Of 99 adults selected randomly from one town, 63 have health insurance. Find a 95% confidence interval for the true proportion of all adults in the town who do not have health insurance.

Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The p-value is 0.024.

The null and alternative hypotheses for the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level are:

H0: p = 0.7 (null hypothesis

)H1: p ≠ 0.7 (alternative hypothesis)

The test is a two-tailed test because the alternative hypothesis includes not equal to (<>) which means either p is less than 0.7 or greater than 0.7

Based on a sample of 500 people, 62% owned cats.

This means that the sample proportion, p = 0.62.

To calculate the p-value, we will use the z-test statistic.

The formula for calculating the z-test statistic is given as:

z = (p - P) / √(PQ/n) where P is the hypothesized proportion (P = 0.7), Q is the complement of P (Q = 1 - P), and n is the sample size.

Using the given values in the formula, we have; z = (0.62 - 0.7) / √(0.7 × 0.3 / 500) = -2.52

The p-value for a two-tailed test at 0.02 level of significance is obtained from the standard normal table.

The area in both tails beyond the z-score of 2.52 is 0.012.

Therefore, the p-value is:

p-value = 2 × 0.012 = 0.024

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In the given situation, "angle 4 is the angle of elevation from the radar tower to the person" is the description of angle 4.In trigonometry, an angle of elevation or inclination is the angle between the horizontal and the line of sight of an observer looking upwards. An angle of depression is the angle between the horizontal and the line of sight of an observer looking downwards.

In the given situation, angle 4 refers to the angle formed between the horizontal and the line of sight from the radar tower to the person. As the angle is formed while looking upwards from the radar tower to the person, it is called the angle of elevation. Hence, the correct description of angle 4 in this situation is "angle 4 is the angle of elevation from the radar tower to the person."

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Answer:

0.25

Step-by-step explanation:

4/16 --> 1/4 and 1/4 = 0.25

It is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space. Let's explain why.

Let A be an m × n matrix, and let x be a nonzero vector in the null space of A, so Ax = 0. We can also say that x is in the null space of A transpose. So x is an element of N(AT).Let’s prove the contradiction that arises from the initial claim by assuming that 3,1,2 is a row vector in the row space of A and 2,1,1 is a column vector in N(AT).We have that A[3 1 2]T = 0 and 2,1,1 is in the null space of A transpose. We also know that if a vector v is in the row space of A, then there exists a vector y such that v = A*y, where y is a column vector. So in this case, we can say that 3,1,2 is in the row space of A if there is a column vector y such that A * y = [3 1 2]T. But if that's the case, then we have the following equation: A* y = [3 1 2]. This can be written as: TA* = [3 1 2]If we then take the transpose of both sides, we have: A* y = [3 1 2]T and TA = [3 1 2]. However, this implies that TA* = TA, which can only be true if A is a symmetric matrix. But A is an m × n matrix, where m and n are not equal, so A cannot be a symmetric matrix. Therefore, it is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space.

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Answer:

12 units

Step-by-step explanation:

1st, I found the distance for the two parallel sides on the hexagon. I counted the lines to be 2 units each, which makes 4 units. And since all sides of a hexagon are equal. All the sides make 12 units, or centimeters. Therefore, the perimeter is 12 units

Answer:

80 minutes.

Step-by-step explanation:

do I need to explain? I hate explaining :(

Answer:

The ratio of perimeter of ABCD to perimeter of WXYZ = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

First, we have to determine the multiplicative factor of the dimensions for both figures.

Considering sides AB and WX,

multiplicative factor = [tex]\frac{12}{8}[/tex]

                                = 1.5

So that:

XY = 6 x 1.5 = 9

YZ = 7 x 1.5 = 10.5

ZW = 7 x 1.5 = 10.5

Perimeter of ABCD = 6 + 7 + 7 + 8

                                = 28

Perimeter of WXYZ = 9 + 10.5 + 10.5 + 12

                                 = 42

The ratio of the perimeters of the two quadrilaterals can be determined as;

ratio = [tex]\frac{perimeter of ABCD}{Perirmeter of WXYZ}[/tex]

       = [tex]\frac{28}{42}[/tex]

       = [tex]\frac{2}{3}[/tex]

The ratio of the perimeter of ABCD to perimeter of WXYZ is [tex]\frac{2}{3}[/tex].

Based on this, a 90% confidence interval for the proportion, p. of adult residents who are parents in this county is 0.787 < p < 0.873.

The point estimate for the proportion is calculated by dividing the number of adults with kids by the total sample size. In this case, the point estimate is 166/200 = 0.83.

To construct the confidence interval, we can use the formula:

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

Where:

p is the point estimate

z is the z-score corresponding to the desired confidence level (90% confidence corresponds to a z-score of approximately 1.645)

n is the sample size

Substituting the values into the formula, we get:

[tex]= 0.83 \pm 1.645 \times \sqrt{\frac{0.83 \times (1-0.83)}{200}}[/tex]

Calculating the values, we can obtain the 90% confidence interval for the proportion of adult residents who are parents.

To construct a 90% confidence interval for the proportion of adult residents who are parents in the county, we can use the sample proportion and the standard error formula. Out of the 200 adult residents sampled, 166 had kids.

we calculate the sample proportion, p-hat:

p-hat = 166 / 200

         = 0.83

Next, we calculate the standard error using the formula:

SE = √((p-hat × (1 - p-hat)) / n)

SE = √((0.83 × (1 - 0.83)) / 200) ≈ 0.025

To construct the confidence interval, we use the formula:

p-hat ± (z × SE)

where, z is the z-score corresponding to the desired confidence level.

For a 90% confidence interval, the z-score is approximately 1.645.

Substituting the values into the formula, we get:

= 0.83 ± (1.645 × 0.025)

Calculating the upper and lower bounds:

Lower bound = 0.83 - (1.645 × 0.025) ≈ 0.787

Upper bound = 0.83 + (1.645 × 0.025) ≈ 0.873

Therefore, the 90% confidence interval for the proportion of adult residents who are parents in the county is approximately 0.787 < p < 0.873.

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Answer:

The A matches the table x+3

The radius of the circle is 144 units.

To find the radius of the circle, we can use the formula that relates the circumference of a circle to its radius and the central angle intercepted by an arc.

The formula is:

Arc length = 2πr * (θ/360)

Where:

Arc length is the length of the intercepted arc

r is the radius of the circle

θ is the central angle in degrees

In this case, we are given that the arc length is 48π and the central angle is 120°. Let's substitute these values into the formula and solve for r:

48π = 2πr * (120/360)

Simplifying the equation:

48 = 2r * (120/360)

48 = r * (1/3)

r = 48 * 3

r = 144

Therefore, the radius of the circle is 144 units.

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Answer:

if x is 16 then 3/4(16) - 12

when you simplify 4 by 16

3(4)-12

12-12=0

9514 1404 393

Answer:

  (d)  512√3

Step-by-step explanation:

The area (A) of a regular hexagon can be computed from its side length (s) using the formula ...

  A = (3√3)/2·s²

Here, the side length is given as ...

  s = 32√3/3 = 32/√3

Then the area is ...

  [tex]A=\dfrac{3\sqrt{3}}{2}\cdot\left(\dfrac{32}{\sqrt{3}}\right)^2=\dfrac{3\sqrt{3}\cdot1024}{2\cdot3}=\boxed{512\sqrt{3}}[/tex]

The area of the hexagon is 512√3 square units.

Answer:

system is:

y = 1/2x

y = 1/2x - 2

No Solution to this system

Step-by-step explanation:

Answer:

mean = 5+9+9+6+6+11+8+4/7 = 8.29

median = 6

mode = 6

range = 11 - 4 = 7

Answer:

Step-by-step explanation:

5 , 9 , 6 , 6 , 11 , 8 , 4

Mean = sum of all data ÷ number of data

         [tex]= \frac{5+9+6+6+11+8+4}{7}\\\\= \frac{49}{7}\\\\= 7[/tex]

Median: To find median, arrange in ascending order and medianis the middle term

4 , 5 , 6 , 6 , 8 , 9 , 11

Middle term = 4th term

Median = 6

Mode: a number that appears most often is mode

6 appears 2 times

Mode = 6

Range:

Range = maximum value - minimum value

          = 11 - 4

          = 7

If the continuous distribution is given then The age of people who have retired represents Normal distribution.

a) The age of people who have retired would likely follow a normal distribution, as it tends to have a symmetric bell-shaped curve.

b) The number of red Smarties in boxes of Smarties would have a discrete distribution, as it can only take on certain whole numbers and cannot be fractionally or continuously measured.

c) The shoe sizes of Stouffvillians may exhibit a bimodal distribution, as there might be two distinct peaks indicating two groups with different average shoe sizes.

d) The wait time between calls to Pizza Pizza could potentially follow an exponential distribution, as it is often used to model the time between events in a Poisson process, such as the arrival of phone calls. The distribution would have a long tail, representing longer wait times occurring less frequently.

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12+85% is $22.20

80%x12=9.6

5%x12=0.6

9.6+0.6=10.2

12+10.2=22.20

 Answer: $22.20  

Answer:

Hi! The answer to your question is B) He can walk 12 miles in 1 minute.

To find Unit rate divide the biggest number by the smallest; Example: [tex]120/10[/tex]

Step-by-step explanation:

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Answer:  h < 6

Step-by-step explanation:

3h - 5 < 13

3h < 18

h < 6

Answer:

h<6

Step-by-step explanation:

If We consider the string w = [tex]CA^pG^pT^pC[/tex], then L ∉ RLs by pumping lemma.

To prove that L ∉ RLs using the RL pumping theorem, we assume L is a regular language and apply the pumping lemma for RLs. Let p be the pumping length of L.

We consider the string w = [tex]CA^pG^pT^pC[/tex], where |w| ≥ p. According to the pumping lemma, we can decompose w into uvxyz such that |vxy| ≤ p, |vy| > 0, and for all k ≥ 0, the string [tex]u(v^k)x(y^k)z[/tex] is also in L.

However, by examining the structure of L, we see that the number of A's and G's is dependent on each other and must match the number of T's.

Since pumping up or down would alter this balance, there is no way to satisfy the condition for all k, leading to a contradiction. Therefore, L cannot be a regular language, and we conclude that L ∉ RLs.

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The average fixed cost of each case will be $25

Average fixed cost = fixed cost / number of cases.

$4500/ 180= $25

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Answer:

$8.75

Step-by-step explanation:

Cost price= $9.75

Selling price= $1.00

profit= C.P-.SP

= 9.75-1.00

= $8.75

The principal should reject her original hypothesis, as the lower bound of the interval is less than 110.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 20 - 1 = 19 df, is t = 2.8609.

The parameters for this problem are given as follows:

[tex]\overline{x} = 108, s = 10, n = 20[/tex]

Then the lower bound of the interval is given as follows:

[tex]108 - 2.8609 \times \frac{10}{\sqrt{20}} = 101.6[/tex]

The upper bound of the interval is given as follows:

[tex]108 + 2.8609 \times \frac{10}{\sqrt{20}} = 114.4[/tex]

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Answer:

The answer is postulate

mode is 4 and the median is also 4

mode is the number that appears the most which is 4 and median is the number that is in the middle when you line up all the numbers in order  (0,2,2,3,3,4,4,4,4,5,5,5,6,6,10)

Answer:

$2000

Step-by-step explanation:

Simple Interest = $70

Rate = 3.5%

Time = 1

Principal = ?

Simple Interest = (Principal × Rate × Time)/100

Principal = (Simple Interest × 100)/(Rate × Time)

Principal = (70 × 100)/(3.5 × 1)

Principal = 7000/3.5

Principal = 14000/7

Principal = 2000

Answer:

I belive the answer is A

Step-by-step explanation:

So any answer with 22t would make sense, so you have A and C. In C though, it is subtracting 22, but since 6195 is the total it would have to include the 22 so it is A.

Answer:

A would be the answer

Step-by-step and