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3 years ago

a hot air ballon was at 2,180 feet. it decended at 120 feet per minute for 9 minutes. what is the balloons new height?

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

7 0

Answer:

The balloons new height is $1,100\ ft$

Step-by-step explanation:

Let

x ----> the number of minutes

y ----> the height of a hot air balloon in feet

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

The slope is equal to

$m=-120\ ft\ per\ minute$ ---> is negative because is a decreasing function

The y-intercept is equal to

$b=2,180\ ft$

substitute

$y=-120x+2,180$

For x=9 minutes

substitute in the linear equation

$y=-120(9)+2,180$

$y=1,100\ ft$

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balu736 [363]

Answer:

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(b) The sample size required is 62.

Step-by-step explanation:

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(a)

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*Use a z-table.

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$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

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(b)

The information provided is:

<em>σ</em> = 4 minutes

MOE = 1 minute

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α = 5%

Compute the critical value of z for α = 5% as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

$=[\frac{1.96\times 4}{1}]^{2}\\\\=61.4656\\\\\approx 62$

Thus, the sample size required is 62.

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