Let's start by finding a common denominator for all of these fractions. In this case, we will use 60.
3/4 = 45/60
2/3 = 40/60
3/5 = 36/60
7/10 = 42/60
13/20 = 39/60
The closest to 45/60 is 42/60/ Therefore, 7/10 is the closest to 3/4
Answer:
Solutions are 2, -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
or 2, -1 + 1.58 i and -1 - 1.58i
(where the last 2 are equal to nearest hundredth).
Step-by-step explanation:
The real solution is x = 2:-
x^3 - 8 = 0
x^3 = 8
x = cube root of 8 = 2
Note that a cubic equation must have a total of 3 roots ( real and complex in this case). We can find the 2 complex roots by using the following identity:-
a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Here a = x and b = 2 so we have
(x - 2)(x^2 + 2x + 4) = 0
To find the complex roots we solve x^2 + 2x + 4 = 0:-
Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2
= -1 +/- (sqrt( -10)) / 2
= -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
Answer:
D. 18.68
Step-by-step explanation:
Applying PEMDAS as order of operations.
Solving the exponents first ![[(\frac{2}{5})^2=\frac{4}{25}]](https://tex.z-dn.net/?f=%5B%28%5Cfrac%7B2%7D%7B5%7D%29%5E2%3D%5Cfrac%7B4%7D%7B25%7D%5D)
Multiplying ![[53\times \frac{4}{25}=8.48]](https://tex.z-dn.net/?f=%5B53%5Ctimes%20%5Cfrac%7B4%7D%7B25%7D%3D8.48%5D)
Dividing ![[27\div \frac{5}{3}=16.2]](https://tex.z-dn.net/?f=%5B27%5Cdiv%20%5Cfrac%7B5%7D%7B3%7D%3D16.2%5D)
Adding and subtracting.
Problem Page Question An urn contains black and pink balls. Four balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all balls drawn from the urn are pink? Round your answer to three decimal places.
Answer:
8.66
Step-by-step explanation:
