Please Help, this is math problems

- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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The rate of change of the area as a function of time is:

A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)

Remember that for a circle of radius R, the area is:

A = 3.14*R^2

Now, if the radius increases at a rate of 4 ft/min, then we can rewrite R as:

R(t) = R₀ + 4ft/min*t

Where t is the time in minutes, and R₀ is the initial radius.

So the area function is:

A(t) = 3.14*(R₀ + 4ft/min*t)^2

The rate of change is given by the differentiation with respect to t, it is:

A'(t) = 2*3.14*(R₀ + 4ft/min*t)*(4ft/min)

A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)

The rate at which the area increases, as a function of time, is given by:

A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)

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Answer:

20

Step-by-step explanation:

EG = EF + FG

Its given in the question that -

• EF = 9

• FG = 11

So,

EG = 9 + 11 = 20

Answer:

27. 18.62

28. 200%

29. 136

30. 50

31. 12.5%

32. 750

33. 5.4

Step-by-step explanation:

The maximum height reached by the ball is 164 feet, the velocity of the ball when it hits the ground is -48 ft/sec, and the acceleration of the ball when it hits the ground is -32 ft/sec^2.

To find the maximum height reached by the ball, the velocity of the ball when it hits the ground, and the acceleration of the ball when it hits the ground, we can analyze the given function s(t) = 64 + 80t - 16t^2.

Now, let's break down the computation into steps:

Step 1: Find the maximum height reached by the ball

The maximum height reached by the ball corresponds to the vertex of the parabolic function s(t) = 64 + 80t - 16t^2. The vertex can be found using the formula t = -b / (2a), where the quadratic function is in the form s(t) = at^2 + bt + c.

In this case, a = -16, b = 80, and c = 64. Substituting these values into the formula, we have:

t = -80 / (2*(-16)) = 80 / 32 = 2.5 seconds.

To find the maximum height, we substitute this value of t back into the function s(t):

s(2.5) = 64 + 80(2.5) - 16(2.5)^2 = 64 + 200 - 16(6.25) = 64 + 200 - 100 = 164 feet.

Therefore, the maximum height reached by the ball is 164 feet.

Step 2: Find the velocity of the ball when it hits the ground

To find the velocity of the ball when it hits the ground, we need to determine the time it takes for the ball to reach a height of 0 feet.

Setting s(t) = 0, we have:

0 = 64 + 80t - 16t^2.

This is a quadratic equation. Solving for t using the quadratic formula, we obtain two possible solutions: t = 4 seconds and t = -1 second. Since time cannot be negative in this context, we discard the negative solution.

Therefore, the ball hits the ground after 4 seconds. To find the velocity at this time, we differentiate the function s(t) with respect to t and evaluate it at t = 4:

s'(t) = 80 - 32t.

s'(4) = 80 - 32(4) = 80 - 128 = -48 ft/sec.

So, the velocity of the ball when it hits the ground is -48 ft/sec, indicating it is moving downward.

Step 3: Find the acceleration of the ball when it hits the ground

The acceleration of the ball can be determined by differentiating the velocity function. Taking the derivative of s'(t) = 80 - 32t with respect to t, we obtain:

s''(t) = -32.

Since the acceleration is constant and independent of time, the acceleration of the ball when it hits the ground is -32 ft/sec^2.

Therefore, the maximum height reached by the ball is 164 feet, the velocity of the ball when it hits the ground is -48 ft/sec, and the acceleration of the ball when it hits the ground is -32 ft/sec^2.

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Answer:

The first, second, and fourth questions.

Step-by-step explanation:

None of these result in an answer of 23, so I'm assuming that you meant 2/3.

"Two gallons of water are needed to fill 3 fish tanks of equal size. How many gallons of water are required for each tank?"

2 gallons divided between 3 tanks is 2 divided by 3, so 2/3.

"Three cats share 2 cans of tuna. How much of a can does each cat receive?"

2 cans divided between 3 cats - it's the same as the above problem, just with cats and tuna cans instead of tanks and gallons of water. Each cat gets 2/3 of a can.

"Two bags of bird seed are split among 5 parrots. What fraction of a bag does each parrot receive?"

2 bags divided between 5 parrots would be 2/5 of a bag for each parrot.

"Two apples are split among 3 people. How much of an apple does each person receive?"

Two apples split among 3 people - like the first 2 questions, this also equals 2/3.

"Three dogs each drink 2 cups of water. How many cups of water do the dogs drink in all?"

Three dogs EACH drink 2 cups of water means that the answer is 2*3=6 cups.

"Three cupcakes are divided among 2 children. How much of a cupcake does each child receive?"

Three cupcakes are split between 2 children - they will each get 3/2 of a cupcake, or 1 1/2.

The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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Answer:

\(\frac{-x^{2}+5x-1}{2x^{2} -x-1}\)

Step-by-step explanation:

The male long jumper's jump, which ranked in the 75th percentile, was approximately 272.436 inches long.

To find the length of the male long jumper's jump at the 75th percentile, we can use the concept of z-scores and the standard normal distribution.

The 75th percentile corresponds to a z-score of 0.674. Using this z-score, we can calculate the distance of the jump by multiplying it by the standard deviation and adding it to the mean:

Distance = (z-score * standard deviation) + mean

Distance = (0.674 * 14) + 263

Distance ≈ 9.436 + 263

Distance ≈ 272.436

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Answer:

0.25 is the probability

Step-by-step explanation:

If there are 13 diamonds in a deck of 52 cards, dividing 13 by 52 will get you 0.25. This is the probability of getting a diamond from the deck of 52 cards.

Answer:

y= -x

Step-by-step explanation:

same deal

-x+b=y

5= -(-5)+b

5= 5+b

b=0

The level of confidence for the given confidence interval is 95% and z-score is 1.96.The calculation involves using the formula for the confidence interval and the given sample proportion and size.

We can use the formula for the confidence interval for a population proportion:

p-hat ± z*(sqrt(p-hat*(1-p-hat)/n))

Where p-hat is the sample proportion, z is the z-score for the desired level of confidence, and n is the sample size.

We're given that p-hat = 0.3 and n = 50. We're also given that the confidence interval is (.1323, .4677), which means that:

p-hat ± z*(sqrt(p-hat*(1-p-hat)/n)) = (.1323, .4677)

We can use the midpoint of the confidence interval as the point estimate for p-hat, which is (0.1323 + 0.4677) / 2 = 0.3.

Substituting the values we have into the equation, we get:

0.3 ± z*(sqrt(0.3*(1-0.3)/50)) = (.1323, .4677)

Simplifying the equation, we get:

z = 1.96

Therefore, the level of confidence for this interval is 95%, since the z-score for a 95% confidence level is 1.96.

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Answer:

The answer is 36

Step-by-step explanation:

=16-4(-5)

=16-(-20)

=36

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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Answer:

The correct answer is B.

Explanation:

The difference of 9 times a number z -  9z - something

and 7 - and 7

Put everything together- 9z - 7

Happy studying! :)

Answer:

Measure of angle B is 70 degrees

Step-by-step explanation:

If they are both supplementary, it means that add up to be 180 degrees

Thus;

5x + 25 + 3x + 19 = 180

8x + 44 = 180

8x = 136

x = 136/8

x = 17

Measure of angle B will be;

3(17) + 19

= 51 + 19 = 70 degrees

Each type of interviewer should be hired in order to maximize the number of interviews are 0 undergraduate students, 16 graduate students, and 4 faculty members and the maximum number of interviews is 644 according to the statistics given.

If n = the number of interviews, then let x = the number of undergraduate students hired, y = the number of graduate students employed, z = the number of faculty members hired.

The purposeful action is:

maximization of n = 30x + 32y + 33z

The limitations are: x + y + z 20; 100x + 150y + 200z 3200; and 0;

The answer is 644 because x = 0, y = 16, z = 4.

To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics given.

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The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer:

A: Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3}

Step-by-step explanation:

C = {(9, 1) (8, -3) (7, 5) (-5, 3)}

The domain is the inputs

Domain: { -5,7,8,9}

The range is the output

Range{ -3,1,3,5}

This is a functions since there is no input that goes to multiple outputs

Answer:

I don't think that there is two same results. sorry I couldn't help

Step-by-step explanation:

for I the answer should be 10 if you replaced each x by 2. f(2) = 3(2) + 4

and for II it will be f-1(4) = 3-1(4) - 4 /5 the answer will be -1.

for III it should be y = 8 or 4

The volume of the rectangular prism is 12 cubic feet.

To find the volume of a rectangular prism, you need to multiply its height by its base area. In this case, the height is given as 2 ft and the base area is given as 6 ft2. So, the volume can be calculated as follows:

Volume = Height x Base area
Volume = 2 ft x 6 ft2
Volume = 12 cubic feet

Therefore, the volume of the rectangular prism is 12 cubic feet.

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13 units is the distance between points.

The length of the code words in this linear code is 4.

To find the length of code words in a linear code, we can use the formula:

Length of code words = log(base 2) of (number of code words)

In this case, the linear code contains exactly 16 code words and the transmission rate is 23.

Using the formula, we can calculate the length of code words as follows:

Length of code words = log(base 2) of 16
Length of code words = 4

Therefore, the length of the code words in this linear code is 4.

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Hope you could understand.

If you have any query, feel free to ask.

5% sales tax of a $1,000.00 item = $950.

Answer: 1,050.00

Step-by-step explanation: 1,000.00+0.05=1,050.00

Answer: 5

Step-by-step explanation:

  8-2b=-2

8-2b-8=-2-8

    -2b=-10

-2b/-2=-10/-2

       b=5

The correct answer is (D) The full length to which it can be extended.

The size classification of an extension ladder indicates the full length to which it can be extended.
An extension ladder's size classification indicates the total length the ladder can reach when its fly section is fully extended.

This helps users determine if the ladder will be long enough for their specific needs when working at height.

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We can conclude that the students did not have any time left to work on homework.

The duration of Mr. K's math class is 1 and 1/4 hours, or 5/4 hours.

We need to determine how much time is left for the kids to do their assignment after working on problems on the board for 55 minutes and 11/12 hours. To achieve this, we must take the time spent solving issues out of the overall class time:

Total class time = 5/4 hours

Time spent on working problems = 55 minutes + 11/12 hours

= (55/60) hours + (11/12) hours

= (11/12 + 55/60) hours

= (11/12 + 11/12) hours

= (22/12) hours

= (11/6) hours

Overall class time minus the amount of time spent solving problems equals the amount of time remaining for homework.

= 5/4 hours - 11/6 hours

= (15/12) hours - (22/12) hours

= (-7/12) hours

We can infer that the kids ran out of time to finish their homework because the response is illogical because we cannot have negative time.

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The chance of rolling two 5s and flipping two heads can be calculated by multiplying the odds together because each cube and coin flip is independent. the probability that Kyle wins the prize is \(1/144\)

The probability of rolling a 5 on a number cube is 1/6, and the probability of flipping heads on a coin is 1/2.

Since each roll of the cube and flip of the coin is independent, we can find the probability of rolling two 5's and flipping two heads by multiplying the probabilities together:

P(rolling two 5's and flipping two heads) = P(rolling a 5) * P(rolling a 5) * P(flipping heads) * P(flipping heads)

\(= (1/6) \times (1/6) \times (1/2) \times (1/2)\)

\(= 1/144\)

Therefore, the probability that Kyle wins the prize is ,\(1/144\) or approximately  \(0.0069\) (rounded to four decimal places).

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