Answer:
She makes $481.92 for a 44 hour week.
Step-by-step explanation:
12.48 * 4 = 49.92
49.92 + 432 = 481.92
A = v/t Multiply both sides by t
A(t) = v Divide both sides by A
t = v / A
Answer: 9.3 × ![10^{7}](https://tex.z-dn.net/?f=10%5E%7B7%7D)
Step-by-step explanation: To write a number in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point.
In this case, we can write 93,000,000 as 9.3000000 and notice that there is only one digit to the left of the decimal point.
Next, we count the number of places the decimal point would need to move to get back to the original number which is 93,000,000.
Since we will need to move the decimal point seven places to the left, we have an exponent of positive 7. Our exponent will be positive because we need to move the decimal point seven places to the right. Now, we can write our number in scientific notation.
9.3 × ![10^{7}](https://tex.z-dn.net/?f=10%5E%7B7%7D)
Answer:
sqrt(73) = 8.54 feet.
Step-by-step explanation:
Remark
My guess is without the legs.
The person bringing it in will not be able to get a table in that is longer than the hypotenuse of a right triangle.
Givens
a = 8
b = 3
c = ??
Formula
a^2 + b^2 = c^2
Solution
8^2 + 3^2= c^2
64 + 9 = c^2
c^2 = 73
c = sqrt(73)
c = 8.54
The table can be no longer than 8 feet 5 inches about.
Notice that
(1 - <em>x</em>)⁵ (1 + 1/<em>x</em>)⁵ = ((1 - <em>x</em>) (1 + 1/<em>x</em>))⁵ = (1 - <em>x</em> + 1/<em>x</em> - 1)⁵ = (1/<em>x</em> - <em>x</em>)⁵
Recall the binomial theorem:
![\displaystyle(a+b)^n = \sum_{k=0}^n\binom nk a^{n-k}b^k](https://tex.z-dn.net/?f=%5Cdisplaystyle%28a%2Bb%29%5En%20%3D%20%5Csum_%7Bk%3D0%7D%5En%5Cbinom%20nk%20a%5E%7Bn-k%7Db%5Ek)
Let <em>a</em> = 1/<em>x</em>, <em>b</em> = -<em>x</em>, and <em>n</em> = 5. Then
![\displaystyle\left(\frac1x-x\right)^5 = \sum_{k=0}^5\binom5k\left(\frac1x\right)^{5-k}(-x)^k = \sum_{k=0}^5 (-1)^k\binom5k x^{2k-5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cleft%28%5Cfrac1x-x%5Cright%29%5E5%20%3D%20%5Csum_%7Bk%3D0%7D%5E5%5Cbinom5k%5Cleft%28%5Cfrac1x%5Cright%29%5E%7B5-k%7D%28-x%29%5Ek%20%3D%20%5Csum_%7Bk%3D0%7D%5E5%20%28-1%29%5Ek%5Cbinom5k%20x%5E%7B2k-5%7D)
We get an <em>x</em> ³ term for
2<em>k</em> - 5 = 3 ==> 2<em>k</em> = 8 ==> <em>k</em> = 4
so that the coefficient would be
![(-1)^4\dbinom54 = \boxed{5}](https://tex.z-dn.net/?f=%28-1%29%5E4%5Cdbinom54%20%3D%20%5Cboxed%7B5%7D)