Suppose the monthly cost of housing for a UNC student is a random variable with mean 690 dollars and standard deviation equal to 113 dollars.a) We will choose 70 UNC students at random and calculate the average monthly housing cost for the group. What will be the mean and standard deviation of the sampling distribution for the sample mean ? Give your answers to 2 decimal places.b) How large a sample is required for the standard deviation of the sampling distribution to be below 10? Your answer should be an integer.

Step-by-step explanation:

For a RIGHT triangle , TanΦ = opposite leg/adjacent leg = height/12

tan 30 = height /12

12 tan 30 = height

12 (sin 30 / (cos 30)  = height

12  *  1/2 / (sqrt(3) /2) = height

6 * 2 / sqrt (3) = 12 /sqrt 3  = 4 sqrt 3

Answer: 6 units

Step-by-step explanation:

To find the height of the right triangle with an angle that measures 30 degrees adjacent to a base of 12, you can use the formula h = (b x sin(theta)), where h is the height, b is the base, and theta is the angle in radians.

First, convert the angle of 30 degrees to radians by multiplying it by pi/180:

theta = 30 degrees x pi/180 = pi/6 radians

Then, substitute the values into the formula:

h = 12 x sin(pi/6) = 12 x 1/2 = 6

Therefore, the height of the right triangle is 6 units.

a) Area = √[s(s-a)(s-b)(s-c)] b) the area of the land 225.83 m^2 c) the total cost for the fencing the land three times at the rate of Rs. 25 per meter of the wire. is  Rs. 43,500

a) The formula to find the area of a triangle when all sides are not equal is Heron's formula:

Area = √[s(s-a)(s-b)(s-c)]

where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides.

To find the semi-perimeter, we add up the three sides and divide by 2:

semi-perimeter = (8+9+10)/2 = 27/2

Now we can substitute into the formula:

b) Area = √[27/2(27/2-8)(27/2-9)(27/2-10)]

= √[27/2(11/2)(9/2)(7/2)]

= √(27^2/4 * 11 * 9 * 7) / 4

= √51030.1875

≈ 225.83 m^2

b) To fence the land three times, we need to find the perimeter of the triangle and multiply by 3:

Perimeter = 8x + 9x + 10x = 27x

We know that the perimeter is 540 m, so we can solve for x:

27x = 540

x = 20

Now we can find the actual lengths of the sides:

8x = 8(20) = 160

9x = 9(20) = 180

10x = 10(20) = 200

The total length of wire needed to fence the land three times is the perimeter multiplied by 3:

Total length of wire = 3(160 + 180 + 200) = 1740 m

The cost of the wire is Rs. 25 per meter, so the total cost is:

Total cost = 1740 * 25 = Rs. 43,500

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Based on this scale factor, the length and width of the kitchen would be: A. 1.8 inches long by 1.8 inches wide.

In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures such as kites, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the side lengths of the image by the side lengths of the pre-image:

Scale factor = length of image (new figure)/length of pre-image (actual figure).

Scale factor = 2/5

For the actual length of kitchen, we have:

Scale factor = New length of kitchen/Actual length of kitchen

Actual length of kitchen = 9/5 = 1.8 in.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The total number of white shirts needed to be added by the store would be 13.

Assuming that x is the number of white shirts that need to be added. After adding these shirts, the total number of shirts in the store will be:

If the probability of selecting a white shirt from all the shirts is 3/5, then we can set up the following equation and solve for x accordingly:

Therefore, the store needs to add 13 white shirts.

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The value of the angle x in the given polygon image is: x = 54°

The formula to find the interior angles of a polygon is:

θ = 180(n - 2)/n

Thus, for a pentagon with 5 sides, we have:

θ = 180(5 - 2)/5

θ = 540/5

θ = 108°

Interior angle of a square is 90 degrees and since angle at a point is 360 degrees then we have:

x + 108 + 108 + 90 = 360

x = 360 - 306

x = 54°

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The given statement is false.

If SS between treatments = 20 and MS between treatments = 10, this means that there are more than two treatment conditions being compared in the ANOVA.

1. SSbetween treatments = 20

2. MSbetween treatments = SSbetween treatments / (k - 1), where k is the number of treatment conditions.

3. In this case, MSbetween treatments = 10

4. Solving for k, we get: 10 = 20 / (k - 1)

5. Rearranging and solving for k, we find that k = 2 + 1, which gives us k = 3.

Since k = 3, there are actually three treatment conditions in the ANOVA, and the statement is false.

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that is not important when estimating population properties using sample data, as even minor issues can significantly impact the accuracy of estimates.

One important issue affecting our ability to estimate the properties of a population when using only sample data is the representativeness of the sample. If the sample is not a good representation of the population, then the estimates based on the sample data may not accurately reflect the true properties of the population. Other factors that can affect estimates' accuracy include the sample size and the sampling method used. However, it is difficult to identify issues that are not important when estimating population properties using sample data, as even minor issues can significantly impact the accuracy of estimates.
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The population of the U.S. in 1820 was 9 million people.

From the given information, we know that the population of the U.S. in 1810, when t = 0, was 7.5 million people. We are also given that the population was growing at a rate of about 2^t million people per decade.

Using this information, we can write a formula for the population P(t) as a function of time t in decades since 1810:

P(t) = 7 + 2^t

To find the population in 1820, which is one decade later than 1810, we need to evaluate P(1), since t is measured in decades since 1810 and 1820 is one decade after 1810.

P(1) = 7 + 2^1

P(1) = 7 + 2

P(1) = 9

Therefore, the population of the U.S. in 1820 was 9 million people.

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Answer: 4/5

Step-by-step explanation:

Sin ∅ = [tex]\frac{opposite}{hypotenuse}[/tex]    

- opposite means, the length of the side opposite of the angle

-trig can only be sued in a right triangle, so the hypotenuse is always the side opposite of the right angle, or the longest side

Your question

sin A= [tex]\frac{32}{40}[/tex]      you can reduce this ratio by 8, meaning you can divide the top and bottom by 8 to get a reduced fraction

sin A = [tex]\frac{4}{5}[/tex]

Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes , the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity).

An exponential equation is an equation in which a variable occurs in the exponent. For example, y = 5x is an exponential equation since the exponent is the variable x (also said as "5 to the power of x"), while y = x5 is not an exponential equation since the exponent is 5 and not a variable.

The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log).

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The value of area and perimeter of the rectangle are 12 units² and 10√7+2√5 units respectively.

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

The area of a rectangle is expressed as;

A = l ×w

and the perimeter = 2(l+w)

The area is calculated as;

A = (2√7-2√5)(3√7 + 3√5)

= 2√7(3√7 + 3√5) -2√5(3√7 + 3√5)

= 42+6√35-6√35-30

= 42-30

= 12 units²

The perimeter is calculated as;

P = 2( l+w)

= 2(2√7-2√5+ 3√7 + 3√5)

= 2( 2√7+3√7+3√5-2√5)

= 2(5√7+√5)

P = 10√7+2√5

therefore the value of area and perimeter of the rectangle are 12 units² and 10√7+2√5 respectively.

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Yes, there is the relationship a function.

b. From the table, all the outputs are found to be either 3, 4 or 5.

The relationship is a function, with each input mapping to one output. Table has a function mapping each input to a single output. However, in option b) some inputs map to the same output.

The numbers 5 and 3 are repeated as outputs for "Kabir" and "Ethan", indicating a non-one-to-one function.

This function's rule is based on the length of the input name and assigned values for each letter, which are added together to find the output.

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Consider the relationship shown in the table.

Input   Output

Kabir       5

Eve           3

Ethan        5

Maya          4

Shawn       5

the new value of the house is $225,500. we can solve this by  substituting the given information into the equation from part (a)

what is equation ?

An equation is a mathematical statement that uses an equal sign to show that two expressions have the same value. Equations are used to represent a wide range of relationships between variables

In the given question,

(a) To write the new value in terms of the old value, we can use the fact that the value decreased by 18%, which means that the new value is equal to 100% - 18% = 82% of the old value. So, we can write:

New value = 0.82 x Old value

(b) To determine the new value, we can substitute the given information into the equation from part (a):

New value = 0.82 x 275,000

New value = 225,500

Therefore, the new value of the house is $225,500.

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The expected value of a discrete probability distribution is also known as the mean or the mathematical expectation.

The expected value of a discrete probability distribution is a concept in probability theory that represents the average value that can be expected from a random variable.

It is a measure of the central tendency of the distribution, and represents the average value of the random variable over many trials. The expected value is calculated by summing the product of each possible outcome and its corresponding probability.

It is a weighted average of all the possible outcomes of a discrete probability distribution, where the probabilities of each outcome are used as weights.

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Neither of these generations are typically associated with multitasking and instant gratification to the same extent as Millennials.

Based on the generational categories commonly used, it is most likely that Meg is a Millennial.

Millennials are known for their proficiency in multitasking and their preference for instant gratification. They have grown up with technology and are comfortable with constant communication through various channels. The Baby Boomer and Gen X generations, on the other hand, did not have the same level of exposure to technology from a young age, and may not prioritize instant gratification in the same way.

Baby Busters is a less common term for the generation born between the late 1950s and mid-1960s, and Golden Boomers typically refer to the leading edge of the Baby Boomer generation (born between 1946 and 1955). Neither of these generations are typically associated with multitasking and instant gratification to the same extent as Millennials.

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We can estimate that there were approximately 388 M&Ms in the bag. 5. The M&M bags may not be distributed as planned for a number of reasons.

When a number is expressed as a fraction of 100, the denominator is always fixed at 100. It is frequently used to convey ratios, proportions, or rates in a way that is easier to grasp and compare.

On a test, for instance, if a student correctly answers 20 of the 25 questions, we can calculate their percentage by dividing 20 by 25, then multiplying the result by 100:

20/25 x 100 = 80%

Given that, you count 97 blue pieces, and they are 25%.

Thus,

0.25x = 97

x = 388

Hence, we can estimate that there were approximately 388 M&Ms in the bag.

5. The M&M bags may not be distributed as planned for a number of reasons. There is a chance that the sample of M&Ms we saw is not entirely representative of the population of M&Ms in the bag due to random sampling error. Another explanation is that there may be some natural fluctuation in the ratios of various colours in each batch of M&Ms because the manufacturing procedure at the factory is not always exact.

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AnswER

410 A

Step-by-step explanation:

To find the 95th quantile of coded weight for a continuous random variable with a given density function fX(x) = 2/16 x, where 0 < x < 4, follow these steps:

1. Find the cumulative distribution function (CDF) by integrating the density function:

F(x) = ∫fX(x) dx = ∫(2/16 x) dx, with limits 0 to x.

2. Calculate the CDF:

F(x) = x^2/16, with limits 0 to x.

3. Find the 95th quantile (0.95) by setting F(x) equal to 0.95:

0.95 = x^2/16

4. Solve for x, the 95th quantile of coded weight:

x^2 = 0.95 * 16
x^2 = 15.2
x = sqrt(15.2)
x ≈ 3.898

So, the 95th quantile of coded weight is approximately 3.898.

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Mollie can expect to lose $1.50 per game played.

What is Mollie's expected profit per game, assuming players play only once?

First, let's calculate the expected revenue per game:

Probability of winning: 0.1

Revenue from winners: $5

Probability of losing: 0.9

Revenue from losers: $0

Expected revenue per game = (0.1 x $5) + (0.9 x $0) = $0.50

Now, let's calculate the expected cost per game:

Cost per game: $2

Expected cost per game = $2

Therefore, Mollie's expected profit per game is:

Expected profit per game = Expected revenue per game - Expected cost per game

Expected profit per game = $0.50 - $2

Expected profit per game = -$1.50

This means that, on average, Mollie can expect to lose $1.50 per game played.

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It is true that A priori tests refer to hypothesis tests that are planned and conducted before conducting an ANOVA (Analysis of Variance) to determine whether there are any significant differences among the groups being compared.

These tests are typically conducted to compare specific group means or to test specific hypotheses based on prior knowledge or research.

A priori tests are preferred over post-hoc tests because they help to minimize the likelihood of making Type I errors (false positives) by reducing the number of tests being conducted. This is important because conducting multiple tests can increase the probability of finding significant results by chance alone.

In conclusion, a priori tests are those that are planned before an ANOVA is calculated and they help to ensure that the hypotheses being tested are both valid and meaningful. They are an important aspect of the research process, and they can help researchers to draw valid conclusions from their data.

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Answer: A. 8x = 32

Step-by-step explanation:

To solve for x in the equation 8x = 32, we need to isolate x on one side of the equation.

We can divide both sides of the equation by 8:

8x/8 = 32/8

Simplifying:

x = 4

Therefore, the solution to the equation 8x = 32 is x = 4.

The solution to the equation 15x + 4 = 10x + 24 is x = 4.

Answer:

A) 8x = 32

Step-by-step explanation:

15x + 4= 10x +24

15x - 10x= 5x

5x + 4 = 24

24 - 4= 20

5x = 20

20/5= 4

X=4

Check options
A) 8x = 32

32/8=4

X=4

The number of  people per square mile live in the city is (A) 5000

Population density is a measurement of the number of people who live in a certain area or region, typically expressed as the number of people per unit of area. It is calculated by dividing the total population of an area by the total land area of that area

To estimate the number of people per square mile in the given city, we can divide its population by its area

Population density ≈ Population ÷ Area

Population density ≈ 279,392 ÷ 50.8

Population density ≈ 5,500

So, the estimated number of people per square mile living in the city is around 5,500. The closest choice to this estimate is A. 5000.

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The arrow notation that describes the translation is (x, y) ⇒ (x + 3, y + 6)

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

W(-2,-6) to W'(4,9)

The translation is the difference between the pairs

So, we have

(x, y) = (9 - 6, 4 + 2)

Evaluate

(x, y) = (3, 6)

Hence, the translation is (x, y) ⇒ (x + 3, y + 6)

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Answer:

35

Step-by-step explanation:

a = # cards antonio has

g = # of cards giancarlo has

g = 3a + 2

3a + 2 -12 = a + 12

3a - 10 = a + 12

2a = 22

a = 22/2 = 11

g = 3(11) + 2 = 35

a) The given proposition "Every homogeneous linear system has a solution" is true.

A homogeneous linear system is in the form Ax = 0, where A is a matrix and x is a vector of unknowns. This system always has at least the trivial solution (x = 0), where all unknowns are set to zero.

b) The given proposition "Let A, B, and C be three matrices of the appropriate sizes. Then, the following holds: AB = AC and A ≠ 0 imply B = C" is true.

If AB = AC and A ≠ 0, we can left-multiply both sides by the inverse of A (A×(-1)). Then, A×(-1)(AB) = A×(-1)(AC) which simplifies to B = C.

c) The given proposition If A ≠ 0 and B ≠ 0 are square matrices of the same order, then AB ≠ 0 is False.

Even if A and B are nonzero square matrices, their product AB could still be a zero matrix. A counterexample is A = [[1, 1], [1, 1]] and B = [[1, -1], [-1, 1]].

d) The given proposition "If A is skew-symmetric, then A×p is skew-symmetric for any positive integer p" is true.

A skew-symmetric matrix A satisfies the property that A×T = -A. By repeatedly multiplying a skew-symmetric matrix A by itself, the resulting matrix A×p will also be skew-symmetric for any positive integer p. This can be proven by induction.

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That the constant of integration C cancels out when we evaluate the definite integral, so we do not need to include it in the final answer.

We can evaluate the definite integral using the power rule of integration, which states that

∫ [tex]x^n dx = (x^(n+1))/(n+1) + C[/tex]

where C is the constant of integration.

So, for the given definite integral, we have:

∫ [tex](1/(5^(50)x^3)) dx[/tex]

[tex]= (-1/2) * (1/(5^(50))) * (1/x^2) + C[/tex]

Evaluating this from x = 1 to x = 1/5, we get:

[tex]= (-1/2) * (1/(5^(50))) * (1/(1/5)^2) - (-1/2) * (1/(5^(50))) * (1/1^2)[/tex]

[tex]= (-1/2) * (5^2) * (5^(50)) + (1/2) * (5^(50))[/tex]

[tex]= - (1/2) * (5^(52)) + (1/2) * (5^(50))[/tex]

[tex]= (1/2) * (5^(50)) * (1 - 5^2)[/tex]

[tex]= (1/2) * (5^(50)) * (-24)[/tex]

[tex]= -12 * (5^(50))[/tex]

So, the value of the definite integral is [tex]-12 * (5^(50))[/tex]. Note that the constant of integration C cancels out when we evaluate the definite integral, so we do not need to include it in the final answer.

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The line-of-sight distance from the television camera to the case of the stadium is [tex]\text{x = 3826.71 m}[/tex]

Given data

From Δ ABC

AB =  The altitude of the blimp is = 400 m

AC = The line-of-sight distance from the television camera to the case of the stadium = x

Now

[tex]\text{sin} \ 6=\dfrac{\text{AB}}{\text{AC}}[/tex]

[tex]x=\dfrac{\text{AB}}{\text{sin} \ 6}[/tex]

[tex]x=\dfrac{400}{\text{sin} \ 6}[/tex]

[tex]\bold{x = 3826.71 \ m}[/tex]

Therefore the line-of-sight distance from the television camera to the case of the stadium.

Answer:

=√2/4

Step-by-step explanation:

[tex]sin(3\pi /4) = \frac{\sqrt{2}}{2} \\\\and \\\\cos(5\pi /3) = \frac{1}{2} \\\\[/tex]

Therefore, sin(3π/4) × cos(5π/3) = √2/2 × 1/2 = √2/4