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siniylev [52]
3 years ago
9

Given the equation of the circle find the center and the radius: (x - 3)2 + (y + 1)2 = 49

Mathematics
1 answer:
marta [7]3 years ago
3 0

Answer:

(3, -1), 7

Step-by-step explanation:

To find the center of this circle:  compare the given equation

(x - 3)^2 + (y + 1)^2 = 7^2   to the standard equation of a circle with center at (h, k):

(x - h)^2 + (y -k)^2 = r^2

From this comparison we see that the center is at

h = 3 and k = -1, and also that r must be 7:    (3, -1), 7

You might be interested in
A survey revealed that 56% of the students at North Valley high school are involved with in a sports team. The survey also showe
oksano4ka [1.4K]

Answer:

The probability that a student who is involved in a sports team also participated in the prom dance = 0.1344

Step-by-step explanation:

56% of the students are involved in a sport team

56% = 0.56

According to the question, it is stated that 24% of the students at the school that are involved in a sports team also participated in the prom dance.

24% = 0.24

This means that we are going to find 24% of the original 56%, since 24% of them also participated in the prom dance.

The probability that a student who is involved in a sports team also participated in the prom dance = 0.24 * 0.56

The probability that a student who is involved in a sports team also participated in the prom dance = 0.1344

5 0
3 years ago
What would be the critical value for a two-tailed, one-sample t test with 26 degrees of freedom (df = 26) and an alpha level (p
Alika [10]

Answer: The critical value for a two-tailed t-test = 2.056

The critical value for a one-tailed t-test = 1.706

Step-by-step explanation:

Given : Degree of freedom : df= 26

Significance level : \alpha=0.05

Using student's t distribution table , the critical value for a two-tailed t-test will be :-

t_{\alpha/2, df}=t_{0.025,26}=2.056

The critical value for a two-tailed t-test = 2.056

Again, Using student's t distribution table , the critical value for a one-tailed t-test will be :-

t_{\alpha, df}=t_{0.05,26}=1.706

The critical value for a one-tailed t-test = 1.706

6 0
3 years ago
Simplify,<br> Rewrite the expression in the form 2n.<br> 2.2.2.2.2.2.2.2<br> 2.2.2.2
Nastasia [14]

Answer: 8/4

Step-by-step explanation: if I’m wrong just watch the video for a hint it helps

6 0
2 years ago
A veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses
Licemer1 [7]

Answer:

Probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.

Step-by-step explanation:

We are given that a veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses with colic is 12 years. The average age of all horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of all horses coming to the veterinary clinic is 8 years.

So, firstly according to Central limit theorem the z score probability distribution for sample means is given by;

                    Z = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \bar X = average age of the random sample of horses with colic = 12 yrs

            \mu = average age of all horses seen at the veterinary clinic = 10 yrs

   \sigma = standard deviation of all horses coming to the veterinary clinic = 8 yrs

         n = sample of horses = 60

So, probability that a sample mean is 12 or larger for a sample from the horse population is given by = P(\bar X \geq 12)

   P(\bar X \geq 12) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } \geq \frac{12-10}{\frac{8}{\sqrt{60} } } ) = P(Z \geq 1.94) = 1 - P(Z < 1.94)

                                                 = 1 - 0.97381 = 0.0262

Therefore, probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.

4 0
3 years ago
Find the solution of this system of equations. Separate the x- and y-values with a comma. x - 4y = 12 and x - y = 0
Elenna [48]
Use elimination and subtitution method to solve the problem.
First, eliminate x and you'll find the value of y
x - 4y = 12
x -  y  = 0
--------------- - (substract)
     -3y = 12
        y = 12/-3
        y = -4

Second, subtitute -4 as y and you'll find the value of x
x - y = 0
x- (-4) = 0
x + 4 = 0
x = -4

The solution
x,y = -4,-4
6 0
3 years ago
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