triangle town wants to build a school that is equidistant from its three cities L,M, and N. Which construction correctly finds the best location of the school? A. Construction Y because point E is the incenter of triangleLMN B. Construction Y because point E is the circumcenter of triangleLMN C. Construction X because point C is the incenter of triangleLMN D. Construction X because point C is the circumcenter of triangleLMN

Answer:

For 1: The first term is 10 and the common difference is

For 2: The value of n is 27

Step-by-step explanation:

The n-th term of the progression is given as:

where,

is the first term, n is the number of terms and d is the common difference

The sum of n-th terms of the progression is given as:

where,

is the sum of nth terms

• For (1):

The 11th term of the progression:

              .......(1)

Sum of first 4 numbers:

             ......(2)

Forming equations:

                 ( × 8)

The equations become:

Solving above equations, we get:

Putting value in equation (1):

Hence, the first term is 10 and the common difference is

• For 2:

The nth term is given as:

Solving the above equation:

Hence, the value of n is 27

Final answer:

The value of n when the nth term of the progression is 49 is 22.

Explanation:

The 11th term of the progression (a11) is 25.

The sum of the first 4 terms (S4) is 49.

The nth term (an) is 49.

Let's find the answers to your questions:

Find the first term of the progression (a1) and the common difference (d):

We know that the nth term of an AP can be expressed as:

an = a1 + (n - 1)d

Substituting the values:

a11 = a1 + (11 - 1)d

25 = a1 + 10d

Now, we need to find a1 and d. We'll also use the information that the sum of the first 4 terms (S4) is 49. In an AP, the sum of the first n terms (Sn) can be expressed as:

Sn = (n/2)[2a1 + (n - 1)d]

For S4:

49 = (4/2)[2a1 + (4 - 1)d]

49 = 2[2a1 + 3d]

Now, we have two equations:

25 = a1 + 10d

49 = 2[2a1 + 3d]

Let's solve this system of equations to find a1 and d.

1. First, rearrange the first equation to isolate a1:

a1 = 25 - 10d

Now, substitute this expression for a1 into the second equation:

49 = 2[2(25 - 10d) + 3d]

Simplify and solve for d:

49 = 2[50 - 20d + 3d]

49 = 2[50 - 17d]

49 = 100 - 34d

34d = 100 - 49

34d = 51

d = 51/34

d = 3/2

2. Now that we have the common difference (d), we can find a1 using the first equation:

a1 = 25 - 10d

a1 = 25 - 10(3/2)

a1 = 25 - 15/2

a1 = (50 - 15)/2

a1 = 35/2

a1 = 17.5

So, the first term of the progression (a1) is 17.5, and the common difference (d) is 3/2.

Find the value of n when the nth term of the progression is 49:

We know that an = 49, and we can use the formula for an in an AP:

an = a1 + (n - 1)d

Substitute the values:

49 = 17.5 + (n - 1)(3/2)

49 - 17.5 = (n - 1)(3/2)

31.5 = (n - 1)(3/2)

To isolate n, multiply both sides by (2/3):

(n - 1)(3/2) = 31.5 * (2/3)

(n - 1) = 21

Now, add 1 to both sides to find n:

n = 21 + 1

n = 22

So, the value of n when the nth term of the progression is 49 is 22.

Learn more about Arithmetic Progression here:

brainly.com/question/35697112

#SPJ3

Answer:

The sample size needed if the margin of error of the confidence interval is to be no more than 0.02.

n= 2015

Step-by-step explanation:

Given the customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion that are dissatisfied

Given data from  past studies, they believe that this proportion will be about 0.28

The proportion of success(p)  = 0.28

We know that the margin of error of 95% of intervals of given proportion

margin of error =  …(i)

Given margin of error = 0.02

Substitute values in equation (i) cross multiplication √n

0.02 √n  = 2√0.28X0.72

On calculation, we get √n = 44.89

squaring on both sides, we get

n = 2015

Conclusion:-

The sample size needed if the margin of error of the confidence interval is to be no more than 0.02.

n= 2015

Answer:

Robin can clean 9828 rooms in 9 days

Step-by-step explanation:

Since Robin can clean 727272 rooms in 666 days, we can find how many rooms she can clean in 1 day by dividing 727272 by 666

number of rooms cleaned by Robin in 1 day = 727272 rooms/666 days = 1092 rooms/day

We can then find how many rooms she can clean in 9 days by multiplying 1092 by 9

1092 rooms/day * 9 days = 9829 rooms

Answer:

54

Step-by-step explanation:

9(6)=54

6(9)=54

54=(30)+(24)  54=54 so it is true

9x6=54

Answer: 0.9726

Step-by-step explanation:

Given :  Females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minutes.

i.e. and

Let x is a random variable to represent the pulse rates.

Formula :

For n= 16 , the probability that her pulse rate is less than 80 beats per minute will be :-

Hence, the required probability = 0.9726

Final answer:

The probability that a randomly selected female's pulse rate is less than 80 beats per minute, given a mean pulse rate of 74.0 and standard deviation of 12.5 beats per minute, is approximately 0.6844, or 68.44%.

Explanation:

This question pertains to the topic of normal distribution in statistics. We know that the average or mean pulse rate for females is 74.0 beats per minute, with a standard deviation of 12.5 beats per minute. We also know that the pulse rate we want to find the probability for is less than 80 beats per minute.

In these situations, we use the formula for the z-score, which is Z = (X - μ) / σ, where X is the value, we're interested in, μ is the mean, and σ is the standard deviation.

Using this formula, we find Z = (80 - 74) / 12.5 = 0.48. After finding the z-score, we can look at the standard normal distribution table to get the probability. The value for Z = 0.48 on the Z table is approximately 0.6844. Therefore, the probability that a randomly selected female's pulse rate is less than 80 beats per minute is approximately 0.6844, or 68.44%.

Learn more about Normal Distribution here:

brainly.com/question/30390016

#SPJ6