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BaLLatris [955]
3 years ago
10

Guys please help me out ASAP, Due today. I

Mathematics
1 answer:
Mice21 [21]3 years ago
5 0

Answer:

T_7 = 11

T_n = 2n- 3

Step-by-step explanation:

Given

S_n = n^2 -2n

T_n = S_n - S_{n-1}

Solving (a): T7

Substitute 7 for n in T_n = S_n - S_{n-1}

T_7 = S_7 - S_{7-1}

T_7 = S_7 - S_6

Calculate S7 and S6

S_n = n^2 -2n

S_7 = 7^2 - 2 * 7 = 35

S_6 = 6^2 - 2 * 6 = 24

So:

T_7 = 35 -24

T_7 = 11

Solving (b): Tn

T_n = S_n - S_{n-1}

Where S_n = n^2 -2n

CalculateS_{n-1}

We have:

S_{n-1} =(n-1)^2 - 2(n-1)

Open brackets

S_{n-1} = n^2 -2n + 1 -2n +2

S_{n-1} = n^2 -2n-2n + 1  +2

S_{n-1} = n^2 -4n + 3

So:

T_n = S_n - S_{n-1}

T_n = n^2 - 2n - (n^2 -4n + 3)

T_n = n^2 - 2n - n^2 +4n - 3

Collect Like Terms

T_n = n^2 - n^2- 2n  +4n - 3

T_n = 2n- 3

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There asking for the equation, and the possible answers are 

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4 0
2 years ago
Statistics show that about 42% of Americans voted in the previous national election. If three Americans are randomly selected, w
MrRa [10]

Answer:

19.51% probability that none of them voted in the last election

Step-by-step explanation:

For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

42% of Americans voted in the previous national election.

This means that p = 0.42

Three Americans are randomly selected

This means that n = 3

What is the probability that none of them voted in the last election

This is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951

19.51% probability that none of them voted in the last election

6 0
2 years ago
A campground consists of 5 square campsites arranged in a line along a beach. The distance from the edge of a campsite to the wa
Anestetic [448]
To answer this question with the choices given, you would substitute the possible answers into your work for the base and the height of each dimension on the entire campground.

To find the length of the campground, you multiply each choice by 5 because there are 5 campsites.

For the width, you add each choice to 4.

Then you multiply the total length by the total width to see if your answer is 950 square yards.

See the attached picture for all the work.

7 0
3 years ago
M∠1 = 80 – x; and
Burka [1]

Answer:

10

Step-by-step explanation:

<em>m∠</em>2 and <em>m∠</em>1 are congruent by the Corresponding Angles Theorem; we set both expressions equal to each other:

[80 - x]° = [90 - 2x]°

+ x° + x°

______________

80° = [90 - x]°

-90° - 90°

__________

−10° = [−x]°

10° = x

I am joyous to assist you anytime.

6 0
2 years ago
Nick goes to the store and buys 22 notebooks for $1.50 each. Then he buys 8 pens for $0.55 each. How much money did he spend in
rosijanka [135]

Answer:

$33 for the notebooks and $4.40 for the pens

Step-by-step explanation:

if u would multiply 33 by 1.50 you would get $33

if u would multiply 8 by 0.55 you would get $4.40

8 0
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