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3 years ago

How do I solve this?

Mathematics

1 answer:

maksim [4K]3 years ago

4 0

Answer:

Answer A represents this

x <= -3 ; x > 9

Step-by-step explanation:

Isolate x on each of the inequalities:

4 x + 4 <= - 8

subtract 4 from both sides

4 x <= - 12

divide both sides by 4 to isolate x completely (notice 4 is positive, so there is NO flipping of the inequality symbol)

x <= -3

This inequality is represented by shading the left section of the number line starting at x = -3 (make sure you draw a SOLID dot to mae clear that the point x = -3 is also included in your drawing.

The other inequality:

11 x - 11 > 88

add 11 to both sides

11 x > 99

divide both sides by 11 to isolate x (notice again that 11 is a positive number, so the inequality doesn't change with the division)

x > 9

This inequality is represented by shadowing the right hand side of the number line starting at x = 9. Make sure you draw an EMPTY dot on the number 9 to indicate that x = 9 is NOT included.

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Estimate quotient using multiple 53÷3

kolezko [41]

It would be 20 because if you estimate 53 you would get 50 so 50÷3 would be clase to 2 and then add 1 zero and you will get 20 so 20 is your answer. Hope this helped. ☺

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3 years ago

A single card is drawn from a deck of 52 cards, find the following

aleksandr82 [10.1K]

Answer:

a. 1/13

b. 1/78

c. 1/4

d. 1/12

e. 1/6

f. 1/4

Step-by-step explanation:

First, lets write some basic data

There are total 52 cards.
26 cards are red and 26 cards are black
Out of 26 red cards; 13 cards are of diamond and 13 cards are of heart
Out of 26 black cards; 13 cards are of spade and 13 cards are of clubs
In spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jack

a. result is a queen

Each set has one queen; 1 of spade, 1 of clubs, 1 of heart, 1 of heart

There are total 4 queens

Total number of cards is 52

Probability = Number of favourable outcomes/total number of outcomes

Probability = 4/52

Probability = 1/13

b. result is a queen result is a face card

From my understanding, this question is result is a queen given that result is a face card.

Queen: 4 cards

Face card means King, Queen and Jack

Each set has one King, one Queen and one Jack

There are total 4 sets

Therefore, there are 4 Kings, 4 Queens and 4 Jacks

Face cards: 12-4 (because 4 queens have already been taken out) = 8

Total number of cards: 52-4 (because 4 queens have already been taken out) = 48

Probability (A|B) = P(A) * P(A|B)

P(A) = result is a queen = 4/52 = 1/13

P(A|B) = result is a face card = 8/48 = 1/6

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/13 * 1/6

Probability (A|B) = 1/78 or 0.01282

c. result is a heart

Out of the 52 cards, there are 26 red cards and out of the 26 red cards, there are 13 cards of heart

Heart = 13 cards

Total number of cards = 52 cards

Probability = Number of favourable outcomes/total number of outcomes

Probability = 13/52

Probability = 1/4

d. result is a heart | result is a red card

Result is a heart = P(A) = 13/52 = 1/4

Result is a red card=26/52 Total number of red cards is 26 but 13 cards (heart) are already taken out so 13 will be subtracted from the numerator and denominator

= 13/39 = 1/3

Result is a heart given that result is a red card P(A|B) = 1/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1/3

Probability (A|B) = 1/12

e. result is a heart result is a black card

Result is a heart = P(A) = 13/52 = 1/4

Result is a black card=26/52 Total number of cards is 52 but 13 cards (heart) are already taken out so 13 will be subtracted from the denominator

= 26/39 = 2/3

Result is a heart given that result is a black card P(A|B) = 2/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 2/3 = 1/6

f. result is a heart result is not a diamond

Result is a heart = P(A) = 13/52 = 1/4

Result is not a diamond = there are 13 diamonds in a deck so cards that are not diamond are 52-13 = 39

Total cards = 52 - 13 (because hearts are already taken out) = 39

= 39/39 = 1

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1 = 1/4

4 0

3 years ago

is it possible to store a 20 foot long pipe in a rectangular room that is 10 feet by 12 feet by 8 feet?

Anastaziya [24]

First we'll consider the floor size.
In a 10 by 12 room the longest pipe that will fit lying on the floor equals the hypotenuse of a 10 by 12 triangle:
hypotenuse² = 10² + 12²
hypotenuse² = 100 + 144
hypotenuse² = 244
hypotenuse = 15.62 feet

Now we have to consider the third dimension (height = 8 feet).
The two sides would be 15.62 and 8
hypotenuse² = 15.62² + 8²
hypotenuse² = 244 + 64 = 308
hypotenuse = 17.55
So, the longest pipe that would fit in that room would be 17.55 feet long.

7 0

3 years ago

Read 2 more answers

If 25 is subtracted from the square of a positive integer, the result is 200. Find the positive

yulyashka [42]

Answer:

150

Step-by-step explanation:

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2 years ago

Find a unit vector that is orthogonal to both i + j and i + k.

kenny6666 [7]

Answer: i - j - k

Step-by-step explanation:

Taking the cross product between two vectors will give you a third vector that is orthogonal(perpendicular) to both vectors.

<1,1,0> x <1,0,1>

$det(\left[\begin{array}{ccc}i&j&k\\1&1&0\\1&0&1\end{array}\right] )$

the determinate of the matrix: <1,-(1),-1>

or: i - j - k

3 0

3 years ago