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a) the 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it is 45.1% to 52.9%

b) a sample size of approximately 1629 people would be recommended to achieve a margin of error of about 1.5% for a 90% confidence level

(a) To calculate a 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it, we can use the sample proportion and the standard error formula. The sample proportion is 49% (0.49) and the sample size is 350.

The margin of error (ME) for a 90% confidence level is approximately 1.645 times the standard error. The standard error is calculated as the square root of (p*(1-p)/n), where p is the sample proportion and n is the sample size.

Using these values, the 90% confidence interval can be calculated as:

p ± ME

= 0.49 ± 1.645 * sqrt(0.49*(1-0.49)/350)

= 0.49 ± 0.039

Therefore, the 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it is 45.1% to 52.9%. We are 90% confident that 45.1% to 52.9% of all Americans who decide not to go to college do so because they cannot afford it.

(b) To determine the required sample size to achieve a margin of error of 1.5% for a 90% confidence level, we can use the formula: n = (Z^2 * p * (1-p)) / (ME^2), where Z is the z-score corresponding to the desired confidence level, p is the estimated proportion, and ME is the desired margin of error.

Substituting the values into the formula, we have:

n = (1.645^2 * 0.49 * (1-0.49)) / (0.015^2)

n ≈ 1629

Therefore, a sample size of approximately 1629 people would be recommended to achieve a margin of error of about 1.5% for a 90% confidence level.


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Answer:

last one "kiki" is true...

Answer:

Option 2 and 4

Step-by-step explanation:

2) Number of science questions = (3/4) of total questions

                              = \(\dfrac{3}{4}*24\)

4) Number of marbles in the jar = (3/4) of the total marbles

                  \(=\dfrac{3}{4}*24\)

Answer:

(4, 2.5)

Step-by-step explanation:

The relationship between the linear correlation coefficient r and the slope b of a regression line is that the value of r will always have the same sign as the value of b. So, the correct option is B.

This means that if the slope is positive, indicating a positive relationship between the variables, the correlation coefficient will also be positive. Similarly, if the slope is negative, indicating a negative relationship between the variables, the correlation coefficient will also be negative. It is important to note that the magnitude of r and the magnitude of b may not necessarily be the same. Therefore, option B is the correct answer.

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The area of the shaded sector of the circle obtained using the radius and the angle of the shaded sector is; \(16\frac{2}{3}\) m²

A sector of a circle is a pie shaped part of a circle, consisting of an arc and two radius of the circle.

The details in the drawing includes;

The diameter of the circle = 20 meters

The radius of the circle, r = (20 meters)/2 = 10 meters

The angle of the shaded region and the 120° angle are supplementary angles, therefore;

The angle of the shaded region, θ = 180° - 120° = 60°

The area of sector is; A = (θ/360) × π·r²

Therefore;

A = (60/360) × π × 10² = π·100/6 = π·(50/3) =

The area of the shaded region is; A = π·(50/3) m² =  (16 2/3)·π m²

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Answer:

588 units^2

Step-by-step explanation:

To find the area of the enlarged rectangle, first find the length and width of the enlarged rectangle.

This is 3.5 multiplied by their original measures:

Length = 3.5 x 8 = 28

Width = 3.5 x 6 = 21

Now, area =. LxW = 588 units^2

Hope this helps

Answer:

588 units squared

Step-by-step explanation:

We have a rectangle that has dimensions 8 units by 6 units.

From the problem, we know that this rectangle has been enlarged by a scale of 3.5. Essentially, to obtain the dimensions of the new, bigger rectangle, we multiply the current length (8 units) by 3.5 and the current width (6 units) by 3.5:

new length = 8 * 3.5 = 28 units

new width = 6 * 3.5 = 21 units

Given this, we can now calculate the area.

The area of a rectangle is denoted by A = lw, where l is the length and w is the width.

Here, the length is l = 28 and the width is w = 21. Plug these in:

A = lw

A = 28 * 21 = 588

The answer is thus 588 units squared.

~ an aesthetics lover

8ln(4) is the area encompassed by the curves y = 2/x, y = 8x, and the x-axis.

To determine the area bounded by the given curves, we must first determine the points of intersection. Because y > 0, we only consider the section of the curve between these two points when we solve y = 2/x and y = 8x.

On integrating y = 2/x with respect to x, we will get the area under the curve. We will use limit x = 1/4 to x = 2. For the area above the x axis, the limits will be x = 1/4 to x = 2 for integration of y = 8x with respect to x.

As a result, the area contained by the curves is equal to the difference between these two areas, which is 8ln(4).

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The time is needed between injections is 3.6 hours, i.e., the drug is to be injected again when the number of milligrams reaches 6 mg.

We have the exponential function of number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is

\(D(h)=25 {e}^{ - 0.4 h}\)

We have to solve for h (the numbers of hours) that would have passed when the D(h) (the amount of medication in the patient's bloodstream) equals 6 mg in order to know when the patient needs to be injected again.

\(6 = 25 {e}^{ - 0.4h} \)

\( \frac{6}{25} = \frac{25}{25} {e}^{ - 0.4h} \)

\(0.24= {e}^{ - 0.4h} \)

Taking logarithm both sides of above equation , we get,

\( \ln(0.24) = \ln( {e}^{ - 0.4h)} \)

Using the properties of natural logarithm,

\( \ln(0.24) = - 0.4h\)

\( - 1.427116356 = - 0.4h\)

\(h = \frac{1.42711635}{0.4} = 3.56779089\)

=> h = 3. 6

So, after 3.6 hours, the patient needs to be injected again.

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Answer:

500! Just multiply 5 x 1 then add the remaining 2 zeros :)

Step-by-step explanation:

Thank you!

Answer:

\(\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}\)

\(5 \times 100 \\ = 500\)

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

ΔABC → ΔA'B'C'

7 up and 6 right

(x - 6, y + 7)

ΔA'B'C' → ΔA''B''C''

Reflection over the x-axis

(x, -y)

Answer:

it's A y-intercept hope it helps

Answer:

The given statement that value 5 is an upper bound for the zeros of the function f(x) = x⁴ + x³ - 11x² - 9x + 18  will be true.

Step-by-step explanation:

Given

\(f\left(x\right)\:=\:x^2\:+\:x^3\:-\:11x^2\:-\:9x\:+\:18\)

We know the rational zeros theorem such as:

if \(x=c\) is a zero of the function \(f(x)\),

then \(f(c) = 0\).

As the \(f\left(x\right)\:=\:x^2\:+\:x^3\:-\:11x^2\:-\:9x\:+\:18\) is a polynomial of degree \(4\), hence it can not have more than \(4\) real zeros.

Let us put certain values in the function,

\(f(5) = 448\), \(f(4) = 126\), \(f(3) = 0\), \(f(2) = -20\),

\(f(1) = 0\), \(f(0) = 18\), \(f(-1) = 16\), \(f(-2) = 0\), \(f(-3) = 0\)

From the above calculation results, we determined that \(4\) zeros as

\(x = -3, -2, 1,\) and \(3\).

Hence, we can check that

\(f(x) = (x+3)(x+2)(x-1)(x-3)\)

Observe that,

\(for x > 3\), \(f(x)\) increases rapidly, so there will be no zeros for \(x>3\).

Therefore, the given statement that value 5 is an upper bound for the zeros of the function f(x) = x⁴ + x³ - 11x² - 9x + 18  will be true.

Answer:

Step-by-step explanation:

A

Answer:

2.27

Step-by-step explanation:

1.98+2.50+3.25 = 7.73 - 10.00 = 2.27

Answer:

$2.27

Step-by-step explanation:

Add the prices together

1.98 + 2.50 + 3.25 = 7.73

Susy owes the cashier $7.73 but payed with a $10 bill, so subtract

10 - 7.73 = 2.27

She should get back $2.27

The correct option: b. Reaction times were the longest when people had to read words presented in colored ink.

A seemingly unimportant phenomena called the Stroop effect explains a great deal about how the brain functions.

Thus, the stroop experiment's findings most accurately represent when respondents used to have to read words given in colorful ink, reaction times tended to be the longest.

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The complete question is-

This following question refers to the outcome of the actual experiment (described on the conclusions slides), not the data generated from your performance in particular (which may or may not have matched the real experimental results).

a. Reaction times were the longest when people had to read words presented in black ink.

b. Reaction times were the longest when people had to read words presented in colored ink.

c. Reaction times were the longest when people had to name the color of colored chips/shapes.

d. Reaction times were the longest when people had to name the color of words presented in colored ink.

The causes of variation which are large in magnitude and are not part of the normal variation are known as Outliers.

What is an Outlier? An outlier is a value that is far greater or less than the majority of other values in a given dataset. These may be due to a variety of factors, including statistical errors or data entry mistakes, but they may also represent actual phenomena that have an impact on the overall results. These causes are not typically part of the normal variation of the process. Thus, outliers are not considered a part of the normal variation.

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Answer:

x = 55

Step-by-step explanation:

total number of degrees in a 6-sided figure is (6-2)x180, which is 720°

720/6 = 120

Each angle of a hexagon measures 120°

2x+10 = 720

2x = 110

x = 55

The given statement "If A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have AX · AY = X · Y" is proved.

Given that A is a n * n order matrix.

And X, Y ∈ Rₙ so,

|X - Y|² = (X - Y) * (X - Y)

|X - Y|² = |X|² - 2 * X * Y + |Y|²

2 * X * Y = |X|² + |Y|² - |X - Y|²

Since A is orthogonal matrix so,

2 * (AX * AY) = |AX|² + |AY|² - |AX - AY|²

2 * (AX * AY) = |X|² + |Y|² - |X - Y|²

2 * (AX * AY) = 2 * X * Y

(AX * AY) =  X * Y

Hence the statement is proved.

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The question is incomplete. The complete question will be -

"Suppose that A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have

AX · AY = X · Y"

The weight of the dog is calculated by multiplying its mass of 40.0 kg with the acceleration due to gravity of 9.80 m/s^2, resulting in a weight of 392 N.

The weight of an object is the force exerted on it due to gravity. The formula to calculate weight is

weight = mass x acceleration due to gravity

In this case, the mass of the dog is 40.0 kg, and the acceleration due to gravity on Earth is 9.80 m/s^2. Plugging these values into the formula, we get

weight = 40.0 kg x 9.80 m/s^2

weight = 392 N (Newtons)

Therefore, the weight of the dog is 392 Newtons.

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Given -

ie, length of the mirror, L = 4 feet and breadth of the mirror, B = 7 feet .

To find -

Solution -

As we know to find the area of rectangle we use the formula, Area = L × B

Hence, we will be doing the same.

Area = 4 × 7

Area = 28 square feet

Answer:

28 sq. feet

Step-by-step explanation:

Given:-

To find:-

Solution:-

Area of rectangular bathroom mirror:- L × B

putting the values ,

Area :- 4 × 7 sq. feet

Area:- 28 sq. feet

Answer:

The number of different ways the car can be built is 31 different ways

Step-by-step explanation:

The given options are'

1), Leather seats, 2) Heated seats, 3) Sunroof, 4) Tinted windows, 5), back up camera

Therefore, the number of different ways the car can be built, n, is given as follows;

n = ₅C₁  + ₅C₂ + ₅C₃ + ₅C₄ + ₅C₅

n = 5 + 10 + 10 + 5 + 1 = 31 different ways

The number of different ways the car can be built = n = 31 different ways

The answer would be 14.3

Answer:

30 miles

Step-by-step explanation:

The equation for the hyperbola described is:(x - 7)² / 9 - (y - 8)² / 1 = 1

Graph:

To graph a hyperbola, we first draw the rectangular axes. Next, we plot the foci and the vertices.

Then, we draw the transverse axis, which connects the two vertices, and mark the center of the hyperbola at the midpoint of the transverse axis. Finally, we draw the asymptotes.

The hyperbola described has foci at (7,2) and (7,10) and vertex at (7,8). Thus, the center of the hyperbola is at (7, 8). Since the transverse axis is vertical and passes through the center, we have a vertical hyperbola.

The distance between the foci is 8 units, which is equal to 2c. Therefore, c = 4.The distance between the center and each vertex is 1 unit, which is equal to a.

Therefore, a = 1. Thus, the value of b can be found using the formula b² = c² - a² = 16 - 1 = 15. Therefore, b = √15 ≈ 3.9.The coordinates of the vertices are (7, 8 ± a) = (7, 7) and (7, 9).

The coordinates of the endpoints of the transverse axis are (7, 8 ± a) = (7, 7) and (7, 9).The equation for the asymptotes is y - 8 = ± b/a (x - 7).

Thus, the equations for the asymptotes are:y - 8 = ± 3.9(x - 7) ⇒ y = ± 3.9x/9 + 22/9 and y = ± 3.9x/9 + 14/9.The graph of the hyperbola is shown below:graph of the hyperbola described.

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Answer:

a. -4

Step-by-step explanation:

142 = -6(5n + 1) - 7n

142 = -6*5n + 1*(-6) - 7n  ==> distributive property

142 = -30n + (-6) - 7n

142 = -30n - 6 - 7n

142 = -30n - 7n - 6

142 = -37n - 6

142 + 6 = -37n - 6 + 6

148 = -37n

-37n/(-37) = 148/(-37)

n=-4 ==> a

Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

For many hotels, including the Grand Hotel Toplice, the price of a room will fluctuate depending on  the time of year. Option B

The rates of hotel rooms tend to fluctuate depending on the demand during different seasons and times of high travel activity.

Hotels have a tendency to increase their room rates during peak tourist seasons or notable holiday periods, namely summer vacations or significant local events.

During times when there is less demand or fewer guests, prices may be decreased in order to entice visitors. The demand for hotel rooms and subsequent price changes can be impacted by factors such as climate, nearby activities, and cultural festivities specific to certain periods.

Generally, the room rates at hotels are not directly influenced by additional elements like the individual's gender, nationality, or the time of day.

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The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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