Answer:
220 N * m or 220 J
Step-by-step explanation:
We have that the work formula would be the applied force multiplied by the distance traveled, that is:
W = F * d
In this case the F is 200 N and the distance is 1.1 meters, therefore we replace:
W = 200 * 1.1
W = 220 N * m = 220 J
Therefore the work carried out by Clarissa and her mom is 200 joules.
Answer:
The area of the region between the two curves by integration over the x-axis is 9.9 square units.
Step-by-step explanation:
This case represents a definite integral, in which lower and upper limits are needed, which corresponds to the points where both intersect each other. That is:
Given that resulting expression is a second order polynomial of the form 
, there are two real and distinct solutions. Roots of the expression are:
and 
.
Now, it is also required to determine which part of the interval 
is equal to a number greater than zero (positive). That is:
and 
.
Therefore, exists two sub-intervals: ![[-5, -4.899]](https://tex.z-dn.net/?f=%5B-5%2C%20-4.899%5D)
and ![\left[4.899,5\right]](https://tex.z-dn.net/?f=%5Cleft%5B4.899%2C5%5Cright%5D)
. Besides, 
in each sub-interval. The definite integral of the region between the two curves over the x-axis is:
![A = \int\limits^{-4.899}_{-5} [{1 - (x^{2}-24)]} \, dx + \int\limits^{4.899}_{-4.899} \, dx + \int\limits^{5}_{4.899} [{1 - (x^{2}-24)]} \, dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5E%7B-4.899%7D_%7B-5%7D%20%5B%7B1%20-%20%28x%5E%7B2%7D-24%29%5D%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5E%7B4.899%7D_%7B-4.899%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5E%7B5%7D_%7B4.899%7D%20%5B%7B1%20-%20%28x%5E%7B2%7D-24%29%5D%7D%20%5C%2C%20dx)
The area of the region between the two curves by integration over the x-axis is 9.9 square units.
Answer:
a. z = 2.00
Step-by-step explanation:
Hello!
The study variable is "Points per game of a high school team"
The hypothesis is that the average score per game is greater than before, so the parameter to test is the population mean (μ)
The hypothesis is:
H₀: μ ≤ 99
H₁: μ > 99
α: 0.01
There is no information about the variable distribution, I'll apply the Central Limit Theorem and approximate the sample mean (X[bar]) to normal since whether you use a Z or t-test, you need your variable to be at least approximately normal. Considering the sample size (n=36) I'd rather use a Z-test than a t-test.
The statistic value under the null hypothesis is:
Z= X[bar] - μ = 101 - 99 = 2
σ/√n 6/√36
I don't have σ, but since this is an approximation I can use the value of S instead.
I hope it helps!
Transpose all the terms in the left hand side of the equation. The equation then becomes,
8x² - 22x - 6 =0
Divide both sides of the equation by 2,
4x² - 11x - 3 = 0
In this equation, A = 4, B = -11, and C = -3
With the variables identified, the quadratic equation can be used to identify the roots,
x = (-B +/- √B² - 4AC) / 2A
The values of x in the equation are,
<em> x = 3 and x = -1/4
</em><em />Thus, the one of the answer to this item is the third choice, x = 3. <em>
</em>
<span>131 3/4 divided by 37/8.
527/4 divided by 31/8.
527/4 divided by 8/31.
1054/31.
34.</span>
