Answer:
Minimum: $25,200
Maximum: $44,800
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
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 question:
What are the minimum and the maximum starting salaries of the middle 95% of the graduates
Minimum: 50 - (95/2) = 2.5th percentile.
Maximum: 50 + (95/2) = 97.5th percentile
2.5th percentile:
X when Z has a pvalue of 0.025. So X when Z = -1.96.
The minimum is $25,200
97.5th percentile:
X when Z has a pvalue of 0.975. So X when Z = 1.96.
The maximum is $44,800
The <em>correct answer</em> is:
maximum: 116
; range: y ≤ 116
Explanation:
This is a quadratic equation in standard form, which is y=ax²+bx+c. The maximum or minimum of a quadratic function is the vertex. To find the x-coordinate of the vertex, we find the axis of symmetry. This is given by the formula x=-b/2a:
x = -32/2(-2) = -32/-4 = 8
To find the y-coordinate, plug this into the equation:
y = -2(8²)+32(8)-12
y=-2(64) + 256 - 12 = -128+256-12 = 128-12 = 116
The coordinates of the vertex are (8, 116).
To determine if this is a maximum or minimum, look at the value of a. It is -2. Since it is negative, this means the parabola opens downward, and the vertex is a maximum.
Since this is a maximum at y=116, this means the range, our y-values, will be less than or equal to this value of 116.
He made about $300 more this week.
Hints:
Step 1: Use Sine law the the angle B.
a/Sin A=b/SinB=c/SinC
24/Sin61^=12/SinB (accross multiply)
SinB=12Sin61^/24
SinB=0.437309853 then convert to degree =25.9 degree( depends on question rounded how many decimal) Read the question it must notes there.
--> Angle C=180-61-25.9=93.1 degree.
Step 2: Use Cosine law to calculate.
c^2=a^2+b^2−2ab⋅cosC
c^2=24^2+12^2-2(24)(12)cos93.1
c^2=720-576(-0.054078812)
c^2=720+31.11494
c^2=751.1494
c=27.4
(Square root take exponent off)
Step-by-step explanation:
