Answer:
The 95% confidence interval for the difference of the two populations means is ( 2.4, 41.6)
Step-by-step explanation:
Confidence intervals are usually constructed using the formula;
point estimate ± margin of error
In this question we are required to construct a 95% confidence interval for the difference of two populations means. The point estimate for the difference of two population means is the difference of their sample means which in this case is 22.
Assuming normality conditions are met, since we have no information on the sample sizes, the margin of error will be calculated as;
margin of error = z-score for 95% confidence * standard deviation of the difference of the sample means
The z-score associated with a 95% confidence interval is 1.96
The standard deviation of the difference of the sample means is given as 10
The 95% confidence interval for the difference of the two populations means is thus;
22 ± 1.96(10) = 22 ± 19.6 = ( 2.4, 41.6)
(-5)(-9) because a negative times a negative equals a positive.
Answer:
Step-by-step explanation:
We have been given that a piece of carpet is 8 feet wide and 12 feet long. The carpet needs to be reduced by a scale factor so that the reduced carpet is 2 feet wide.
First of all, let us find the scale factor by which the width of carpet has been reduced.
Dividing both sides by 8 ft we will get,
Let us find the length of carpet after reduced by a scale factor of 
.
Now we will multiply the reduced length and width of carpet to find the area of reduced carpet.
Therefore, the area of reduced carpet is 6 square feet.
The center-radius form of the circle equation is in the format
(x – h)²+ (y – k)² = r²
with the center being at the point (h, k) and the radius being "r"
So, just plug in the (-5,3) and you get:
(x+5)²+(y-3)²=16
