Given that 3/4 of a track team are girls and 3/4 of these girls are in 8th grade, we can multiply the two fractions to find the fraction of the whole track team that are 8th-grade girls, which is 9/16.
Explanation:The question involves two instances of finding 3/4 of a group. Initially, we are given a track team and we are told that 3/4 of the team are girls. If we let the total number of students in the team equal 1 (or 100%), then the fraction representing the girls is 3/4. Further, 3/4 of these girls are in 8th grade. Therefore, to find the fraction of 8th-grade girls out of the whole team, we multiply the two fractions together as follows: 3/4 * 3/4 = 9/16. This means that 9 out of 16 students are 8th-grade girls, assuming that the track team consists of 16 students. If the track team doesn't consist of 16 students, we can interpret the 9 out of 16 as a ratio.
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The fraction of the track team that are grade 8 girls is [tex]\(\frac{9}{16}\)[/tex].
To find the fraction of the track team that are grade 8 girls, we need to multiply the fraction of the team that are girls by the fraction of those girls who are in grade 8.
Let's denote the total number of students on the track team as [tex]\(T\)[/tex]. According to the information given:
- About[tex]\(\frac{3}{4}\)[/tex] of the students on the track team are girls. So the number of girls on the track team is [tex]\(\frac{3}{4}T\)[/tex].
- About [tex]\(\frac{3}{4}\)[/tex] of these girls are in grade 8. Therefore, the number of grade 8 girls is [tex]\(\frac{3}{4} \times \frac{3}{4}T = \frac{9}{16}T\)[/tex].
Thus, the fraction of the track team that are grade 8 girls is [tex]\(\frac{9}{16}\)[/tex]. This is found by dividing the number of grade 8 girls by the total number of students on the track team:
[tex]\[ \frac{\text{Number of grade 8 girls}}{\text{Total number of students on the track team}} = \frac{\frac{9}{16}T}{T} = \frac{9}{16} \][/tex]
Therefore, the fraction of the track team that consists of grade 8 girls is[tex]\(\frac{9}{16}\)[/tex].
1/20=0.05. Which calculation is NOT a way to find 14/20?
a. 0.5+0.05
b. 0.75−0.05
c. 14÷20
d. 14·0.05
The calculation that is NOT a relevant way to find the value of 14/20 is given by option a: 0.5 + 0.05.
Let's find the value of 14/20 first:
To find 14/20, divide 14 by 20:
14 ÷ 20 = 0.7
Now, let's check each calculation:
a. 0.5 + 0.05 = 0.55 (Not relevant to finding 14/20)
b. 0.75 - 0.05 = 0.7 (Relevant, as this gives us 14/20)
c. 14 ÷ 20 = 0.7 (Relevant, as this is the correct calculation for 14/20)
d. 14 × 0.05 = 0.7 (Relevant to finding 14/20)
Therefore, the calculation that is NOT a way to find 14/20 is option a: 0.5 + 0.05.
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Aiko is finding the sum (4 + 5i) + (–3 + 7i). She rewrites the sum as (–3 + 7)i + (4 + 5)i. Which statement explains the mathematical property that she made an error using?
Answer:
Given the expression: [tex](4+5i)+(-3+7i)[/tex]
Aiko rewrites the equation by factoring out the [tex]i[/tex] from the expression and this wrote it as,
[tex](-3+7)i+(4+5)i[/tex]
but this is wrong because [tex]i[/tex] is an imaginary number which is with a number 5 and 7.
Therefore, Aiko cannot factor out the [tex]i[/tex] because it is not present in both numbers -3 and 4
She could rewrote it as
[tex](4-3)+i(5+7)[/tex]
So, she incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
Add. Simplify the answer to lowest terms before entering the numerator and denominator in their boxes. 11/16 + 3/16
Answer:
The answer is 7/8.
Step-by-step explanation:
If you add 11/16 to 3/16, you'll get 14/16. 14/16 has two numbers that are divisible by 2, so when you divide 14/16 by 2 you'll get 7/8 which is 14/16 in a simplified form. 7 is prime and you can't divide it down any more, but 8 i'snt the same way. The rule is, whatever you do to one side, you have to do to the other. You can divide 8, but not 7; therefore, you cannot simplify the fraction any further.
To add fractions with the same denominator, simply add the numerators together, while keeping the denominator the same.
Explanation:To add fractions with the same denominator, simply add the numerators together, while keeping the denominator the same. In this case, we have 11/16 + 3/16. The denominators are already the same, so we can add the numerators: 11 + 3 = 14. The fraction 14/16 cannot be simplified further.
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A marble is drawn at random from the bag shown below. The bag contains 3 green, 4 yellow, 5 blue, and 8 pink marbles.What is P(not pink)?
Answer: [tex]\dfrac{3}{5}[/tex]
Step-by-step explanation:
Given : The number of pink marbles in bag= 8
Total number of marbles in bag= [tex]4+5+8+3=20[/tex]
Now, the number of marbles that are not pink =[tex]20-8=12[/tex]
We know that the formula to find the probability is :-
[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Similarly, [tex]\text{P(not pink)}=\dfrac{12}{20}=\dfrac{3}{5}[/tex]
does the point given below occur on the line shown. Can you show the work please
$14.30 watch ; 6 3/4% sales tax
Find the average rate of change of a function that contains the points (-2,3) and (2,5).
A. -2
B. 1/2
C. -1/2
D. 2
Three hikers equally shared gallon of water. Explain how you would use an area model to find the amount of water each hiker drank.
Answer:
Draw a square and shade half of it. Then draw 2 lines to divide the square into 3 equal parts. There will be one shaded piece in each group, and there are 6 pieces total, so the answer is 1
6
of a gallon.
Step-by-step explanation:
You have 4 dimes, 5 quarters, and 3 pennies in your pocket. What is the probability of reaching in and randomly picking out a dime or a quarter? Express your answer as a fraction in lowest terms.
The probability of picking a dime or a quarter is 3/4
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, you have 4 dimes, 5 quarters, and 3 pennies in your pocket.
There are a total of 4 + 5 + 3 = 12 coins in your pocket.
The probability of picking a dime or a quarter can be calculated as the sum of the probability of picking a dime and the probability of picking a quarter. Since the coins are selected randomly, each coin has an equal chance of being picked.
The probability of picking a dime is 4/12 or 1/3, since there are 4 dimes in the pocket out of a total of 12 coins.
The probability of picking a quarter is 5/12, since there are 5 quarters in the pocket out of a total of 12 coins.
Therefore, the probability of picking a dime or a quarter is:
P(dime or quarter) = P(dime) + P(quarter)
P(dime or quarter) = 4/12 + 5/12
P(dime or quarter) = 9/12
P(dime or quarter) = 3/4
So the probability of picking a dime or a quarter is 3/4, or three-fourths.
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With a speed of 55 mph, a driver drives through a tunnel in 1 minute. How long would it take him to get through the same tunnel with a speed of 45 mph?
You borrowed $25 from your mom to buy close a week later you repaid her $13 write an expression to show how much money you owe
During a day a student spends 7 hours sleeping, ¹/4 of the day studying and of the time travelling. What fraction of the day is left for other things?
Answer:
[tex]\dfrac{5}{24}[/tex]
Step-by-step explanation:
Time Spent Sleeping=7 hoursTime Spent Studying=[tex]\frac{1}{4}[/tex] of the dayTime Spent Travelling=[tex]\frac{1}{4}[/tex] of the dayThere are 24 hours in a day, therefore:
Time Spent Studying=[tex]\frac{1}{4}[/tex] X 24 =6 HoursTime Spent Travelling=[tex]\frac{1}{4}[/tex] X 24 =6 HoursThe total hour used for sleeping, studying and travelling=7+6+6=19 hours
Hours used for other things=24-19=5 hours
Therefore, the fraction of the day used for other things=[tex]\dfrac{5}{24}[/tex]
n the figure, 2004-02-04-06-00_files/i0250000.jpg. If the ratio of the perimeter of to that of is 3:2 and the sum of the perimeters of the two triangles is 110, find the perimeter of each triangle.
A.
perimeter of = 66
perimeter of = 44
B.
perimeter of = 73
perimeter of = 37
C.
perimeter of = 37
perimeter of = 73
D.
perimeter of = 44
perimeter of = 66
Answer:
Perimeter of triangle 1 = p1 = 66
Perimeter of triangle 2 = p2 = 44
the quotient of a and c is 8. The product of a and c is 2. The quotient of a and b is -16. The product of a and b is -1. The quotient of b and c is -0.5. What is value of a,b, and c?
To find the values of a, b, and c, we can use the given information and solve the system of equations.
Explanation:To find the values of a, b, and c, we can use the given information and solve the system of equations.
From the first two statements, we have a/c = 8 and a*c = 2. This allows us to solve for a and c.
Similarly, from the next two statements, we have a/b = -16 and a*b = -1. Using these equations, we can find the values of a and b.
Finally, the last statement gives us b/c = -0.5, and we can use this equation to find the value of c.
Substituting the appropriate values for a, b, and c, we find that a = 1, b = 0.0211, and c = -0.0211.
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Me.ford drove 483 miles during his trip. How many hundreds are in this number
How do you fact prime numbers
Final answer:
Factoring prime numbers is not applicable as they are already in their simplest form. In calculations involving exponents with prime numbers, exponent rules can be used to simplify or alter the expression. Understanding these rules empowers you to verify the results and improve your mental math skills.
Explanation:
Prime numbers are the building blocks of the number system, but interestingly, they cannot be factored further since they have only two distinct divisors: one and themselves. Therefore, the concept of factoring prime numbers doesn't apply because they are already in their simplest form. However, when you work with exponents and prime bases, such as in 24 × 10¹², you can manipulate the expression by using exponent rules to simplify or alter its form.
Exponents represent how many instances a base number is multiplied by itself. For example, 10³ equals 10 × 10 × 10, which is 1,000. Similarly, when you see an operation like (53)4, you can multiply the exponents (3 × 4) to understand this as 512, which is 5 multiplied by itself 12 times.
Mastering these concepts avoids confusion and allows for mathematical operations to be performed more readily in your head. Calculators handle these numbers with ease, but understanding the rules lets you confirm the accuracy of your work and can help in developing a life-long skill.
I need to know what does untethers mean
What is 1920 divided by 12
what is 29.5 multiplied 2.6
Fourteen of the kids in a class are girls. Eight of the kids wear blue shirts. Two of the kids are neither girls nor wear a blue shirt. If five of the kids are girls who wear blue shirts, how many kids are there in the class?
zack made this table for his survey? grape 16, orange 10, berry 9, apple 12 how many votes were cast?
neil has 3 partially full cans of white paint. They contain 1/3 gallion, 1/5 gallion, and 1/2 gallion of paint. about how much paint does neil have in all
Neil has approximately [tex]\( 1 \frac{1}{30} \)[/tex] gallons of white paint in total.
Let's calculate the total amount of paint step by step:
1. Convert fractions to a common denominator:
[tex]- \( \frac{1}{3} \) gallon = \( \frac{10}{30} \) gallons[/tex]
[tex]- \( \frac{1}{5} \) gallon = \( \frac{6}{30} \) gallons[/tex]
[tex]- \( \frac{1}{2} \) gallon = \( \frac{15}{30} \) gallons[/tex]
2. Add the amounts of paint in the cans:
[tex]\( \frac{10}{30} + \frac{6}{30} + \frac{15}{30} = \frac{31}{30} \) gallons[/tex]
3. Simplify the fraction:
[tex]\( \frac{31}{30} = 1 \frac{1}{30} \) gallons[/tex]
Thus, Neil has approximately [tex]\( 1 \frac{1}{30} \)[/tex] gallons of white paint in total.
To find out how much paint Neil has in total, we first converted the fractions to a common denominator of 30 to make them easier to add. This gave us [tex]\( \frac{10}{30} \) gallons, \( \frac{6}{30} \)[/tex] gallons, and [tex]\( \frac{15}{30} \)[/tex] gallons for the three cans, respectively. Adding these fractions together gives[tex]\( \frac{31}{30} \)[/tex] gallons. To simplify, we divide 31 by 30, resulting in[tex]\( 1 \frac{1}{30} \)[/tex] gallons. Thus, Neil has approximately [tex]\( 1 \frac{1}{30} \)[/tex] gallons of white paint in total.
complete question
neil has 3 partially full cans of white paint. They contain 1/3 gallion, 1/5 gallion, and 1/2 gallion of paint. about how much paint does neil have in all
Idk what the properties are I need help
solve the equation 20x-5y=10 for y
Plot the line for the equation on the graph. y−4=−14(x−5)
Answer:
Hopefully this helps other people! :) I got it right on the test!
find −3(2.5−k)+0.5(7+8k)
The total charge on 7 particles is −42 units. All the particles have the same charge.
What is the charge on each particle? (1 point)
6 units
5 units
−5 units
−6 units
Your answer would be -6! -42= -6 divided by 7 or 7 X -6= -42
Find the ending balance: Principal: $600
Interest Rate:5%
Time: 6 Years
What's 140,250 rounded to the nearest 100,000
Sofia wants to place a sticker 2 ½ inches long in the center of a switch box that is 3 ¾ inches wide. About how far from the edge will she place the sticker?