Find the inner product for (-8,2) (4.5,18) and state whether the vectors are perpendicular.

Mathematics

1 answer:

Anna71 [15]2 years ago

3 0

Answer: 0; Yes

Step-by-step explanation:

-8 x 4.5 = -36

2 x 18 = 36

-36 + 36 = 0

since the product is zero, the vectors are perpendicular

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A gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than

Neko [114]

Answer:

The probability that no more than 70% would prefer to start their own business is 0.1423.

Step-by-step explanation:

We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.

Let $\hat p$ = sample proportion of people who prefer to start their own business

The z-score probability distribution for the sample proportion is given by;

Z = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, p = population proportion who would prefer to start their own business = 72%

n = sample of 18-29 year-olds = 600

Now, the probability that no more than 70% would prefer to start their own business is given by = P( $\hat p$ $\leq$ 70%)

P( $\hat p$ $\leq$ 70%) = P( $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ $\leq$ $\frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } }$ ) = P(Z $\leq$ -1.07) = 1 - P(Z < 1.07)