What is the range of this function?

An orange is shot up into the air with a catapult. The function h given by

Mrrafil [7]

Answer:

Velocity = 59 feet/second

Step-by-step explanation:

h(t) = 15 + 60t – 16t2

Time t = 1 second

Let's substitute time into the equation to get the distance

h(t) = 15+60(1)-16(1)²

h(t) = 15 + 60 - 16

h(t) = 59 feet

Speed or velocity = distance/time

Distance = 59 feet

Time = 1 second

Velocity = 59/1

Velocity = 59 feet/s

7 0

3 years ago

5x^2 +3 = -122 a. no solution b. -5 c. +‐5 d. +- 25

Finger [1]

Answer:

I put it in the calc and it got

x=5i,−5i

6 0

3 years ago

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For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains

AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

$f(x) = (1-p)^{x}p$

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

$\mu = \frac{1-p}{p}$

The standard deviation of the geometric distribution is given by the following formula:

$\sigma = \sqrt{\frac{1-p}{p^{2}}$

In this problem, we have that:

$p = 0.383$

So

$\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61$

$\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05$

(a) What is the probability that a drought lasts exactly 3 intervals?

This is $f(3)$

$f(x) = (1-p)^{x}p$

$f(3) = (1-0.383)^{3}*(0.383)$

$f(3) = 0.09$

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is $P = f(0) + f(1) + f(2) + f(3)$

$f(x) = (1-p)^{x}p$

$f(0) = (1-0.383)^{0}*(0.383) = 0.383$

$f(1) = (1-0.383)^{1}*(0.383) = 0.236$

$f(2) = (1-0.383)^{2}*(0.383) = 0.146$

Previously in this exercise, we found that $f(3) = 0.09$

So

$P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855$

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is $P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4)$ .

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

$P(X \leq 3) + P(X \geq 4) = 1$

$0.855 + P(X \geq 4) = 1$

$P(X \geq 4) = 0.145$

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

8 0

3 years ago

Is (4,-2), (1,-1), (0,0), (1,1), (4,2) a function?

Ilia_Sergeevich [38]

No this data set is not a function because two points have x coordinates of 4

Hope this helps

7 0

3 years ago

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What is the length of Arc AB, if the radius of Circle L is 12 inches?

grigory [225]

Hello :
The circumference of the circle is 24π inches

The length of the arc is (100/360)×24π = 20.93 inches
(The complete circumference would cover 360°. Angle ALB is 100°)

6 0

3 years ago