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3 years ago

P = 14.7e-0.21x, where x is the number of miles above sea level. To the nearest foot, how high

Mathematics

1 answer:

AlladinOne [14]3 years ago

5 0

9514 1404 393

Answer:

13064 feet

Step-by-step explanation:

We can rewrite the formula so that x is in feet. Equating the new formula to 8.743 PSI, we have ...

8.743 = 14.7e^(-0.21x/5280)

Dividing by 14.7 and taking natural logs, we have ...

ln(8.743/14.7) = -0.21x/5280

Multiplying by the inverse of the coefficient of x gives ...

x = 5280·ln(8.743/14.7)/-0.21 ≈ 13064.0806

The peak of the mountain is about 13,064 feet high.

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ACTIVITY

marin [14]

Answer:

4 feet of wall should be on each side of the painting.

Step-by-step explanation:

Given that a 4 foot wide painting should be centered on a 12 foot wide wall, to determine how many feet (X) should be on each side of the painting, the following equation must be solved:

(Total wide of the wall - wide of the painting) / 2 = X

(12 - 4) / 2 = X

8/2 = X

4 = X

Therefore, 4 feet of wall should be on each side of the painting.

7 0

3 years ago

Let X equal the number of flips of a fair coin that are required to observe

Nataliya [291]

Answer:

(a) I attached a photo with the diagram.

(b) $f(x) = \big( \frac{1}{2} \big)^{x-1}$

(d) 4

(e) $k^2/2$

Step-by-step explanation:

(a) I attached a photo with the diagram.

(b) The easiest way to think about this part is in terms of combinatorics. Think about it like this.

To begin with, look at the three each level of the three represents a possible outcome of throwing the coin n-times. If you throw the coin 3 times at the end in total there are 8 possible outcomes. But The favorable outcomes are just 2.

1 - Your first outcome is HEADS and all the others are different except the last one.

2 - Your first outcome is TAILS and all the others are different except the last one.

Therefore the probability of the event is

$f(x) = P(X=x) = \frac{2}{2^x} = \frac{1}{2^{x-1}} = \big( \frac{1}{2} \big)^{x-1}$

(c)

P(X = 0) = 0 because it is not possible to have two consecutive tails or heads.

$E(X > 4) = 1 - P(X \leq 3) = 1 - ( P(X = 0 ) + P(X = 1) + P(X = 2) + P(X = 3))\\= 1 - ( \frac{1}{2} + \frac{1}{4} ) = \frac{1}{4}$

(d)

Remember that this is a geometric distribution therefore

$E[X] = p/(1-p)$ , in this case $p = 1/2$ so $E[X] = 1$ and

$E[X+1]^2 = ( E[X] +1 )^2 = (1+1)^2 = 2^2 = 4$

Also

(e)

This is a geometric distribution so its variance is

$Var(X) = \frac{1-p}{p^2} = 1/2 / 1/4 = 1/2$

And using properties of variance

$Var(kX - k ) = Var(kX) = k^2 var(X) = k^2 /2$

3 0

3 years ago

Noah raised $54, which is 60% of his fundraising goal to support the animal shelter.

zmey [24]

Answer:

make shur your using fractions

54 60

x 100 cross multiply

54(100) 60(x)

5400 60x

divided both by 60

5400/60 60/60

90 1

= $90

then you go

54 60

90 100

and use a caculater to see if your answer is coorect

you just fowllow the steps to see if you get 90

Step-by-step explanation:

3 0

3 years ago

A country has a total biocapacity of 6.21 ha/person, a biocapacity of grazing land of 0.85 ha/person, and a biocapacity of fores

leonid [27]

Answer:

44.8 %

Step-by-step explanation:

Let p = the number of people. Then

Total biocapacity = 6.21p ha

Grazing biocapacity = 0.85p ha

Forest biocapacity = <u>2.53p </u>

Grazing + forest = 2.78p ha

$\text{Percent grazing + forest} = \dfrac{\text{grazing + forest}}{\text{Total}} \times 100 \, \% \\\\= \dfrac{\text{2.78p ha}}{\text{6.21p ha}} \times 100 \, \% = \mathbf{44.8 \,\%}$

6 0

3 years ago

5xthe power of x...................

Alex777 [14]

Answer:

$5x^{x}$

3 0

3 years ago