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3 years ago

Of 15 possible books, you plan to take 6 with you on vacation. How many different collections of 6 books can you take?

Mathematics

1 answer:

Mekhanik [1.2K]3 years ago

6 0

Answer:

5005

Step-by-step explanation:

6 C 15

(6, 15)

15! / (6! x 9!)

The answer is 5005

C is just a way to say the order the books are picked in is random and ! means factorial. Factorial is when you multiply all the previous numbers up to the number it is. For example, 5! = 1 x 2 x 3 x 4 x 5 and 2! = 1 x 2

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If two objects travel through space along two different curves, it’s often important to know whether they will collide. (Will a

galina1969 [7]

Answer:

Both objects collide at t=3 in the point <9,9,9>

Step-by-step explanation:

Collision Of Moving Objects

Two objects can describe different trajectories in the space. Those trajectories can intersect in one or more points but it doesn't mean they collide. Collision occurs if they are in the same position at the same time. If we know the positions as a function of time of each object, we could try so find if, for a given time, they are in the same position.

The positions of two object are given as

$r1(t)=$

$r2(t)=$

Let's find out if there is at least one value of t that makes both positions to be the same. We can try by equating one of the three coordinates and testing if the value of t make both have the same x,y,z coordinate. Let's try equating the x-components of both

$t^2=4t-3$

Rearranging

$t^2-4t+3=0$

Factoring

$(t-1)(t-3)=0$

We found two solutions

$t=1,\ t=3$

for t=1 the x-coordinates are

$x1=t^2=1$

$x2=4t-3=1$

For t=3

$x1=t^2=9$

$x2=4t-3=9$

Now we'll test both values in the y-coordinates

$y1=7t-12$

$y2=t^2$

For t=1

$y1=-5$

$y2=1$

Thus they don't collide at t=1. Let's try t=3

$y1=7(3)-12=9$

$y2=3^2=9$

Now let's try the z-coordinate for t=3

$z1=t^2=9$

$z2=5t-6=9$

Since the three coordinates match, we can say both objects collide at t=3 in the point <9,9,9>

6 0

3 years ago

5x^{2} -60 = 20 Solve by using the quadratic formula PLZ help

almond37 [142]

Answer: x=4,-4 Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula

3 0

3 years ago

An instructor believes the distribution of scores on her final exam will have mean 62 and standard deviation 7. Fred is a studen

OLga [1]

Answer:

a) $P(47$

And then the probability that Fred will not score between 47 and 77 is

1-0.968 = 0.0321

b) $P(45$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(62,7)$

Where $\mu=62$ and $\sigma=7$

We are interested on this probability on the probability that Fred will not score between 47 and 77. So we can begin finding this probability

$P(47$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(47$

And we can find this probability on this way:

$P(-2.143$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-2.143$

And then the probability that Fred will not score between 47 and 77 is

1-0.968 = 0.0321

Part b

$P(45$

And we can find this probability on this way:

$P(-2.429$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-2.429$

7 0

3 years ago

June 14th Jim Thompson Homework

pogonyaev

Seriously, how do those two images put on brainly? :/

3 0

2 years ago

Read 2 more answers

which set of numbers can represent the side lengths, in centimeters, of a right triangle?a. 8,12,15b. 10,24,26c. 12,20,25d. 15,1

Mama L [17]

Answer:

Step-by-step explanation:

Pythagorean theorem (applicable on right triangles only) says:

$a^{2}+b^{2}=c^{2}$

Where $a$ and $b$ are the two legs of the triangle and $c$ is the length of the hypotenuse [THE LONGEST SIDE].

We can square each leg on the triangle and take the sum, if that is equal to the square of the longest side, we have a right triangle. Let's check for all of these.

$8^{2}+12^{2}\\=64+144\\=208$