Answer:
Radius: [tex]r =\frac{\sqrt {21}}{6}[/tex]
[tex]Center = (-\frac{3}{2}, -\frac{2}{3})[/tex]
Step-by-step explanation:
Given
[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]
Solving (a): The radius of the circle
First, we express the equation as:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where
[tex]r = radius[/tex]
[tex](h,k) =center[/tex]
So, we have:
[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]
Divide through by 9
[tex]x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0[/tex]
Rewrite as:
[tex]x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}[/tex]
Group the expression into 2
[tex][x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}[/tex]
[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]
Next, we complete the square on each group.
For [tex][x^2 + 3x][/tex]
1: Divide the [tex]coefficient\ of\ x\ by\ 2[/tex]
2: Take the [tex]square\ of\ the\ division[/tex]
3: Add this [tex]square\ to\ both\ sides\ of\ the\ equation.[/tex]
So, we have:
[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]
[tex][x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]
Factorize
[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]
Apply the same to y
[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}[/tex]
Add the fractions
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]
Recall that:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
By comparison:
[tex]r^2 =\frac{7}{12}[/tex]
Take square roots of both sides
[tex]r =\sqrt{\frac{7}{12}}[/tex]
Split
[tex]r =\frac{\sqrt 7}{\sqrt 12}[/tex]
Rationalize
[tex]r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}[/tex]
[tex]r =\frac{\sqrt {84}}{12}[/tex]
[tex]r =\frac{\sqrt {4*21}}{12}[/tex]
[tex]r =\frac{2\sqrt {21}}{12}[/tex]
[tex]r =\frac{\sqrt {21}}{6}[/tex]
Solving (b): The center
Recall that:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where
[tex]r = radius[/tex]
[tex](h,k) =center[/tex]
From:
[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]
[tex]-h = \frac{3}{2}[/tex] and [tex]-k = \frac{2}{3}[/tex]
Solve for h and k
[tex]h = -\frac{3}{2}[/tex] and [tex]k = -\frac{2}{3}[/tex]
Hence, the center is:
[tex]Center = (-\frac{3}{2}, -\frac{2}{3})[/tex]
consider the line (d) with equation y = –2x+6
determine the coordinates of B, the intersection point of (d) andy'Oy.
Answer:
i dont know sry need points sry
Step-by-step explanation:
Can someone please help me out pleaseeeee !!!!!
Answer:
Step-by-step explanation:
0: -2
1: -4
2: -6
Find the annual percentage yield of a saving account that pays 2.75% compounded quarterly
Answer:
The annual percentage yield is of 2.78%.
Step-by-step explanation:
Annual percentage yield of an account:
The annual percentage yield of an account compounded n times during the year with a decimal interest rate of r is given by:
[tex]Y = (1+\frac{r}{n})^n - 1[/tex]
Pays 2.75% compounded quarterly
This means that [tex]r = 0.0275, n = 4[/tex]. So
[tex]Y = (1+\frac{r}{n})^n - 1[/tex]
[tex]Y = (1+\frac{0.0275}{4})^4 - 1[/tex]
[tex]Y = 0.0278[/tex]
0.0278 = 2.78%
The annual percentage yield is of 2.78%.
Billy ate 30% of a pizza and Bonnie ate 3/8 of a pizza who ate more
5.5.3 Suppose X and Y have a bivariate normal distribution with , , , , and . Determine the following. Round your answers to three decimal places (e.g. 98.765). (a) Enter your answer in accordance to the item a) of the question statement (b) Enter your answer in accordance to the item b) of the question statement (c) Enter your answer in accordance to the item c) of the question statement
The question is incomplete. The complete question is :
Suppose X and Y have a bivariate normal distribution with [tex]$\sigma_X = 0.04, \sigma_Y = 0.08, \mu_X = 3.00, \mu_Y = 7.70$[/tex] and ρ = 0.
Determine the following. Round your answers to three decimal places (e.g. 98.765).
(a). [tex]$P(2.90 < X < 3.10) =$[/tex]
(b). [tex]$P(7.60 < X < 7.80) =$[/tex]
(c). P(2.90 < X < 3.10, 9.60 < Y < 7.80) =
Solution :
We have
[tex]$X \sim N (\mu_X=3, \sigma_X^2=0.04^2)$[/tex] and
[tex]$Y \sim N (\mu_Y=7.7, \sigma_Y^2=0.08^2)$[/tex]
a). The required probability is
[tex]$P(2.90 < X < 3.10) =$[/tex] [tex]$P\left(\frac{2.9-3}{0.04}< Z < \frac{3.1-3}{0.04}\right)$[/tex]
= P(-2.5 < Z < 2.5) = P(Z < 2.5) - P(Z < -2.5)
= P(Z < 2.5) - [1-P(Z < 2.5)]
= 2P(Z < 2.5) - 1
= 2(0.99379) - 1
= 0.98758
≈ 0.988
b). The required probability is
[tex]$P(7.6 < X < 7.8) =$[/tex] [tex]$P\left(\frac{7.6-7.7}{0.08}< Z < \frac{7.8-7.7}{0.08}\right)$[/tex]
= P(-1.25 < Z < 1.25) = P(Z < 1.25) - P(Z < -1.25)
= P(Z < 1.25) - [1-P(Z < 1.25)]
= 2P(Z < 1.25) - 1
= 2(0.89435) - 1
= 0.7887
≈ 0.789
c). Since, ρ = 0, so the X and Y are independent. Thus the required probability is :
P(2.90 < X < 3.10, 9.60 < Y < 7.80) = P(2.9 < X < 3.1) x P(7.6 < Y < 7.8)
= (0.98758)(0.7887)
= 0.77890
≈ 0.779
Solve each equation by completing the square :
(x +y )(x -y), if x = -3, y=-5
PLS NO FILES OR I AM REPORTING YOU
Answer:
-16
Step-by-step explanation:
(X + Y)
= (-3 + -5)
= -8
(X - Y)
= (-3 - -5)
= 2
Because they're still in brackets in this form:
(-8) (2)
You multiply them both and you'll get the answer:
-16
hope this helped!
how much of a circle does a 100 degree angle turn through
Answer: 5/18
Step-by-step explanation: A circle is 360 degrees so if you are turning 100 degrees... you would get 100/360 of the way around the circle.
100/360 = 5/18
PLEASE HELP!!! ILL GIVE BRAINLIEST !! Which is the correct answer ? 100 POINTS !! EXPLAIN.
Which statement is best supported by the Information in the box
plots?
A The median of the data for Student 1 is less than the medianof the data for Student2
B. The interquartile range of the data for Student 1 is equal to the
interquartile range of the data for Student 2
C. The range of the data for Student 1 is greater than the range
of the data for Sludent 2
D. The lowest grade for Student 1 is greater than the lowest
grade for Student 2
Answer:Interquartile Range (IQR) ... IQR: Step 1: Put the data in order from least to greatest. ... If the number of data points is even, the median is the average of the middle two data points. ... The first quartile is the median of the data points to the left of the median in the ... Is it possible for the IQR to be less than the given data points?
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
can someone actually help me :)
Answer:1 + 1
Step-by-step explanation:because 1+1 is 1+1
Please please help please
Answer:
4 times larger
Step-by-step explanation:
PLZ ANSWER NO FAKE LINKS
Answer:
Draw a Rectangle with 3/10 at the bottom and 1/2 at the top
Step-by-step explanation:
Have a Nice Day!
How many cubes with side lengths of 1/4 cm does it take to fill the prism?
Answer:2 14
Step-by-step explanation:
9514 1404 393
Answer:
135
Step-by-step explanation:
The prism is 9/4 cm = 9×(1/4 cm) = 9 cubes wide.
The prism is 3/4 cm = 3×(1/4 cm) = 3 cubes deep.
The prism is 5/4 cm = 5×(1/4 cm) = 5 cubes high.
The number of cubes that will fill the prism is ...
9 × 3 × 5 = 135 . . . cubes to fill the prism
D is greater than E and less than C.
C and D are opposites.
At least one number is greater than A.
HELP
Answer:
?
Step-by-step explanation:
Please can someone help me thank you
Answer:
(a) Rome= 11 degrees
Munich= 5 degrees
Difference = 11-5 = 6 degrees
(b)
Oslo= 2 degrees
At 6pm= 2+5= 7 degrees
What is the volume of a cylinder with base radius 2 and height 5?
Either enter an exact answer in terms of 3.14 for pi
Answer:
V ≈ 62.83
Step-by-step explanation:
Cylinder Formulas in terms of r and h
Calculate the volume of a cylinder:
V = πr2h
Calculate the lateral surface area of a cylinder (just the curved outside):
L = 2πrh
Calculate the top and bottom surface area of a cylinder (2 circles):
T = B = πr2
Total surface area of a closed cylinder is:
A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
Solution
V=πr 2h = π · 22 · 5 ≈ 62.83185
Therefore, the volume of the cylinder in the nearest tenths is V ≈ 62.83
Pls help I’ll pay u 30$ if it’s right
Answer:
8 5 7 1 3 2 4 6
Step-by-step explanation:
my Cashsap kinqcollin
Answer now please ♀️
Answer:
8/15
Step-by-step explanation:
In a right triangle, where B is an acute angle, the tan B is equal to the measure of the side opposite B divided by the measure of the shorter side at B
tanB = 16/30 = 8/15
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use
Answer:
The advertisement should use 16 minutes.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.
This means that [tex]m = 3.5, \mu = \frac{1}{3.5} = 0.2857[/tex]
What number of minutes should the advertisement use?
The values of x for which:
[tex]P(X > x) = 0.01[/tex]
So
[tex]e^{-\mu x} = 0.01[/tex]
[tex]e^{-0.2857x} = 0.01[/tex]
[tex]\ln{e^{-0.2857x}} = \ln{0.01}[/tex]
[tex]-0.2857x = \ln{0.01}[/tex]
[tex]x = -\frac{\ln{0.01}}{0.2857}[/tex]
[tex]x = 16.12[/tex]
Rounding to the nearest number, the advertisement should use 16 minutes.
Which of the following letters is NOT line symmetric?
1. A
2. E
3. G
4. Y
Answer:
G
Step-by-step explanation:
Answer:
its G
Step-by-step explanation:
Perform the indicated operation and write the answer in the form a + bi.
(9+ i)(-6+5i)
Answer:
-59 + 39i
Step-by-step explanation:
Apply the Distributive Property of Multiplication:
(9)(-6) + (9)(5 i) - 6i - 5 (recall that i^2 = -1)
or:
-54 + 45i - 6i - 5, or
-59 + 39i
PLS HELP!
2x + 4 > 8
2x 4 =- 8
2 x + 4 = 8 2x+4=8 2x+4=8. Subtract 4 from both sides. Simplify 8 − 4 8-4 8−4 to 4. Divide both sides by 2.
Which expression is equivalent to the expression given below?
-3.5(2 - 1.5n) 14.5n
-7 - 6n
A.
-7 + 0.75n
B.
-7 - 9.75n
c.
-7 – 9.5n
D
Step-by-step explanation:
- 35/10(2-15n/10) 145n/10 - 7 - 6n
-70/10 +35*15n/100.145n/10 -7-6n
-7 + 525n/100.145n/10 -7- 6n
-14 +5.25n .14.5n -6n
-14 +76.125n^2 -6n is final answer
10th grade Geometry Question, I will give brainliest. NEED HELP ASAP!
Answer:
- 1 + 5 + 2 y is your answer I am the teacher
Select the measures that are equal. Select all that apply.pls help me i beg you
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer: all of dem except for 6
Step-by-step explanation:
Pls help me , ASAP , TIA
Answer:
Step-by-step explanation:
Arrange your numbers in numerical order.
Count how many numbers you have.
If you have an odd number, divide by 2 and round up to get the position of the median number.
If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
Which of the following is equal to 5 1/3
Answer:
C
Step-by-step explanation:
The 3 would go on the outside.
Juan deposited $450 in an account that earned 7.5% simple interest.
- He did not make additional deposits and he didn't withdraw any money from the account.
What was the balance in Juan's investment account after 3 years?
Answer:
$551.25
Step-by-step explanation:
$450 x 7.5% = 33.75
33.75 x 3 = 101.25
101.25 + 450 = 551.25