Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
Where 
and 
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel and we got:
first, rewrite 54 as 6•9
next, rewrite 42 as 6•7
then, that gets you 6x^2 -6•7x- 6•9
lastly, factor out the common term (6)
and then you get 6(x^2-7x-9)
<u>please mark as brainliet <3</u>
Straight line depreciation applies the same amount of depreciation in each year.
Our Depreciation Base is 21,000 - 1,000 = 20,000
The useful life is 5 years, so each year we depreciate 20,000 ÷ 5 = 4,000
Book Value is Cost - Accumulated Depreciation
After Year 1:
Book Value = 21,000 - 4,000 = 17,000
Answer is A) 17,000
<h3>Equation : x + y = 170 and y = 2x - 40</h3><h3>The weight of Bill is 70 pounds and weight of mark is 100 pounds</h3>
<em><u>Solution:</u></em>
Let the weight of Bill be "x"
Let the weight of mark be "y"
Given that,
Mark and Bill have a combined weight of 170 pounds
Therefore,
x + y = 170 ------- eqn 1
Mark weighs 40 pounds less than twice Bill's weight
y = 2x - 40 ------- eqn 2
<em><u>Substitute eqn 2 in eqn 1</u></em>
x + 2x - 40 = 170
3x = 170 + 40
3x = 210
x = 70
<em><u>Substitute x = 70 in eqn 2</u></em>
y = 2(70) - 40
y = 140 - 40
y = 100
Thus weight of Bill is 70 pounds and weight of mark is 100 pounds
Answer:
Option D: 6x-14 is the correct answer.
Step-by-step explanation:
Given that:
Length of the box = L = 2x-2
Width of the box = W = x-5
Perimeter is defined by the sum of length of all sides of the box.
Perimeter of the box = P = 2L + 2W
Perimeter of box = 2(2x-2) + 2(x-5)
Perimeter = 4x-4+2x-10
Perimeter = 6x-14
The perimeter of the box is 6x-14.
Hence,
Option D: 6x-14 is the correct answer.
