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4 years ago

Find the minimum or maximum value of f (x) = x2 - 6x + 13.

Mathematics

1 answer:

Greeley [361]4 years ago

7 0

Minimum value is (3, 4)

It is the minimum value because the coefficient of x^2 is positive.

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The table shows the height of a ball that was dropped from a 380-foot tower. What was the ball's rate of fall during the first 3

Alex

Answer:

60ft/s

Step-by-step explanation:

To find the rate

rate = f(3) - f(0)

-------------

3-0

rate = 200-380

---------------

3-0

rate = -180/3 = -60 ft/s

The negative tells us it is falling

The fall falls 60ft/s

8 0

4 years ago

Read 2 more answers

Let P be between M and N use the segment addition postulate to solve for X

marta [7]

Step-by-step explanation:

given,

MP = x - 8

PN = 3x - 9

MN = 21

we know,

according to segment addition postulate AB + BC = AC

now,

MP + PN = MN

→ x - 8 + 3x - 9 = 21

→ 4x - 17 = 21

→ 4x = 21 + 17

→ 4x = 38

→ x = 38/4 = 9

→ x = 9

therefore, value of x is 9.

hope this answer helps you dear! take care

5 0

3 years ago

Gail has $5,500 that she wants to put in a new savings account. She is

katrin [286]

Answer: Neighborhood Bank - 0.65% interest, compounded weekly

Step-by-step explanation:

6 0

3 years ago

Solve the equation: 5 - (t + 3) = - 1 + 2t - 3)<br> Show your work.<br> HELPPP MEEE PLEASSEEE !!!!

Finger [1]

Answer

t = 2

Step-by-step explanation

Simplify 5-(t+3).

-t+2=-1+2t-3

Subtract 3 from -1

-t+2=2t-4

Move all terms containing to the left side of the equation.

-3t+2=-4

Move all terms not containing t to the right side of the equation.

-3t=-6

Divide each term by -3 and simply.

t = 2

5 0

3 years ago

The probability that a single radar station will detect an enemy plane is 0.65.

taurus [48]

Answer:

a) We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.

b) If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

Step-by-step explanation:

For each station, there are two two possible outcomes. Either they detected the enemy plane, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

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 combinatios 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.

In this problem, we have that:

The probability that a single radar station will detect an enemy plane is 0.65. This means that $n = 0.65$ .

(a) How many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station?

This is the value of n for which $P(X = 0) \leq 0.02$ .

n = 1.

$P(X = 0) = C_{1,0}.(0.65)^{0}.(0.35)^{1} = 0.35$

n = 2

$P(X = 0) = C_{2,0}.(0.65)^{0}.(0.35)^{2} = 0.1225$

n = 3

$P(X = 0) = C_{3,0}.(0.65)^{0}.(0.35)^{3} = 0.0429$

n = 4

$P(X = 0) = C_{4,0}.(0.65)^{0}.(0.35)^{4} = 0.015$

We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.

(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?

The expected number of sucesses of a binomial variable is given by:

$E(x) = np$

So when $n = 7$

$E(x) = 7*(0.65) = 4.55$

If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

6 0

3 years ago