Answer:
3/4
Step-by-step explanation:
f(0) - f(3) / 0 - 3
f(0) = -4
f(3) = 9/4 - 16/4 = -7/4
f(0) - f(3) = [-4 - (-7/4)]
f(0) - f(3) = [-16/4 + 7/4]
f(0) - f(3) = -9/4
-9/4 ÷ -3 = -9/4 · -1/3 = 3/4
Answer:
<h3>
f(x) = - 4x² - 20x + 56 </h3>
Step-by-step explanation:
f(x) = a(x - x₁)(x - x₂) - factored form of the equation of the parabola with zeros x₁ and x₂
x-intercepts at (2,0) and (-7,0) means zeros: x₁=2 and x₂=-7
So:
f(x) = a(x - 2)(x + 7) - factored form of the equation of the parabola with x-intercepts at (2,0) and (-7,0)
The parabola passing through point (1, 32) means if x=1 then f(x)=32
Then:
32 = a(1 - 2)(1 + 7)
32 = a(-1)(8)
32 = - 8a
a = - 4
Therefore the equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32):
<u> f(x) = -4(x - 2)(x + 7) </u>
Expanding to standard form:
f(x) = -4(x - 2)(x + 7)
f(x) = -4(x² + 7x - 2x - 14)
<u> f(x) = -4x² - 20x + 56 </u>
X + 367 = 860
x = 860 - 367
x = 493
The dog had 493 bones to start with.
Answer:
Salary: $90,500
Step-by-step explanation:
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
An employee was having their annual appraisal and the manager indicated that the employee salary for next year has a Z-score of 1.24. Approximately how much will this employee be paid next year in salary?
This is X when . So
Rouded to the nearest hundred of dollars:
Salary: $90,500
Answer: Symmetrical, Bell-shaped
Step-by-step explanation:
The Normal Probability Distribution is very popular among all because of its unique mathematical characteristics like
- Normal distributions are symmetric.
- They are unimodal (i.e. it has only one mode).
- All mean, median, mode are equal.
- It is symmetrical around center where mean, median and mode lies.
- Its curve is always a bell shaped curve.
Hence, the major characteristics of a normal probability distribution:
Symmetrical, Bell-shaped