Answer:
a) The sampling distirbution has a mean of 135 and a standard deviation of 1.732.
b) The sampling distribution is also bell shaped, centered in the population mean. It has less spread that the population distribution because the standard deviation is smaller.
c) P(X>140)=0.002
Step-by-step explanation:
a) We are taking samples of size n=3, as we are taking 3 readings daily.
Each reading has a mean of 135 and a standard deviation of 3.
The sampling distribution depends on the population parameters and the sample size.
The mean of the sampling distribution is equal to the population mean. In this case, the mean of the sampling distribution is 135.
The standard deviation depends on the standard deviation of the population and the sample size, and is calculated as:
b) The sampling distribution is also bell shaped, centered in the population mean. It has less spread that the population distribution because the standard deviation is smaller.
c) The probability that the sample mean exceeds 140 can be calculated using the standard normal distribution.
First, we have to calculate the z-score for X=140. We use for this the mean and standard deviation of the sampling distribution.
With this z-score, we can look up the probabilty in the standard normal distribution
㏒3(9)=㏒3(3)²=2
(2x)²=16 (the exponent 2 in this equation is the result of step 1)
2x=4
x=2
<span>A factor is a divisor - a number that will evenly divide into another number. The greatest common factor of two or more numbers is the largest factor that both numbers have in common.One way to determine the greatest common factor is to find all the factors of the numbers and compare them.
The factors of 64 are 1, 2, 4, 8, 16, 32, and 64.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
The common factors are 1, 2, 4, and 8. Therefore, the greatest common factor is 8.
The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.
The prime factors of 64 are 2, 2, 2, 2, 2, and 2.
The prime factors of 72 are 2, 2, 2, 3, and 3.
The prime factors in common are 2, 2, and 2, so the greatest common factor is 2 x 2 x 2 = 8.
SummaryA factor is a divisor - a number that will evenly divide into another number. The greatest common factor of two or more numbers is the largest factor that both numbers have in common.
Summary:
The common factors of 64 and 72 are 1, 2, 4, and 8.
The greatest common factor of 64 and 72 is 8.
Or in the short term; the answer is 8</span>
Answer:
A)
58/3 = 19.33 hours
B)
84.00 hours
C)
2074.29 miles
Step-by-step explanation:
Under the assumption the earth is a perfect circle, then in a complete rotation ( 24 hours) the earth will rotate through 360 degrees or 2π radians.
A)
In one day or 24 hours the earth rotates through 360 degrees. We are required to determine the duration it takes to rotate through 290 degrees. Let x be the duration it takes the earth to rotate through 290 degrees, then the following proportions hold;
(24/360) = (x/290)
solving for x;
x = (24/360) * 290 = 58/3 = 19.33 hours
B)
In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it will takes the Earth to rotate through 7π radians. Let x be the duration it takes the earth to rotate through 7π radians, then the following proportions hold;
(24/2π radians) = (x/7π radians)
Solving for x;
x = (24/2π radians)*7π radians = 84 hours
C)
If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;
circumference = 2*π*R = π*D
= 7920*3.142
= 24891.43 miles
Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;
(24891.43miles)/(24 hours) = 1037.14 miles/hr
The distance covered by the point in 2 hours will thus be;
1037.14 * 2 = 2074.29 miles
