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2 years ago

The square root of 8?

Mathematics

1 answer:

Hoochie [10]2 years ago

8 0

Answer:

√8 8n sure form= √ 4 ×√2

= 2×√2

= 2√2

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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

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

8 0

2 years ago

Mallory puts $1.00 in a jar. The following week, she puts 2 times that original amount in the jar. For each of the next six week

Burka [1]

The relationship of the ordered pair that represents Mallory savings is a nonlinear relationship.

Let x represents the number of weeks, and y represents the amount put in the jar, each week.

So, we have the following highlights for 6 weeks.

Week 1: (1, 1)
Week 2: (2,2)
Week 3: (3,4)
Week 4: (4,8)
Week 5: (5,16)
Week 6: (6,32)

The ordered pairs can then be represented as:

$(x,y) = (1,1)(2,2)(3,4)(4,8)(5,16)(6,32)$

As the x values increase, the y values increase too, but the y values do not increase at a constant rate.

This means that the relationship is not linear; it is an exponential relationship.

Hence, the relationship is a nonlinear relationship.

Read more about linear relationships at:

brainly.com/question/7040405

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2 years ago

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Write a number that has a zero in the tens place. Draw a quick picture for your number

natali 33 [55]

400 hope that helped

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3 years ago

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Work out m and c for the line: y = 1 − 3 x

wolverine [178]

Answer:

m=-3

c=1

Step-by-step explanation:

y=mx+c

m is -3 which is the coefficient of x and c is the intercept 1

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2 years ago

Deanna was solving the following equation, 5(x + 2) - 4 = 16.

zaharov [31]

Answer:

Add 4 to each side

Step-by-step explanation:

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3 years ago