Expand and simplify (2+3i)(4-I)

Answers

Answer 1

Answer: $(2+3i)(4-i)=\n8-2i+12i+3=\n11+10i$

Answer 2

Answer: (2 + 3i)(4 - i)
8 - 2i + 12i - 3i²
8 + 10i - 3(-1)
8 + 10i + 3
8 + 3 + 10i
11 + 10i

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(a2 - b)3 Evaluate the expression if a = -2 and b = 5.

Answers

Answer: -1

Step-by-step explanation: I took the quiz

Answer:

B) -27

Step-by-step explanation:

(-2^(2)-5)3

The distribution of heights for adult men in a certain population is approximately normal with mean 70 inches and standard deviation 4 inches. Which of the following represents the middle 80 percent of the heights ? A. 2.5% B. 5% C. 16% D. 1%

Answers

The interval that represent the middle 80% of the heights (inches) is [64.88, 75.12].

Step-by-step explanation:

Given :

Mean -- $\rm \mu = 70 \; inches$

Standard Deviation -- $\rm \sigma = 4 \; inches$

Calculation :

We want to know an interval in which the probability that a height falls there is 0.8.

In such interval, the probability that a value is higher than the right end of the interval is

$\rm P(x>z) = \frac {1-0.8}{2} = 0.1$

If x is the distribuition of heights, then we want y such that P(x > y) = 0.1.

$Z = (x-\mu)/(\sigma)$

Now, let

$U = (y-70)/(4)$

We have

$\rm 0.1 = P(x>y)= P((x-70)/(4) > (y-70)/(4))=P(Z>U)=1-\phi(U)$

$\phi (U) = 1-0.1=0.9$

by looking at the table, we find that U = 1.28, therefore

$(y-70)/(4)=1.28$

$1.28* 4 + 70 = y$

$y=75.12$

The other end of the interval is the symmetrical of 75.12 respect to 70, hence it is

70- (75.12-70) = 64.88.

The interval that represent the middle 80% of the heights (inches) is [64.88, 75.12].

For more information, refer the link given below

brainly.com/question/10729938?referrer=searchResults

Answer:

The interval (meassured in Inches) that represent the middle 80% of the heights is [64.88, 75.12]

Step-by-step explanation:

I beleive those options corresponds to another question, i will ignore them. We want to know an interval in which the probability that a height falls there is 0.8.

In such interval, the probability that a value is higher than the right end of the interval is (1-0.8)/2 = 0.1

If X is the distribuition of heights, then we want z such that P(X > z) = 0.1. We will take W, the standarization of X, wth distribution N(0,1)

$W = (X-\mu)/(\sigma) = (X-70)/(4)$

The values of the cumulative distribution function of W, denoted by $\phi$ , can be found in the attached file. Lets call $y = (z-70)/(4)$ . We have

$0.1 = P(X > z) = P((X-70)/(4) > (z-70)/(4)) = P(W > y) = 1-\phi(y)$

Thus

$\phi(y) = 1-0.1 = 0.9$

by looking at the table, we find that y = 1.28, therefore

$(z-70)/(4) = 1.28\nz = 1.28*4+70 = 75.12$

The other end of the interval is the symmetrical of 75.12 respect to 70, hence it is 70- (75.12-70) = 64.88.

The interval (meassured in Inches) that represent the middle 80% of the heights is [64.88, 75.12] .

How do i factor the quadratic expression 4x^2-11x=3

Answers

4x² - 11x = 3
4x² - 11x - 3 = 0
4x² -12x + x - 3 = 0
4x (x - 3) + 1(x - 3) = 0
(x - 3) (4x + 1) = 0
Using zero product property,
Either,
x - 3 = 0
x = 3
Or,
4x + 1 = 0
4x = -1
x = -1/4

$4 x^(2) -11x-3=0$
(4x+1)(x-3)=0
We can solve for x by setting each parentheses equal to 0
x= -1/4
x= 3

How do I get the original price if after you discount by 5% the new price is 57