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3 years ago

What is the distance between points A(3, 8) and B(-3, 4)?

Mathematics

1 answer:

max2010maxim [7]3 years ago

8 0

Answer:

About 7.2 OR (7.211102551)

Step-by-step explanation:

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Determine which of the lines, if any, are parallel or perpendicular. Explain.

jonny [76]

Line A. line B. line C. it’s A

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3 years ago

What term refers slope

Serga [27]

In y = mx+b, m is the term that refers to slope

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3 years ago

Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Nastasia [14]

Answer:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

Step-by-step explanation:

Given

$9 < x < 10$ --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

$v = x^3$

For a uniform distribution, we have:

$x \to U(a,b)$

and

$f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.$

$9 < x < 10$ implies that:

$(a,b) = (9,10)$

So, we have:

$f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Solve

$f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Recall that:

$v = x^3$

Make x the subject

$x = v^\frac{1}{3}$

So, the cumulative density is:

$F(x) = P(x < v^\frac{1}{3})$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$ becomes

$f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.$

The CDF is:

$F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx$

Integrate

$F(x) = [v]\limits^{v^\frac{1}{3}}_9$

Expand

$F(x) = v^\frac{1}{3} - 9$

The density function of the volume F(v) is:

$F(v) = F'(x)$

Differentiate F(x) to give:

$F(x) = v^\frac{1}{3} - 9$

$F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}$

$F'(x) = \frac{1}{3}v^{-\frac{2}{3}}$

$F(v) = \frac{1}{3}v^{-\frac{2}{3}}$

So:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

8 0

3 years ago

Katie is playing a game using a 26-card deck that contains the black suits of the cards, which are 13 clubs and 13 spades. She c

Vladimir [108]

Answer:

The probability that Katie will draw a face card on her next turn is 3/13, or approximately 23%.

Step-by-step explanation:

In a regular deck, there are four suits (clubs, spades, hearts and diamonds). Each suit has 13 cards that go from 2 - 10 plus the Ace, King, Queen and Jack. Since Katie is playing using a 26-card deck of only two suits, then there are only two kings, two queens and two jacks in the entire deck. In order to find probability, we form a fraction where the denominator is the total number of outcomes, in this case 26, and the numerator is the number of desired outcomes, in this case the total number of face cards in the deck - 6. So, the probability that Katie will choose a face card on the next turn is 6/26, which simplifies to 3/13 in lowest terms.

4 0

3 years ago

Read 2 more answers

What is 24.2% of 120

katen-ka-za [31]

Answer:

29.04

Step-by-step explanation:

Multiply: 120*.242=29.04

It's multiplied by .242 bc if you want to turn a percentage into a decimal you need to move the decimal twice to the left. So, 24.2 becomes .242.

3 0

3 years ago