If x2 = 30, what is the value of x?

Suppose that 3 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 3 are diamonds?

Marat540 [252]

There are 13 diamonds in the deck, so $\dbinom{13}3$ ways of drawing 3 diamonds.

There is a total of $\dbinom{52}3$ ways of drawing any 3 cards from the deck.

So the probability of drawing 3 diamonds is

$\dfrac{\binom{13}3}{\binom{52}3}=\dfrac{11}{850}\approx0.012941$

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

5 0

3 years ago

The period 7 (in seconds) of a pendulum is given by T = 2pi√( L divided by 32) where L stands for the length (in feet) of the pe

oksano4ka [1.4K]

Answer:

128 feet

Step-by-step explanation:

$t = 2\pi \sqrt{\frac{l}{32} }$

So now we will substitute the values of T and π into the equation.

$12.56 = 2 \times 3.14 \sqrt{ \frac{l}{32} }$

$12.56 = 6.28 \sqrt{ \frac{l}{32} }$

Divide both sides by 6.28

$2 = \sqrt{ \frac{l}{32} }$

Square both sides.

$4 = \frac{l}{32}$

Multiply both sides by 32

$l = 4 \times 32 \\ l = 128 \: feets$

5 0

1 year ago

Fraction less than 1/2

fiasKO [112]

1/4 is the answer is is a lower fraction

8 0

3 years ago

Read 2 more answers

Is the mean age at which American children learn to walk less than 15 months? A study of 40 American children found a mean walki

Sonbull [250]

Answer:

We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.

Null hypothesis: $\mu \geq 15$

Alternative hypothesis: $\mu$

And for this case the best answer would be:

H 0 : μ ≥ 15 vs. Ha : μ < 15

Step-by-step explanation:

We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.

Null hypothesis: $\mu \geq 15$

Alternative hypothesis: $\mu$

And for this case the best answer would be:

H 0 : μ ≥ 15 vs. Ha : μ < 15

And the data given from the sample is:

$\bar X = 13.2$ represent the sample mean

$\sigma$ represent the population deviation

$n = 40$ represent the sample size

And the statistic would be given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

8 0

4 years ago

4x-y=20 and -2x-2y=10

lara31 [8.8K]

You can use Substitution to solve this problem:

4x-y=20

-y=-4x+20

y=4x-20

Now you have two equations, and you use the first one to substitute into the second one.

y=4x-20 and -2x-2y=10

-2x-2(4x-20)=10

-2x-8x+40=10

-10x+40=10

-10x=-30

-x=-3

x=3

Now that we have figured out what x is, we can substitute x in to one of the equations to figure out y.

4x-y=20 x=3

4(3)-y=20

12-y=20

-y=8

y=-8

<em><u>So your answer would be x=3 and y=-8</u></em>

6 0

3 years ago