Consider the equation below:

Mathematics

1 answer:

klemol [59]3 years ago

6 0

A. Four times a number increased by two is equal to twice the difference between the number and three

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A rocket is launched into the air and follows the path, h (t) = -3 * t^2 + 12 * t

DanielleElmas [232]

check the picture below.

so, the rocket will come back to the ground when h(t) = 0, thus

$\bf h(t)=-3t^2+12t\implies \stackrel{h(t)}{0}=-3t^2+12t\implies 0=-3t(t-4)\\\\[-0.35em]~\dotfill\\\\0=-3t\implies 0=t\impliedby \textit{0 seconds when it took off from the ground}\\\\[-0.35em]~\dotfill\\\\0=t-4\implies 4=t\impliedby \textit{4 seconds later, it came back down}$

8 0

4 years ago

Suppose a large shipment of laser printers contained 18% defectives. If a sample of size 340 is selected, what is the probabilit

Anestetic [448]

Answer:

The probability that the sample proportion will be greater than 13% is 0.99693.

Step-by-step explanation:

We are given that a large shipment of laser printers contained 18% defectives. A sample of size 340 is selected.

Let $\hat p$ = the sample proportion of defectives.

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 of defective laser printers = 18%

n = sample size = 340

Now, the probability that the sample proportion will be greater than 13% is given by = P( $\hat p$ > 0.13)

P( $\hat p$ > 0.13) = P( $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }$ > $\frac{0.13-0.18}{\sqrt{\frac{0.13(1-0.13)}{340}} }$ ) = P(Z > -2.74) = P(Z < 2.74)