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3 years ago

Which equation represents a circle with a center at (-4,9) and a diameter of 10 units?

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

7 0

Answer:

$(x+4)^2 + (y-9)^2 = 25$

Step-by-step explanation:

To write the equation of a circle, use the formula $(x-h)^2+(y-k)^2 = r^2$ where the center of the circle is (h, k).

This means the equation is $(x--4)^2 + (y-9)^2 = r^2\\\(x+4)^2 + (y-9)^2 = r^2$ .

Find the radius r by dividing the diameter of 10 in 2. The radius is 5.

So the equation of the circle is $(x+4)^2 + (y-9)^2 = 25$

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Yuri surveyed a random sample of 75 students in his school about their favorite color. Of the students surveyed, 49 chose lavend

Svetllana [295]

Answer:

A 600.

Step-by-step explanation:

(49/75) * 900

= 588.

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3 years ago

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A coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces. A random sample of 15 co

Luda [366]

Answer:

We conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

Step-by-step explanation:

We are given that a coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces.

A random sample of 15 containers were weighed and the mean weight was 31.8 ounces with a sample standard deviation of 0.48 ounces.

Let $\mu$ = mean weight of coffee in its containers.

SO, Null Hypothesis, $H_0$ : $\mu \geq$ 32 ounces {means that the mean weight of coffee in its containers is at least 32 ounces}

Alternate Hypothesis, $H_A$ : $\mu$ < 32 ounces {means that the mean weight of coffee in its containers is less than 32 ounces}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean weight = 31.8 ounces

s = sample standard deviation = 0.48 ounces

n = sample of containers = 15

So, the test statistics = $\frac{31.8 -32}{\frac{0.48}{\sqrt{15} } }$ ~ $t_1_4$

= -1.614

The value of t test statistics is -1.614.

Now, at 0.01 significance level the t table gives critical value of -2.624 at 14 degree of freedom for left-tailed test.

Since our test statistic is more than the critical value of t as -1.614 > -2.624, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

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3 years ago

What is the value of m in this equation -4(m+6)=-8

Darina [25.2K]

-4m-24=-8
(add 24 to both sides)
-4m=16
(divide by -4 on both sides)
m=-4

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Simplify (3x − 5) − (5x + 1). (2 points)

Verizon [17]

The correct answer is B. -2x-6

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3 years ago

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Can some please help with this? :)

den301095 [7]

Answer:

Step-by-step explanation:

The stuff that is yellow is the answer!

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