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marshall27 [118]

3 years ago

14

There is a bag filled with 5 blue and 4 red marbles. A marble is taken at random from the bag, the colour is noted and then it i

s replaced. Another marble is taken at random. What is the probability of getting 2 of the same colour?

1 answer:

liberstina [14]3 years ago

5 0

The probability is 60% that you will get the same colour twice because one colour has more marbles that the other coloured marble.

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A long year end status report for work is 136 pages long. You need to print 19 copies for a meeting next week. How much is the p

tatyana61 [14]

Answer:

$19.60

Step-by-step explanation:

Given data

number of pages= 136 pages

number of copies = 19 copies

Hence 19 copies make a total of = 136*19

=2584 pages

hence if 500 pages cost $3.80

then 2584 pages will cost x

cross multiply

500x= 2584*3.8

500x=9819.2

Divide both sides by 500

x= 9819.2/500

x= 19.6384

x=$19.60

It will cost $19.60

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Adrian ordered a blue-denim jacket for $69.75 and 2 sweaters for $55 each. With 7% sales tax and shipping below, how much was hi

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3 years ago

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Using the image, determine the length of each arc.<br> m RC=<br> m CBR =

Montano1993 [528]

<u>Given</u>:

Given that the measure of ∠CDR = 85°

We need to determine the measure of $\widehat{RC}$ and $\widehat{CBR}$

<u>Measure of arc RC:</u>

Since, we know that if a central angle is formed by two radii of the circle then the central angle is equal to the intercepted arc.

Thus, we have;

$m\angle CDR = m \widehat{RC}$

Substituting the values, we get;

$85^{\circ} = m \widehat{RC}$

Thus, the measure of $\widehat{RC}$ is 85°

<u>Measure of arc CBR:</u>

We know that 360° forms a full circle and to determine the measure of arc CBR, let us subtract the values 360 and 85.

Thus, we have;

$m\widehat{CBR}=360^{\circ}-m \widehat{RC}$

Substituting the values, we have;

$m\widehat{CBR}=360^{\circ}-85^{\circ}$

$m\widehat{CBR}=275^{\circ}$

Thus, the measure of $\widehat{CBR}$ is 275°

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Amber and her friend Nathan are saving to buy a video game that costs $65. Amber earns $12 per week for babysitting and spends $

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Answer:65 divided [(12-4)+(15-8)]

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3 years ago

Determine determine whether the following geometric series converges or diverges. if the series converges find its sum.

Lilit [14]

For starters,

$\dfrac{3^k}{4^{k+2}}=\dfrac{3^k}{4^24^k}=\dfrac1{16}\left(\dfrac34\right)^k$

Consider the $n$ th partial sum, denoted by $S_n$ :

$S_n=\dfrac1{16}\left(\dfrac34\right)+\dfrac1{16}\left(\dfrac34\right)^2+\dfrac1{16}\left(\dfrac34\right)^3+\cdots+\dfrac1{16}\left(\dfrac34\right)^n$

Multiply both sides by $\frac34$ :

$\dfrac34S_n=\dfrac1{16}\left(\dfrac34\right)^2+\dfrac1{16}\left(\dfrac34\right)^3+\dfrac1{16}\left(\dfrac34\right)^4+\cdots+\dfrac1{16}\left(\dfrac34\right)^{n+1}$

Subtract $S_n$ from this:

$\dfrac34S_n-S_n=\dfrac1{16}\left(\dfrac34\right)^{n+1}-\dfrac1{16}\left(\dfrac34\right)$

Solve for $S_n$ :

$-\dfrac14S_n=\dfrac3{64}\left(\left(\dfrac34\right)^n-1\right)$

$S_n=\dfrac3{16}\left(1-\left(\dfrac34\right)^n\right)$

Now as $n\to\infty$ , the exponential term will converge to 0, since $r^n\to0$ if $0$ . This leaves us with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{k=1}^n\frac{3^k}{4^{k+2}}=\sum_{k=1}^\infty\frac{3^k}{4^{k+2}}=\frac3{16}$

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3 years ago

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