-3 > x
The values that make this inequality true are those that are less than -3. The inequality does not include -3.
Answer:
d) 5/3 x
Step-by-step explanation:
You substitute a for 2c and b for 5d, so your equation will look like this:
c/d - 2c/5d = x
Then you just simplify into x by making c/d into 5c/5d so you have a common denominator.
5c/5d - 2c/5d = x
3c/5d = x
5/3 is your answer
Answer:
Yes. The male and female consumers differ in the amounts they spend.
Step-by-step explanation:
We can express the null and alternative hypothesis as:
![H_0: \mu_m=\mu_w\\\\H_1: \mu_m\neq\mu_w](https://tex.z-dn.net/?f=H_0%3A%20%5Cmu_m%3D%5Cmu_w%5C%5C%5C%5CH_1%3A%20%20%5Cmu_m%5Cneq%5Cmu_w)
It is assumed a significance level of 0.05.
The standard deviation of the difference of means is calculated as:
![s=\sqrt{\frac{s_m^2}{n_m} +\frac{s_w^2}{n_w} } =\sqrt{\frac{35^2}{40} +\frac{20^2}{30} } =\sqrt{30.625+13.333} =\sqrt{43.958} =6.63](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cfrac%7Bs_m%5E2%7D%7Bn_m%7D%20%2B%5Cfrac%7Bs_w%5E2%7D%7Bn_w%7D%20%7D%20%3D%5Csqrt%7B%5Cfrac%7B35%5E2%7D%7B40%7D%20%2B%5Cfrac%7B20%5E2%7D%7B30%7D%20%7D%20%3D%5Csqrt%7B30.625%2B13.333%7D%20%3D%5Csqrt%7B43.958%7D%20%3D6.63)
The test statistic is
![t=\frac{(M_m-M_w)-0}{s}=\frac{135.67-68.64}{6.63}=10.11](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%28M_m-M_w%29-0%7D%7Bs%7D%3D%5Cfrac%7B135.67-68.64%7D%7B6.63%7D%3D10.11)
The degrees of freedom are:
![df=n_1+n_2-2=40+30-2=68](https://tex.z-dn.net/?f=df%3Dn_1%2Bn_2-2%3D40%2B30-2%3D68)
The P-value for t=10.11 is P=0, so it is smaller than the significance level. The null hypothesis is rejected.
We can conclude that male and female consumers differ in the amounts they spend.