The area of the region bounded by the parabola x = y² + 2 and the line y = x - 8 is; -125/6
<h3>How to find the integral boundary area?</h3>
We want to find the area of the region bounded by the parabola x = y² + 2 and the line y = x - 8.
Let us first try to found the two boundary points.
Put y² + 2 for x in the line equation to get;
y = y² + 2 - 8
y² - y - 6 = 0
From quadratic root calculator, we know that the roots are;
y = -2 and 3
Thus, the area will be the integral;
Area = ∫³₋₂ (y² - y - 6)
Integrating gives;
¹/₃y³ - ¹/₂y - 6y|³₋₂
Plugging in the integral boundary values and solving gives;
Area = -125/6
Read more about Integral Boundary Area at; brainly.com/question/23277151
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Answer:
It is likely that the birth weight of a random baby boy will be between 3.2 and 3.4 kg because the probability of this event is large enough.
Step-by-step explanation:
Population mean=μ=3.3.
S.E=0.1.
n=36.
If the probability of the birth weight of a random baby boy will be between 3.2 and 3.4 kg is larger than the it will be likely. The probability can be calculated by normal distribution because sample size is large enough.
Z-score for 3.2 kg=3.2-3.3/0.1=-1
Z-score for 3.4 kg=3.4-3.3/0.1=1
P(-1<Z<1)=P(-1<Z<0)+P(0<Z<1)
P(-1<Z<1)=0.3413+0.3413
P(-1<Z<1)=0.6826
The probability of the birth weight of a random baby boy will be between 3.2 and 3.4 kg is 68.26%. So. it is likely that the birth weight of a random baby boy will be between 3.2 and 3.4 kg as the probability is large enough.
Answer:
F(5)= 37
Step-by-step explanation:
F(x)= 6x + 7
F(5)= 6(5) +7
F(5)=30+7
F(5)=37
It’ll be length= 12ft width= 26ft
(76-24)/2= width
Answer:
<em>~ Jill needs a minimum score of 90% to recieve an average of at least 92% on all her math quizzes ~</em>
Step-by-step explanation:
1. The table shows that her past weeks math quiz scores are: 92, 96, 94, 88
2. If she were to get a mean, or average, of at least 92, we could set up an equation to determine the minimum score she will recieve on her next quiz:
92 + 96 + 94 + 88 + x/ 5 = 92 ⇒ <em>(where x is the minimum score she should recieve on her next quiz to get an average of at least 92%)</em>
3. Now let us solve this equation for x through simple algebra ⇒
92 + 96 + 94 + 88 + x/ 5 = 92 ⇒
370 + x/5 = 92 ⇒
x/5 + 74 = 92 ⇒
x/5 = 18
x = 90
4. <em>Jill needs a minimum score of 90% to recieve an average of at least 92% on all her math quizzes</em>