78=.75x or $78 is 75% of the original price before the discount 78/.75=x x=104 is the original price proof 104-(.25*104)=78 104-26=78 78=78
Answer:
40
Step-by-step explanation:
angles QPR and RPS are complimentary, so they equal 90, or angle QPS, so you can set up the equations like so:
7x - 9 + 4x + 22 = 90
Combine like terms:
11x + 13 = 90
Subtract 13 from each side:
11x = 77
Divide each side by 11:
x=7
Then use this value in the angle that you are finding:
7(7) - 9
49 - 9
40
40 is your answer
Hope this helps!
Answer:
m<R = 22.62°
Step-by-step explanation:
Reference angle = R
Opposite = 5 cm
Hypotenuse = 13 cm
Apply the trigonometric function SOH:
Sin R = Opp/Hyp
R = 22.6198649°
m<R = 22.62° (nearest hundredth)
(a) Average time to get to school
Average time (minutes) = Summation of the two means = mean time to walk to bus stop + mean time for the bust to get to school = 8+20 = 28 minutes
(b) Standard deviation of the whole trip to school
Standard deviation for the whole trip = Sqrt (Summation of variances)
Variance = Standard deviation ^2
Therefore,
Standard deviation for the whole trip = Sqrt (2^2+4^2) = Sqrt (20) = 4.47 minutes
(c) Probability that it will take more than 30 minutes to get to school
P(x>30) = 1-P(x=30)
Z(x=30) = (mean-30)/SD = (28-30)/4.47 ≈ -0.45
Now, P(x=30) = P(Z=-0.45) = 0.3264
Therefore,
P(X>30) = 1-P(X=30) = 1-0.3264 = 0.6736 = 67.36%
With actual average time to walk to the bus stop being 10 minutes;
(d) Average time to get to school
Actual average time to get to school = 10+20 = 30 minutes
(e) Standard deviation to get to school
Actual standard deviation = Previous standard deviation = 4.47 minutes. This is due to the fact that there are no changes with individual standard deviations.
(f) Probability that it will take more than 30 minutes to get to school
Z(x=30) = (mean - 30)/Sd = (30-30)/4.47 = 0/4.47 = 0
From Z table, P(x=30) = 0.5
And therefore, P(x>30) = 1- P(X=30) = 1- P(Z=0.0) = 1-0.5 = 0.5 = 50%
A. place a closed circle on -4 and shade to the right.
