Answer:
24 times
Step-by-step explanation:
P(5 or 6) = 2/6
2/6 = x/72
cross-multiply:
6x = 144
x = 24
um half hour? because at 4mph youll get 4 miles in an hour so 2 miles, is half the rate which makes it half hour
Answer:
Step-by-step explanation:
Given is a system of equations as
We have 5 variables and 3 equations
a) coefficient matrix of this system is
1 -4 0 -1 0\\
0 1 0 -2 0\\
0 0 0 1 2\\
We find that x3 has no coefficient in any of the equations so we can omit x3 and write as equations for 4 variables as
1 -4 -1 0\\
0 1 -2 0\\
0 0 1 2\\
b) Augmented matrix is
1 -4 -1 0\\ 7
0 1 -2 0\\
3
0 0 1 2\\3
c) For row operations to ehelon form
we can do R1+4R2 = R1
We get
1 0 -9 0 \\ 19
0 1 -2 0 \\ 3
0 0 1 2 \\ 3
Now let us do R1 = R1+9R3 and R2 = R2+2R3
1 0 0 0 \\ 46
0 1 0 0 \\ 9
0 0 1 2 \\ 3
d) We find that there are infinite solutions to the system in parametric form, since x4 and x5 are linked with only one equation
e) x1 = 46, x2 = 9, x4+2x5 =3
Or x1 =46, x2 =9, x4 = 3-2x5, x5 = x5 is the parametric solution
Answer: B) There is not convincing evidence because the interval contains 0.
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Explanation:
The 98% confidence interval (-0.36, 0.22) means we are 98% confident that the difference of proportions p1-p2 is somewhere between those two endpoints of -0.36 and 0.22 Values in this interval are possible values of p1-p2.
Note how 0 is in this interval. So it's possible that p1 - p2 = 0. Because of this, we fail to reject the null hypothesis. The null in this case is that p1 - p2 = 0 which can be restated as p1 = p2. The null is the assumption that the two population proportions (p1 and p2) are the same.
The alternative hypothesis is that p1-p2 is not zero. If we got a confidence interval like (0.22, 0.55), this example doesn't have 0 in the interval, then that would mean we reject the null since its unlikely that p1-p2 is equal to zero.
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In short,
- If the confidence interval contains 0, then you fail to reject the null
- If the confidence interval doesn't contain 0, then you reject the null.
In this case, we fail to reject the null and we don't have enough evidence to show that p1 = p2 is false. So for now, we assume it's true.
