Let be the amount (gal) of the 40% slime solution you end up using. You want to end up with 120 gal of the 50% solution, so that you would use
gal of the 70% solution.
You want the final solution to consist of 50% slime, or 60 gal of slime. Each gal of the 40% solution contributes 0.4 gal of slime, while each gal of the 70% solution contributes 0.7 gal of slime. This means
so the answer is B.
Answer:
Area = 13.15 square units
Step-by-step explanation:
Let the given vertices be represented as follows:
A(2, -1, 1) = 2i - j + k
B(5, 1, 4) = 5i + j + 4k
C(0, 1, 1) = 0i + j + k
D(3, 3, 4) = 3i + 3j + 4k
(i) Let's calculate the vectors of all the sides:
AB = B - A = (5i + j + 4k) - (2i - j + k)
AB = 5i + j + 4k - 2i + j - k [Collect like terms]
AB = 3i + 2j + 3k
BC = C - B = (0i + j + k) - (5i + j + 4k)
BC = 0i + j + k - 5i - j - 4k [Collect like terms]
BC = -5i + 0j - 3k
CD = D - C = (3i + 3j + 4k) - (0i + j + k)
CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]
CD = 3i + 2j + 3k
DA = A - D = (2i - j + k) - (3i + 3j + 4k)
DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]
DA = -i - 4j - 3k
AC = C - A = (0i + j + k) - (2i - j + k)
AC = 0i + j + k - 2i + j - k [Collect like terms]
AC = -2i + 2j
BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)
BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]
BD = -2i + 2j
(ii) From the results in (i) above, we can deduce that;
AB = CD This implies that AB || CD [AB is parallel to CD]
AC = BD This implies that AC || BD [AC is parallel to BD]
(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram
<u>Now let's calculate the area</u>
To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.
In this case, we'll choose AB and AC
Area = |AB X AC|
Where;
<u></u>
AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)
AB X AC = - 6i - 6j + 10k
|AB X AC| =
|AB X AC| =
|AB X AC| = 13.15
Area = 13.15 square units.
<u></u>
<u></u>
<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.
Answer:
a) 0.0668 = 6.68% probability that a domestic airfare is $550 or more
b) 0.1093 = 10.93% probability than a domestic airfare is $250 or less
c) 0.6313 = 63.13% probability that a domestic airfare is between $300 and $500
d) The cost for the 3% highest domestic airfares are $592 and higher.
Step-by-step explanation:
Problems of normally distributed samples are solved using 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 problem, we have that:
a. What is the probability that a domestic airfare is $550 or more (to 4 decimals)?
This is 1 subtracted by the pvalue of Z when X = 550. So
has a pvalue of 0.9332
1 - 0.9332 = 0.0668
0.0668 = 6.68% probability that a domestic airfare is $550 or more
b. What is the probability than a domestic airfare is $250 or less (to 4 decimals)?
This is the pvalue of Z when X = 250. So
has a pvalue of 0.1093
0.1093 = 10.93% probability than a domestic airfare is $250 or less
c. What if the probability that a domestic airfare is between $300 and $500 (to 4 decimals)?
This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 300. So
X = 500
has a pvalue of 0.8519
X = 300
has a pvalue of 0.2206
0.8519 - 0.2206 = 0.6313
0.6313 = 63.13% probability that a domestic airfare is between $300 and $500
d. What is the cost for the 3% highest domestic airfares?
At least the 97th percentile, so at least X when Z has a pvalue of 0.97. So X when Z = 1.88.
The cost for the 3% highest domestic airfares are $592 and higher.