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2 years ago

5

P and q are two arithmetic sequences. The first four terms of sequence P are 2,6,10,14. The nth term of sequence Q is 145-3n. Th

e rth term of sequence P has the same values as the rth term of sequence Q. Work out the value of r.

1 answer:

Tomtit [17]2 years ago

5 0

Answer:

r = 21

Step-by-step explanation:

nth of sequence P :

$T_{n} = 4n -2$

$r^{th} term$ : $4r-2=145-3r\\4r+3r=145+2\\7r=147\\r=21$

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3 years ago

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4 years ago

Suppose you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. If you randomly

mina [271]

Answer:

(a) The probability you pass the exam is 0.0000501.

(b) The expected number of correct guesses is 7.5.

(c) The standard deviation is 2.372.

Step-by-step explanation:

We are given that you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. And you randomly guess on all 30 questions.

Since there is an assumption of only 1 correct choice out of 4 which means the above situation can be represented through binomial distribution;

$P(X =x) = \binom{n}{r}\times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,3,......$

where, n = number of trials (samples) taken = 30

r = number of success = at least 60%

p = probbaility of success which in our question is the probability

of a correct answer, i.e; p = $\frac{1}{4}$ = 0.25

Let X = Number of questions that are correct

So, X ~ Binom(n = 30 , p = 0.25)

(a) The probability you pass the exam is given by = P(X $\geq$ 18)

Because 60% of 30 = 18

P(X $\geq$ 18) = P(X = 18) + P(X = 19) +...........+ P(X = 29) + P(X = 30)

= $\binom{30}{18}\times 0.25^{18}\times (1-0.25)^{30-18} + \binom{30}{19}\times 0.25^{19}\times (1-0.25)^{30-19} +.......+ \binom{30}{29}\times 0.25^{29}\times (1-0.25)^{30-29} + \binom{30}{30}\times 0.25^{30}\times (1-0.25)^{30-30}$

= 0.0000501

(b) The expected number of correct guesses is given by;

Mean of the binomial distribution, E(X) = $n \times p$

= $30 \times 0.25$ = 7.5

(c) The standard deviation of the binomial distribution is given by;

S.D.(X) = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{30 \times 0.25 \times (1-0.25)}$

= $\sqrt{5.625}$ = 2.372

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4 years ago