Use five different colors to paint the four rectangles A, B, C and D shown in the figure. No two rectangles sharing an edge can be the same color. How many ways are there to color the rectangles?
Answer:
260 ways
Step-by-step explanation:
There are 3 scenarios.
Scenario #1, all colors used are different. A, B, C, and D each have their own individual color.
In this case, there would be 5x4x3x2=120 ways for this to happen.
(Since each color is different, after one is chosen there are only n-1 colors left, hence why it is 5x4x3x2)
Scenario #2, EITHER A&C OR B&D are the same color (Diagonal rectangles share no edges so they share a color).
In this case, there would be 2(5x4x1x3)=120 ways for this to happen. (Since we have two options, either A&C or B&D share a color, we multiply (5x4x1x3) by two to represent both options. Since the diagonal pairs must share one color, if, for example, A's color has been chosen from 5 options, C has only 1 option to choose from because it MUST match A's color)
Scenario #3, BOTH A&C AND B&D are the same color, meaning only 2 colors are used.
In this case, there would be 5x4x1x1=20 ways for this to happen.
(If A is already one color, B must choose a color from the remaining 4 options, C must match A so it has 1 option, similarily D must match B so it also has only 1 option, hence 5x4x1x1)
Now we add up all possible scenarios.
120+120+20=260 ways
A total of 60 boys and girls attended a basketball game. There were twice as many girls at the game as there were boys,
How many boys were at the game?
Answer:
let the no. of boys be x
no. of girls = 2x
According to the question,
x + 2x = 60
=> 3x = 60
=> x = 60/3
=> x = 20
Thus, there were 20 boys at the game
Answer:
boys:20 girls:40
Step-by-step explanation:
because 40 +20=60
Find m
A. 17
B. 42
C. 48
D 90
Answer:
A
Step-by-step explanation:
PLEASE HELP ME WITH THIS
Answer:
1
Step-by-step explanation:
angles on a straight line are 180 so u do 180 minus 47 gives u 133
The sum of x and 4 is greater than the difference of 2x and 3. Find x
Answer:
3 i think
Step-by-step explanation:
add 3 and 4 =7
or
multiply 2 and 3= 6 and subtract 3 = 3
Lena got three “hits” in her last seven times at bats, so her chance of getting a hit is 3/5. Theoretical or Experimental?
Answer:
HMM LOOKS LIKE A FRACTION PROBLM IM NOT SURE KIND OF TIERD RN SO UM .........3x+7=3/5 try this in calculated
Step-by-step explanation:
✌
During what month do people sleep the least? Will mark brainliest for the correct answer!!!
Answer:
February, it's the shortest month after all.
Answer: February
Step-by-step explanation: People sleep the least amount of time in February because it is the shortest month out off all the months. Your welcome :)
(18 – ab) + 4b
If a = -2 and b = -5
Answer:
-12
Step-by-step explanation:
First, substitute the variables with the numbers.
(18-(-2*-5))+4(-5)
Using the order of operations, solve in the parentheses before anything else.
(18-(-2*-5))+4(-5)
(18-(10))+4(-5)
We can now multiply 4 by -5.
(18-(10))+4(-5)
(18-10)-20
It's probably easier if we subtract 10 from 18 before subtracting 20.
(18-10)-20
8-20
-12
Hope this helps you out!! Have a wonderful day c:
Can someone please explain to me how to get this into standard form?
Answer:
12-5 is 7 standard form + 7
Step-by-step explanation:
Which set is finite?
A the set of all factors of 20
B. the set of all multiples of 20
C. the set of all integers less than 20
D. the set of all integers greater than 20
E. the set of all fractions less than 20.
=======================================================
Explanation:
Let's go through the answer choices
A) The factors of 20 are 1,2,4,5,10,20. This list does not go on forever, so this set is finite.B) The multiples of 20 are 20,40,60,80,100,... and this list does go on forever. Simply add 20 to the last value to get the next one. This set is not finite, so it is infinite.C) This set is infinite as well because there are infinitely many negative integers. Any negative number is smaller than a positive number.D) There are infinitely many integers, so there are infinitely many integers greater than 20. This set is infinite.E) It's the same idea as before. This set is infinite. There are infinitely many rational numbers smaller than 20.A boat, which moves at 12 miles per hour in water without a current, goes 45 miles upstream and 45 miles
back again in 8 hours. Find the speed of the current to the nearest tenth.
The speed of the current is
miles per hour.
Given:
Speed in still water = 12 miles per hour
Distance travel in upstream = 45 miles
Distance travel in downstream = 45 miles
Total time = 8 hours
To find:
The speed of current.
Solution:
Let the speed of current be x miles per hour.
Speed in upstream = (12-x) miles per hour
Speed in downstream = (12+x) miles per hour
We know that,
[tex]Time=\dfrac{Distance }{Speed}[/tex]
Time to cover 45 miles in upstream = [tex]\dfrac{45}{12-x}[/tex]
Time to cover 45 miles in downstream = [tex]\dfrac{45}{12+x}[/tex]
Total time is 8 hours. So,
[tex]\dfrac{45}{12-x}+\dfrac{45}{12+x}=8[/tex]
[tex]45\left (\dfrac{1}{12-x}+\dfrac{1}{12+x}\right)=8[/tex]
Taking LCM, we get
[tex]45\left (\dfrac{12+x+12-x}{12^2-x^2}\right)=8[/tex]
[tex]45\left (\dfrac{24}{144-x^2}\right)=8[/tex]
[tex]\dfrac{45\times 24}{8}=144-x^2[/tex]
On further simplification, we get
[tex]45\times 3=144-x^2[/tex]
[tex]135=144-x^2[/tex]
[tex]x^2=144-135[/tex]
[tex]x^2=9[/tex]
Taking square root on both sides.
[tex]x=\pm \sqrt{9}[/tex]
[tex]x=\pm 3[/tex]
Speed cannot be negative. So, x=3 only.
Therefore, the speed of the current is 3 miles per hour.
Rafael is making cookies by following a recipe that calls for 2.375 cups of flour, .75 cup of sugar and, 2.125 cups of chocolate chips. Rafael only wants to make 60% of the original recipe. How many cups of flour, sugar, and chocolate chips will he need in total?
CAN SOMONE PLEASE HELP ME ASAP ILL MARK BRAINLIST !!!!
I honestly don't know try 10 or 12 sorry I couldn't help you further
The length of a rectangle is five inches less than twice its width. If the
rectangle has a perimeter of 80 inches, find the length and width. *
Width 5, Length 35
Width 10, Length 30
Width 15, Length 25
O Width 20, Length 20
Answer:
10 width and 30 length.
Step-by-step explanation
multiply 30x2 which is 60 and 10x2 which is 20 and 60+20=80.
Answer:
Jasisnotcute
Step-by-step explanation:
Im telling you they really arent.
Answer is Z though.
200 g of water at 60 ° C are mixed with 300 g of water at 20 ° C. What is the temperature of the mixture?
the temperature of the mixture will be 60°
D
Question 12
(-3, 3) and (2, -7)
What is the slope of the line?
Answer:
m=-2
Step-by-step explanation:
adam spent $3.42 orange juice .orange juice cost 0.12 per ounce .how many ounces of orange juice did adam buy
Answer
I think it would be 2,850
Answer:
28.5
Step-by-step explanation:
0.12 x 28.5 = 3.42
That means he bought 28.5 ounces
Which of the following scenarios could be represented by the equation below?
1,000 + 1,200m = 1,500 + 1,175m
To rent an apartment at Cedar Ridge Apartments, Eli has to pay a security deposit of $1,000 and $1,500 a month in rent, m. To rent an apartment at Northview Apartments, Andrew has to pay a security deposit of $1,200 and $1,175 a month in rent, m. How many months will it take for Eli and Andrew to have spent the same amount on their apartment deposit and rent?
To rent an apartment at Cedar Ridge Apartments, Eli has to pay a security deposit of $1,000 and $1,500 a month in rent, m. To rent an apartment at Northview Apartments, Andrew has to pay a security deposit of $1,200 and $1,175 a month in rent, m. How many months will it take for Eli and Andrew to have spent the same amount on their apartment deposit and rent?
To rent an apartment at Cedar Ridge Apartments, Eli has to pay a security deposit of $1,000 and $1,200 a month in rent, m. To rent an apartment at Northview Apartments, Andrew has to pay a security deposit of $1,175 and $1,500 a month in rent, m. How many months will it take for Eli and Andrew to have spent the same amount on their apartment deposit and rent?
To rent an apartment at Cedar Ridge Apartments, Eli has to pay a security deposit of $1,000 and $1,200 a month in rent, m. To rent an apartment at Northview Apartments, Andrew has to pay a security deposit of $1,175 and $1,500 a month in rent, m. How many months will it take for Eli and Andrew to have spent the same amount on their apartment deposit and rent?
To rent an apartment at Cedar Ridge Apartments, Eli has to pay a security deposit of $1,200 and $1,000 a month in rent, m. To rent an apartment at Northview Apartments, Andrew has to pay a security deposit of $1,500 and $1,175 a month in rent, m. How many months will it take for Eli and Andrew to have spent the same amount on their apartment deposit and rent?
To rent an apartment at Cedar Ridge Apartments, Eli has to pay a security deposit of $1,200 and $1,000 a month in rent, m. To rent an apartment at Northview Apartments, Andrew has to pay a security deposit of $1,500 and $1,175 a month in rent, m. How many months will it take for Eli and Andrew to have spent the same amount on their apartment deposit and rent?
To rent an apartment at Cedar Ridge Apartments, Eli has to pay a security deposit of $1,000 and $1,200 a month in rent, m. To rent an apartment at Northview Apartments, Andrew has to pay a security deposit of $1,500 and $1,175 a month in rent, m. How many months will it take for Eli and Andrew to have spent the same amount on their apartment deposit and rent?
To rent an apartment at Cedar Ridge Apartments, Eli has to pay a security deposit of $1,000 and $1,200 a month in rent, m. To rent an apartment at Northview Apartments, Andrew has to pay a security deposit of $1,500 and $1,175 a month in rent, m. How many months will it take for Eli and Andrew to have spent the same amount on their apartment deposit and rent?
Had this same question on my math test.
Four classmates went bowling. Each paid $2.00 to rent shoes and bowled g games, paying $3.50 per player for each game. Which expression shows how many dollars they paid in all?
A. 4(2) + 3.5g
B. 4(3.5) + 2g
C. 4(2 +3.5)g
D. 4(2) + 4(3.5g)
Answer:
its A
Step-by-step explanation:
Answer:
The answer is D!
Step-by-step explanation:
When you answer the question you have 4 players who pay $3.5 per player each game the formula would be 4(3.5g). The you have to calculate in the money they paid to rent shoes which is 4x2 or 4(2) so when you combine the equations you get D)4(2)+4(3.5g)!!!
HOPE THIS HELPS!!
What is the 'K' (Constant of Proportionality) for a straight line that goes through the origin with a point of (3, 30).
Answer:
k = 10
Step-by-step explanation:
The constant of proportionality of a graph in Mathematics is simply the ratio of y to x which can be called the slope.
It's given by; k = y/x
We are given; y = 30 and x = 3.
Thus;
k = 30/3
k = 10
Life me kbhi sad mt hona kitne log agree hai
Please please help!!
Answer:
y +4 = 1/5(x +5)
Step-by-step explanation:
The equation of a line with slope m through point (h, k) in point-slope form is ...
y -k = m(x -h)
You have m=1/5, (h, k) = (-5, -4). Putting these values into the formula gives ...
y -(-4) = (1/5)(x -(-5))
y +4 = 1/5(x +5)
The quadratic equation given describes the area of the shaded region of each figure. Use the equation to find for the length and width of the figure
(s-2) (s+6) = 153
Answer:
Step-by-step explanation:
To find the length and width of the figure given the equation (s-2) (s+6) = 153, we will find the equivalent value of s by factoring.
(s-2) (s+6) = 153
s²+6s-2s-12 = 153
s²+4s-12-153 = 0
s²+4s-165 = 0
s²+15s-11s-165 = 0
s(s+15)-11(s+15) = 0
s+15(s-11) = 0
s+15 = 0 and s-11 = 0
s = -15 and 11
s cannot be negative
Hence s = 11
The length of the figure is s
The width is s+6
Length = 11
Width = 11+6 = 17
Hence the length of the figure is 11 and the width is 17
A(n)=7+(n-1)(11)
A(2)=
A(4)=
A(11)=
Answer:
A(2)= 18, A(4)= 40, A(11)= 117
someone helppp pleasee
Answer:
He first made the mistake when multiplying 3(5-4x)
He accidentally put 15+12 x
It should be 15-12x
The answer would then come out to be x=2
-5= 2x+3(5-4x)
-5= 2x+15-12x
-5= -10x+15 Can i get brainliest please?
-20= -10x
2= x
explain how to graph an equation in slope-intercept form.
Answer: explain how to graph an equation in slope-intercept form.
Step-by-step explanation: To graph a linear equation in slope-intercept form, we can use the information given by that form. For example, y=2x+3 tells us that the slope of the line is 2 and the y-intercept is at (0,3). This gives us one point the line goes through, and the direction we should continue from that point to draw the entire line.
NEED ASAP GIVE YOU LOTS OF POINTS
Answer:
A
Step-by-step explanation:
Trust me
Answer: the Answer is A
Step-by-step explanation: I used a graphing calculator
Can someone help me slove for d
Answer:
D=23
Step-by-step explanation:
This is a 90 degree angle
90-39=51
51-5=46
46/2=23
Ali must mix 6 tablespoons of plant food for every 2 gallons of water if she has 6 gallons of water how much plant food should she use
Gary had a 40% discount for new tires. The sale price of a tire was $96.25. What was the original price of the tire? Round to the nearest cent.
Answer:
$57.75
Step-by-step explanation:
96.25 x .40 = 38.5
96.25 - 38.5 = 57.75
The original price of the tire will be equal to $160.4.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Gary had a 40% discount for new tires. The sale price of a tire was $96.25.
Let the original price of the tire be x. Now form the equation to have the price of the tire,
x ( 0.60 ) = $96.25
x = $96.25 / 0.60
x = $160.4
Therefore, the original price of the tire will be equal to $160.4.
To know more about percentages follow
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