a study is to be made to estimate the proportion of residents of a certain city and its suburbs who favor the construction of a nuclear power plant near the city. how large a sample is needed if one wishes to be at least ​% confident that the estimate is within of the true proportion of residents who favor the construction of the nuclear power​ plant?

Estimated change in momentum of the boy after he lands without rebounding is equal to 0 kgm/s approximately.

Height of the wall = 3meters

To estimate the change in momentum of the boy when he lands without rebounding,

Use the principle of conservation of momentum.

The change in momentum of an object is equal to the product of its mass and the change in velocity.

Here, the boy's mass is not given, but we can assume it to be negligible compared to the change in velocity.

This implies, focus on the change in velocity alone.

When the boy jumps from a wall 3m high, he undergoes free fall due to gravity.

The final velocity of an object in free fall can be calculated using the equation,

v² = u² + 2as,

where,

v = final velocity (unknown)

u = initial velocity (0 m/s, as the boy jumps from rest)

a = acceleration due to gravity (-9.8 m/s²)

s = displacement (3 m, height of the wall)

Rearranging the equation, we get,

⇒ v² = 0 + 2(-9.8)(3)

⇒ v² = -58.8

⇒ v ≈ -7.67 m/s

Since the boy lands without rebounding, his final velocity is approximately -7.67 m/s,

Considering downward motion as negative.

The change in momentum can be calculated by multiplying the mass assumed to be negligible with the change in velocity,

⇒ Change in momentum = mass × change in velocity

⇒ Change in momentum ≈ 0 × (-7.67) kgm/s

⇒ Change in momentum ≈ 0 kgm/s

Therefore, the estimate of the change in momentum of the boy when he lands without rebounding is approximately 0 kgm/s.

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The expression that is equivalent to √10 / (4√8) is given as √5 / 8

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

Given the equation:

√10 / (4√8)

Simplifying:

= √10 / (4√(4 * 2))

= √10 / (8√2)

= √5 / 8

The expression that is equivalent to √10 / (4√8) is given as √5 / 8

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Answer:

C and D are parallel

Step-by-step explanation:

If b⊥c and b⊥d, then that means that they are both parallel because they both have a 90 degree anglewith line B.

Answer:

| | (Parallel)

Step-by-step explanation:

I'm assuming that is what it is asking. if b and c are perpendicular, that means they form 90 degrees on all angles. The same for b and d. So if both c and d are perpendicular to b, then they are parallel.

If scores on an exam follow an approximately normal distribution with a mean of 74.3 and a standard deviation of 7.4 points, approximately 28.19% of students scored below 70 points on the exam.

To find the percentage of students who scored below 70 points on the exam, we need to calculate the area under the normal distribution curve to the left of 70.

First, we need to standardize the score of 70 using the formula z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.

z = (70 - 74.3) / 7.4 = -0.5811

We can then use a standard normal distribution table or a calculator to find the area under the curve to the left of z = -0.5811. This area corresponds to the percentage of students who scored below 70 points on the exam.

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -0.5811 is approximately 0.2819.

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The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.

Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)

$1,000 | 2% | 1 year | $20

$5,000 | 4% | 2 years | $400

$10,000 | 3.5% | 3 years | $1,050

$2,500 | 1.5% | 6 months | $18.75

$7,000 | 2.25% | 1.5 years | $236.25

To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.

For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.

For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.

For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.

For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.

For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.

These calculations show the interest earned for different savings principals, interest rates, and time periods.

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Answer:

3n-9=18 because the number which is times the 3 is 9

The solution is Option D.

The equation which represents the statement 9 less than 3 times a number is 18 will be 3n - 9 = 18

The equation is 3n - 9 = 18

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

Now , the value of A is 18

A = 9 less than 3 times a number is 18

A = 3n - 9

And the value of A is 18 , so substituting the value in the equation , we get

A = 18

3n - 9 = 18

Therefore , the equation is 3n - 9 = 18

Hence , The equation which represents the statement 9 less than 3 times a number is 18 will be 3n - 9 = 18

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Answer:

Step-by-step explanation:

a)  Sum = - 6

Product = - 16

Factors = (-8) ; (2   {-8 + 2 = -6  ; (-8) * 2 = -16}

y = x² - 6x - 16

     = x²  + 2x - 8x - 16

     = x(x + 2) - 8(x + 2)

    = (x +2)(x -8)

b) y = 0

(x +2 )(x -8) = 0

x + 2 = 0  ;   x -  8 = 0

x = -2       ;  x = 8

(-2) ; 8 are the zeros.

Your pay for the first week of January, given that you worked 10 hours of overtime is option a. $550

To solve this problem, we need to do the calculation for your total pay for the first week of January.

We will multiply the normal working hour by hourly wages:

For the first 40 hours, you would earn a total of

40 * $10.00 = $400=400.

For the 10 hours of overtime, you would earn a total of

10 * $10.00 * 1.5 = $100*1.5=150,

since you get the time and a half for anything over 40 hours. Therefore, your pay for the first week of January would be

$400 + $150 = $400+150=550.

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For the first week of January your pay was $550

The correct answer is an option a. $550

In this question we have been given that hourly wage is $10.00 per hour.

And you get time and a half for anything over 40 hours.

Since the deadline is approaching for a project at work and you are asked to put in more than the normal 40 hours of work for the first week of January.

We need to find the total pay for the first week of January.

Given that,  you get time and a half for anything over 40 hours.

This means, for overtime pay:

per hour regular pay + half of regular pay

= 10 + 5

= $15

So, the overtime wage is $15.00 per hour.

Your hourly wage is $10.00 per

Using unitary method, for the first 40 hours, you would earn a total of:

40 * $10.00

= $400

For the 10 hours of overtime, you would earn a total of

10 * $15

= $150

So, your pay for the first week of January would be

$400 + $150

= $550.

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The rate of change or essentially the slope is a numerical value that describes the direction and the steepness of the line.

To find the slope, we just need any two points on the line

       --> Let's pick (0,2) and (2,6)

The slope's equation = \(\frac{y2-y1}{x2-x1}\)

Let's plug the known quantities into the equation

     \(\frac{y2-y1}{x2-x1}=\frac{6-2}{2-0} =\frac{4}{2} =2\)

Therefore the rate of change is 2 km/trip

Hope that helps!

The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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Answer:

$216

Step-by-step explanation

We know that we are paying 80% of the price of the airpods (20% off) so we can multiply the full price by 0.8.

250 * 0.8

This will give us 200.

Now, we need to add the sales tax which is 8%.

Simply multiply the 200 by 1.08 since we are paying the 200$ plus an extra 8% of the cost.

200 * 1.08 = $216

I hope this helped.

Answer:

x= -2

Step-by-step explanation:

Hope this helps.

Answer:

-102 = (-8×6 -8×-4x) -5x ( this is only for explanation write only this way as given below)

-102 = -48+32x -5x

-102 = -48+27x

-102+48= 27x

-54 = 27x

x = -54/27

x = -2 Ans

Hope you like it!

The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.

First, let's analyze the number of significant figures in the given values:

- 3.4876 has five significant figures.

- 4.11 has three significant figures.

- 1.2 has two significant figures.

To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:

4.11 + 1.2 = 5.31

Now, we divide 3.4876 by 5.31:

3.4876 / 5.31 = 0.6567037...

Now, let's determine the number of significant figures in the result.

Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.

In this case, the value with the fewest significant figures is 5.31, which has three significant figures.

Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

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Answer:

6.7

Step-by-step explanation:

Answer:

Radius = 2.1 in.

Step-by-step explanation:

Pythagorean Theorem

•a²+4²=4.5²

•a²+16=20.25

•Subtract 16 from both sides

•a²=4.25

•Remove the square root

•√a²=√4.25

•a=2.06155

EXPLANATION

In order to turn -2x + 10y = 2 into slope-intercept form:

First, as we know, the generic slope-intercept form is:

y= mx + b

where m is the slope and b is the y-intercept

Going back to our equation:

-2x + 10y = 2

Adding +2x to both sides:

-2x + 2x + 10y = 2 + 2x

Adding similar terms:

10y = 2 + 2x

Dividing both sides by 10:

10y/10 = 2/10 + 2x/10

Simplifying:

y = 1/5 + x/5 --> Slope-intercept form

Answer:

y= -21x/19 x≠0

Step-by-step explanation:

(I just reviewed this!) Combined like terms and used Pemdas for Order of Operations. Canceled out -21x with -21 and we know that x is not equal to 0. If you need more help there are some sites like Khan Academy.

Answer:

62.22%

Step-by-step explanation:

First, find how many total marbles there are:

12 + 11 + 17 + 5

= 45

Then, find how many marbles that are not blue:

12 + 11 + 5

= 28

Then, divide 28 by 45, and multiply by 100

(28/45) x 100

= 62.22% is the probability of not choosing a blue marble

Answer:

FG = 16

Step-by-step explanation:

∆FEG is congruent to ∆GEH. Therefore,

FG = HG

Find x

x + 11 = 3x + 1 (substitution)

Collect like terms

x - 3x = -11 + 1

-2x = -10

Divide both sides by -2

x = -10/-2

x = 5

✔️FG = x + 11

Plug in the value of x

FG = 5 + 11

FG = 16

Answer:

Solution,

2(4x+3)=10x-2

or,8x+6=10x-2

or,8x-10x=-2-6

or,-2x=-8

or,X=-8/-2

X=4

Hope it helps

Good luck on your assignment

Answer:

x = 4

Step-by-step explanation:

First you want to distribute the terms:

2(4x+3) = 10x-2

8x+6 = 10x-2

then combine like terms:

8x+6 = 10x-2

-8x         -8x

6 = 2x-2

+2      +2

8 = 2x

x = 4

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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The algebraic expression for the word phrase is 12 + z/4

The word phrase is given as:

twelve more than the quotient of a number z and 4

The quotient of a number z and 4 is represented as:

z/4

So, we have:

twelve more than z/4

twelve more means 12 +

So, we have:

12 + z/4

Hence, the algebraic expression for the word phrase is 12 + z/4

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Answer:

x=62° y = 92°

Step-by-step explanation:

x° and 118° are same side interior angles.

So,

x+118 = 180

Subtract 118 on both sides,

x = 180 - 118 = 62

x = 62°

Angles inside the triangle are y, 22 and x

x + y + 22 = 180

But , x = 62°

So, 62 + 22 + y = 180

88 + y = 180

Subtract 88 on both sides,

y = 180 - 88 = 92°

Given the point: (15, -15)

We will express the point in polar notation

the formulas to convert from rectangular to polar are as follows:

so, the polar form will be as follows:

So, the answer will be:

Answer:

288

Step-by-step explanation:

You multiply each number like 16 x 6 x3 and get 288 which equals the amount of different options

Answer:

Step-by-step explanation:

To find the total area of the track, we need to calculate the area of each section and then add them together.

Area of a semi-circle with radius 31m:

A = (1/2)πr^2

A = (1/2)π(31m)^2

A = 4795.4m^2

Area of a rectangle with length 92.7m and width 31m (the straight parts):

A = lw

A = (92.7m)(31m)

A = 2873.7m^2

To find the total area, we need to add the areas of the two semi-circular ends and the two straight sections:

Total area = 2(Area of semi-circle) + 2(Area of rectangle)

Total area = 2(4795.4m^2) + 2(2873.7m^2)

Total area = 19181.6m^2

Rounding this to 1 decimal place, we get:

Total area ≈ 19181.6 m^2

Therefore, the total area of the track is approximately 19181.6 square meters.

The test that would be conducted to see if the claim that the mean price of SUVs in the region is $45,000 is true would be a one-sample t-test.

The kind of test conducted to determine if the mean price of SUVs in the region is $45,000 is a hypothesis test, specifically a one-sample t-test or z-test, depending on the sample size and available information about the population's standard deviation. This test compares the sample mean price to the claimed mean price to assess whether there's significant evidence to support or refute the claim.

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Answer:

Kami sold 28 large figurines

Step-by-step explanation:

L = number of large figurines

S = number of small figurines

L+S = 70   since he sold 70 figurines

12L  = 8S  since the amount  of money  collected for the large figurines is equal to the amount of money for the small figurines

L+S = 70  

12L  = 8S

Divide by 8

12/8 L = S    

3/2 L = S

Substitute this into the first equation

L+S = 70

L + 3/2 L = 70

Get a common denominator

2/2 L + 3/2L = 70

5/2 L = 70

Multiply each side by 2/5

2/5 * 5/2 L = 70 * 2/5

L = 28

Kami sold 28 large figurines

Answer:

67% is subtracted

Step-by-step explanation:

Answer: a. pi=3.1, sqrt of 3=1.7, 2*sqrt of 3=3.5, sqrt of 5=2.2

b. sqrt of 3, sqrt of 5, pi, 2*sqrt of 3

Step-by-step explanation: Hi there.

1. Calculate the value of each (value shown above; sqrt= square root)

2. Order them from smallest to biggest.

The area of the region bounded by the curve r = e^(θ/2) and the sector π ≤ θ ≤ 3π/2 can be found by integrating the equation for the area of a sector and subtracting the area of the triangle formed by the origin and the two points where the curve intersects the sector.

The resulting integral is: A = (1/2)∫π^(3π/2) (e^(θ/2))^2 dθ - (1/2)(e^(π/2))^2 - (1/2)(e^(3π/2))^2Simplifying and evaluating the integral and the two triangle areas gives:  A = 2(e^3/2 - e^π/2) ≈ 7.737 Therefore, the area of the region bounded by the curve r = e^(θ/2) and the sector π ≤ θ ≤ 3π/2 is approximately 7.737 units^2.

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