the sum of a number and 11

To find the coefficient of the term with t^6 in the expansion of (x - 2)^12 without expanding the entire binomial, we can use the binomial theorem.

The binomial theorem states that the term at index k in the expansion of (a + b)^n can be calculated using the formula: C(n, k) * a^(n-k) * b^k. where C(n, k) represents the binomial coefficient, given by: C(n, k) = n! / (k! * (n - k)!). In this case, a = x and b = -2. We are interested in finding the term with t^6, so we need to find the k value that satisfies n - k = 6.

In the expansion of (x - 2)^12, the term with t^6 will have the following form: C(12, k) * x^(12-k) * (-2)^k. To find the k value that corresponds to t^6, we solve the equation n - k = 6: 12 - k = 6. Simplifying, we find: k = 12 - 6 = 6. Therefore, the term with t^6 in the expansion of (x - 2)^12 is given by: C(12, 6 ) * x^(12-6) * (-2)^6. C(12, 6) represents the binomial coefficient, which is calculated as: C(12, 6) = 12! / (6! * (12 - 6)!). Plugging in the values, we have: C(12, 6) = 924. Therefore, the term with t^6 in the expansion of (x - 2)^12 is: 924 * x^6 * (-2)^6. Simplifying further, we get: 924 * x^6 * 64. Finally, the simplified expression is: 59040 * x^6

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We want to evaluate the limit;

Answer:

5 power 3

Step-by-step explanation:

the answer of 5 power 2 is 25,multiply by 5 to get 125,make 5 the base to get your answer

Answer:

5^3

Step-by-step explanation:

5x5^2= 25x5=125

Now that is equivalent to 5^3

5x5x5=125

The surface area of a cube is changing at a rate of 200 cm²/sec when each edge is 5 centimeters, and it is changing at a rate of 600 cm²/sec when each edge is 15 centimeters.

(a) To find how fast the surface area is changing when each edge is 5 centimeters, we need to calculate the rate of change of the surface area with respect to time. The surface area of a cube is given by the formula S = 6a², where S is the surface area and a is the length of each edge.

Given that each edge is expanding at a rate of 8 centimeters per second, we can write da/dt = 8 cm/sec. We need to find dS/dt, the rate at which the surface area is changing.

Using the chain rule, we have dS/dt = dS/da * da/dt. Taking the derivative of the surface area formula, we get dS/da = 12a.

Substituting the values, we have dS/dt = 12a * da/dt = 12(5) * 8 = 480 cm²/sec.

Therefore, the surface area is changing at a rate of 480 cm²/sec when each edge is 5 centimeters.

(b) Similarly, when each edge is 15 centimeters, we have a = 15 cm. Using the same process as before, we find dS/dt = 12a * da/dt = 12(15) * 8 = 1440 cm²/sec.

Therefore, the surface area is changing at a rate of 1440 cm²/sec when each edge is 15 centimeters.

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Answer:

95°

Step-by-step explanation:

Here we have angles of 30° and 55°, so the remaining angle is:

100%

$55 = $55. Or in other terms:

100% = 100%

$55 is the maximum number of the problem, which would be 100%. So, they are asking what the maximum is. Which is 100%.

100%

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer: %100

Step-by-step explanation:

55 is the number you are using and the highest number is 55 so it will be %100

The mean of the sampling proportion is 0.03 and the standard deviation of the sampling proportion is 0.008 if the probability that a student forgets to bring their ID with them when they take their SAT is 3%. and a random sample of 500 students was selected.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

We have:

p = 0.03

n = 500 students

\(\rm {\hat p} - Normal\)

So the mean:

\(\rm \mu _\hat p \ = \ p \ = \ 0.03\)

For standard deviation:

\(\rm \sigma_p = \sqrt{\frac{pq}{m} }\)

q = 1 - p = 1 - 0.03 = 0.97

\(\rm \sigma_p = \sqrt{\frac{0.03\times 0.97}{500} }\)

\(\rm \sigma_p = 0.008\)

Thus, the mean of the sampling proportion is 0.03 and the standard deviation of the sampling proportion is 0.008 if the probability that a student forgets to bring their ID with them when they take their SAT is 3%. and a random sample of 500 students was selected.

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The probability that the weight limit will be exceeded when there are exactly 40 passengers and 3 crew members on board is 0.031.

Mean = 196 × 43

Mean = 8428

Std. Dev. = 63 × √(43)

Std. Dev. = 63 × 6.56

Std. Dev. = 413.28

Here, μ = 8428, σ = 413.1186 and x = 9200. We must calculate P(X ≥ 9200).

he central limit theorem states that, for a sufficiently large sample size, the sample mean of all observations will be approximately normally distributed, regardless of the distribution of the population from which it was sampled.

The Central Limit Theorem is used to get the associated z-value.

z = (x - μ)/σ

z = (9200 - 8428)/413.28

z = 772/413.28

z = 1.87

Therefore,

P(X ≥ 9200) = P(z ≤ (9200 - 8428)/413.1186)

P(X ≥ 9200) = P(z ≤ 772/413.1186)

P(X ≥ 9200) = P(z ≥ 1.87)

P(X ≥ 9200) = 1 - 0.9693

P(X ≥ 9200) = 0.031

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The complete question is:

A small jet can carry up to 40 passengers and 3 crew members. There is a weight restriction of 9200 pounds on board. The combined weight of each passenger (or crew member) and his luggage has a mean of 196 pounds, with a standard deviation of 63 pounds. What is the probability that the weight limit will be exceeded when there are exactly 40 passengers and 3 crew members on board? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

Answer:

D

Step-by-step explanation:

from what I could tell, it sounds like D would be correct

Answer: $7,291.14

Step-by-step explanation: To calculate the value of the car in 2020, you can use the formula y = 20,000(0.85)^10.

Here, y represents the value of the car in 2020, 20,000 is the initial value of the car, and 0.85 is the depreciation rate. The exponent 10 represents the number of years that have passed, so the formula calculates the value of the car after 10 years by multiplying the initial value by the depreciation rate raised to the power of 10.

To perform this calculation, you can calculate 0.85^10 first, and then multiply that result by 20,000:

0.85^10 = (0.85)(0.85)(0.85)...(0.85) (10 times)

      = 0.364569708

y = 20,000 * 0.364569708

 = 7,291. 139416

So the value of the car in 2020 would be approximately $7,291.14.

Considering the definition of an equation and the way to solve it, the number of points Carlos scored in the last game is 19.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being:

and knowing that in the last game, Fabio had 7 points less than 2 times as many points as Carlos, the equation to determine the number of points Carlos scored in the last game is:

2C - 7= F

Fabio scored 31 points in the game. So you get:

2C - 7= 31

Solving:

2C= 31 + 7

2C= 38

C= 38 ÷ 2

C=19

Finally, the number of points Carlos scored in the last game is 19.

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Answer:

b probably

Step-by-step explanation:

Answer:

1 1/8

Step-by-step explanation:

1. Keep, change, flip

3/4 x 3/2

2. Multiply

3/4 x 3/2= 9/8

3. Simplify

9/8= 1/18

Answer:

Christina will pay $82.71 after tax

Answer:

Put a dot on 7 on the y axis then draw a horizontal line through y=7

Step-by-step explanation:

(1), Yes, it is appropriate to use the normal approximation as np and n(1-p) both exceed 10. (2), The z-score for the probability of less than 27% of people in a sample of 82 having high blood pressure is approximately 1.2727.

Part 1 Yes, it is appropriate to use the normal approximation to find the probability that more than 48% of the people in the sample have high blood pressure. The conditions for using the normal approximation are satisfied when both np and n(1 - p) are greater than or equal to 10.

In this case,

np = 37 * 0.2 = 7.4

and

n(1 - p) = 37 * 0.8 = 29.6,

both of which are greater than 10.

part 2  To find the probability that less than 27% of the people in a sample of 82 have high blood pressure, we can use the normal approximation.

To calculate the z-score for the probability of less than 27% of the people in a sample of 82 having high blood pressure, we can use the formula:

z = (x - μ) / (σ / √n)

Where:

x is the sample proportion (0.27)

μ is the population proportion (0.20)

σ is the population standard deviation (sqrt(0.2 * 0.8) = 0.4)

n is the sample size (82)

Plugging in the values, we have:

z = (0.27 - 0.20) / (0.4 / √82)

z = 0.07 / (0.4 / 9.055)

z ≈ 1.2727

Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to this z-score. The probability that less than 27% of the people in the sample of 82 have high blood pressure is the cumulative probability to the left of z = 1.2727.

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--The given question is incomplete, the complete question is given below " High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high blood pressure is 0.2. A sample of 37 U.S. adults is chosen. Use the TI-84 Plus Calculator as needed. Round the answer to at least four decimal places.  Part 1  Is it appropriate to use the normal approximation to find the probability that more than 48% of the people in the sample have high blood pressure? It (Choose one) appropriate to use the normal curve, since np - Choose one) and n(1 - p) = (Choose one) 10.

Part 2  Find the probability that less than 27% of the people in the sample of 82 have high blood pressure. The probability that less than 27% of the people in the sample of 82 have high blood pressure is"--

Answer:

17/24

Step-by-step explanation:

hope this helped:)

Answer: i think it is 17/24

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

20 / 2 = 10

10 - 4 = 6

Answer:

8??

Step-by-step explanation:

Answer:

7 feet long

Step-by-step explanation:

This set up will give a right angle triangle where;

Length of the ladder is the hypotenuse = x

The distance of the ladder to the house is the adjacent = 3 feet

Angle of elevation theta = 72 degrees

Using the CAH in trigonometry identity;

cos theta = adjacent/hypotenuse

cos 72 = 3/hyp

hyp = 3/cos72

hyp = 3/0.4258

hyp = 7.05 feet

Hence the ladder is approximately 7 feet long

Answer:

I need the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample is the part of the population that somebody wants to study. therefore, the sample is the 100 male students interviewed

Answer:

Step-by-step explanation:

It's not proportional because for every 1 month there's supposed to be 3 pounds, but it shows that when she was 3 months she is 6 pounds soits not proportional because it shows she grows 3 times at first but then by 3 months she grows 1/3

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

mean is $11

median is $10

Step-by-step explanation:

Answer:

You can Ask nicely about that,

we are not doing your homework for you.

if you have question, put it on the question.

not giving us a doc.

We do not want anything returned

Thankyou

Answer:

All results in the explanation

Step-by-step explanation:

To make the equation of the line, we only need two points. Select from the table the points (-1,4) and (3,9).

First, find the slope of the line:

We know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

\begin{gathered}\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\\\end{gathered}m=x2−x1y2−y1

Substituting:

\displaystyle m=\frac{9-4}{3+1}=\frac{5}{4}m=3+19−4=45

This value is used in the slope-point form of the line:

\displaystyle y-k=\frac{5}{4}(x-h)y−k=45(x−h)

Where (h,k) is a point from the table, select for example (3,9):

\displaystyle y-9=\frac{5}{4}(x-3)y−9=45(x−3)

Operate:

\displaystyle y=\frac{5}{4}\cdot x-\frac{5}{4}\cdot 3+9y=45⋅x−45⋅3+9

\displaystyle y=\frac{5}{4}\cdot x+\frac{-15+36}{4}y=45⋅x+4−15+36

The equation of the line is:

\boxed{\displaystyle y=\frac{5}{4}\cdot x+\frac{21}{4}}y=45⋅x+421

Now complete the table.

For x=0:

\displaystyle y=\frac{5}{4}\cdot 0+\frac{21}{4}y=45⋅0+421

y=\frac{21}{4}y=421

For x=15

\displaystyle y=\frac{5}{4}\cdot 15+\frac{21}{4}y=45⋅15+421

\displaystyle y=\frac{75}{4}+\frac{21}{4}=\frac{96}{4}=24y=475+421=496=24

y=24

For y=1.5, find x:

\displaystyle 1.5=\frac{5}{4}\cdot x+\frac{21}{4}1.5=45⋅x+421

Operate:

\displaystyle 1.5-\frac{21}{4}=\frac{5}{4}\cdot x1.5−421=45⋅x

Multiply by 4:

\displaystyle 6-21=5 x6−21=5x

Solve:

x=-15/5=-3x=−15/5=−3

x=-3

Answer:

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

perimeter = 2(length + width)

In this case, the length is 14.3 yards and the width is 12 yards. Substituting these values into the formula, we get:

perimeter = 2(14.3 + 12)

perimeter = 2(26.3)

perimeter = 52.6 yards

Therefore, the perimeter of the rectangle is 52.6 yards.

The area of a rectangle is given by the formula:

area = length x width

Substituting the length and width values, we get:

area = 14.3 x 12

area = 171.6 square yards

Therefore, the area of the rectangle is 171.6 square yards.

Andy weighs 44lbs. He is to receive 1tsp of medicine for every 15 kg he weighs. How many cc's will he receive? Round to the nSolution:Given,Andy weighs 44 lbs.Convert 44 lbs into kg.1 pound = 0.45359237 kg44 pounds = 19.958 kg1 tsp is given for every 15 kg he weighs.1 tsp = 5 cc (Approximately)Therefore, 19.958 kg will get,(1/15) * 1 tsp = (1/15) * 5 cc = 0.33333 cc (approximately)Therefore, the number of cc's Andy will receive = 0.33333 cc (Approximately)Aspirin 600mg is orderedYou have available gr v tablets. How many tablets will you give? Round to nearest whole numberSolution:Given,Aspirin 600 mg is ordered.You have available gr v tablets.1 gram = 1000 mg600 mg = 0.6 gTherefore, 0.6 g of aspirin is ordered.1 tablet contains gr v= 0.324 g (approx)Therefore, the number of tablets will be given = 0.6 g / 0.324 g ≈ 2The number of tablets to be given = 2 tablets (approximately).The doctor has ordered Tylenol 650mg. You have available Tylenol elixir g g/15cc. How many tsp will you give? Round to nearest whoSolution:Given,Tylenol 650 mg is ordered.Tylenol elixir is available.1 g = 1000 mg1 g / 15 cc = 0.0666667 g/ccTherefore, Tylenol elixir is 0.0666667 g/cc.Hence, the number of tsp will be given is 2 tsp (approx).A 55lb child is to receive liquid ampicillin 5mghkg of body weight. How many cc's will she receive if the ampicillin bottle is labeled 150mg/5 ce? Round to the nearest tenth.Solution:Given,The weight of the child is 55 lbs.1 pound = 0.45359237 kgTherefore, the weight of the child in kg is,55 lbs × 0.45359237 kg = 24.947 kgThe liquid ampicillin is 5 mg/kg.Therefore, the amount of liquid ampicillin will be given,24.947 kg × 5 mg/kg = 124.735 mg = 0.124735 gThe ampicillin bottle is labeled 150 mg/5 cc.Therefore, the amount of liquid to be given,150 mg/5 cc = 30 mg/ccTherefore, the number of cc's of liquid ampicillin to be given,0.124735 g × 1,000 mg/1 g × 1 cc/30 mg = 4.1581 cc ≈ 4.2 ccTherefore, the number of cc's of liquid ampicillin to be given is 4.2 cc (Approximately).

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Based on the fact that Troop 175 wants the bathrooms to be halfway between the cabins and the mess hall, the coordinates of the bathrooms will be (1, 1).

First, what are the coordinates for the cabins and mess hall?

Mess hall:

= (-4, -1)

Cabins:

= (6, 3)

The halfway point is:

= ( (-4 + 6)/2 , (-1 + 3) / 2)

= (2 / 2, 2/2)

= (1, 1)

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