Answer:
m<BXY = 36degrees
Step-by-step explanation:
If XY bisects ∠AXB, then;
<AXY + <BXY = <AXB
Given
m∠AXY = (3x^2 - 12)°
m∠AXB = -18x°
Required
Find m∠BXY.
From the formula above;
Find m∠BXY = <AXB - <AXY
m<BXY = -18x - (3x^2-12)
m<BXY = -18x - 3x^2 + 12
m<BXY = -3x^2 -18x + 12
Also <AXY = m<BXY
3x^2 - 12 = -3x^2 -18x + 12
6x^2 + 18x -24 = 0
x^2+3x-4 = 0
Factorize
x = -3±√9+16/2
x = -3±5/2
x = -3+5/2 and -3-5/2
x = 2/2 and -8/2
x = 1 and -4
Substitute x = 1 into m<BXY
m<BXY = -3x^2 -18x + 12
m<BXY = -3(1)^2 -18(1) + 12
m<BXY = -3 -18+ 12
m<BXY = -9
when x= -4
m<BXY = -3(-4)^2 -18(-4) + 12
m<BXY = -3(16) +72+ 12
m<BXY = -48+84
m<BXY = 36degrees
Answer:
Step-by-step explanation:
The mean, , is 90 and the standard deviation, , is 12. We are looking for the probability that the variable X will fall between 57 and 105. We use the z-score table for this, AFTER we find the z scores. The formula to find the z-scores for us is:
and we fill in accordingly:
which simplifies to
and we will break them up into 2 different sets as follows:
P(-2.75 ≤ z ≤ 0) + P(0 ≤ z ≤ 1.25)
and based on the fact that z scores are given from 0 on up, we are going to convert the first one by using the logic that if z is greater than -2.75 but less than 0, by symmetry, z is greater than 0 but less than 2.75:
P(0 ≤ z ≤ 2.75) + P(0 ≤ z ≤ 1.25) and we go to the z-score table.
Locate 2.7 down along the left side and move over til you're under the .05; that gives us the z-score for 2.75 which is .4970. Do the same for 1.25 to get a z-score of .3944. Add them together to get a final z-score that covers the range of values for X:
.4970 + .3944 = 0.8914
1. x = 25 inches
2. Triangle c
You are told that sprinklers run for the same amount of time. lets refer to this time as T.
you are told that 4 sprinkles run one at a time for 50 minutes total. that means that T should be 50/4 = 12.5 minutes = 12 minutes and 30 seconds