Answer:
7.5 seconds.
Step-by-step explanation:
Substitute the distace 220m in the given equation:
d = 19t + t^2
200 = 19t + t^2
t^2 + 19t - 200 = 0
t = [-19 +/- sqrt(19^2 - 4*1*-200)] / 2
t = -19 +/- sqrt(1161) / 2
t = ( -19 +/- 34.07) / 2
t = 7.535 seconds
Answer:
-2.92178
Step-by-step explanation:
Given the function 
The average,A is calculated using the formula;
![A=\frac{1}{b-a}\int\limits^a_b F(x)\, dx \\\\A=\frac{1}{7-1}\int\limits^7_1 3x \ Sin \ x\, dx \\\\\\=\frac{3}{6}\int\limits^7_1 x \ Sin \ x\, dx \\\\\#Integration\ by\ parts, u=x, v \prime=sin(x)\\=0.5[-xcos(x)-\int-cos(x)dx]\limits^7_1\\\\=0.5[-xcos(x)-(-sin(x))]\limits^7_1\\\\=0.5[-xcos(x)+sin(x)]\limits^7_1\\\\=0.5[-6.82595--0.98240]\\\\=-2.92178](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7Bb-a%7D%5Cint%5Climits%5Ea_b%20F%28x%29%5C%2C%20dx%20%5C%5C%5C%5CA%3D%5Cfrac%7B1%7D%7B7-1%7D%5Cint%5Climits%5E7_1%203x%20%5C%20Sin%20%5C%20x%5C%2C%20dx%20%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7B3%7D%7B6%7D%5Cint%5Climits%5E7_1%20x%20%5C%20Sin%20%5C%20x%5C%2C%20dx%20%5C%5C%5C%5C%5C%23Integration%5C%20%20by%5C%20%20parts%2C%20u%3Dx%2C%20v%20%5Cprime%3Dsin%28x%29%5C%5C%3D0.5%5B-xcos%28x%29-%5Cint-cos%28x%29dx%5D%5Climits%5E7_1%5C%5C%5C%5C%3D0.5%5B-xcos%28x%29-%28-sin%28x%29%29%5D%5Climits%5E7_1%5C%5C%5C%5C%3D0.5%5B-xcos%28x%29%2Bsin%28x%29%5D%5Climits%5E7_1%5C%5C%5C%5C%3D0.5%5B-6.82595--0.98240%5D%5C%5C%5C%5C%3D-2.92178)
Hence, the average of the function is -2.92178
Answer:
p-value (0.0208) is less than alpha = 0.05 reject H0.
Step-by-step explanation:
we have the following data:
sample size = n = 75
x, the number to evaluate is 45
the sample proportion would be: x / n = 45/75
p * = 0.6
Now, the null and alternative hypotheses are:
H0: P = 0.72
Ha: P no 72
two tailed test
statistic tes = z = (p * - p) / [(p * (1-p) / n)] ^ (1/2)
replacing we have:
z = (0.6 - 0.72) / [(0.72 * (1-0.72) / 75)] ^ (1/2)
z = -2.31
p-vaule = 2 * p (z <-2.31)
using z table, we get:
p-vaule = 2 * (0.0104)
p-vaule = 0.0208
Therefore, p-value (0.0208) is less than alpha = 0.05 reject H0.
Yes you will regroup because 8+3 equals 11 so you would bring the 1 down and add the other to the 4 and 2
