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sammy [17]
3 years ago
6

Refer to the accompanying data set of mean​ drive-through service times at dinner in seconds at two fast food restaurants. const

ruct a 95​% confidence interval estimate of the mean​ drive-through service time for restaurant x at​ dinner; then do the same for restaurant y. compare the results.

Mathematics
1 answer:
Anton [14]3 years ago
4 0

Step-by-step explanation:

Assuming the data is as shown, restaurant X has a mean service time of 180.56, with a standard deviation of 62.6.

The standard error is SE = s/√n = 62.6/√50 = 8.85.

At 95% confidence, the critical value is z = 1.960.

Therefore, the confidence interval is:

180.56 ± 1.960 × 8.85

180.56 ± 17.35

(163, 198)

Restaurant Y has a mean service time of 152.96, with a standard deviation of 49.2.

The standard error is SE = s/√n = 49.2/√50 = 6.96.

At 95% confidence, the critical value is z = 1.960.

Therefore, the confidence interval is:

152.96 ± 1.960 × 6.96

152.96 ± 13.64

(139, 167)

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How to answer this? A farmer had 455 ducks and chickens. He sold 2/5 of the ducks and bought another 104 chickens. As a result,
julia-pushkina [17]

Answer:

(a) 25

(b) $4816

Step-by-step explanation:

Let's say the starting amount of ducks is d, and the starting amount of chickens is c. Since there are only ducks and chickens, we can say that d + c= 455.

Next, the farmer sells 2/5 of the ducks, so we subtract 2/5 of the ducks so that the ending duck amount is d - (2/5)d = (3/5) d

After that, the farmer buys another 104 chickens, so we add 104 chickens to the current amount of chickens to get the ending chicken number as 104+c

Given the ending duck and chicken count, we can say that the ending farm animal count (we can represent this as a) is (3/5)d + 104 + c = a

The number of ducks is 2/3 the total number of animals at the end, so (3/5)d = (2/3)a

Let's list our equations out so it is easier to solve:

d+c = 455

(3/5)d + 104 + c = a

(3/5)d = (2/3)a

We have three equations and need to solve for three variables. One common variable in all three equations is d, so it might help if we put everything in terms of d.

Starting with d+c=455, if we subtract d from both sides, we get c=455-d. We can substitute this in the second equation to get

(3/5)d + 104 + 455 - d = a

-(2/5)d + 559 = a

(3/5)d = (2/3)a

Next, we can substitute for a. If we multiply both sides by 3 and then divide by 2 in (3/5)d = (2/3)a , we get

(9/10)d = a

Substitute that in to the second equation to get

-(2/5)d + 559 = (9/10) d

-(4/10)d + 559 = (9/10) d

add (4/10)d to both sides to isolate the variable and its coefficient

(13/10)d = 559

multiply both sides by (10/13) to isolate the coefficient

d = 430

Therefore, the starting number of ducks is 430 and the starting amount of chickens is 455-430 = 25

For (b), 2/5ths of the ducks are sold, so this is (430) * (2/5) = 172. Each duck is sold for 28 dollars, so this is 172*28=$4816 as the total price

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2 years ago
The equation of the circle is (x+8)^2+(y+9)^2=169. Which of the following are the center and the radius of the circle
ipn [44]
The equation for a circle is (x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center and r is the radius
(x + 8)^2 + (y + 9)^2 = 169
Since the equation is -h and -k, I will rewrite in terms of -h and -k.
(x - -8)^2 + (y - -9)^2 = 13^2
The center is (-8, -9) and the radius = 13
Let me know if you need me to explain further.
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Answer:

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Step-by-step explanation:

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