Answer:
-1/3
Step-by-step explanation:
The product of 10 and a number is 3 less than the number.
Ok, lets call this number x.
10x = x-3 is how to algebraically write this out.
now, lets subtract x from both sides
9x = -3
Divide by 9
x = -1/3
Answer:
Step-by-step explanation:
9514 1404 393
Answer:
M = 7x² +21
Step-by-step explanation:
Subtract the unwanted terms on the left from both sides.
(-7x² +6x -16) + M = 6x +5
M = 6x +5 -(-7x² +6x -16)
M = 7x² +21 . . . . simplify
Answer:
The value of the test statistic is 4.70.
Step-by-step explanation:
The hypothesis for this test can be defined as follows:
<em>H</em>₀: Men do not spend more than women on St. Patrick's day, i.e. μ₁ = μ₂.
<em>H</em>ₐ: Men spend more than women on St. Patrick's day, i.e. μ₁ > μ₂.
The population standard deviations are not known.
So a <em>t</em>-distribution will be used to perform the test.
The test statistic for the test of difference between mean is:
![t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s^{2}_{1}}{n_{1}}+\frac{s^{2}_{2}}{n_{2}}} }](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%5Cbar%20x_%7B1%7D-%5Cbar%20x_%7B2%7D%7D%7B%5Csqrt%7B%5Cfrac%7Bs%5E%7B2%7D_%7B1%7D%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7Bs%5E%7B2%7D_%7B2%7D%7D%7Bn_%7B2%7D%7D%7D%20%7D)
Given:
![\bar x_{1}=55\\s_{1}=18\\n_{1}=90\\\bar x_{1}=44\\s_{1}=16\\n_{1}=86](https://tex.z-dn.net/?f=%5Cbar%20x_%7B1%7D%3D55%5C%5Cs_%7B1%7D%3D18%5C%5Cn_%7B1%7D%3D90%5C%5C%5Cbar%20x_%7B1%7D%3D44%5C%5Cs_%7B1%7D%3D16%5C%5Cn_%7B1%7D%3D86)
Compute the value of the test statistic as follows:
![t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s^{2}_{1}}{n_{1}}+\frac{s^{2}_{2}}{n_{2}}} }=\frac{55-44}{\sqrt{\frac{15^{2}}{90}+\frac{16^{2}}{86} }}=4.70](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%5Cbar%20x_%7B1%7D-%5Cbar%20x_%7B2%7D%7D%7B%5Csqrt%7B%5Cfrac%7Bs%5E%7B2%7D_%7B1%7D%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7Bs%5E%7B2%7D_%7B2%7D%7D%7Bn_%7B2%7D%7D%7D%20%7D%3D%5Cfrac%7B55-44%7D%7B%5Csqrt%7B%5Cfrac%7B15%5E%7B2%7D%7D%7B90%7D%2B%5Cfrac%7B16%5E%7B2%7D%7D%7B86%7D%20%7D%7D%3D4.70)
Thus, the value of the test statistic is 4.70.