There are 5000 words in some story. The word "the" occurs 254 times, and the word "States" occurs 92 times. Suppose that a word is selected at random from the U.S. Constitution. • (a) What is the probability that the word "States"? (1 point) • (b) What is the probability that the word is "the" or "States"? (1 point) (c) What is the probability that the word is neither "the" nor "States"? (1 point)

The sample space for rolling a fair seven-sided die is.

Probability theory defines sample space as the complete set consisting of all possible outcomes which can be produced by some random experiment or process.

It is commonly represented by the letter S, and it forms the base for different probability calculations.

In this case, the experiment is rolling of die assuming the die is labelled such that each face has the numbers as 1, 2, 3, 4, 5, 6, and 7 then the sample space would be

S = {1, 2, 3, 4, 5, 6, 7}

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Answer:

88 is the answer to the question

A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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The confidence interval methods for the mean are robust against departures from​ normality, meaning they work well with distributions that​ aren't normal, provided that departures from normality are not too extreme.

A confidence interval for a mean is a range of values that is likely to contain a population mean with a certain level of confidence.

We use the following formula to calculate a confidence interval for a mean:

Confidence Interval = x  +/-  z*(s/√n)

where:

x: sample mean

z: the chosen z-value

s: sample standard deviation

n: sample size

They work well with distributions that​ aren't normal, provided that departures from normality are not too extreme.

This means that the methods of this section are not robust against poor sampling method.

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A student need a raw score of 36.

We can find the raw score (R) of the student by substituting A = 60 into the the formula and then solve for R. That is:

A = 10√R

√R = 60/10

√R = 6

R = 6²

R = 36

Thus, a student need a raw score of 36 to get a passing grade after her score is adjusted.

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Answer:

-27

Step-by-step explanation:

3^4=81

square root of 81 is 9

-6^2=36

9-36=-27

Step-by-step explanation:

association is non linear, it has the shape of a quadratic function.

if it was a neg linear association, you'd see a right line with a neg slope (values of y would decrease as values of x increase)

Answer:  x < 4 and x > -4

===================================================

Work Shown:

-2 | x | > -8

| x | < -8/(-2)

| x | < 4

-4 < x < 4

-4 < x and x < 4

x < 4 and x < -4

x < 4 and x > -4

Side note: the inequality sign flips in the 2nd step because we divided both sides by a negative number. Also, I used the rule that \(| x | < k\) leads to\(-k < x < k\) only when k is positive.

The picture of the drawing of triangle ABC with vertices at A(1,6), B (1,1) and C (5,1) is attached below.

A triangle is known to be a kind of a polygon that is made up of three edges and also made up of  three vertices.

It is regarded as a key shapes in geometry as its vertices is often denoted with A, B, and C.

The points will be taken as: A(1,6),  B(1,1) and C (5,1)

=AB + BC = AC

Therefore, The picture of the drawing of triangle ABC with vertices at A(1,6), B (1,1) and C (5,1) is attached below.

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Regardless of whether statement (1) or statement (2) is true, the difference between the median of Set A and the range of Set B is 44.5.

To answer the question, let's consider each statement separately:

(1) All numbers in Set B are prime numbers:

Since the first four numbers in Set B are 2, 3, 5, and 7, which are all prime numbers, we can conclude that all numbers in Set B are prime numbers.

For Set A, we know that it consists of all positive integers less than 100. The median of Set A would be the middle value when the numbers are arranged in ascending order. Since the set consists of consecutive integers, the median would be the average of the two middle numbers. In this case, the two middle numbers are 49 and 50, so the median would be (49 + 50) / 2 = 49.5.

The range of Set B is the difference between the largest and smallest values in the set. The largest value in Set B is 7, and the smallest value is 2, so the range is 7 - 2 = 5.

Therefore, the difference between the median of Set A (49.5) and the range of Set B (5) is 49.5 - 5 = 44.5.

(2) Each element in Set B is divisible by exactly two factors:

Since each element in Set B is divisible by exactly two factors, it implies that all elements in Set B are prime numbers. The analysis and calculations for Set A and Set B would be the same as in the first case.

Therefore, the difference between the median of Set A (49.5) and the range of Set B (5) is still 49.5 - 5 = 44.5.

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Answer:

90° is correct answer. :)

Answer:

A = 63 m^2

Step-by-step explanation:

The area of a parallelogram is bh

A = bh

The base is 9 and the height is 7

A = 9*7

A = 63 m^2

Answer:

2^12

Step-by-step explanation:

\(16^3= (2^4)^3=2^{(4\cdot 3)}=2^{12}\)

Hope this helps!

Answer:2^12

Step-by-step explanation:

First we find out the expression given

16^3= 4096

Then the options

2^11=2048

2^12=4096

2^64= 18446744073709551616

As you can see only 2^12 equals to 4096

Making 2^12 the answer

Hope my explanation helps!

Answer:

Why did you put the anwer if you want someone to answer it?

Step-by-step explanation:

-m-

The price of the Motorcycle, not including the tax, is $11,500

The price of the motorcycle before the tax, we need to subtract the tax amount from the total price, including the tax. Let's denote the price of the motorcycle before tax as P.

Given:

Tax rate = 12.5%

Tax amount = $1437.50

We know that the tax amount is equal to 12.5% of the price of the motorcycle:

Tax amount = 0.125 * P

We can set up the equation and solve for P:

0.125 * P = $1437.50

To isolate P, divide both sides of the equation by 0.125:

P = $1437.50 / 0.125

Performing the calculation:

P = $11,500

Therefore, the price of the motorcycle, not including the tax, is $11,500.

Tax amount = 0.125 * $11,500 = $1437.50

The tax amount matches the given information, confirming that the price of the motorcycle before tax is indeed $11,500.

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Answer:   B.x^3+4x^2-19x+14 is correct

Step-by-step explanation:

(x + 7)(x2 – 3x + 2)

Multiplying both

x^3-3x^2+2x+7x^2-21x+14

x^3+4x^2-19x+14

After expanding the given equation, the equivalent expression is found to be \(x^3 + 4x^2 -19x +14\)

The correct answer is B

Given expression:

\((x + 7)(x^2 - 3x + 2)\)

To find:

The given expression can be expanded as follows;

\((x + 7)(x^2 - 3x + 2)\\\\remove \ the \ bracket \ by \ multiplying \ through \ with \ "x" \ and \ "7"\\\\x(x^2 - 3x + 2) + 7(x^2 - 3x + 2)\\\\x^3 - 3x^2 + 2x + 7x^2 - 21x+ 14\\\\simplify \ further \ by \ collecting \ similar \ terms \ together\\\\x^3 + (-3x^2 + 7x^2)+ (2x-21x) + 14\\\\x^3 + 4x^2 - 19x+ 14\)

Thus, the equivalent expression of the given equation is \(x^3 + 4x^2 -19x +14\)

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The probability of selecting chocolate of the first type at random is 1/3.

Since there are three types of chocolates with 6 pieces each, there are a total of 18 chocolates in the box.

The probability of selecting chocolate of the first type is the number of chocolates of the first type divided by the total number of chocolates in the box.

Since there are 6 chocolates of the first type, the probability of selecting a chocolate of the first type is:

Probability = (Number of chocolates of the first type) / (Total number of chocolates)

= 6 / 18

= 1/3

Therefore, the probability of selecting chocolate of the first type at random is 1/3.

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There are a total of 56 different ways that 5 cellular telephones can be selected from 8 cellular phones.

This can be calculated using the combination formula:

C(n,k) = n! / (k! * (n-k)!)

where n is the total number of items, and k is the number of items being selected.

Plugging in the values for this problem:

C(8,5) = 8! / (5! * (8-5)!)

= 8! / (5! * 3!)

= (8 * 7 * 6 * 5!)/ (5! * 3!)

= (8 * 7 * 6)/ (3 * 2 * 1)

= 56

Therefore, there are 56 different ways that 5 cellular telephones can be selected from 8 cellular phones.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we can use the right Riemann sum method.

The width of each rectangle, Δx, is given by the interval width divided by the number of rectangles.

In this case, Δx = (π/2 - 0)/4 = π/8.

To calculate the right endpoint values, we evaluate f(x) at the right endpoint of each rectangle.

For the first rectangle, the right endpoint is x = π/8.

For the second rectangle, the right endpoint is x = π/4.

For the third rectangle, the right endpoint is x = 3π/8.

And for the fourth rectangle, the right endpoint is x = π/2.

Now, let's calculate the area for each rectangle by multiplying the width (Δx) by the corresponding height (f(x)):

Rectangle 1: Area = f(π/8) * Δx = 5cos(π/8) * π/8

Rectangle 2: Area = f(π/4) * Δx = 5cos(π/4) * π/8

Rectangle 3: Area = f(3π/8) * Δx = 5cos(3π/8) * π/8

Rectangle 4: Area = f(π/2) * Δx = 5cos(π/2) * π/8

Now, let's calculate the values:

Rectangle 1: Area = 5cos(π/8) * π/8 ≈ 0.2887

Rectangle 2: Area = 5cos(π/4) * π/8 ≈ 0.3142

Rectangle 3: Area = 5cos(3π/8) * π/8 ≈ 0.2887

Rectangle 4: Area = 5cos(π/2) * π/8 ≈ 0

Finally, to estimate the total area, we sum up the areas of all four rectangles:

Total Area ≈ 0.2887 + 0.3142 + 0.2887 + 0 ≈ 0.8916

Therefore, the estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

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Answer:

first one, hope this helped

Step-by-step explanation:

Answer:

168

Step-by-step explanation:

24x7=168

Answer:

In total, the amount of milk every kid combined drank is 672 ounces.

Step-by-step explanation:

If four kids drank 24 ounces of milk for seven days, you would solve it as follows:

First, the amount all the kids drink in one day combined is 96 ounces.

If they drink 96 per day, and they do so for a week (7 days), then that is 96 × 7 because its 96 seven times.

7 × 96 = 672

Answer:

\(x < - 21\)

Step-by-step explanation:

1. Multiply both sides by 3.

\(x < - 7 \times 3\)

2. Simplify 3 × 7 to 21.

\(x < - 21\)

therefor, the answer is x < -21

Answer:

Step-by-step explanation:

Slope intercept form

y + 7 = 3(x  + 4)                 Change all the double minuses to pluses.

y + 7 =  3x + 12                  Remove the brackets.

y + 7 - 7 = 3x + 12-7           Subtract 7 from both sides

y = 3x + 5

Slope

Whatever number is in front of the x is the slope Answer: 3

y intercept

Whatever comes after the plus sign (or minus sign) is the y intercept. It is a single number.  Answer: 5

x intercept.

This occurs when y = 0

0 = 3x + 5                      Subtract 5 from both sides

-5 = 3x + 5 -5

-5 = 3x                            Divide by 3

-5/3 = 3x / 3

-5/3 = x                          

Answer: x_intercept = -5/3

Answer:

angle bac is the answer

Step-by-step explanation:

both rays emanate from the shared point 'a', which will be the vertex of angle bac

Answer:

length of a rectangular is 4x

breadth of a rectangular is 3x

perimeter is 140m

perimeter of rectangular is

put the value and you got the value of x

then;

find area

\(area = l \times b\)

then put the value of length and breadth and x also

then you got the answer...

Answer:

-33/10z-11

Step-by-step explanation:

Answer:

No. She should have multiplied 12 and One-half to solve

6 yards

Step-by-step explanation:

Number of girls = 12

Each girl needs = 1/2 yard of strings

Suzie workings:

12/1 ÷ 1/2

= 12/1 × 2/1

= 24/1

= 24 yards

No. She should have multiplied 12 and One-half to solve

Correct workings:

Total strings needed for 12 girls = 12 × 1/2 yards

= (12*1)/2

= 12/2

= 6 yards

Answer:

The answer is A.

Step-by-step explanation:

I got it right on Edge 2021.

Answer:

C x = 66 : y = 17

Step-by-step explanation:

since 2x - 3 and 129 are vertical angles you know that they are equal so you can make the equation 2x -3 = 129 you add 3 to both sides to get 2x = 132 then you decide by 2 to get x = 66