The ratio of athletes in the two teams is 3:2. After 12 athletes move from first team to second, the ratio is 5:4. Find the number of athletes on each team originally.
Answers:
team one = 162team two = 108=========================================================
Explanation:
The ratio 3:2 scales up to 3x:2x for some positive whole number x.
This tells us that the first team has 3x people and the second team has 2x people. We'll subtract 12 from the first team and add 12 to the second team to represent 12 people moving.
3x becomes 3x-122x becomes 2x+12The new team counts 3x-12 and 2x+12 represent team 1 and team 2. Those expressions are in the new proportion 5:4.
This means....
(team 1 new count)/(team 2 new count) = 5/4
(3x-12)/(2x+12) = 5/4
4(3x-12) = 5(2x+12)
12x-48 = 10x+60
12x-10x = 60+48
2x = 108
x = 108/2
x = 54
From this, we then can say:
team 1 original count = 3x = 3*54 = 162team 2 original count = 2x = 2*54 = 108The two subtotals add to 162+108 = 270 players overall.
If we were to subtract 12 from team 1, and add 12 to team 2, then,
team 1 new count = 162-12 = 150team 2 new count = 108+12 = 120The ratio 150:120 then reduces to 5:4 when we divide both parts by the GCF 30. This helps confirm we have the correct answer.
Answer:
162 athletes108 athletesStep-by-step explanation:
Each ratio can be expressed using two numbers that have the same sum. The sum in the first given ratio is 3+2 = 5, and in the second ratio, it is 5+4 = 9. The least common multiple of 5 and 9 is 45, so we can express both ratios so they have a sum of 45:
3 : 2 = 3(9) : 2(9) = 27 : 18
5 : 4 = 5(4) : 4(5) = 25 : 20
Here, we observe that the second ratio has numbers that look like 2 was moved from the numerator to the denominator. (27 -2 = 25; 18 +2 = 20) The problem statement tells us 12 athletes were moved, so multiplying the first ratio by 12/2 = 6 will tell us the numbers of players on each original team:
first team = 27×6 = 162 athletes
second team = 18×6 = 108 athletes
pls help worth a lot of points best answer gets brainiest
Answer:
21/16 gallons per minute
Step-by-step explanation:
HOPE YOU HAVE THE BEST WEEKENDDDD
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Answer:
Ans = 42
Step-by-step explanation:
just substitute the variables with their respective value
x² + 2y ÷ w + 3z
= 5² + 2(8) ÷ 2 + 3(3)
= 25 + 16 ÷ 2 + 9 <bear in mind, have to do multiplication/division before addition/substraction>
= 25 + 8 + 9
= 42
Find the product of 51 and -2.5.
Use the distributive property to rewrite and solve.
The first step is done for you.
51(-2.0) + 51(-0.5)
What is the next step in using the distributive property to solve this equation?
A) -102 + 25.5
B) 102 + (-25.5)
C) -102 + (-25.5)
D) -102 + (-25)
Answer:
A. -102 + 25.5.
Step-by-step explanation:
After multiplying 51 by -2.0, you will get -102. When multiplying 51 by -0.5, you get 25.5. A is the next step in this equation. (Optional answer: read this when this is also in your quiz. -102 + 25.5 = 127.5).
hope this helped.
Describe how to determine if a number is a solution to an equation.
Step-by-step explanation:
Determine whether a number is a solution to an equation.
Substitute the number for the variable in the equation.
Simplify the expressions on both sides of the equation.
Determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.
Hoped that helped:P
help me it's algebra and dont tell me to look at the lesson :)
Let b be the number of blue beads and g the number of green beads that Giovanni can use for a belt.
He's supposed to use a total of between 70 and 74 beads, so
70 ≤ b + g ≤ 74
The ratio of green beads to blue beads is g/b, and this ratio has to be between 1.4 and 1.6, so
1.4 ≤ g/b ≤ 1.6
For completeness, Giovanni must use at least one of either bead color, so it sort of goes without saying that this system must also include the conditions
b ≥ 0
g ≥ 0
(These conditions "go without saying" because they are implied by the others. g/b is a positive number, so either both b and g are positive, or they're both negative. But they must both be positive, because otherwise b + g would be negative. I would argue for including them, though.)
7 to 10
Round the decimal to the nearest hundredth, then make that a percent
PLS HELP ME!! THIS IS URGENT!!!
Answer:
no b is the correct answer
Answer:
Step-by-step explanation:
im pretty sure its b
Drag and drop the fractions to order them from least to greatest.
-3/7
-4/5
2/3
1/4
Answer:
-4/5, -3/7, 1/4, 3/2
Step-by-step explanation:
I took the test these are the right answers
1/3 + 4/6 +6/18 = ?
pls help
5th grade math
Proportional relationship between x y cabbage
Answer:
10 pounds cost $4.00
Step-by-step explanation:
how do i find x and y
Answer:
The x is the x-axis, which is a horizontal line. The y is the y-axis, which is a vertical line. The y-axis goes up or down, while the x-axis goes left or right.
hope this helped.
have a great day!
The question is attached.
A factory that manufacturers school supplies will not sell any ruler whose actual length is more than 0.05% different than it's intended length.
Determine the smallest possible length of a 12-inch ruler that would meet this qualification. inches
Answer: 11.994
Step-by-step explanation:
0.05%(0.0005) x 12 = 0.006
12 - 0.006 = 11.994 inches
I = prt
Time = 3 years
Interest Rate = 5%
Principal = $7,430
Use the information to answer the question.
How much interest is paid?
1.$111.45
2.$1,114.50
3.$11,145
4.$111,450
Help Please
Step-by-step explanation:
S.I = PRT
=$7430×(5÷100)× 3
=$1114•50
You have the cards numbered 1-10 in front of you.Each time you select a card,it is returned.What is the probability of selecting a 3 and then an even number
Answer:
[tex]Both \: the \: moon \: and \: earth \: are \: in \: \\ the \: shape \: of \: spheres. \\ Surface\: area \: of \: a \: sphere \: of \: radius \: 'r' \\ [/tex]
Let d1 be the diameter of the moon and d2 and be the diameter of the earth.Let r1 be the radius of the moon and r2 be the radius of the earth.
[tex]given \: d1 = \frac{1}{4}d2 \\ = > 2r1 = \frac{1}{4} ×2r2 \\ =>r1 = \frac{1}{4}×r2 \\ Now, \: ratio \: of \: \: their \: surface \: areas \: is: \\ = s1: s2 \\ = r {1}^{2}: r {2}^{2} \\ = {1}^{2 } : {4}^{2 } \\ =1:16[/tex]
hope it helps you
Why is it important to use the order of operations to evaluate algebraic expressions?
PLEASE HELP ME I AM ON A TEST PLEASE!!!!!!!!!!!!
the first screenshot is the top of the page
the second is the bottom of the page
Answer:
1st. Add 5 each time so 5 times 12 = 60 so
5
10
15
20
25
30
35
40
45
50
55
60
2: H = 5M
Step-by-step explanation:
Answer:
5 457
Step-by-step explanation:
he closing amount of the Dow Jones Industrial Average on the stock market for four days is shown in the table below.
Date
Closing amount (in points)
01/27
13,895.98
01/28
13,881.93
01/29
13,954.4
01/30
13,860.42
Which best represents the greatest amount of change that took place from one day to the next day over the four-day period?
a loss of 93.98 points
a loss of 72.47 points
a gain of 72.47 points
a gain of 93.98 points
Answer:
C) a gain of 72.47 points
Step-by-step explanation:
because on 1/28 it has 13,881.93 and the next day 1/29 it has 13,954.4
subtract 13,954.4 - 13,881.93= 72.47
72.47 is the greatest amount change
And it can’t be 93.98 because in the instructions it said one day to the next not 2 day’s in advance
Jean is x years old and jonathan is y years old how many years older is jean then jonathan. How old was jean 5 years ago
Answer:
x - y is the difference in the kids' ages
x - 5 represents Jean's age 5 years ago
Step-by-step explanation:
If Jean is older, write her age (x) before Jon's age (y): x - y. This is as far as we can go with the limited info you have shared.
Jean is x years old, so 5 years ago her age was x - 5.
Last week, Adriana made a batch of peanut butter ice cream from scratch. She used 2 cups of peanut butter and 6 cups of cream. It was so good that she made another batch this week. This time, she used 3 cups of peanut butter and 9 cups of cream. Which batch had a stronger peanut butter flavor?
Answer:
They are the same
Step-by-step explanation:
Both times they used the ratio of 1:3 for the peanut butter to cream, so they will taste the same.
Answer the following questions
In a city, there are 16 swimming pools. On weekends, 6 of the pools are open.
George says the ratio of pools open on weekends to the total number of pools is 6:16.
Emma says the ratio of pools open on weekends to the total number of pools is 6:11.
Which student is correct? Explain.
Answer:George
Step-by-step explanation: George is correct because Emma said that the total number of pools in the city is 11 even though it says there are 16 pools in the city, but she got the number of how many are open, George is right because it says what is the ratio of pools open on the weekends to the total amount of pools, and it says there are 6 pools open on the weekend and there are 16 pools in the city in total so he would do 6:16.
George is correct they said that the ratio of pools open on weekends to the total number of pools is 6:16.
What are ratios and proportions?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls) One-quarter are boys and three-quarters are girls.
Given that In a city, there are 16 swimming pools. On weekends, 6 of the pools are open.
George says the ratio of pools open on weekends to the total number of pools is 6:16.
Emma says the ratio of pools open on weekends to the total number of pools is 6:11.
George is right that the ratio of the open pools to the total pools will be 6:16.
To know more about ratios and proportions follow
https://brainly.com/question/2914376
#SPJ2
plz help Solve for x.
x+(−1.8)=−5.37
Answer:
-3.57
Step-by-step explanation:
PLEASE HELP I AM TIMED !
Answer:
the graph does not represent a function
simplify 7 1/3 - 5 8/9 + 8 1/2
]Show all work
Answer:
38 7/18
Step-by-step explanation:
The LCD of denominators 3, 9 and 2 is 72; all three of these divide evenly into 72. Rewriting the original problem, we get
7 24/72 - 5 64/72 + 8 36/72
Rewriting the original quantities as improper fractions, we get
22/3 - 53/9 + 17/2
Applying the LCD, we get
24(22) 8(53) 17(36) 2764
----------- - ----------- + ---------- = ------------ = 38 7/18
72 72 72 72
[tex]7\frac{1}{3}-5\frac{8}{9}+8\frac{1}{2}= \frac{22}{3}-\frac{53}{9} +\frac{17}{2} = \frac{132}{18}-\frac{106}{18}+\frac{153}{18} =\frac{132-106+153}{18} =\frac{179}{18}=9\frac{17}{18}[/tex]
ok done. Thank to me :>
Blacks car has traveled 100 miles in 1 an 1/4 hours. How many miles per hour in Blacks car traveling?
Answer:
[tex]\huge\boxed{\sf v = 80\ mph}[/tex]
Step-by-step explanation:
Given Data:
Distance = S = 100 miles
Time = t = 1 1/4 hours = 1.25 hours
Required:
Speed = v = ? mph
Formula:
v = S/t
Solution:
v = 100 / 1.25
v = 80 mph
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH180732) 48,504 ÷ 16
33) Is the sum of 15,398 + 7,292 even or odd? Why?
34) Is the product of 312,234 x 8,987 even or odd? Why?
I need all of these answers by today!!
Answer:
48,504 ÷ 16 = 3031.5
Even because the answer is 22690, which is an even number (All numbers ending in 0 are even)
Even because the answer is 2806046958, which is even (All numbers ending in 8, including 8 itself, are even)
plz help me! whats the answer? i have no idea how to do this! the second picture, or the one that shows the set percentages, is the rest of the info you need to know, plz help!
Answer:
you answer is 1,090
Step-by-step explanation:
part is ,327
of whole,x
percent,30
327over x = 30 over 100
327*100=30x
32700=30x
÷30-÷30
= 1090x
do 1090 8s the overall answer
Wich ratio is equivalent to 14:4?
A. 21:8
B. 35:15
C. 49:14
D. 7:3
Answer:
C
Step-by-step explanation:
To calculate the left side of the ratio, our calculator multiplies the right side by 14 and then divides the product by 4. To calculate the right side of the ratio, our calculator multiplies the left side by 4 and then divides the product by 14. Answers are rounded to two decimals if necessary.