All categories

2 years ago

Evan randomly selects 30 marbles from a bag. His data is given in the table.

Mathematics

1 answer:

Igoryamba2 years ago

3 0

The probability of selecting a yellow marble is #of yellow marbles/total # of marbles= 6/30 or .2 or 20%

If there are 300 marbles in the bag, a good estimate for the total number of red marbles in the bag is 90.

9/30=.3 = the percentage of red marbles
.3(300) = 90

You might be interested in

Test for convergence

Elan Coil [88]

You've established that

$\displaystyle\sum_{n\ge1}\frac1{2^n}\le\int_1^\infty\frac{\mathrm dx}{2^x}$

so all you need to do is compute the integral. Rewrite the integrand as

$\dfrac1{2^x}=2^{-x}=e^{\ln2^{-x}}=e^{-x\ln2}$

and replace $y=-x\ln2$ , so that $\mathrm dy=-\ln2\,\mathrm dx$ . Then

$\displaystyle\int_{x=1}^{x\to\infty}\frac{\mathrm dx}{2^x}=\int_{y=-\ln2}^{y\to-\infty}e^y\,\frac{\mathrm dy}{-\ln 2}=\frac1{\ln2}\int_{-\infty}^{-\ln2}e^y\,\mathrm dy$

By the fundamental theorem of calculus, this evaluates to

$\dfrac1{\ln2}e^y\bigg|_{y\to-\infty}^{y=-\ln2}=\dfrac1{\ln2}\left(e^{-\ln2}-\lim_{y\to-\infty}e^y\right)=\dfrac{e^{-\ln2}}{\ln2}=\dfrac{\frac12}{\ln2}=-\dfrac1{2\ln2}=\dfrac1{\ln4}$

and so the series converges.

You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.

4 0

3 years ago

Need help quiiickkkk

OLEGan [10]

Answer:

100 beats per minute

Step-by-step explanation:

If it takes 28.8 secs for the piano to play 48 beats, then it would take 60 secs (1 minute) to play x number of beats.

To find the value of x, which is the number of beats the piano makes per minute, let's set the proportion as shown below:

28.8 secs = 48 beats

60 secs = x beats

Cross multiply

28.8*x = 60*48

28.8x = 2,880

Divide both sides by 28.8

x = 2,880/28.8

x = 100

✅Thus, if the Piano plays 48 beats in 28.8 secs, therefore, the tempo of the piano in beats per minute would be 100 BPM

7 0

3 years ago

Respond using complete sentences and math language. Mike told his friend Jacky that 16 + 5 * 2 - 3 = 23. Jacky disagrees, she sa

slava [35]

22 hope this help enjoy ya day

4 0

3 years ago

Read 2 more answers

Monica wants to save at least $399 to buy a new laptop computer. She has $284 saved already. Which options below will allow her

german

Answer:

She is given $205 and spends $57.

She earns $580 and spends $422.

She is given $38 and earns $42.

She earns $56 and is given $59.

Step-by-step explanation:

You just have to do the math.

4 0

3 years ago

Write down the inequality described by "half of x is no more than six", and solve it<br>

Montano1993 [528]

X/.5 > 6
(the > has a line under it but idk how to type that lol)

5 0

3 years ago