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Free_Kalibri [48]

4 years ago

5

How many five-card hands (drawn from a standard deck) contain exactly three fives? (A five-card hand is any set of five differen

t cards.)

1 answer:

VashaNatasha [74]4 years ago

4 0

Answer:

4512.

Step-by-step explanation:

We are asked to find the number of five-card hands (drawn from a standard deck) that contain exactly three fives.

The number of ways, in which 3 fives can be picked out of 4 available fives would be 4C3. The number of ways in which 2 non-five cards can be picked out of the 48 available non-five cards would be 48C2.

$4C3=\frac{4!}{3!(4-3)!}=\frac{4*3!}{3!*1}=4$

$48C2=\frac{48!}{2!(48-2)!}=\frac{48*47*46!}{2*1*46!}=24*47=1128$

We can choose exactly three fives from five-card hands in $4C3*48C3$ ways.

$4C3*48C3=4*1128=4512$

Therefore, 4512 five card hands contain exactly three fives.

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1) A TV is on sale for 20% off. If the sale price is $700, what is the original

barxatty [35]

Answer:

140

Step-by-step explanation:

20% of 700

so 20/100 * 700

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140

4 0

4 years ago

Find the values of y = c(x) = for x = 0, 0.008, 0.027, 0.064, 0.125, 0.216, 0.343, 0.512, , 0.729, and 1.

kondaur [170]

c(x) is a function, then we will solve the problem for two different functions.

1. If $c(x)=\frac{x}{0.5}+x$

Then

$y=c(x)$

$y=\frac{x}{0.5}+x$

Using each of the values for x we have.

When x=0 the result is: $y=\frac{0}{0.5}+0=0$

When x=0.008 the result is: $y=\frac{0.008}{0.5}+0.008=0.016+0.008=0.024$

When x=0.027 the result is: $y=\frac{0.027}{0.5}+0.027=0.054+0.027=0.081$

When x=0.064 the result is: $y=\frac{0.064}{0.5}+0.064=0.128+0.064=0.192$

When x=0.125 the result is: $y=\frac{0.125}{0.5}+0.125=0.25+0.125=0.375$

When x=0.216 the result is: $y=\frac{0.216}{0.5}+0.216=0.432+0.216=0.648$

When x=0.343 the result is: $y=\frac{0.343}{0.5}+0.343=0.686+0.343=1.029$

When x=0.512 the result is: $y=\frac{0.512}{0.5}+0.512=1.024+0.512=1.536$

When x=0.729 the result is: $y=\frac{0.729}{0.5}+0.729=1.458+0.729=2.187$

When x=1 the result is: $y=\frac{1}{0.5}+1=2+1=3$

2. If $c(x)=sin(x)+2x$

Then

$y=c(x)$

$y=sin(x)+2x$

Using each of the values for x we have.

When x=0 the result is: $y=sin(0)+2(0)=0$

When x=0.008 the result is: $y=sin(0.008)+2(0.008)=0.000139+0.016=0.016139$

When x=0.027 the result is: $y=sin(0.027)+2(0.027)=0.000471+0.054=0.054471$

When x=0.064 the result is: $y=sin(0.064)+2(0.064)=0.001117+0.128=0.129117$

When x=0.125 the result is: $y=sin(0.125)+2(0.125)=0.002182+0.25=0.252182$

When x=0.216 the result is: $y=sin(0.216)+2(0.216)=0.003769+0.432=0.435769$

When x=0.343 the result is: $y=sin(0.343)+2(0.343)=0.005986+0.686=0.691986$

When x=0.512 the result is: $y=sin(0.512)+2(0.512)=0.008936+1.024=1.032936$

When x=0.729 the result is: $y=sin(0.729)+2(0.729)=0.012723+1.458=1.470723$

When x=1 the result is: $y=sin(1)+2(1)=0.017452+2=2.017452$

7 0

3 years ago

8 what place value is the 8 on

Vika [28.1K]

Ones place. (I would appreciate if you vote brainiest answer)

3 0

4 years ago

P ( rolling a 5 or rolling a 4 ) on a die or fair number cube. Find the probability of these mutually exclusive events.

pentagon [3]

Answer: I believe it the probability of this would be 1/3.

Step-by-step explanation: This is mainly because if the chances of rolling a 5 or a 4 on a die or fair numbered cube, which contains 6 sides, then landing on 5 or 4 would be 2 out of the six chances it would land on those two numbers. Hope this helps!

3 0

3 years ago

A random sample of 56 lithium batteries has a mean life of 645 hours with a population standard deviation of 31 hours. Compute t

bearhunter [10]

Answer: A. (636.9, 653.1)

Step-by-step explanation:

Given : Sample size : n=56

Significance level : $\alpha: 1-0.95=0.05$

Critical value : $z_{0.05}=1.96$

Sample mean : $\overline{x}=645\text{ hours}$

Standard deviation : $\sigma= 31\text{ hours}$

The 95% confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=645\pm (1.96)\dfrac{31}{\sqrt{56}}\\\\=645\pm8.1\\\\=(636.9, 653.1)$

Hence, 95% confidence interval for population mean is (636.9, 653.1).

8 0

3 years ago