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2 years ago

The Venn diagram shows all of the elements in sets A, B and ξ. Find the elements in (A ∩ B) U (A U B)’

1 answer:

8 0

This is impossible to answer without knowing what the sets A and B contain (and what ξ even refers to - universal set?).

However, we have

(A U B)' = A' ∩ B'

so that

(A ∩ B) U (A U B)' = (A ∩ B) U (A' ∩ B') = (A U A') ∩ (B U B')

If ξ is indeed the universal set, then both A U A' = ξ and B U B' = ξ, so we end up with ξ ∩ ξ = ξ.

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Sarah would like to make a 6 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of a mixture that is 80%

ivolga24 [154]

Answer:

a. The system of equations that models the situation is....

$0.80x+0.50y=3.60\\\\ 0.20x+0.50y=2.40$

b. The solution to the system: x = 2 and y = 4

The amount of 80/20 mixture is 2 pounds and the amount of 50/50 mixture is 4 pounds.

Step-by-step explanation:

Suppose, the amount of 80/20 mixture is $x$ pounds and the amount of 50/50 mixture is $y$ pounds.

So, the amount of peanuts in 80/20 mixture $= 0.80x$ pound and the amount of almonds in 80/20 mixture $=0.20x$ pound.

And the amount of peanuts in 50/50 mixture $=0.50y$ pound and the amount of almonds in 50/50 mixture $=0.50y$ pound.

Now, Sarah would like to make a 6 pounds nut mixture that is 60% peanuts and 40% almonds.

So, the amount of peanuts in that mixture $=(6\times 0.60)=3.60$ pounds

and the amount of almonds in that mixture $=(6 \times 0.40)= 2.40$ pounds.

So, the system of equations will be.........

$0.80x+0.50y=3.60 ...................(1)\\\\ 0.20x+0.50y=2.40...................(2)$

Subtracting equation (2) from equation (1), we will get.....

$(0.80x+0.50y)-(0.20x+0.50y)=3.60-2.40\\ \\ 0.60x=1.20\\ \\ x= \frac{1.20}{0.60}=2$

Now, plugging this $x=2$ into equation (1), we will get......

$0.80(2)+0.50y=3.60\\ \\ 1.60+0.50y=3.60\\ \\ 0.50y=3.60-1.60=2\\ \\ y=\frac{2}{0.50}=4$

So, the amount of 80/20 mixture is 2 pounds and the amount of 50/50 mixture is 4 pounds.

7 0

3 years ago

Help me out pleaseeee

gladu [14]

4x - y = 5 --> 4x = y + 5

substitute

4x + 4y = -4

(y + 5) + 4y = -4

5y + 5 = -4

5y = -9

y = -1.8

solve x

4x = y + 5 = -1.8 + 5 = 3.2

x = 3.2/4 = 0.8

6 0

2 years ago

The function f(x) = 4(4)x represents the growth of a fly population every year in a remote swamp. Jackie wants to manipulate the

otez555 [7]

Around the rate would be 0.10

4 0

2 years ago

Read 2 more answers

On a given day, 36 of the 445 students in a school were absent. What was the appproximate absentee rate that day?

Nata [24]

Answer: The approximate absentee rate that day would be 8.09%.

Step-by-step explanation:

Since we have given that

Number of students who were absent = 36

Total number of students = 445

We need to find the approximate absentee rate that day :

Rate of absentee of that day would be

$\dfrac{\text{Number of absentee}}{\text{Total number of students}}\times 100\\\\=\dfrac{36}{445}\times 100\\\\=8.09\%$

Hence, the approximate absentee rate that day would be 8.09%.

5 0

2 years ago

I need some help with this two.

andrey2020 [161]

Answer: a = 2168 miles

b= $3360.40

Hope this helps!

6 0

2 years ago

Read 2 more answers