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3 years ago

What is the equation, in standard form, of a circle with center (−5, 8) and radius 5?

Mathematics

1 answer:

skad [1K]3 years ago

3 0

Answer:

( x + 5 )² + ( y - 8 )² = 25

Step-by-step explanation:

Standard form for the equation of a circle - ( x - h )² + ( y - k )² = r²

Where r = radius and Center is located at ( h , k )

We are given that the center is at ( -5 , 8 )

Thus, h = -5 and k = 8

We are also given that the radius = 5

Thus, r = 5

Now we just plug all of the given values into the standard form equation

( x - (-5))² + ( y - 8 )² = 5²

*simplify*

in - ( - 5 ) the two negative sign cancel out and it turns into + 5

5² = 25

Thus, the equation is ( x + 5 )² + ( y - 8 )² = 25

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Mr. Falk is going to replace the carpet in his basement. The basement is

Rzqust [24]

<h3>Answer: 1728 dollars</h3>

==========================================================

Explanation:

1 yard = 3 feet

We'll divide by 3 to convert from feet to yards

27 feet = 27/3 = 9 yards
18 feet = 18/3 = 6 yards

The basement is 9*6 = 54 square yards in floor area.

At $32 per square yard, the total cost to carpet the floor is 32*54 = 1728 dollars.

7 0

3 years ago

Iron deficiency anemia is an important nutritional health problem in the U.S. A dietary assessment was performed on 51 boys 9-11

Bond [772]

Answer:

a) Null hypothesis: $\mu = 14.44$

Alternative hypothesis: $\mu \neq 14.44$

b) $t=\frac{12.50-14.44}{\frac{4.75}{\sqrt{51}}}=-2.917$

The degrees of freedom are given by:

$df =n-1= 51-1=50$

Now we can calculate the p value taking in count the alternative hypothesis

$p_v =2*P(t_{50}$

Since the p value is lower than the significance $\alpha=0.05$ we have enough evidence to reject the null hypothesis and the true mean is significantly different from 14.44

c) $12.50 -2.01 \frac{4.75}{\sqrt{51}}= 11.163$

$12.50 +2.01 \frac{4.75}{\sqrt{51}}= 13.837$

Step-by-step explanation:

Information given

$\bar X=12.50$ represent the mean for the daily iron intake

$s=4.75$ represent the sample deviation

$n=51$ sample size

$\mu_o =14.44$ represent the reference value

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value for the test

Part a

We want to test if the mean iron intake among the low-income group is different from that of the general population, the system of hypothesis would be:

Null hypothesis: $\mu = 14.44$

Alternative hypothesis: $\mu \neq 14.44$

Part b

Since we don't know the population deviation the statistic would be given by:

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

Replacing the info we got

$t=\frac{12.50-14.44}{\frac{4.75}{\sqrt{51}}}=-2.917$

The degrees of freedom are given by:

$df =n-1= 51-1=50$

Now we can calculate the p value taking in count the alternative hypothesis

$p_v =2*P(t_{50}$

Since the p value is lower than the significance $\alpha=0.05$ we have enough evidence to reject the null hypothesis and the true mean is significantly different from 14.44

Part c

The confidence interval would be given by:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$