Answer:
132
Step-by-step explanation:
First, find how many beats are in a minute by creating a proportion:
[tex]\frac{11}{5}[/tex] = [tex]\frac{x}{60}[/tex]
Cross multiply and solve for x:
5x = 660
x = 132
So, there are 132 beats in one minute.
This means the constant of proportionality is 132.
The proportional relation is y= 2.2x
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Neena counts 11 beats in 5 seconds
So, x=11 and y=5
Using the proportionality
y = k x
k= y/x
k= 11/5
k= 2.2
Hence, the proportional relation is y= 2.2x
Learn more about proportion here:
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Problem 9.4 Given the system of equations -3x2 + 7x3 = 4 x1 + 2x2 - x3 = 0 5x1 -2 x2 = 3 (a) Compute the determinant. (b) Use Cramer’s rule to solve for the x’s. (c) Use Gauss elimination with partial pivoting to solve for the x’s. As part of the computation, calculate the determinant in order to verify the value computed in (a) (d) Substitute your results back into the original equations to check your solution.
- 3 x₂ + 7 x₃ = 3
x₁ + 2 x₂ - x₃ = 0
5 x₁ - 2 x₂ = 3
(a) I suppose this is asking for the determinant of the coefficient matrix.
[tex]\begin{vmatrix}0&-3&7\\1&2&-1\\5&-2&0\end{vmatrix}[/tex]
Using a cofactor expansion along the first row, this reduces to
[tex]0\begin{vmatrix}2&-1\\-2&0\end{vmatrix}-(-3)\begin{vmatrix}1&-1\\5&0\end{vmatrix}+7\begin{vmatrix}1&2\\5&-2\end{vmatrix}= 3(0 - (-5))+7(-2-10)=\boxed{-69}[/tex]
(b) Using Cramer's rule, we have
[tex]x_1=\dfrac{\begin{vmatrix}\mathbf 3&-3&7\\\mathbf 0&2&-1\\\mathbf 3&-2&0\end{vmatrix}}{\begin{vmatrix}0&-3&7\\1&2&-1\\5&-2&0\end{vmatrix}}[/tex]
[tex]x_2=\dfrac{\begin{vmatrix}0&\mathbf 3&7\\1&\mathbf 0&-1\\5&\mathbf 3&0\end{vmatrix}}{\begin{vmatrix}0&-3&7\\1&2&-1\\5&-2&0\end{vmatrix}}[/tex]
[tex]x_3=\dfrac{\begin{vmatrix}0&-3&\mathbf 3\\1&2&\mathbf 0\\5&-2&\mathbf 3\end{vmatrix}}{\begin{vmatrix}0&-3&7\\1&2&-1\\5&-2&0\end{vmatrix}}[/tex]
That is, solving for n-th variable consists of dividing [the determinant of the coefficient matrix with its n-th column replaced with the right side of the system, the numbers in boldface,] by [the determinant of the coefficient matrix].
Compute each determinant:
[tex]\begin{vmatrix}\mathbf 3&-3&7\\\mathbf 0&2&-1\\\mathbf 3&-2&0\end{vmatrix}=3\begin{vmatrix}2&-1\\-2&0\end{vmatrix}+3\begin{vmatrix}-3&7\\2&-1\end{vmatrix}=3(0-2)+3(3-14)=-39[/tex]
(expanding along the first column)
[tex]\begin{vmatrix}0&\mathbf 3&7\\1&\mathbf 0&-1\\5&\mathbf 3&0\end{vmatrix}=-1\begin{vmatrix}3&7\\3&0\end{vmatrix}+5\begin{vmatrix}3&7\\0&-1\end{vmatrix}=-1(0-21)+5(-3-0)=6[/tex]
(again, along the first column)
[tex]\begin{vmatrix}0&-3&\mathbf 3\\1&2&\mathbf 0\\5&-2&\mathbf 3\end{vmatrix}=-1\begin{vmatrix}-3&3\\-2&3\end{vmatrix}+5\begin{vmatrix}-3&3\\2&0\end{vmatrix}=-1(-9-(-6))+5(0-6)=-27[/tex]
(first column)
So, we get the solution
[tex]x_1=\dfrac{-39}{-69}=\boxed{\dfrac{13}{23}},x_2=\dfrac6{-69}=\boxed{-\dfrac2{23}},x_3=\dfrac{-27}{-69}=\boxed{\dfrac9{23}}[/tex]
(c) Using elimination:
- 3 x₂ + 7 x₃ = 3
x₁ + 2 x₂ - x₃ = 0
5 x₁ - 2 x₂ = 3
Swap the first two equations:
x₁ + 2 x₂ - x₃ = 0
- 3 x₂ + 7 x₃ = 3
5 x₁ - 2 x₂ = 3
Add -5(equation 1) to equation 3:
x₁ + 2 x₂ - x₃ = 0
- 3 x₂ + 7 x₃ = 3
- 12 x₂ + 5 x₃ = 3
Add -4(equation 2) to equation 3:
x₁ + 2 x₂ - x₃ = 0
- 3 x₂ + 7 x₃ = 3
- 23 x₃ = -9
Multiply through equation 3 by -1/23:
x₁ + 2 x₂ - x₃ = 0
- 3 x₂ + 7 x₃ = 3
x₃ = 9/23
Add -7(equation 3) to equation 2:
x₁ + 2 x₂ - x₃ = 0
- 3 x₂ = 6/23
x₃ = 9/23
Multiply through equation 2 by -1/3:
x₁ + 2 x₂ - x₃ = 0
x₂ = -2/23
x₃ = 9/23
Add -2(equation 2) and equation 3 to equation 1:
x₁ = 13/23
x₂ = -2/23
x₃ = 9/23
2,940 ÷ 48 pls help
i need to get the answer
Answer:
61.25
Step-by-step explanation:
48 goes into 2940 that many times.
Hope this helped :)
Answer:
61.25
Step-by-step explanation:
2,940 / 48 = 61.25
Hope this helps.
translate the sentence into an equation
The sum of 6 times a number and 2 is equal to 3
Answer:
6x + 2 = 3
Step-by-step explanation:
x would represent the unknown number
The sum refers to addition
6 times a number would be 6x (you can use any variable, but for this example I'm using x)
When you put it all together, it is 6x + 2 = 3
The required equation is 6x + 2 = 3.
It is required to find the equation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers
Given:
The sum of 6 times a number and 2 equals 3.
According to given question we have,
Let the number be x.
6 times a number would be
6x
The sum of 6 times a number and 2 equals 3.
6x + 2 = 3.
Therefore, the required equation is 6x + 2 = 3.
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13-22 super easy help please wee thank you!
the answer to the equation is -9
what is the slope of the line thru passes thru (1,1) and (9,6)
Answer: 0.6
Step-by-step explanation:
x1=1
x2= 9
y1=1
y2=6
SLOPE OF THE LINE
= y2-y1/x2-x1
= 6-1/9-1
=5/8
=0.6
You work for a swimming pool cleaning service. The pool you are cleaning holds 15,000 gallons of water. The cleaning solution you have to add to the pool calls for a ratio of 1:6,000 (1oz to 6,000 gallons of water). What is the ratio of solution you must use for this specific pool?
Answer:
The answer would be 2.5 oz. of solution
Step-by-step explanation:
If you need 1:6,000 ratio and the pool you are cleaning is 15,000 then you divide 15,000 by 6,000 and you get what your ratio should be
What is the value of x? Round to the nearest tenths place....
Answer:
x = 12.64911064
Step-by-step explanation:
a^2 + b^2 = c^2
8^2 + b^2 = 14^2
36 + b^2 = 196
-74.25
That the right answer
Answer:
Okay...
Step-by-step explanation:
I’LL MARK BRAINLEST! :)
Answer:
9.1
Step-by-step explanation:
I think this because it is 9 boxes away from the other points, plus it sloped a bit...
Answer:
9.1
Step-by-step explanation:
Distance=[tex]\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]
=[tex]\sqrt{(4-3)^{2} +(-5-4)^{2} }[/tex]
=[tex]\sqrt{(1)^{2}+(-9)^{2} }[/tex]
=[tex]\sqrt{1+81}[/tex]
=[tex]\sqrt{82}[/tex]
≈9.1
Pleaseeeee helppppp meeeeee
What is the price per pound of the beans ? Explain how you know that your answer is reasonable.
Answer:
we need numbers please
Answer:
$1.76
Step-by-step explanation:
:)
the simple interest on $15000 for three months at 10% per annum is
9514 1404 393
Answer:
$375
Step-by-step explanation:
The interest formula for simple interest is ...
I = Prt . . . . on amount P, at annual rate r for t years.
Here, t = 3/12 = 1/4, r = 0.10, P = $15,000, so the interest is ...
I = $15,000·0.10·0.25 = $375
The simple interest is $375.
what is 35% as a fraction
Answer:
7/20
Step-by-step explanation:
Sub to SZ Lexrn if that does not show search up shiyo on vr and first vid is them please help out , thx bye . If you do it cmt and ill make a post for yall for 100 points, please bro..
Answer:
Ooooook?
Step-by-step explanation:
Fine
What is the distance between the points -30, -10 and -30, 19 in the xy plane?
A: 9 units
B: 20 units
C: 29 units
D: 49 units
Answer:
29 units..
Step-by-step explanation:
well i don't know how to insert an image of the answer...but I did it...its (c): 29 units
rove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r = a b and s = c d for some ---Select--- a, b, c, and d with ---Select--- . Write r − s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r − s = Both the numerator and the denominator are integers because ---Select--- . In addition, bd ≠ 0 by the ---Select--- . Hence r − s is a ---Select--- of two integers with a nonzero denominator, and so by definition of rational, r − s is rational.
Answer:
Step-by-step explanation:
Question:
Prove the following statement directly from the definitions.
The difference of any two rational numbers is a rational number.
Answer, see attachment for proof.
Which is the correct comparison symbol to make the number sentence true ( )? 6.53 _____ 6.534
Answer:
<
Step-by-step explanation:
6.53 < 6.534
Helppp need help (p.s: Zearn
(50×20) - (1×20)
Step-by-step explanation:
there is 50 twenties (20) so its 50 × 20 and 1 twenty is 20
Which number is less than 85.2 ?
086
0 85.02
O 85.8
0 85.30
Which proportion can be used to show that the slope of JL is equal to the slope of MP? (sorry for the horrible quality)
Answer:
The proportion can be used to show that the slope of JL is equal to the slope of MP is [tex]\frac{0-4}{-4-(-7)}[/tex] = [tex]\frac{-4-8}{-1-(-10)}[/tex] ⇒ G
Step-by-step explanation:
The rule of the slope of a line is [tex]m=\frac{y2-y1}{x2-x1}[/tex] , where (x1, y1) and (x2, y2) are two points on the line
∵ The coordinates of the point J are (-7, 4)
∵ The coordinates of the point L are (-4, 0)
∴ x1 = -7 and y1 = 4
∴ x2 = -4 and y2 = 0
→ Substitute them in the rule above to find the slope of LJ
∴ [tex]m_{JL}=\frac{0-4}{-4-(-7)}[/tex]
∵ The coordinates of the point M are (-10, 8)
∵ The coordinates of the point P are (-1, -4)
∴ x1 = -10 and y1 = 8
∴ x2 = -1 and y2 = -4
→ Substitute them in the rule above to find the slope of MP
∴ [tex]m_{MP}=\frac{-4-8}{-1-(-10)}[/tex]
∵ The slope of JL = the slope of MP
∴ [tex]\frac{0-4}{-4-(-7)}[/tex] = [tex]\frac{-4-8}{-1-(-10)}[/tex]
The proportion can be used to show that the slope of JL is equal to the slope of MP is [tex]\frac{0-4}{-4-(-7)}[/tex] = [tex]\frac{-4-8}{-1-(-10)}[/tex]
if a number contains decimal places then it is an irrational number
Answer:
sometimes true
Step-by-step explanation:
Administrators at Riverview High School surveyed a random sample of 100 of their seniors to see how
seniors at the school felt about the lunch offering at the school's cafeteria.
Identify the population and sample in this setting.
Choose 1 answer:
А
The population is all high school seniors in the world; the sample is all of the seniors at
Riverview High.
B
The population is all students at Riverview High; the sample is all of the seniors at Riverview
High.
The population is all seniors at Riverview High; the sample is the 100 seniors surveyed.
Answer:
C. The population is all seniors at Riverview High; the sample is the 100 seniors surveyed.
Step-by-step explanation:
The Population in statistical terms refers to the objects, people, organisms, etc that a researcher wishes to study. Usually, the population is so large that it might be difficult for the researcher to study all of them. To solve this problem, a sample is thus obtained from the population in such a way that participants have an equal chance of being chosen for the study. The result gotten from this sample can then be generalized to the entire population.
In the example provided, all the seniors at Riverview High are the population under study. The 100 seniors chosen from this population are the sample.
The population in this setting is all seniors at Riverview High and the sample is the 100 seniors surveyed.
What is a Population?
A population is the party of interest in an experiment. It is from a population the sample is derived. A population consists of all the members of the group.
What is a Sample?A sample is a smaller group of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.
To learn more about population, please check: https://brainly.com/question/12982972
To pay for a $23,600 motorcycle, Raphael made a down payment of $3300 and took out a loan for the rest .on the loan, he paid monthly payments of $364.77 for 5 years. what was the total amount Rafael ended up paying for the motorcycle including the down payment and monthly payments? how much interest did Raphael pay on the loan?
Answer:
-Total amount Rafael ended up paying for the motorcycle: $25,186.2
-Interest: $1,586.2
Step-by-step explanation:
You can find the total amount Rafael ended up paying by adding up the down payment plus the result of multiplying the monthly payment for the number of months he paid:
Total payment=3,300+(364,77*60)
Total payment=3,300+21,886.2
Total payment=25,186.2
Now, to calculate the amount of interest that Raphael paid on the loan, you should subtract the price of the motorcycle from the total amount Raphael paid:
Interest=$25,186.2-$23,600
Interest=$1,586.2
Help me with this math problem because I’m too lazy to do it thank you if you do answer
Answer:
D. 30x + 120 ≤ 250
Step-by-step explanation:
Since we know that he bought one pair of shoes for $120 you would subtract 250-120=130 though you cant divide 130 into 30 so you would use ≤ so your answer is 30x + 120 ≤ 250
x= how many shirts he buys.
There is a line that includes the point (-7, 9) and has a slope of -1/7.
What is its equation in slope intercept form?
Answer:
y=-(1)/(7)x+8
Step-by-step explanation:
answer 2 questions about equations A and B A. 5x=20 B. x=4 1.) how can we get equation B from equation A
Answer:
Multiply/divide both sides by the same non-zero constant
Step-by-step explanation:
5x = 20
Divide each side by 5
5x/5 = 20/5
x = 4
Which shows all the factors pairs of 16?
I don't understand what you are talking about, but I can list you the factor pairs of 16!
16=1,16; 2,8; 4,4
Thise are all the factor pairs
Answer:
1 x 16,
2 x 8
4 x 4
Factors of 16: 1, 2, 4, 8, 16
PLZ HELP!!!!!
how can 28/8 be a decimal?
Answer:
What is 28/8 as a decimal you ask? Converting the fraction 28/8 into a decimal is very easy.
To get 28/8 converted to decimal, you simply divide 28 by 8. Don't worry. You don't need to get the calculator out, because we did this for you.
28/8 as a decimal is:
3.5
PLEASE HELP!!! ALGEBRA! For a concert 5,000 tickets were sold, and the proceeds were $72,000. Tickets for children 16 and younger were $10, adults were $20, and seniors 60 and older were $15. There were 3 times more children than seniors at the concert. What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the concert?
Answer:
( c + a + s) = 5000
(10c + 20a + 15s) = 72000
c = 3s
Step-by-step explanation:
Number of tickets sold = 5000
Proceeds from ticket Sale = $72,000
Tickets for children 16 and younger = $10
Adults = $20
seniors 60 and older = $15
Let :
number of children, c ;
adults, a;
seniors, s,
There were 3 times more children than seniors at the concert ; c = 3s
Total number of attendees = 5000 ;
( c + a + s) = 5000
Total proceeds or revenue
(10c + 20a + 15s) = 72000
Seven subtracted from the product of three and a number is 23. What is the number?
Answer:
Step-by-step explanation:
If the number is 10 so
Product of 10 and 3 = 10 x 3 = 30
Subtracting by 7 = 30 - 7 = 23
So the number is 10
Video games made up 77.8% of the total revenue for a small specialty store.
A) 0.0778 B) 7.78 C) 77.8
D) 0.778
Timod at home while attending classes
Answer:
D
Step-by-step explanation:
This is saying 77.8% percent out of 100, therefore we right it like D
I hope this helped, please mark Brainliest, thank you!
