A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%. What is the minimum sample size needed?.

Answer:

C. Infinite Solutions

Step-by-step explanation:

In order to solve this we fist have to simplify the equation so we do the following:

\(\frac{1}{7}(63n -77) = -11 + 9n\\\\(\frac{1}{7})(7)(63n - 77) = (7)(-11 + 9n) \\\\63n - 77 = -77 + 63n\\63n - 77 = 63n - 77\)

From here we know that any value of n is the solution of this equation so the answer is option C.

Answer:

A. -4

Step-by-step explanation:

Perpendicular lines have negative slopes

so you would have to flip the fraction and change the sign

so 1/4x = -4/1x or -4x

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Answer:

TYSM!! I wanted to know how to calculate the kinetic energy of an object for so long!

A pendulum at the top of its swing, when it stops moving does not have any speed and therefore it has no kinetic energy.

Kinetic energy is the energy an object has because of its motion. If we want to accelerate an object, then we must apply a force.

Given that, Kinetic energy = 1/2 × mass × velocity²

If the kinetic energy of the pendulum at the top of its swing is 0, then this tells us that the velocity of the pendulum at that point is 0.

Here, mass m = 0, This shows that the pendulum has no mass and

velocity (v) = 0 meaning the velocity is zero, it is stopped at once.

The velocity that is moving one way or direction can be said to be in a positive direction or positive velocity.

It does slows down when it reaches the top of its swing then move again back to the opposite direction making it to move in the opposite or negative direction with negative velocity. This make a positive velocity and a negative velocity which has pass through to be zero.

Therefore, a pendulum at the top of its swing, when it stops moving does not have any speed and therefore it has no kinetic energy.

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60.5 is mean

61 is median

65 is interquartile range

14 is range

Answer:

60.5 is mean.

_________________

61 is median.

_________________

65 is interquartile range.

_________________

14 is range.

Answer:  Rational

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

The least number of computers that must be shipped is 10.

In order to determine the least number of computers that must be shipped, the equation that represents the cost of shipping should be equal to the selling price of the computers.

3000 + 100x = 400x

In order to determine the value of x, take the following steps:

3000 = 400x - 100x

3000 = 300x

x = 3000 / 300

x = 10

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The slope-intercept equation of the line that passes through (3, 8) and is parallel to the y-axis is x = 3.

We can find the slope-intercept equation of the line that satisfies the given conditions by first determining the equation of the y-axis, which is x = 0.

Since the line is parallel to the y-axis, it has an undefined slope.

Therefore, its equation is of the form x = k, where k is some constant.

Since the line passes through the point (3, 8), we can find its equation by setting x = 3.

This gives us the point-slope form of the equation as follows: x - 3 = 0.

To find the slope-intercept form of the equation, we can solve for x: x = 3, which is our y-intercept.

Thus, the slope-intercept equation of the line that satisfies the given conditions is x = 3.

This means that the line is vertical and passes through the point (3, 8).

It is worth noting that vertical lines have undefined slopes, and their equations cannot be expressed in slope-intercept form.

Instead, they are expressed as x = k, where k is some constant.

The slope-intercept equation of the line that passes through (3, 8) and is parallel to the y-axis is x = 3. The line is vertical and passes through the point (3, 8). The equation of the y-axis is x = 0, which serves as a reference line for the line in question. Vertical lines have undefined slopes, and their equations cannot be expressed in slope-intercept form.

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The quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

The time taken by substance to reduce to its half of its initial concentration is called half life period.

We will use the half- life equation N(t)

N e^{(-0.693t) /t½}

Where,

N is the initial sample

t½ is the half life time period of the substance

t2 is the time in years.

N(t) is the reminder quantity after t years .

Given

N = 13g

t = 350 years

t½ = 1599 years

By substituting all the value, we get

N(t) = 13e^(0.693 × 50) / (1599)

= 13e^(- 0.368386)

= 13 × 0.691

= 8.98

Thus, we calculated that the quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

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Answer:

-1

Step-by-step explanation:

Slope formula: (y₂ - y₁) / (x₂ - x₁)

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

= -1

To analyze the investment decision between Machine A and Machine B, various financial metrics are calculated. The payback period, accounting rate of return, net present value, and internal rate of return are determined. Based on these calculations, the suitable machine is chosen, considering the payback period, cost of capital, and other factors.

The payback period of both machines is calculated by determining the time required to recover the initial investment. It is expressed in years, months, and days. The machine with the shorter payback period indicates a faster return on investment.
Using the payback period as the sole criterion for decision-making, the machine with the shorter payback period should be chosen. However, it's important to note that the payback period does not consider the time value of money or the profitability beyond the payback period.
The accounting rate of return on average investment for Machine A is calculated by dividing the average annual profit by the average investment cost, expressed to two decimal places. This metric provides an indication of the profitability of the investment.
The net present value (NPV) of each machine is calculated by discounting the expected cash flows using the company's cost of capital (12%). NPV represents the present value of the expected cash inflows and outflows associated with the investment. The machine with the higher NPV indicates a higher value addition to the company.
The internal rate of return (IRR) of Machine B is determined using interpolation. IRR is the discount rate that equates the present value of expected cash flows to the initial investment. It indicates the profitability and return on investment of Machine B.
Considering all these factors and the company's cost of capital, a comprehensive evaluation can be made to determine the most suitable machine for investment.

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Answer:

A.) Y.

Step-by-step explanation:

I'm not sure how to explain.

The best prediction for the number of Algaes after 30 days is; 543 Algaes

We are given the formula for the future amount as;

Future amount = I(1 + r)^(t)

Where;

I is initial amount

r is rate of increment

t is number of periods of compounding = 30/3 = 10

Thus;

Future amount = 46(1 + 0.28)¹⁰

Future amount = 543 algaes

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Answer:50

Step-by-step explanation:

3/5 = 3 ÷ 5 = 0.6

30 ÷ 0.6 = 50

otra explicacion:

30/1 ÷ 3/5= 30/1 x 5/3 = 150/3 = 50

The function un(x,t) = e^(-αn^2t/l^2) sin(nx/l) is a solution of the heat equation for any positive integer n.

To verify that the function un(x,t) satisfies the heat equation, we need to show that it satisfies the partial differential equation and the initial condition.

The heat equation is given by ∂u/∂t = α (∂^2u/∂x^2), where u(x,t) is the temperature distribution, α is the thermal diffusivity, and ∂ and ∂^2 represent partial derivatives. Let's evaluate the function un(x,t) to check if it satisfies the heat equation.

Partial derivative with respect to t:

∂un/∂t = (∂/∂t) (e^(-αn^2t/l^2) sin(nx/l))

= -αn^2/l^2 e^(-αn^2t/l^2) sin(nx/l)

Second partial derivative with respect to x:

∂^2un/∂x^2 = (∂/∂x) (-αn^2/l^2 e^(-αn^2t/l^2) sin(nx/l))

= -n^2/l^2 e^(-αn^2t/l^2) cos(nx/l)

Now, let's substitute these derivatives into the heat equation:

∂un/∂t = α (∂^2un/∂x^2)

-αn^2/l^2 e^(-αn^2t/l^2) sin(nx/l) = α(-n^2/l^2 e^(-αn^2t/l^2) cos(nx/l))

The exponential terms cancel out, and we are left with:

-sin(nx/l) = -cos(nx/l)

Since the equation holds true for all x and t, we can conclude that un(x,t) = e^(-αn^2t/l^2) sin(nx/l) is indeed a solution of the heat equation.

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Answer:

-19 degrees

Step-by-step explanation:

13+6=19

you would need to add the negative since it said dropped in temperature and the temperature was already negative.

LCM of 156 and 168 is

\(2184\)

\(Find \: the \: prime \: factorization \: of \: 156 \\ 156 = 2 \times 2 \times 3 \times 13 \\ \)

\(Find \: the \: prime \: factorization \: of \: 168 \\ 168 = 2 \times 2 \times 2 \times 3 \times 7\)

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM

LCM = 2×2×2×3×7×13

LCM = 2184

Answer:

I think -1.5 -0.1 0.8 1.1

Answer:

-1.5 || -0.1 || 0.8 || 1.1

Explanation:

Since it is from least to greatest, let's compare the 2 negative numbers -1.5 and -0.1.

-1.5 has a 1 in its first place while -0.1 has a 0. This means that -1.5 is smaller because the further a number is on the negative number line the smaller it is.

So, -1.5 is the smallest, then -0.1.

-1.5 || -0.1

Now we compare the 2 positive numbers 0.8 and 1.1.

0.8 has a 0 in its first place and 1.1 has a 1 in its first place. Because the numbers are positive, the number with the biggest digit in in front of the decimal is greater.

So, in this case 1.1 is greater than 0.8.

0.8 || 1.1

In order it is:

-1.5 || -0.1 || 0.8 || 1.1

\(\displaystyle\bf 1\frac{1}{3} -3\frac{5}{6} +5\frac{1}{9} =5+1-3+\frac{1^{/6}}{3} +\frac{1^{/2}}{9} -\frac{5^{/3}}{6}\\\\\\\ =3+\frac{6+2-15}{18} =3-\frac{7}{18}=\boxed{2\frac{11}{18} }\)

The percentage of students who scored between 340 and 458 on the exam is 47.1%, rounded to 3 significant figures.

To solve this problem, we need to standardize the values of 340 and 458 using the given mean and standard deviation. We can then use the standard normal distribution table or a calculator to find the area under the standard normal curve between the standardized values.

The standardized value for 340 is:

z = (340 - 458) / 59 = -1.998

The standardized value for 458 is:

z = (458 - 458) / 59 = 0

Using a standard normal distribution table or a calculator, we can find that the area under the standard normal curve between -1.998 and 0 is approximately 0.471. This means that about 47.1% of the students scored between 340 and 458 on the exam.

Therefore, the percentage of students who scored between 340 and 458 on the exam is 47.1%, rounded to 3 significant figures.

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The coefficients obtained by the student may be less efficient and have larger standard errors compared to the professor's regression.

If the student enters each observation twice, resulting in a sample size of 100 instead of the original 50, the assumption of independent observations is violated in Ordinary Least Squares (OLS) regression. The OLS assumption assumes that the observations are independent, meaning that the value of one observation does not depend on the value of another observation.

In this case, the student's dataset contains repeated observations, which introduces dependence between observations. This violation of the independence assumption can lead to biased and inconsistent parameter estimates in the regression analysis.

Regarding the slope coefficients, if the student runs a regression using the duplicated data, the estimated coefficients may be different from the professor's regression. The duplication of observations inflates the sample size, potentially affecting the precision and accuracy of the estimates.

However, the direction and overall relationship between the variables may still be captured by the student's regression, although the estimates may not be as reliable.

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Answer:

square root of 282, and in decimal form its 16.79, rounded

Step-by-step explanation:

hi

The answer to work for part a) is 2. The value that is used in hypothesis testing to compare a test statistic to the rejection region is known as a critical value. The critical value differs depending on the level of significance selected for the test and the test’s degree of freedom.

The value that is used in hypothesis testing to compare a test statistic to the rejection region is known as a critical value. The critical value differs depending on the level of significance selected for the test and the test’s degree of freedom. For this particular question, the critical value can be calculated using the Z-distribution formula since the sample size is greater than or equal to 30.

Thus, the answer to work for part a) is 2.

Explanation: Given that the population standard deviation is known to be 1.28 screens, The sample size is 89 with a sample mean of 10.59 screens. The hypothesis test can be represented as follows:

H0: µ ≤ 5 Ha: µ > 5

To determine whether there is sufficient evidence to conclude that the mean number of screens per household is greater than 5, a Z-test can be used. The test statistic is calculated as follows:

Z = (X - µ) / (σ / sqrt(n))

Where X = 10.59,

µ = 5,

σ = 1.28,

n = 89.

Substituting the values in the above equation, we get

Z = (10.59 - 5) / (1.28 / sqrt(89))

= 33.97

Since the alternative hypothesis is one-tailed, the critical value for the test can be calculated using the Z-distribution formula as follows:

Critical value = Zα

where α is the level of significance. For instance, for a 5% level of significance, α = 0.05, and the corresponding critical value is 1.64. Since the calculated test statistic is greater than the critical value, the null hypothesis can be rejected at a 5% level of significance.

Hence, there is sufficient evidence to conclude that the mean number of screens per household is greater than 5.

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Answer:

x = 4

Step-by-step explanation:

x + 8 = 3x

8 = 2x

x = 4

So, the answer is x = 4

Answer:

-5.46

Step-by-step explanation:

-8.24 + 3.7

3.7 can also be written as 3.70

-8.24 + 3.70

3.70

-8.24

____

-5.46

The answer is -5.46

c. 5x4=20

4x4=16 items.

Answer:

1/2000

Step-by-step explanation:

To answer the questions using the Empirical Rule, we can apply the properties of a normal distribution.

a) According to the Empirical Rule, for a bell-shaped distribution, approximately 68% of the data lies within one standard deviation of the mean, approximately 95% lies within two standard deviations, and approximately 99.7% lies within three standard deviations.

Since the mean weight is 65 ounces and the standard deviation is 8 ounces, we can determine the range within which 95% of the widget weights lie.

1 standard deviation = 8 ounces

2 standard deviations = 2 * 8 = 16 ounces

So, 95% of the widget weights lie between (65 - 16) and (65 + 16) ounces.

95% of the widget weights lie between 49 and 81 ounces.

b) To find the percentage of widget weights that lie between 41 and 81 ounces, we need to calculate how many standard deviations each value is from the mean.

For 41 ounces:

Z = (41 - 65) / 8 = -3 standard deviations

For 81 ounces:

Z = (81 - 65) / 8 = 2 standard deviations

Since the Empirical Rule states that approximately 95% of the data lies within two standard deviations of the mean, we can conclude that approximately 95% of the widget weights lie between 41 and 81 ounces.

c) To find the percentage of widget weights that lie below 73 ounces, we calculate how many standard deviations 73 is from the mean.

Z = (73 - 65) / 8 = 1 standard deviation

Using the Empirical Rule, approximately 68% of the data lies within one standard deviation of the mean. Therefore, approximately 68% of the widget weights lie below 73 ounces.

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