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uysha [10]
3 years ago
7

Which of the following integers is a solution to the inequality below?

Mathematics
1 answer:
natta225 [31]3 years ago
7 0
I am not sure, but I checked my answer and I am right. Hope this helps, thank you :) !!

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Determine each of the following.
castortr0y [4]

Answer:

(a) \{1,2,3,4,5,6,7,8,9,10\}

(b) 10

(c) \{\}

(d) 0

(e) 1024

Step-by-step explanation:

(a)

A = {x ∈ Z | 0 < x, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

0                ... (1)

x^2\leq 100

Taking square root on both sides.

-\sqrt{100}\leq x\leq \sqrt{100}

-10\leq x\leq 10             .... (2)

Using (1) and (2) we get

0

Since x ∈ Z,

A=\{1,2,3,4,5,6,7,8,9,10\}

(b)

We need to find the value of  | {x ∈ Z | 0 < x, x² ≤ 100}| or |A|. It means have to find the number of elements in set A.

|A|=10

| {x ∈ Z | 0 < x, x² ≤ 100}| = 10

(c)

B = {x ∈ Z | x > 10, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

x>10                ... (3)

x^2\leq 100

It means

-10\leq x\leq 10             .... (4)

Inequality (3) and (4) have no common solution, so B is null set or empty set.

B=\{\}

(d)

We need to find the value of |{x ∈ Z | x > 10, x² ≤ 100}| or |B|. It means have to find the number of elements in set B.

|B|=0

|{x ∈ Z | x > 10, x² ≤ 100}| = 0

(e)

We need to find the value of | P(A) |. P(A) is the power set of set A.

Number of elements of a power set is

N=2^n

where, n is the number of elements of set A.

We know that the number of elements of set is 10. So the value of |P(A)| is

|P(A)|=2^{10}

|P(A)|=1024

Therefore |P(A)|=1024.

7 0
3 years ago
If a = 12 and B = 43 degrees, find c.
ludmilkaskok [199]

Answer:

74

Step-by-step explanation:

You subtract 43 from 12 you get 31 then you add 43 and 31 you get 74 bye

8 0
3 years ago
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Is 100 MG less than 10g
pantera1 [17]
There are 1000 grams in a gram  and 1000 times 10 is 10000 so yes 100 mg is less than a 10g
3 0
3 years ago
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How to multiple decimals by decimals.
puteri [66]

Answer:

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

7 0
2 years ago
Sarah has 24 cups of rice. She puts an equal amount of rice into 5 bowls. Sarah eats 1/7 of a bowl of rice. How many cups of ric
Lelechka [254]
5/17 cups of rice she ate that’s how many
8 0
2 years ago
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