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nasty-shy [4]
3 years ago
9

Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.

Mathematics
1 answer:
nalin [4]3 years ago
8 0

Answer:

  • Hannah: 2.11 is a terminating decimal that can be written as 2 11/100. Rational numbers can be expressed as fractions.

Step-by-step explanation:

<u>The answer choices are:</u>

  • <u>Gus</u>: 2.11 repeats because there are two 1s.
  • <u>Gus</u>: 2.11 is a repeating decimal because it stops.
  • <u>Hannah</u>: 2.11 is a rational number because it's a decimal.
  • <u>Hannah</u>: 2.11 is a terminating decimal that can be written as 2 11/100. Rational numbers can be expressed as fractions.

<u>The correct one is:</u>

  • Hannah: 2.11 is a terminating decimal that can be written as 2 11/100. Rational numbers can be expressed as fractions.
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Scilla [17]

Answer:

Hi!~I~am~beinggreat78,~and~I~will~help~you!

Let's start by breaking down the problem.

This is how it should look. ↓

60 ÷ 20 ⇒ + 3 ⇒ x * 5^2

What does that <em>x</em> mean? <em>x</em> is just a substituted value for the first 2 equations.

Now, we can solve.

60 ÷ 20 = 3

Add 3

3 + 3 = 6

Now, multiply 6 times 5 squared. What does 5 squared mean? 5 squared is just 5 times itself once. You most likely want to solve 5 squared before multiplying.

5^2~or~5 * 5 = 25

And now for the last step, multiply 25 times 6

25 * 6 = 150

With that information, the problem is solved! Your answer is 150

6 0
2 years ago
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What is the value of x when y = 16? y = 0.25x + 11
cestrela7 [59]

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3 years ago
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Factorise: a squared +8a -20
Vaselesa [24]
Factor out the 4 in both equations
8a^2-20^2=(2^2 times a^2 times 2)-(2^2 times 5)
therefor it is also equal to
(2a)^2 times 2-(2^2 times 5)
we can force it into a difference of 2 perfect squares which is a^2-b^2=(a-b)(a+b)
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3 years ago
Musa ships cars into Ghana, Nigeria and Benij republic from the United States of America. The import duty costs are 10%, 25% and
babunello [35]

The Benz C300 markup should be $15525. The markup price for the new Toyota Highland should be $43470

Step-by-step explanation:

For the used Benz C300

Initial price $12,000

Apply import duty for Nigeria which is 25%, which is similar to increasing the price by 25%

100% +25%=125%

12000*125/100 = $15000

Apply the 15% profit

100%+15%=115%

15000*115/100 =$17250

Apply the 10% discount, reducing the price by 10%

100%-10%=90%

17250*90/100 =$15525

The Benz C300 markup should be $15525

For the Toyota Highlander

Initial price = $30,000

Apply import duty for Nigeria for new cars, which is 40%, which is similar to increasing the car price by 40%

100%+40%=140%

30,000*140/100 =$42000

Apply the 15% profit

15%+100%=115%

115/100*42000 =$48300

Apply the 10% discount

100%-10%=90%

48300*90/100=$43470

The markup price for the new Toyota Highland should be $43470

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Percentage increase and decrease :brainly.com/question/11537235

Keywords : cars, import duty, cost, minimum profit, discount, reseller

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6 0
2 years ago
Prove each of the following statements below using one of the proof techniques and state the proof strategy you use.
pochemuha

Answer:

See below

Step-by-step explanation:

a) Direct proof: Let m be an odd integer and n be an even integer. Then, there exist integers k,j such that m=2k+1 and n=2j. Then mn=(2k+1)(2j)=2r, where r=j(2k+1) is an integer. Thus, mn is even.

b) Proof by counterpositive: Suppose that m is not even and n is not even. Then m is odd and n is odd, that is, m=2k+1 and n=2j+1 for some integers k,j. Thus, mn=4kj+2k+2j+1=2(kj+k+j)+1=2r+1, where r=kj+k+j is an integer. Hence mn is odd, i.e, mn is not even. We have proven the counterpositive.

c) Proof by contradiction: suppose that rp is NOT irrational, then rp=m/n for some integers m,n, n≠. Since r is a non zero rational number, r=a/b for some non-zero integers a,b. Then p=rp/r=rp(b/a)=(m/n)(b/a)=mb/na. Now n,a are non zero integers, thus na is a non zero integer. Additionally, mb is an integer. Therefore p is rational which is contradicts that p is irrational. Hence np is irrational.

d) Proof by cases: We can verify this directly with all the possible orderings for a,b,c. There are six cases:

a≥b≥c, a≥c≥b, b≥a≥c, b≥c≥a, c≥b≥a, c≥a≥b

Writing the details for each one is a bit long. I will give you an example for one case: suppose that c≥b≥a then max(a, max(b,c))=max(a,c)=c. On the other hand, max(max(a, b),c)=max(b,c)=c, hence the statement is true in this case.

e) Direct proof: write a=m/n and b=p/q, with m,q integers and n,q nonnegative integers. Then ab=mp/nq. mp is an integer, and nq is a non negative integer. Hence ab is rational.

f) Direct proof. By part c), √2/n is irrational for all natural numbers n. Furthermore, a is rational, then a+√2/n is irrational. Take n large enough in such a way that b-a>√2/n (b-a>0 so it is possible). Then a+√2/n is between a and b.

g) Direct proof: write m+n=2k and n+p=2j for some integers k,j. Add these equations to get m+2n+p=2k+2j. Then m+p=2k+2j-2n=2(k+j-n)=2s for some integer s=k+j-n. Thus m+p is even.

7 0
2 years ago
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