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2 years ago

Write the standard equation of a circle with center (-1, 4) and radius 5

Mathematics

1 answer:

Wittaler [7]2 years ago

7 0

Answer:

(x + 1)² + (y - 4)² = 25

Step-by-step explanation:

The general equation for a circle is given by the formula;

x² + y² + 2hx + 2ky + c = 0 ......equation 1.

Where the center is C(-h, -k)

Also, the standard form of the equation of a circle is;

(x - h)² + (y - k)² = r² ......equation 2.

Where;

h and k represents the coordinates of the centre.

r represents the radius of the circle.

Given the following data;

h = -1

k = 4

r = 5

Substituting into eqn 2, we have;

(x - {-1})² + (y - 4)² = 5²

Simplifying further, we have;

(x + 1)² + (y - 4)² = 25

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The mayor is interested in finding a 98% confidence interval for the mean number of pounds of trash per person per week that is

saul85 [17]

Solution :

Given :

Sample mean, $\overline X = 34.2$

Sample size, n = 129

Sample standard deviation, s = 8.2

a. Since the population standard deviation is unknown, therefore, we use the t-distribution.

b. Now for 95% confidence level,

α = 0.05, α/2 = 0.025

From the t tables, T.INV.2T(α, degree of freedom), we find the t value as

t =T.INV.2T(0.05, 128) = 2.34

Taking the positive value of t, we get

Confidence interval is ,

$\overline X \pm t \times \frac{s}{\sqrt n}$

$34.2 \pm 2.34 \times \frac{8.2}{\sqrt {129}}$

(32.52, 35.8)

95% confidence interval is (32.52, 35.8)

So with $95 \%$ confidence of the population of the mean number of the pounds per person per week is between 32.52 pounds and 35.8 pounds.

c. About $95 \%$ of confidence intervals which contains the true population of mean number of the pounds of the trash that is generated per person per week and about $5 \%$ that doe not contain the true population of mean number of the pounds of trashes generated by per person per week.