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Rama09 [41]
3 years ago
15

Find the center and radius for the circles with the following equation x^2+y^2-4x+6y+11=0

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
7 0
Rearrange x²+y²-4x+6y=-11 I'll tell you an easy way. take the coefficient of x and divide it by -2 and the coefficient of y and divide it by -2  so -4 ÷-2 = 2           6÷-2= -3 (2,-3) is the center of the circle to know the radius √2² + -3² + -11  =√2  The Radius equals √2
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Draw graphs of the following lines: The line through (-5, 2) having the slope of -3
Ivanshal [37]
What you want to do here is take this information and plug it into point-slope form. any time you're given a point and a slope, you generally want to plug it into this equation: y - y1 = m(x - x1).

in this equation, m is your slope and (x1, y1) is a given point. plug in your info--slope of -3 and (-5, 2).

y - 2 = -3(x + 5)

that is the equation of your line. however, if you want to graph it, this doesn't really make much sense to you. convert it to slope-intercept form, y = mx + b, by solving for y.

y - 2 = -3(x + 5) ... distribute -3
y - 2 = -3x - 15 ... add 2
y = -3x - 13 is your equation.

to graph this, and any other y = mx + b equation, you want to start with your y-intercept if it's present. your y intercept here is -13, which means the line you wasn't to graph crosses the y-axis at y = -13, or (0, -13). put a point there.

after you've plotted that point, you use your slope to graph more. remember that your slope is "rise over run"--you rise up/go down however many units, you run left/right however many units. if your slope is -3, you want to go down 3 units, then go to the right 1 unit. remember that whole numbers have a 1 beneath them as a fraction. -3/1 is your rise over 1.
6 0
3 years ago
Read 2 more answers
What is the correlation coefficient for the data shown in the table?
xxTIMURxx [149]

Answer:

The correlation coefficient is -1

Step-by-step explanation:

Here, we want to get the correlation coefficient for the given dataset

from the table, what do we observe?

As x is increasing by 5 units;

y is decreasing by 5 units

What this mean is that there is a negative correlation between both

Thus, what we have here is that, since the rate of increase/decrease on both ends is of equal magnitude but opposite signs, we can conclude that the correlation coefficient is -1

8 0
2 years ago
Read 2 more answers
A common blood test performed on pregnant women to screen for chromosome abnormalities in the fetus measures the human chorionic
goldfiish [28.3K]

Answer:

(a) The proportion of women who are tested, get a negative test result is 0.82.

(b) The proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.

Step-by-step explanation:

The Bayes' theorem states that the conditional probability of an event <em>E</em>_{i}, of the sample space <em>S,</em> given that another event <em>A</em> has already occurred is:

P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum\liits^{n}_{i=1}{P(A|E_{i})P(E_{i})}}

The law of total probability states that, if events <em>E</em>₁, <em>E</em>₂, <em>E</em>₃... are parts of a sample space then for any event <em>A</em>,

P(A)=\sum\limits^{n}_{i=1}{P(A|B_{i})P(B_{i})}

Denote the events as follows:

<em>X</em> = fetus have a chromosome abnormality.

<em>Y</em> = the test is positive

The information provided is:

P(X)=0.04\\P(Y|X)=0.90\\P(Y^{c}|X^{c})=0.85

Using the above the probabilities compute the remaining values as follows:

P(X^{c})=1-P(X)=1-0.04=0.96

P(Y^{c}|X)=1-P(Y|X)=1-0.90=0.10

P(Y|X^{c})=1-P(Y^{c}|X^{c})=1-0.85=0.15

(a)

Compute the probability of women who are tested negative as follows:

Use the law of total probability:

P(Y^{c})=P(Y^{c}|X)P(X)+P(Y^{c}|X^{c})P(X^{c})

          =(0.10\times 0.04)+(0.85\times 0.96)\\=0.004+0.816\\=0.82

Thus, the proportion of women who are tested, get a negative test result is 0.82.

(b)

Compute the value of P (X|Y) as follows:

Use the Bayes' theorem:

P(X|Y)=\frac{P(Y|X)P(X)}{P(Y|X)P(X)+P(Y|X^{c})P(X^{c})}

             =\frac{(0.90\times 0.04)}{(0.90\times 0.04)+(0.15\times 0.96)}

             =0.20

Thus, the proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.

6 0
3 years ago
Dylan borrowed $2100 from the bank for 15 months. The bank discounted the loan at 2.6%. How much was the interest? $ State your
melomori [17]

Answer:

actual rate of interest is 2.08 %

Step-by-step explanation:

Given data

borrowed = $2100

time = 15 months

rate = 2.6%

to find out

interest and receive from the bank and actual rate of interest

solution

we know bank discounted the loan at 2.6%

so interest will be 2.6% of $2100

that is  = 2.6/100 × 2100

interest = $54.60

so receive from the bank  is  borrowed money - interest

receive = 2100 - 54.60

receive from the bank is $2045.40

and we can say that interest is directly proportional to time

so interest of 12 months / interest of 15 month = 12 month time/ 15 month time

here  interest of 12 months = 12/15 ×  interest of 15 month

interest of 12 months = 12/15 × 54.60

interest of 12 months is $43.68 (annually)

now we can calculate actual rate of interest

that is = interest / borrowed money × 100

actual rate of interest = 43.68/2100 × 100

actual rate of interest is 2.08 %

6 0
2 years ago
A) A club is considering changing its bylaws. In an initial straw vote on the issue, 24 of the 40 members of the club favored th
lora16 [44]

Answer:

38,38,380

Step-by-step explanation:

GIVEN: A club is considering changing its laws. In an initial straw vote on the issue, 24 of the 40 members of the club favored the change and 16 did not. A committee of six is to be chosen from the 40 club members to devote further study to the issue.

TO FIND: How many committees of six can be formed from the club membership.

SOLUTION:

Total number of members =40

Total members to be chosen =6

To select committee of 6 members from 40 =^{40}C_6

                                                                       =\frac{40!}{34!6!}

                                                                      =38,38,380

Hence 38,38,380 different committee can be formed.

7 0
3 years ago
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