A random sample of 92 sophomores are asked whether they plan to attend Homecoming. Of these, 51 sophomores said they will attend. What is the margin of error at 90% confidence and its interpretation?

The ordered pairs of the given graph are;

(-2, 3), (4, 2), (0, -3), (2, -5), (-5, -4)

An ordered pair is defined as a composition of the x coordinate and the y coordinate, having two values written in a fixed order within parentheses.

Ordered Pair = (x, y)

Where;

x = abscissa, the distance measure of a point from the primary axis “x”

y = ordinate, the distance measure of a point from the secondary axis “y”

Thus the ordered pairs of the given graph are;

(-2, 3), (4, 2), (0, -3), (2, -5), (-5, -4)

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The length of the square base is thus [tex]2 x 3\sqrt{2}/2 = 3\sqrt{2}[/tex] = A

Consequently, a hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape. It is created by precisely cutting a spherical along its diameter, leaving behind two identical hemispheres.

EXPLANATION; Let ABCDE be the pyramid with ABCD as the square base. Let O and M be the center of square ABCD and the midpoint of side AB respectively. Lastly, let the hemisphere be tangent to the triangular face ABE at P.

Notice that triangle EOM has a right angle at O. Since the hemisphere is tangent to the triangular face ABE at P, angle EPO is also 90 degree. Hence, triangle EOM is similar to triangle EPO.

OM/2 = 6/EP

OM = 6/EP x 2

OM = [tex]6\sqrt{6^2 - 2^2} x 2 = 3\sqrt{2}/2}[/tex]

The length of the square base is thus [tex]2 x 3\sqrt{2}/2 = 3\sqrt{2}[/tex] = A

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The solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3

The statement is given as:

5x+3 is greater than or equal to x-9

Express as an inequality

5x + 3 >= x - 9

Collect the like terms

5x - x >= -9 - 3

Evaluate the like terms

4x > = -12

Divide both sides by 4

x >= -3

Hence, the solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3

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Using sampling concepts, the population being studied is all visitors that are flying to the state of Hawaii.

The problem is incomplete, but researching it on a search engine, it asks for us to identify who is the population of this study.

In this problem, a set of visitors traveling to Hawaii were sampled, hence the population being studied is all visitors that are flying to the state of Hawaii.

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Answer:

-7 i + 43

Step-by-step explanation:

Simplify the following:

(-4 i + 3) (6 i + 7) - (-3 i + 2)

(3 - 4 i) (7 + 6 i) = 3×7 + 3×6 i - 4 i×7 - 4 i×6 i = 21 + 18 i - 28 i + 24 = 45 - 10 i:

(-10 i + 45) - (-3 i + 2)

-(-3 i + 2) = 3 i - 2:

45 - 10 i + (3 i - 2)

45 - 10 i - 2 + 3 i = (45 - 2) + (-10 i + 3 i) = 43 - 7 i:

Answer:  -7 i + 43

Her commission for the week was $234.

It is given the total earning in past week = $3,925  and jean earns 4% for the first $2000

So, the commission = $2000 x 4/100  = $80

To find additional sales, the formula to refer is

Add –on sales = total sales – base sales

                          = 3,925 – 2000

                          = 1,925

For the $1,925 sales, Jeans earns 8% commission, Her commission

                                                     = 1,925*0.08    = $154

So, the total commission = $80 + $154  = $234

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The information is no complete yet. The additional fact that is needed to prove that both triangles are congruent by SAS is: AD ≅ CD.

The Side-Angle-Side (SAS) is a triangle congruence theorem that is used to prove that two triangles are congruent to each other if they have two pairs of corresponding congruent sides and a pair of included congruent angles.

The diagram given gives us the following information:

A pair of congruent sides - BD ≅ BD

A pair of congruent angles - <ADB ≅ CDB.

Thus, the information is no complete yet. The additional fact that is needed to prove that both triangles are congruent by SAS is: AD ≅ CD.

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a)

[tex]z=4.658\\p_v=P(z > 4.65)=1-P(z < 4.65)=1.581x*10^{-6}[/tex]

b) By assuming a significance level of α = 0.05 and observing that [tex]p_v[/tex] > α, we can reject the null hypothesis at this level of significance. And in this instance, it makes sense that more than 50% of Americans believe that the Civil War still has an impact on American politics and political life.

c) The confidence interval at 90% would be shown (0.527;0.593).

About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.

a)

1) The presented data and the notation "n=1507" refer to the random sample of Americans, "X" denoting the proportion of those Americans in the sample who believe that the Civil War is still significant to American politics and political life, and "p cap" denoting the estimated number of those Americans.

Since the problem specifies that majority  α=0.05 represents the significance threshold, [tex]p_0[/tex] is the number that we wish to test (no given, but is assumed)

Z would stand for the statistic (interesting variable), and [tex]p_v[/tex] for the p value (variable of interest)

P is the percentage of the public that believes that the Civil War still has an impact on American politics and political life.

2) Useful concepts and formulas

The allegation that more Americans than 50% believe the Civil War is still significant to American politics and political life needs to be tested through a hypothesis (Majority). :

Alternative Hypothesis: p[tex]\geq[/tex] 0.5

Null Hypothesis: p[tex]\leq[/tex] 0.5

The proportion is thought to have a normal distribution.

This test for the percentage of union membership has one tail higher.

Verify whether the sample conforms to the presumptions required for the test to be applied.

a) The random sample must be representative; in this situation, there is no mention of this issue, but it is safe to presume that it exists.

b) The sample size must be sufficient.

[tex]np_0=1507*0.5=753.5 > 10\\n(1-p_0)=1507*(1-0.5)=753.5 > 10[/tex]

3. Determine the statistic.

The formula used to calculate the statistic is as follows:

[tex]z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }= \frac{0.56-0.5}{\sqrt{\frac{0.5(1-0.5)}{1507} } }=4.658[/tex]

P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]

According to the alternative hypothesis, the following would be the p value:

P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]

Using this formula, the confidence interval would be determined.

p ± [tex]z_{\frac{\alpha }{2}}\sqrt{\frac{p(1-p)}{n} }[/tex]

With the value of [tex]\alpha[/tex] and [tex]\alpha _2[/tex], we can get the quantile necessary for the interval in the normal standard distribution for the 90% confidence interval.

[tex]z_{\frac{\alpha }{2} }=2.58[/tex]

adding the following to the formula for the confidence interval:

[tex]0.56-2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.527\\0.56+2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.593[/tex]

Also provided would be the 90% confidence interval (0.527;0.593).

About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.

And because the interval does not contain the value of 0.5, we can conclude that, at a 90% level of confidence, the percentage of Americans who believe that the Civil War is still relevant to American politics and political life is higher than 0.5. This result is consistent with the result of part b.

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Answer:

Fe2 is elemental iron and Fe2O3 is a compound

Answer:

Step-by-step explanation:

Fe2 is elemental iron and Fe2O3 is a compound of iron and oxygen.

The square root of 255 is approximately 15.969.

Given,

Root 255, [tex]\sqrt{255}[/tex]

We have to find the square root of the number:

Square root of a number:

A number multiplied by itself is the square root of that number. Or we may say that after adding a number to itself, we must calculate its square root in order to go back to the original number. The square root of p, if it is a positive integer, is represented by p, so that p = q.

Now,

√255 = 15.9687194227

Which is approximately equals to 15.969

That is,

The square root of 255 is approximately 15.969

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Answer: q(r(5))= 3

Step-by-step explanation: sub in 5 for x in r(x). Once you do that, you'll get -3 for r(5). Now sub in the value of r(5), -3, for x in q(x). Then you'll end up with -9 once the equation has been evaluated.

Answer:

d:1

Step-by-step explanation:

the answers will always be negative and the other side will always be positive

The volume of the sphere is 2144.7cm³.

Given that a sphere with radius 8 cm.

As we all know that the volume of sphere is 4/3πr³.

We will find the volume of sphere by substituting the value of radius in the formula, we get

Volume=4/3 πr³

Now, we will substitute r=8 cm in above formula, we get

V=(4/3)π(8 cm)³

V=(4/3)π(512)cm³

Now, we will simplify this by multiply by 4, we get

V=(2048/3)πcm³

Now, we will simplify it by dividing it with 3, we get

V=682.66π cm³.

As we know, the value of π is 3.14.

So, we will substitute this value and simplify it, we get

V=682.66×3.14

V=2144.66 cm³

Hence, the volume of the sphere when the radius is 8cm is 2144.7 cm³.

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Four numbers has a sum of 1764 and the value of one of those numbers is 1029.

Use algebraic expressions to solve for the value of n.

Algebraic expression is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc).

One of the four numbers is already denoted as variable n. Let m be the sum of the three other numbers.

If the sum of the four numbers is 1,764, then:

n + m = 1764

If n is 40% more than the sum of the other three numbers, then:

n = 40% m + m

n = 1.4 m

Substitute n from the 2nd equation to the 1st equation.

n + m = 1764

1.4 m + m = 1764

2.4 m = 1764

m = 735

Recall that n = 1.4 m.

n = 1.4 (735)

n = 1029

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Answer: 7

Step-by-step explanation:

(fg)(-1/3)=

f(g(-1/3))=

f(3(-1/3) + 1)=

f(-1 + 1)=

f(0)=

0²- 7=7

x(5) is approximately equal to 1.466.

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The equation which represents the net profit of the charity organization is y = 45x-810.

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Answer:

put 244 add 7e8ue

Step-by-step explanation:

i53838 divede 73838

Answer:

(25,20) , (45,36)

Step-by-step explanation:

I THINK??

Answer: an acute angle so it bout 55

Step-by-step explanation:

Answer:

The number will be x

Step-by-step explanation:

2(x + 4) = 3(x - 2)

2x + 8 = 3x - 6

14 = x

Answer:

Step-by-step explanation:

if * means multiplication

the equivalent expression will be :

[tex]\frac{2.14}{2.2} = \frac{7}{7} = 7[/tex]

If the * means power :

then equivalent expression will be

[tex]\frac{2^{14} }{2^{2} } = 2^{(14-2)} =2^{12}[/tex]

Answer:

[tex]6.45*10^{-9}[/tex]

Step-by-step explanation:

Answer:

k = 4.33

Step-by-step explanation:

Cos 30 = 0.8660

Tan 60 = 1.732

2 Tan 60 = 2 (Tan 60)

2 Tan 60 = 2 (1.732)

2 Tan 60 = 3.464

Cos 30 + Tan 60  = 0.8660 + 3.464 = 4.33

k = 4.33