Answer:
257 is prime.
Step-by-step explanation:
To evaluate if a number is prime, we just need to evaluate it for the prime numbers that are equal or lesser than the said number's square root.
In this case, √257 = 16.03 so we just need to see if 257 is divisible by <u>2, 3, 5, 7, 11 and 13</u> (the prime numbers that come before 16)
- 257 is odd, so it is not divisible by 2.
- The sum of its digits is 14, therefore, it is not divisible by 3.
- 257 ends in 7, therefore it's not divisible by 5.
- 257/ 7 = 36.71 so it's not divisible by 7.
- 257/ 11 = 23.36 so it's not divisible by 11
- Finally 257 / 13= 19.76 so it's not divisible by 13.
Therefore, 257 is prime.
Answer: The approximate solution is (-0.36, 2.08).
Given system of equations : x+5y=10 and 3x+y=1
X + 3y = 7
x = -3y + 7
2x + 4y = 8
2(-3y + 7) + 4y = 8
-6y + 14 + 4y = 8
-2y = 8 - 14
-2y = - 6
y = -6/-2
y = 3
x + 3y = 7
x + 3(3) = 7
x + 9 = 7
x = 7 - 9
x = -2
solution is (-2,3)
Answer:
34
Step-by-step explanation:
Since the pennies need to be kept under the pillow in order to be doubled, we're really looking for the day the girl will wake up with 5 billion pennies under her pillow.
The general formula of that geometric sequence will be: t = 1 + 2^(n-1)
We need to find the value of n when t will be over 5,000,000,000.
So, the equation becomes:
5,000,000,001 = 1 + 2^(n-1)
(n-1) * log(2) = log(5,000,000,000)
n-1 = log(5,000,000,000) / log(2)
n-1 = 22.25
n = 33.25
Since it has to be complete days, and we have to reach over 5 billion, then we round it up to 34.
So hmmm let's see
she has a monthly income of 120 from investments, now, there are 12 months in a year, so her yearly income from investments are 120*12 or
$1440
she plays on a band, and makes 200 a week, now, there are 52 weeks in a year, so her yearly income from band playing is 200 * 52, or
$10400
her total annual income is 49696, now, if we subtract the band and investment income, we'd be left over with only what comes from her job payrate
so 49696 - 1440 - 10400 is 37856
so, she makes from her job, $37856 annually
now, she only works 28 hours weekly, how much is that yearly? well, 52 weeks in a year, she works 28*52 hours a year, let us divide 37856 by that
37856 ÷ ( 28 * 52) well, it ends up as 26
so, her hourly payrate is $26 per hour
now, she wants to ask for a raise, to make 51880 annually
well, if we check the difference of 51880 and 49696, that'd leave us with the difference in pay, or the raise annual amount
51880 - 49696 = 2184
ok, so she wants $2184 annually more from her work
how much is that in the hours she works annually? well 2184 ÷ ( 28 * 52)
