Answer: 43.5
Step-by-step explanation:
Find f(-5) if f(x) =|x+1|
2 answers:
Answer:
Step-by-step explanation:
Given an Absolute value function , it is important to remember that the absolute value of "x" is the distance from zero to "x", therefore:
In this case you have this Absolute value function:
In order to find it is necessary to substitute
into this function.
Therefore, you get:
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a. The probability that on a randomly selected day, the jail population
is greater than 750,000 is 20.1%
b. The probability that on a randomly selected day, the jail population is
between 600,000 and 700,000 is 43.2%
Step-by-step explanation:
The given is:
1. The average daily jail population in the United States is 706,242
2. The distribution is normal and the standard deviation is 52,145
3. We need to find the probability that on a randomly selected day,
the jail population is greater than 750,000
4. We need to find the probability that on a randomly selected day,
the jail population is between 600,000 and 700,000
a.
At first find z-score
∵ z = (x - μ)/σ, where x is the score, μ is the mean and σ is the standard
deviation
∵ x = 750,000 , μ = 706,242 and σ = 52,145
∴ z = ≅ 0.84
Use the normal distribution table of z to find the area to the right of
the z-value
∵ The corresponding area to z-score of 0.84 is 0.79955
- But we are interested in x > 750,000, we need the area to the
right of z-score
∴ P(x > 750,000) = 1 - 0.79955 = 0.2005
∴ P(x > 750,000) = 0.2005 × 100% = 20.1%
The probability that on a randomly selected day, the jail population is
greater than 750,000 is 20.1%
b.
We will find z-score for 600,000 < x < 700,000
∵ z = ≅ -2.04
∵ z = ≅ -0.12
Use the normal distribution table of z to find the area between
the two z-values
∵ The corresponding area to z-score of -2.04 is 0.02068
∵ The corresponding area to z-score of -0.12 is 0.45224
- To find P(600,000 < x < 700,000) subtract the two values above
∴ P(600,000 < x < 700,000) = 0.45224 - 0.02068 = 0.4316
∴ P(600,000 < x < 700,000) = 0.4316 × 100% = 43.2%
The probability that on a randomly selected day, the jail population is
between 600,000 and 700,000 is 43.2%
Learn more:
You can learn more about z-score in brainly.com/question/7207785
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Answer:
The maximum height of the rocket is 256 feet
Step-by-step explanation:
The vertex form of the quadratic function f(x) = ax² + bx + c is
f(x) = a(x - h)² + k, where
- (h, k) is the vertex point
- h =
and k = f(h)
- (h, k) is a minimum point if a > 0 and a maximum point if a < 0
Let us use these rules to solve the question
∵ h(t) = -16t² + 128t
→ Compare it by the form of the quadratic function above
∴ a = -16 and b = 128
∵ a < 0
∴ The vertex (h, k) is a maximum point
∴ The maximum height of the rocket is the value of k
→ Use the rule of h above to find it
∵ h = =
∴ h = 4
→ Substitute x in the equation by the value of h to find k
∵ k = h(h)
∴ k = -16(4)² + 128(4)
∴ k = -256 + 512
∴ K = 256
∴ The maximum height of the rocket is 256 feet