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VLD [36.1K]
3 years ago
12

Find the area bounded by the curves x = y2 - 4y and x = 2y - y2. Your work must include an integral in one variable.

Mathematics
1 answer:
kaheart [24]3 years ago
4 0
<span>The curves x = y^2 - 4y and x = 2y - y^2 are two parabolas with vertices (-4,2) and (1,1), respectively.
</span>
The solutions (0,0) and (-3,3) of system \left \{ {{x = y^2 - 4y } \atop {x = 2y - y^2 }} \right. give the common points of these parabolas.
The area is calculated in the image.
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Identify the factors of the quadratic equation below.
baherus [9]

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7 0
3 years ago
michele is 52 inches tall. her father is 6 feet and 3 inches tall. exactly how many inches taller is michele
Studentka2010 [4]

Answer:

michelle is 23 inches shorter than her dad

Step-by-step explanation:

3 0
3 years ago
Find the lateral area of the pyramid to the nearest whole number.
son4ous [18]

Answer:

The correct answer is first option.  204 m²

Step-by-step explanation:

Formula:-

Lateral surface area of square pyramid = 4 * area  of triangle

<u>To find the slant height of triangle(l)</u>

l = √(6² + 6²) = 6√2

To find the area of triangle

Area = bh/2

b = 12 m

h =  6√2

Area = (12 * 6√2)/2 = 36√2

<u>To find the lateral surface area of Prism</u>

Lateral surface area of square pyramid = 4 * area  of triangle

= 36√2 * 4 = 203.64 ≈ 204 m²

First answer is the correct option

7 0
3 years ago
A grinding wheel manufacturer designed a new grinding wheel. Repeated tests were conducted on wheels of approximately the same w
sergejj [24]

Answer:

a) a=225 +0.674*16.5=236.121

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

b) P(X \geq 3) = 1-P(X

c) P(\bar X \geq 225)=1- P(\bar X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:

X \sim N(225,16.5)  

Where \mu=225 and \sigma=16.5

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674=\frac{a-225}{16.5}

And if we solve for a we got

a=225 +0.674*16.5=236.121

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

X\sim Bin(n=10, p=0.25)

And we want this probability:

P(X \geq 3) = 1-P(X

We can find the individual probabilities like this:

P(X=0)=(10C0)(0.25)^0 (1-0.25)^{10-0}=0.0563

P(X=1)=(10C1)(0.25)^1 (1-0.25)^{10-1}=0.1877

P(X=2)=(10C2)(0.25)^2 (1-0.25)^{10-2}=0.2816

P(X \geq 3) = 1-P(X

Part c

For this case we know that the distribution for the sample mean is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And we want this probability:

P(\bar X \geq 225)

And for this case we can use the complement rule and the z score given by:

z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And if we replace we got:

P(\bar X \geq 225)=1- P(\bar X

4 0
3 years ago
Solve by Substitution
anastassius [24]

Answer:

-9x-10y=12  \ -----(1)\\\\-3x+3=y  \ ------(2)\\\\substitute \ y \ in \ (1)\\\\-9x -10(-3x+3) =12\\\\-9x+30x-30=12\\\\21x= 12+30\\21x=42\\x=2\\\\\\substitute \ x \ in  \ (2)\\-3\cdot 2+3=y\\-6+3=y\\y=-3

x= 2, y = -3

7 0
3 years ago
Read 2 more answers
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