Answer:
The smallest positive integer is 3.
Step-by-step explanation:
In order to detect if a number is a perfect square, you firstly have to write the number as a product of its prime factor. If the prime factors of the number appear in an even number of times, then it's a perfect square. For example, if we want to detect if 36 is a perfect square we have to write 36 as a product of its prime factors. Doing this, we have:
36 = 2 x 2 x 3 x 3 = 2² x 3². From here, we see that the prime factors of 36 – 2 and 3 – appear twice which is an even number of times. Hence, it's a perfect square.
Now let us go back to our number:
N = 2^10 x 3^5
Obviously, N is not a perfect square because one of it's prime factors, 3, appears 5 times which is an odd number of times. In order to make it a perfect square, we have to multiply it by a certain number of 3's such that it will appear in an even number of times. Since the least positive integer is required, then we have to multiply by the least number of 3 that will make 3^5 even. Obviously, one 3 is the least needed to make 3^5 appear even number of times, because 3^5 x 3 = 3^6.
Therefore we have
N x 3 = 2^10 x 3^5 x 3 = 2^10 x 3^6.
Since there are 7 days in a week and he slept the same amount of time each day, we can determine the number of hours he slept each day by dividing the number of hours he slept the whole week, 91 hours, and the number of days he slept. So you would get 91/7, which is 13. So Mac slept 13 hours each day. Hope this helps.
Answer:
8 minutes if Jane was assumed to be stationary
Step-by-step explanation:
The question is on relative speed
First find the distance covered by Jane when Sally left school
Speed=Distance/Time ⇒⇒ Distance=Time×Speed
Time=10minute=10/60 hrs
Jane's speed= 12mph
Distance covered by Jane when Sally left school was= 12 ×10/60 = 2miles
So, when Sally left school, Jane was 2 miles away. To find the time Sally requires to catch up with Jane;
Time=Distance/speed
Time of meeting =2/15 hrs ⇒⇒ 2/15 × 60 =8minutes
Answer:
w-9
Step-by-step explanation:
Plug in w = 9 to each equation
9+5=14
5+9=14
23-9=14
9-9=0
All except for w-9 have a solution of 14
Let
s-------> the amount of money Layla deposits
we know that
so
therefore
<u>the answer is</u>
She could deposit
She could deposit