

So, we have:

\(\mathbf{\bar x = 200 \times 85\%}\)

\(\mathbf{\bar x = 170}\)

(b) The standard deviation

This is calculated as:

\(\mathbf{\sigma = \sqrt{np(1 - p)}}\)

So, we have:

\(\mathbf{\sigma = \sqrt{170 \times (1 - 85\%)}}\)

\(\mathbf{\sigma = \sqrt{170 \times 15\%}}\)

\(\mathbf{\sigma = \sqrt{25.5}}\)

Take square roots

\(\mathbf{\sigma = 5.05}\)

Hence, the mean and the standard deviation of C are 170 and 5.05 respectively

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The area of the surface obtained by rotating the curve x = 2e^(2y) from y = 0 to y = 3 about the y-axis is approximately 366.11 square units.

To find the area of the surface, we can use the formula for the surface area of revolution. Given the equation x = 2e^(2y), we need to rotate this curve about the y-axis.

The surface area formula is given by A = 2π∫[a,b] x(y) √(1 + (dx/dy)^2) dy, where [a,b] represents the interval of integration.

First, we find dx/dy by differentiating x = 2e^(2y) with respect to y:

dx/dy = 4e^(2y)

Next, we substitute the values into the surface area formula:

A = 2π∫[0,3] (2e^(2y)) √(1 + (4e^(2y))^2) dy

Simplifying the expression inside the integral:

A = 2π∫[0,3] (2e^(2y)) √(1 + 16e^(4y)) dy

To evaluate the integral, we can make a substitution by letting u = 1 + 16e^(4y). Then, du/dy = 64e^(4y), and solving for e^(4y), we get e^(4y) = (du/64).

Substituting these values into the integral:

A = 2π∫[u(0),u(3)] (2e^(2y)) √(u) (du/64)

Now, we need to find the limits of integration. For y = 0, u = 1 + 16e^(4(0)) = 1 + 16 = 17.

For y = 3, u = 1 + 16e^(4(3)) = 1 + 16e^12.

Substituting the limits and evaluating the integral:

A = 2π(1/64)∫[17,1 + 16e^12] (2e^(2y)) √(u) du

A = (π/32)∫[17,1 + 16e^12] e^(2y)√(u) du

Performing the integration will yield the final result for the surface area.

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If the area contains several small hills each with base elevation of 2,105 ft and summit elevations of 2,345 ft, 2,456 ft, and 2,565 ft, then the maximum relief in the area is 460 ft.

To calculate the maximum relief in the area with several small hills having base elevation of 2,105 ft and summit elevations of 2,345 ft, 2,456 ft, and 2,565 ft, follow these steps:

1. Find the difference in elevation between the highest summit and the base elevation: 2,565 ft - 2,105 ft = 460 ft
2. Compare this difference to the differences for the other summits: 2,456 ft - 2,105 ft = 351 ft and 2,345 ft - 2,105 ft = 240 ft.
3. Identify the largest difference, which represents the maximum relief.

The maximum relief in the area is 460 ft.

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Step-by-step explanation:

Parallel lines cut by a transversal coloring activity is an activity that helps students understand the pattern of angles when parallel lines are cut by a transversal. The activity involves coloring the angles formed by the parallel lines and the transversal in different colors. This helps students identify the different types of angles formed and their relationships with each other.

Answer:

So there are infinite solutions along the line y = 2x-1

Step-by-step explanation:

10x=5y+5

y=2x-1

Substitute y into the first equation

10x = 5(2x-1) +5

10x = 10x-5+5

10x = 10x

This is always true

So there are infinite solutions along the line y = 2x-1

Answer: Choice C.

How many 1/4-meter long pieces of ribbon are needed to have a total of 3 1/2 meters of ribbon.

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

Explanation:

Let's consider a similar problem without the fractions.

Let's say you want to know how many 2 meter lengths of ribbon you can cut from an overall length of 24 meters. That would be 24 ÷ 2 = 12 pieces total.

So we divide the two values (large ÷ small)

The same idea applies to this problem as well. The larger amount (3 & 1/2 meters) is what we cut up, and each slice is 1/4 of a meter. To find the number of pieces, we would compute 3 1/2÷1/4

Note: it might help to convert the mixed number 3 & 1/2 to the improper fraction 7/2

Answer:

znvipahgvahgv

Step-by-step explanation:

Answer:

Miguel needs 1,369/9 square inch of carpeting

Step-by-step explanation:

Here, we want to know the size of carpeting needed to cover the floor

What we have to do here is to find the area of the bedroom floor

Mathematically, we have this as the product of the dimensions of the floor;

This will give;

12 1/3 inches * 9 1/4 inches

= 37/3 * 37/3 = 1,369/9 square inches

Answer:

Step-by-step explanation:

The circumference is given by the formula ...

  C = πd

Using the given numbers, the circumference is ...

  C = (3.14)(20 ft) = 62.8 ft

__

The area is given by the formula ...

  A = πr² . . . . . where radius r is half the diameter

Using the given numbers, the area is ...

  A = 3.14(10 ft)² = 314 ft²

Answer:

4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

a = 3, b = 5, c = 1

b - c

Step 2: Evaluate

If a group of 10 friends has 5 toy soldiers in average and it increases to 6 with an addition of a friend, the new friend will be having 16 toy soldiers.

Therefore, the answer is 16.

It is given that a group of 10 friends has 5 toy soldiers in average. Average is the ratio of total number of toy soldiers to number of friends. Therefore,

Total number of toy soldiers = average × 10

= 5 × 10

= 50

When Lee joins the group, the average increases to 6 and number of friends increases to 11. So

New total number of toy soldiers = 6 × 11

= 66

The new total number of toy soldiers is obtained by adding the number of toy soldiers Lee have with the initial total number of toy soldiers.

Therefore, the number of toy soldiers Lee have is obtained by

= 66 - 50

= 16

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Answer:

HF, GH, FG largest to smallest

Step-by-step explanation:

HFGHFG

Answer:

The slope is 2

Step-by-step explanation:

Answer:

\(5x - 6 = 44 \\ \longrightarrow \: 5x = 44 + 6 \\ \longrightarrow \: 5x = 50 \\ dividing \: both \: sides \: by \: 5 \: \\ \\ \longrightarrow \: \cancel\frac{5x}{5} = \cancel\frac{50}{5} \\ \\ \longrightarrow \:\boxed{ x = 10}\)

hope helpful! :)

Answer:

Step-by-step explanation:

5x - 6 = 44

5x = 50

x = 10

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

check

5 x 10 - 6 = 44     (remember pemdas)

44 = 44

the answer is good

Answer:

y=3x+4

Step-by-step explanation:

Slope-intercept form is written as y=mx+b

m = the slope

slope is rise over run or (y2-y1)/(x2-x1). We need to choose which y value is y2 and the corresponding x value is the x2. If -2 is y2, then:

x2 = -2

y1 = 1

x1 = -1

then plug in the values.

(-2-1)/(-2-(-1))

-3/-1 = 3

m =3

then plug in values for the first equation. you can use any point on the line.

y = 3x+b

4 = 3*0 +b

4=0+b

b = 4

then write it with out x or y

y = 3x+4

Answer:

x = 1

y = 0

Step-by-step explanation:

You did a great job solving one of the equations for a single variable. You solved for x. But what your paper shows is that...it jind of looks like you were going to substitute the 2y+1 into y. BUT you need to substitute it into x.

-4x + 3y = -4

x = 2y + 1

Fill in 2y + 1 into x in the first equation.

-4(2y+1) + 3y = -4

Now you have an equation in one variable. There are only y's in this equation. Next, distribute.

-8y - 4 + 3y = -4

combine like terms.

-5y - 4 = -4

add 4 to both sides.

-5y = 0

divide by -5

y = 0

It's okay that it cam out to be zero. Its fine!

y=0

Put it back in one of the original equations to find x.

x = 2y + 1

x = 2(0) + 1

x = 1

The solution is

x=1

y=0

You can write this as an ordered pair.

(1,0)

Answer:

85%

Step-by-step explanation:

just because thats the answer

No, f(x, y) = 3x - 3y^2 is not a harmonic function.

A harmonic function is a twice continuously differentiable function f(x, y) that satisfies the Laplace equation:
                                                                            ∂²f/∂x² + ∂²f/∂y² = 0.

Let's check if f(x, y) = 3x - 3y^2 satisfies the Laplace equation:
∂²f/∂x² = ∂/∂x(3) = 0
∂²f/∂y² = ∂/∂y(-6y) = -6
∂²f/∂x² + ∂²f/∂y² = 0 + (-6) = -6 ≠ 0

Since the Laplace equation is not satisfied, f(x, y) = 3x - 3y^2 is not a harmonic function.

As for finding a corresponding analytic function, an analytic function is a function that is locally given by a convergent power series. Since f(x, y) is not a harmonic function, there is no corresponding analytic function.

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Holy will take 13/5 or 2.6 hours to finish the bookcase.

The relation between time and work is

Work Done = Time Taken × Rate of Work ·

or, Rate of Work = 1 / Time Taken ·

or, Time Taken = 1 / Rate of Work ·

Now it is given that,

Time taken by Fritz to build a bookcase =  8 hours

So, Bookcase build by Fritz in 1 hour = 1/8

Similarly,

Time taken by Holly to build a bookcase =  10 hours

So, Bookcase build by Holly in 1 hour = 1/10

So, bookcase build in 3 hours

Fritz = 3/8

Holly = 3/10

Total bookcase build in 3 hours =  3/8 + 3/10 =  27/40

So. remaining work =  1 - 27/40 =  13/40

Thus, Time taken by Fritz to complete the bookcase =  8 * (13/40) hours

                                                                                         =  13/5 or 2.6 hours

Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.

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Yes, the series converges and the value is 1/41.

We can use the ratio test to determine the convergence of the series:

\(lim\) n→∞ |(5(n+1) / 210(n+1)) / (5n / 210n)| =\(lim\) n→∞ |5/(210(1 + 1/n))| =5/210 < 1

Since the limit is less than 1, the series converges by the ratio test.

To determine its value, we can use the formula for the sum of a geometric series:

S = a/(1-r)

where S is the sum, a is the first term, and r is the common ratio.

In this case, a = 5/210 and r = 5/210, so

S = (5/210)/(1-5/210) = (5/210)/(205/210) = 5/205 = 1/41

Therefore, the series converges to 1/41. Answer: converges; value if convergent: 1/41

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Answer:

the answer is 86!

hope this helped

Answer:

the answer to your question is 86

Answer:

B

Step-by-step explanation:

make sure calculator is in degrees mode and insert equation to get -7.5

Answer:

Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):

2.6

Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.

In short: 2.6 rounded to the nearest whole number is 3.

Answer:

what do you need help with?

Step-by-step explanation:

Answer:

y=7x+26

Step-by-step explanation:

First we have to find the slope of the lines.

(-4,-2)      

(-3,5)    

Our slope is going to equal 7

then we take a point and use it to find the equation

y--2=7(x--4)

y+2=7x+28

y=7x+26

Answer:

The tree is 9.1 meters high.

Step-by-step explanation:

We can use the Pythagorean Theorem to solve this problem. Let T be the height of the tree. We can set up the following equation:

4.2^2 + T^2 = 6.5^2

Solving for T, we get:

T = sqrt(6.5^2 - 4.2^2)

T = sqrt(41.25 - 17.64)

T = sqrt(23.61)

T = 4.878

Since the height of the tree is measured to the nearest tenth, we can round this value to 9.1 meters.

The possible values of the solutions to the inequality 5x + 5 ≥ −9 are: I, II, and III.

To find the possible values of the solution to a given inequality, solve the inequality given using the properties of equality to isolate the variable.

Given the inequality:

5x + 5 ≥ −9

Subtract 5 from both sides:

5x + 5 - 5 ≥ −9 - 5 [subtraction property of inequality]

5x ≥ -14

Divide both sides by 5

5x/5 ≥ -14/5

x ≥ -2.8

This means that all the possible values of x are greater than or equal to -2.8.

1, 4, and 6 are greater than -2.8, therefore, the values of the solutions are: I, II, and III.

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The probability that a student is in choir, given that the student is in the school musical is (c) 56%

From the question, we have the following parameters that can be used in our computation:

School musical and choir = 18%

School musical = 32%

The requird probabilty is calculated as

P = School musical and choir/School musical

Substitute the known values in the above equation, so, we have the following representation

P = 18%/32%

Evaluate

P = 56%

Hence, the probability is (c) 56%

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