Cost of the article = $27.50
Amount of city sales tax = (27.50 x 6%) = $1.65
Amount of excise tax = (27.50 x 8%) = $2.20
From my knowledge, we pay city sales tax and federal excise tax when we buy something, so the total cost would be $31.35
Answer:
![24=4k](https://tex.z-dn.net/?f=24%3D4k)
![k=6](https://tex.z-dn.net/?f=k%3D6)
Step-by-step explanation:
For this exercise it is important to remember that "Times as great as" indicates multiplication.
Therefore, "4 times as great as" can be expressed as following:
![4k](https://tex.z-dn.net/?f=4k)
So, the statement "24 is 4 times as great as" indicates that 24 is equal to
.
Knowing this, you can write the following equation:
![24=4k](https://tex.z-dn.net/?f=24%3D4k)
In order to solve for "k", you can divide both sides of the equation by 4. Then, you get the following result:
![\frac{24}{4}=\frac{4k}{4}\\\\k=6](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7B4%7D%3D%5Cfrac%7B4k%7D%7B4%7D%5C%5C%5C%5Ck%3D6)
Answer:
x = 14
Step-by-step explanation:
Given that,
2:7 is expressed in the form for 4:x.
We need to find the value of x.
2:7 must be equated to 4:x.
So,
![2:7=4:x\\\\or\\\\\dfrac{2}{7}=\dfrac{4}{x}\\\\x=\dfrac{7\times 4}{2}\\\\x=14](https://tex.z-dn.net/?f=2%3A7%3D4%3Ax%5C%5C%5C%5Cor%5C%5C%5C%5C%5Cdfrac%7B2%7D%7B7%7D%3D%5Cdfrac%7B4%7D%7Bx%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B7%5Ctimes%204%7D%7B2%7D%5C%5C%5C%5Cx%3D14)
So, the value of x is equal to 14.
Answer: The value of test statistic is 0.696.
Step-by-step explanation:
Since we have given that
![n_1=1399\\\\x_1=411\\\\p_1=\dfrac{x_1}{n_1}=\dfrac{411}{1399}=0.294](https://tex.z-dn.net/?f=n_1%3D1399%5C%5C%5C%5Cx_1%3D411%5C%5C%5C%5Cp_1%3D%5Cdfrac%7Bx_1%7D%7Bn_1%7D%3D%5Cdfrac%7B411%7D%7B1399%7D%3D0.294)
Similarly,
![n_2=759, x_2=211\\\\p_2=\dfrac{x_2}{n_2}=\dfrac{211}{759}=0.278](https://tex.z-dn.net/?f=n_2%3D759%2C%20x_2%3D211%5C%5C%5C%5Cp_2%3D%5Cdfrac%7Bx_2%7D%7Bn_2%7D%3D%5Cdfrac%7B211%7D%7B759%7D%3D0.278)
At 0.01 level of significance.
Hypothesis are :
![H_0:P_1=P_2=0.5\\\\H_a:P_1\neq P_2](https://tex.z-dn.net/?f=H_0%3AP_1%3DP_2%3D0.5%5C%5C%5C%5CH_a%3AP_1%5Cneq%20P_2)
So, the test statistic value would be
![z=\dfrac{(p_1-p_2)-(P_1-P_2)}{\sqrt{\dfrac{P_1Q_1}{n_1}+\dfrac{P_2Q_2}{n_2}}}\\\\z=\dfrac{0.294-0.278}{\sqrt{0.5\times 0.5(\dfrac{1}{1399}+\dfrac{1}{759})}}\\\\z=\dfrac{0.016}{0.023}=0.696](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%28p_1-p_2%29-%28P_1-P_2%29%7D%7B%5Csqrt%7B%5Cdfrac%7BP_1Q_1%7D%7Bn_1%7D%2B%5Cdfrac%7BP_2Q_2%7D%7Bn_2%7D%7D%7D%5C%5C%5C%5Cz%3D%5Cdfrac%7B0.294-0.278%7D%7B%5Csqrt%7B0.5%5Ctimes%200.5%28%5Cdfrac%7B1%7D%7B1399%7D%2B%5Cdfrac%7B1%7D%7B759%7D%29%7D%7D%5C%5C%5C%5Cz%3D%5Cdfrac%7B0.016%7D%7B0.023%7D%3D0.696)
Hence, the value of test statistic is 0.696.