Using proportions, it is found that the number of books that was left over was of 505.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The number of books received by Marie is given by:
M = 772 - 345 = 427.
Melanie received one-sixth of Marie, hence:
Me = 427/6 = 71.
The total amount is 25 times Melanie's amount, hence:
T = 25 x 71 = 1775.
The amount left over is:
L = 1775 - (772 + 427 + 71) = 505
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Four graphs are shown below:
Four graphs named Graph A, Graph B ,Graph C and Graph D are shown with scale along x axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 100 at increments of 10. All the graphs have 0,12 and 1,20 and 2,28 and 3,31 and 4,42 and 5,53 and 6,61 and 7,72 and 8,88 and 9,83 and 10,92. A straight line joins 0, 12 and 6,100 in Graph A. A straight line joins 0, 12 and 10, 50 in Graph B. A straight line joins 0, 10.5 and 10, 95 in Graph C. A straight line joins 0, 30 and 8,100 in Graph D.
Which graph best shows the line of best fit?
Graph A
Graph B
Graph C
Graph D
The graph that best shows the line of best fit is graph (c)
How to determine the best graph?A graph that shows the appropriate line of best fit has the following properties:
The line of best fit has equal approximately points on either sideThe line of best fit touches as many points as possibleThe graph that satisfies the above highlights is the graph (c)
Hence, the graph that best shows the line of best fit is graph (c)
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Answer:
c
Step-by-step explanation:
New Zealand consists of hundreds of islands. Most of the population lives on the North Island, which has an area of 1.14x105 square kilometers, and the South Island, which has an area of 151,000 square kilometers.
· Which island has a greater area? How many square kilometers greater is it? Express your answer in scientific notation.
· The population of the North Island and South Island combined is about 4.8 x 106. Find the approximate population density in people per square kilometer, rounded to the nearest unit. Explain your steps
Answer:
151,000
Step-by-step explanation:
1.14×105=119.7
151,000
Q4. The diagram shows a triangle inside a rectangle.
2x
All measurements are given in centimetres.
Show that the total area, in cm², of the shaded regions is 18x - 30
3x-5
Diagram NOT
accurately drawn
The prove to show that the area of the shaded portion is 18x - 30 is as follows: 3x² + 13x - 30 - 3x² + 5x = 18x - 30
How to find the area of the shaded region?The area of the shaded region can be represented as follows:
area of the shaded region = area of rectangle - area of triangle
Therefore,
area of the rectangle = (x + 6)(3x - 5)
area of the rectangle = 3x² - 5x + 18x - 30
area of the rectangle = 3x² + 13x - 30
area of triangle = 1 / 2 × 2x × 3x - 5
area of triangle = 3x² - 5x
Therefore,
area of the shaded portion = 3x² + 13x - 30 - 3x² + 5x
area of the shaded portion = 18x - 30
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Which of the following tables represents a function?
Reason:
Choices A, C and D have repeated x values. It allows us to rule them out.
Table A has x = 6 repeating. Table C has x = 3 and x = -3 repeated. Table D has x = 4 and x = 5 show up twice each.
Whenever we have repeated x values, it indicates we do not have a function. A function is only possible when each x value goes to exactly one y value only.
Table A has the input x = 6 lead to y = 2 and y = -2 at the same time. Table C and table D are a similar story. So this is another way to rule out choices A, C and D.
Luckily table B has no repeated x values. Each x input leads to exactly one and only one y output. Therefore, table B is a function.
Side Note: the y values can repeat, but the function won't be one-to-one.
The coordinates (1, 1), (1, 3), (3, 3), and (x, y) form a square when graphed on a coordinate plane. Which ordered pair would be the fourth vertex of the square? A (3, 1) B (1,3) C (3,5) D (3, 0
)
Answer:
3,1
....................................
-7–2.1n=-3.5n PLEASE ANSWER
Answer:
n=5
Step-by-step explanation:
-7-2.1n=-3.5n
+2.1n +2.1n
-7 = -1.4n
/-1.4 /-1.4
n=5
Hope this helps!
If not, I am sorry
Answer:
b = - 1.25
Step-by-step explanation:
-7 - 2.1n = 3.5n
-7 = 3.5n + 2.1n
-7 = (3.5+2.1)n
-7 = 5.6n
-7/5.6 = n
n = -1.25
Check:
-7 -(2.1*-1.25) = 3.5*-1.25
-7 + 2.625 = -4.375
A circle has a area of 49 pie cm2 work out its radius
Area of a circle: pi x r^2
49 pi = pi x r^2
49 = r^2
r = +/- 7
---In this case, the radius is a measurement, so the answer must be positive.
r = 7
Hope this helps!
Stan wants to start an ira that will have $250,000 in it when he retires in 25 years. how much should he invest semiannually in his ira to do this if the interest is 6% compounded semiannually? assume an annuity due. round to the nearest cent. a. $2,151.82 c. $2,303.29 b. $2,216.91 d. $4,556.68
Answer:A
Step-by-step explanation:
What is the slope intercept form of the 2 points (-6,-3) and (6,-7)
1/2x-20-x = 3(2x - 1) - (2x - 1)
Answer:
x = -4
Step-by-step explanation:
1/2x - 20 - x = 6x -3 -2x +1
-1/2x -20 = 4x -2
-1/2x -4x = -2 +20
-9/2x = 18
9/2x = -18
9x = -36
x = -4
Give brainliest please!
hope this helps :)
PLEASE ASAPPP 50 POINTS
Answer:
A,B,C,J,K,M
A=B,L is parallel to K
C=J
1. Solve the equation using square roots.
x² +10=9
Answer:
x=±√−1 (NO REAL SOLUTION)Step-by-step explanation:
x² + 1 = 0
1× x²+1=0
x=±√(−1×1)
x=±√−1 (NO REAL SOLUTION)
Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions as the one shown.
8x + 7y = 39
4x – 14y = –68
Answer:
Sample Response: Using the linear combination method, you can multiply the first equation by 2 and add the equations to get 20x = 10. Dividing both sides by 20, x = 1/2. To solve for y, substitute 1/2 for x in the equation 8x + 7y = 39 to get 4 + 7y = 39. Solving this equation, y = 5. Checking this in the other equation, 4(1/2) – 14(5) = –68 results in 2 – 70 = –68 or –68 = –68. The solution of the system shown is (1/2, 5). The system 8x + 7y = 39 and 20x = 10 is formed by replacing 4x –14y = –68 by a sum of it and a multiple of 8x + 7y = 39. Since 20(1/2) = 10, the system 8x + 7y = 39 and 20x = 10 also has a solution of (1/2, 5).
Hope this was helpful..
n of the following are factors of x² - 7x - 30 ?
a
(x-3) (x - 10)
B
(x-3) (x + 10)
C
(x - 15) (x + 2)
D
(x - 10) (x + 3)
Answer:
D
Step-by-step explanation:
Solve system of equation using elimination by addition.
Will give brainliest!!
Answer:
x = 2
y = -1
Step-by-step explanation:
You can add together the equations so the x term cancels out:
-3x + 5y = -11
+ (3x + 7y = -1)
The -3x and 3x cancel out, 5y and 7y add to 12y, and -11 and -1 add to -12:
12y = -12
Divide by 12 on both sides to get
y = -1
We can substitute this value into one of the equations to solve for x:
3x + 7y = -1
3x +7(-1) = -1
3x - 7 = -1
3x = 6
x = 2
Name the types of angles shown.
L
M
Check all that apply.
A. straight angle
B. right angle
c. supplementary angles
D. complementary angles
Answer:
Ans : A. Straight angle
Step-by-step explanation:
Brainliest me pls
#KEEPSAFE
#STUDYWELL
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Brain
Can someone please help me witht his question (i will give brainliest)
Answer:
n = 3
Step-by-step explanation:
there are 80 people in choir
half are women , that is 40
quarter of number of women are men , that is 10
number of children = 80 - 40 - 10 = 80 - 50 = 30
number of children : number of men = 30 : 10 ( divide both parts by 10 )
children : men = 30 : 10 = 3 : 1 ← in simplest form
with n = 3
Answer:
30
Step-by-step explanation:
=> number of people in the choir = 80
=> number of women in the choir = half the total people = 80/2 = 40
=> number of men in the choir = one quarter of the number of women =
(1/4)*40 = 40/4 = 10
=> for the number of children,
we subtract the sum of number of men and women from the total
people = 80 - (40+10) = 80 - 50 = 30
number of children = 30
hope this helps :)
Eva wants to estimate the number of rabbits on a farm.
On Monday, she catches 50 rabbits.
These rabbits are tagged and then released.
On Tuesday, she catches 100 rabbits.
12 of these rabbits have tags on them.
Estimate the number of rabbits on the farm.
Estimate the number of rabbits on the farm will be 417 rabbits.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
Eva wants to estimate the number of rabbits on a farm.
On Monday, she catches 50 rabbits.
These rabbits are tagged and then released.
On Tuesday, she catches 100 rabbits.
12 of these rabbits have tags on them.
Then estimate the number of rabbits on the farm that will be
Let n be the number of total rabbits. Then we have
12n = 50 x 100
n = 5000 / 12
n = 416.67
n ≅ 417
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How many times longer is the wavelength of a sound wave with a frequency of 20 waves per second than the wavelength of a sound wave with a frequency of 16,000 waves per second?
The sound wave with a frequency of 20 waves/sec is 800 longer than the wavelength of a sound wave with a frequency of 16,000 waves/sec
Calculating wavelengthFrom the question, we are to determine how many times longer is the first sound wave compared to the second sound water
Using the formula,
v = fλ
∴ λ = v/f
Where v is the velocity
f is the frequency
and λ is the wavelength
For the first wave
f = 20 waves/sec
Then,
λ₁ = v/20
For the second wave
f = 16,000 waves/sec
λ₂ = v/16000
Then,
The factor by which the first sound wave is longer than the second sound wave is
λ₁/ λ₂ = (v/20) ÷( v/16000)
= (v/20) × 16000/v)
= 16000/20
= 800
Hence, the sound wave with a frequency of 20 waves/sec is 800 longer than the wavelength of a sound wave with a frequency of 16,000 waves/sec
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Can someone help me with this??
Which triangles are similar?
15
28
62
28
17
Triangle A
37
15
53
9
16
Triangle B
Triangle C
OA. Triangles B and C
OB. Triangles A and B
C. Triangles A and C
D. Triangles A, B, and C
62°
34
Answer:
triangle A andC are the same
6. What is an equation of the line that passes through the point (6,8)
and is perpendicular to a line with equation y = 3
2x + 5?
(1) y − 8 = 2(x − 6)
(3) y + 8 =
2(x + 6)
(2) y - 8 = -(x − 6)
-
(4) y + 8 =
− ½(x + 6)
Answer:
x = 6
Step-by-step explanation:
y = 3 is a horizontal line parallel to the x- axis and passing through all points with a y- coordinate of 3
A line perpendicular to this will be a vertical line parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (6, 8 ) with x- coordinate 6 , then
x = 6 ← equation of perpendicular line
Graph the equation y =3/5 x on the coordinate plane.
Step-by-step explanation:
See above graph.......
Evaluate each function.
14) g(x)= 3x² - 1; Find g(-3)
Answer:
g(-3)= 26
Step-by-step explanation:
g(x)= 3x² - 1
g(-3) means use -3 for x in the given equation.
g(-3)= 3(-3)² - 1
g(-3)= 3(9) - 1
g(-3)= 27 - 1
g(-3)= 26
An account has $26,000 after 15 years. The account received 2.3 percent interest compounded continuously. How much was deposited initially. Show all work.
The intital amount deposited was $18485.82.
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
An account has $26,000 after 15 years. The account received 2.3 percent interest compounded continuously.
A = 26000
R = 0.02.3
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
[tex]26000 = p(1 + \dfrac{2.3}{100})^{15}\\\\26000 = p \times 1.4064\\\\\P= 18485.82[/tex]
Therefore, the intital amount deposited was $18485.82.
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PLEASE HELPPPPP ME, IVE BEEN STUCK ON THIS ONE!!..
Answer:
C. 9 minutes 30 seconds
Step-by-step explanation:
well you could estimate it or just add 2.5 to 6.9 and you would get pretty close to the answer
Have a good day! :)
someone please help me to learn new things i am a 5th grade student and im hoping to learn new things in math
Answer:
Here you go!
Step-by-step explanation:
Do tell if it still seems difficult.
:)
Set A= 1, 3, 4, 5, 9, 10, 11
Set B= 2, 4, 6, 7, 11, 12
What is the union of sets A and B?
Answer:
1 ,2,3,4,5,6,7,9,10,11,12 is the union
Answer:
A U B = {1,2,3,4,5,6,7,9,10,11,12}
Step-by-step explanation:
Union of sets is a set containing all elements that are in A or B.
A = {1,3,4,5,9,10,11}
B= {2,4,6,7,11,12}
A U B = {1,2,3,4,5,6,7,9,10,11,12}
What are some examples of a linear system
Answer:
Describe the middle class of Central America. Mention jobs, homes, and education.ury
Step-by-step explanation:
20(6x4) Can you pls help me
Answer:
480
Step-by-step explanation:
We will use the order of PEMDAS. First, everything in parenthesis must be completed. Since 6x4 is in parenthesis, we multiply it and get 24.
Since we now have 20(24). We can multiply them by each other.
A trick to do this manually is to notice that 20 is 10 x 2, meaning that in reality this equation is 10 x 2 x 24. Multiply 2 x 24 = 48, and 48 x 10 = 480.