Answer:
1000 balls
(there are infinitely many solutions to this question; you can scale up 1000, use a different total, etc.)
Step-by-step explanation:
there are, of course, multiple possible numbers,
but the easiest way is to go with 1000, because we can say 375 / 1000 and 400 / 1000
(0.4 + 0.275 + 0.225 = 1)
400 out of 1000 balls are red (400/1000 = 4/10 = 0.4)
375 out of 1000 balls are green (375/1000 = 3.75/10 = 0.375)
225 out of 1000 balls are yellow (225/1000 = 2.25/10 = 0.225)
the question never gave detail as to if the answer should be the <em>lowest</em><em> </em>number of possible balls, so this value is possible.
So, a possible number of balls in this bag is 1000.
Their total points for the first 10 games were
(10) x (35) = 350 total .
Their total points after 11 games were
(11) x (33) = 363 total .
They must have scored (363 - 350) = 13 points in that 11th game.
I hate to say it, but these kids and their coach are in the wrong game.
Answer:
The other side was decreased to approximately .89 times its original size, meaning it was reduced by approximately 11%
Step-by-step explanation:
We can start with the basic equation for the area of a rectangle:
l × w = a
And now express the changes described above as an equation, using "p" as the amount that the width is changed:
(l × 1.1) × (w × p) = a × .98
Now let's rearrange both of those equations to solve for a / l. Starting with the first and easiest:
w = a/l
now the second one:
1.1l × wp = 0.98a
wp = 0.98a / 1.1l
1.1 wp / 0.98 = a/l
Now with both of those equalling a/l, we can equate them:
1.1 wp / 0.98 = w
We can then divide both sides by w, eliminating it
1.1wp / 0.98w = w/w
1.1p / 0.98 = 1
And solve for p
1.1p = 0.98
p = 0.98 / 1.1
p ≈ 0.89
So the width is scaled by approximately 89%
We can double check that too. Let's multiply that by the scaled length and see if we get the two percent decrease:
.89 × 1.1 = 0.979
That should be 0.98, and we're close enough. That difference of 1/1000 is due to rounding the 0.98 / 1.1 to .89. The actual result of that fraction is 0.89090909... if we multiply that by 1.1, we get exactly .98.
Answer:
a^3-b^3
Step-by-step explanation:
(a−b)(a2+ab+b2)
=(a+−b)(a2+ab+b2)
=(a)(a2)+(a)(ab)+(a)(b2)+(−b)(a2)+(−b)(ab)+(−b)(b2)
=a3+a2b+ab2−a2b−ab2−b3
=a3−b3