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3 years ago

The container that holds the water for the football team is

Mathematics

1 answer:

Rom4ik [11]3 years ago

3 0

Answer:

30 Gallons

Step-by-step explanation:

Okay so you need to start by making an equation for yourself. Since the container starts at 1/10 of the total, you want to start by saying 1/10x. Then you add 12 gallons of water to make it half full. So 1/10x + 12 = 1/2x where x is the total amount that can fit in the container.

1/10x + 12 = 1/2x (Move your x's to the same side.)

12 = 1/2x - 1/10x (Find a common denominator.)

12 = 5/10x - 1/10x (Simplify/)

12 = 4/10x (Multiply both sides by 10; your demoninator)

120 = 4x (Divide)

x = 30

Your container holds 30 gallons.

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Find the number of elements in A 1 ∪ A 2 ∪ A 3 if there are 200 elements in A 1 , 1000 in A 2 , and 5, 000 in A 3 if (a) A 1 ⊆ A

lina2011 [118]

Answer:

a. 4600

b. 6200

c. 6193

Step-by-step explanation:

Let $n(A)$ the number of elements in A.

Remember, the number of elements in $A_1 \cup A_2 \cup A_3$ satisfies

$n(A_1 \cup A_2 \cup A_3)=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)$

Then,

a) If $A_1\subseteq A_2, n(A_1 \cap A_2)=n(A_1)=200$ , and if $A_2\subseteq A_3, n(A_2\cap A_3)=n(A_2)=1000$

Since $A_1\subseteq A_2\; and \; A_2\subseteq A_3, \; then \; A_1\cap A_2 \cap A_3= A_1$

$n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-200-200-1000-200=4600$

b) Since the sets are pairwise disjoint

$n(A_1 \cup A_2 \cup A_3)=\\n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\200+1000+5000-0-0-0-0=6200$

c) Since there are two elements in common to each pair of sets and one element in all three sets, then

$n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-2-2-2-1=6193$

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2 years ago

Which of the following statements are true about the graph of f(x) = 6(x + 1)2 -9?

Sphinxa [80]

Answer:

Step-by-step explanation:

a. The vertex is (1, -9). False. The vertex is (-1, -9).

b. The graph opens upward. True. That coefficient '6' is positive.

c. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units. False. It's DOWN 9 units.

d. The graph is steeper than the graph of f(x) = x^2. True. The given function increases 6 times faster than does x^2.

e. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.

Let's put f(x) = 6(x + 1)^2 -9 into standard form. Expanding the first term, we get f(x) = 6(x^2 + 2x + 1) - 9, or f(x) = 6x^2 + 12x + 6 - 9. YES, TRUE

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2 years ago

Convert 7500cm to meters

olya-2409 [2.1K]

Answer: 75 meters

Step-by-step explanation: In this problem, we're asked to convert 7,500 centimeters into meters which means we use the conversion factor for centimeters and meters.

Conversion factor ⇒ <em>100 centimeters = 1 meter</em>

Next, notice that we're converting from a smaller unit "centimeters" to a larger unit "meters" and when we convert from a smaller unit to a larger unit we divide by the conversion factor.

So we divide 7,500 by the conversion factor which is 100.

7,500 ÷ 100 = 75

Therefore, 7,500 centimeters = 75 meters.

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Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper. The per

Fantom [35]

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3 years ago

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