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3 years ago

What is the value of 7x(3x+x), when x =8?

Mathematics

2 answers:

abruzzese [7]3 years ago

3 0

If x equals 8, 7(8) times (24 + 8), simplifying to 56 times 32

the answer is 1792

timofeeve [1]3 years ago

3 0

It is a bit confusing, so i will do the equation both ways:

1 way :

7·8(3·8+8)
=7·8(24+8)
=7·8(32)
=56(32)
=1960

2 way:

7(3·8+8)
7(24+8)
7(32)
224

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3 years ago

In a random sample of 11 residents of the state of New York, the mean waste recycled per person per day was 2.9 pounds with a st

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Answer:

80% confidence interval for the mean waste recycled per person per day for the population of New York is [2.495 , 3.305].

Step-by-step explanation:

We are given that a random sample of 11 residents of the state of New York, the mean waste recycled per person per day was 2.9 pounds with a standard deviation of 0.98 pounds.

Firstly, the pivotal quantity for 80% confidence interval for the true mean waste recycled per person per day for the population of New York is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean waste recycled per person per day = 2.9 pounds

s = sample standard deviation = 0.98 pounds

n = sample of residents = 11

$\mu$ = true mean waste recycled per person per day

Here for constructing 80% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 80% confidence interval for the true mean, $\mu$ is ;

P(-1.372 < $t_1_0$ < 1.372) = 0.80 {As the critical value of t at 10 degree of

freedom are -1.372 & 1.372 with P = 10%}

P(-1.372 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 1.372) = 0.80

P( $-1.372 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $1.372 \times {\frac{s}{\sqrt{n} } }$ ) = 0.80

P( $-\bar X -1.372 \times {\frac{s}{\sqrt{n} }$ < - $\mu$ < $-\bar X +1.372 \times {\frac{s}{\sqrt{n} }$ ) = 0.80

P( $\bar X -1.372 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +1.372 \times {\frac{s}{\sqrt{n} }$ ) = 0.80

80% confidence interval for $\mu$ = [ $\bar X -1.372 \times {\frac{s}{\sqrt{n} }$ , $\bar X +1.372 \times {\frac{s}{\sqrt{n} }$ ]

= [ $2.9 -1.372 \times {\frac{0.98}{\sqrt{11} }$ , $2.9 -1.372 \times {\frac{0.98}{\sqrt{11} }$ ]

= [2.495 , 3.305]

Therefore, 80% confidence interval for the mean waste recycled per person per day for the population of New York is [2.495 , 3.305].

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