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Sedbober [7]
3 years ago
15

Filipe was playing with a triangle on a coordinate plane. The triangle's area is 24 square units. The largest circle he can fit

in the triangle is centered at (0,0) and passes through the point (1.2,1.6). Approximately what percentage of the triangle does the circle cover?
Mathematics
2 answers:
Natali5045456 [20]3 years ago
6 0

Answer:

52.36%

Step-by-step explanation:

I did this problem on a test

Nuetrik [128]3 years ago
4 0

Answer:

52.36%

Step-by-step explanation:

First you need to find the radius of the circle. You can do this by using the Pythagorean theorem, which states a^2+b^2=c^2. In this case a and b are equal to 1.2 and 1.6, and c is the radius of the circle. Plugging in we get 1.2^2+1.6^2=c^2 or 1.44+2.56=c^2 or 4=c^2. Finding the square root of both sides of the equation, we find that 2=c. Now that we have the radius, we can find the area of the circle. The area of a circle is expressed as πr^2, and plugging in 2 for r we get an area of 4π, or ~12.56637. Now all we do is divide 12,56637 by 24 and get what percentage of the area of the triangle the circle covers, which is roughly 0.5236, or 52.36%

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A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi
Luden [163]

Answer:

Null hypothesis:\mu \leq 3.3  

Alternative hypothesis:\mu > 3.3  

z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768  

Since is a one right tailed test the p value would be:  

p_v =P(z>1.768)=0.039  

Step-by-step explanation:

Data given and notation

\bar X=3.4 represent the sample mean  

\sigma=0.4 represent the population deviation for the sample

n=50 sample size  

\mu_o =3.3 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses to be tested  

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:  

Null hypothesis:\mu \leq 3.3  

Alternative hypothesis:\mu > 3.3  

Compute the test statistic  

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

We can replace in formula (1) the info given like this:  

z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768  

P value

Since is a one right tailed test the p value would be:  

p_v =P(z>1.768)=0.039  

6 0
3 years ago
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Answer:

y=4, x=8

Step-by-step explanation:

system:

x+y = 12, x=2y

convert to 1 variable, simplify:

2y+y=12

3y=12

y=4

x=2y=4*2=8

6 0
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Answer:

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Step-by-step explanation:

im good like that :)

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4 0
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Answer:

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