<span>Per capita consumption of bottled water is approximately normally distributed with a mean of 34.7 and a standard deviation of 13 gallons. You will need the Z-score table to convert it into percentiles
</span><span>a. what is the probability that someone consumed more than 35 gallons of bottled water?
Z score of 35 gallons would be:
Z= (score-mean) / standard deviation
Z= (35-34.7) /13
Z= 0.02
The percentile of Z=0.02 is 0.</span>5080 which means 50.8% people consume lower than 35 gallons per year. Then, the number of people consume higher than 35 gallons would be: 100%- 50.8%= 49.2%<span>
b. what is the probability that someone consumed between 30 and 40 gallons of bottled water?
To count this, you need to find the number of people in 40 gallons percentile and subtract it with 30 gallons percentile
</span>Z= (score-mean) / standard deviation
Z= (40-34.7) /13
Z= 0.41 ==> 65.91 percentile<span>
</span>Z= (score-mean) / standard deviation
Z= (30-34.7) /13
Z= -0.36 ==> 35.94 percentile
<span>
The probability that someone is consuming 30-40 gallon would be: 65.91%-35.94%= 29.97%
c. what is the probability that someone consumed less than 30 gallons of bottled water?
This question can be answered using the equation of the previous question
</span>Z= (score-mean) / standard deviation
Z= (30-34.7) /13
Z=-0.36 = 35.94 percentile<span>
The probability of someone consume less than 30 gallons would be: 35.94%
d. 99 % of people consumed less than how many gallons of bottled water?
</span><span>This question asking for 99% percentile value. To solve it, you need to reverse the step from the previous question. The Z score of 99 percentile is 3.09. Then, the number of gallons for 99 percentile would be:
score= mean + (Z * standard deviation)
score= 34.7 + (3.09*13)
score= 34.7 + 40.17
score= 74.87
</span>
2c^5 + 44c^4 + 242c^3
Take out common factors.
= 2c^3(c^2 + 22c + 121)
( Refer for attachment for next step )
= 2c^3(c + 11)(c + 11)
= 2c^3(c + 11)^2
Answer:
3
Step-by-step explanation:
Answer: y = x + 2 OR f(x) = x + 2
Step-by-step explanation:
Calculating slope:
Remember rise over run; when going from one point to another point, in this case from (-3, -1) to (0,2), locate the distance moved in the x and y directions. This scenario moves 3 up and 3 right, meaning a positive slope of one. However, if the line was directed left, your slope would be negative.
Finding y-intercept:
Where does the line intersect the y-axis and have a x-value of 0? This is your y-intercept --> (0,2).
Write Equation:
y = mx +b
y = 1x + 2
y = x + 2 <em>(your final answer)</em>
This is the question:
A
bicycle manufacturing company makes a particular type of bike.
Each
child bike requires 4 hours to build and 4 hours to test.
Each
adult bike requires 6 hours to build and 4 hours to test.
With
the number of workers, the company is able to have up to 120 hours of building
time and
100 hours of testing time for a week.
If
c represents child bikes and a represents adult bikes,
determine
which system of inequality best explains whether the company can build 10 child
bikes and 12 adult bikes in the week
Now you
can state the system of inequalities from the statements
1) First inequality based on the hours availble
to buiding
Each
child bike requires 4 hours, e<span>ach
adult bike requires 6 hours to build and </span>the company is able to have up to 120 hours of building =>
4c + 6a ≤ 120
2) Second inequality based of the hours available to testing.
Each
child bike requires 4 hours to test, each
adult bike 4 hours to test and the company is able to have up 100 hours of testing time for a week =>
4c + 4a ≤ 100
Then the two inequalities are:
4c + 6a ≤ 1204c + 4a ≤ 100<span>
The answer is Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100Which you can verify by replacing in both equations 10 for c and 12 for a. Look:
1) 4(10) + 6(12) = 40 + 72 = 112 ≤ 1202) 4(10) + 4(12) = 40 + 48 = 88 ≤ 100</span>
