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Jet001 [13]
3 years ago
6

A box contains 9 blueberry muffins, 4 banana muffins, and 5 pumpkin muffins. You pick one muffins from the box at random. What i

s the probability of selecting a pumpkin muffin?
Mathematics
1 answer:
Law Incorporation [45]3 years ago
4 0

Answer: 5 in 18 or 27.7%

Step-by-step explanation:

There are 18 muffins, 5 of which are pumpkin

Multiply 5 by 100, then divide by the total number of muffins to find the percent chance of picking a pumpkin one

(5 x 100) / 18

500 / 18

27.77777777...

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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
3 years ago
Using the expression 10 x 2/5 as an example, describe how to multiply a whole number by a fraction that is less than one.
Schach [20]
To multiply a whole number by a fraction less than one, you have to rewrite the whole number in the expression as a fraction by putting a one under it.
For example, in 10 x 2/5, you would rewrite the 10 to 10/1 x 2/5.
Then, you would multiply the top and bottom of the two fractions. In this case, it would be 10 x 2 and 1x5. This would result in 20/5.
Finally, you would simplify this fraction by dividing. The final answer is 4.
5 0
2 years ago
Read 2 more answers
You are going to play a game where you bet a dollar and get to flip a coin ten (10) times. If you get four (4) heads in a row, y
klio [65]

Answer:

Approximately 4,000 times

Step-by-step explanation:

If you're flipping a coin to get 4 heads out of 10 and you times it by 10,000 then you would have a probable win rate of 4,000.

3 0
3 years ago
A penguin is standing 3 feet above sea level and then<br> dives down 10 feet. What is its depth?
ValentinkaMS [17]

Answer:

7 feet below sea level

Step-by-step explanation:

he was at 3 then you subtract 10 feet because he dives.

7 0
3 years ago
Read 2 more answers
0.05% as a fraction in simplest form
fiasKO [112]
0.05=5/100
5/100=1/20
3 0
3 years ago
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