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maw [93]
3 years ago
9

Problem 2 Find all the divisors of the number 2,310. How do you know that you found them all?​

Mathematics
1 answer:
elena-s [515]3 years ago
8 0

9514 1404 393

Answer:

  1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42,

  55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310

Step-by-step explanation:

The trailing digit is 0, and the sum of digits is 6, so we know the number is divisible by 2, 3, 5. Dividing out those factors, we get a quotient of 77, which is 7×11. This means the prime factorization is ...

  2×3×5×7×11 = 2310

There are 5 prime factors, each with an exponent of 1, so the total number of divisors is 2^5 = 32. We will have found them all when all 32 are listed.

  1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42,

  55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310

Of course, the pairwise products working toward the center from the ends of the list are all 2310.

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One survey showed that among 785 randomly selected subjects who completed four years of college, 18.3% smoke and a 98% confidenc
Valentin [98]

Answer

a. True

Step-by-step explanation:

Based on this survey we estimate that about 18.3\% of the college students smokes. And a 98\% confidence interval is [15.1\% ; 21.6\%].  So we know that our estimative for the smoking rate is in the confidence interval with 98\% certainty. We also know the estimative for the smoking rate in the general population is 27\%. So we can write the two possible hypothesis:

H_0 = Smoking rate is equal to 27\%.

H_1 = Smoking rate is not equal to 27\%.

We will reject the null hypothesis (H_0) if the estimate doesn't fall into the confidence interval for the college students smoking rate.

Since this condition holds we reject the null hypothesis. So with 98\% certainty we say that the smoking rate for the general population is different than the smoking rate for the college students.

6 0
3 years ago
Consider a small ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let X and Y
harina [27]

Answer:

Expected revenue from the single trip is $ 13.14

Step-by-step explanation:

                              y

p(x,y)                   0               1                                 2                g(x)

x    0           0.025              0.015                       0.010            0.05

1                  0.050            0.030                        0.020           0.1  

2                   0.115             0.075                        0.050           0.24

3                  0.150              0.090                      0.060             0.3

<u>4                   0.100             0.060                     0.040              0.2 </u>

h(y)              0.325              0.27                       0.18  

E (x+Y) = E(X) +E(Y)

E(X)= ∑ xi g(x)i

       = ( 0*0.05) + (1*0.1) + (2* 0.24) + (3*0.3) + (4*0.2)

        = 0 + 0.1+ 0.48 + 0.9+0.8

        =2.28

E(Y)= ∑yi h(y)

      = (0* 0.325) + (1*0.27) + (2*0.18)    

       = 0 +0.27+ 0.36

        = 0.63

E (x+Y) = E(X) +E(Y)

             = 2.28 + 0.63

                = 2.91

But the equation is 3x+ 10y

E(3x+ 10y)= 3E(x) + 10 E(y)

                   = 3(2.28) + 10 (0.63)

                       = 6.84 +6.3

                         = 13.14

Expected revenue from the single trip is $ 13.14

5 0
3 years ago
The perimeter of the rectangular playing field is 460 yards. The length of the field is 5 yards less than quadruple the width. W
Tpy6a [65]

Answer:

multiply 460 by 5

Step-by-step explanation:

460 * 5 = 2,300

8 0
3 years ago
Solve -2z – 5 &gt; 3 for z.
Natasha2012 [34]

Hi,

- 2z - 5 > 3

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7 0
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The first one because 2% as a decimal I'd 0.2
3 0
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