equivalent - equal in value, amount, function, meaning

2 tons and 500 pounds is equivalent to

2 tons and 500 pounds is equivalent to
1 ton equals 2000 pounds.
So 2 tons equal 2(2000) = 4000 pounds.
Add this to 500 pounds, we get:
4000 + 500 = [B]4,500 pounds[/B].

A large storage container is filled with 44.9 quarts of water. One quart of water is equivalent to 3

A large storage container is filled with 44.9 quarts of water. One quart of water is equivalent to 32 fluid ounces. How many fluid ounces of water are stored in the container? Round your answer to the nearest whole number.
44.9 quarts * 32 fluid ounce / quart = 1,436.8
if we found to the nearest whole number, we round up since 0.8 is greater than 0.5, so we get:
[B]1,437 fluid ounces[/B]

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Writ

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Write two equivalent expressions for the total cost of 9 accessory package. Then find the cost.
Let c be the number of cleats, s be the number of shin guards, and b be the number of balls. We have the following cost function for 9 accessory packages:
[B]9(25c + 14s + 12b)[/B]
But if we multiply through, we get an equivalent expression:
[B]225c + 126s + 108b[/B]

A recipe calls for 2 ½ cup of flour, but Paul only has 2 ?. How much more flour does he need?

A recipe calls for 2 ½ cup of flour, but Paul only has 2 ?. How much more flour does he need?
Convert to improper fractions
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%261%2F2&frac2=3%2F8&pl=Simplify']2 & 1/2 [/URL]= 5/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%261%2F6&frac2=3%2F8&pl=Simplify']2 & 1/6[/URL] = 13/6
[URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=5%2F2&pl=Equivalent+Fractions']Convert 5/2 to an equivalent fraction with a denominator[/URL] of 6:
15/6
[URL='https://www.mathcelebrity.com/fraction.php?frac1=15%2F6&frac2=13%2F6&pl=Subtract']We subtract 13/6 from 15/6[/URL]
15/6 - 13/6 = 2/6
2/6 = [B]1/3[/B]

An analysis of the final test scores for Managerial Decision Making Tools reveals the scores follow

An analysis of the final test scores for Managerial Decision Making Tools reveals the scores follow the normal probability distribution. The mean of the distribution is 75 and the standard deviation is 8. The instructor wants to award an "A" to students whose score is in the highest 10 percent. What is the dividing point for those students who earn an "A"?
Top 10% is equivalent to the 90th percentile.
Using our [URL='http://www.mathcelebrity.com/percentile_normal.php?mean=+75&stdev=8&p=+90&pl=Calculate+Percentile']percentile calculator[/URL], the 90th percentile cutoff point is [B]85.256[/B]

Carlos was asked to write an equivalent equation to 2x/5 = 1 - x. he wrote it as 2x = 1 - 5x. do you

Carlos was asked to write an equivalent equation to 2x/5 = 1 - x. he wrote it as 2x = 1 - 5x. do you agree with his conclusion? explain your answer for x
Cross multiply
2x/5 = 1 - x
2x = 5(1 - x)
2x = 5 - 5x
I disagree with his conclusion. He forgot to multiply the 5 through to [B]both terms[/B]

Equivalent Fractions

Given a fraction, this will determine equivalent fractions

Explain why 1/2 and 3/6 are equivalent

Explain why 1/2 and 3/6 are equivalent.
Multiply any number by 1, and we get the same number.
Multiply 1/2 by 3/3 which is 1
(1 * 3)/(2 *3) = 3/6

if 3/15 is equivalent to 45/a, find a

if 3/15 is equivalent to 45/a, find a.
Set up the proportion:
3/15 = 45/a
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=45&den1=15&den2=a&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
a = [B]225[/B]

Is 20% equivalent to 2/5?

Is 20% equivalent to 2/5?
Let's compare fractions to fractions:
20% equals 1/5 from our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=20&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage-decimal-fraction calculator[/URL].
1/5 < 2/5 so these fractions are [B][I]not equivalent[/I][/B].

Is 5 over 3 equivalent to 9 over 6?

Is 5 over 3 equivalent to 9 over 6?
Using our fraction [URL='http://www.mathcelebrity.com/fraction.php?frac1=5/3&frac2=9/6&pl=Compare']comparison calculator[/URL]:
[B]5/3 > 9/6[/B]

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An em

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An employee in the Amazon distribution center earns about $13 an hour. The estimated lifespan of the employee is 71 years. If the employee worked 24 hours a day, every day of the year from the moment of his birth, how many lifespans would it take for him to earn wages equivalent to Jeff Bezos' net worth? Round the answer to the nearest whole number.
Calculate earnings per lifespan:
Earnings per lifespan = lifespan in years * Annual Earnings
Earnings per lifespan = 71 * 13 * 24 * 365 <-- (24 hours per day * 365 days per year)
Earnings per lifespan = 8,085,480
Calculate the number of lifespans needed to match Jeff Bezos earnings:
Number of lifespans = Jeff Bezos Net Worth / Earnings Per Lifespan
Number of lifespans = 143,100,000,000 / 8,085,480
Number of lifespans = [B]17,698.39 ~ 17,699[/B]

Ordered Pair

This calculator handles the following conversions:

* Ordered Pair Evaluation and symmetric points including the abcissa and ordinate

* Polar coordinates of (r,θ°) to Cartesian coordinates of (x,y)

* Cartesian coordinates of (x,y) to Polar coordinates of (r,θ°)

* Quadrant (I,II,III,IV) for the point entered.

* Equivalent Coordinates of a polar coordinate

* Rotate point 90°, 180°, or 270°

* reflect point over the x-axis

* reflect point over the y-axis

* reflect point over the origin

* Ordered Pair Evaluation and symmetric points including the abcissa and ordinate

* Polar coordinates of (r,θ°) to Cartesian coordinates of (x,y)

* Cartesian coordinates of (x,y) to Polar coordinates of (r,θ°)

* Quadrant (I,II,III,IV) for the point entered.

* Equivalent Coordinates of a polar coordinate

* Rotate point 90°, 180°, or 270°

* reflect point over the x-axis

* reflect point over the y-axis

* reflect point over the origin

Proportion

1) Calculates the missing link of 2 equivalent proportions or ratios.

2) Also determines if two numerical proportions that you entered such as 1/10=6/12 are equivalent or*not* equivalent.
Note: You can use all allowable operators such as =,<,≤,>,≥

2) Also determines if two numerical proportions that you entered such as 1/10=6/12 are equivalent or

Rational Number Subtraction

Subtracting 2 numbers, this shows an equivalent operations is adding the additive inverse. p - q = p + (-q)

The expression (5x - 2)/(x + 3) is equivalent to which of the following?

The expression (5x - 2)/(x + 3) is equivalent to which of the following?
[LIST]
[*]A) (5 - 2)/3
[*]B) 5 - 2/3
[*]C) 5 - (2/(x + 3))
[*]D) 5 - (17/(x + 3))
[/LIST]
Let's start with an integer x = 2. Plug that into our original expression, and we get:
(5(2) - 2)(2 + 3)
(10 - 2)/5
8/5
So what we do next is, take x = 2, and plug it into answer choices A-D, and see which one results in 8/5
A) 3/3 = 1 <-- Nope
B) Since 5 is 15/3, we have 15/3 - 2/3 = 13/3 which is over 4, so Nope
C) 5 - (2/(2 + 3)) = 5 - (2/5). Since 5 is 25/5, we have 25/5 - 2/5 = 23/5. <-- Nope
D) 5 - (17/(2 + 3)) = 5 - 17/5. Since 5 is 25/5, we have 25/5 - 17/5 = 8/5 <-- YES
Since 8/5 = 8/5, our answer is [B]D) 5 - (17/(x + 3))[/B]

True False Equations

Determines if a set of addition and subtraction of numbers on each side of an equation are equivalent.
Also known as true or false equations

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 intege

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 integers. What is the difference of the product minus the sum?
Let the 3 consecutive positive integers be:
[LIST=1]
[*]x
[*]x + 1
[*]x + 2
[/LIST]
The product is:
x(x + 1)(x + 2)
The sum is:
x + x + 1 + x + 2 = 3x + 3
We're told the product is equivalent to:
x(x + 1)(x + 2) = 16(3x + 3)
x(x + 1)(x + 2) = 16 * 3(x + 1)
Divide each side by (x + 1)
x(x + 2) = 48
x^2 + 2x = 48
x^2 + 2x - 48 = 0
Now subtract the sum from the product:
x^2 + 2x - 48 - (3x + 3)
[B]x^2 - x - 51[/B]

Which of the following is equivalent to 3(2x + 1)(4x + 1)?

Which of the following is equivalent to 3(2x + 1)(4x + 1)?
[LIST]
[*]A) 45x
[*]B) 24x^2 + 3
[*]C) 24x^2 + 18x + 3
[*]D) 18x^2 + 6
[/LIST]
First, [URL='https://www.mathcelebrity.com/binomult.php?term1=2x%2B1&term2=4x%2B1&pl=Expand+Product+of+2+Binomials+using+FOIL']multiply the binomials[/URL]:
We get 8x^2 + 6x + 1
Now multiply this polynomial by 3:
3(8x^2 + 6x + 1) = [B]24x^2 + 18x + 3, answer C[/B]

Which of the following is equivalent to 9^3/4?

Which of the following is equivalent to 9^3/4?
Since 9 is 3^2, we have 3^(3*2/4) which is 3^6/4
Since 6/4 is 3/2, we have:
3^(3/2)
Since 3/2 is 1 + 1/2, we have:
3^1*sqrt(3)
[B]3*sqrt(3) or option D.[/B]

Which of the following is equivalent to the sum of the expression a^2 - 1 and a + 1?

Which of the following is equivalent to the sum of the expression a^2 - 1 and a + 1?
A) a^2 + a
B) a^3 - 1
C) 2a^2
D) a^3
a^2 - 1 + a + 1
The 1's cancel, so we're left with:
[B]a^2 + a - Answer A[/B]

You have 30 DONUTS. 1/6 of them are Boston Cream. 2/5 of them are Maple. 3/10 of them are Chocolate

You have 30 DONUTS. 1/6 of them are Boston Cream. 2/5 of them are Maple. 3/10 of them are Chocolate Dip and 1/3 are Sprinkled. IS THIS EVEN POSSIBLE?? How many donuts OVER or UNDER am I? (Show your work and use EQUIVALENTS.)
We use 30 as our common denominator. Let's get [I]equivalent fraction[/I]s for each donut type with a denominator of 30:
[LIST]
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=1%2F6&pl=Equivalent+Fractions']1/6[/URL] = 5/30
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=2%2F5&pl=Equivalent+Fractions']2/5 [/URL]= 12/30
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=3%2F10&pl=Equivalent+Fractions']3/10[/URL] = 9/30
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=1%2F3&pl=Equivalent+Fractions']1/3[/URL] = 10/30
[/LIST]
Add up our numerators of the common denominator of 30:
5 + 12 + 9 + 10 = 36
So our fraction is 36/30. This makes our scenario [B]impossible[/B]. Fractions of the donut should add up to 1. Which would mean our numerators need to sum to 1 or less. Since 36 > 30, this scenario is [B]impossible.[/B]