Answer:
The system has zero solutions.
Cost of hosting the tournament : $1,000
If it rains, the club will lose the investment: $ -1,000
If it is sunny, the club will collect $4,500 ; profit: 4,500 - 1000 = 3,500
chance of rain is 20%
-1,000 * 20% = -200
3,500 * 80% = 2,800
2,800 - 200 = 2,600 Choice C.
Answer:
x=12
Step-by-step explanation:
This is an equilateral triangle. That means all the angles are equal
There are three angles and they add to 180. 180/3 =60. Each angle is equal to 60
4x+12 =60
Subtract 12 from each side
4x+12-12 = 60-12
4x = 48
Divide by 4
4x/4 =48/4
x=12
The anchor of the guy wire is 12.06 meters away form base of electrical pole.
Further explanation:
The whole given scenario forms a right angle triangle. The pole is standing straight so it is the perpendicular while the guy wire goes from the top of pole to the anchor so it will be the hypotenuse. We have to finds the base.
Pythagoras theorem will be used.
Pythagoras theorem states that:

Given
Base=?
Perpendicular=12.4 m
Hypotenuse = 17.3 m
Putting the values

The anchor of the guy wire is 12.06 meters away form base of electrical pole.
Keywords: Pythagoras theorem, Hypotenuse
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Answer:
a) Mean = 133, Standard deviation = 2.5
b) Normal distribution
c) 0.0026
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 4
Mean = 133
Standard deviation = 5
a) Mean and the standard deviation of the sampling distribution of the sample mean for the four observations each day.
The sampling distribution has a mean equal to the population mean

The standard deviation of the sampling distribution is given by:

b) Shape of the sampling distribution
Central limit theorem:
When a large sample is drawn from a normal distribution, then the distribution of sample means approaches a normal distribution.
Since the distribution is normal, the sampling distribution of the sample mean will be bell shaped and follow a normal distribution.
c) P(sample mean exceeds 140)
Calculation the value from standard normal z table, we have,
0.0026 is the probability that the sample mean exceeds 140.