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djyliett [7]
2 years ago
15

In November, the rain in a certain valley tends to fall in storms of several days duration. The unconditional probability of rai

n on any day of the month is 0.600. But the probability of rain on a day that follows a rainy day is 0.900, and the probability of rain on a day following a nonrainy day is 0.300. Find the probability of rain on November 1 and 2. but not on November 3. Find the probability of rain on November 1 and 2, but not on November 3.​
Mathematics
1 answer:
Mumz [18]2 years ago
4 0

Answer:

0.0594 = 5.94% probability of rain on November 1 and 2, but not on November 3.​

Step-by-step explanation:

Rain on November 1:

0.9 of 0.6(rain on Oct 31).

0.3 of 0.4(not rain on Oct 31).

Rain on November 2:

Considering rain on November 1, 0.9 probability of rain.

Rain on November 3:

Considering rain on November 2, 0.1 probability of rain.

Find the probability of rain on November 1 and 2, but not on November 3.​

Multiplicating the probabilities:

p = (0.9*0.6+0.3*0.4)*0.9*0.1 = 0.0594

0.0594 = 5.94% probability of rain on November 1 and 2, but not on November 3.​

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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
2 years ago
You guys can have these free points :)))
fiasKO [112]

Answer:

ok

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Gia opened two savings accounts at two diffrent banks. One account earns an annual 3.4% simple interest, and the other earns hal
dsp73

Interest from first account is :

I_1 = \dfrac{p\times r \times t}{100}\\\\I_1 = \dfrac{509\times 3.4\times 3}{100}\\\\I_1 =\$ 51.918

Interest form second account is :

I_2 = \dfrac{p\times r\times t}{100}\\\\I_2 = \dfrac{509\times 1.7\times 3}{100}\\\\I_2 =  \$25.959

So, total interest is :

I = I_1 + I_2 \\\\I = 51.918 + 25.959\\\\I = \$77.877

Therefore, total interest is $77.877 .

5 0
3 years ago
Chris paid $36 for 3 tanktops and 2 shirts. a shirt cost 3 times as much as a tank top. how much did chris pay for the 2 shirts?
devlian [24]

Answer:

$72

Step-by-step explanation:

36/3=12

1 tanktop=$12

12*3=36

1 shirt equals=$36

36*2=72

2 shirts=$72

4 0
3 years ago
Please tell me the answer as quick as possible! Stuck here badly :(
olga2289 [7]

63degrees

Step-by-step explanation:

there are multiple ways to do this

for one, angle a = angle e (corresponding angles)

angle f + angle e = 180 degrees (angles on a straight line)

angle f = 180 degrees - angle e where angle e = angle a = 117degrees

so angle f = 63 degrees.

4 0
3 years ago
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