The relationship between arc, radius, and central angle in radians is:
Θ = s/r
So just plugging in the values:
Θ = (5π/3)/7 = 5π/21 ≈ 0.748 or 0.7
Answer: Hello mate!
you put every number twice, I will consider that in this problem we have:
225 gallons of water initial with 5 pounds of sugar. then each minute you add 20 gallons of water and 4 pounds of sugar.
the concentration is defined as pounds of sugar divided by the gallons of water. The gallons of water are 225 initially and 20 per minute, this is written as 225 + 20tt, where t is the minutes. The pounds of sugar is 5 + 4 per minute, then this can be written as 5 + 4t
this is the equation that describes the concentration in pounder per gallon after t minutes.
Answer:
At 95% confidence level, the difference between the proportion of freshmen using steroids in Illinois and the proportion of seniors using steroids in Illinois is -7.01135×10⁻³ <
< 1.237
Step-by-step explanation:
Here we are required to construct the 95% confidence interval of the difference between two proportions
The formula for the confidence interval of the difference between two proportions is as follows;
![\hat{p}_1-\hat{p}_2\pm z^{*}\sqrt{\frac{\hat{p}_1\left (1-\hat{p}_1 \right )}{n_{1}}+\frac{\hat{p}_2\left (1-\hat{p}_2 \right )}{n_{2}}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D_1-%5Chat%7Bp%7D_2%5Cpm%20z%5E%7B%2A%7D%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D_1%5Cleft%20%281-%5Chat%7Bp%7D_1%20%20%5Cright%20%29%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7B%5Chat%7Bp%7D_2%5Cleft%20%281-%5Chat%7Bp%7D_2%20%20%5Cright%20%29%7D%7Bn_%7B2%7D%7D%7D)
Where:
![\hat{p}_1 = \frac{34}{1679}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D_1%20%20%3D%20%5Cfrac%7B34%7D%7B1679%7D)
n₁ = 1679
n₂ = 1366
at 95% confidence level = 1.96
Plugging in the values, we have;
![\frac{34}{1679}- \frac{24}{1366} \pm 1.96 \times \sqrt{\frac{ \frac{34}{1679}\left (1- \frac{34}{1679}\right )}{1679}+\frac{\frac{24}{1366} \left (1-\frac{24}{1366} \right )}{1366}}](https://tex.z-dn.net/?f=%5Cfrac%7B34%7D%7B1679%7D-%20%5Cfrac%7B24%7D%7B1366%7D%20%5Cpm%201.96%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%20%5Cfrac%7B34%7D%7B1679%7D%5Cleft%20%281-%20%5Cfrac%7B34%7D%7B1679%7D%5Cright%20%29%7D%7B1679%7D%2B%5Cfrac%7B%5Cfrac%7B24%7D%7B1366%7D%20%5Cleft%20%281-%5Cfrac%7B24%7D%7B1366%7D%20%20%20%5Cright%20%29%7D%7B1366%7D%7D)
Which gives;
-7.01135×10⁻³ <
< 1.237.
At 95% confidence level, the difference between the proportion of freshmen using steroids in Illinois and the proportion of seniors using steroids in Illinois = -7.01135×10⁻³ <
< 1.237.
Answer:
-20
Step-by-step explanation: