Stefanie swam four-fifths of a lap in the morning and seven-fifteenths of a lap in the evening. How much farther did Stefanie swim in the morning than in the evening?

The variance of the binomial distribution with n = 900 and p = 0.95 is approximately 32.54. Option B is correct.

The binomial distribution describes the probability of obtaining a certain number of successes in a fixed number of independent trials. The variance of a binomial distribution is a measure of how spread out the distribution is. The formula for variance is np(1-p), where n is the number of trials and p is the probability of success on each trial.

In this case, the variance of a binomial distribution with parameters n and p is given by the formula Var(X) = np(1-p).

Plugging in n = 900 and p = 0.95, we get:

Var(X) = 9000.95(1-0.95)

Var(X)  = 900 x 0.0475

Var(X) = 42.75

Rounding this to the nearest hundredth, we get approximately 32.54. Therefore, the answer is option B: 32.54.

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The increase in the volume of the cone is 1,544.78 cm³.

Volume of a cone = 1/3πr²h

1/3 x 8² x 6 x π = 128π cm³

Volume of a cone = 1/3πr²h

1/3 x 17.60² x 6 x π = 619.52π cm³

619.52π cm³ - 128π cm³ = 491π cm³ = 491 x 22/7 = 1,544.78 cm³

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One should budget $60 for fuel to cover the 500-mile trip.

Given that your vehicle gets 25 miles per gallon (mpg), you can calculate the total number of gallons required for the 500-mile trip by dividing the total miles by the mileage per gallon:

Total gallons = Total miles / Mileage per gallon

Total gallons = 500 miles / 25 mpg

Total gallons = 20 gallons

Now that you know you need 20 gallons of gas for the trip, you can calculate the total cost by multiplying the number of gallons by the cost per gallon:

Total cost = Total gallons × Cost per gallon

Total cost = 20 gallons × $3/gallon

Total cost = $60

Therefore, you should budget $60 for fuel to cover the 500-mile trip.

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Answer: 36.5 miles

Step-by-step explanation:

It looks like you have the right idea! You simply need to divide the 438 miles by the 12 days to find the miles traveled per day. This results in 438 / 12 = 36.5

Answer:

$ 30

$ 20

Step-by-step explanation:

Sea el costo fijo xy el costo por km sea y suponiendo que es el mismo para ambos taxis.

De la pregunta obtenemos las dos ecuaciones

\(x+8y=190\quad ...(i)\)

\(x+5y=130\quad ...(ii)\)

Aplicando \((i)-(ii)\)

\(8y-5y=190-130\\\Rightarrow 3y=60\\\Rightarrow y=\dfrac{60}{3}\\\Rightarrow y=20\)

Sustituyendo en \((ii)\)

\(x+5y=130\\\Rightarrow x+5\times 20=130\\\Rightarrow x=130-100\\\Rightarrow x=30\)

Entonces, el costo fijo es de $ 30 y el costo por km es de $ 20.

Therefore, we would use a chi-squared distribution with 12 degrees of freedom to conduct the hypothesis test of the sample.

The degrees of freedom for a chi-squared test of independence with a contingency table with r rows and c columns can be calculated as (r-1)(c-1). In this case, we have a contingency table with 3 rows and 7 columns, so the degrees of freedom would be (3-1)(7-1) = 12. A chi-squared test of independence is a statistical test used to determine if there is a relationship between two categorical variables. It is commonly used to analyze contingency tables, which are tables that display the frequency distribution of two or more categorical variables.

The degrees of freedom (df) for a chi-squared test of independence with a contingency table are calculated using the formula (r-1)(c-1), where r is the number of rows in the table and c is the number of columns.

In this case, we have a contingency table with 3 rows and 7 columns. Therefore, r = 3 and c = 7.

Substituting these values into the formula, we get:

df = (r-1)(c-1)

= (3-1)(7-1)

= 2 x 6

= 12

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Answer:

\(\displaystyle d = \sqrt{82}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 5)

Point (-8, 4)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

0.522

0.063

Step-by-step explanation:

6 x 8.7 = 52.2

6 x 1.05 = 6.3

If we move them both two decimal places then...

0.522

0.063

To determine the sets (U) and (H), let's go through each case:

(i) Determining the sets (U):

U = {} Since U is an empty subset, (U) will also be an empty set.

U = {1}

The set (U) will contain all elements x in X such that xh = x for each element h in G.

Here, the set (U) will be {1, 2, 3} since every permutation in G fixes the element 1.

U = {2}

Similarly, the set (U) will be {1, 2, 3} since every permutation in G fixes the element 2.

U = {3}

Again, the set (U) will be {1, 2, 3} since every permutation in G fixes the element 3.

U = {1, 2}

In this case, (U) will contain the elements that are fixed by every permutation in G.

The set (U) will be {3} since only the permutation (3) fixes both elements 1 and 2.

U = {1, 3}

The set (U) will also be {2} since only the permutation (2) fixes both elements 1 and 3.

U = {2, 3}

Similarly, (U) will be {1} since only the permutation (1) fixes both elements 2 and 3.

U = {1, 2, 3}

In this case, (U) will be the set of all elements x in X since every permutation in G fixes all elements.

(ii) Determining the sets (H):

To determine the sets (H), we need to consider each subgroup H of G:

H = {}

Since H is an empty subgroup, (H) will also be an empty set.

H = {(1)}

The set (H) will contain the elements x in X such that h(x) = x for each element h in H.

Here, (H) will be {1} since only the identity permutation fixes the element 1.

H = {(2)}

Similarly, (H) will be {2} since only the identity permutation fixes the element 2.

H = {(3)}

(H) will be {3} since only the identity permutation fixes the element 3.

H = {(1), (2)}

In this case, (H) will be the set of elements fixed by both the identity permutation and the transposition (1 2).

The set (H) will be {3} since only the transposition (1 2) fixes the element 3.

H = {(1), (3)}

(H) will be {2} since only the transposition (2 3) fixes the element 2.

H = {(2), (3)}

Similarly, (H) will be {1} since only the transposition (1 3) fixes the element 1.(iii) Determining the Galois elements with respect to (7, 0):

The Galois elements with respect to (7, 0) will be the set of all elements x in X such that x^7 = x (or h(x) = x for the permutation (7, 0)).

Since (7, 0) is not a permutation in G, there are no elements in X that satisfy this condition. Thus, the Galois elements with respect to (7, 0) will be an empty

Set X = {1,2,3}, and define G := Sym(X) (the group of the six permutations of X). For each of the eight subsets U of X, define y(U) to be the set of all permutations g of X satisfying u⁹ = u (or g(u) = u) for each element u in U. For each of the six subgroups H of G, define (H) to be the set of all elements x in X satisfying xh = x (or h(x) = x) for each element h in H. (i) Determine, for each of the eight subsets U of X, the set (U). (ii) Determine, for each of the six subgroups H of G, the set (iii) Determine the galois elements with respect to (7,0). (H).

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Answer:

taking away

Step-by-step explanation:

Performing a change of scale we will see that the actual distance is 4 miles.

We know that the scale is:

3/4 inch = 2 miles.

And the distance that Nicole found on the map is (1 + 1/2) inches.

We can rewrrite the scale as:

1 inch = (4/3)*2 miles

1 inch = (8/3) miles.

Then the actual distance will be:

distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.

The correct option is A.

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Answer:

1. 8x +40

2. -6m -18

3. -5x -1

Step-by-step explanation:

please mark as brainlyest

what is the question your trying to find, if you could repile to this so I can try to figure it out. (I'll be heading off soon)

Answer: 9/56

Step-by-step explanation:

Answer:

A because we need the amount of time she played soccer for so we need to add the 2 days together

Step-by-step explanation:

Uma pay in order to replace her stuff as $1000.

According to the scenario, Uma's possessions worth $5,600 were stolen or destroyed due to the burglary. Since this amount is less than the coverage limit, Uma will be eligible for reimbursement from her insurance policy. However, she will still need to pay the deductible.

To calculate how much Uma will pay to replace her stolen items, we need to subtract the deductible from the total loss. In this case, Uma's total loss is $5,600, and her deductible is $1,000. Therefore, the amount she needs to pay out of pocket is $1,000.

To summarize, Uma's insurance policy will cover the remaining amount after she pays the deductible. In this scenario,

Uma will receive reimbursement for

=> ($5,600 - $1,000) = $4,600

from her insurance company.

She can use this amount to replace her stolen or destroyed possessions.

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Answer:

no

Step-by-step explanation:

its is not a solution, however if the equal sign actually looks like

\( \leqslant \)

then it would be yes

Answer:

Not a solution

Step-by-step explanation:

( x, y ) = ( - 3, 4 )

x = - 3

y = 4

Substitute the values of x and y in the equation,

y = 3x + 107

4 = 3 ( - 4 ) + 107

4 = - 12 + 107

4 = 107 - 12

4 ≠ 95

Therefore,

( - 3, 4 ) is not a solution to the

equation y = 3x + 107.

Since the test statistic (-2.24) falls outside the range of the critical values (-1.96 to 1.96), we reject the null hypothesis.

What is sign test?

The sign test is a non-parametric statistical test used to determine whether the median of a distribution is equal to a specified value. It is a simple and robust method that is applicable when the data do not meet the assumptions of parametric tests, such as when the data

The given problem can be solved using the one-sample sign test to test the null hypothesis that the mean of the population is 19.4 minutes against the alternative hypothesis that it is not 19.4 minutes.

(a) Using Table I:

Step 1: Set up the hypotheses:

Null hypothesis (H0): The mean of the population is 19.4 minutes.

Alternative hypothesis (H1): The mean of the population is not 19.4 minutes.

Step 2: Determine the test statistic:

We will use the sign test statistic, which is the number of positive or negative signs in the sample.

Step 3: Set the significance level:

The significance level is given as 0.05.

Step 4: Perform the sign test:

Count the number of observations in the sample that are greater than 19.4 and the number of observations that are less than 19.4. Let's denote the count of observations greater than 19.4 as "+" and the count of observations less than 19.4 as "-".

In the given sample, there are 5 observations greater than 19.4 (18.1, 20.3, 19.3, 19.5, and 20.0), and 15 observations less than 19.4 (18.3, 15.6, 16.8, 17.6, 16.9, 17.0, 16.5, 18.6, 18.8, 19.1, 17.5, 18.5, and 18.0).

Step 5: Calculate the test statistic:

The test statistic is the smaller of the counts "+" or "-". In this case, the test statistic is 5.

Step 6: Determine the critical value:

Using Table I, for a significance level of 0.05 and a two-tailed test, the critical value is 3.

Step 7: Make a decision:

Since the test statistic (5) is greater than the critical value (3), we reject the null hypothesis.

(b) Using the normal approximation to the binomial distribution:

Alternatively, we can use the normal approximation to the binomial distribution when the sample size is large. Since the sample size is 20 in this case, we can apply this approximation.

Step 1: Set up the hypotheses (same as in (a)).

Step 2: Determine the test statistic:

We will use the z-test statistic, which is calculated as (x - μ) / (σ / √n), where x is the observed number of successes, μ is the hypothesized value (19.4), σ is the standard deviation of the binomial distribution (calculated as √(n/4), where n is the sample size), and √n is the standard error.

Step 3: Set the significance level (same as in (a)).

Step 4: Calculate the test statistic:

Using the formula for the z-test statistic, we get z = (5 - 10) / (√(20/4)) ≈ -2.24.

Step 5: Determine the critical value:

For a significance level of 0.05 and a two-tailed test, the critical value is approximately ±1.96.

Step 6: Make a decision:

Since the test statistic (-2.24) falls outside the range of the critical values (-1.96 to 1.96), we reject the null hypothesis.

Rework Exercise 16.16 using the signed-rank test based on Table X:

To provide a more accurate solution, I would need additional information about Exercise 16.16 and Table X.

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The probability that a randomly selected Riverside High School student is in twelfth grade is 0.4 and it can be determined by using probability.

The two-way table shows the estimated number of students who will enroll in three area high schools next year.

A 5-column table has 4 rows.

The first column has entries Mount Woodson High School, Valley High School, Riverside High School, Total number of students.

The second column is labeled Tenth grade with entries 110, 180, 160, 450.

The third column is labeled Eleventh grade with entries 120, 150, 140, 410.

The fourth column is labeled Twelfth grade with entries 80, 120, 200, 400.

The fifth column is labeled Total with entries 310, 450, 500, 1,260.

What is the probability that a randomly selected Riverside High School student is in twelfth grade?

The first column has entries Mount Woodson High School, Valley High School, Riverside High School, Total number of students.

The number of randomly selected Riverside High School students is in twelfth grade = 200,

And Total number of students in Riverside High School is = 500

Therefore,

The probability that a randomly selected Riverside High School student is in twelfth grade is,

\(\rm P(12th \ grade \students ) = \dfrac{Number \ of \ students \ in \ 12th \ grade }{Total\ number \ of \ students}\\\\ P(12th \ grade \students ) = \dfrac{200}{500}\\\\ P(12th \ grade \students )= 0.4\)

Hence, The required probability that a randomly selected Riverside High School student is in twelfth grade is 0.4.

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Answer:

C

Step-by-step explanation:

When arranging indistinguishable objects in such a way that no two objects are in the same row or column, the number of possible arrangements depends on the dimensions of the grid.

The number of ways to arrange indistinguishable objects without any repetitions in a grid, such that no two objects are in the same row or column, depends on the dimensions of the grid. Let's assume the grid has M rows and N columns. In this case, the number of possible arrangements can be determined using combinatorics.

To find the total number of arrangements, we start with the first column. There are M choices for the first object in this column. Moving to the second column, there are M-1 choices since we need to avoid repetition within the same row. Continuing this process, the number of choices decreases by 1 for each subsequent column.

Therefore, the total number of arrangements can be calculated as M x (M-1) x (M-2) x ... x (M-N+1), where N is the number of columns. This can be further simplified as M! / (M-N)!, where "!" represents the factorial operation.

In conclusion, when arranging indistinguishable objects in a grid such that no two objects are in the same row or column, the number of possible arrangements depends on the dimensions of the grid. By applying combinatorial principles, the total number of arrangements can be calculated using the formula M! / (M-N)!.

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Power is the probability that a test correctly rejects a false null hypothesis​.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes—how likely they are—whenever we're uncertain of how an event will turn out.

Power is inversely related to the probability of making a type 2 error (β) which is rejecting the alternative hypothesis when it is true.

The equation of power is:

Power=1-β

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The dealers included in the sample are dealers 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, and 98.

To use systematic random sampling, we need to choose a starting point and a sampling interval. In this case, we are starting with the third dealer in the list, so we need to skip the first two dealers.

Let's assume that the dealers are numbered 1 to 100 in the list. Since we are starting with the third dealer, our starting point is dealer 3. We also need to choose a sampling interval of 5, since we want to select every fifth dealer.

To find out which dealers are included in the sample, we can use the following formula:

Sampled Dealers = Starting Point + (Sampling Interval * Number of Samples)

Using the formula, we can calculate the dealers that are included in the sample as follows:

Sampled Dealers = 3 + (5 * n)

where n is the number of samples.

If we want to select a sample of 20 dealers, we can substitute n = 1 to 20 into the formula to get the following list of dealers:

3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98

Therefore, the dealers included in the sample are dealers 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, and 98.

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The total cost to buy the sedan now would be $326.60.

Total cost refers to the overall cost of production, which includes both fixed and variable components of the cost.

To calculate the total cost to buy the sedan based on the mileage driven, we need to multiply the excess mileage by the cost per mile.

Excess mileage = Total mileage - Allowed mileage

Excess mileage = 48,266 miles - 45,000 miles

Excess mileage = 3,266 miles

Cost for excess mileage = Excess mileage * Cost per mile

Cost for excess mileage = 3,266 miles * $0.10/mile

Cost for excess mileage = $326.60

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Answer:

Since the trianges are similar

then:

Answer:

B

Step-by-step explanation:

The correct option is A) quantitative data.

The stem-and-leaf plot is used to display the distribution of quantitative data.

Stem-and-leaf plots are very useful graphical techniques to represent data of numeric values. It is a way to represent quantitative data graphically with precision and accuracy, and its detailed structure can show the distribution of data.

Each number in a data set is split into a stem and a leaf, where the stem is all digits of the number except the rightmost, and the leaf is the last digit of the number.

Then the stems are listed vertically, and the leaves of each number are listed in order beside the corresponding stem, allowing you to view the overall shape of the data and identify outliers and patterns.

Thus, stem-and-leaf plot is used to display the distribution of quantitative data.

Therefore, the correct option is A) quantitative data.

The stem-and-leaf plot is used to display the distribution of quantitative data.

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Answer:

x^2 - 4x + 5 = 0

Step-by-step explanation:

:)

x = (2 + i) and (2 - i) are the roots of the quadratic equation f(x) = x² - 4x + 5.

The values of variables satisfying the given quadratic equation are called its roots.

Given  (2 + i) and (2 - i) are roots of the quadratic equation.

Let the quadratic equation be f(x).

(x - (2 + i)) and (x - (2 -i)) are the factors of f(x).

Since, f(x) is a quadratic equation, it has only two roots.

f(x) = (x - (2 + i))(x - (2 - i))

f(x) = x² - (2 - i)x - (2 + i)x + (2 - i)(2 + i)

f(x) = x² - 2x + ix - 2x - ix + 4 - i²

f(x) = x² - 4x + 4 + 1

f(x) = x² - 4x + 5

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we find that you would need to deposit approximately $15,000 to have a retirement fund of $93,447 after 41 years, assuming no additional deposits are made to the account.

To calculate the amount you need to deposit now to have a retirement fund of $93,447 after 41 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment (retirement fund)
P = the principal amount (the initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years

In this case, the future value (A) is $93,447, the annual interest rate (r) is 3% (0.03 in decimal form), the number of times interest is compounded per year (n) is 365 (since it is compounded daily), and the number of years (t) is 41.

Plugging in these values into the formula, we get:

93,447 = P(1 + 0.03/365)^(365*41)

To find the principal amount (P), we can isolate it on one side of the equation. Dividing both sides by (1 + 0.03/365)^(365*41), we have:

P = 93,447 / (1 + 0.03/365)^(365*41)

Calculating this expression, we find that you would need to deposit approximately $15,000 to have a retirement fund of $93,447 after 41 years, assuming no additional deposits are made to the account.

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