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3 years ago

Which is an equation of a circle with center ( -5, -7) that passes through the point ( 0, 0 ) brainly

Mathematics

1 answer:

nika2105 [10]3 years ago

3 0

Answer:

(x+5)^2+(y+7)^2=74

Step-by-step explanation:

So we are given this (x+5)^2+(y+7)^2=r^2

We need to find r so just plug in your point (0,0) for (x,y) and solve for r :)

(0+5)^2+(0+7)^2=r^2

25+49=r^2

74=r^2

So the answer is (x+5)^2+(y+7)^2=74

You might be interested in

What is the distance from the point (a, −b, −4) to the origin?

laiz [17]

Answer:

$\sqrt{a^2+b^2+16}$

Step-by-step explanation:

The distance (d) between two points in 3 dimensions is ...

d = √((x2 -x1)² +(y2 -y1)² +(z2 -z1)²)

Then the distance between (a, -b, -4) and (0, 0, 0) is ...

d = √((a -0)² +(-b -0)² +(-4 -0)²)

= √(a² +b² +16)

6 0

3 years ago

Suppose a consumer product researcher wanted to find out whether a highlighter lasted longer than the manufacturer's claim that

rosijanka [135]

Answer:

C) t = 2.635; p = 0.006; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours.

Step-by-step explanation:

Data given and notation

$\bar X=14.5$ represent the sample mean

$s=1.2$ represent the sample standard deviation

$n=40$ sample size

$\mu_o =14$ represent the value that we want to test

$\alpha=0.05$ 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.

We need to conduct a hypothesis in order to check if the mean is higher than 14, the system of hypothesis would be:

Null hypothesis: $\mu \leq 14$

Alternative hypothesis: $\mu > 14$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-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".

Calculate the statistic

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

$t=\frac{14.5-14}{\frac{1.2}{\sqrt{40}}}=2.635$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=40-1=39$

Since is a one side test the p value would be:

$p_v =P(t_{(39)}>2.635)=0.006$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis