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3 years ago

Please Answer ASAP ! Which point lies on the circle represented by the equation x2 + (y − 12)2 = 252?

Mathematics

1 answer:

Ivahew [28]3 years ago

6 0

Answer:

Point (20 , -3) lies on the circle ⇒ (A)

Step-by-step explanation:

The point which lies on the circle must satisfy the equation of the circle

The equation of the circle is x² + (y - 12)² = 25²

<em>Take the left hand side and substitute x and y by the coordinates of each point the answer must equal the right hand side</em>

<em />

A. (20 , -3)

∵ x = 20

∵ y = -3

∴ (20)² + (-3 - 12)² = 400 + (-15)² = 400 + 225 = 625

∵ The right hand side is 25²

∵ 25² = 625

∴ The left hand side = The right hand side

∴ Point (20 , -3) satisfy the equation of the circle

∴ Point (20 , -3) lies on the circle

B. (-7 , 24)

∵ x = -7

∵ y = 24

∴ (-7)² + (24 - 12)² = 49 + (12)² = 49 + 144 = 193

∵ The right hand side is 25² = 625

∴ Point (-7 , 24) does not lie on the circle

C. (0 , 13)

∵ x = 0

∵ y = 13

∴ (0)² + (13 - 12)² = 0 + (1)² = 0 + 1 = 1

∵ The right hand side is 25² = 625

∴ Point (0 , 13) does not lie on the circle

D. (-25 , -13)

∵ x = -25

∵ y = -13

∴ (-25)² + (-13 - 12)² = 625 + (-25)² = 625 + 625 = 1250

∵ The right hand side is 25² = 625

∴ Point (-25 , -13) does not lie on the circle

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3 years ago

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The numbers of new CDs is 30 and the old CDs is 21.

To solve this problem, we have to write a system of equations in which we would know the numbers of each types of CD she bought.

<h3>System of Equations</h3>

This is used to solve a series or complex of word problems in which we can represent in a mathematical statements;

Let n represents numbers of new CDs
Let u represents numbers of old CDs

The equations can be represented as

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Making n the subject of formula

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we can put equation (iii) into equation (ii)

$15n + 6u =576\\n = 51 - u\\15(51 - u) + 6u = 576\\765-15u + 6u = 576\\collect like terms\\765-576=15u - 6u\\189=9u\\9u/9 = 189/9\\u = 21$

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2 years ago

A random sample of size n1= 25, taken from a normal population with a standard deviation σ1= 5, has a mean X1= 80. A second rand

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Answer:

The 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X_1 =80$ represent the sample mean 1

$\bar X_2 =75$ represent the sample mean 2

n1=25 represent the sample 1 size

n2=36 represent the sample 2 size

$\sigma_1 =5$ sample standard deviation for sample 1

$\sigma_2 =3$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =80-75=5$

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.88$