Answer:
The 95% confidence interval for the difference of means is (7.67, 16.33).
The estimate is Md = 12.
The standard error is sM_d = 2.176.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the difference between means.
The sample 1 (this year's sales), of size n1=36 has a mean of 53 and a standard deviation of 12.
The sample 2 (last year's sales), of size n2=49 has a mean of 41 and a standard deviation of 6.
The difference between sample means is Md=12.
The estimated standard error of the difference between means is computed using the formula:
The degrees of freedom are:
The critical t-value for a 95% confidence interval and 83 degrees of fredom is t=1.989.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the difference of means is (7.67, 16.33).
Answer:
15.73
Step-by-step explanation: I just kinda guessed and got it right.
Answer:
Step-by-step explanation:
Let the angles be 4x , 5x
4x + 5x = 180 { supplementary}
9x = 180
x = 180/9
x = 20
Larger angle= 5x = 5* 20 = 100
Answer:
Area of composite figure = 216 cm²
Hence, option A is correct.
Step-by-step explanation:
The composite figure consists of two figures.
1) Rectangle
2) Right-angled Triangle
We need to determine the area of the composite figure, so we need to find the area of an individual figure.
Determining the area of the rectangle:
Given
Length l = 14 cm
Width w = 12 cm
Using the formula to determine the area of the rectangle:
A = wl
substituting l = 14 and w = 12
A = (12)(14)
A = 168 cm²
Determining the area of the right-triangle:
Given
Base b = 8 cm
Height h = 12 cm
Using the formula to determine the area of the right-triangle:
A = 1/2 × b × h
A = 1/2 × 8 × 12
A = 4 × 12
A = 48 cm²
Thus, the area of the figure is:
Area of composite figure = Rectangle Area + Right-triangle Area
= 168 cm² + 48 cm²
= 216 cm²
Therefore,
Area of composite figure = 216 cm²
Hence, option A is correct.
