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3 years ago

8

Diego‘s mother is twice as old as he is. She is also as old as the sum of the ages of Diego and both of his younger twin brother

s. The twins are 11 years old. Find the age of Diego.

1 answer:

Pavel [41]3 years ago

5 0

Diego's age is 22
And his mother's age is 42

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Four times the sum of a number and 15 is at least 120. Find all possible solutions for x

zloy xaker [14]

First translate the English phrase "Four times the sum of a number and 15 is at least 120" into a mathematical inequality.

"Four times..." means we're multiplying something by 4.

"... the sum of a number and 15..." means we're adding an unknown and 15 and then multiplying the result by 4.

"... is at least 120" means when we substitute the unknown for a value, in order for that value to be in the solution set, it can only be less than or equal to 120.

So, the resulting inequality is 4(x + 15) ≤ 120.

Simplify the inequality.

4(x + 15) ≤ 120
4x + 60 ≤ 120 <-- Using the distributive property
4x ≤ 60 <-- Subtract both sides by 60
x ≤ 15 <-- Divide both sides by 4

Now that we have the inequality in a simplified form, we can easily see that in order to be in the solution set, the variable x can be no bigger than 15.

In interval notation it would look something like this:

[15, ∞)

In set builder notation it would look something like this:

{x | x ∈ R, x ≤ 15}

It is read as "the set of all x, such that x is a member of the real numbers and x is less than or equal to 15".

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Identify the terms themselves for the following expression. (separate ur terms with a comma)

Zinaida [17]

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The surface area 5cm x 14cm x 6cm

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A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience i

s344n2d4d5 [400]

Answer:

5.3%

Step-by-step explanation:

The final probability is calculated by means of the quotient of the specific combinations and the total of total combinations

Let's start with the specific ones,

First the number of combinations of 4 of the 30 students getting a spot, i.e .:

A combinations are equal to:

nCx = n! / x! * (n-x)!

Replacing:

30C4 = 30! / (4! * 26!) = 27405

Segundo the number of combinations of the other audience members filling the other 4 (8-4) spots n = 110, 140 - 30

110C4 = 110! / (4! * 106!) = 5773185

Now the total combinations of possible 8 contestants from the audience

140C8 = 140! / (8! * 132!) = 2.98 * 10 ^ 12

Finally, the probability is equal to:

P = (30C4 * 110C4) / 140C8

replacing:

P = 27405 * 5773185 / 2.98 * 10 ^ 12

P = 0.053

Therefore the probability is 5.3%

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Fraction equivalent to 3/12

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