A plumber has a 40-ft piece of a PVC pipe. How many 7/5-foot pieces can be cut from the 40-foot piece ?

All of these equations will be set up as: h(t) = $-\frac{g}{2}t^{2}$ +v₀t + h₀ where g represents gravity, v₀ represents initial velocity, and h₀ represents initial height. When working with ft/sec, g = 32. So, -g/2 = -16

1a) Length of time to reach its maximum height means you are looking for the x-value of the vertex (aka Axis Of Symmetry).

h(t) = -16t² + 160t

AOS: x = $\frac{-b}{2a}$ = $\frac{-160}{2(-16)}$ = 5

Answer: 5 sec

1b) Length of time to fall to the ground means you are looking for the x-intercept when height (y-value) = 0.

h(t) = -16t² + 160t

0 = -16t² + 160t

0 = -16t(t - 10)

0 = -16t 0 = t - 10

t = 0 t = 10

t = 0 is when it started, t = 10 is when fell to the ground.

Answer: 10 sec

2c) Same concept as 1a

h(t) = -16t² + 288t

AOS: x = $\frac{-b}{2a}$ = $\frac{-288}{2(-16)}$ = 9

Answer: 9 sec

2d) Same concept as 1b

h(t) = -16t² + 288t

0 = -16t² + 288t

0 = -16t(t - 18)

0 = -16t 0 = t - 18

t = 0 t = 18

Answer: 18 sec

3e) Same concept as 1a

h(t) = -16t² + 352t

AOS: x = $\frac{-b}{2a}$ = $\frac{-352}{2(-16)}$ = 11

Answer: 11 sec

3f) Same concept as 1b

h(t) = -16t² + 352t

0 = -16t² + 352t

0 = -16t(t - 22)

0 = -16t 0 = t - 22

t = 0 t = 22

Answer: 22 sec

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Researchers are interested in determining whether more women than men prefer the beach to the mountains. In a random sample of 2

exis [7]

Answer:

$SE=\sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

$SE=\sqrt{\frac{0.52(1-0.52)}{300} +\frac{0.45 (1-0.45)}{200}}=0.0455$

The margin of error would be:

$M = z* SE = 2.576*0.0455=0.1172$

$(0.45-0.52) - 0.1172=-0.047$

$(0.45-0.52) + 0.1172=0.187$

So then the correct option for this case would be:

a. − 0.07 ± 0.1172

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion of men

$\hat p_A =0.52$ represent the estimated proportion of men

$n_A= 300$ the random sample for male

$p_B$ represent the real population proportion of female

$\hat p_B =0.45$ represent the estimated proportion of female

$n_B =200$ the random sample for female

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_B -\hat p_A) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.576$

The standard error is given by: