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a. The minimum sample size needed is 601.

b. The minimum sample size needed using a prior study is 304.

c. The difference between the results from parts (b) and (a) shows that a preliminary estimation of the population proportion can lower the necessary minimum sample size.

The signed, fractional number of standard deviations above the mean value that an event is above is expressed by the dimensionless variable known as the z-score. Among other names, it is also referred to as the normal score, z-value, and standard score. Z-scores are indicative of values that are higher than the mean and lower than the mean.

(a) To find the minimum sample size needed assuming that no prior information is available, we can use the formula:

n = (Zα/2)² *\(\hat p \hat q\)/ E²

where Zα/2 is the z-score corresponding to the desired level of confidence (90% confidence corresponds to a z-score of 1.645), \(\hat p\) is the sample proportion (unknown), \(\hat q = 1 - \hat p\), and E is the maximum error of estimation (2% of the true proportion, or 0.02).

Plugging in the values, we get:

n = (1.645)² * 0.5*0.5 / 0.02² ≈ 601

Consequently, 601 is the required minimum sample size.

(b) To find the minimum sample size needed using a prior study that found that 42% of the respondents said they think Congress is doing a good or excellent job, we can use the formula:

n = (Zα/2)² * \(\hat p \hat q\) / E²

where now we have a preliminary estimate of the population proportion, \(\hat p = 0.42, and \hat q = 1 - \hat p.\)

Plugging in the values, we get:

n = (1.645)² * 0.42*0.58 / 0.02² ≈ 304

Therefore, the minimum sample size needed using a prior study is 304.

(c) The result from part (b) is smaller than the result from part (a), indicating that having a preliminary estimate of the population proportion can reduce the minimum sample size needed. This is because a preliminary estimate can provide a starting point for the sample size calculation, and reduce the variability of the sampling distribution.

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Answer:

NO WRONG (6T)(5S)+7 IS WRONG YOU ARE SOPOSED TO ADD THAT 6+5=11      11+7=18    18 DIVIDED BY 7=2.5

Step-by-step explanation:

SORRY FO CAPLOCK THAT HOW I TYPE SIR

The length of the unknown sides of the triangles are as follows:

CD = 10√2

AC = 10√2

BC =  10

AB = 10

Since, Triangle ACD

ΔACD is a right angle triangle.

Therefore, Pythagoras theorem can be used to find the sides of the triangle.

c² = a² + b²

where

c = hypotenuse side = AD = 20

a and b are the other 2 legs

lets use trigonometric ratio to find CD,

cos 45 = adjacent / hypotenuse

cos 45 = CD / 20

CD = 1 / √2 × 20

CD = 20 / √2 = 20√2 / 2 = 10√2

Hence,

20² - (10√2)² = AC²

400 - 100(2)  = AC²

AC² = 200

AC = √200 = 10√2

Triangle ABC

ΔABC is a right angle triangle too. Therefore,

AB² + BC² = AC²

Using trigonometric ratio,

cos 45 = BC / 10√2

BC = 10√2 × cos 45

BC = 10√2 × 1 / √2

BC = 10√2 / √2 =  10

Hence,

(10√2)² - 10² = AB²

200 - 100 = AB²

AB² = 100

AB = 10

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Answer:

3 cookies

Step-by-step explanation:

After he gave nine cookies to teachers,he have 39 cookies left.He shared 36 cookies to his 18 classmates at the rate of 2 cookies per person.Then,3 cookies remained.I may be wrong but,it is answer according to me.

hope it helps u and keep smiling :)

Answer:

20

Step-by-step explanation:

we expect to have the smae outcome so we just multiply the out puts by 5 to see what would happen after 125 draws

Answer:

it would be “>”, 100% guaranteed.

Answer:

answer is >

Step-by-step explanation:

hope this is helpful

Answer:

inverse operations is with oppisite operations that undo each other.

open circle is circle not filled in to show that the point is a border value and is not included as part of the solution set.  

like terms is terms that have the same varible raised to the same exponent.

ordered pair is a group of two numbers written in the form (x, y) where the x value represents a horizontal position.

the last one numeric expressions is an expression involving only constants

Step-by-step explanation:

Answer:

inverse operations is with oppisite operations that undo each other.

open circle is circle not filled in to show that the point is a border value and is not included as part of the solution set.  

like terms is terms that have the same varible raised to the same exponent.

ordered pair is a group of two numbers written in the form (x, y) where the x value represents a horizontal position.

the last one numeric expressions is an expression involving only constants

Step-by-step explanation:

The value of fluid ounce in millimeter can be calculated by mutliplyin by 29.574 so 12 fluid ounce is 354.882 millileters.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

Per ounce, there are 29.5735296 millilitres (ml) (oz). As a result, the conversion formula for oz to ml is as follows:

ounce x 29.5735296 = ml

The following is the response to the question "What is 12 oz to ml?" when we enter 12 oz into our formula:

12 x 29.5735296

= 354.8823552 12 oz

≈ 354.882 ml

We have also changed the answer to "12 oz to ml?" into a fraction for your convenience. The fractional response to "12 oz to ml?" is as follows:

12 oz ≈ 354 15/17 ml

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The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.

The volume of the building will be calculated by the formula -

Volume = length × breadth × height

Thus, keeping the value of each component of building in the formula to find the volume of the building.

Volume of building = 255 × 255 × 42

Performing multiplication on Right Hand Side of the equation to find the value of volume

Volume of building = 2,731,050 feet³

Therefore, the volume of the building is 2,731,050 feet³.

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Answer:

ײ + y²=1

144 96

a)

b)No.

Step-by-step explanation:

Answer:

\( m = \frac{ \sqrt[3]{243b} }{17} \)

Answer:

Slope of the line is \(-\frac{8}{3}\).

Step-by-step explanation:

Given points are:

(10, 3) and (7, 11)

Here,

x1 = 10 and y1 = 3

x2 = 7 and y2 = 11

Slope of a line is given by

\(m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{11-3}{7-10}\\\\m = \frac{8}{-3}\)

Therefore,

Slope of the line is \(-\frac{8}{3}\).

Answer: the answer is A

Step-by-step explanation:

hope it helps

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Step-by-step explanation:

We have:

f(x) = -5x√4

g(x) = 19x√4

To find (f+g)(x), we add f(x) and g(x) as follows:

(f+g)(x) = f(x) + g(x)

= (-5x√4) + (19x√4)

= (19-5)x√4

= 14x√4

Therefore, (f+g)(x) = 14x.

To find (f-g)(x), we subtract g(x) from f(x) as follows:

(f-g)(x) = f(x) - g(x)

= (-5x√4) - (19x√4)

= (-19-5)x√4

= -24x√4

Therefore, (f-g)(x) = -24x.

To evaluate f+g and f-g for x=16, we substitute x=16 in the expressions we found above:

(f+g)(16) = 14(16) = 224

(f-g)(16) = -24(16) = -384

Therefore, f+g = 224 and f-g = -384 for x=16.

Answer:

(-2, -2)

Step-by-step explanation:

You can isolate one variable, x or y, from any of the given equations and substitute to find the solution.

Let's isolate y from 4x + 3y = -14.

To do this, we can substract 4x to get 3y = -4x - 14.

Then, we divide both sides of the equation by 3 to result in y = -4/3x - 14/3.

Next, substitute -4/3x - 14/3 for y in 8x + 10y = -36.

The equation then becomes 8x + 10(-4/3x - 14/3) = -36.

Multiply the quantity in the parentheses by the given number 10, and the equation is now 8x + (-40/3x) + (-140/3) = -36.

Solve the equation by adding like terms.

8x + -40/3x = -16/3x

-16/3x + -140/3 = -36

You can multiply both sides of the equation by -3 to remove the fraction and negative.

16x + 140 = 108

16x = -32

x = -2

Finally, substitute x in any of the equations to find y.

4(-2) + 3y = -14

-8 + 3y = -14

3y = -6

y = -2

So, the solution is (-2, -2).

To find the solution of the given system of equations, use the method of elimination.

To find the solution of the given system of equations, we can use the method of elimination. Multiply the first equation by 2 to make the coefficients of y in both equations equal:

8x + 6y = -28

8x + 10y = -36

Now subtract the first equation from the second equation:

(8x + 10y) - (8x + 6y) = -36 - (-28)

4y = -8

Divide both sides of the equation by 4:

y = -2

Substitute the value of y into either of the original equations:

4x + 3(-2) = -14

4x - 6 = -14

4x = -8

x = -2

So the solution to the system of equations is (-2, -2).

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Answer:

I hope this helps you...

please mark me as brainliest..

Answer:

He's moving 10 meters a second, and the slope is 1/1

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

3•(-6)=-18

3•(-11)=-33

3•(-14)=-42

3•(-9)=-27

Answer:

B. [ -18 -33]

[ -42 -27]

you have to distribute the x3 to all four numbers in the matrix

For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.

The given system of equations is:

Equation 1: x + 3y = h

Equation 2: -4x + ky = -9

For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.

Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.

For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.

To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.

Solving this equation for ok, we've got:

-1/3 = 4/k

-1 = 12/k

k = -12

Substituting k = -12 returned into the equation -1/3 = 4/k, we've:

-1/3 = 4/(-12)

-1/3 = -1/3

Since the equation holds real for any value of h, there aren't any restrictions at the price of h.

Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

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The system of equations has no solution when k is equal to 12. The value of h can be any real number.

To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.

The given system of equations is:

x + 3y = h

-4x + ky = -9

We can rewrite the second equation as:

-4x + ky = -9

Dividing both sides of the equation by -4, we get:

x - (k/4)y = 9/4

Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.

Therefore, for the system to have no solution, k must be equal to 12.

As for the value of h, it can be any real number since it does not affect the slopes of the lines.

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One possible value of ∠U is 80° (to the nearest degree).

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

To find the possible values of ∠U, we can use the Law of Cosines:

c² = a² + b² - 2ab cos(C)

Where c is the side opposite the angle we want to find (∠U), a and b are the other two sides, and C is the angle opposite side c.

In this case, we want to find ∠U, so we'll use side u as c and sides t and s (which we don't know yet) as a and b, respectively:

u² = t² + s² - 2ts cos(U)

Substituting the given values, we get:

340² = 620² + s² - 2(620)(s)cos(U)

Simplifying:

115600 = 384400 + s² - 1240s cos(U)

Subtracting 384400 and rearranging:

s² - 1240s cos(U) + 268800 = 0

Now we can use the quadratic formula to solve for s:

s = [1240 cos(U) ± √(1240² cos²(U) - 4(1)(268800))]/(2)

Simplifying under the square root:

s = [1240 cos(U) ± √(1537600 cos²(U) - 1075200)]/(2)

s = [1240 cos(U) ± √(409600 cos²(U) + 1742400)]/(2)

s = [620 cos(U) ± √(102400 cos²(U) + 435600)]

Since s must be positive, we can discard the negative solution, and we have:

s = 620 cos(U) + √(102400 cos²(U) + 435600)

Now we can use the fact that the sum of angles in a triangle is 180° to find ∠U:

∠U = 180° - ∠T - ∠S

Since we know ∠T = 110°, we just need to find ∠S. We can use the Law of Sines to do this:

sin(S)/s = sin(T)/t

sin(S) = (s/t)sin(T)

Substituting the values we know:

sin(S) = (620 cos(U) + √(102400 cos²(U) + 435600))/620 * sin(110°)

sin(S) ≈ (1.481 cos(U) + 2.225)/6.959

Now we can use a calculator to find the arcsin of both sides to get ∠S:

∠S ≈ arcsin((1.481 cos(U) + 2.225)/6.959)

Finally, we can substitute the values we found for ∠S and ∠T into the equation we found earlier for ∠U:

∠U = 180° - 110° - arcsin((1.481 cos(U) + 2.225)/6.959)

Simplifying:

∠U = 70° - arcsin((1.481 cos(U) + 2.225)/6.959)

Now we can use trial and error or a graphing calculator to find the values of ∠U that satisfy this equation. One possible solution is:

∠U ≈ 80°

Therefore, one possible value of ∠U is 80° (to the nearest degree).

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First, we can simplify the expression inside the parentheses by dividing both the numerator and the denominator by their greatest common factor, which is 8a^2b^2:

(8a^3b^2/16a^2b^3) = (a/2b)

Now, we can substitute this expression back into the original expression and simplify:

(8a^3b^2/16a^2b^3)^4 = [(a/2b)^4] ^4

= (a^4/16b^4) ^4

= a^16/16^4b^16

= a^16/65536b^16

Therefore, the simplified expression is a^16/65536b^16.

In statistics, a bell-shaped distribution is known as a normal distribution, and it is characterized by a symmetrical shape. The mean and standard deviation are important parameters in a normal distribution, and they are used to calculate the range within which a certain percentage of the data lie.

Specifically, for a normal distribution, about 68% of the data lie within one standard deviation of the mean in either direction.

Given the mean of 14.0 inches and the standard deviation of 0.1 inches, we can calculate the range within which 68% of the outside diameters lie. To do this, we need to calculate the range between the mean minus one standard deviation and the mean plus one standard deviation. This gives us a range of 13.9 inches to 14.1 inches.

Therefore, the correct answer is 13.8 and 14.2 inches is incorrect, and the correct range is 13.9 and 14.1 inches.

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Answer:

Paul should be wearing a light jacket appropriate for about 59 F or 15 °C

Step-by-step explanation:

If it is 4:00 a.m. in Honolulu when it is 2:00 p.m. in London, then the difference between times is:

\(d=14-4\\d=10\ hours\)

London is 10 hours ahead of Honolulu.

If Paul left Honolulu at 12:00 p.m, the corresponding time in London was:

\(t=12+10\\t=22 = 10:00\ p.m.\)

Since he arrived in London at 1:00 p.m. at Friday, the flight time was:

\(F= (24-22)+13\\F=15\ hours\)

The flight took 15 hours in total. If the temperature was 30°C when he boarded the flight and it decreases at a rate of 1°C per hour, the temperature when Paul arrives in London is:

\(T=30-(15*1)\\T=15^oC\)

Converting it to Fahrenheit

\(T=(15*\frac{9}{5})+32 \\T=59\ F\)

Paul should be wearing a light jacket appropriate for about 59 F or 15 °C

Answer:

d

Step-by-step explanation:

We can use the standard normal distribution table or calculate the z-score and find the corresponding area under the curve. The percentage of the population for X ≥ 124.75 is approximately 3.86%.

To find the percentage of the population for X ≥ 124.75, we need to calculate the z-score, which represents the number of standard deviations an observation is from the mean. The formula for the z-score is:

z = (X - μ) / σ

In this case, X is 124.75, μ is 100, and σ is 15. Plugging in these values, we get:

z = (124.75 - 100) / 15 = 1.65

Using the standard normal distribution table or a calculator, we can find the area under the curve to the right of the z-score of 1.65. The area represents the percentage of the population for X ≥ 124.75.

From the standard normal distribution table, we find that the area to the right of the z-score 1.65 is approximately 0.0495. Multiplying this by 100, we get 4.95%.

However, since we are interested in X ≥ 124.75, we need to consider the area to the left of the z-score of 1.65 and subtract it from 1. This gives us:

1 - 0.0495 = 0.9505

Multiplying 0.9505 by 100, we find that the percentage of the population for X ≥ 124.75 is approximately 95.05%. Therefore, the percentage of the population for X ≥ 124.75 is approximately 3.86%.

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Answer:

yes that is true

Step-by-step explanation:

Answer: No

Step-by-step explanation:

9 is not a solution because 9 times -3 would be -27.

hope this helps :)

We can count the days from July 31 to the end of the year, then add the days from the start of the year to January 3, to determine the number of days between those dates and January 3 of the next year.

From July 31 to December 31, there are 0 days in August.

September is a 30 day month.

October is 31 days long.

30 days are in November.

A 31-day month, December.

Total number of days from July 31 to December 31 is 122 days (0 + 30 + 31 + 30 + 31).

January 1 through January 3: Since January includes 31 days, there are 3 days between January 1 and January 3.

Days in total are 122 + 3 = 125.

Consequently, the right response is not

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