A tree casts a shadow of 24 ft. At the same time, a 6 ft adult casts a shadow of 2 ft. what is the hight of the tree?

Yanka [14]

The answer is the 3rd one

6 0

3 years ago

If there is an 80% chance of rain and a 10% chance of wind and rain, what is the probability that it is windy, given that it is

dalvyx [7]

13% (apex) is the correct answer

4 0

4 years ago

Suppose a basketball player has made 231 out of 361 free throws. If the player makes the next 2 free throws, I will pay you $31.

statuscvo [17]

Answer:

The expected value of the proposition is of -0.29.

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either the player will make it, or he will miss it. The probability of a player making a free throw is independent of any other free throw, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Suppose a basketball player has made 231 out of 361 free throws.

This means that $p = \frac{231}{361} = 0.6399$

Probability of the player making the next 2 free throws:

This is P(X = 2) when n = 2. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{2,2}.(0.6399)^{2}.(0.3601)^{0} = 0.4095$

Find the expected value of the proposition:

0.4095 probability of you paying $31(losing $31), which is when the player makes the next 2 free throws.

1 - 0.4059 = 0.5905 probability of you being paid $21(earning $21), which is when the player does not make the next 2 free throws. So

$E = -31*0.4095 + 21*0.5905 = -0.29$

The expected value of the proposition is of -0.29.

3 0

3 years ago

The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $3, sales will reach 6000 Fun Noodles per day d

Salsk061 [2.6K]

PART A:
The generic equation of the line is:
y-yo = m (x-xo)
First we look for the slope of the line:
m = (y2-y1) / (x2-x1)
m = ((5000) - (6000)) / (4-3)
m = -1000
Then, we substitute any point in the generic equation:
(xo, yo) = (4, 5000)
Substituting:
y-5000 = (- 1000) (x-4)
Rewriting:
y = -1000x + 4000 + 5000
y = -1000x + 9000
The equation is:
y = -1000x + 9000

PART B:
For the price of 3.50 we have:
y = -1000 * (3.5) +9000
y = 5500

6 0

3 years ago

Select the correct answer from each drop-down menu.

kifflom [539]

Answer:

0.83
0.9
steeper than
slower than

Step-by-step explanation:

Letting t=1 in Ted's equation, we find that he climbs 5/6 stairs in 1 second. As a decimal, 5/6 ≈ 0.83.

Michael climbs 9 stairs in 10 seconds so his rate is ...

... (9 stairs)/(10 seconds) = (9/10) stairs/second = 0.9 stairs/second

Michael's graph will be a line with a slope of 0.9; Ted's graph will be a line with a slope of about 0.83, so the line on Michael's graph is steeper.

Ted climbs fewer stairs per second, so his rate is slower than Michael's.

_____

<em>Comment on the problem</em>

You're being asked to compare two different rates that are associated with two different people. First the comparison is one way, then it is the other way. This can be confusing. It might be helpful to draw and label a simple chart to help you keep it straight. (The attachment is such a chart scribbled on a bit of scratch paper. It is sufficient for the purpose.)

3 0

3 years ago