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Elza [17]
4 years ago
12

Water coming out from a fountain is modeled by the function f(x) = −x2 + 8x + 2 where f(x) represents the height, in feet, of th

e water from the fountain at different times x, in seconds.
What does the average rate of change of f(x) from x = 1 to x = 4 represent, options AWhat does the average rate of change of f(x) from x = 1 to x = 4 represent?
options: The water travels an average distance of 3 feet from 1 second to 4 seconds.
The water travels an average distance of 2 feet from 1 second to 4 seconds.
The water rises up with an average speed of 3 feet per second from 1 second to 4 seconds.
The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds.
Mathematics
1 answer:
andrew-mc [135]4 years ago
6 0
f(x)=-x^{2} +8x+2
Average rate of change from x = 1 to x = 4 = \frac{f(4)-f(1)}{4-1}= \frac{( -4^{2}+8(4)+2)-(- 1^{2}+8(1)+2)}{3}= \frac{(-16+32+2)-(-1+8+2)}{3}= \frac{18-9}{3}= \frac{9}{3}=3

This means that the water rises up with an average speed of 3 feet per second from 1 second to 4 seconds
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{y|y≥−2}

Step-by-step explanation:

The domain is {x|x∈R}

The range is {y|y≥−2}

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Find negative square root of 16
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-4

-4×-4=16

Step-by-step explanation:

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Any athlete who fails the Enormous State University's women's soccer fitness test is automatically dropped from the team. Last y
castortr0y [4]

Using conditional probability, it is found that there is a 0.7873 = 78.73% probability that Mona was justifiably dropped.

Conditional Probability

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • P(A \cap B) is the probability of both A and B happening.
  • P(A) is the probability of A happening.

In this problem:

  • Event A: Fail the test.
  • Event B: Unfit.

The probability of <u>failing the test</u> is composed by:

  • 46% of 37%(are fit).
  • 100% of 63%(not fit).

Hence:

P(A) = 0.46(0.37) + 0.63 = 0.8002

The probability of both failing the test and being unfit is:

P(A \cap B) = 0.63

Hence, the conditional probability is:

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.63}{0.8002} = 0.7873

0.7873 = 78.73% probability that Mona was justifiably dropped.

A similar problem is given at brainly.com/question/14398287

3 0
3 years ago
What is the percent increase between getting a high school scholarship and bachelors degree when high school scholarship is $421
gogolik [260]

Answer:

The percent increase between getting a high school scholarship and bachelor's degree is <u>59.14%</u>.

Step-by-step explanation:

Given:

High school scholarship is $421.

Bachelor's degree is $670.

Now, to find the percent increase between a high school scholarship and bachelor's degree.

So, we get the amount of increase between a high school scholarship and bachelor's degree.

670-421=249.

<em>Thus, the amount of increase = $249</em>.

Now, to get the percent increase between a high school scholarship and bachelor's degree:

\frac{249}{421}\times 100

=\frac{24900}{421}

=59.14\%.

Therefore, the percent increase between getting a high school scholarship and bachelor's degree is 59.14%.

7 0
3 years ago
Solve for points. identify the vertex and indicate whether it is max or min.
Keith_Richards [23]

Answer:

min at (3, 0 )

Step-by-step explanation:

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x_{vertex} = - \frac{b}{2a}

y = (x - 3)² = x² - 6x + 9 ← in standard form

with a = 1 and b = - 6 , then

x_{vertex} = - \frac{-6}{2} = 3

substitute x = 3 into the equation for corresponding value of y

y = (3 - 3)² = 0² = 0

vertex = (3, 0 )

• if a > 0 then vertex is minimum

• if a < 0 then vertex is maximum

here a = 1 > 0 then (3, 0 ) is a minimum

4 0
2 years ago
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