A study of 420,000 cell phones user found that 0.0317% of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0327% for those not using cell phones. Compute parts (a) and (b)

a. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system
______%

1. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among these not using cell phones ? Why and why not?
A. No, because 0.0327% is not included in the confidence interval.
B. No, because 0.0327% is included in the confidence interval.
C. Yes, because 0.0327% is included in the confidence interval.
D. Yes, because 0.0327% is not included in the confidence interval.

Sum of two interiors =Exterior

Use simple way

Angle beside x

Measure of x

Answer:

x = 44°

Step-by-step explanation:

According to the Exterior Angle Theorem of a triangle, the external angle is equal to the sum of the two interior opposite angles of a triangle.  

This is because the interior angles of a triangle sum to 180° and angles on a straight line sum to 180°.

⇒ x = ∠CAB + ∠BCA

⇒ x = 14° + 30°

⇒ x = 44°

Proof

Interior angles of a triangle sum to 180°

⇒ ∠CAB + ∠ABC + ∠BCA = 180°

⇒ 14° + ∠ABC + 30° = 180°

⇒ ∠ABC = 180° - 14° - 30°

⇒ ∠ABC = 136°

Angles on a straight line sum to 180°

⇒ ∠ABC + x = 180°

⇒ 136° + x = 180°

⇒ x = 180° - 136°

⇒ x = 44°

Answer: The answer is: 693 ft^3 or 693ft cubed

Answer:

A.

Step-by-step explanation:

The first question equals 729 and it is the highest, I reccomend using photomath.

Answer:

A

Step-by-step explanation:

-y = -2x+5

y = 2x-5

3x+2(2x-5)= -3

The mean is greater than the median, which in turn is less than the mode, in a unimodal skewed right distribution. Therefore, option c) is the correct answer.

The terms mean, median, and mode are commonly used in statistics to measure the central tendency of a set of

values or a dataset.  The mean is calculated by dividing the sum of all the numbers in a dataset by the total number of

items in the dataset. The mean is the average of the dataset. The median is the middle number in a dataset when the

data is arranged in ascending or descending order. Half of the values are higher than the median, and half are lower.

The mode is the value that appears most frequently in a dataset. If there are two values that occur with the same

frequency, the dataset is referred to as bimodal, and if there are more than two values that occur with the same

frequency, the dataset is referred to as multimodal. In a unimodal skewed right distribution, the mean is greater than

the median, which in turn is less than the mode. Therefore, the correct answer is option c) greater, less than.

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It is proved that if f has a zero at 0 and if Ref(z) > 0 for every ze aD(0; 1), then f has a pole in D(0; 1).

The problem is based on Complex Analysis.

Let U CC be a region containing D(0; 1) and let f be a meromorphic function on U, which has no zeros and no poles on aD(0; 1).

If f has a zero at 0 and if Ref(z) > 0 for every ze aD(0; 1), we need to prove that f has a pole in D(0; 1).

We know that f is meromorphic function on U and we are given that it has a zero at 0. So, we can write the Laurent expansion of f around 0 as: f(z) = anzn+ ... + a1z + a0 + b1z + ... where an ≠ 0 and the expansion is valid in a deleted neighborhood of z=0. This implies that f(z) has a pole of order m at 0 where m is the largest non-negative integer such that am ≠ 0.

Suppose that m = 0 and f(z) has a removable singularity at 0 then by Riemann’s theorem f(z) is bounded in some deleted neighborhood of z = 0 which implies that Ref(z) ≤ M, a contradiction to Ref(z) > 0 for every ze aD(0; 1).

Hence, f(z) has a pole at 0. Therefore, f has a pole in D(0; 1). Hence, we have proved that if f has a zero at 0 and if Ref(z) > 0 for every ze aD(0; 1), then f has a pole in D(0; 1).

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The data set is the most clustered around its mean is

A.4, 10, 8, 6

To determine which data set is the most clustered around its mean, we can calculate the mean and the standard deviation for each data set.

calculate the mean and standard deviation for each data set

Data Set A: 4, 10, 8, 6

Mean: (4 + 10 + 8 + 6) / 4 = 28 / 4 = 7

Standard Deviation: √[(4-7)^2 + (10-7)^2 + (8-7)^2 + (6-7)^2] / 4 ≈ 1.58

Data Set B: 11, 3, 10, 4

Mean: (11 + 3 + 10 + 4) / 4 = 28 / 4 = 7

Standard Deviation: √[(11-7)^2 + (3-7)^2 + (10-7)^2 + (4-7)^2] / 4 ≈ 3.87

Data Set C: 2, 9, 13, 4

Mean: (2 + 9 + 13 + 4) / 4 = 28 / 4 = 7

Standard Deviation: √[(2-7)^2 + (9-7)^2 + (13-7)^2 + (4-7)^2] / 4 ≈ 4.27

Data Set D: 11, 2, 9, 6

Mean: (11 + 2 + 9 + 6) / 4 = 28 / 4 = 7

Standard Deviation: √[(11-7)^2 + (2-7)^2 + (9-7)^2 + (6-7)^2] / 4 ≈ 3.27

Comparing the standard deviations, we find that data set A has the smallest standard deviation of approximately 1.58. this indicates that the data points in Data Set A are the closest to the mean, making it the most clustered around its mean.

Therefore, the answer is A. 4, 10, 8, 6.

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Answer:

11

Step-by-step explanation:

first u 90 minus 67 equals 23

and if u times 11 by 4 equal 44

minus 21 equals 23 which would make the equation true

hope this helped

Answer:

6 feet tall.

Step-by-step explanation:

The boy is 4 ft tall, but he casts a 6 ft long shadow. You need to find how long a shadow would be if a person/thing was just 1 ft tall.

To do this, you would need to divide 4 by 4, and 6 by 4 as well.

6/4 is 1.5, or 1 and a half.

If a person (or a thing) is 1 foot tall, the statue will cast 1 and a half feet long shadow.

The statue casts a 9 ft long shadow.

Since we already figured out 1 ft = 1 and 1/2 ft shadow, and since the statue casts a 9 foot long shadow, you need to divide 9 by 1.5.

(You'll get 6.)

This means that the statue is 6 feet tall, and it casts a 9 foot long shadow.

Answer:

C

Step-by-step explanation:

All you do is take the number choices and plug it into the equation. For example if you take A and plug it in the equation would look like -5(-5) < 25 and -5 times -5 is 25 so you know 25 is equal to 25 not less than.

If you plug in C you get -5(-4) < 25 and -5 times -4 is 20 and 20 is indeed less than 25

The average cost AC when x = 90 is $1, and the derivative C'(x) when x = 90 is $0.41.

The average cost function AC and the derivative of the total cost function C'(x) can be found using the given total cost function C(x) = 0.01x + 0.4x + 50, where x represents the number of units produced and sold.

To find the average cost AC, we divide the total cost C(x) by the quantity x:

AC = C(x) / x

Substituting the given total cost function C(x) = 0.01x + 0.4x + 50, we have:

AC = (0.01x + 0.4x + 50) / x

Simplifying, we get:

AC = (0.41x + 50) / x

When x = 90, we substitute this value into the equation:

AC = (0.41 * 90 + 50) / 90

AC = (36.9 + 50) / 90

AC = 86.9 / 90

AC ≈ $0.97 ≈ $1 (rounded to two decimal places)

To find the derivative C'(x), we differentiate the total cost function C(x) with respect to x:

C'(x) = d/dx (0.01x + 0.4x + 50)

C'(x) = 0.01 + 0.4

C'(x) = 0.41

When x = 90, we substitute this value into the equation:

C'(90) = 0.41

Therefore, the derivative C'(x) when x = 90 is $0.41.

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Answer: Online discussions have a better portrayal of other cultures

Step-by-step explanation:

Unless you are very antisocial then the only good thing that an online group shares is being able to stay safe from corona virus and the ability to speak with each other from different perspectives. Lets say hypothetically I was in a bear watching group where everybody took pictures and discussed bears. If I lived in North Michigan I would see black bears and brown bears. If I lived in more of an arctic region I would see polar bears. You can see how this would throw in a little more content to discuss. Which bears are bigger? Which bears live longer? Which bears have heavier coats? This obviously does not only apply to bears. Books, sports, video games, cars, and more all have different miniature cultures in different states or countries.

Answer:

Facilitating an online conversation may require even more work, so that participants continue engaging with one  another online.

Step-by-step explanation:

Answer:

The domain of a function is the set of the possible input values of the function. For example: consider the function f(x) = cos x, the domain of the function is the set of possible values of x.

The cosine function takes x values from all real numbers.

Therefore, the domain of the cosine function is a real numbers.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the first one cant be a triangle

im pretty sure the second one can

the third one can

im pretty sure the fourth one cant

Answer:

B - Her monthly average would have increased by $19.57. ... Katie works as a waitress and records her monthly tips in the table shown below. If Katie decided not to work the month of November, how would her five month average compare to her six month ... Lisa is currently taking physics as one of her electives in school.

Step-by-step explanation:

Answer:

Nov. ✔ = Feb.

Oct. ✔ < Dec.

Jan. ✔ > Nov.

Step-by-step explanation:

Edge 2022

Answer:

I think its C

Step-by-step explanation:

The center of the sphere can be found by taking the average of the coordinates of points A and B, and the radius of the sphere is half the distance between points A and B.

Let's denote point A as (2, 1, 5) and point B as (6, 2, 22). We want to find the set of points P such that the distance from P to A is twice the distance from P to B.

We can express this condition mathematically as:

|PA| = 2|PB|

Using the distance formula, we can rewrite this equation as:

[tex]\sqrt{(x - 2)^2+ (y - 1)^2 + (z - 5)^2} = 2\sqrt{(x - 6)^2 + (y - 2)^2 + (z - 22)^2}[/tex]

Simplifying the equation, we have:

[tex](x - 2)^2 + (y - 1)^2 + (z - 5)^2 = 4((x - 6)^2 + (y - 2)^2 + (z - 22)^2)[/tex]

Expanding and combining like terms, we get:

[tex]3x^2 + 3y^2 + 3z^2 - 28x - 10y - 96z = 273[/tex]

This equation represents the equation of a sphere. The center of the sphere can be found by taking the average of the coordinates of points A and B, which gives us the center (4, 1.5, 13.5). The radius of the sphere is half the distance between points A and B, which is the square root of 273 divided by 2.

Therefore, the set of all points satisfying the given condition is a sphere with center (4, 1.5, 13.5) and radius √(273/2).

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The z-score table shows that for a z-score of 15.1, the p-value is approximately zero (p < 0.0001). Hence, the p-value for this sample is p < 0.0001.

Given that the population is normally distributed and the standard deviation is σ = 5.2.

A sample of size n = 64 is obtained with the sample mean of M = 78.5.

Test statistic = (Sample mean - population mean) / (Standard error of the mean) = (78.5 - µ) / (σ /√n)

Where µ = population mean = 0σ = 5.2n = 64.

The formula for the standard error of the mean is; σM = σ/√n = 5.2/√64 = 0.65.

Substituting in the test statistic equation,

Test statistic = (78.5 - 0) / 0.65 = 121.54.

P-value is the probability of obtaining the observed sample mean or a more extreme value from the null hypothesis.

Assuming a significance level of α = 0.05 and the null hypothesis H0: µ = 0 (Population mean), we can obtain the p-value from the z-score table.z-score = (sample mean - population mean) / standard deviation = (78.5 - 0) / 5.2 = 15.1

The z-score table shows that for a z-score of 15.1, the p-value is approximately zero (p < 0.0001).Hence, the p-value for this sample is p < 0.0001.

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(a) To prove that B\A = (AB)* using only the above equations and equivalences, we need to show that B\A is equivalent to (AB)*.

First, we will show that B\A is a subset of (AB)*.

Let x be an element of B\A. Then, x is in B and x is not in A. Therefore, x is in AB and not in A. This means that x is in (AB)*. Thus, we have shown that B\A is a subset of (AB)*.

Next, we will show that (AB)* is a subset of B\A.

Let x be an element of (AB)*. Then, x is in AB or x is not in AB.

If x is in AB, then x is in B and x is in A. Therefore, x is not in B\A.

If x is not in AB, then x is not in A or x is not in B. Therefore, x is not in A and x is in B. This means that x is in B\A.

Thus, we have shown that (AB)* is a subset of B\A.

Since we have shown that B\A is a subset of (AB)* and (AB)* is a subset of B\A, we can conclude that B\A = (AB)*.

(b) To prove that B* A* = (AB)*, we need to show that B* A* is a subset of (AB)* and (AB)* is a subset of B* A*.

First, we will show that B* A* is a subset of (AB)*.

Let x be an element of B* A*. Then, x is in (B*) and x is in (A*).

If x is in B*, then x is in B or x is not in B.

If x is in A*, then x is in A or x is not in A.

If x is in B and x is in A, then x is in AB.

If x is not in B and x is not in A, then x is not in AB.

If x is in B and x is not in A, then x is in B\A.

If x is not in B and x is in A, then x is in A\B.

Therefore, we have shown that x is in (AB)*.

Next

Given:

The function is:

[tex]f(x)=x^2-16[/tex]

To find:

The inverse of the function.

Solution:

We have,

[tex]f(x)=x^2-16[/tex]

Step 1: Substitute [tex]f(x)=y[/tex].

[tex]y=x^2-16[/tex]

Step 2: Interchange x and y.

[tex]x=y^2-16[/tex]

Step 3: Isolate y.

[tex]x+16=y^2[/tex]

[tex]\pm \sqrt{x+16}=y[/tex]

[tex]y=\pm \sqrt{x+16}[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex].

[tex]f^{-1}(x)=\pm \sqrt{x+16}[/tex]

Therefore, the inverse function of the given function is [tex]f^{-1}(x)=\pm \sqrt{x+16}[/tex].

Answer:

Step-by-step explanation:

The degree of f(x) is 0.

Its leading coefficient is 13 and the type is constant. Because the function is constant,

f(x = 13 when x --> -∞ and

f(x) = 13  when x --> ∞ .

(How? Because I'm smart like that!! :D)

Answer:

yay

Step-by-step explanation:

yayyayyayyayyayyyayyayayayyayaya

Answer:

D. 5x2 + 28x + 21

Step-by-step explanation:

First you want to find the area of the white rectangle

Then find the area of the beings rectangle

Then subtract beings minus white.

                                     Sorry it’s +21. The first answer in your list

                                      then thats correct

...............................................................................................................................................

5x^2+28x+21 confirmed from Cortez himself

The amount of sales tax is $87.79.

Given a total purchase price of a sofa as $1,254.07 and state taxes of 7%.

We are required to calculate the amount of sales tax.

The amount of sales tax can be calculated by multiplying the purchase price by the sales tax rate.

Let's represent the sales tax rate by `r`.

Therefore, the sales tax formula is expressed as:

Sales tax = r * purchase price

In this case, the rate of the sales tax `r` is 7%.

Therefore, we have:r = 7% = 0.07

Now we substitute the values given into the formula:

Sales tax = 0.07 * $1,254.07= $87.79

Therefore, the amount of sales tax is $87.79.

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The family members were 3 adults and 2 children.

We have given that the,

A family of 10 purchased tickets to the county fair.

Tickets for adults cost $6 and tickets for children cost $3

Total cost is $42.

We have to determine how many family members were adults and children

(3 x 10) + (2 x 6)

30+12=42

Therefore we get 3 adults and 2 children.

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Answer:

The f(x) domain is the set of all values for the function and the function spectrum is the set of all values for which f is defined.

Step-by-step explanation:

Answer:

Domain = all real numbers

Range = y ≥ -4

Step-by-step explanation:

Domain is the x-values, and for parabolas it is almost always all real numbers.

Range is the y-values, and the lowest it gets is -4.

The eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1 are λ₁ = -1, λ₂ = 1, and λ₃ = -1. The corresponding eigenspaces are E₁ = span{[-1, 1, 0]}, E₂ = span{[1, 1, 1]}, and E₃ = span{[-1, 1, 2]}.

Eigenvalues and eigenvectors play a fundamental role in linear algebra, particularly in the study of matrices.

The eigenvalues of a matrix are the values λ for which the equation A = λ has nontrivial solutions, where A is the given matrix and is a non-zero vector. The eigenspace associated with an eigenvalue is the set of all eigenvectors corresponding to that eigenvalue.

To find the eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1, we need to solve the characteristic equation det(A - λI) = 0, where A is the given matrix, λ is an eigenvalue, and I is the identity matrix.

The characteristic equation in this case is (-2 - λ)(λ² + 1) + (1 - λ)(-1) = 0. Simplifying this equation yields λ³ - 2λ² - 2 = 0. This is a cubic equation, and we can use a calculator or Wolfram Alpha to find its roots, which are λ₁ = -1, λ₂ = 1, and λ₃ = -1.

Once we have the eigenvalues, we can find the corresponding eigenvectors by solving the equation (A - λ) = 0 for each eigenvalue.

For λ₁ = -1, solving (A + ) = 0 gives us the eigenvector [-1, 1, 0]. For λ₂ = 1, solving (A - ) = 0 gives us the eigenvector [1, 1, 1].

Finally, for λ₃ = -1, solving (A + ) = 0 gives us the eigenvector [-1, 1, 2]. These eigenvectors span the eigenspaces E₁, E₂, and E₃, respectively.

In summary, the eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1 are λ₁ = -1, λ₂ = 1, and λ₃ = -1. The corresponding eigenspaces are E₁ = span{[-1, 1, 0]}, E₂ = span{[1, 1, 1]}, and E₃ = span{[-1, 1, 2]}.

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Answer:

x - 3 > 10

There were more than

13

board games in Anne's cabinet to start.

Step-by-step explanation:

The variable x represents how many board games were in Anne's cabinet to start. Since she has already picked out 3 board games to bring, the expression x–3 represents how many board games are still in the cabinet.

And, since Anne has more than 10 board games still in her cabinet, x–3 must be greater than 10.

This inequality shows the relationship.

x–3>10

Now, solve for x.

x–3

> 10

x–3+3

> 10+3 Add 3 to both sides

x

> 13 Simplify

So, there were more than 13 board games in Anne's cabinet to start.

The radius of a circle is half of its diameter so the radius of a circle with a diameter of 240 mm is 120.00 mm. Option D is the correct answer.

To find the radius of a circle with a given diameter, you can follow these steps:

Given that the diameter is 240 mm, divide it by 2 to obtain the radius. Recall that the radius is half the length of the diameter.

Radius = Diameter / 2

In this case, Radius = 240 mm / 2 = 120 mm.

Therefore, the radius of the circle with a diameter of 240 mm is 120.00 mm.

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