The surface inside the circles will be painted green. The surface outside the circles will be painted white. What is the ratio of green paint to white paint?
A. π : (4 - π)
B. (4 - π) : π
C. π : (π - 4)
D. π^2 : (4 - π^2)
Answers
Answer:
The ratio of green paint to white paint is A. [tex]\pi:(4-\pi)[/tex]
Step-by-step explanation:
To find the ratio of green paint to white paint we need to divide the surface that will be painted green by the surface that will be painted white.
In the graph we can see 4 equal circles. Let be ''R'' the radius of the circles.
We can also see a square. The side of the square is 4R (because the length of the side is 4 times the radius of any circle).
The surface of a circle which radius is ''R'' is equal to :
[tex]\pi .R^{2}[/tex]
The surface inside this 4 circles is equal to :
[tex]4.\pi .R^{2}[/tex]
The surface [tex]4.\pi .R^{2}[/tex] will be painted green.
The surface outside the circles is equal to [tex]4.\pi .R^{2}[/tex] subtracted to the area of the square.
The area of the square is :
[tex](4R)^{2}=16R^{2}[/tex] ⇒
[tex]16R^{2}-4.\pi.R^{2}[/tex] is the surface that will be painted white.
If we make the division between the surfaces :
[tex]\frac{GreenSurface}{WhiteSurface}[/tex] ⇒
[tex]\frac{4.\pi .R^{2}}{16R^{2}-4.\pi .R^{2}}[/tex]
[tex]\frac{(4R^{2}).\pi}{(4R^{2}).(4-\pi)}=\frac{\pi}{4-\pi}[/tex]
We find that the ratio of green paint to white paint is [tex]\pi:(4-\pi)[/tex]
Related Questions
Which property is used in the problem below?
2(x+4)=2x+8
the associative property
the commutative property
the distributive property
the additive identity property
Answers
the answer is The distributive property hoped I helped
The perimeter of a rectangle is 68cm the length is 4cm less than three time its width write a system of equation to find the dimension of the rectangle
Answers
A wise man once said, "500 reduced by 3 times my age is 200." What is his age?
Answers
_________________________________________________________
Explanation:
_________________________________________________________
Let "x" represent the numerical value of [the man's age].
500 - 3x = 200 ; Solve for "x" ;
Subtract "500" from each side of the equation:
500 - 3x - 500 = 200 - 500 ;
to get:
- 3x = -300 ;
Now, divide each side of the equation by "-3" ; to isolate "x" on one side of the equation; & to solve for "x" ;
- 3x / -3 = -300 / -3 ;
x = 100 .
_______________________________________________________
The answer is: " 100 " .
_______________________________________________________
What is the second term in the binomial expansion of (2r – 3s)12? –73,728r11s 73,728r11s 608,256r10s2 –608,256r10s2?
Answers
Solution:
A is the correct option.
Explanation:
We have been given that [tex](2r - 3s)^{12}[/tex]
The [tex]r^{th}[/tex] term of a binomial expansion [tex](a+b)^n[/tex] is given by
[tex]t_r=^{n}C_{r-1}a^{n-r+1}b^{r-1}[/tex]
For the given binomial expansion, we have
[tex]a=2r,b=-3s,r=2,n=12[/tex]
On plugging this value in the above formula, we have
[tex]t_2=^{12}C_{2-1}(2r)^{12-2+1}(-3s)^{2-1}\\\\t_2=^{12}C_1 (2r)^{11}(-3s)^{1}\\\\t_2=\frac{12!}{1!11!}(2)^{11}r^{11}(-3)s\\\\t_2=12\cdot (2)^{11}(-3)r^{11}s\\\\t_2=-73728r^{11}s[/tex]
Therefore, the second term is -73728r^11 s
A is the correct option.
Bruno is designing his next skateboard. the skateboard store has 333 types of grip tape, 131313 types of decks, 777 types of trucks, 4 types of bearings, and 2 types of wheels. how many different skateboards can bruno create
Answers
Answer:
2184 is what i got.
Step-by-step explanation:
The volume of a cylinder is 1323pi cmcubed. The radius of the base of the cylinder is 7 cm. What is the height of the cylinder? The height of the cylinder is nothing cm. (Simplify your answer.)
Answers
h=V /(πr²)
h=27/π -exact value
h=1323/(3.14*(7)²)= 8.6 cm - approximate value
The height of the cylinder with a given volume of 1323
cmcubed and a radius of 7 cm, divide the volume by the area of the base. The correct height is 27 cm.
The height of a cylinder given its volume and the radius of its base. To find the height, we'll use the formula for the volume of a cylinder, which is V = ()h, where V is the volume, is the radius and h is the height.
Step-by-step calculation:
The volume of the cylinder is given as 1323cmcubed.
The radius (r) of the base of the cylinder is given as 7 cm.
Plugging these values into the formula: 1323cm³= (7 cm)² imes h.
Simplify the equation: 1323cm³ = 49cm² imes h.
Divide both sides by 49cm² to find the height: h = 1323cm³ / 49cm².
The resulting height is therefore 27 cm, which is the solution to the problem.
The height of the cylinder is 27 cm.
triangle ABC is similar to Triangle XYZ. AB=5x+25, BC=7x+44, YZ=29, XZ=45, XY=14 Find x
Answers
============================================================
Explanation:
Triangle ABC is similar to Triangle XYZ. This means that
AB/BC = XY/YZ
is one proportion we can form
Plug in the given expressions and then isolate x
AB/BC = XY/YZ
(5x+25)/(7x+44) = 14/29
29(5x+25) = 14(7x+44)
29(5x)+29(25) = 14(7x)+14(44)
145x+725 = 98x+616
145x-98x = 616-725
47x = -109
x = -109/47
note: its possible your teacher made a typo since we got a negative fraction here. I would ask your teacher to double check.
How much greater is the median number of pairs of shoes in the inventory at the Golf pro Shop than the median number of pairs of shoes in the inventory at the Tennis Pro Shop?
Answers
To get this answer, you find the median of the golf pro shop data (a = 40) and the median of the tennis pro shop data (b = 20). Then you subtract to get a-b = 40-20 = 20. The median of any box plot is the vertical line inside the box plot.
Answer:
20
Step-by-step explanation:
If a population has a birth rate of 40 individuals per 1,000 per year and a death rate of 30 individuals per 1,000 per year, how will the population change each year
Answers
Video games are on sale for 35% off if a particular game regularly sells for $99.50 what is the sales price
Answers
To find the sales price, multiply $99.50 by 35% to get the discount amount of $34.83, then subtract that from the original price, resulting in a sales price of $64.67.
Explanation:To calculate the sales price of a video game that has a discount of 35%, first determine the amount of the discount by multiplying the original price by the percentage of the discount. The original price of the video game is $99.50. Therefore, you calculate $99.50 × 0.35 to find the discount amount.
The discount amount is $34.825. Next, subtract the discount amount from the original price to find the sales price: $99.50 - $34.825 equals the sales price.
It's also important to round the discount to the nearest cent as currency, resulting in a discount of $34.83. Thus, the sale price of the video game will be $99.50 - $34.83, which equals $64.67.
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Michael, a freelance editor, charges the rates shown in the table below to edit manuscripts. The cost per page increases as the quality of editing improves. Michael also gives a 5% discount if the entire amount is paid up front. A 2 column table with Type of Editing and Cost per page as the column headings. Express Proofreading costs 2.20 dollars, Basic Proofreading 2.80 dollars, Extended Proofreading 3.90 dollars, and Deep Editing 12 dollars Maria has a 25-page manuscript. The equation below shows the relationship between the total cost of editing 25 pages, T, and the cost per page, c, if she gets the 5% discount: 25c − 0.05(25c) = T Using the equation, what is the best quality of editing that Maria can get done for a maximum of $66.50?
Answers
25c -.05(25c) = 66.50
0.95*25*c = 66.50
c = 66.50/(0.95*25) = 2.80
The best quality of editing that Maria can afford is ...
Basic Proofreading
Consumer reports stated that the sodium content, in milligrams, for a two tablespoon serving for 10 different brands is as follows: 120, 50, 120, 140, 150, 150, 110, 249, 171, 60 What is the mean of the data set? Type a numerical answer in the box. a0
Answers
1320/10 = 132
The mean is 132.
HELP ASAP PLEASE!1!! Determine the factors of a2b + 2a2 + 3b + 6. (b + 3)(a2 + 2) (b + 2)(a2 + 3) (ab + 2)(a + 3) (ab + 3)(a + 2)
Answers
Hope this helps!
Answer:
B. (b + 2)(a2 + 3)
Step-by-step explanation:
Broderick answered 21 of the 25 questions on his history test correctly. What decimal represents the fraction of problems he answered incorrectly?
Answers
84 hundredths
Which number is irrational A)25.23 B) 8 C)square root of 48
Answers
Reason:
=> √48 = √(2×2×2×2×3) = 4√3
As, we know√3 is irrational therefore √48 is also irrational no.
Hope this helps!
Short answer: C.
Why?
When a number is irrational, that means it goes on forever. It can't be A, because we know the end is .23. It can't be B because that is just a whole number. The only one that would make sense is answer choice C. √48.
Hope this helped you! ♥
Which box plot represents the data?
30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40
Answers
The box plot representing the data set 5, 5, 10, 15, 25, 25, 30, 35, 40, 40, 45, 50 will have the values at 5 (minimum), 12.5 (Q1 - 25th percentile), 25 (median), 37.5 (Q3 - 75th percentile), and 50 (maximum). The data is arranged in ascending order, divided into quartiles, and the median of each quartile is found.
Explanation:To determine which box plot represents the data, we need to obtain the five-number summary of the data which includes the minimum, Q1 (25th percentile), median (Q2 - 50th percentile), Q3 (75th percentile), and the maximum.
Arrange the data in ascending order: 5, 5, 10, 15, 25, 25, 30, 35, 40, 40, 45, 50Determine the minimum and maximum: Minimum is 5, Maximum is 50 Find the median (Q2): With 12 numbers, the median is the average of the 6th and 7th value, so (25+25)/2 = 25 Q1 is the median of the lower half of data (not including Q2): The median of 5, 5, 10, 15, 25, 25 is (10+15)/2 = 12.5 Q3 is the median of the upper half of data (not including Q2): The median of 30, 35, 40, 40, 45, 50 is (35+40)/2 = 37.5Therefore, the box plot that represents this data will have values at 5 (minimum), 12.5 (Q1), 25 (median), 37.5 (Q3), and 50 (maximum).
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Will constructed a figure on a graph using coordinates: M(2,3),N (8,3),AND
(5,2)
How long is the line segment M N in Will's graph?
Answers
convert the following complex number into its polar representation 2+2i
Answers
2+2i
simplifying the above we get
2(1+i)
dividing through above through by √2
=2*√2(1/√2+i/√2)
but
1/√2=cos (π/4)=sin (π/4)
thus our expression will be:
=2√2(cos (π/4)+isin (π/4))
Answer:
[tex]z=2\sqrt{2}(cos{\frac{\pi}{4}}+isin{\frac{\pi}{4}})[/tex]
Step-by-step explanation:
The given complex number is:
[tex]2+2i[/tex]
Now, the polar from of the complex number [tex]z=a+ib[/tex] is [tex]z=r(cos{\theta}+isin{\theta})[/tex].
Finding the absolute value of r:
[tex]r=|z|={\sqrt{2^2+2^2}[/tex]
[tex]r=\sqrt8[/tex]
[tex]r=2\sqrt{2}[/tex]
Now, find the value of argument,
Using formula, [tex]{\theta}=tan^{-1}(\frac{b}{a})[/tex]
[tex]{\theta}=tan^{-1}({\frac{2}{2})[/tex]
[tex]{\theta}=tan^{-1}(1)[/tex]
[tex]{\theta}={\frac{\pi}{4}}[/tex]
Thus, the polar form is:
[tex]z=2\sqrt{2}(cos{\frac{\pi}{4}}+isin{\frac{\pi}{4}})[/tex]
which is the required polar form.
i need help so bad asap
Answers
Substitute x=2 and y=2
2•2+3=3•2+1 ✔️
Substitute x=4 and y=4
11=13 ❌
Substitute x=3 and y= 3
9=10 ❌
Substitute x=5 and y= 5
13=16 ❌
If there is a very strong correlation between two variables, then the coefficient of correlation must be
Answers
Final answer:
If there is a very strong correlation between two variables, then the coefficient of correlation must be close to 1 or -1.
Explanation:
The correlation coefficient measures the strength and direction of the relationship between two variables. If there is a very strong correlation between two variables, then the coefficient of correlation must be close to 1 or -1. A correlation coefficient of 1 indicates a perfect positive correlation, meaning the variables increase and decrease together.
A correlation coefficient of -1 indicates a perfect negative correlation, where one variable increases while the other decreases.
There are 7 performers who are to present their acts at a variety show. One of them insists on being the first act of the evening. If this request is granted, how many different ways are there to schedule the appearances?
Answers
for the second, 6 choices
third, 5
fourth,4.....
You have to multiple them together :
1*6*5*4*3*2*1=720ways
there are 720 ways to schedule this show
Since one of the seven performers insists on being the first act, the remaining six performers can be arranged in '6!' (factorial of 6) ways. Therefore, there are 720 different ways to schedule the appearances of the variety show.
Explanation:This problem is a permutation problem. Since one performer insists on being the first act of the evening, this leaves 6 other acts that can be arranged in any order. In permutation, if you have 'n' different items, they can be arranged in 'n!' (n factorial) ways. The factorial of a number n, denoted as 'n!', is the product of all positive integers less than or equal to n.
In this case, 6 performers can be arranged in '6!' ways. The factorial of 6 (6!) is 6 * 5 * 4 * 3 * 2 * 1 = 720. Therefore, there are 720 different ways to schedule the appearances of the remaining 6 acts after the first performer has gone on.
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Which of the following equations could be used to solve the given equation?
9x + 26 + 7x - 17 = 2x + (-3x) + 5x
16x + 9 = 0
16x + 9 = 4x
16x + 11 = 4x
Answers
16x + 9 = 4x
Its B
Answer: The correct option is (B) [tex]16x+9=4x.[/tex]
Step-by-step explanation: We are given to select the correct equation that could be used to solve the following equation :
[tex]9x+26+7x-17=2x+(-3x)+5x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the correct equation, we need to simplify the given equation (i).
From equation (i), we get
[tex]9x+26+7x-17=2x+(-3x)+5x\\\\\Rightarrow (9+7)x+(26-17)=2x-3x+5x\\\\\Rightarrow 16x+9=(2-3+5)x\\\\\Rightarrow 16x+9=4x.[/tex]
Thus, the required equation is [tex]16x+9=4x.[/tex]
Option (B) is CORRECT.
Need help on this as soon as possible!
Answers
Area of the base of the prism: Ab=Area of the equilateral triangle
Height of the prism: h=6
Ab=A triangle= sqrt(3)/4*s^2
Ab=sqrt(3)/4*3^2
Ab=sqrt(3)/4*9
Ab=9 sqrt(3)/4
V=Ab*h
V=[9 sqrt(3)/4](6)
V=54 sqrt(3) /4
V=27 sqrt(3) / 2
V=27/2 sqrt(3)
Danielle ran 3 1/8 miles on Tuesday and 4 and 1/2 miles on Wednesday and 5 1/4 miles on Thursday how far did Danielle run all together this
Answers
3 1/8
4 1/2
5 1/4
the common denominator would be 8. so multiply all the fractions by the number that would give you 8 on the bottom of the fraction
1/8 x 1 = 1/8
1/2 x 4 = 4/8
1/4 x 2 = 2/8
now you would set up your problem
3 1/8 + 4 4/8 + 5 2/8
first add the fractions
1/8 + 4/8 + 2/8 = 7/8
then add the whole numbers
3 + 4 + 5 = 12
now put the number and fractions together and you have your answer
12 and 7/8
2/3 (a-b) =c, solve for a
Answers
Find 2 positive real numbers that differ by 1 and have a product of 1
Answers
B) x * y =1
B) y = 1/x
A) x -(1/x) = 1
Multiplying both sides by "x"
A) x^2 -1 = x
A) x^2 -x -1 = 0
Solving by the quadratic formula
x = 1.618 and
y = .618
Interestingly, the number 1.6180339... is called the "phi ratio" or the "golden ratio".
https://en.wikipedia.org/wiki/Golden_ratio
Factor the trinomial below.
x2 – 14x + 45
A. (x – 3)(x + 15)
B. (x – 5)(x + 9)
C. (x – 5)(x – 9)
D. (x – 3)(x – 15)
Answers
The answer is C.
[tex] {x}^{2} - 14x + 45 = (x - 9)(x - 5)[/tex]
To find our answer we are looking for 2 integers. The sum of the integers must be -14 (since it must be equal to the number before the variable x). The product of both integers must be 45. Now we can conclude we are looking for the numbers -9 and -5.
[tex] - 9 + - 5 = - 9 - 5 = - 14 \\ - 9 \times - 5 = 45[/tex]
(Remember that multiplying 2 negatives makes you end up with a positive.)
~ Hope this helps you!
Predict the vital capacity of a 20-year-old 5'5" female who weighs 120 pounds using the equation below: vc = (0.041) h - (0.018) a - 2.69
Answers
The predicted vital capacity of a 20-year-old, 5'5" female, using the provided equation, is approximately 3.97 liters.
Explanation:To predict the vital capacity of this 20-year-old 5'5" female who weighs 120 pounds using the given equation, we first need to convert the height from feet to centimeters since standard medical measurements are usually in metric units. The conversion is 1 foot = 30.48 cm. Therefore, 5'5" = 5*30.48 cm + 5*2.54 cm = 165.1 cm. Now we can substitute the height (h) and age (a) into the equation: vc = (0.041) h - (0.018) a - 2.69 = (0.041*165.1) - (0.018*20) - 2.69 ≈ 3.97 Liters. Therefore, the predicted vital capacity of this 20-year-old 5'5" female is approximately 3.97 liters.
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help a brother out lol
Answers
[tex]( \frac{g}{f} )(x)= \frac{x^2-6}{3x+1} [/tex]
Since the denoinatorcan't be zero:
[tex]3x+1 \neq 0[/tex]
[tex]x \neq - \frac{1}{3} [/tex]
We can conclude that the correct answer is A. [tex]\frac{x^2-6}{3x+1} [/tex] [tex]x \neq - \frac{1}{3}[/tex]
Coach miller bought 5.15 pounds of ground beef to make burgers The cost of ground beef is $3.40 for each pound.What was the total cost for all of the ground beef?
Answers
The total cost of the ground beef bought by Coach Miller is calculated by multiplying the quantity (5.15 pounds) by the price per pound ($3.40). The total cost comes to $17.51.
Explanation:The subject of the question is a practical application of multiplication in Mathematics. Coach Miller bought 5.15 pounds of ground beef at a rate of $3.40 per pound. To calculate the total cost, you simply need to multiply the quantity (5.15 lbs) by the price per unit ($3.40/lb).
So the calculation will be: 5.15 (pounds) × $3.40 (cost per pound) = $17.51 So, the total cost for all of the ground beef would be $17.51.
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