Answer:
B ∪ C = (-∞, ∞)
B ∩ C = [1, 7)
Step-by-step explanation:
B ∪ C: The union of two sets or intervals is the set of elements which are in <em>either </em>set.
B ∩ C: The intersection of two sets or intervals is the set of elements which are in <em>both </em>sets.
<u>Interval notation symbols</u>
Square brackets [ ]: both endpoints are included in the set.
Round brackets ( ): both endpoints are excluded in the set.
Round, square ( ]: left endpoint is excluded and right endpoint is included in the set.
Square, round [ ): left endpoint is included and right endpoint is excluded in the set.
Given:
- B = {z | z ≥ 1}
- C = {z | z < 7}
Therefore,
B = [1, ∞)
C = (-∞, 7)
Therefore, B ∪ C = (-∞, ∞)
As z is either less than 7, or equal to or more than 1 then the intersection is:
B ∩ C = {z | 1 ≤ z < 7} = [1, 7)
Answer:
1/2
Step-by-step explanation:
Given:
sinx=-1/2
cosy=√3/2
finding x
x=sin^-1(-1/2)
x=-π/6
x=-30°
finding y
cosy=√3/2
y=cos^-1(√3/2)
y=π/6
y=30°
Now finding cos(x-y)
cos(-π/6-π/6)
=cos(-π/3)
=1/2!
3 + 1/4x = 2.....subtract 3 from both sides
1/4x = 2 - 3
1/4x = -1...multiply both sides by 4, eliminating the 4 on the left side
x = -1 * 4
x = -4
Answer:
The expression for the change received = $20 - 3 J
Step-by-step explanation:
The cost of 1 juice bottle = $3
Let us assume the number of juice bottles bought = J
The amount of bill paid = $20
Now, the cost of J juice bottles = J x ( Coat of 1 juice bottle)
= J x ( $3) = 3J
Now, the Change Returned = $20 bill - The cost of J juice bottles
= $20 - 3 J
or, Change Returned = $20 - 3 J
Hence, the expression for the change received = $20 - 3 J
Answer:
Take each sale price of each product and divide it by its original price. Subtract from 1. Then multiply by 100.
Step-by-step explanation:
A percent is a portion of 100 or the total. We find the percent we pay by taking each sales price and dividing it by the original price. To find the percent off we take that same number and subtract from 1. This will give a decimal which we can convert to a % by multiplying by 100.