How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 41 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: x = 35, s = 18.

Answer:

x^2 - 64

Step-by-step explanation:

A difference of squares is a special product in the form (a^2 - b^2)..their factored form is (a - b)(a + b)..

Thus here a = x and b = 8, thus if x + 8 is a factor, then x - 8 is also a factor..

(x + 8)(x - 8) <-- expand this out using difference of squares rules..

= (x)^2 - (8)^2 

= x^2 - 64 <-- answer...

You could also expand that using FOIL (FOIL - first, outer, inner, last)..

(x + 8)(x - 8) 

= (x)(x) + (x)(-8) + (8)(x) + (8)(-8) 

= x^2 - 8x + 8x - 64 <-- the -8x and 8x cancels out..leaving you with..

= x^2 - 64

The difference of squares that has a factor of x+8 is x² - 64.

An algebraic identity is an equality that holds for any values of its variables.

For example, the identity ( x + y )² = x² + 2xy + y²

(x+y)² = x² + 2xy + y²

(x+y)²=x²+2xy+y² holds for all values of x and y.

As, Difference of two squares

x² - y² = (x - y)(x + 8)

So, for difference of squares that has (x -8) as one of the factor.

The other factor is (x + 8)

So, we can write

(x - 8)(x + 8) = x² - 8²

                    =  x² - 64.

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Answer:

7

Step-by-step explanation:

63 ÷ 9 = 7

Answer:

-6 and +8

Step-by-step explanation:

Hi there,

The best way to think about these is the fact that the sum is very small, but the product is big. So, these numbers must:

1. have a large absolute difference, since their sum is so small

2. the numbers are relatively close to each other in magnitude. Otherwise, you wouldn't get such a big product.

-6 * 8 = -48

-6 + 8 = +2

This makes sense, because they have a large absolute difference of 14 (8+6). Also, as absolute value +6 and +8 are pretty close to each other.

Keep practicing and have fun.

Answer:

A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. so its A

Step-by-step explanation:

i looked it up and i think this is right :)

Answer:

The area of a sector of a circle = 19.2325

Step-by-step explanation:

Explanation:-

Given θ be the measure of angle and radius of circle

The area of a sector of a circle (see diagram)

                                        [tex]A = \frac{theta}{360} \pi r^{2}[/tex]

Given the radius of circle 'r' = 7cm and given angle θ = 45°

The area of a sector of a circle

                                      [tex]A = \frac{45}{360} \pi( 7)^{2}[/tex]

  Use pi =3.14

                                      [tex]A = \frac{45X 3.14( 7)^{2}}{360}[/tex]

                                      A = 19.2325

Final answer:-

The area of a sector of a circle = 19.2325

Answer:

  $7.54

Step-by-step explanation:

Using the two-point form of the equation of a line, we can write the equation for the number tickets (t) as a function of price (p).

  t = (t2 -t1)/(p2 -p1)(p -p1) +t1

  t = (930 -1160)/(7 -5)(p -5) +1160

  t = -230/2(p -5) +1160

  t = -115p +1735 = -115(p -15 2/23)

The revenue from ticket sales will be the product of the price and the number of tickets sold:

  r = pt = p(-115)(p -15 2/23)

This is the equation of a downward-opening parabola with zeros at p=0 and p=15 2/23. The vertex of the parabola (maximum revenue) will be found at a ticket price halfway between these values. The price for maximum revenue is ...

  (0 +15 2/23)/2 = 7 25/46 ≈ 7.54

Rosalie should charge $7.54 per ticket to obtain the most revenue.

Answer:

x=test value before , y = test value after

The system of hypothesis for this case are:

Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]

Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]

If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:

Null hypothesis: [tex]\mu_d = 0[/tex]

Alternative hypothesis: [tex]\mu_d \neq 0[/tex]

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

Let put some notation  

x=test value before , y = test value after

The system of hypothesis for this case are:

Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]

Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]

If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:

Null hypothesis: [tex]\mu_d = 0[/tex]

Alternative hypothesis: [tex]\mu_d \neq 0[/tex]

Answer:

By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 190

Standard deviation = 14

Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?

148 = 190 - 3*14

So 148 is 3 standard deviations below the mean.

232 = 190 + 3*14

So 232 is 3 standard deviations above the mean

By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232

Answer:

The vertex of the function is at (2,3).

Step-by-step explanation:

I graphed the equation on the graph below.

If this answer is correct, please make me Brainliest!

The vertex of the graph of the function [tex]f(x)=2(x-2)^2+3[/tex] is at (2, 3). This is obtained by comparing the given function of the graph with the vertex form function of a parabola.

Given that the function of the graph is [tex]f(x)=2(x-2)^2+3[/tex].

We have the vertex form as [tex]y=a(x-h)^2+k[/tex]

So, the graph shows a parabola for the given equation.

On comparing the given equation with the vertex form,

f(x)=y, a=2, h=2, and k=3.

Then, (h, k)=(2, 3)

It is shown in the graph below.

Therefore, the vertex of the graph is at the point (2, 3).

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Answer:

line graph

Step-by-step explanation:

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.5

For the alternative hypothesis,

p < 0.5

Considering the population proportion, probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

P = 42/100 = 0.42

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

n = 400

z = (0.42 - 0.5)/√(0.5 × 0.5)/400 = - 3.2

Recall, population proportion, p = 0.5

We want the area to the left of 0.5 since the alternative hypothesis is lesser than 0.5. Therefore, from the normal distribution table, the probability of getting a proportion < 0.5 is 0.00069

So p value = 0.00069

Since alpha, 0.05 > than the p value, 0.00069, then we would reject the null hypothesis.

Therefore, there is significant evidence to conclude that that less than 50% of people under the age of 25 check social media sites right after they wake up.

Answer:

the interest amount is $240

Step-by-step explanation:

I hope it helps.

Answer:

The probability that the mean amplifier output would be greater than 364.8 watts in a sample of 52 amplifiers is 0.3156

Step-by-step explanation:

Mean output of amplifiers = 364

Standard deviation = [tex]\sigma[/tex] = 12

We have to find the probability that the mean output for 52 randomly selected amplifiers will be greater than 364.8. Since the population is Normally Distributed and we know the value of population standard deviation, we will use the z-distribution to solve this problem.

We will convert 364.8 to its equivalent z-score and then finding the desired probability from the z-table. The formula to calculate the z-score is:

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

x=364.8 converted to z score for a sample size of n= 52 will be:

[tex]z=\frac{364.8-364}{\frac{12}{\sqrt{52} } }=0.48[/tex]

This means, the probability that the output is greater than 364.8 is equivalent to probability of z score being greater than 0.48.

i.e.

P( X > 364.8 ) = P( z > 0.48 )

From the z-table:

P( z > 0.48) = 1 - P(z < 0.48)

= 1 - 0.6844

= 0.3156

Since, P( X > 364.8 ) = P( z > 0.48 ), we can conclude that:

The probability that the mean amplifier output would be greater than 364.8 watts in a sample of 52 amplifiers is 0.3156

The mean of a distribution indicates its central tendency, with more observations clustering around this central value in a normally distributed dataset.

When examining various distributions, the mean of each distribution is a critical value that gives information about the central tendency of the data. In a normally distributed dataset, the mean is at the peak of the bell curve, suggesting that more observations cluster around this central value.

As for different types of distributions, such as binomial or normal, knowing the mean helps us compare them effectively.

For instance, if both distributions are normal with the same mean, they will overlap, but varying standard deviations will affect the spread of the data around that mean. The larger the standard deviation, the wider the distribution.

Additionally, the concept of skewness also affects the mean. In a positively skewed distribution, the mean is higher than the median, while in a negatively skewed distribution, the mean is less than the median. Considering skewness helps gauge the data's asymmetry and the mean's position relative to other central tendency measures.

Understanding the characteristics of a probability distribution, especially the normal distribution, which is symmetrical about its mean, is fundamental in statistics. The probability density functions have properties that allow us to predict the likelihood of outcomes within a range, expressed through confidence intervals or the standard deviation.

Answer:

See explaination

Step-by-step explanation:

Kindly check attachment for the step by step solution of the given problem.

Answer:

The second number is 40

Step-by-Step:

There is a pattern in the ratio table: you need to multiply the first number by 4, and the answer is the second number. So if the first number is 10, you will need to multiply that by 4 to get the second number. So the second number is 40

Answer:

  $4,508.64

Step-by-step explanation:

The compound interest formula can answer this for you.

  A = P(1 +r/n)^(nt)

where A is the account balance, P is the principal invested (4000), r is the annual interest rate (.02), n is the number of times per year interest is compounded (4), and t is the number of years (6).

Putting the given values into the formula, doing the arithmetic tells us ...

  A = $4000(1 +.02/4)^(4·6) = $4000·1.005^24 ≈ $4,508.64

There will be $4,508.64 in the account at the end of 6 years.

Answer:

its 9 to 12 is greater than 4 to 6.

Step-by-step explanation:

As per the given question, the correct option is the ratio 9 to 12 is greater than 4 to 6.

In comparing the ratios 9 to 12 and 4 to 6, we first need to simplify both ratios. The ratio 9 to 12 can be simplified by dividing both numbers by their greatest common divisor, which is 3. This gives us a simplified ratio of 3 to 4.

Similarly, the ratio 4 to 6 can be simplified by dividing both numbers by their greatest common divisor, which is 2, giving us a simplified ratio of 2 to 3.

If we convert both ratios to decimals by dividing the first number by the second in each pair, we'll find that 9/12 = 0.75 and 4/6 = 0.67, which shows that the first ratio is greater. Therefore, we find that the correct statement is the ratio 9 to 12 is greater than 4 to 6.

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Answer:

a) Eᶜ = {13,14,15,16,17,18}

The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

b) P(Eᶜ) = (1/2) = 0.5

P(Upper E Superscript c) = (1/2) equals 0.5

Step-by-step explanation:

The set that represents the universal set with all the sample spaces is set S and is given by

Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

S = {7,8,9,10,11,12,13,14,15,16,17,18}

Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSet

Event E = {7,8,9,10,11,12}

a) Find Eᶜ

Eᶜ is the complement of event E; it includes all the outcomes in the universal set, S, that are not in the event E

Eᶜ = {13,14,15,16,17,18}

The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

b) P(Upper E Superscript c) = P(Eᶜ)

= n(Eᶜ) ÷ n(S)

Each outcome is equally likely, hence,

n(Eᶜ) = number of outcomes in the event Eᶜ = 6

n(S) = number of outcomes in the set S = 12

P(Eᶜ) = (6/12) = (1/2) = 0.5

Hope this Helps!!!

Answer:

196

Step-by-step explanation:

7 x 13 = 91 + 105

Answer:

1323

Step-by-step explanation:

Answer:

P(Y and R) = P(Y)*P(R) + P(R)*P(Y)

P(Y and R) = 16/125 = 0.128 = 12.8%

Step-by-step explanation:

There are 8 Yellow marbles in the bag

There are 9 Green marbles in the bag

There are 3 Purple marbles in the bag

There are 5 Red marbles in the bag

The total number of marbles in the bag are

Total marbles = 8 + 9 + 3 + 5 = 25

We want to find the probability of selecting two marbles that is one Yellow marble and one Red marble from the bag.

The probability of selecting a Yellow marble is given by

P(Y) = number of Yellow marbles/total number of marbles

P(Y) = 8/25

The probability of selecting a Red marble is given by

P(Y) = number of Red marbles/total number of marbles

P(Y) = 5/25

P(Y) = 1/5

It is possible that the first marble selected is Yellow and the second is Red, and it is also possible that first marble selected is Red and the second is Yellow.

P(Y and R) = P(Y)*P(R) + P(R)*P(Y)

P(Y and R) = (8/25)*(1/5) + (1/5)*(8/25)

P(Y and R) = 16/125

P(Y and R) = 0.128

P(Y and R) = 12.8%

Answer:

probability of selecting one yellow and one red = 2/15

Step-by-step explanation:

We are told there are;

8 yellow marbles

9 green marbles

3 purple Marbles

5 red Marbles

Since two Marbles are selected,

Number of ways of selecting one yellow and one red is:

C(8,1) x C(5,1) = 8!/(1!(8 - 1)!) x 5!/(1!(5 - 1)!)

This gives 40

Now, the total number of Marbles in the question will be;

8 + 9 + 3 + 5 = 25 Marbles

Thus, number of ways to select any two Marbles from the total is;

C(25,2) = 25!/(2!(25 - 2)!) = 300

Thus; probability of selecting one yellow and one red = 40/300 = 2/15

Answer:

I.

Scalene triangle

Step-by-step explanation:

Answer:

3/20

Step-by-step explanation:

because there is only 3 purple socks out of 20 socks total

Answer:

p^7

Step-by-step explanation:

p^5⋅p^2  =   p ^(5+2) =  p^7

Answer:

y  =  0.5x + 10

Step-by-step explanation:

Step 1 :

Identify the independent and dependent variables.

The independent variable (x) is the square footage of floor space.

The dependent variable (y) is the monthly rent.

Step 2 :

Write the information given in the problem as ordered pairs.

The rent for 600 square feet of floor space is $750 :

(600, 750)

The rent for 900 square feet of floor space is $1150 :

(900, 1150)

Step 3 :  

Find the slope.  

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute (600, 750) for (x₁, y₁) and (900, 1150) for (x₂, y₂).

m  =  (1150 - 750) / (900 - 600)

m  =  400 / 300

m  =  4/3

Step 4 :  

Find the y-intercept.

Use the slope 4/3 and one of the ordered pairs (600, 750).

Slope-intercept form :  

y  =  mx + b

Plug m = 4/3,  x = 600 and y = 750.  

750  =  (4/3)(600) + b

750  =  (4)(200) + b

750  =  800 + b

-50  =  b

Step 5 :  

Substitute the slope and y-intercept.

Slope-intercept form

y  =  mx + b  

Plug m = 4/3 and b = -50

y  =  (4/3)x + (-50)

y  =  (4/3)x - 50  

Problem 2 :

Hari’s weekly allowance varies depending on the number of chores he does. He received $16 in allowance the week he did 12 chores, and $14 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.

Solution :  

Step 1 :

Identify the independent and dependent variables.

The independent variable (x) is number of chores Hari does per week

The dependent variable (y) is the allowance he receives per week.  

Step 2 :

Write the information given in the problem as ordered pairs.

For 12 chores, he receives  $16 allowance :  

(12, 16)

For 8 chores, he receives  $14 allowance :  

(8, 14)

Step 3 :  

Find the slope.  

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute (12, 16) for (x₁, y₁) and (8, 14) for (x₂, y₂).

m  =  (14 - 16) / (8 - 12)

m  =  (-2) / (-4)

m  =  1/2

m  =  0.5

Step 4 :  

Find the y-intercept.

Use the slope 0.5 and one of the ordered pairs (8, 14).

Slope-intercept form :  

y  =  mx + b

Plug m = 0.5,  x = 8 and y = 14.  

14  =  (0.5)(8) + b

14  =  4 + b

10  =  b

Step 5 :  

Substitute the slope and y-intercept.

Slope-intercept form

y  =  mx + b  

Plug m = 0.5 and b = 10

y  =  0.5x + 10

Answer:

f(-2) = 0

Step-by-step explanation:

If x + 2 is a factor, then f(x) = 0 when x + 2 = 0.

x + 2 = 0

x = -2

f(-2) = 0

For the polynomial, f(0) = 2 and f(-2) = 0.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given x+2 is a factor,

And values of x from the options are x = 0, -2 and 2.

We will put the values of x to the factor,

f(0) = 0 +2 = 2

f(-2) = -2 +2 = 0

f(2) = 4

Therefore from the result only two options satisfy the factor and those are f(0) = 2 and f(-2) = 0.

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Answer:

x=3

Step-by-step explanation:

24-9

15/5

3

x=3

Answer:

x = 3

Step-by-step explanation:

3 * 5 + 9 =24

Answer:

The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%

Step-by-step explanation:

Average time to find a new job for someone over 55 years = μ = 22 weeks

Standard deviation = σ = 2 weeks

We have to find the probability that if 8 workers are selected at random what will be the probability that it will take them more than 20 weeks to find a job. So, this means that the sample size is n = 8.

Since, the distribution is normal and we have the value of population standard deviation, we will use the z-distribution to find the desired probability. For this, first we need to convert the value (20 weeks) to its equivalent z-score. The formula to calculate the z-score is:

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

x = 20, converted to z-score will be:

[tex]z=\frac{20-22}{\frac{2}{\sqrt{8}}}=-2.83[/tex]

Thus, probability of time being greater than 20 weeks is equivalent to probability of z score being greater than - 2.83.

i.e.

P( X > 20 ) = P( z > -2.83 )

Using the z-table we can find this probability:

P( z > -2.83 ) = 1 - P( z < -2.83)

= 1 - 0.0023

= 0.9977

Since, P( X > 20 ) = P( z > -2.83 ), we can conclude that:

The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%

The probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 99.77%.

To solve this problem, we need to use the concepts of the sampling distribution of the sample mean and the properties of the normal distribution. Here are the steps to find the probability that the average time for eight workers over the age of 55 to find a job is more than 20 weeks:

Step 1: Understand the given data

- Mean time[tex](\(\mu\))[/tex] = 22 weeks

- Standard deviation [tex](\(\sigma\))[/tex] = 2 weeks

- Sample size [tex](\(n\))[/tex]  = 8 workers

The sample mean [tex]\(\bar{X}\)[/tex] for a sample of size (n) from a normal distribution with mean [tex]\(\mu\)[/tex] and standard deviation [tex]\(\sigma\)[/tex] is itself normally distributed with:

- Mean:[tex]\(\mu_{\bar{X}} = \mu\)[/tex]

- Standard deviation: [tex]\(\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}\)[/tex]

Calculate the standard deviation of the sample mean:

[tex]\[\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{8}} = \frac{2}{2.828} \approx 0.707\][/tex]

We want to find the probability that the sample mean [tex]\(\bar{X}\)[/tex] is greater than 20 weeks. First, we convert this to a Z-score:

[tex]\[Z = \frac{\bar{X} - \mu_{\bar{X}}}{\sigma_{\bar{X}}}\][/tex]

Calculate the Z-score for [tex]\(\bar{X} = 20\)[/tex]  weeks:

[tex]\[Z = \frac{20 - 22}{0.707} = \frac{-2}{0.707} \approx -2.83\][/tex]

Using standard normal distribution tables or a Z-score calculator, we find the probability that (Z) is less than -2.83.

The cumulative probability for (Z = -2.83) is approximately 0.0023. This represents the probability that the sample mean is less than 20 weeks. However, we want the probability that the sample mean is more than 20 weeks:

[tex]\[P(\bar{X} > 20) = 1 - P(\bar{X} \leq 20) = 1 - 0.0023 = 0.9977\][/tex]

The probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 0.9977, or 99.77%.

Therefore, we can conclude that there is a very high probability (99.77%) that the average time for these eight workers to find a job is more than 20 weeks.

Answer:

Step-by-step explanation:

Please kindly go through the attached file for a step by step approach to the question.

The question discusses a scenario where the voltage output of a microphone, denoted by X, has a uniform distribution from -1 to 1. A hard limiter is applied which limits the output of X (denoted as Y) between -0.5 and 0.5, regardless of X's value.

We have been given that X is a uniform distribution from -1 to 1. This essentially means that each value between -1 and 1 has an equal probability of occurring. A 'hard limiter' is applied with cutoff values of -0.5 and 0.5. Hence, the output Y is related to X as follows:

This indicates that any voltage output greater than 0.5 or less than -0.5 will be limited, leading Y to fluctuate only between -0.5 and 0.5, irrespective of the value of X. Thus, the 'hard limiter' acts as a sort of boundary for the voltage output.

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