Y = -2x - 7
slope = -2 (parallel shares the same slope, -2)
Option A:
y = -2x + 7
slope = -2
At (3, 1)
y = -2(3) + 7 = 1
Answer: Option A
Answer:
2, 4, 6, and 8, respectively
Step-by-step explanation:
The rule says that 2 times the x value, which we are given, equals to y, which we must find. So all we hve to do is multiply each of the given x values by two to get the y value.
Answer:
720ft²
Step-by-step explanation:
Wall 1&2 = lh = 15*10=150
Wall 3&4 = wh = 12*10=120
Ceiling = lw = 12*15=180
120+150+120+150+180=720ft²
Answer:
1) p1=0.83
2) p2=0.81
3) Option B
4) p=0.82
5) s=0.03
6) z=0.67
7) P=0.50
8) Do not reject H0
Step-by-step explanation:
1) The proportion of Republicans who think the full-body scans should be applied in airports is equal to the ratio between the republicans that think it should over the total Republicans in the poll:
![p=X/n=258/311=0.83](https://tex.z-dn.net/?f=p%3DX%2Fn%3D258%2F311%3D0.83)
2) The proportion of Democrats who think the full-body scans should be applied in airports is equal to:
![p=X/n=294/363=0.81](https://tex.z-dn.net/?f=p%3DX%2Fn%3D294%2F363%3D0.81)
3) As we want to know if there is a difference in the proportions calculated, not if one is higher or lower than the other, the correct option is B:
![H_0:p_1-p_2=0\\\\H_a:p_1-p_2\neq0](https://tex.z-dn.net/?f=H_0%3Ap_1-p_2%3D0%5C%5C%5C%5CH_a%3Ap_1-p_2%5Cneq0)
4) The pooled estimate of a proportion is the average of both proportions:
![\bar{p}=\frac{p_1+p_2}{2}= \frac{0.83+0.81}{2}=0.82](https://tex.z-dn.net/?f=%5Cbar%7Bp%7D%3D%5Cfrac%7Bp_1%2Bp_2%7D%7B2%7D%3D%20%5Cfrac%7B0.83%2B0.81%7D%7B2%7D%3D0.82)
5) The standard error can be calculated as:
![s=\sqrt{\frac{\bar{p}(1-\bar{p})}{n_1} +\frac{\bar{p}(1-\bar{p})}{n_2}} \\\\s=\sqrt{\frac{0.82*0.18}{311} +\frac{0.82*0.18}{363}} \\\\s=\sqrt{0.00047+0.00041} =\sqrt{0.00088}=0.03](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cfrac%7B%5Cbar%7Bp%7D%281-%5Cbar%7Bp%7D%29%7D%7Bn_1%7D%20%2B%5Cfrac%7B%5Cbar%7Bp%7D%281-%5Cbar%7Bp%7D%29%7D%7Bn_2%7D%7D%20%5C%5C%5C%5Cs%3D%5Csqrt%7B%5Cfrac%7B0.82%2A0.18%7D%7B311%7D%20%2B%5Cfrac%7B0.82%2A0.18%7D%7B363%7D%7D%20%5C%5C%5C%5Cs%3D%5Csqrt%7B0.00047%2B0.00041%7D%20%3D%5Csqrt%7B0.00088%7D%3D0.03)
6) The z-statistic can be calculated as:
![z=\frac{p_1-p_2}{s}=\frac{0.83-0.81}{0.03}=\frac{0.02}{0.03}=0.67](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bp_1-p_2%7D%7Bs%7D%3D%5Cfrac%7B0.83-0.81%7D%7B0.03%7D%3D%5Cfrac%7B0.02%7D%7B0.03%7D%3D0.67)
7) The P-value for z=0.67 is P=0.50 (from the standard normal distribution table).
![2P(Z>|z|)=0.50286](https://tex.z-dn.net/?f=2P%28Z%3E%7Cz%7C%29%3D0.50286)
8) If the significance level is 0.01, the P-value is bigger than the significance level. The effect is not significanct. The null hypothesis is not rejected.
There is not enough evidence to say that both proportions are different.
A. Do not reject H0
Answer:
- 33 1/3 liters of 30%
- 16 2/3 liters of 45%
Step-by-step explanation:
Let x represent the liters of 45% solution needed. Then the amount of HCl in the mix is ...
0.45x +0.30(50 -x) = 0.35(50)
0.15x = 0.05(50) . . . . . simplify, subtract 0.30(50)
x = (0.05/0.15)(50) = 50/3 = 16 2/3 . . . liters of 45% HCl
33 1/3 liters of 30% and 16 2/3 liters of 45% HCl are needed.
_____
<em>Comment on the solution</em>
You may notice that the general solution to a mixture problem of this sort is that the fraction of the mix that is the highest contributor is ...
(mix % - low %) / (high % - low %) = (.35 -.30) / (.45 -.30) = .05/.15 = 1/3