Ask question

Ask question

All categories

4 years ago

13

A wallet contains five $10 bills, three $5 bills, six $1 bills, and no larger denominations. If bills are randomly selected one-

by-one from the wallet, what is the probability that at least two bills must be selected to obtain the first $10 bill?

1 answer:

Black_prince [1.1K]4 years ago

6 0

Answer:

$\frac{4}{21}$

Step-by-step explanation:

Another way of phrasing this question is this; if only two bills are selected without replacement, what is the probability that at one of the two bills will be a $10 bill:

P(One $10 bill) = P(picking a $10 bill first then another type) + (picking another

type then a $10 bill)

= $\frac{5}{15}*\frac{10}{14}+\frac{10}{15} *\frac{5}{14} = \frac{4}{21}$

You might be interested in

You eam (4x + 12) points after completing x levels of a video game and

EastWind [94]

Answer: (4x+12) - (2x-5)

Step-by-step explanation: The (4x+12) is positive and the (2x-5) is negative.

5 0

3 years ago

Find all possible values of α+

const2013 [10]

Answer:

$\rm\displaystyle 0,\pm\pi$

Step-by-step explanation:

please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation

===========================

we want to find all possible values of α+β+γ when <u>tanα+tanβ+tanγ = tanαtanβtanγ</u><u> </u>to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma )$

factor out tanγ:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)$

divide both sides by tanαtanβ-1 and that yields:

$\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}$

multiply both numerator and denominator by-1 which yields:

$\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)$

recall angle sum indentity of tan:

$\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta )$

let α+β be t and transform:

$\rm\displaystyle \tan( \gamma ) = - \tan( t)$

remember that tan(t)=tan(t±kπ) so

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi )$

therefore <u>when</u><u> </u><u>k </u><u>is </u><u>1</u> we obtain:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi )$

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi )$

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

$\rm\displaystyle \gamma = - \alpha - \beta \pm \pi$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }$

<u>when</u><u> </u><u>i</u><u>s</u><u> </u><u>0</u>:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 )$

likewise by Opposite Angle Identity we obtain:

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 )$

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

$\rm\displaystyle \gamma = - \alpha - \beta \pm 0$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }$

and we're done!

8 0

3 years ago

Read 2 more answers

In the figure below, ∠ABC ≅ ∠DEC and ∠GFE ≅ ∠DCE. Point C is the point of intersection between segment AG and segment BD, while

I am Lyosha [343]

Answer:

See Below.

Step-by-step explanation:

We are given that:

$\angle ABC \cong \angle DEC\text{ and } \angle GFE \cong \angle DCE$

By vertical angles:

$\displaystyle \angle DEC\cong \angle GEF\text{ and } \angle DCE\cong \angle ACB$

Hence, by substitution:

$\displaystyle \angle ABC\cong \angle GEF\text{ and } \angle GFE\cong \angle ACB$

Then by Angle-Angle Similarity:

$\Delta ABC \sim \Delta GEF$

8 0

3 years ago

Math Help PLZ!!!!!!!!!

VMariaS [17]

Answer: C

<u>Step-by-step explanation:</u>

f(x) = 2x + 1 ⇒ 2x + 1

<u>- g(x) = -(x² - 7) </u>⇒ <u>-x² + 7 </u>

(f-g)(x) = -x² + 2x + 8

4 0

3 years ago

Which graph represents a reflection across the x-axis of g(x) = 3/4(3)x?

Basile [38]

Answer: B the arrow should be pointing to the negative side

Step-by-step explanation:

6 0

3 years ago