The answer is b I just took the test
Answer:
90% confidence interval for the mean commute time of working adult Calgary residents is between a lower limit of 26.72 minutes and an upper limit of 30.28 minutes.
Step-by-step explanation:
Confidence Interval = Mean + or - Error margin (E)
mean = 28.5 minutes
sd = 24.2 minutes
n = 500
degree of freedom = n - 1 = 500 - 1 = 499
confidence level = 90%
t-value corresponding to 499 degrees of freedom and 90% confidence level = 1.64801
E = t × sd/√n = 1.64801 × 24.2/√500 = 1.78
Lower limit = mean - E = 28.5 - 1.78 = 26.72 minutes
Upper limit = mean + E = 28.5 + 1.78 = 30.28 minutes
90% confidence interval is between 26.72 and 30.28 minutes.
<u>Given the 45-90-45 triangle property:</u>
Hyopentuse = 9√2, therefore:
Base = 9 + 9 = 18 m
Height = 9 m
Area of the top triangle = 1/2 (9) (18) = 81 m²
Area of the bottom triangle = 1/2(6)(18) = 54 m²
Tota area = 81 + 54 = 135 m²
Answer: 135 m²
Answer:
See explanations below
Step-by-step explanation:
Given the simultaneous equations;
2x - 3y = 9... 1
2x + y = 13 ... 2
From 2;
y = 13-2x
Substitute into 1;
2x - 3(13-2x) = 9
2x -39 + 6x = 9
8x - 39 = 9
8x = 9+39
8x = 48
x = 6
Since y = 13-2x
y = 13-2(6)
y = 13-12
y = 1
The soluton to the system of equation is (6, 1)
Given the equations;
99x + 101y = 499; .... 1 * 101
101x + 99 y = 501 ... 2 * 99
______________
9999x + 10,201y = 50,399
9999x + 9801y = 49,599
Subtract
10201y - 9801y = 50399-49599
400y = 800
y = 2
Substitute y = 2 into 1;
From 1;
99x + 101y = 499
99x + 101(2) =499
99x +202 = 499
99x = 499 - 202
99x = 198
x = 198/99
x =2
Hence the solution is (2,2)
For the equations;
49x - 57y = 172 .... * 57
57x - 49y = 252 __ * 49
____________________
2793x -3249y = 9804
2793x - 2401y = 12348
Subtract
-3249y+2401y = 9804-12348
-848y = -2544
y = 3
Substitute into 1;
49x - 57y = 172
49x - 57(3) = 172
49x - 171 = 172
49x = 171+172
49x = 343
x = 7
Hence the solution is (7, 3)
Each person needs to buy at least 3 tickets, because 2 is too small
2(1.50) = 3 and 3(75) = $225
You need $250!
3(1.50) = 4.50 and 4.50(75) = $337.50
It's more than $250, but that's how it would have to be if they each buy an equal amount of tickets
