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2 years ago

For what values of x is the inequality 2/3 + x/3 >1 true?

Mathematics

1 answer:

Travka [436]2 years ago

6 0

Answer:

Step-by-step explanation:

$\frac{2}{3}$ + $\frac{x}{3}$ > 1 ( multiply through by 3 to clear the fractions )

2 + x > 3 ( subtract 2 from both sides )

x > 1

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If you draw four cards at random from a standard deck of 52 cards, what is the probability that all 4 cards have distinct charac

mezya [45]

There are $\binom{52}4$ ways of drawing a 4-card hand, where

$\dbinom nk = \dfrac{n!}{k!(n-k)!}$

is the so-called binomial coefficient.

There are 13 different card values, of which we want the hand to represent 4 values, so there are $\binom{13}4$ ways of meeting this requirement.

For each card value, there are 4 choices of suit, of which we only pick 1, so there are $\binom41$ ways of picking a card of any given value. We draw 4 cards from the deck, so there are $\binom41^4$ possible hands in which each card has a different value.

Then there are $\binom{13}4 \binom41^4$ total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is

$\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761$

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2 years ago

Write an equation in the form y= mx + b to represent the graph.

mixas84 [53]

Y=x-2

..........................
.

5 0

3 years ago

What is the measure of angle X?

Alinara [238K]

Using one of the above equations, you can find the value of x.
tan x = 84/13 => x = tan-¹(84/13)
x = 81.20°

Hope that helps

4 0

3 years ago

Read 2 more answers

A)<br> Identify all x-values not in the domain of<br> y=(x² – 4x²) / (3x² - 6x – 24)

True [87]

Answer:

x ≠ 4 or -2

Step-by-step explanation:

the denominator cannot be zero, so factor the bottom equation to get the zeros and those are the domain restrictions.

3x^2 - 6x - 24 ≠ 0

3(x^2 - 2x - 8) ≠ 0 (factor out a 3)

3(x - 4)(x + 2) ≠ 0 (factor equation)

x ≠ 4, x ≠ -2 (use zero product property to find zeros)

3 0

3 years ago

Jacob distributed a survey to his fellow students asking them how many hours they spent on the Internet in the past day. He also

Anna35 [415]

The linear equation B. y = -x +7.5 best describes the given model. The mood rating for a student that spent 5.5 hours online would be 2.

Step-by-step explanation:

Step 1; We plot the points that fall on the line and that lie on an exact x or y coordinate. The following 4 points are plotted (0.5, 7), (2, 5.5), (2.5, 5) and (3.5, 4). We substitute the values of x in the given equations to see which best describes the model.

Step 2; When y = x + 7.5, we get the coordinates as (0.5, 8), (2, 9.5), (2.5, 10) and (3.5, 11).

When y = -x + 7.5, the coordinates are (0.5, 7), (2, 5.5), (2.5, 5) and (3.5, 4).

When y = $\frac{-1x}{2}$ + 7.5, the coordinates are (0.5, 7.25), (2, 6.5), (2.5, 6.25) and (3.5, 5.75).

So equation 2 has the closest values to the actaul graph.

Step 3; By substituting x = 5.5, y = -(5.5) + 7.5 = 7.5 - 5.5 = 2.

8 0

3 years ago