What is the quotient of 2/3 divided into 1/5?

The height of a tree in feet over x years is modeled by the function f(x). f(x)=301+29e−0.5x which statements are true about the

Karo-lina-s [1.5K]

Given this equation:

$f(x)=301+29^{-0.5x}$

That represents the height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.

The tree's maximum height is limited to 30 ft.

As shown in figure below, the tree is not limited, so this statement is false.

The tree is initially 2 ft tall

The tree was planted in x = 0, so evaluating the function for this value, we have:

 $f(0)=301+29^{-0.5(0)}=301+1=302ft$

So, the tree is initially $\boxed{302ft}$ tall.

Therefore this statement is false.

Between the 5th and 7th years, the tree grows approximately 7 ft.

if x = 5 then:

 $f(5)=301+29^{-0.5(5)}=301ft$ 

if x = 7 then:

$f(7)=301+29e^{0.5(7)}=301ft$

So, between the 5th and 7th years the height of the tree remains constant
:
$\Delta=f(7)-f(5)=301-301=0ft$

This is also a false statement.

After growing 15 ft, the tree's rate of growth decreases.

It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term $29^{-\infty}$ approaches zero.

Therefore this statement is also false.

Conclusion: After being planted this tree won't grow.

4 0

2 years ago

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A 90 percent confidence interval is to be created to estimate the proportion of television viewers in a certain area who favor m

Dominik [7]

Answer:

This means that the first interval, with 9000 viewers, is 3 times as narrower as the second interval, with 1000 viewers.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The width of the interval is:

$W = 2z\sqrt{\frac{\pi(1-\pi)}{n}}$

In this sample:

Two 90% intervals, with different lenghts. So both have the same values for z an $\pi$

Interval A:

9000 viewers.

So the width is

$W_{A} = 2z\sqrt{\frac{\pi(1-\pi)}{9000}}$

Interval B:

100 viewers

So the width is

$W_{B} = 2z\sqrt{\frac{\pi(1-\pi)}{1000}}$

Relationship between the widths:

$R = \frac{W_{A}}{W_{B}} = \frac{2z\sqrt{\frac{\pi(1-\pi)}{9000}}}{2z\sqrt{\frac{\pi(1-\pi)}{1000}}} = \frac{\sqrt{1000}}{\sqrt{9000}} = \frac{\sqrt{1}}{\sqrt{9}} = \frac{1}{3}$

This means that the first interval, with 9000 viewers, is 3 times as narrower as the second interval, with 1000 viewers.

8 0

3 years ago

HELp Plz god bless you and your grades

zavuch27 [327]

Answer:

a

Step-by-step explanation:

3 0

2 years ago

A scale drawing of a car uses a scale of 2cm =1m. What is the length of the car on the drawing if the actual car measures 4 m?

marusya05 [52]

Answer:

The answer is 8cm.

Step-by-step explanation:

The scale drawing uses a ratio of 2cm:1m. If the actual car is 4 meters long, you would multiply 2 by 4 to get 8cm. The actual new ratio on the map is 8cm:4m, which is equivalent to the one in the problem.

3 0

3 years ago

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Which statement is true? 5/8>1\2 5/8=1/2 5/8<1/2

Leokris [45]

Answer: 5/8>1/2

Step-by-step explanation:

First you must have a common denominator.

Change 1/2 to 4/8

(1/2 = 4/8)

Second:

5/8 ? 4/8

5/8 is greater than 1/4 (aka 1/2)

so

5/8 > 1/2

7 0

3 years ago