The fractions 9/6 and 21/14 are proportional because both simplify to the same value, which is 1.5. Cross-multiplication also confirms their proportionality as the cross products are equal.
Explanation:To determine if the fractions 9/6 and 21/14 are proportional, we can simplify each fraction or cross-multiply to see if we end up with an equivalent value. If two ratios are proportional, this means they are equivalent to each other when reduced to simplest form, or the cross products are equal.
Simplifying 9/6, we get 1.5, and simplifying 21/14, we also get 1.5. Since both simplified fractions result in the same value, 9/6 and 21/14 are indeed proportional.
We can also cross multiply to verify: (9×14) should be equal to (6×21). This results in 126 = 126, confirming that both ratios are indeed proportional.
Final answer:
The ratios 9/6 and 21/14 are proportional because both simplify to the same ratio 3/2, and cross-multiplication yields equal products, confirming proportionality.
Explanation:
To determine if the ratios 9/6 and 21/14 are proportional, we simplify each ratio. The ratio 9/6 simplifies to 3/2 and the ratio 21/14 simplifies to 3/2 as well. Since both simplified ratios are equal, we can confirm that 9/6 and 21/14 are indeed proportional ratios.
Another way to check for proportionality is to cross-multiply and see if the products are equal. Multiplying 9 times 14 and 6 times 21 gives us 126 in both cases, which reaffirms our conclusion. Thus, based on these methods, the given ratios are proportional.
What is 4.8 times 3.7
Which property should be used next in this solution process?
3x+2+3=7(x−1)−4
3x+5=7(x−1)−4
The solution of d + s > -3 is d > -7. What is the value of s?
Curtis is packing to move. He finds 23 photo albums in the attic and 45 albums in a closet. If he divides them equally among 4 boxes, how many albums will he put in each box?
Answer:
68 divide by 4
Step-by-step explanation:
Dipping your spoon into the bowl 4 times, what is the probability that you randomly select at least 1 heart
Probability randomly select at least 1 heart is 5 / 14
Probability based questions:Given question is incomplete, complete question is as follows;
Number of hearts = 5
Number of clover = 3
Number of stars = 4
Number of moons = 2
Find:
Probability randomly select at least 1 heart
Computation:
Total item = 5 + 3 + 4 + 2
Total item = 14
Probability randomly select at least 1 heart = 5 / 14
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The distance a car travels on a flat highway is directly proportional to the quantity of gas consumed.
A Lexus travels miles on gallons of gas.
What is the constant of proportionality, and what are it units
The distance a car travels is directly proportional to the quantity of gas consumed. To find the constant of proportionality, set up a proportion using the given values. The units for the constant of proportionality will be miles per gallon.
Explanation:In this problem, we are given that the distance a car travels, in miles, is directly proportional to the quantity of gas consumed, in gallons. We are also given that a Lexus travels x miles on y gallons of gas. To find the constant of proportionality, we can set up a proportion using the given values:
x/y = miles/gallons
Using this proportion, we can solve for x and y. The constant of proportionality, which represents the distance a car travels per gallon of gas, will be the value of x when y = 1. The units for the constant of proportionality will be miles per gallon.
21k – 3n + 9p > 3p + 12
6 friends share 3 small pies equally
Each friend will get 1/2 of a pie when it is divided into equal.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that, 6 friends share 3 small pies equally.
Total number of pies = 3
Total number of friends = 6
Since, the number of pie is less than number of friends, no one will get 1 pie each.
Divide 3 pies in to 6 equal parts.
Each friend will get 3/6 pies.
After simplifying, each friend will get 1/2 pie.
That is, each will get half of a pie.
Hence each of the friend will get one half of a pie.
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Your question is incomplete. Probably, the correct question is as follows.
6 friends share 3 small pies equally. What fraction of a pie does each friend get?
The research of Eich and Metcalf would suggest that if you were really happy when you were learning math, you should be _________ when taking the math exam to do well.
How much would $400 be worth after 16 years, if it were invested at 3% interest compounded annually? (Use the formula below and round your answer to the nearest cent.)
A(t)=P(1+ r/n)^nt
Final answer:
Using the compound interest formula A(t) = P(1 + r/n)^(nt) with the values P = $400, r = 3%, n = 1, and t = 16 years, the investment would grow to $722.44.
Explanation:
To calculate how much $400 would be worth after 16 years when invested at a 3% interest rate compounded annually, we can use the compound interest formula A(t) = P(1 + r/n)^(nt). In this formula, P represents the principal amount ($400), r is the annual interest rate (3% or 0.03), n is the number of times interest is compounded per year (1 for annually), t is the number of years the money is invested (16 years), and A(t) is the amount of money accumulated after t years, including interest.
To solve for A(t), we substitute the values into the formula:
A(t) = 400(1 + 0.03/1)^(1×16)
A(t) = 400(1 + 0.03)^16
A(t) = 400(1.03)^16
After calculating the power term:
A(t) = 400(1.80611123467)
Finally, we multiply the principal amount by the factor:
A(t) = $722.44
The $400 investment at 3% interest compounded annually would be worth $722.44 after 16 years.
Upon graduation from college, Warren Roberge was able to defer payment on his $22,000 student loan for 3 months. Since the interest will no longer be paid on his behalf, it will be added to the principal until payments begin. If the interest is 6.94 % compounded monthly , what will the principal amount be when he must begin repaying his loan?
Using the compound interest formula, we calculate that after 3 months, the new principal amount that Warren Roberge will owe on his student loan is $22,000(1 + 0.0694/12)^(12*0.25).
Explanation:To find the principal amount that Warren Roberge will owe when he begins repaying his student loan, we need to consider the interest compounding monthly over the 3-month deferment period. The formula for compound interest is: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time in years.
In this case, P = $22,000, r = 6.94/100 = 0.0694, n = 12 (since the interest is compounded monthly), and t = 3/12 = 0.25 (since the deferment period is 3 months, or 0.25 years).
Substituting these values into the formula, we find that A = $22,000(1 + 0.0694/12)^(12*0.25).
Therefore, after 3 months, the principal amount that Warren will owe on his student loan will be A.
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When Warren Roberge begins repaying his student loan after a 3-month deferment, the principal amount will be $22,038.07.
To calculate the principal amount when he starts repaying, we need to account for the accrued interest during the deferment period.
Calculate the monthly interest rate,Calculate the interest accumulated over the 3-month deferment period,Add the accrued interest to the principal:
Interest rate,
6.94% / 12 (months)
= 0.579%
$22,000 * 0.579% * 3 months
=127.38*3
= $38.07
Principal amount,
$22,000 + $38.07
= $22,038.07
A newspaper writers compensation package includes the total cost of a $150 per month health insurance plan the total cost of a $55 per month life insurance plan and a salary of 45,000 per year what would the yearly value of the compensation package be
Answer:
The answer is: $ 47,460.
Step-by-step explanation:
$ 150 x 12 month health insurance plan = 1800 $
$ 55 x 12 month life insurance plan = $ 660
With an annual salary of $ 45,000 + Health Insurance $ 1800 + Life insurance $ 660 = $ 47460
The answer is: $ 47,460.
Timmy writes the equation f(x) = 1/4x – 1. He then doubles both of the terms on the right side to create the equation g(x) = x – 2. How does the graph of g(x) compare to the graph of f(x)? The line of g(x) is steeper and has a higher y-intercept. The line of g(x) is less steep and has a lower y-intercept. The line of g(x) is steeper and has a lower y-intercept. The line of g(x) is less steep and has a higher y-intercept.
In 33,294 how is the value of the 3 in the ten thousands place related to the value of the 3 in the thousands place ?
Answer:
The value of the 3 in the ten thousands place is 10 times the value of the 3 in the thousands place.
Step-by-step explanation:
Let's see the value of each algarism in this number.
33294.
4 is the unit. So the value of the 4 in this number is [tex]4 \times 10^{0}[/tex]
9 is the tenth. So the value of the 9 in this number is [tex]9 \times 10^{1} = 90[/tex]
2 is the centh. So the value of the 2 in this number is [tex]2 \times 10^{2} = 200[/tex]
3 is the thousanth. So the value of the second 3(from the start to the end) in this number is [tex]3 \times 10^{3} = 3000[/tex]
3 is also the ten thousanths. So the value of the first 3 is this number is [tex]3 \times 10^{4} = 30000[/tex]
So
[tex]33294 = 30000 + 3000 + 200 + 90 + 4[/tex]
how is the value of the 3 in the ten thousands place related to the value of the 3 in the thousands place ?
[tex]\frac{3 \times 10^{4}}{3 \times 10^{3}} = 10[/tex]
The value of the 3 in the ten thousands place is 10 times the value of the 3 in the thousands place.
John is running in a race.The race is 25 miles long. After two hours,John has run 7 miles.How many miles does John have left to run?
A carpenter cut a board 3 3/4 feet long to make a shelf. Before he cut the board, it was 10 1/2 feet long.
How long is the remaining piece of the board?
Enter your answer, as a mixed number in simplest form
The remaining piece of the board was [tex]6\frac{3}{4}[/tex] feet.
What are mixed fractions?A fraction represented with its quotient and remainder is a mixed fraction.
Given that, a carpenter cut a board 3 3/4 feet long to make a shelf, before he cut the board, it was 10 1/2 feet long.
[tex]3\frac{3}{4} = \frac{15}{4} \\10\frac{1}{2} = \frac{21}{2}[/tex]
[tex]\frac{21}{2} - \frac{15}{4} \\= \frac{27}{4} \\= 6\frac{3}{4}[/tex]
Hence, The remaining piece of the board was [tex]6\frac{3}{4}[/tex] feet.
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The mean plus or minus one standard deviation defines the ________ percent probability range of a normal distribution. 82 68 95 50 90
Pierre deposits $9,000 in a certificate of deposit that pays 8% interest, compounded semiannually. How much interest does the account earn in the first six months? What is the balance after six months?
Final answer:
Pierre earns $360 in interest on his $9,000 certificate of deposit after the first six months, with a balance of $9,360.
Explanation:
Pierre deposits $9,000 in a certificate of deposit (CD) that pays an 8% interest rate, compounded semiannually. To calculate the interest earned in the first six months and the balance after six months, we follow these steps:
Determine the semiannual interest rate by dividing the annual rate by two. Since the annual rate is 8%, the semiannual rate is 4% or 0.04 in decimal form.
Calculate the interest for the first semiannual period (first six months) by multiplying the principal amount by the semiannual interest rate: $9,000 * 0.04 = $360.
The interest earned in the first six months is $360.
To find the new balance after six months, add the interest earned to the initial deposit: $9,000 + $360 = $9,360.
The balance of Pierre's certificate of deposit after six months is $9,360.
of the 125 students in 5th grade, 3/5 of them have a mobile phone. How many students do not have a mobile phone.
Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5:2:3. How much of each juice is needed to make 25 liters of this punch?
Answer:
5:2:3....added = 10
Step-by-step explanation:
5/10(25) = 125/10 = 12.5 liters of pear juice
2/10(25) = 50/10 = 5 liters pineapple juice
3/10(25) = 75/10 = 7.5 liters plum juice
how to turn 7.5% into a fraction in simplest form
Nitrogen and oxygen are the most abundant gases in Earth’s atmosphere. A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule. Which statements describe writing 0.00000000003 in scientific notation? Check all that apply.
Answer:
(these are the answer choices ppl)
The exponent is negative.
The exponent is positive.
The coefficient is 0.3.
The exponent represents the number of places the decimal moves.
The decimal moves to the right.
(its a, d, e)
0.00000000003 in scientific notation is 3.0 x 10^-11.
Explanation:The number 0.00000000003 can be converted to scientific notation by moving the decimal point to the right until there is only one non-zero digit to the left of the decimal point. In this case, we would move the decimal point 11 places to the right to get 3.0 x 10-11. The exponent, -11, indicates how many places the decimal point was moved.
So, the correct statement would be:
0.00000000003 in scientific notation is 3.0 x 10-11.
suppose that a small pump can empty a swimming pool in 60 hours and that a large pump can empty a pool in 40 hours. working together, how long will it take to empty the pool?
To determine the time it takes for a small and large pump to empty a swimming pool together, their rates are added to find a combined rate, and the inverse of this combined rate gives the time required. Calculations show the two pumps can empty the pool in 24 hours.
Calculating Time to Empty a Pool with Two Pumps
When the small pump operates alone, it can empty a swimming pool in 60 hours, while the large pump can do this in 40 hours. To find how long they will take to empty the pool when working together, we need to calculate their combined rate of emptying the pool.
The rate of the small pump is 1/60 pools per hour, and the rate of the large pump is 1/40 pools per hour. To find their combined rate, we simply add these rates together:
Combined rate = (1/60) + (1/40) pools per hourConverting both fractions to have a common denominator, we get:
Combined rate = (1/60) + (1/40) = (2/120) + (3/120) = (5/120) pools per hourThe inverse of the combined rate gives us the time to empty one pool:
Time = 1 / (5/120) = 120/5 = 24 hours.Therefore, the small and large pumps working together will empty the pool in 24 hours.
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the distance in 1.5 h. Car B traveled 15 mph faster than Car A. How fast did Car B travel? (The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.) Enter your answer for the box.
What is the equation of this line in standard form? −6x+11y=13 −6x+7y=−17 −6x+11y=−13 −11x+6y=−13 Number graph that ranges from negative five to five on the x and y axes. A line passes through the labeled points begin ordered pair negative four comma negative one end ordered pair and begin ordered pair one and begin fraction one-half end fraction comma, two end ordered pair
6 x - 1 1 y = - 1 3
The wall at the front entrance to the rock and roll hall of fame and museum in cleveland, ohio, is an isosceles triangle. the triangle has a vertex angle of 102 degrees. what is the measure of the base angles? answer
The measure of the base angles is 39° respectively.
An Isosceles triangle is a triangle that has two equal sides.
Note: The base angle of an isosceles triangle is equal.
From the question,
The sum of the angle in a triangle is 180°.
⇒ a+b+c = 180°............... Equation 1
Given:a = 102°b = c = x = base angle of the isosceles triangle.Substitute these values into the equation.
102+x+x = 180102+2x=180Solve for x.
2x = 180-1022x = 78x = 78/2x = 39°Hence, the measure of the base angles is 39° respectively.
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Which phrase describes the algebraic expression x - 21.5?
a. 21.5 decreased by x
b. x more than 21.5
c. 21.5 minus x
d. x less 21.5
Answer:
option D
Step-by-step explanation:
Given : the algebraic expression x - 21.5
a. 21.5 decreased by x
the expression becomes 21.5 - x
b. x more than 21.5
more than means we add , so expression becomes 21.5 +x
c. 21.5 minus x
For minus we use subtraction symbol,
so the expression becomes 21.5 -x
d. x less 21.5
x less 21.5 , we subtract 21.5
so the expression becomes x - 21.5 . that is the given expression
The correct phrase that describes the algebraic expression [tex]\( x - 21.5 \)[/tex] is b. x more than 21.5.
To understand why option b is correct, let's break down the expression and the meanings of each option:
The expression [tex]\( x - 21.5 \)[/tex] means that you start with an unknown quantity x and subtract 21.5 from it. This results in a new quantity that is the original x minus 21.5.
Now, let's consider each option:
a. "21.5 decreased by ( x )" suggests that ( x ) is being subtracted from 21.5, which would be written as ( 21.5 - x ). This is not the same as the given expression.
b. ( x ) more than 21.5 correctly implies that you have the quantity ( x ) and you are adding something to it to get a total that is more than 21.5 by that amount. Since we are subtracting a positive number from ( x ), the result is indeed ( x ) minus some amount, which means ( x ) is more than (x - 21.5 ).
c. "21.5 minus ( x )" is equivalent to option a and suggests that ( x ) is being subtracted from 21.5, which is not the same as the given expression.
d. "( x ) less 21.5" suggests that 21.5 is being subtracted from ( x ), but the wording is incorrect. The correct phrase would be "( x ) less than 21.5,"" but even then, it would imply that ( x ) is the smaller quantity, which is not what the expression ( x - 21.5 ) indicates.
Therefore, the correct interpretation of the expression ( x - 21.5 ) is that it represents ( x ) more than 21.5, which aligns with option b.
what fraction did she spend on petrol ,she spent £30 on petrol in total ,how much did she spend
Leo is adding gravel to the edge of his driveway he order six bags of gravel for $252 how much would it cost if orders eight bags instead
It would cost $756 if orders eight bags of gravel instead.
252x 3= 756
what is the value of (2³)²