In this question, i think we have to determine all the three angles of a triangle.
Since the three angles of a triangle are p,q and r.
Since, angle measure of q is one third of p, which implies
Angle measure of r is the difference of p and q, which implies
(Equation 1)
By using the angle sum property of a triangle which states that the sum of all the angles of a triangle is 
p+q+r=
Substituting the value of r from Equation 1,
p+q+p-q=
2p=
p=
Since
Since, r=p-q
r =
Answer:27 pieces were sold at the original price.
63 pieces were sold at the new price
Step-by-step explanation:
Let x represent the number of pieces of pottery that was sold at the original price.
Let y represent the number of pieces of pottery that was sold at the new price.
They sold some of their pottery at the original price of $9.50 for each piece. This means that the amount that they got from selling x pieces of pottery at the original price would be 9.5x
They later decreased the price of each piece by $2. This means that the new price was 9.5 - 2 = $7.5
This means that the amount that they got from selling x pieces of pottery at the new price would be 7.5y
If they sold all 90 pieces and took in $729, then the equations are
x + y = 90
9.5x + 7.5y = 729 - - - - - - - - - -1
Substituting x = 90 - y into equation 1, it becomes
9.5(90 - y) + 7.5y = 729
855 - 9.5y + 7.5y = 729
- 9.5y + 7.5y = 729 - 855
- 2y = - 126
y = - 126/- 2 = 63
Substituting y = 63 into x = 90 - y, it becomes
x = 90 - 63 = 27
Answer:
35 is the integer that represents the change in number of gallons of water in the tank after 7 days
Step-by-step explanation:
The water tank leaks 5 gallons in one day.
So if there is leakage of 5 gallons a day, then after 7 days the total leakage will be:
Total Leakage = Leakage per day * Total number of days
= 5 Gal/day * 7 day
= 35 Gallons
So, 35 is the integer that represents the change in number of gallons of water in the tank after 7 days ..
Answer:
a) 90.695 lb
b) 85.305 lb
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) The 65th percentile
X when Z has a pvalue of 0.65. So X when Z = 0.385.
(b) The 35th percentile
X when Z has a pvalue of 0.35. So X when Z = -0.385.
