This is the sum of the arithmetic sequence:
10 - 2 + 6 + 14 + ... + 110
where: a 1 = - 10, d = 8
a n = 110
a n = a 1 + ( n - 1 ) * d
110 = - 10 + ( n - 1 ) * 8
110 = - 10 + 8 n - 8
110 + 10 + 8 = 8 n
128 = 8 n
n = 128 : 8
n = 16
∑ n = n/2 * ( a 1 + a n )
∑ 16 = 16/2 * ( -10 + 110 ) = 8 * 100 = 800
Answer:
The sum is 800.

7 0

3 years ago

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According to a survey, 74% of households said that they have never purchased organic fruits or vegetables. Suppose that this res

Andreyy89

Answer:

(a) S = {0, 1, 2, ..., 10}

(b) 0.256

Step-by-step explanation:

It is provided that, 74% of households said that they have never purchased organic fruits or vegetables.

(a)

X = the number of households in a random sample of 10 who have never purchased organic fruits or vegetables.

X follows a binomial distribution.

The sample space of X is:

S = {0, 1, 2, ..., 10}

(b)

Compute the probability that exactly 7 households in a random sample of 10 will say that they have never purchased organic fruits or vegetables as follows:

$P(X=7)={10\choose 7}(0.74)^{7}(1-0.74)^{10-7}$

$=120\times 0.121513\times 0.017576\\\\=0.25628549856\\\\\approx 0.256$

Thus, the probability that exactly 7 households in a random sample of 10 will say that they have never purchased organic fruits or vegetables is 0.256.

6 0

4 years ago