Answer:
p = 8
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 4 + 5p and d = 5, then
a₁ + 8d = 4 + 5p, that is
a₁ + 8(5) = 4 + 5p
a₁ + 40 = 4 + 5p ( subtract 40 from both sides )
a₁ = 5p - 36
a₂ = 5p - 36 + 5 = 5p - 31
a₃ = 5p - 31 + 5 = 5p - 26
a₄ = 5p - 26 + 5 = 5p - 21
Given that the sum of the first 4 terms = 7p - 10, then
5p - 36 + 5p - 31 + 5p - 26 + 5p - 21 = 7p - 10, that is
20p - 114 = 7p - 10 ( subtract 7p from both sides )
13p - 114 = - 10 ( add 114 to both sides )
13p = 104 ( divide both sides by 13 )
p = 8
A) The side length is 5 units since 5*5*5 = 125. You can guess and check to see which value multiplies with itself three times to get 125. Or you can take the cube root of 125 to get 5. You can type in 125^(1/3) to indicate you want the cube root of 125
b) The volume is 64 cubic units. Multiply the side length 4 by itself three times: 4*4*4 = 64.
Answer:
5. r(x) is f(x) translated down 16 units
7. g(x) is f(x) vertically scaled by a factor of 2/5
Step-by-step explanation:
5. Adding a number to a function value translates that value up by the amount of the number. If the number is negative, the translation is downward. Adding -16 to x^2 translates the graph down 16 units.
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7. Multiplying a function value vertically scales the graph of the function by the multiplying factor. For factors greater than 1, the result is a vertical expansion; for factors less than 1, the result is vertical compression. Here, the function f(x) = x^2 is multiplied by 2/5, so the resulting g(x) is vertically scaled by a factor of 2/5 (compressed).
For a parabola, the effect is to make the graph appear "wider." Values some distance from the line of symmetry that would have been vertically off the page now appear on the page. Hence, the horizontal extent of the graph on the page has increased.
Answer:
(a) The Expected value of the job satisfaction score for senior executives is 4.05.
(b) The Expected value of the job satisfaction score for middle managers is 3.84.
(c) The Variance of job satisfaction scores for executives and middle managers is 1.13
(d) The Standard Deviation of job satisfaction scores for both probability distributions 1.11 and 1.06.
Step-by-step explanation:
Explanation with steps is in the following attachments.
Answer:
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Step-by-step explanation:
Hope this helps!
