Your class tutorial has 12 students, who are supposed to break up into 4 groups of 3 students each. Your Teaching Assistant (TA) has observed that the students waste too much time trying to form balanced groups, so he decided to pre-assign students to groups and email the group assignments to his students. (a) Your TA has a list of the 12 students in front of him, so he divides the list into consecutive groups of 3. For example, if the list is ABCDEFGHIJKL, the TA would define a sequence of four groups to be ({A, B, C},{D, E, F},{G, H, 1},{J, K, L}). This way of forming groups defines a mapping from a list of twelve students to a sequence of four groups. This is a k-to-1 mapping for what k? (b) A group assignment specifies which students are in the same group, but not any order in which the groups should be listed. If we map a sequence of 4 groups, ({A, B, C},{D, E, F}, {G, H, I }, {J, K, L}), into a group assignment {{A, B, C},{D, E, F}, {G, H, 1},{J, K, L}}, this mapping is j-to-1 for what j? (c) How many group assignments are possible? (d) In how many ways can 3n students be broken up into n groups of 3?

-8x-2(5+4x)

Step-by-step explanation:

-8x-10-8x -8x-8x-10 -16x-10

Answer:

The answer is 1/11

Step-by-step explanation:

Explanation is in the picture above

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Answer:

d=18 feet

Step-by-step explanation:

The volume of a sphere is represented by the equation [tex]V=\frac{4}{3}\pi r[/tex]³, where r is the radius. If the volume is 972[tex]\pi[/tex],

[tex]972\pi =\frac{4}{3}\pi r[/tex]³

Divide [tex]\pi[/tex] from each side,

[tex]972=\frac{4}{3} r[/tex]³

Multiply each side by 3/4 to get rid of the fraction,

[tex]r[/tex]³[tex]=729[/tex]

Using the cube root, we find that 729 is actually a perfect cube.

[tex]r=9[/tex]

Now, the diameter is 2 times the radius, so

9×2=18

So, the measure of the diameter is 18 feet.

Answer:

100in

Step-by-step explanation:

1/2 *10*5=25

4(25)=100

Answer:

The correct statement is B (are very sensitive to change in price)

Step-by-step explanation:

Option B is correct because of the following reason -:

The degree to which a rise in price affects the quantity demanded or supplied is known as elasticity. In the case of elastic demand and supply, as the price rises, the quantity demanded falls and the quantity supplied rises more than proportionally. Inelastic price elasticity of demand and supply, on the other hand, induces a less than proportional change in quantity as prices change.

Hence , the correct option is B .

Answer:

3x10 15x2 5x6

Step-by-step explanation:

Answer:

20 boys

Step-by-step explanation:

If there are 4 boys for every 3 girls, multiply both numbers by 5 (3*5 = 15) to find the number of boys.

Answer:

20

Step-by-step explanation:

4/3 = ?/15

multiply both sides by 15

15*4/3 = ?

? = 20

Type I Error: A Type I error is the first kind of error that can occur when testing a hypothesis. A Type I error occurs when a null hypothesis is rejected even when it is accurate.

If we make a Type I Error on this test, it would mean that we reject a null hypothesis that is true. This mistake would be made if we made a decision to reject the null hypothesis when there is no significant evidence to support that decision. The null hypothesis is the hypothesis that claims no change or no difference between the groups being compared. Null hypothesis is the opposite of the alternative hypothesis which is the hypothesis that claims that there is a difference between groups being compared.

In this context, making a Type I Error would mean that we reject the null hypothesis which is that all groups of voters would agree that workers who have illegally entered the US should be allowed to keep their jobs and apply for US citizenship. Making this error would mean we have come to the conclusion that they do not agree, which would be incorrect.

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Answer:

A x<1125

Step-by-step explanation:

Answer:

find which one my guy im trying to get infinite awnseres srryyyyy

Step-by-step explanation:

Answer:

Post the question along with this

Answer: D) a rotation of 180 degrees Clockwise about the center of the parallelogram

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The perimeter of the square has to be only positive values, and so there has to be restrictions on the values. We can rule out answers A and B. Because the perimeter the values of x have to be less than 4. If they were greater than 4, then 4x>16. So we can rule out answer d. The correct answer is C.

Answer:

7. 7.1+5.4+2.9=15.7

10.3+5.4=15.7

8. 373.4 - 152.9 = 220.5

373.4 - 153 = 220.4

220.4 - 0.1 = 220.5

9. 18.25 + 7.99 + 4.75 = 30.99

10. 1.05 + 3 + 4.28 + .95 = 9.28

11. 302.504

12 50.5

Answer:

Fraction form: (-1/2, 7/2) Decimal form: -.5, 3.5)

Step-by-step explanation:

use the midpoint formula of: (x1 + x2/2 , y1 + y2/2) in order to get (x,y) coordinates.

Let's call endpoint C x1 and y1. So 6=x1 and -1=y1.

This makes endpoint D x2 and y2. So -7=x2 and 8=y2.

Now plug it in and simplify!

x-coordinates: (6+-7)/2 = (6-7)/2 = -1/2 or -.5

y-coordinates: (-1+8)/2 = (8-1)/2 = 7/2 or 3.5

the midpoint of endpoints C and D is (-1/2, 7/2)

**decimal form: (-.5, 3.5)

Answer:

8 laps in 70 seconds is faster.

Step-by-step explanation:

If we divide 70/8 and 98/12 we get the following:

70/8= 8.75

98/12=8.16

8.75>8.16

The unit rate is 1 lap in 8.75 seconds and 1 lap in 8.16 seconds

Therefore, 3 is 6 1/2 of 19.5. Therefore, 30% of 9 is 2.7.  Therefore, 42% of 30 is 12.6. Therefore, 54 is 4 1/2 of 243. Therefore, 1.92 milligrams of antibiotic should be added to 4.8 mL of solution at this rate.

To find the number that is 6 1/2 times 3, we can set up the equation: x = 6 1/2 * 3. Multiplying 6 by 3 gives us 18, and 1/2 of 3 is 1.5. Adding these results, we get x = 19.5. Therefore, 3 is 6 1/2 of 19.5.

To find 30% of 9, we multiply 9 by 0.30 (or 30% written as a decimal). The calculation is 9 * 0.30 = 2.7. Therefore, 30% of 9 is 2.7.

To find 42% of 30, we multiply 30 by 0.42 (or 42% written as a decimal). The calculation is 30 * 0.42 = 12.6. Therefore, 42% of 30 is 12.6.

To find the number that is 4 1/2 times 54, we can set up the equation: x = 4 1/2 * 54. Multiplying 4 by 54 gives us 216, and 1/2 of 54 is 27. Adding these results, we get x = 243. Therefore, 54 is 4 1/2 of 243.

If the recommended rate is 0.8 mg per 2 mL of solution, we can set up a proportion to find the amount of antibiotic for 4.8 mL: (0.8 mg / 2 mL) = (x mg / 4.8 mL). Cross-multiplying and solving for x gives us x = (0.8 mg / 2 mL) * 4.8 mL = 1.92 mg. Therefore, 1.92 milligrams of antibiotic should be added to 4.8 mL of solution at this rate.

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Answer:

Step-by-step explanation:

5 boys

Answer:

me

Step-by-step explanation:

beceaus im the best Guy

Answer:嘿，我不知道答案，但這段文字很酷

Answer:

For real???

Step-by-step explanation:

Tysm!! <3 you deserve so much!

Answer:thanks

Step-by-step explanation:

Answer:

− 6 + 3 0 − 4

Answer:

do you mean simplify the expression?

-6x+4(-2+8y)- 2y+ 4

-6x - 8 + 32y - 2y + 4

-6x + 30y + 4 - 8

-6x + 30y - 4

Answer:

19. B

20. C

Step-by-step explanation:

The probability to consume more than 13 pizzas per month is 0.3707 and more than 110 pizzas in a random sample of size 10 is 0.9646.

The number of pizzas consumed per month by university students is normally distributed with a mean of 12 and a standard deviation of 3.

A. Probability that more than 13 pizzas consumed by students:

For finding the probability, we need to find the Z-score first.

z = (x - μ) / σz = (13 - 12) / 3z = 0.3333

Now, we have to use the z-table to find the probability associated with the z-score 0.3333.

The area under the normal distribution curve to the right of 0.3333 is 0.3707 (rounded off to 4 decimal places).

Thus, the probability that a student consumes more than 13 pizzas per month is 0.3707.

B. Probability that more than 110 pizzas consumed in a random sample of size 10:

Let x be the number of pizzas consumed in the random sample of size 10.

Then, the distribution of x is a normal distribution with the mean = 10 × 12 = 120 and standard deviation = √(10 × 3²) = 5.4772

We have to find the probability that the total number of pizzas consumed is greater than 110. i.e. P(x > 110).

For finding the probability, we need to find the Z-score first.z = (110 - 120) / 5.4772z = -1.8257

The area under the normal distribution curve to the right of -1.8257 is 0.9646 (rounded off to 4 decimal places).

Thus, the probability that more than 110 pizzas are consumed in a random sample of size 10 is 0.9646.

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The correct answer is option D. Since A and B are mutually exclusive events, the probability that both A and B occur is 0. In other words, P(A&B) = 0.

When two events, A and B, are mutually exclusive, it means that they cannot occur simultaneously. If one event happens, the other event cannot happen at the same time. In this scenario, the correct answer is option D, which states that the probability of both events A and B occurring together is 0, i.e., P(A&B) = 0.

To understand this concept, consider a simple example. Let's say event A represents flipping a coin and getting heads, while event B represents flipping a coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, it is impossible for both events A and B to occur simultaneously. Therefore, the probability of both A and B occurring together is 0. In summary, when events A and B are mutually exclusive, the correct answer is option D, which states that the probability of both A and B occurring together is 0, i.e., P(A&B) = 0.

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Answer:

x = 3, 2

Step-by-step explanation:

Answer: x = 3, 2

Step-by-step explanation:

The required probability is 0.2023.

Given random variable X with binomial distribution with n=150 and p=0.6.

The binomial distribution with parameters n and p has probability mass function:

$$f(x)= \begin{cases} {n\choose x} p^x (1-p)^{n-x} & \text{for } x=0,1,2,\ldots,n, \\ 0 & \text{otherwise}. \end{cases}$$

Now the mean, μ = np = 150 × 0.6 = 90 and standard deviation, σ = √(npq) = √(150 × 0.6 × 0.4) = 6

Using the normal approximation,

we have:

$$\begin{aligned}P(X ≥ 95) &\approx P\left(Z \geq \frac{95 - \mu}{\sigma}\right)\\ &\approx P(Z \geq \frac{95 - 90}{6})\\ &\approx P(Z \geq 0.8333) \end{aligned}$$

Using the standard normal table, the area to the right of 0.83 is 0.2023.

Therefore, P(X ≥ 95) = 0.2023.

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According to the given information, the required probability is 0.2019.

The random variable has a binomial distribution with n = 150 and p = 0.6.

We can use the normal approximation to the binomial distribution to find the probability P(X ≥ 95).

Normal Approximation:

The conditions for the normal approximation to the binomial distribution are:

np ≥ 10 and n(1 - p) ≥ 10

The expected value of the binomial distribution is given by the formula E(X) = np

and the variance is given by the formula [tex]Var(X) = np(1 - p)[/tex].

Let X be the number of successes among n = 150 trials each with probability p = 0.6 of success.

The random variable X has a binomial distribution with parameters n and p, i.e., X ~ Bin(150, 0.6).

The expected value and variance of X are:

[tex]E(X) = np = 150(0.6) = 90[/tex],

[tex]Var(X) = np(1 - p) = 150(0.6)(0.4) = 36[/tex].

The probability that X takes a value greater than or equal to 95 is:

[tex]P(X ≥ 95) = P(Z > (95 - 90) / (6))[/tex]

where Z ~ N(0,1) is the standard normal distribution with mean 0 and variance 1.

[tex]P(X ≥ 95) = P(Z > 0.8333)[/tex]

We can use a standard normal distribution table or a calculator to find this probability.

Using a standard normal distribution table, we find:

[tex]P(Z > 0.8333) = 0.2019[/tex]

Thus, [tex]P(X ≥ 95) = 0.2019[/tex] (rounded to four decimal places).

Therefore, the required probability is 0.2019.

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Based on estimated sales of 2,000 cups of coffee per week and the amount of coffee required for each cup size, it is recommended to purchase approximately 46.875 pounds of coffee.

To determine the amount of coffee needed for 2,000 cups of coffee per week, we need to consider the size of each cup and the amount of coffee required for each size.

According to the information provided, small cups use 1 shot of espresso, medium cups use 2 shots, and large cups use 3 shots.

Since each shot requires approximately 7 grams of coffee (or about 1/64 of a pound), a small cup would require approximately 1/64 of a pound, a medium cup would require approximately 2/64 (or 1/32) of a pound, and a large cup would require approximately 3/64 of a pound.

Let's calculate the total amount of coffee required for 2,000 cups based on these proportions. Assuming a certain distribution of cup sizes, we can estimate the average number of shots per cup.

Let's assume that 40% of the cups are small, 40% are medium, and 20% are large.

With these proportions, we can calculate the total amount of coffee required.

(0.4 * 2,000 * 1/64) + (0.4 * 2,000 * 2/64) + (0.2 * 2,000 * 3/64) = 62.5 + 125 + 46.875 = 234.375

Therefore, to meet the estimated sales of 2,000 cups of coffee per week, it is recommended to purchase approximately 46.875 pounds of coffee.

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Answer:

it is A

Step-by-step explanation:

i remember doing this in middle school.

The remainder when f(x) = 2x3 - 12x2 + 11x + 2 is divided by x - 5 is 7.

We can use the remainder theorem to find the remainder when a polynomial is divided by a linear factor.

The remainder theorem states that the remainder when a polynomial f(x) is divided by x - a is f(a). In this case, the polynomial is f(x) = 2x3 - 12x2 + 11x + 2 and the linear factor is x - 5. So, the remainder is f(5).

To find f(5), we can simply substitute x = 5 into the polynomial. This gives us f(5) = 2(5)3 - 12(5)2 + 11(5) + 2 = 7.

Therefore, the remainder when f(x) = 2x3 - 12x2 + 11x + 2 is divided by x - 5 is 7.

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