The probability distribution of number of televisions per household in a small town is given below.

x 0 1 2 3
​P(x) ​ 0.05 0.15 0.25 0.55


a. Find the probability of randomly selecting a household that has one or two televisions.
b. Find probability of randomly selecting a household that has one or two televisions

Answer: No, the orders are not independent.

Step-by-step explanation:

If event 1 has some possible outcomes, suppose that we choose a given outcome 1 with a probability P1, and event 2, also with different possible outcomes, we can select an outcome 2, that has a probability P2, and the two events are independent (meaning that the outcome in event 1 does not affect the outcome in event 2, and vice versa)

Then the probability of outcome 1 and outcome 2 happening at the same time is equal to the product of their individual probabilities.

P = P1*P2.

In this case, event 1 is the selection of the pizza, and outcome 1 is the selection of the square pizza, with a probability of 55%.

Event 2 is the selection of the drink, outcome 2 is the order of a soft drink, with a probability of 72%.

If those two events were independent, then the probability that a customer orders a square pizza and a soft drink would be:

P = 0.55*0.72 = 0.396 (or 39.6%)

But we know that the actual probability is 48%.

So this is larger, which means that the outcomes are not independent.

Answer:

x could be 3 or 1

Step-by-step explanation:

x²+3=4x

x²-4x+3=0

(x-3)(x-1)

x could be 3 or 1

The values could be 1 or 3.

In this exercise, you're required to write a mathematical (algebraic) expression for the given word problem and determine which values could be the unknown number.

Translating the word problem into an algebraic expression, we have;

[tex]n^{2} = 4n - 3\\\\n^{2} - 4n + 3 = 0[/tex]

We would solve the quadratic equation by using the factorization method;

[tex]n^{2} - 3n -n + 3 = 0\\\\n(n - 3) - 1(n - 3) = 0\\\\(n - 1)(n - 3) = 0[/tex]

Therefore, the values could be 1 or 3.

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Answer:

slope = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (4, 2)

m = [tex]\frac{2-1}{4-0}[/tex] = [tex]\frac{1}{4}[/tex]

Answer:

the answer would be 1/4

Step-by-step explanation:

Step-by-step explanation:

cot x / (1 + csc x)

Multiply by conjugate:

cot x / (1 + csc x) × (1 − csc x) / (1 − csc x)

Distribute the denominator:

cot x (1 − csc x) / (1 − csc²x)

Use Pythagorean identity:

cot x (1 − csc x) / (-cot²x)

Divide:

(csc x − 1) / cot x

Answer:

84 beads

Step-by-step explanation:

She had 98 beads and lost all but fourteen. So it would be 98 - 14 which would get you 84 beads that the girl has lost

Answer:

1.649 approximately 2

Step-by-step explanation:

S.d = standard deviation = 0.5

Time taken = lead time = 2 weeks

Mean = demand for week = 5 boxes

We are required to find the safety stock to maintain at 99% service level.

At 99% level, the Z value is equal to 2.326.

Therefore,

Safety stock = z × s.d × √Lt

= 2.326 × 0.5 x √2

= 1.649

Which is approximately 2.

Answer:

The Taylor series of f(x) around the point a, can be written as:

[tex]f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....[/tex]

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

[tex]fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}[/tex]

In this exercise we must calculate the Taylor series for the given function in this way;

[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]

The Taylor series of f(x) around the point a, can be written as:

[tex]f(x) = f(a) + f'(a)(x-a)+\frac{1}{2!} f''(a)(x-a)^2+....[/tex]

Here we have:

[tex]f(x) = 4cos(x)\\a = 7\pi[/tex]

Then, let's calculate each part:

[tex]f(a) = 4cos(7\pi) = -4\\df/dx = -4sin(x)\\(df/dx)(a) = -4sin(7\pi) = 0\\(d^2f)/(dx^2) = -4cos(x)\\(d^2f)/(dx^2)(a) = -4cos(7\pi) = 4[/tex]

Here we already can see two things:

1) The odd derivatives will have a sin(x) function that is zero when evaluated in [tex]x=7\pi[/tex].

2) We also can see that the sign will alternate between consecutive terms.

So we only will work with the even powers of the series:

[tex]f(x) = -4 + (1/2!)*4*(x - 7\pi)^2 - (1/4!)*4*(x - 7\pi)^4 + ....[/tex]

So we can write it as:

[tex]f(x)=\sum f_n[/tex]

Such that the n-th term can written as:

[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]

See more abour Taylor series at: brainly.com/question/6953942

Answer:

answer below

Step-by-step explanation:

1. price per gallon of gasoline and total cost of gasoline

2. distance from a door and height of a wheelchair ramp

perfect positive linear relationship:

this is a relation that exists between two variables. The pearson correlation is used to check this relationship and if the relationship is 1.0 then it is established that a positive linear relationship exists

negative linear relationship

this is a relationship between variables where the pearson correlation is less than 0. if the value is -1.0 then a negative linear relatioship exists.

price per gallon of gasoline and total cost of gasoline move in the same direction so it is positive.

distance from a door and height of a wheelchair ramp are negative because they do not move in the same direction.

Answer:

Hey there!

True. You use individuals rules, pieces of evidence, and experimentally found ideas that can be combined to form a general mathematical statement.

Let me know if this helps :)

Answer:

x = ±2

Step-by-step explanation:

log 7 (x^2 + 11) = log 7 15

We know that log a ( b) = log a(c)   means b =c

x^2 + 11 = 15

Subtract 11 from each side

x^2 = 15-11

x^2 =4

Take the square root of each side

sqrt(x^2) =±sqrt(4)

x = ±2

Answer:

4

Step-by-step explanation:

"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.

Answer:

Step-by-step explanation:

The summary of the given statistics data include:

sample size n = 400

sample mean [tex]\overline x[/tex] = 6.86

standard deviation = 4.37

Level of significance ∝ = 0.01

Population Mean [tex]\mu[/tex] = 6.00

Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

To start with the hypothesis;

The null and the alternative hypothesis can be computed as :

[tex]H_o: \mu = 6.00 \\ \\ H_1 : \mu \neq 6.00[/tex]

The test statistics for this two tailed test can be computed as:

[tex]z= \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt {n}}}[/tex]

[tex]z= \dfrac{6.86 - 6.00}{\dfrac{4.37}{\sqrt {400}}}[/tex]

[tex]z= \dfrac{0.86}{\dfrac{4.37}{20}}[/tex]

z = 3.936

degree of freedom = n - 1

degree of freedom = 400 - 1

degree of freedom = 399

At the level of significance ∝ = 0.01

P -value = 2 × (z < 3.936)  since it is a two tailed test

P -value = 2 × ( 1  - P(z ≤ 3.936)

P -value = 2 × ( 1  -0.9999)

P -value = 2 × ( 0.0001)

P -value =  0.0002

Since the P-value is less than level of significance , we reject [tex]H_o[/tex] at level of significance 0.01

Conclusion: There is sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is  5.00 km.

Answer: Find answers in the attachment files

Step-by-step explanation:

Answer:

= - 54

Step-by-step explanation:

- 99 + 3^2•5

- 99 + 9 × 5

- 99 + 45

= - 54

Answer:

Philomena would make more than $14.06 interest in the second month

Step-by-step explanation:

We are not told how much Philomena put initially, but what we are told is that she has more now as she has been making interests.

This means that if the percent interest remains the same, the amount will definitely have to be more.

For example, let's say we had $10 and we had 10% interest that means we now add $1 to make $11. Since we now have $11, 10 percent of that is $1.1. so now we have $11 + $1.1 = $12.1 which is more than $11.

Thus,Philomena would make more than $14.06 interest in the second month.

Answer:

More than 14.06

Step-by-step explanation:

apesex

Answer:

Those ratios could be 3:1

Step-by-step explanation:

[tex] - 3x - 3 = - 3(x + 1) \\ - 3x - 3 = - 3x - 3 \\ - 3x + 3x = - 3 + 3 \\ 0 = 0[/tex]

Step 1: Use 3 to open the bracket

Step 2 : Collect like terms and simplify

Answer = 0

Answer:

3

Step-by-step explanation:

[tex] \sqrt[4] {27} \cdot \sqrt[4] {3} = [/tex]

[tex] = \sqrt[4] {27 \cdot 3} [/tex]

[tex] = \sqrt[4] {3^3 \cdot 3^1} [/tex]

[tex] = \sqrt[4] {3^4} [/tex]

[tex] = 3 [/tex]

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of a rectangle = l × w

where

l is the length

w is the width

From the question

The length of a rectangle six times its width which is written as

l = 6w

Area = 150cm²

Substitute these values into the formula for finding the area

That's

150 = 6w²

Divide both sides by 6

w² = 25

Find the square root of both sides

width = 5cm

Substitute this value into l = 6w

That's

l = 6(5)

length = 30cm

So the perimeter of the rectangle is

2(30) + 2(5)

= 60 + 10

Hope this helps you

Answer:

Reject H₀.

Step-by-step explanation:

In this case, we need to test whether the average student spent less than the recommended amount of time doing homework in statistics.

The provided data is:

S = {20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27}

Compute the sample mean:

[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{12}\cdot [20+29+...+27]=23.167[/tex]

The population standard deviation is σ = 7.

The hypothesis for the test is:

H₀: The average student does not spent less than the recommended amount of time doing homework, i.e. μ ≥ 24.

Hₐ: The average student spent less than the recommended amount of time doing homework, i.e. μ < 24.

(A)

Compute the standardized test statistic value as follows:

[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]

  [tex]=\frac{23.167-24}{7/\sqrt{12}}\\\\=-0.412[/tex]

Thus, the standardized test statistic value is -0.412.

(B)

The significance level of the test is:

α = 0.07

The critical value of z is:

z₀.₀₇ = -1.476

The rejection region is:

(-∞, -0.1476)

(C)

Compute the p-value as follows:

[tex]p-value=P(Z<-0.412)=0.34[/tex]

*Use a z-table.

Thus, the p-value is 0.34.

(D)

Since, p-value = 0.34 > α = 0.07, the null hypothesis was failed to be rejected at 7% level of significance.

Thus, the correct option is (A).

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The correct option is  D

Step-by-step explanation:

From the question the question we are told that

    The researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe.

Generally a confidence interval states to what extent the chances of the true population is within the a given range

 So the 95% confidence interval given in the question as 52.5% and 59.5%  means that the chances of the true population mean being with this given range is 95%

 So given that the the true population mean is within this range then it means that the population mean will be greater than 50%

   So  the statement that best describe and interprets this result is

The results show significant statistical support that most U.S. adults (over 50%) believe that the U. S. Federal government is not doing enough to keep U.S. election safe.

Using concepts of circles, it is found that the angle measure of each slice is of 72º.

--------------------------------------------

--------------------------------------------

5 equal slices, thus:

[tex]\frac{360}{5} = 72[/tex]

The angle measure of each slice is of 72º.

A similar problem is given at https://brainly.com/question/16746988

Answer

Is it C I may have done my math wrong lol

Step-by-step explanation:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of a line given two points first find the slope of the line and use the formula

y - y1 = m( x - x1) to find the Equation of the line using any of the points given

Slope of the line using points

(3,2) and (4,6) is

[tex]m = \frac{6 - 2}{4 - 3} = \frac{4}{1} = 4[/tex]

So the equation of the line using point

( 3 , 2 ) and slope 4 is

Hope this helps you

Answer:

[tex]\boxed{2y^{2} - y - 15}[/tex]

Step-by-step explanation:

Use the FOIL technique in order to distribute the terms properly. FOIL stands for First Terms, Outside Terms, Inside Terms, and Last Terms. In order to properly distribute, multiply the common terms based on the steps in the FOIL technique. So, in this case:

Therefore, multiply the terms:

Then, add or subtract based on the signs:

2y² - 6y + 5y - 15

Then, add like terms to finish simplifying the expression. This leaves you with 2y² - y - 15.

Answer:

2y2 – y – 15

Step-by-step explanation:

(2y + 5)(y – 3)

= 2y(y – 3) + 5(y – 3)

= 2y2 – 6y + 5y – 15

= 2y2 – y –15

Answer:

(a) 2,162,160

(b) 3,003

Step-by-step explanation:

(a) order matters

You can choose from 14 for the first pick. Then you have 13 left for the second pick. Then you have 12 left for the third pick. Keep going until you have 9 left for the 6th pick. The number when order matters is:

total = 14 * 13 * 12 * 11 * 10 * 9 = 2,162,160

(b) Order does not matter

Start with the same number as above for picking 6 out of 14. Since order does not matter, we divide by the number of ways you can arrange 6 items.

Since there are 6! ways of arranging 6 items,

total = 2,162,160/6! = 3,003

The number of ways when the order matters are 121080960.

The number of ways when order does not matters are 3003.

Given,

Choose 6 colors, without replacement, from 14 distinct colors.

We have to find:

- How many ways can this be done, if the order of the choices matters.

- How many ways can this be done if the order of the choices does not matter.

We use permutation when the order of the arrangements matters.

It is given by:

[tex]^ nP_r[/tex] = n! / r!

We use combination when order does not matter.

It is given by:

[tex]^nC_{r}[/tex] = n! / r! (n-r)!

Find the number of ways when order matters.

We have,

n = 14 and r = 6

[tex]^{14}P_{6}[/tex]

= 14! / 6!

= (14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6!) / 6!

= 4 x 13 x 12 x 11 x 10 x 9 x 8 x 7

= 121080960

Find the number of ways when order does not matter.

We have,

n = 14 and r = 6

[tex]^{14}C_{6}[/tex]

= 14! / 6! 8!

= 14 x 13 x 12 x 11 x 10 x 9 / 6 x 5 x 4 x 3 x 2

= 7 x 13 x 11  x 3  

= 3003

Thus,

The number of ways when the order matters are 121080960.

The number of ways when order does not matters are 3003.

Learn more about combination here:

https://brainly.com/question/28134115

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Answer:

x = 10°, y = 10° and z = 160°

Step-by-step explanation:

Given : m∠BAC = 85°

            CA ≅ CB and BD ≅ CD

In the given ΔABC,

Since, CA ≅ CB

Angles opposite to these equal sides will be equal in measure.

m∠BAC ≅ m∠ABC ≅ 85°

Since, sum of interior angles of a triangle = 180°

m∠BAC + m∠ABC + m∠BCA = 180°

85° + 85° + m∠BCA = 180°

m∠BCA = 180° - 170°

m∠BCA = 10°

x = 10°

In ΔBDC,

Since, BD ≅ DC [Given]

Opposite angles to these equal sides will be equal in measure.

Therefore, x° = z° = 10°

Since, x° + y° + z° = 180°

10° + y° + 10° = 180°

y = 180 - 20°

y = 160°

[tex]p^2 - 10pq + 16q^2=\\p^2-2pq-8pq+16q^2=\\p(p-2q)-8q(p-2q)=\\(p-8q)(p-2q)[/tex]

Answer:

(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.

(b) The simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).

(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].

(d) The probability that only one of the three is a man is 0.375.

(e) The probability that all three are women is 0.125.

Step-by-step explanation:

We are given that three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.

(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.

(b) As we know that the gender of each person is noted by the county clerk, which means one is male and another female.

So, the simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).

Here, M is denoted for male and F for female.

(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].

Because there is 50-50 chance of selecting males or females.

(d) The probability that only one of the three is a man is given by;

The total cases in the sample space = 8

Number of cases of only one man out of three = 3

So, the required probability =  [tex]\frac{3}{8}[/tex] = 0.375.

(e) The probability that all three are women is given by;

The total cases in the sample space = 8

Number of cases of all three are women = 1

So, the required probability =  [tex]\frac{1}{8}[/tex] = 0.125.