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3 years ago

given that (y+2) (y+3) and (2y^2+1) are consecutive terms of an arithmetic progression, find the possible value of y

Mathematics

1 answer:

mafiozo [28]3 years ago

8 0

Answer:

-3/2 and 1

Step-by-step explanation:

Given the arithmetic sequence (y+2) (y+3) and (2y²+1), the common difference is gotten by taking the difference in their terms. For example if we have 3 terms T1, T2, T3... the common difference d = T2-T1 = T3-T2

From the sequence given;

T1 = y+2, T2 = y+3 and T3 = 2y²+1

d = y+3-(y+2) = 2y²+1- (y+3)

open the parenthesis

y+3-y-2 = 2y²+1- y-3

1 = 2y²+1- y-3

1 = 2y²- y-2

2y²- y-2-1 = 0

2y²- y-3 =0

Factorize the resulting expression

2y²- y-3 =0

2y²- 2y+3y-3 =0

2y(y-1)+3(y-1) = 0

(2y+3)(y-1) = 0

2y+3 = 0 and y-1 = 0

2y = -3 and y =1

y = -3/2 and 1

Hence the possible values of y are -3/2 and 1

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stira [4]

we have

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$24p-18p-2p=10-6-12$

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3 years ago

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Suppose you can somehow choose two people at random who took the SAT in 2014. A reminder that scores were Normally distributed w

Sindrei [870]

Answer:

22.29% probability that both of them scored above a 1520

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 1497, \sigma = 322$

The first step to solve the question is find the probability that a student has of scoring above 1520, which is 1 subtracted by the pvalue of Z when X = 1520.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1520 - 1497}{322}$

$Z = 0.07$

$Z = 0.07$ has a pvalue of 0.5279

1 - 0.5279 = 0.4721

Each students has a 0.4721 probability of scoring above 1520.

What is the probability that both of them scored above a 1520?

Each students has a 0.4721 probability of scoring above 1520. So

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22.29% probability that both of them scored above a 1520

8 0

3 years ago

What is the minimum number of clients the travel agent should survey? Note that z=1.96 for a 95% confidence interval.

slega [8]

Answer:

121

Step-by-step explanation:

Given data as per the question

Standard deviation = $\sigma$ = 840

Margin of error = E = 150

Confidence level = c = 95%

For 95% confidence, z = 1.96

based on the above information, the minimum number of clients surveyed by the travel agent is

$n = (\frac{z\times \sigma}{E})^2$

$= (\frac{1.96\times 840}{150})^2$

= 120.47

= 121

hence, the 121 number of clients to be surveyed

Therefore we applied the above formula to determine the minimum number of clients

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3 years ago

SOLVE x^4 − 15x^2 − 16 = 0 What are the roots of the equation?

kakasveta [241]

Answer:

roots : 4, -4, i, -i

Step-by-step explanation:

This gets a bit tricky.

We have to substitude x^2 as u in this problem.

Now to rewrite x^4 − 15x^2 − 16 = 0 with u, we get

u^2 - 15u - 16 = 0

( u - 16) (u + 1)

U = 16

U = -1

This is not the end of the problem.

Now we have to substitute x^2 back to u.

x^2 = 16 --> we get the roots 4 and -4

x^2 = -1 --> we get the roots i and -i

tadah!

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2 years ago

Find the perimeter. Use 3.14 for pi.

balu736 [363]

Step-by-step explanation:

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3 years ago

given that (y+2) (y+3) and (2y^2+1) are consecutive terms of an arithmetic progression, find the possible value of y​

given that (y+2) (y+3) and (2y^2+1) are consecutive terms of an arithmetic progression, find the possible value of y