A right triangle has legs measuring 18 in. and 26 in. What is the length of the hypotenuse? Round to the nearest tenth. A) 18.8 in. B) 31.6 in. C) 44.0 in. D) 100.0 in.

To test the effectiveness of touch therapists, a hypothesis test can be conducted using a significance level of 0.05. The test statistic is calculated by comparing the observed success rate to the expected success rate under the null hypothesis. If the test statistic falls within the critical region, the null hypothesis can be rejected and it can be concluded that the touch therapists are effective.

To test the claim that touch therapists use a method equivalent to random guesses, a hypothesis test can be conducted using a significance level of 0.05. In this case, the null hypothesis would state that the therapists' success rate is no better than random chance, while the alternative hypothesis would state that the therapists are effective. The test statistic can be calculated using the observed success rate and the expected success rate under the null hypothesis. If the test statistic falls within the critical region, which is determined by the significance level, then the null hypothesis can be rejected, suggesting that the touch therapists are indeed effective.

First, let's calculate the expected success rate under the null hypothesis. Since the therapists are guessing randomly, the probability of guessing correctly is 0.5. Therefore, the expected success rate can be calculated by multiplying the total number of trials by the probability of guessing correctly:

Expected success rate = 0.5 * 264 = 132

Next, we can calculate the test statistic using the observed success rate and the expected success rate:

Test statistic = (observed success rate - expected success rate) / sqrt(expected success rate * (1 - expected success rate) / number of trials)

Substituting the values into the formula:

Test statistic = (105 - 132) / sqrt(132 * (1 - 132/264) / 264) = -3.181

Finally, we can compare the test statistic to the critical value. The critical value can be obtained from the Z-table or using statistical software. If the test statistic falls within the critical region (i.e., if it is less than the negative critical value), then we can reject the null hypothesis and conclude that the touch therapists are effective.

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To test the claim that touch therapists use a method equivalent to random guesses, a hypothesis test can be conducted. The data provided is used to calculate the p-value, which is found to be less than 0.05. This suggests that touch therapists are effective.

To test the claim that touch therapists use a method equivalent to random guesses, we can use a hypothesis test. The null hypothesis is that the therapists' accuracy is due to random chance, while the alternative hypothesis is that they are effective. We can use a binomial hypothesis test with a significance level of 0.05. Using the given data, the therapists were correct in 105 out of 264 trials. Calculating the p-value, we find that it is less than 0.05, which means we reject the null hypothesis. Therefore, the results suggest that touch therapists are effective.

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Answer:

x = 5 and -2

Step-by-step explanation:

This question wants the roots, which are when y = 0.

Set the equation equal to 0:

y=x2-3x-10

0=x2-3x-10

Now we can factor this (or use our calculators).

0=(x-5)(x+2)

Separate these by the Zero Product Property.

0 = x-5

x = 5

0 = x+2

x = -2

Answer:

-2 and 5

b on edu 2020

Step-by-step explanation:

edu 2020

Answer:

The correct answer is 0.1714 .

Step-by-step explanation:

There are 6 men and 4 women to be interviewed for jobs.

Total number of arrangements in which they can be called for the interview process is 10!.

Number of ways any two women are interviewed before any man is 4 × 3 × 8!. = 12 × 8!.

Number of ways any three women are interviewed before any man is 4 × 3 × 2 × 7!. = 24 × 7!.

Number of ways all the women are interviewed before any man is 4! × 6!.

Required number of ways in which at least two women being interviewed before any man is given by 12 × 8! + 24 × 7! + 4! × 6! = 864 × 6!.

Required probability is 864 × 6! ÷ 10! = 0.1714

The probability that no man will be interviewed until at least two women have been interviewed is [tex]\( \bxed{\frac{2}{15}} \).[/tex]

Step 1

We may utilise the concept of permutations to estimate the likelihood that no man will be interviewed until at least two women have been interviewed.

Let us examine the case where a minimum of two women are interviewed before a guy is examined. This implies that women must have the first two places in the interview process. Men and women may be appointed to the other positions in any order, following these two positions.

Let's figure out how many options there are to choose the first two slots for women, given that there are four women and six men:

Step 2

Number of ways to select the first woman: [tex]\(4\)[/tex]

Number of ways to select the second woman: [tex]\(3\)[/tex] (since one woman has already been selected for the first position)

The total number of ways to select the first two positions for women is [tex]\(4 \times 3 = 12\).[/tex]

Step 3

After these two positions have been filled with women, the remaining 8 positions (6 men + 2 women) can be filled with the remaining people (4 men + 2 women) in any order. This can be calculated using the permutation formula:

[tex]\[ nPr = \frac{{n!}}{{(n-r)!}} \][/tex]

Where n is the total number of people and r is the number of positions to be filled.

For our scenario, [tex]\( n = 6 + 4 = 10 \)[/tex] and [tex]\( r = 8 \)[/tex]. So, the number of ways to fill the remaining 8 positions is:

[tex]\[ 10P8 = \frac{{10!}}{{(10-8)!}} = \frac{{10!}}{{2!}} = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \][/tex]

Step 4

Now, let's calculate the total number of ways to select the positions for all 10 people:

[tex]\[ 10! \][/tex]

Consequently, the ratio of the number of favourable results to the total number of outcomes represents the likelihood that no guy will be interviewed until at least two women have been interviewed:

[tex]\[ \text{Probability} = \frac{{12 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}}{{10!}} \]\[ \text{Probability} = \frac{{12}}{{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}} \]\[ \text{Probability} = \frac{{12}}{{10!/(10-8)!}} \]\[ \text{Probability} = \frac{{12}}{{10P8}} \]\[ \text{Probability} = \frac{{12}}{{10 \times 9}} \]\[ \text{Probability} = \frac{2}{15} \][/tex]

So, the probability that no man will be interviewed until at least two women have been interviewed is [tex]\( \bxed{\frac{2}{15}} \).[/tex]

Answer:

5/36

Step-by-step explanation:

This is in fractions so that's what i did and its simplified as well

Answer:

The population will be 64 times larger after 96 hours.

Leave a comment if you'd like a more in-depth explanation.

Answer:

64  times as large as the original population.

Step-by-step explanation:

Answer:

1 unit

Step-by-step explanation:

If the circumference is 6, then the arc measured by a 60 degree angle, which is 1/6 of 360, represents 1/6 of the total circumference. Thus the answer is 1.

Answer:

[tex]Unit Price =\$2.5 \:per\: gallon[/tex]

Step-by-step explanation:

15 Gallon of Gas costs $37.50

To determine the Unit Price, we divide the Total Cost by the number of gallons of gas bought.

Unit Price

[tex]=\dfrac{\$37.50}{15gallons}\\Unit Price =\$2.5 \:per\: gallon[/tex]

Answer:

Price per gallon = $2.5 per gallon

Step-by-step explanation:

Given;

Price of 15 gallons = $37.50

Number of gallons = 15

Price per gallon = 37.50/15 = $2.5

Answer:

x = 1.67 about  and y = 4.67 about

Step-by-step explanation:

y = 4x-2 and y = x+3

4x - 2 = x + 3

3x = 5

x = 5/3 = 1.67  about

y = 5/3 + 3 = 5/3 + 9/3 = 14/3 = 4.667

Answer:

1 and 7/10 pounds

Step-by-step explanation:

add.

Answer:

1 and 7/10 pounds

Step-by-step explanation:

Answer:

At Maximum point;

x(max) = 50

p(max) = $100

Maximum revenue = $5,000

Step-by-step explanation:

The price function is;

p(x) = 200 − 2x

where

p is the price (in dollars) at which exactly x trucks will be rented per day.

The revenue function R(x) can be written as;

R(x) = p(x) × x

Substituting p(x) equation;

R(x) = (200-2x)x

R(x) = 200x-2x^2 ........1

To maximize R(x), at maximum point dR/dx = 0

differentiating equation 1;

dR/dx = 200 - 4x = 0

4x = 200

x = 200/4

x = 50

Substituting x = 50 into p(x)

p(50) = 200 - 2(50) = $100

p = $100

Maximum revenue is;

R = p × x = $100×50

R = $5,000

At the level of the maximum point, the value of x(max) should be 50 and the value of p(max) should be $100, Also, Maximum revenue = $5,000.

Since

The price function is;

p(x) = 200 − 2x

Here,

p refer to the price (in dollars) at which exactly x trucks should be rented per day.

Now

The revenue function R(x) should be

R(x) = p(x) × x

Now

R(x) = (200-2x)x

R(x) = 200x-2x^2 ........1

Now

To maximize R(x), at maximum point dR/dx = 0

So,

dR/dx = 200 - 4x = 0

4x = 200

x = 200/4

x = 50

Now

Substituting x = 50 into p(x)p(50) = 200 - 2(50) = $100

p = $100

Now

Maximum revenue is;

R = p × x = $100×50

R = $5,000

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Answer:

  [tex]\dfrac{z}{4}\text{ or }z/4\text{ or }z\div 4[/tex]

Step-by-step explanation:

"The quotient of z and 4" means "z divided by 4." That can be written several ways, as shown above.

Step-by-step explanation:

Given points

( x1 , y1 ) = ( 0, 4)

And

( x2 , y2 ) = ( - 4 , - 3 )

Now

Slope(m)

= ( y2 - y1 ) / ( x2 - x1 )

= ( - 3 - 4) / ( -4 - 0)

= - 7 / - 4

= 7/4

Answer:

m=7/4

Step-by-step explanation:

Answer: the first one

Step-by-step explanation: base×width×height

Answer:

The first choices.

Step-by-step explanation:

The solid is a rectangular prism which means V=l × w × h

Answer:

(7,0)

Step-by-step explanation:

you can 0 in for Y in order to find the x-axis

0=-x+7

-7=-x

x=7

Answer:

(7, 0)

Step-by-step explanation:

We are trying to find the location that the equation crosses the x-axis.

This location is also known as the x-intercept.

To find the x-intercept, you can just set y in the equation to 0 and then solve for x.

0 = -x + 7

-x = -7

x = 7

So, the x-intercept is 7.

X-intercepts always have a y of 0 by definition, so it can be found at the point (7, 0)

Answer:

Probability that the 44 randomly selected laptops will have a mean replacement time of 3.6 years or less is 0.0092.

Yes. The probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.

Step-by-step explanation:

We are given that the replacement times for the model laptop of concern are normally distributed with a mean of 3.8 years and a standard deviation of 0.4 years.

He then randomly selects records on 44 laptops sold in the past and finds that the mean replacement time is 3.6 years.

Let [tex]\bar X[/tex] = sample mean replacement time

The z-score probability distribution for sample mean is given by;

            Z = [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean replacement time = 3.8 years

            [tex]\sigma[/tex] = standard deviation = 0.4 years

            n = sample of laptops = 44

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the 44 randomly selected laptops will have a mean replacement time of 3.6 years or less is given by = P([tex]\bar X[/tex] [tex]\leq[/tex] 3.6 years)

 P([tex]\bar X[/tex] [tex]\leq[/tex] 3.6 years) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] [tex]\leq[/tex] [tex]\frac{3.6-3.8}{\frac{0.4}{\sqrt{44} } }} }[/tex] ) = P(Z [tex]\leq[/tex] -3.32) = 1 - P(Z < 3.32)

                                                            = 1 - 0.99955 = 0.0005 or 0.05%          

So, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.32 in the z table which has an area of 0.99955.

Hence, the required probability is 0.0005 or 0.05%.

Now, based on the result above; Yes, the computer store has been given laptops of lower than average quality because the probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.

Answer:

a. [tex]f(x)= 1.25\ \ \ \ , \ for \ 31.8\leq x\leq 32.6[/tex]

[tex]b. \ P(X=32)=0\\P(X>32.3)=0.375\\P(X<31.8)=0[/tex]

c. No.  Delicious Candy isn't violating any government regulations

Step-by-step explanation:

a.

-A uniform distribution is given by the formula:

[tex]f(x)=\frac{1}{b-a} \ \ \ for \ \ \ a\leq x\leq b[/tex]

#we substitute our values in the formula above to determine the distribution:

[tex]f(x)=\frac{1}{b-a}\\\\=\frac{1}{32.6-31.8}\\\\=1.25\\\\\therefore f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6[/tex]

Hence, the probability density function for the box's weight is given as: [tex]f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6[/tex]

b. The probability of the box's weight being exactly 32 ounces is obtained by integrating f(x) over a=b=32:

[tex]f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32}_{32} {1.25} \, dx \\\\\\=[1.25x]\limits^{32}_{32}\\\\\\=1.25[32.0-32.0]\\\\\\=0[/tex]

Hence,  the probability that a box weighs exactly 32 ounces is 0.000

ii.The probability that a box weighs more than 32.3 is obtained by integrating f(x) over the limits 32.3 to 32.6 :

[tex]f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32.6}_{32.3} {1.25} \, dx \\\\\\=[1.25x]\limits^{32.6}_{32.3}\\\\\\=1.25[32.6-32.3]\\\\\\=0.375[/tex]

Hence, the probability that a box weighs more than 32.3 ounces is 0.3750

iii. The probability that a box weighs less than 31.8 is 0.000 since the weight limits are [tex]31.8\leq x\leq 32.6[/tex].

-Any value above or below these limits have a probability of 0.000

c. Let 32 ounces be the government's stated weight.

[tex]1.25(32.6-32)=0.75\\\\0.75>0.60[/tex]

Hence, Delicious Candy isn't violating any government's regulations.

(a): The required probability density function for the weight of the box of chocolate is 1.25

(b):  The probability that a box weighs (1) exactly 32 ounces is 0

and  (2) more than 32.3 ounces is 0.375

(c): Therefore, Delicious Candy does not violate government regulation.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. Probability can range in from 0 to 1.

Given that,

The uniform distribution between [tex]a = 31.8[/tex] ounce and [tex]b = 32.6[/tex] ounce

Part(a):

The probability density function for the weight of the box of chocolate is,

[tex]\frac{1}{b-a}=\frac{1}{32.6-31.8} \\=1.25[/tex]

Part(b):

(1) P(exactly 32 ounces) = 0, because this is a continuous distribution.

(2) P(more than 32.3 ounces) =[tex]1.25\times (32.6-32.3)=0.375[/tex]

Part(c):

The stated weight of Delicious Candy =  2 pounds

That is, [tex]2\times 16=32[/tex] ounces

P(a candy weigh at least as much as stated) = P(at least 32)

[tex]1.25\times (32.6-32)=0.75[/tex]

So, 75% of candies weigh at least as much as stated.

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Answer:

6

Step-by-step explanation:

Data provided as per the question below:-

Number of students = 4025

Lockers = 805

The calculation of  the largest number of students who must necessarily share a locker is shown below:-

Largest number of students = ((Number of students - 1) ÷ Lockers) + 1

= ((4026 - 1) ÷ 805) + 1

= (4025 ÷ 805) + 1

= 5 + 1

= 6

Answer:

i dont see no angle

Step-by-step explanation:

Angles can be named according to their measure in degrees or position on a plane. Angles are always counted to be positive in the counter-clockwise direction and negative in the clockwise direction.

The name of an angle in Mathematics can vary based on its measure and location. Angles are generally named according to their measure in degrees, and they can be categorized as acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (180 degrees), reflex (greater than 180 degrees), or full (360 degrees).

Angles can also be referred to in terms of their position on a Cartesian plane: angles in the first quadrant are positive and less than 90; in the second quadrant, they are more than 90 but less than 180; in the third quadrant, they exceed 180 but are less than 270; and in the fourth quadrant, they are greater than 270 but less than 360 degrees.

This consistently maintains the rule that angles are defined as positive in the counter-clockwise direction, and negative in the clockwise direction. For example, an angle of 30° south of west is the same as the global angle 210°, or it can also be expressed as −150° relative to the positive x-axis.

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Answer:

Check the explanation

Step-by-step explanation:

US has a comparative advantage in producing rice.

This means US's opportunity cost of producing rice is less than that of Korea.

Korea's opportunity cost of producing rice will be given as:

For producing 9 units of Rice, Korea gives up 5 cars.

For producing 1 unit of rice's, Korea will give up 5/9 units of car.

Kindly check the image below.

If the U.S. has a comparative advantage in producing rice, then [tex]\( X > \frac{54}{7} \).[/tex]

The correct answer is option B.

Comparative advantage in the context of international trade is determined by the opportunity cost of producing one good over another. If the U.S. has a comparative advantage in producing rice, it implies that the U.S. can produce rice at a lower opportunity cost compared to Korea. To analyze the situation, let's consider the production figures provided:

In the U.S., the opportunity cost of producing one unit of rice is 6/7 units of cars. In Korea, the opportunity cost of producing one unit of rice is X/9 units of cars. Since the U.S. has the comparative advantage in rice production, X/9 (opportunity cost for Korea) should be greater than 6/7 (opportunity cost for the U.S.).

Mathematically, this can be expressed as:

[tex]\[ \frac{X}{9} > \frac{6}{7} \][/tex]

To simplify the comparison, multiply both sides of the inequality by 9 to get:

[tex]\[ X > \frac{54}{7} \][/tex]

Therefore, the correct statement is [tex]\( X > \frac{54}{7} \)[/tex] making option B the correct option.

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The question discusses a survey of US teens and their online interaction. It's emphasizing on the statistical data that shows approximately 57% of surveyed teens reported making new friends online. Other data are also relevant to highlight various aspects of teens internet usage.

The question is about a survey conducted on US teens, where 1060 were randomly selected and it was found that 605 of them have made a new friend online. This is relevant to statistics, a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

To calculate the percentage of teens making friends online, it is calculated as follows: (Number of teens reporting making new friends online / Total number of teens surveyed) * 100 = (605/1060) * 100 = 57.08%. This implies that approximately 57% of the surveyed teens reported making new friends online.

The other data provided discuss various aspects of teen internet usage, including use of social media, smartphone adoption, and experiences with digital relationships. The given data can be used to set up and test various statistical hypotheses about teen behavior relating to internet use.

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Answer:

Step-by-step explanation:

x = 7

so 2x is 2 x 7

The answer is 14

Answer:

14

Step-by-step explanation:

when x is 7 then 2x is 7*2

7*2=14

Answer:

No, H is not a subspace of the vector space V.

Step-by-step explanation:

A matrix is a rectangular array in which elements are arranged in rows and columns.

A matrix in which number of columns is equal to number of rows is known as a square matrix.

Let H denote set of all 2×2  idempotent matrices.

H is a subspace of a vector space V if [tex]u+v \in H[/tex] for [tex]u,v \in V[/tex] and   [tex]cu \in H[/tex].

Let [tex]A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}[/tex]

As [tex]A^2=A\times A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}\begin {pmatrix}1&0\\0&1 \end{pmatrix}=\begin {pmatrix}1&0\\0&1 \end{pmatrix}=A[/tex], A is idempotent.

So, [tex]A \in H[/tex]

[tex]A+A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}+\begin {pmatrix}1&0\\0&1 \end{pmatrix}=\begin {pmatrix}2&0\\0&2\end{pmatrix} \\ \left ( A+A \right )^2=\begin {pmatrix}2&0\\0&2\end{pmatrix}\begin {pmatrix}2&0\\0&2\end{pmatrix}=\begin {pmatrix}4&0\\0&4\end{pmatrix}\neq A[/tex]So, A+A is not idempotent and hence, does not belong to H.

So, H is not a subspace of the vector space V.

Yes, H is a subspace of the vector space V. It satisfies the conditions of closure under addition, closure under scalar multiplication, and contains the zero vector.

Yes, H is a subspace of the vector space V. In order for a set to be considered a subspace, it must satisfy three conditions: it must be closed under addition, closed under scalar multiplication, and contain the zero vector. Let's check if H satisfies these conditions:

Since H satisfies all three conditions, it is a subspace of the vector space V.

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Answer:

12+4x

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

8 slices of a pizza cut into 16 pieces is a half of the pizza. A half is 0.5

Find the solution in the attachments

In this exercise we have to use the knowledge of finance and thus plot a graph, this way we have that it corresponds to:

A)[tex]q= 0 \ or \ q=1[/tex]

B) The graph bellow.

C) The points of the grapg bellow.

Knowing that:

[tex]total \ cost = (variable \ cost \ per \ unit + final \ cost \ per \ unit * produced)[/tex]

The data that was informed is;

A) The result is:

[tex]T= (3+2)*9\\T= 59[/tex]

Break even points one the points at which total cost are equal to :

[tex]T(q)= Y_T(9)\\5q= 5\sqrt{9}\\q=\sqrt{9}\\ q= 0 or q=1[/tex]

B) One plot of total cost are total revenue are ploted below. The blue curve is of total revenue and real graph is of total cost.

C) With the graph, it's closes that from q=0 ot q=1. Total revenue dominantes total cost and beyond a=1 the total cost dominands total revenue.

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Answer:

330 degrees.

Step-by-step explanation:

 π radians / 180 degrees = 1

(11 π)/6  radians  *  180  / π  =   11 * 180 / 6  =  11 * 30 = 330 degrees.

After converting into degree we get;

⇒ 11 pi /6 radians = 330 degree

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

The expression is,

⇒ 11 pi /6 radians

Now, To change into degree we can multiply by 180 / π in the given expression as;

⇒ 11 pi /6 radians

⇒ 11 π /6 × 180 / π degree

⇒ 330 degree

Thus, After converting into degree we get;

⇒ 11 pi /6 radians = 330 degree

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Answer:

The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is (0.4894, 0.5706)..

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1004, \pi = 0.53[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.53 - 2.575\sqrt{\frac{0.53*0.47}{1004}} = 0.4894[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.53 - 2.575\sqrt{\frac{0.53*0.47}{1004}} = 0.5706[/tex]

The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is (0.4894, 0.5706)..

The 99% confidence interval for the proportion of American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is approximately 0.502 to 0.558.

To calculate the 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems, we can use the formula:

CI = p ± Z * sqrt((p * (1-p)) / n)

Where:

CI = Confidence interval

p = Proportion of respondents who blamed Barack Obama a great deal or a moderate amount

Z = Z-score corresponding to the desired confidence level

n = Sample size

Given that 53% of respondents blamed Barack Obama a great deal or a moderate amount and the sample size is 1,004, we can calculate the confidence interval as follows:

CI = 0.53 ± Z * sqrt((0.53 * (1-0.53)) / 1004)

Since we want a 99% confidence interval, the corresponding Z-score is 2.58 (obtained from a standard normal distribution table).

Plugging in the values:

CI = 0.53 ± 2.58 * sqrt((0.53 * (1-0.53)) / 1004)

Calculating the standard deviation and rounding to 2 decimal places:

CI = 0.53 ± 2.58 * sqrt(0.53 * 0.47 / 1004)

CI = 0.53 ± 2.58 * sqrt(0.2491 / 1004)

CI = 0.53 ± 2.58 * 0.0157

The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is approximately 0.502 to 0.558.

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Given:

The given expression is [tex]18^{x^{2}+4 x+4}=18^{9 x+18}[/tex]

We need to determine the solution of the given expression.

Solution:

Let us solve the exponential equations with common base.

Applying the rule, if [tex]a^{f(x)}=a^{g(x)}[/tex] then [tex]f(x)=g(x)[/tex]

Thus, we have;

[tex]x^{2}+4 x+4=9 x+18[/tex]

Subtracting both sides of the equation by 9x, we get;

[tex]x^{2}-5 x+4=18[/tex]

Subtracting both sides of the equation by 18, we have;

[tex]x^{2}-5 x-14=0[/tex]

Factoring the equation, we get;

[tex]x^2-7x+2x-14=0[/tex]

Grouping the terms, we have;

[tex](x^2-7x)+(2x-14)=0[/tex]

Taking out the common term from both the groups, we get;

[tex]x(x-7)+2(x-7)=0[/tex]

Factoring out the common term (x - 7), we get;

[tex](x+2)(x-7)=0[/tex]

[tex]x+2=0 \ and \ x-7=0[/tex]

   [tex]x=-2 \ and \ x=7[/tex]

Thus, the solution of the exponential equations is x = -2 and x = 7.

Hence, Option C is the correct answer.