Answer:
Step-by-step explanation:
Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.
1) (2-6i)+(4+2i)
open the parenthesis
= 2-6i+4+2i
collect like terms
= 2+4-6i+2i
= 6-4i
2) (6+5i)(9-2i)
= 6(9)-6(2i)+9(5i)-5i(2i)
= 54-12i+45i-10i²
= 54+33i-10i²
In complex number i² = -1
= 54+33i-10(-1)
= 54+33i+10
= 54+10+33i
= 64+33i
3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i
= 2/3-9i*3+9i/3+9i
=2(3+9i)/(3-9i)(3+9i)
= 6+18i/9-27i+27i-81i²
= 6+18i/9-81(-1)
= 6+18i/9+81
= 6+18i/90
= 6/90 + 18i/90
= 1/15+1/5 i
4) For (3 − 5i)(7 − 2i)
open the parenthesis
= 3(7)-3(2i)-7(5i)-5i(-2i)
= 21-6i-35i+10i²
= 21-6i-35i+10(-1)
= 21-41i-10
= 11-41i
Answer: 336cm^3
Step-by-step explanation: First of all. We can combine the two different 4's to make this one shape so it is easier to calculate. We know to get volume it is l * w * h=v. So we just plug in the values. We have 8*3*14. Now just multiply. 8*3*14 = 336
Answer:
x=20
Step-by-step explanation:
Rewrite the equation as
x
/32
=
5/
8
Multiply both sides of the equation by 32
32 ⋅ x /32 = 32 ⋅ 5/8
Simplify both sides of the equation.
Cancel the common factor of
32
Cancel the common factor.
<h3><u>
32·</u> x/<u>32</u> · 5/8
</h3>
Rewrite the expression.
x = 32 ⋅ 5/8
Simplify
32⋅5/8
Cancel the common factor of
8
Factor 8 out of 32
x = 8 ( 4 ) ⋅ 5/8
Cancel the common factor.
Rewrite the expression.
x = 4 ⋅ 5
Multiply 4 by 5
Answer: a) There are 42% chances that both units will meet their objectives.
b) There are 88% chances that one or the other but not both of the units will be successful.
Step-by-step explanation:
Since we have given that
Probability that the Red unit will successfully meet its objectives = 60% = P(R)
Probability that Blue unit will successfully meet its objectives = 70% = P(B)
Probability that only Red unit will be successful = P(only Red) = 18%
As we know that
Hence, there are 42% chances that both units will meet their objectives.
the probability that one or the other but not both of the units will be successful is given by
Hence, there are 88% chances that one or the other but not both of the units will be successful.
Yes, James is correct.
Think of a pizza. If there are 5 slices and you have all 5 of them, then you have the whole pizza.
Now, instead of the pizza having 5 slices, it now has 10. Since the pizza is still the same size, the pieces are going to smaller. If you have 9 slices out of the 10, you won't have the whole pizza.
This is why 5/5 is greater than 9/10.
