The researchers are in short of budget so they would like to minimize the respondents needed for their research. They decided to use σ = 0.4 with CL = 92.5% but they are undecided on 1% and 2% margin of error. Help the researchers on choosing between the two margin of errors if their best of interest is the least possible number of respondents. [6 points]
(a) Find Z.
(b) Determine the 2 sample sizes.
(c) Write your conclusion.

The mean is ≈ 8.793. The variance is approximately 9.641. The standard deviation is approximately 2.964

Given frequency table:

Value: 2 3 6 9 12

Frequency: 3 6 9 7 4

a) Mean:

\(\[\text{{Mean}} = \frac{{\text{{Sum of (Value * Frequency)}}}}{{\text{{Total number of observations}}}}\]\[\text{{Mean}} = \frac{{(2 \times 3) + (3 \times 6) + (6 \times 9) + (9 \times 7) + (12 \times 4)}}{{3 + 6 + 9 + 7 + 4}}\]\[\text{{Mean}} = \frac{{189}}{{29}}\]\)

≈ 8.793

b) Variance:\(\[\text{{Variance}} = \frac{{(3 \times (2 - \text{{Mean}})^2) + (6 \times (3 - \text{{Mean}})^2) + (9 \times (6 - \text{{Mean}})^2) + (7 \times (9 - \text{{Mean}})^2) + (4 \times (12 - \text{{Mean}})^2)}}{{29}}\]\)

 ≈ 8.793

c) Standard Deviation:

\(\[\text{{Standard Deviation}} = \sqrt{{\text{{Variance}}}}\]\)

Therefore, the standard deviation is approximately \(\sqrt{8.793} \approx 2.964\)

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Given that a circle with radius 20 has a corresponding angle of 305°.

To find the coordinates of a point on the circle, we use the formula:`(r cos (θ), r sin (θ))`Here, `r = 20` and `θ = 305°`.

Substituting the values of `r` and `θ` in the formula, we get:`(20 cos (305°), 20 sin (305°))`

Using the values of trigonometric ratios, we can write:cos(305°) = cos(360° - 305°) = cos(55°) ≈ -0.5736sin(305°) = sin(360° - 305°) = sin(55°) ≈ 0.8192

Hence, the coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`.

The coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`

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Answer: The unit value of a cubic centimeter (cm^3) is the same as the metric measurement of a milliliter (mL).

This is because 1 milliliter is equal to 1 cubic centimeter. In other words, if you have a cube that measures 1 centimeter on each side, its volume would be 1 cubic centimeter, which would also be equivalent to 1 milliliter of volume.

This relationship between cm^3 and mL is commonly used in scientific and medical measurements involving liquids and gases.

The unit value of a cubic centimeter (cc) is equivalent to one milliliter (mL) in the metric system. Both cubic centimeters and milliliters are used to measure volume, and their conversion is straightforward: 1 cc = 1 mL.

The metric system uses base units such as meters, liters, and grams, and applies prefixes like kilo-, centi-, and milli- to indicate larger or smaller units of measurement.
Cubic centimeters are often used to measure the volume of solid objects or the capacity of containers, while milliliters are more commonly used to measure the volume of liquids. However, both units represent the same volume and can be used interchangeably.
It is important to understand the difference between volume measurements and other metric measurements, such as length or mass. For instance, meters are used to measure length or distance, and grams are used to measure mass or weight. These units cannot be directly converted to cubic centimeters or milliliters, as they represent different physical properties.
In summary, a cubic centimeter (cc) is a unit of volume in the metric system that is equivalent to one milliliter (mL). Both units can be used to measure volume, and they have a simple conversion of 1 cc = 1 mL. Understanding the relationship between these units and other metric measurements is essential for accurately quantifying and comparing different physical properties.

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Answer:

The product is 6112

because u multiply the numbers together

Step-by-step explanation:

Answer:

6×6=36

Step-by-step explanation:

2×3=5

6×10=60

50×10=50

Answer: Simple random sample

Step-by-step explanation: This will be the most representative of the 150 ninth graders.

The sample that is the most representative of the 150 ninth graders is

Simple random space

It is the total number of possible outcomes from a given set.

We have,

Number of 9th grader students = 150

Number of students to survey = 20

Sample that is the most representative of the 150 ninth graders.

= Simple random space

This means,

The 20 students will be selected randomly.

Thus,

Sample random space is the most representative of the 150 ninth graders.

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Answer/Step-by-step explanation:

Common ratio of a sequence can be gotten by dividing any of the consecutive term in a sequence, by the term before it.

Thus,

For the sequence, \( 3, 9, 27. . . \) : \( a_1 = 3 \)

\( r = \frac{9}{3} = 3 \)

For the sequence, \( 8, 4, 2, 1. . . \) : \( a_1 = 8 \)

\( r = \frac{4}{8} = \frac{1}{2} \)

For the sequence, \( -16, 64, -256 . . \) : \( a_1 = -16 \)

\( r = \frac{64}{-16} = -4 \)

Answer:

1) not a function

2) Function

3) Function

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Pemdas you do the 3x6 first then add the twelve. you would be at 30 1/3 of that is 10 then you subtract the 5

Option 3 is correct.

The formula needed for Excel to calculate the monthly payment needed to pay off a mortgage for a house that costs

189,000with a fixed APR of 3.1

=PMT(3.1/12,32*12,-189000)

This formula uses the PMT function in Excel, which stands for "Present Value of an Annuity." The PMT function calculates the monthly payment needed to pay off a loan or series of payments with a fixed annual interest rate (the "APR") and a fixed number of payments (the "term").

In this case, we are calculating the monthly payment needed to pay off a mortgage with a fixed APR of 3.1% and a term of 32 years. The formula uses the PMT function with the following arguments:

Rate: 3.1/12, which represents the annual interest rate (3.1% / 12 = 0.0254)

Term: 32*12, which represents the number of payments (32 years * 12 payments per year = 384 payments)

Payment: -189000, which represents the total amount borrowed (the principal amount)

The PMT function returns the monthly payment needed to pay off the loan, which in this case is approximately 1,052.23

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To calculate the point estimate, we divide the number of individuals in the sample who smoked marijuana within the last year (328) by the total number of individuals in the sample (920).

Point Estimate = Number of individuals who smoked marijuana / Total number of individuals in the sample

Point Estimate = 328 / 920 ≈ 0.357

Therefore, the point estimate is approximately 0.357.

The correct answer is d. 0.357.

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Answer: (a) The English system of units used in surveying:

Length: The basic unit of length is the foot (ft).

Area: The basic unit of area is the square foot (ft²).

Volume: The basic unit of volume is the cubic foot (ft³).

Angles: The basic unit of angles is degrees (°).

(b) The SI (International System of Units) system of units used in surveying:

Length: The basic unit of length is the meter (m).

Area: The basic unit of area is the square meter (m²).

Volume: The basic unit of volume is the cubic meter (m³).

Angles: The basic unit of angles is the degree (°) or the radian (rad).

It's worth noting that while the English system is still used in some countries, the SI system is the globally recognized and widely adopted system of measurement.

Step-by-step explanation:

the values of m and b for the best least-squares fit line are m = 5.2 and b = -8.To find the values of m and b for the straight line that provides the best least-squares fit to the data, we need to complete the table and use the formulas for calculating the slope (m) and y-intercept (b).

First, let's complete the table by calculating the xy column:

X    y    xy

1    8    8

2    10   20

3    12   36

4    3    12

  Σχ=10   Σy=20   Σxy=76

Now, we can use the formulas:

m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)

b = (Σy - m(Σx))/n

Plugging in the values from the table:

m = (76 - (10)(20)/4) / (30 - (10)²/4)

  = (76 - 200/4) / (30 - 100/4)

  = (76 - 50) / (30 - 25)

  = 26 / 5

  = 5.2

b = (20 - 5.2(10))/4

  = (20 - 52)/4

  = -32/4

  = -8

Therefore, the values of m and b for the best least-squares fit line are m = 5.2 and b = -8.

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9514 1404 393

Answer:

  a) profit has a typical curve: negative at low volume, and again at very high volume.

  b) $239,407

Step-by-step explanation:

a) The graph is negative below x=1.58, so the break-even point is 158 toys sold. The profit declines steeply above 533 toys sold, to again go negative for 774 toys sold. This sort of curve seems fairly typical.

__

b) The profit is a maximum of $239,407 when 533 toys are sold.

Answer:

if y = 2x then

-3x+8y=26

-3x + 8·2x= 26

-3x+16x=26

13x=26

x = 26/13= 2

Answer:

Im only doing this to message people and really this is easy dig deeper

Step-by-step explanation:

Answer:

i cant read that,

Step-by-step explanation:

The cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).

We can use the fοrmula fοr the area οf a triangle, which is:

area = (base * height) / 2

We knοw that the base AB has a length οf 16 units, sο we can find the height by rearranging the fοrmula:

height = (2 * area) / base

height = (2 * 80) / 16

height = 10

Sο, pοint B is at (4, 0) and pοint C is at (x, y) where the height frοm A tο BC is 10 units and the length οf BC is 16 units.

We can use the Pythagοrean theοrem tο find the cοοrdinates οf pοint C:

\(x^2 + y^2 = BC^2\)

\(x^2 + y^2 = 16^2\)

\(x^2 + y^2 = 25\)

Alsο, we knοw that the height frοm A tο BC is 10 units, sο the distance between pοint A and the line BC is 10 units. The slοpe οf the line BC is -y/x (rise οver run), sο the equatiοn οf the line BC is:

\(y = (-y/x) * (x - 4)\)

\(y = (-y/x) * x + (y/x) * 4\)

\(y + (y/x) * x = (y/x) * 4\)

\(y(x/x + 1) = (y/x) * 4\)

\(y + x = 4y/x\)

\(x^2 + xy = 4y\)

\(y = (x^2) / (4 - x)\)

Nοw we can substitute this expressiοn fοr y intο the equatiοn\(x^2 + y^2 = 256:\)

\(x^2 + ((x^2) / (4 - x))^2 = 256\)

Sοlving this equatiοn gives twο pοssible values fοr x: x = 8 οr x = -4.

If x = 8, then y = 16/3, and if x = -4, then y = -16.

Therefοre, the cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).

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The profit function, P(x), is given by the difference between the revenue function R(x) and the cost function C(x), so P(x) = -0.4x³ + 1000x² + 400x +500.

Therefore, the correct answer is OA.

To find the profit function, we need to subtract the cost function from the revenue function.

Cost function: C(x) = 400x² + 600x

Revenue function: R(x) = -0.42x³ + 600x² + 200x + 500

To find the profit function P(x), we subtract C(x) from R(x):

P(x) = R(x) - C(x)

P(x) = (-0.42x³ + 600x² + 200x + 500) - (400x² + 600x)

Simplifying the expression, we combine like terms:

P(x) = -0.42x³ + 600x² + 200x + 500 - 400x² - 600x

P(x) = -0.42x³ + (600x² - 400x²) + (200x - 600x) + 500

P(x) = -0.42x³ + 200x² - 400x + 500

Therefore, the profit function is P(x) = -0.42x³ + 200x² - 400x + 500.

Matching the options given:

OA. P(x) = -0.4x³ + 1000x² + 400x + 500 (incorrect)

OB. P(x) = 0.4x³ - 200x² + 800x + 500 (incorrect)

OC. P(x) = 0.4x³ + 200x² + 800x + 500 (incorrect)

OD. P(x) = -0.4x³ + 200x² - 800x + 500 (incorrect)

None of the options provided match the derived profit function, so the correct answer is not among the given options.

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Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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\(3\leqslant |x+2|\leqslant 6\implies \begin{cases} 3\leqslant |x+2|\\\\ |x+2|\leqslant 6 \end{cases}\implies \begin{cases} 3 \leqslant \pm (x+2)\\\\ \pm(x+2)\leqslant 6 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(3\leqslant +(x+2)\implies \boxed{3\leqslant x+2}\implies 1\leqslant x \\\\[-0.35em] ~\dotfill\\\\ 3\leqslant -(x+2)\implies \boxed{-3\geqslant x+2}\implies -5\geqslant x \\\\[-0.35em] ~\dotfill\\\\ +(x+2)\leqslant 6\implies \boxed{x+2\leqslant 6}\implies x\leqslant 4 \\\\[-0.35em] ~\dotfill\\\\ -(x+2)\leqslant 6\implies \boxed{x+2\geqslant -6}\implies x\geqslant -8\)

Answer:

Flip the sign.

Step-by-step explanation:

For example if it was -2<3 youd flip the sign when you get your answer. So it would be -2>3 except itd be your answer. I just made this problem up but flip the sign!

Answer:

3.5 hours*3.25 mph=11.375 miles

11.375 miles/3.45 mi/hr=3.297 hours or 3.30 hours, about 12 minutes faster.

Step-by-step explanation:

(i) The probability of both events A and B happening, P(A and B), is 0.12. (ii) The probability of either event A or event B happening, P (A or B), is 0.58.

First, let's define what it means for events to be independent. Two events A and B are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. In other words, the probability of both events occurring together is equal to the product of their individual probabilities: P (A and B) = P(A) x P(B).

Using this formula, we can find the probability of both events occurring together:
P (A and B) = P (A) x P(B) = 0.3 x 0.4 = 0.12

Now let's find the probability of either event occurring. We can use the formula P (A or B) = P (A) + P(B) - P(A and B).
We already know that P(A) = 0.3 and P(B) = 0.4, and we just found that P (A and B) = 0.12. Plugging those values into the formula, we get:
P (A or B) = 0.3 + 0.4 - 0.12 = 0.58
So, the probability of either event occurring is 0.58.
In summary:
(i) P (A and B) = 0.12
(ii) P (A or B) = 0.58

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A 95% confidence interval to estimate the population proportion of retired baseball players who used steroids is: (1.9216, 0.2784)

The formula for confidence interval for proportion is:

CI = p ± z√(p(1 - p)/n)

where:

p is sample proportion

n is sample size

z is z-score at confidence level

n = 100

p = 20/100 = 0.2

z-score at 95% CL = 1.96

Thus:

CI = 0.2 ± 1.96√(0.2(1 - 0.2)/100)

CI = 0.2 ± 0.0784

CI = (1.9216, 0.2784)

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Answer:

a = 5

b = 5

Step-by-step explanation:

Answer:

so, you said withdrawal of $25 which means to take out of an account, but then you said OPPOSITE, so the opposite of withdrawal (take) is to put back (earn). so, it would be 25.