a fair coin is tossed 25 times. what is the probability that at most 22 heads occur?
a) 0.999922
b) 0.000078
c) 0.999990
d) 0.000069
e) 0.000010

Step-by-step explanation:

14x-3=4x+13+6x+2(sum of two interior angle is equal to exterior)

14x-4x-6x=13+2+13

4x=28

x=28/4

x=7

14x-13=14*7-13=85

4x+13=4*7+13=85

6x+2=6*7+2=44

To summarize: If points a and b are in a straight line, the distance traveled and the displacement will be the same. If points a and b are not in a straight line, the distance traveled will be greater than the displacement.

The distance traveled refers to the total length covered during the journey, regardless of the direction taken. On the other hand, displacement refers to the change in position from the starting point to the ending point, taking into account the direction of travel.

Neglecting the curvature of the corners implies that the path taken is a straight line. In this case, the distance traveled and the displacement will be the same if the points a and b are in a straight line.

If points a and b are not in a straight line, then the distance traveled will be greater than the displacement. This is because the distance traveled considers the entire path covered, while displacement only considers the change in position.

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9514 1404 393

Answer:

  x = -9

Step-by-step explanation:

The value 13-8x apparently is the measure of the arc in degrees. That is the same as the measure of the central angle, shown as 85°. Then we have ...

  85 = 13 -8x

  72 = -8x . . . . . . subtract 13

  x = -9 . . . . . . . . divide by -8

The value of x is -9.

Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

To calculate this probability, we need to use the cumulative binomial probability formula:

P(X ≤ k) = Σ(i=0 to k) (n choose i) p^i (1-p)^(n-i)

Where:
- X is the number of heads obtained
- k is the number of heads we want to calculate the probability for (in this case, the same number of heads obtained)
- n is the total number of coin flips (10 in this case)
- p is the probability of getting heads on a single flip (0.5 for a fair coin)
- (n choose i) is the binomial coefficient, which represents the number of ways to choose i heads out of n flips

For this problem, we want to calculate P(X ≤ 10), since we're interested in the probability of obtaining as many heads as we did or less. Plugging in the values, we get:

P(X ≤ 10) = Σ(i=0 to 10) (10 choose i) 0.5^i 0.5^(10-i)
          = (10 choose 0) 0.5^0 0.5^10 + (10 choose 1) 0.5^1 0.5^9 + ... + (10 choose 10) 0.5^10 0.5^0
          = 0.00098 + 0.00977 + 0.04395 + 0.11719 + 0.20508 + 0.24609 + 0.20508 + 0.11719 + 0.04395 + 0.00977 + 0.00098
          = 0.9453

Therefore, the probability of obtaining as many heads as we did or less when flipping a fair coin 10 times is 0.9453.

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We need to use 2 cups of lemon juice and 8 cups of water to get a total of 10 cups of lemonade.

We know that the lemonade recipe is:

1 cup of lemon juice and 4 cups of water.

This gives us a total of:

1 cup + 4 cups =  5 cups of lemonade.

Then if we want 10 cups of lemonade, we just need to use the double of each one of the ingredients.

this is:

2*(1 cup) = 2 cups of lemon juice

2*(4 cups) = 8 cups of water.

We need to use 2 cups of lemon juice and 8 cups of water to get a total of 10 cups of lemonade.

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Answer:

1/2

Step-by-step explanation:

For three coin tosses, the posible outcomes are:

[(HHH), (HHT), ( THH), (HTH), ( THT), (TTH), (HTT), (TTT)

The outcomes where there are at least 2 tails are:

(TTT), (TTH), (THT), (HTT)

So, the probability that the coin will land tails at least 2 times is 4/8 or 1/2

Answer:

the probability that the first groupmate you meet has studied some statistics is 0.45

Step-by-step explanation:

From the information given :

A professor divided the students in her business class into three groups

Let consider then to be :

Group            Statistics Class

A                    Never taken a statistics class

B                    Taken one statistics class

C                     Taken two or more statistics class.

If 55% of the students have never taken a statistics class,

Then ;

P(A) = 0.55

25% have taken only one semester of a statistics class

Then P(B) = 0.25

and the rest have taken two or more semesters of statistics

Then P(C) = 1 - 0.55 -0.25

P(C) = 1 - 0.80

P(C) = 0.20

The objective is to determine the probability that the first groupmate you meet has studied some statistics

The probability of the first groupmate you meet has studied some statistics = 1 - P(never taken a statistics course)

Let the  probability of the first groupmate you meet that  has studied some statistics be P(D)

Then P(D) = 1 -  P(A)

P(D) = 1 - 0.55

P(D) = 0.45

the probability that the first groupmate you meet has studied some statistics is 0.45

Aid in the elimination of metabolic byproducts, excess electrolytes (for example, salt and potassium), and urea, a waste product generated during the digestion of ingested protein. Sweating helps to regulate body temperature.

Maintain a regular body temperature. Joints should be lubricated and cushioned. Safeguard your spinal cord and other delicate structures. Wastes can be eliminated by urine, sweat, and bowel motions. Dehydration can also cause a decrease in strength and stamina. It is the most common cause of heat exhaustion. At this point, you should be able to reverse dehydration by consuming extra fluids. Chronic dehydration might impair your kidney function and raise your risk of kidney stones. Water also helps with normal bowel function, muscular performance, and clean, young skin. Failure to drink enough water, on the other hand, can result in dehydration and negative symptoms such as weariness, headache, reduced immunity, and dry skin.

Here,

Assist in the elimination of metabolic byproducts, excess electrolytes (for example, salt and potassium), and urea, a waste product generated during the digestion of ingested protein. Sweating regulates body temperature.

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The content dimension of a message deals with the what of a message, while the relational dimension of a message deals with the how of a message is the correct answer.

Content dimensions is a generic concept to have multiple variants of a content node. It involves the information being explicitly discussed. The content repository supports any number of dimensions. The content dimension is the meaning of the actual message itself.

"Relational dimension of communication is a concept in which we have similar weight and impact as that of the message. This concept deals with the quality or nature of the relationships and networks."

Hence we can conclude that the content dimension of a message deals with the what of a message, while the relational dimension of a message deals with the how of a message is the correct answer.

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A)the density of |x| is f(|x|) = 1/(1-0) = 1. B) the density of p|x| is f(p|x|) = 1/(p-0) = 1/p. C) the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0. D) the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

(a) To find the density of |x|, we need to consider the range of values that |x| can take. Since x is uniformly distributed on the interval (-1, 1), the absolute value of x can take values between 0 and 1. The density function of |x| is given by f(|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = 1. Therefore, the density of |x| is f(|x|) = 1/(1-0) = 1.

(b) To find the density of p|x|, we need to consider the range of values that p|x| can take. Since x is uniformly distributed on the interval (-1, 1), p|x| can take values between 0 and p. The density function of p|x| is given by f(p|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = p. Therefore, the density of p|x| is f(p|x|) = 1/(p-0) = 1/p.

(c) To find the density of -ln|x|, we need to consider the range of values that -ln|x| can take. Since x is uniformly distributed on the interval (-1, 1), -ln|x| can take values between 0 and ∞. The density function of -ln|x| is given by f(-ln|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a  = 0 and b = ∞. Therefore, the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0.

(d) To find the density of sin(x), we need to consider the range of values that sin(x) can take. Since x is uniformly distributed on the interval (-1, 1), sin(x) can take values between -sin(1) and sin(1). The density function of sin(x) is given by f(sin(x)) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = -sin(1) and b = sin(1). Therefore, the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

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a. The probability that the drills are all completed by 11:40 am is very close to 0.
b. The probability that the drills are not completed by 12:10 pm is also very close to 0.

a. To find the probability that the drills are all completed by 11:40 am, we need to calculate the total time required to complete the drills. Since there are 35 drills and each drill takes an average of 6 minutes, the total time required is 35 * 6 = 210 minutes.

Now, we need to calculate the z-score for the desired completion time of 11:40 am (which is 700 minutes). The z-score is calculated as (desired time - average time) / standard deviation. In this case, it is (700 - 210) / 35 = 14.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of 14. However, the z-score is extremely high, indicating that it is highly unlikely for all the drills to be completed by 11:40 am. Therefore, the probability is very close to 0.

b. To find the probability that drills are not completed by 12:10 pm (which is 730 minutes), we can calculate the z-score using the same formula as before. The z-score is (730 - 210) / 35 = 16.

Again, the z-score is very high, indicating that it is highly unlikely for the drills not to be completed by 12:10 pm. Therefore, the probability is very close to 0.

In summary:
a. The probability that the drills are all completed by 11:40 am is very close to 0.
b. The probability that the drills are not completed by 12:10 pm is also very close to 0.

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The given system of linear differential equations x' * (t) = [[2, 1], [1, 1]] * x(t) can be written as x' * (t) = A * x(t), where A is the matrix [[2, 1], [1, 1]]. We need to find the eigenvalues and eigenvectors of A.

First, let's find the eigenvalues. We solve the characteristic equation det(A - λI) = 0, where I is the identity matrix: det([[2, 1], [1, 1]] - λ[[1, 0], [0, 1]]) = 0

Expanding the determinant, we get:

(2 - λ)(1 - λ) - 1 = 0

λ² - 3λ + 1 = 0

Using the quadratic formula, we find the eigenvalues:

λ₁ = (3 + sqrt(5))/2

λ₂ = (3 - sqrt(5))/2

Next, we find the corresponding eigenvectors. For each eigenvalue, we solve the equation (A - λI)v = 0:

For λ₁ = (3 + sqrt(5))/2:

[[2 - (3 + sqrt(5))/2, 1], [1, 1 - (3 + sqrt(5))/2]] * [[v₁₁], [v₁₂]] = [[0], [0]]

Simplifying the matrix equation, we get:

[[(1 - sqrt(5))/2, 1], [1, (1 - sqrt(5))/2]] * [[v₁₁], [v₁₂]] = [[0], [0]]

Solving this system of equations, we find the eigenvector [[v₁₁], [v₁₂]].

Similarly, for λ₂ = (3 - sqrt(5))/2, we solve the equation:

[[(1 + sqrt(5))/2, 1], [1, (1 + sqrt(5))/2]] * [[v₂₁], [v₂₂]] = [[0], [0]]

Solving this system of equations, we find the eigenvector [[v₂₁], [v₂₂]].

Finally, we have found the vectors [[d₁], [d₂]] = [[(3 - sqrt(5))/2], [(3 + sqrt(5))/2]], [[v₁₁], [v₁₂]], and [[v₂₁], [v₂₂]].

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Answer:

it’s already in it’s simplest form

Answer:what

Step-by-step explanation:what does this mean

579 MPa is 0.1446.

The probability that a randomly chosen sample of glass will break at less than 579 MPa can be found using the Normal Distribution. Using the mean and standard deviation given, we can calculate the probability that a randomly chosen sample will have a fracture strength of less than 579 MPa. This is calculated using the formula P(X < 579) = 1 - P(X > 579) = 1 - 0.8554 = 0.1446.

Therefore, the probability that a randomly chosen sample of glass will break at less than 579 MPa is 0.1446.

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dz/dt for the given function z = sin(x)cos(y), where x = t and y = 2/t, is equal to cos(t)cos(2/t) + 2sin(t)sin(2/t)/\(t^{2}\)

To find dz/dt using the chain rule, we need to differentiate z with respect to x and y separately, and then multiply the derivatives by the corresponding derivatives of x and y with respect to t. Given z = sin(x)cos(y), where x = t and y = 2/t, let's calculate dz/dt.

First, differentiate function z with respect to x:

∂z/∂x = cos(x)cos(y)

Next, differentiate z with respect to y:

∂z/∂y = -sin(x)sin(y)

Now, differentiate x = t with respect to t:

dx/dt = 1

Differentiate y = 2/t with respect to t:

dy/dt = -2/\(t^{2}\)

Now, applying the chain rule, we have:

dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)

= cos(x)cos(y)(1) + (-sin(x)sin(y))(-2/\(t^{2}\))

= cos(t)cos(2/t) + 2sin(t)sin(2/t)/\(t^{2}\)

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Answer:

multiply

Step-by-step explanation:

2345567 in the subtract 578431111

The measure angle EBF is (5b-24)°.

Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.

Give that, m∠ABF =(7b-24)° and m∠ABE =2b°.

From the figure,

m∠ABF =m∠ABE + m∠EBF

(7b-24)°=2b° + m∠EBF

m∠EBF = 7b-24-2b

m∠EBF = (5b-24)°

Therefore, the measure angle EBF is (5b-24)°.

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Based on the histogram shown, of the following, which is closest to the average (arithmetic mean) number of seeds per is option (c) 5.

Explanation: Looking at the histogram, we can see that the bar for 5 seeds has the highest frequency, which means that the number of apples with 5 seeds is the highest. Therefore, it is most likely that the average number of seeds per apple is closest to 5.

Based on the given histogram, we can conclude that the option closest to the average number of seeds per apple is (c) 5.
Based on the histogram shown, the closest average (arithmetic mean) number of seeds per apple is option (b) 4.

To find the average (arithmetic mean) number of seeds per apple from the histogram, follow these steps:

1. Determine the frequency of each number of seeds (how many apples have a certain number of seeds).
2. Multiply each number of seeds by its frequency.
3. Add up the products from step 2.
4. Divide the sum from step 3 by the total number of apples (the sum of frequencies).

Based on the given information and the calculation steps, the closest average (arithmetic mean) number of seeds per apple is 4, which corresponds to option (b).

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If you eliminate your discretionary expenses, you can save $592.88 per month.

To calculate your total realized income, we can start by finding your gross income per week and then multiply it by the number of weeks in a month.

Gross income per week:

$11.75/hr * 40 hr/wk = $470/week

Gross income per month:

$470/week * 4 weeks = $1,880/month

Now, let's calculate your deductions:

FICA (7.65%):

$1,880/month * 7.65% = $143.82/month

Federal tax withholding (10.75%):

$1,880/month * 10.75% = $202.30/month

State tax withholding (7.5%):

$1,880/month * 7.5% = $141/month

Total deductions:

$143.82/month + $202.30/month + $141/month = $487.12/month

To find your total realized income, subtract the total deductions from your gross income:

Total realized income:

$1,880/month - $487.12/month = $1,392.88/month

Next, let's calculate your fixed expenses. Fixed expenses typically include essential costs such as rent, utilities, insurance, and loan payments. Since we don't have specific values for your fixed expenses, let's assume they amount to $800/month.

Fixed expenses:

$800/month

Finally, to calculate your discretionary expenses, we'll subtract your fixed expenses from your total realized income:

Discretionary expenses:

$1,392.88/month - $800/month = $592.88/month

If you eliminate your discretionary expenses, you can put the entire discretionary expenses amount towards savings each month:

Savings per month:

$592.88/month

Therefore, if you eliminate your discretionary expenses, you can save $592.88 per month.

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As the interest rate increases from 10 percent to 11 percent, the present value of the bond decreases from $1,074.47 to $1,058.31. Conversely, when the interest rate decreases to 9 percent, the present value increases to $1,091.19. This is because the discount rate used to calculate the present value is inversely related to the interest rate, meaning that as the interest rate increases, the present value decreases, and vice versa.

To compute the present value of a five-year, 10 percent coupon bond with a face value of $1,000, we need to discount the future cash flows (coupon payments and face value) by the appropriate interest rate.

Step 1: Calculate the present value of each coupon payment.
Since the bond has a 10 percent coupon rate, it pays $100 (10% of $1,000) annually. To calculate the present value of each coupon payment, we need to discount it by the interest rate.

Using the formula: PV = C / (1+r)^n
Where PV is the present value,

C is the cash flow,

r is the interest rate, and

n is the number of periods.

At an interest rate of 10 percent, the present value of each coupon payment is:
PV1 = $100 / (1+0.10)^1 = $90.91

Step 2: Calculate the present value of the face value.
The face value of the bond is $1,000, which will be received at the end of the fifth year. We need to discount it to its present value using the interest rate.

At an interest rate of 10 percent, the present value of the face value is:
PV2 = $1,000 / (1+0.10)^5 = $620.92

Step 3: Calculate the total present value.
To find the present value of the bond, we need to sum up the present values of each coupon payment and the present value of the face value.
Total present value at an interest rate of 10 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,074.47

When the interest rate goes to 11 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 11 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,058.31

When the interest rate goes to 9 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 9 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,091.19

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The total cost  of he meat with tax and tip is $ 22.42

To calculate the total cost with tax and tip, we need to follow these steps:

multiply the meal cost by the tip rate. when  the tip rate is 18%, we have:

Tip amount = $19.00 * 0.18 = $3.42

Add the meal cost, sales tax, and tip amount to get the total cost:

Total cost = Meal cost + Sales tax + Tip amount

= $19.00 + $3.42

= $ 22.42

Therefore, the total cost with tax and tip is $22.42

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Answer:

$1,015

Step-by-step explanation:

Given that:

Weekly earning = $625

Commission = 12% of sales

sales made last week = $3250

Last week earning = weekly earning + commision on sale

Commission on sale = 12% of sales

Commission on sale = (0.12 * 3250) = $390

Last week earning = weekly earning + commision on sale

Last week earning = $625 + $390 = $1,015

Answer:

A credit card you have to pay back the money you spend to the credit card company.

While with a debit card it takes money straight out of your bank account.

Answer:

x < -7

Step-by-step explanation:

Divide both sides by 3

simplify

add 4 to both sides

Answer:

x<-7

Step-by-step explanation:

The correct answer is e(x) = np. The expected value for a binomial probability distribution is given by the formula e(x) = np, where n represents the number of trials and p represents the probability of success in each trial.

The expected value is a measure of the average or mean outcome of a binomial experiment. It represents the number of successful outcomes one would expect on average over a large number of trials.

The formula e(x) = np arises from the fact that the expected value of a binomial distribution is the product of the number of trials (n) and the probability of success (p) in each trial. This is because in a binomial experiment, the probability of success remains constant for each trial.

Therefore, to calculate the expected value of a binomial probability distribution, we multiply the number of trials by the probability of success in each trial, resulting in e(x) = np.

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The probability is 1/5.

There are 3 red marbles and 3 white marbles, for a total of 6.

The probability that the first marble is red is:

P(red) = 3/6

The probability that the second marble is also red is:

P(red') = 2/5 (because now there are 2 red marbles and a total of 5).

The joint probability is:

P = (3/6)*(2/5) = 1/5

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6/50 fraction of all people in the company are women under age of 30 In a company where the ratio of men to women i 3:2.

In a company the ratio of men to women  3:2

30% of the women are under the age of 30.

suppose there are 500 people in the company

then 300 are men and 200 are women

30% of 200 = 200*30/100= 60 women are under 30

60/500= 6/50 women are under 30

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The given steps are general suggestions to resolve the error message "Windows photo viewer can't display this picture because there might not be enough memory available on your computer," but their effectiveness may vary based on individual cases.

The error message suggests that there might not be enough memory available on your computer to display the picture using Windows Photo Viewer. This can be caused by a number of factors, such as the size of the image file or the amount of RAM installed on your computer.

Here are a few steps you can try to resolve the issue:

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