MATHEMATICS COLLEGE

Find the 1000th term for the sequence

Answers

Answer 1

Answer:

Answer:

D. 7017

Step-by-step explanation:

if 24 is the first term, find 7x999, or 7x1000-7 and add 24

however a better way would be to use the formula

value=a+(n-1)d

a = the first term in the sequence (24)

n = the amount of terms you need (1000)

d = the common difference between terms (7)

Related Questions

From the records of a health-insurance companies in Pennsylvania, it is known that 58% of the accounts include dental coverage. A researcher would like to take a random sample of 500 accounts to review. Find the standard deviation of the sample proportion in this situation. Give your answer to 4 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."
The commute times (in minutes) of 30 employees are listed below. (a) Find Qi, Q3, and the interquartile range (IQR). (b) Find the fences and determine if there are any outliers in the sample. 20 4 45 48 52 55 56 60 63 65 67 68 6 70 74 75 77 78 79 80 81 82 8 85 87 88 90 92 95 99
2 mi. yd. I'm confused
The minimum monthly payment for Cody's credit card is 2% of his balance or $20, whichever is higher. If Cody's balance at the end of his last billing cycle was $870, what is his minimum monthly payment?
DJ Davon is making a playlist for work; he is trying to decide what 12 songs to play and in what order they should be played. If he has his choices narrowed down to 14 blues, 25 country, and 21 disco songs, and he wants to play an equal number of blues, country, and disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Suppose that P dollars in principal is invested for t years at the given interest rates with continuous compounding. Determine the amount that the investment is worth at the end of the given time period.=P$10,000, =t112 yr

(a) 1% interest

(b) 4% interest

(c) 4.5% interest

Answers

Answer: (a )$30648.54 (b)$882,346.73 (c) $1,544,700.15

Step-by-step explanation:

Formula: $A=Pe^(rt)$ , where P= principal , r=rate of interest, t= time

Given : P= $10,000, t = 112 years

(a) r = 1% = 0.01

$A=(10000)e^(0.01*112)$

$A=(10000)e^(1.12)=10000(3.06485420)\approx 30648.54$

Hence, Amount = $30,648.54

(b) r = 4% = 0.04

$A=(10000)e^(0.04*112)$

$A=(10000)e^(4.48)=10000(88.2346726757)\approx 882346.73$

Hence, Amount = $882,346.73

(c) r = 4.5% = 0.045

$A=(10000)e^(0.045*112)$

$A=(10000)e^(5.04)=10000(154.470015026)\approx 1544700.15$

Hence, Amount = $1,544,700.15

Final answer:

For 1% interest, the investment will be worth $10100.50. For 4% interest, it will be worth $10420.96, and for 4.5% interest, it will be worth $10451.65.

Explanation:

To determine the amount that an investment is worth at the end of a given time period with continuous compounding, we can use the formula A = P * e^(rt), where A is the final amount, P is the principal, r is the interest rate, and t is the time in years.

(a) For 1% interest:

A = 10000 * e^(0.01 * 1) = $10100.50

(b) For 4% interest:

A = 10000 * e^(0.04 * 1) = $10420.96

A = 10000 * e^(0.045 * 1) = $10451.65

Learn more about Continuous compounding here:

brainly.com/question/32594953

#SPJ11

The integral $\pi\int\limits^2_1 {(1-(lnx)^(2)) } \, dx$ represents the volume of a solid obtained by rotating a region around y=-1. Evaluate.

Answers

Answer:

V = π (-2 (ln 2)² + 4 ln 2 − 1)

V ≈ 2.55

Step-by-step explanation:

V = π ∫₁² (1 − (ln x)²) dx

V/π = ∫₁² (1 − (ln x)²) dx

V/π = ∫₁² dx − ∫₁² (ln x)² dx

V/π = x |₁² − ∫₁² (ln x)² dx

V/π = 1 − ∫₁² (ln x)² dx

To evaluate the second integral, integrate by parts.

If u = (ln x)², then du = 2 (ln x) / x dx.

If dv = dx, then v = x.

∫ u dv = uv − ∫ v du

= (ln x)² x − ∫ x (2 (ln x) / x) dx

= x (ln x)² − 2 ∫ ln x dx

Integrate by parts again.

If u = ln x, then du = 1/x dx.

If dv = dx, then v = x.

∫ u dv = uv − ∫ v du

= x ln x − ∫ x (1/x dx)

= x ln x − ∫ dx

= x ln x − x

Substitute:

∫ (ln x)² dx = x (ln x)² − 2 ∫ ln x dx

∫ (ln x)² dx = x (ln x)² − 2 (x ln x − x)

∫ (ln x)² dx = x (ln x)² − 2x ln x + 2x

Substitute again:

V/π = 1 − ∫₁² (ln x)² dx

V/π = 1 − (x (ln x)² − 2x ln x + 2x) |₁²

V/π = 1 + (-x (ln x)² + 2x ln x − 2x) |₁²

V/π = 1 + (-2 (ln 2)² + 4 ln 2 − 4) − (-1 (ln 1)² + 2 ln 1 − 2)

V/π = 1 − 2 (ln 2)² + 4 ln 2 − 4 + 2

V/π = -2 (ln 2)² + 4 ln 2 − 1

V = π (-2 (ln 2)² + 4 ln 2 − 1)

V ≈ 2.55

In a University of Wisconsin (UW) study about alcohol abuse among students, 100 of the 40,858 members of the student body in Madison were sampled and asked to complete a questionnaire. One question asked was, "On how many days in the past week did you consume at least one alcoholic drink?" a. Identify the population and the sample. b. For the 40,858 students at UW, one characteristic of interest was the percentage who would respond "zero" to this question. For the 100 students sampled, suppose 29% gave this response. Does this mean that 29% of the entire population of UW students would make this response? Explain.

Answers

Answer:

a) The population is 40,858 students and the sample is 100.

b) No

Step-by-step explanation:

a) The population would be the 40,858 members of the student body. Since we are only applying the questionnaire to 100 students, the sample would be 100.

b) 29% of the students answered "zero" to the question on how many days in the past week they consumed at least one alcoholic drink. This means that 29 out of 100 students gave this answer. However, this doesn't mean that 29% of the entire population of UW would give this response. Why is that? Because our sample is very small so it might not be representative of the whole population. Equally, the results from such a sample cannot be exactly the same results we would get from an entire population.

Rita earns $18.00 per hr. If she gets a 6% raise, what will be her new hourly wage?

Answers

Answer:

19.06

Step-by-step explanation:

Take her wage and multiply by the percent increase

18*.06 =1.08

Add this to her original wage

18+1.06

19.06 is the new wage

Circletowns limits forms perfect circular shape it has a population of 20,000 and a population density of 480 people per square kilometers

Answers

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Twelve different video games showing substance use were observed and the duration of times of game play (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the sample data to construct a 98% confidence interval estimate of sigma, the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution.4,757 4,509 4,221 4,486 4,935
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5,043 4,038

Answers

Answer:

Step-by-step explanation:

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