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2 years ago

Which is the solution to the inequality 1/4+x<5/8

Mathematics

1 answer:

Masteriza [31]2 years ago

7 0

Answer:

x<3/8

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Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

x+1/4<5/8

Step 2: Subtract 1/4 from both sides.

x + 1/4 - 1/4 < 5/8 - 1/4

x<3/8

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In the equation (x^2+y)^5, what is the coefficient of the term x^4y^3? what is the coefficient of the same term in the expansion

lys-0071 [83]

$\displaystyle
(x+y)^n=\sum_{k=0}^n\binom{n}{k}x^{n-k}y^k$

$\displaystyle
(x^2+y)^n=\sum_{k=0}^n\binom{n}{k}x^{2n-2k}y^k\\
n=5\\
k=3\\\\\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdor5}{2}=10$

----------------------------------------------------

$\displaystyle
(3x^2+y)^n=\sum_{k=0}^n\binom{n}{k}(3x)^{2n-2k}y^k=\sum_{k=0}^n\binom{n}{k}\cdot 3^{2n-2k}\cdot x^{2n-2k}y^k\\\\
n=5\\
k=4\\\\
\binom{5}{3}\cdot3^{2\cdot5-2\cdot4}=10\cdot3^{2}=10\cdot9=90$

<u>It's 90</u>

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2 years ago

In a school contest, each student draws a number from 1 to 5 out of a large basket. The outcomes are shown in the table below.

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The answer is 88/407

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a restaurant has an all-you-can-eat buffet. They charge $13.95 per person. what is the constant of proportionality?

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Step-by-step explanation:

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2 years ago

Max has 5.50. He has eight more quarters than he does nickels. He had four times as many dimes as he has nickels. How many quart

Oliga [24]

Answer:

<h2>There are 13 quarters, 5 nickels and 20 dimes.</h2>

Step-by-step explanation:

Givens

Max has $5.50.
He has eight more quarters than he does nickels.
He had four times as many dimes as he has nickels.

From these statements, we can deduce algebraical expressions to solve the problem. Let's call $q$ quarters, $n$ nickels and $d$ dimes.

$q=n+8$ (8 more quarters than nickels)

$d=4n$ (he has four times as many dimes as he has nickels).

$0.25q+0.05n+0.10d=5.50$ (Max has a total of $5.50, one quartes is $0.25, one nickel is $0.05 and one dime is $0.10).

Let's replace the first two expressions into the third equation

$0.25(n+8)+0.05n+0.10(4n)=5.50\\0.25n+2+0.05n+0.40n=5.50\\0.70n=5.50-2\\n=\frac{3.50}{0.70}\\ n=5$

There are 5 nickels.

Now, we use this value to find the number of quarters

$q=5+8=13$

There are 13 quarters.

Also, $d=4(5)=20$

There are 20 dimes.

Therefore, there are 13 quarters, 5 nickels and 20 dimes.

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2 years ago