Answer:
(x - 7)² + (y - 5)² = 116
Step-by-step explanation:
equation of a circle:
(x - h)² + (y - k)² = r²
where (h,k) is the centre and r is the radius
centre is the midpoint of the diameter:
(h,k) = (11+3)/2 , (-5+15)/2
(h,k) = (7,5)
diameter = sqrt[(15--5)² + (3-11)²]
diameter = sqrt(464) = 4sqrt(29)
radius = ½ diameter
radius = 2sqrt(29)
r² = 116
equation:
(x - 7)² + (y - 5)² = 116
Answer:
[x-7]^2 + [y-5]^2= 116
Step-by-step explanation:
General equation of a circle is
[x2 - xo]^2 + [y2- yo]^2 = r^2
Where xo and yo are coordinates of the circle at the origin.
But xo = [x2 + x1]/2
= 11 + 3 / 2 = 7
yo = [y2 + y1] / 2 = [-5 + 15] /2 = 5
x2= 11, x2= 3; y1= -5, y2= 15
[11-7]^2 + [15-5]^2 =
16+ 100=116 = r^2
From the expression below;
[x2-xo]^2 + [y2-yo] ^2 = r^2
[x1-xo]^2 + [y1-yo] ^2 = r^2
[x-7]^2 + [y-5]^2= 116
what are the coordinates of the vertex of the parabola described by the equation below? y=7(x+5)^2-4
Answer:
[tex] y= 7(x+5)^2 -4[/tex]
The vertex form for a parabola is given by this expression:
[tex] y = a(x-h)^2 +k[/tex]
By direct comparison we see that for this case:
[tex] a = 7, h = -5 and k=-4[/tex]
And we know from the general expression that the vertex is:
[tex] V= (h,k)[/tex]
So then the vertex for this case is:
[tex] V= (-5,-4)[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] y= 7(x+5)^2 -4[/tex]
And we need to take in count that the vertex form for a parabola is given by this expression:
[tex] y = a(x-h)^2 +k[/tex]
By direct comparison we see that for this case:
[tex] a = 7, h = -5 and k=-4[/tex]
And we know from the general expression that the vertex is:
[tex] V= (h,k)[/tex]
So then the vertex for this case is:
[tex] V= (-5,-4)[/tex]
Expression is a trinonmial
Answer:
A: The expression is a trinomial with a degree of 4.
Step-by-step explanation:
The expression has three parts, so it's a tronomial.
The largest exponent is 4, so it has a degree of 4.
Answer:
Yea he is right it is a
Step-by-step explanation:
A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from. The Lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups. One group received vaccinations; the other did not. During the following year, only 333 of 2455 vaccinated children had ear infections, compared to 499 of 2452 unvaccinated children in the control group. a) Are the conditions for inference satisfied? b) Find a 95% confidence interval for the difference in rates of ear infection. c) Use your confidence interval to explain whether you think the vaccine is effective.
Step-by-step explanation:
Random: stated
a) Conditions met Random: stated
Normal: [tex]n_{1} p_{1}=333>10[/tex]
[tex]n_{1}\left(1-p_{1}\right)=2122[/tex]
[tex]n_{2} p_{2}=499>10[/tex]
[tex]n_{2}\left(1-p_{2}\right)=1953[/tex]
Independent: Sample is less than of population.
b) (0.047,0.089) Use 2 -prop interval function of graphing utility
[tex]x_{1}: 333[/tex]
[tex]n_{1}: 2455[/tex]
[tex]x_{2}: 499[/tex]
[tex]n_{2}: 2452[/tex]
[tex]C-[/tex]Level : 0.95
c) The vaccine appears to be effective because we are 95% confident that the proportion of infants without the vaccine who got ear infections was 4.7% to 8.9% more than infants who are vaccinated.
Simplify -r+8(-5r-2)
Answer:
-41r - 16
Step-by-step explanation:
Step 1 :
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
-5r - 2 = -1 • (5r + 2)
Equation at the end of step 2 :
-r + -8 • (5r + 2)
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
-41r - 16 = -1 • (41r + 16)
System of Equations: Solve for (x,y) given the system of linear equations "X 1 point
- y = 4" and "x + y = 4".
Answer:
(x, y) = (4, 0)
Step-by-step explanation:
It looks like you want to solve ...
x - y = 4x + y = 4Adding the two equations gives ...
2x = 8
x = 4 . . . . divide by 2
Then ...
y = 4 - x = 0
The solution is (x, y) = (4, 0).
_____
If you think about what you're seeing when you read the equations, you realize that adding or subtracting y gives the same result. Hence y=0 and x=4.
if 6a/2=12, then a =
Answer:
a = 4
Step-by-step explanation:
Multiply by 2 on each side
6a = 24
a = 4
Hector has three weeks
HELP ASAP!!
Mr. Washington has a sign that is in the shape of a trapezoid. Some of the dimensions of the sign are shown. What is the area of Mr. Washington’s sign?
A) 24 sq. Ft.
B) 36 sq. Ft.
C) 42 sq. Ft.
D) 48 sq. Ft.
Answer:
Answer shown from explanation
Step-by-step explanation:
Area of trapezium =1/2 * sum of parallel side * height = 1/2. *(6+12) *4= 36sqft
Which statement describes the system of equations?
(3x-4y=-35
(3x + 4y = 5
It has one solution (-5.5).
It has one solution (5, -5).
The system has no solution.
The system has infinitely many solutions.
Answer:
one solution
Step-by-step explanation:
3x - 4y = -35
3x + 4y = 5
6x = -30
x = -5
3(-5) + 4y = 5
-15 + 4y = 5
4y = 20
y = 5
(-5, 5)
The system of equations has one solution (-5.5) which is correct option (A).
What is the equation?The equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
What is linear equation?A linear equation is defined as an equation in which the highest power of the independent variable is always one.
Given the system of equations as :
3x - 4y = -35
3x + 4y = 5
Addition the both equations
3x - 4y + 3x + 4y = -35 + 5
6x = -30
Divided by 6 both the sides,
x = -30/6
x = -5
Substitute the value of x =2 in the equation 3x + 4y = 5
So, 3(-5) + 4y = 5
-15 + 4y = 5
4y = 20
Divided by 4 both the sides,
y = 20/4
y = 5
So, It has one solution x = -5 and y = 5
Hence, the system of equations has one solution (-5.5).
Learn more about equation here:
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B =
Round your answer to the nearest hundredth.
please help
Answer:
26.39
Step-by-step explanation:
sin B = 4/9
B = inverse sin 4/9 = 26.387
Find the value of x.
72 + 24x = 288
Answer:
X = 9
Step-by-step explanation:
1. Subtract 72 from both sides.
24x = 216
2. Divide 24 on both sides
x = 9
Answer:
X = 9
Step-by-step explanation:
We have to separate the like terms
72 + 24x = 288
24x = 288 - 72
24x = 216
We then divide both sides by 24
X = 9
Given the following system of equations:
6X1 - 6x2 - 4x3 = 0
X1 - 7x2 - 6x3 = 2
X1 +5x2 + nx3 = -2
Rewrite the system in Ax = b format and determine the following:
a. By reduction of the augmented matrix [A|b] to ref, find a value for n such that the system is consistent with an infinite number of solutions.
b. Based on your solution in part A, identify the rank of matrix A and rank of the augmented matrix [A|b].
c. Based on the value of the rank, how many equations (the row vectors of the augmented matrix [Ab]) are linearly independent?
d. Using your solution in part A, solve the system of equations using Gauss-jordan elimination.
Answer:
Step-by-step explanation:
Given:-
- The following system of equations is given:
[tex]6x_1 - 6x_2 -4x_3 = 0\\\\x_1 - 7x_2 -6x_3 = 0\\\\x_1 - 5x_2 -nx_3 = 0\\[/tex]
Solution:-
- The matrix equation consists of coefficient matrix "A" and a variable matrix " x ". These two matrices undergo multiplication to yield a solution column vector "b".
- The matrix A, is a symmetrical square matrix with its elements representing the coefficients of each variable as follows:
[tex]A = \left[\begin{array}{ccc}a_1_1&a_1_2&a_1_3\\a_2_1&a_2_2&a_2_3\\a_3_1&a_3_2&a_3_3\end{array}\right][/tex]
- Where the elements first subscript denotes the equation number and second subscript denotes the variable number.
[tex]A = \left[\begin{array}{ccc}6&-6&-4\\1&-7&-6\\1&5&n\end{array}\right][/tex]
- Similarly, the variable matrix " X " is a column vector that lists all the variables in the the system of equations in a ascending order.
[tex]X = \left[\begin{array}{c}x_1&x_2&x_3\end{array}\right][/tex]
- The solution vector " b " is the corresponding solution or any number written on the right hand side of the equals to sign " = " :
[tex]b = \left[\begin{array}{c}0&2&-2\end{array}\right][/tex]
- Now, we can express the given system in the asked format:
[tex]A*X = b\\\\\left[\begin{array}{ccc}6&-6&-4\\1&-7&-6\\1&5&n\end{array}\right]*\left[\begin{array}{c}x_1&x_2&x_3\end{array}\right] = \left[\begin{array}{c}0&2&-2\end{array}\right][/tex]
- The augmented matrix is a matrix that combines the coefficient matrix " A " and the solution vector " b ". A solution vector "b" as an extra column to the coefficient matrix:
[tex][ A | b ]\\\\ \left[\begin{array}{ccccc}6&-6&-4&|&0\\1&-7&-6&|&2\\1&5&n&|&-2\end{array}\right][/tex]
- Now we will perform row reduction operation such that the system is consistent and has infinite number of solution.
- Row operation: R3 - R2 & R1/6
[tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\1&-7&-6&|&2\\0&12&n+6&|&-4\end{array}\right][/tex]
- Row operation: R2 - R1 & R3 / 12
[tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&-6&-\frac{16}{3} &|&2\\0&1&\frac{n+6}{12} &|&-\frac{1}{3}\end{array}\right][/tex]
- Row operation: R2 / 6
[tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&-1&-\frac{8}{9} &|&\frac{1}{3} \\0&1&\frac{n+6}{12} &|&-\frac{1}{3}\end{array}\right][/tex]
For the above system to be consistent and have infinite many solution then the coefficient of " x3 " for the 2nd and 3rd row must be equal:
[tex]-x_2 - ( \frac{n+6}{12})*x_3 = \frac{1}{3}[/tex]
[tex]-x_2 - ( \frac{8}{9})*x_3 = \frac{1}{3}[/tex]
The coefficient of " x_3 " must be equal:
[tex]( \frac{n+6}{12}) = \frac{8}{9} \\\\\\\n = \frac{14}{3}[/tex]
- The augmented matrix in reduced form becomes:
[tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&1&\frac{8}{9} &|&-\frac{1}{3} \\0&0&0 &|&0\end{array}\right][/tex]
Answer: Rank = Number of non-zero rows = 2
- The number of linearly independent rows are equal to the rank of the augmented matrix.
Hence,
Answer: Number of linearly independent rows = 2
Row operation: R1 + R2
[tex]\left[\begin{array}{ccccc}1&0&\frac{2}{9} &|&-\frac{1}{3} \\0&1&\frac{8}{9} &|&-\frac{1}{3} \\0&0&0 &|&0\end{array}\right][/tex]
- The variable "x_3" will take any arbitrary value for which the solution holds infinitely many solutions.
[tex]x_2 + \frac{8}{9}*x_3 = -\frac{1}{3} \\\\x_2 = - ( \frac{8}{9}*x_3 + \frac{1}{3} )\\\\x_1 + \frac{2}{9}*x_3 = -\frac{1}{3} \\\\x_1 = - ( \frac{2}{9}*x_3 + \frac{1}{3} )\\[/tex]
- Taking x_3 = α:
Answers:
[tex]x_1 = -\frac{1}{3} + \frac{2}{9} \alpha \\\\x_2 = -\frac{1}{3} + \frac{8}{9} \alpha[/tex]
How to you write 5,678,209 in expand form
Maribel surveyed 55 people to find out their favorite types of music. The results are shown in the bar graph. Based on the information in the graph, which types of music were chosen by 40% of the people surveyed
Answer:
B. Jazz and opra
Step-by-step explanation:
40 percent of 55 is 22. Find whatever is equal to 22
B) Jazz & Opera music combo were chosen by 40% of people surveyed
Calculation of percentage respondentsGiven : Total respondents = 55
So, 40% of total respondents = 40% of 55 = 22
County & Opera are chosen by 15 + 10 = total 25 respondents, ie not equal to 40%
Jazz & Opera are chosen by 12 + 10 = total 22 respondents, ie equal to 40%
Jazz, Opera, Rock & Country, Jazz, Rock are totally more respondents.
To learn more about Percentage Respondents, refer https://brainly.com/question/8191920?referrer=searchResults
circle is centered at (-4,-7)The circle passes through the point (-5,-9) . What is its radius?
Answer:
r = sqrt of 5 or 2.2
Step-by-step explanation:
(1)²+(2)²=r²
5 = r²
r = sqrt of 5 or 2.2
An online movie store made $1,494 on
poster sales last week. It charged $18 for
each poster. How many posters did the
store sell?
Answer:
83 posters
Step-by-step explanation:
$1,494/$18 = 83
Answer:
An online movie store made $1,494 on poster sales last week.
It charged $18 for each poster.
=> The number of sold posters:
N = 1494/18 = 83
Hope this helps!
:)
The slope of a line passing through (-3,-6) and (-6,-6)
Answer:
M=0
Step-by-step explanation:
Nick score on six scientist are listed below 87,93,82,91,93,85
As a bonus the science teacher was going to add three points each test how does the mean of the new test scores compare with the mean of the original test scores??
Answer:
Mean of original test scores is 88.5
Mean of test scores , with three marks added to each score is 91.5
The mean of the test score with three marks added to each score is higher than the original mean of score is increased by three .
Explanation : hope it works out !!
2 lines intersect and create VERTICAL angles. One of the angles measures (3n-28) degrees and the other angle measures 83 degrees. What is the value of n? (show your work in numbers)
Answer:
n is 41.67 degrees
Step-by-step explanation:
At the intersection point of two lines, there are two angles, a and b. The sum of these two angles is 180.
In this question:
One of the angles is (3n - 28)
The other is 83.
Then
[tex]3n - 28 + 83 = 180[/tex]
[tex]3n + 55 = 180[/tex]
[tex]3n = 180 - 55[/tex]
[tex]3n = 125[/tex]
[tex]n = \frac{125}{3}[/tex]
[tex]n = 41.67[/tex]
What value of x is in the solution set of 4x - 12 <16 + 8x?
Step-by-step explanation:
4x - 12 < 16 + 8x
Bringing like terms on one side
-12 - 16 < 8x - 4x
-28 < 4x
-28/4 < x
-7 < x
ANYONE PLZZ THIS DUE IN AN HOUR!!!! Will mark the brainliest
Answer:
Option C is correct.
Step-by-step explanation:
The area of 1 side of the divider is approximately 8 x 3 = 24 < 25
Hope this helps!
:)
Find g(x) if it is known that g(2t)=8t−1. (IWILLMARKBRAINLIEST)
Answer:
g(x) = 4x - 1
Step-by-step explanation:
We have that:
[tex]g(x) = ax + b[/tex]
So
[tex]g(2t) = a*(2t) + b[/tex]
Equaling both sides:
[tex]g(2t) = 8t - 1[/tex]
[tex]a*(2t) + b = 8t - 1[/tex]
b = -1.
And
[tex]2a = 8[/tex]
[tex]a = \frac{8}{2}[/tex]
[tex]a = 4[/tex]
Then
g(x) = 4x - 1
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answer:
d.
Step-by-step explanation:
x^2 because their is no other x^2
2x because their is no more x.
-7+1 equals -6
Answer:
D
Step-by-step explanation:
(f + g)(x) means that you add the two functions together, which results in (f + g)(x) = 2x + 1 + x² - 7 = D) x² + 2x - 6. Hope this helps!
4. A small high school holds its graduation ceremony in the gym. Because of seating constraints, students are limited to a maximum of four tickets to graduation for family and friends. The vice principal knows that historically 30% of students want four tickets, 25% want three, 25% want two, 15% want one, and 5% want none. (a) Let X ¼ the number of tickets requested by a randomly selected graduating student, and assume the historical distribution applies to this rv. Find the mean and standard deviation of X. (b) Let T ¼ the total number of tickets requested by the 150 students graduating this year. Assuming all 150 students’ requests are independent, determine the mean and standard deviation of T. (c) The gym can seat a maximum of 500 guests. Calculate the (approximate) probability that all students’ requests can be accommodated. [Hint: Express this probability in terms of T. What distribution does T have?]
Answer:
(a) The mean and standard deviation of X is 2.6 and 1.2 respectively.
(b) The mean and standard deviation of T are 390 and 180 respectively.
(c) The distribution of T is N (390, 180²). The probability that all students’ requests can be accommodated is 0.7291.
Step-by-step explanation:
(a)
The random variable X is defined as the number of tickets requested by a randomly selected graduating student.
The probability distribution of the number of tickets wanted by the students for the graduation ceremony is as follows:
X P (X)
0 0.05
1 0.15
2 0.25
3 0.25
4 0.30
The formula to compute the mean is:
[tex]\mu=\sum x\cdot P(X)[/tex]
Compute the mean number of tickets requested by a student as follows:
[tex]\mu=\sum x\cdot P(X)\\=(0\times 0.05)+(1\times 0.15)+(2\times 0.25)+(3\times 0.25)+(4\times 0.30)\\=2.6[/tex]
The formula of standard deviation of the number of tickets requested by a student as follows:
[tex]\sigma=\sqrt{E(X^{2})-\mu^{2}}[/tex]
Compute the standard deviation as follows:
[tex]\sigma=\sqrt{E(X^{2})-\mu^{2}}\\=\sqrt{[(0^{2}\times 0.05)+(1^{2}\times 0.15)+(2^{2}\times 0.25)+(3^{2}\times 0.25)+(4^{2}\times 0.30)]-(2.6)^{2}}\\=\sqrt{1.44}\\=1.2[/tex]
Thus, the mean and standard deviation of X is 2.6 and 1.2 respectively.
(b)
The random variable T is defined as the total number of tickets requested by the 150 students graduating this year.
That is, T = 150 X
Compute the mean of T as follows:
[tex]\mu=E(T)\\=E(150\cdot X)\\=150\times E(X)\\=150\times 2.6\\=390[/tex]
Compute the standard deviation of T as follows:
[tex]\sigma=SD(T)\\=SD(150\cdot X)\\=\sqrt{V(150\cdot X)}\\=\sqrt{150^{2}}\times SD(X)\\=150\times 1.2\\=180[/tex]
Thus, the mean and standard deviation of T are 390 and 180 respectively.
(c)
The maximum number of seats at the gym is, 500.
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.
Here T = total number of seats requested.
Then, the mean of the distribution of the sum of values of X is given by,
[tex]\mu_{T}=n\times \mu_{X}=390[/tex]
And the standard deviation of the distribution of the sum of values of X is given by,
[tex]\sigma_{T}=n\times \sigma_{X}=180[/tex]
So, the distribution of T is N (390, 180²).
Compute the probability that all students’ requests can be accommodated, i.e. less than 500 seats were requested as follows:
[tex]P(T<500)=P(\frac{T-\mu_{T}}{\sigma_{T}}<\frac{500-390}{180})\\=P(Z<0.61)\\=0.72907\\\approx 0.7291[/tex]
Thus, the probability that all students’ requests can be accommodated is 0.7291.
(256)^0.16*(256)^0.09 Answer of this pls
Answer:
4
Step-by-step explanation:
[tex]256^{0.16}\cdot 256^{0.09}=\\256^{0.16+0.09}=\\256^{0.25}=\sqrt[4]{256}=4[/tex]
Hope this helps!
nequality
Imagine the polynomial function shown represents the
profits, in y dollars, earned by the production of x
widgets.
What is the minimum number of widgets for the
company to earn more than 50 dollars?
widgets
Answer:
The minimum number of widgets for the company to earn more than 50 dollars = 104 widgets.
Step-by-step explanation:
Complete Question
Inequality
Imagine the polynomial function shown represents the profits, in y dollars, earned by the production of x widgets.
y = -0.04x² + 40x - 3600
What is the minimum number of widgets for the company to earn more than 50 dollars?
Solution
For the profit to be more than 50
y > 50
-0.04x² + 40x - 3600 > 50
-0.04x² + 40x - 3650 > 0
0.04x² - 40x + 3650 < 0
(x - 898.4) (x - 101.6) < 0
Using the inequality table to obtain the required solution to this inequality
Eqn | x < 101.6 | 101.6 < x < 898.4 | x > 898.4
(x - 898.4) | -ve | - ve | + ve
(x - 101.6) | -ve | + ve | + ve
(x-898.4)(x-101.6) | +ve | - ve | +ve
Hence, the inequality that satisfies the equation of (x - 898.4) (x - 101.6) < 0, that is, negative, is 101.6 < x < 898.4.
And from this range, the minimum number of widgets for the company to earn more than 50 dollars = 102 widgets.
But 102 widgets give a profit of 13 dollars, 103 widgets give a profit of 47 dollars and it is until 104 widgets that the profits exceed 50 dollars truly.
Hope this Helps!!!
Answer:4
Step-by-step explanation:
An army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a high failure rate after it has been repaired and reinstalled in the system. The shop floor supervisor believes that having standard work procedures in place will reduce the time required for troubleshooting this component. Time (in minutes) required troubleshooting this component without and with the standard work procedure is recorded for a sample of 19 employees. In order to determine if having a standard work procedure in place reduces troubleshooting time, they should use
a. a one-tailed paired t-test.
b. a two-tailed test of two independent means.
c. a one-tailed test of two independent means.
d. a two-tailed paired t-test.
e. a test of two proportions.
Answer:
A. a one-tailed paired t-test.
Step-by-step explanation:
The stem-and-leaf plot shown displays the weights, in pounds, of the dogs in an animal shelter.
What is the median weight for the dogs in the animal shelter?
A.33 pounds
B.44 pounds
C.48 pounds
D.49 pounds
What is a requirement of supplementary angles
Answer:
They both need to add up 180 degreesStep-by-step explanation:
Answer:
Supplementary angles are angles that add up to 180° so they need to add up to 180 degrees.
Step-by-step explanation:
Plsplzplzplzplz help
Answer:
Step-by-step explanation:
Hi Sorry this took so long!
1. True
A=hbb /2 or Half of Base times Height.
2.False it would be 63
A= b * h
3.True
A=a+b/2 * h
Hope this helps!