Answer:
x1=7,
x2=6
Step-by-step explanation:
x²-13x+42=0
a=1, b=-13, c=42
x1,2=(-b+-sqrt(b^2-4ac)) /2a
x1,2=(-(-13)+-sqrt((-13)^2-4*1*42))/2*1
x1,2=(13+-sqrt (169-168))/2
x1,2=(13+-sqrt(1))/2
x1,2=(13+-1)/2
x1=(13+1)/2, x2=(13-1)/2
x1=14/2, x2=12/2
x1=7, x2 =6
Problem 1
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Explanation:
Complementary angles add to 90
(angle1)+(angle2) = 90
(5x+6)+(68-x) = 90
4x+74 = 90
4x = 90-74
4x = 16
x = 16/4
x = 4
So,
angle1 = 5x+6 = 5(4)+6 = 26
angle2 = 68-x = 68-4 = 64
Note how
angle1+angle2 = 26+64 = 90
to help check our answer
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Problem 2
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Explanation:
The shortest side of a triangle is always opposite the smallest angle.
The longest side of a triangle is always opposite the largest angle.
Based on those two facts, we can say the shortest side is BC (since angle A = 53 is the smallest angle) and the longest side is AB (since angle C = 70 is the largest)
The order from smallest to largest is
BC, AC, AB
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Problem 3
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Explanation:
Use the reverse of the idea from problem 2. We know that AC is the smallest side which must mean that angle B is the smallest angle. Since BC is the largest side, angle A must be the largest angle.
The order of the angles is B < C < A
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Problem 4
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Explanation:
The same side exterior angles must be supplementary to have parallel lines.
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Problem 5
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Explanation:
Use the same idea as problem 2. The smallest angle is opposite the smallest side. The smallest side is 48, so angle G being opposite of that side, is the smallest angle.
Angle O would be the largest as it is opposite the largest side DG = 70
Answer:
The risk premium is positive, indicating a preference for certainty over risk.
Step-by-step explanation:
The risk premium is a measure of how much someone is willing to pay to avoid a risky situation or to insure against potential losses. It is the difference between the expected value of a gamble (or lottery) and the guaranteed (certain) outcome.
In this case, you're dealing with a decision maker who has initial wealth of 4 and faces the following lottery:
Option A: A loss of 2 with a probability of 1/2
Option B: A gain of 2 with a probability of 1/2
Let's calculate the expected value of this lottery:
Expected Value (EV) = (Probability of Option A) * (Value of Option A) + (Probability of Option B) * (Value of Option B)
EV = (1/2) * (-2) + (1/2) * (2)
EV = -1 + 1
EV = 0
The expected value of this lottery is 0. This means that, on average, the decision maker doesn't expect to gain or lose wealth; it's a fair game in terms of expected value.
Now, to calculate the risk premium, we compare this lottery to a certain outcome. In this case, the certain outcome is keeping the initial wealth of 4.
Risk Premium = Guaranteed Outcome - Expected Value of Lottery
Risk Premium = 4 - 0
Risk Premium = 4
The risk premium is 4, which means that the decision maker is willing to pay up to 4 to avoid taking this lottery. This is because the lottery is a risky proposition, and the decision maker values the certainty of keeping their initial wealth at 4 over the gamble, even though, on average, the gamble doesn't result in a gain or loss. Therefore, the risk premium is positive, indicating a preference for certainty over risk.
9x2 + 15x
(Points : 1)
x(3x + 5)
3x(3x + 5)
9x(x + 5)
3x2(3x + 5)
Question 4.
4.
Factor.
20mn − 30m
(Points : 1)
2m − 3
10m(2n − 3)
10mn(2m + 3n)
10n(2m − 3)
Question 5.
5.
Factor.
8x2y2 − 4x2y − 12xy
(Points : 1)
4(2xy − 4x2y − 12xy)
4(8x2y2 − x − 12xy)
4x2y2(2xy − xy −3)
4xy(2xy − x − 3)
Answer:
3: 3 x ( 3 x + 5 ) or B
4: 10 m ( 2 n − 3 ) or B
5: 4 x y ( 2 x y − x − 3 ) or D
Answer:
The answer is skewed distribution.
Step-by-step explanation:
Which phrase accurately describes a distribution that's bell-shaped but not symmetric?
Skewness is defined as asymmetry in a statistical distribution where the curve appears distorted or skewed either to the left or to the right, but not in the center.
When distributions possess a bell shape but is not centered, then they are called skewed distributions.
B. 12.24 pounds
C. 53.44 pounds
D. 78.92 pounds
12. Theresa worked 9 hours on Monday and 7 hours on Wednesday. Her total pay was $116.00. What is her rate per hour?
A. $16.57
B. $8.29
C. $7.25
D. $12.89