Eleven years ago, you deposited $3,200 into an account. seven years ago, you added an additional $1,000 to this account. you earned 9.2 percent, compounded annually, for the first 4 years and 5.5 percent, compounded annually, for the last 7 years. how much money do you have in your account today? $8,666.67 $7,411.90 $7,717.29 $8,073.91 $8,708.15

The population standard deviation of the weights of the defensive tackles is approximately 3.96 pounds.

Here, we have to calculate the population standard deviation,

Calculate the mean:

Mean = (204 + 215 + 207 + 212 + 214 + 208) / 6

Mean = 1260 / 6

Mean = 210 pounds

Calculate the squared differences between each weight and the mean:

[tex](204 - 210)^2 = 36\\(215 - 210)^2 = 25\\(207 - 210)^2 = 9\\(212 - 210)^2 = 4\\(214 - 210)^2 = 16\\(208 - 210)^2 = 4[/tex]

Find the mean of the squared differences:

Mean of squared differences = (36 + 25 + 9 + 4 + 16 + 4) / 6

Mean of squared differences = 94 / 6

Mean of squared differences = 15.67

Take the square root of the mean of squared differences:

Population standard deviation = √(15.67)

Population standard deviation ≈ 3.96 pounds

So, the population standard deviation of the weights of the defensive tackles is approximately 3.96 pounds.

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Answer: The Mean

The mean is when you add up all of those grades and divide by the amount of exams.

18^3 = 5832 (volume of crate)

3^3 = 27 ( volume of small cubes)

5832/27 = 216 cubes ( divide volumes to get number of cubes)

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[tex]\textsf{Using the distributive property, \textbf{a(b+c)=ab+ac}, expand the given expression:}[/tex]

[tex].\qquad\bullet\sf{4x(2x-6)=4x*2x-4x*6=8x^2-24x}[/tex]

[tex]\sf{\bf{$Answer: 8x^2-24x}}[/tex]

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Answer:

b

Step-by-step explanation:

Answer:

C.  

buying it at a 10% discount without sales tax

Step-by-step explanation:

the 2 angls need to equal 180 degrees

 so 2x-y +  60 = 180

 and 2x+y + 40 = 180

 using the choices you have

 answer is B x = 65, y = 10

 when you use those values they both equal 180

To find the probabilities using the normal table and R's pnorm function, follow these steps: (a) p r(z ≤ 1.45) is 0.9265 or 92.65%. (b) p r(z > −1.28) is 0.8997 or 89.97%. (c) p r(−0.674 ≤ z < 1.036) is 0.6017 or 60.17%. (d) p r(z > 0.836) is 0.2013 or 20.13%.

To find the probabilities using the normal table and r's pnorm function, we can follow these steps:

For (a) p r(z ≤ 1.45), we can use the normal table or the pnorm function in R to find the area to the left of 1.45. The area is 0.9265 or 92.65%.

For (b) p r(z > -1.28), we can find the area to the left of -1.28 using the normal table or the pnorm function in R, which is 0.1003 or 10.03%. To find the area to the right of -1.28, we subtract this value from 1. The area is 0.8997 or 89.97%.

For (c) p r(-0.674 ≤ z < 1.036), we can find the area to the left of -0.674 using the normal table or the pnorm function in R, which is 0.2514 or 25.14%. To find the area to the left of 1.036, we can use the normal table or the pnorm function in R, which is 0.8531 or 85.31%. The difference between these two values gives us the area between the z-scores, which is 0.8531 - 0.2514 = 0.6017 or 60.17%.

For (d) p r(z > 0.836), we can find the area to the left of 0.836 using the normal table or the pnorm function in R, which is 0.7987 or 79.87%. To find the area to the right of 0.836, we subtract this value from 1. The area is 0.2013 or 20.13%.

To derive an identity for 2sin2θ using the cosine double-angle identity cos(2θ) = 1 − 2sin²θ, we can rearrange the equation and substitute the value of sin²θ to obtain the identity 2sin²θ = 1 - cos(2θ).

To derive an identity for 2sin2θ using the cosine double-angle identity cos(2θ) = 1 − 2sin²θ, we can start by rearranging the equation to solve for sin²θ. This gives us sin²θ = (1 - cos(2θ))/2.

Next, we can substitute this value into the expression for 2sin²θ. This gives us 2sin²θ = 2(1 - cos(2θ))/2 = 1 - cos(2θ).

Therefore, the identity for 2sin²θ is 1 - cos(2θ).

The number of combinations that will result in a sum of 7 is:

1 + 6

6 + 1

2 + 5

5 + 2

3 + 4

4 + 3

For a total of 6 combinations per roll. While the total number of combinations per roll are:

6 * 6 = 36

Hence the probability that the sum is 7 would be:

Probability = 6 / 36 = 1 / 6

For a succession of three times, the overall probability that each three rolls will be a sum of 7 is:

Overall probability = (1/6) * (1/6) * (1/6)

Overall probability = 1/216 = 4.63 x 10^-3 = 0.463%

Final answer:

The probability of rolling a sum of 7 three times in succession using two balanced dice is 1/216.

Explanation:

To determine the probability that on each of the three rolls of two balanced dice, the sum of the two numbers that appear will be 7, we first need to identify the probability of rolling a sum of 7 with a single roll of two dice. There are six ways to roll a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of possible outcomes when rolling two dice is 6*6 = 36. Therefore, the probability of rolling a sum of 7 on one roll is P(sum=7) = 6/36 = 1/6.

Since each roll is independent of the others, the probability of this event occurring three times in succession is the product of the individual probabilities. Thus:

Therefore, the probability of all three rolls resulting in a sum of 7 is:

P(Three 7's in a row) = P(First roll is 7) * P(Second roll is 7) * P(Third roll is 7) = (1/6) * (1/6) * (1/6) = 1/216.

Answer:

A

Step-by-step explanation:

it has the same slope and the same y-intercept