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3 years ago

Hye Lim drank 4/3 gallons of water in 11/2 hours. At this rate, how long will it take her to drink 4 gallons of water?

Mathematics

1 answer:

snow_lady [41]3 years ago

3 0

Answer:

16.5 hours

Step-by-step explanation:

Here is the explanation. As Hye drinks 4/3 gallons of water in 11/2 hours, we have a constant rate. There are 12 thirds in 4, so we are trying to find how long it takes Hye to drink 12/3 gallon. In this case, 4/3x3=12/3, so we multiply 11/2 by 3 as well, which gives us 33/2 hours. 33/2 in decimal form is 16.5 hours. Hope it helps!

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Holly has watched 39% of a movie that is 122 minutes long.

Scilla [17]

9514 1404 393

Answer:

48 minutes

Step-by-step explanation:

39% of 122 is ...

0.39 × 122 = 47.58 ≈ 48

Holly has watched about 48 minutes of the movie.

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3 years ago

How many square feet of carpet will we need for this hole??

vaieri [72.5K]

Bottom = 2x5 = 10ft
Middle = 2x6 ( 4+2) = 12
Top 4x2= 8
10ft+12ft+8ft= 30ft squared

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3 years ago

What is the slope of the line?

serious [3.7K]

-8/5x is the slope of the line.

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3 years ago

Let H be the set of all polynomials having degree at most 4 and rational coefficients. Determine whether H is a vector space. If

Verizon [17]

Answer:

Yes. It is a vector space over the field of rational numbers $\mathbb{Q}$

Step-by-step explanation:

An element $p$ of the set $H$ has the form

$p(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}$

where $a_{0},a_{1},a_{2},a_{3},a_{4}$ are rational coefficients.

The operations of addition and scalar multiplication are defined as follows:

$p(x)+q(x)=(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+x_{4}x^4)+(b_{0}+b_{1}x+b_{2}x^{2}+b_{3}x^{3}+b_{4}x^{4})=(a_{0}+b_{0})+(a_{1}+b_{1})x+(a_{2}+b_{2})x^{2}+(a_{3}+b_{3})x^{3}+(a_{4}+b_{4})x^{4}$

$\lambda p(x)=\lambda (a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4})=\lambda a_{0}+\lambda a_{1}x+\lambda a_{2}x^{2}+\lambda a_{3}x^{3}+\lambda a_{4}x^{4}$

The properties that $H$ , together the operations of vector addition and scalar multiplication, must satisfy are:

Conmutativity
Associativity of addition and scalar multiplication
Additive Identity
Additive inverse
Multiplicative Identity
Distributive properties.

This is not difficult with the definitions given. The most important part is to show that $H$ has a additive identity, which is the zero polynomial, that is closed under vector addition and scalar multiplication. This last properties comes from the fact that $\mathbb{Q}$ is a field, then it is closed under sum and multiplication.

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3 years ago

60% mark up of 95 cents

Olegator [25]

the answer would be 1.52 because first, we would turn 60% into a decimal (.60) and then, we would multiply .95x.60 and we would get .57

next, we would add .95 and .57 together to get 1.52

7 0

3 years ago