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VashaNatasha [74]
3 years ago
7

For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distin

ct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1,000, what is the maximum possible sum of the length of x and the length of y?
Mathematics
1 answer:
creativ13 [48]3 years ago
7 0

Answer:

16

Step-by-step explanation:

We must find integers x, y with the most amount of prime divisors, not necessarily distinct, such that x + 3y < 1,000.

Obviously, this is achieved when the divisor is the least prime 2. So, we must find integers n, m such that

\large 2^n + 3*2^m < 1,000  

since \large 2^10 = 1,024 , then <em>n must be 9</em>. For n=9 we find the greatest integer m such that  

\large 2^9 + 3*2^m  

and<em> we find m=7 </em>

 and  \large x=2^9 , \large y=2^7  are the numbers we are looking for and the sum of their length is 9+7 = 16.

So, 16 is the maximum possible sum of the length of x and the length of y.

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A company is approached by a new warehouse management systems vendor to adopt a new system. The vendor claims that the warehouse
Ludmilka [50]

Answer:

a

     The null hypothesis  is  H_o  :  \mu  = 180

      The alternative hypothesis is  H_a :  \mu  <  180

b

The decision rule is  fail to reject the null hypothesis

The conclusion

There no sufficient evidence to support the vendor claim  that the warehouse management system reduces the average pick, pack, and ship time to below 3 minutes(180 seconds) per order through bin location and routing optimization

Step-by-step explanation:

From the question we are told that

     The population mean is  \mu  =  3 \  minutes =  180 \  seconds

     The sample  size is  n =  25

     The excel sheet is show on the first uploaded image

     The level of significance is  \alpha =  0.05

     The null hypothesis  is  H_o  :  \mu  = 180

      The alternative hypothesis is  H_a :  \mu  <  180

Generally the sample mean is mathematically represented as

        \= x  =  \frac{156 + 136 + \cdots  + 181}{25}

=>      \= x  = 173.2

Generally the standard deviation is mathematically represented as

      \sigma  =  \sqrt{\frac{\sum  (x_i - \= x )^2 }{n} }

=>    \sigma  =  \sqrt{\frac{  (156 - 173.2 )^2 + (136 - 173.2 )^2  + \cdots + (181- 173.2 )^2  }{25} }

=>    \sigma  =  24.261

Generally the test statistics is mathematically represented as

      t =  \frac{\= x  -  \mu }{\frac{\sigma}{\sqrt{n} } }

=>   t =  \frac{173.2 -  180 }{\frac{24.261}{\sqrt{25} } }

=>   z = -1.40    

Generally p-value is mathematically represented as

  p-value  =  P(Z <  z)

=>  p-value  =  P(Z < -1.40)

From the z-table  

   P(Z < -1.40) =  0.080757

=>   p-value  = 0.080757

From the obtained value we that  p-value >  \alpha

The decision rule is  fail to reject the null hypothesis

The conclusion

There no sufficient evidence to support the vendor claim  that the warehouse management system reduces the average pick, pack, and ship time to below 3 minutes(180 seconds) per order through bin location and routing optimization

   

5 0
2 years ago
What is the mean ( average) of the data set: 3/4, 13/5 , 14/10, and 6/24?
irinina [24]
Add them all together and divide by the number of variables here there are four and the answer is 1.25 or 5/4
3 0
2 years ago
Read 2 more answers
Question 3 (Multiple Choice Worth 1 points)
Evgen [1.6K]

Answer:

g(x) = x + 6

Step-by-step explanation:

The parent function is given as:

f(x) = x + 8

We want to find a new function that results after shifting f(x), 2 units to the right.

Let that function be g(x), then

g(x) = f(x - 2)

We replace x by x-2 in f(x) to get:

g(x) = x - 2 + 8

When we simplify, we obtain:

g(x) = x + 6

8 0
3 years ago
What is the value of z?
VashaNatasha [74]

Answer:

z = 61

Step-by-step explanation:

The exterior angle is congruent (equal to) the sum of the 2 farthest angles from it, so you can set the equation like this:

z + z - 11 = z + 50

Add like terms, which would be the 2 "z's" on the left side:

2z - 11 = z + 50

Then subtract the z on the right side from both sides:

2z - 11 = z + 50

-z          -z

___________

z - 11 = 50

Add 11 to both sides:

z - 11 = 50

  + 11    +11

________

z = 61

6 0
2 years ago
Select all of the rational numbers from the list.
topjm [15]

Step-by-step explanation:

Rational numbers

7/8, square root of 25

6 0
2 years ago
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