Estimate 10/12 - 3/8 using benchmark values. Your equation must show the estimate for each fraction and for the solution.
1 answer:
Answer:
The estimated values of given fraction are 1/2, 1/4 and 1/2 for benchmark values 1/2, 1/4 and 1/8 respectively.
Step-by-step explanation:
The given expression is
Case 1: Let the benchmark value be 1/2.
10/12 > 3/4 so we round it to 1.
1/4 ≤ 3/8 ≤ 3/4 so we round it to 1/2.
Estimating the solution:
1 - 1/2 = 1/2
Case 2: Let the benchmark value be 1/4.
5/8 ≤ 10/12 < 7/8 so we round it to 3/4.
3/8 ≤ 3/8 < 5/8 so we round it to 2/4.
Estimating the solution:
3/4 - 2/4 = 1/4
Case 3: Let the benchmark value be 1/8.
13/16 ≤ 10/12 < 15/16 so we round it to 7/8.
5/16 ≤ 3/8 < 7/16 so we round it to 3/8.
Estimating the solution:
7/8 - 3/8 = 1/2
Therefore the estimated values of given fraction are 1/2, 1/4 and 1/2 for benchmark values 1/2, 1/4 and 1/8 respectively.
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Answer:
95% two-sided confidence interval for the true mean heights of men is [168.8 cm , 181.2 cm].
Step-by-step explanation:
We are given that the heights of 40 randomly chosen men are measured and found to follow a normal distribution.
An average height of 175 cm is obtained. The standard deviation of men's heights is 20 cm.
Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;
P.Q. = ~ N(0,1)
where, = sample average height = 175 cm
= population standard deviation = 20 cm
n = sample of men = 40
<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>
So, 95% confidence interval for the true mean, is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%
level of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for </u> = [
,
]
= [ ,
]
= [168.8 cm , 181.2 cm]
Therefore, 95% confidence interval for the true mean height of men is [168.8 cm , 181.2 cm].
<em>The interpretation of the above interval is that we are 95% confident that the true mean height of men will be between 168.8 cm and 181.2 cm.</em>
Answer:
D. As the sample size is appropriately large, the margin of error is ±0.15
Step-by-step explanation:
The number of students in the sample, n = 32 students
The percentage of the students that preferred studying abroad, = 25%
The confidence level for the study = 95%
As a general rule, a sample size of 30 and above are taken as sufficient
The z-value at 95% confidence level, z = 1.96
The margin of error of a proportion formula is given as follows;
Therefore, we get;
Therefore, the correct option is that as the sample size is appropriately large, the margin of error is ±0.15.
Answer:
- attached graph
- Horizontal Asymptote: y = 5
- twon whole number points are (4,4) and (5,1)
Step-by-step explanation:
- Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote
y = -4^(x-4) + 5
= -4^(4-4) + 5
= -4^(0) + 5
= -1 + 5
= 4
y = -4^(x-4) + 5
= -4^(5-4) + 5
= -4^(1) + 5
= -4 + 5
= 1
