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Aloiza [94]
3 years ago
7

Kaitlin has 46 coins in her coin collection . She has albums that can hold 5 coins per page. The albums have 6 pages each. How m

any of these albums will kaitlin need if she fills each page with her coins
Mathematics
1 answer:
Mademuasel [1]3 years ago
6 0

Answer:

Hence, kaitlin will need 2 albums if she fills each page with her coins.

Step-by-step explanation:

The given information is:

Kaitlin has 46 coins in her coin collection.

She has albums that can hold 5 coins per page.

The albums have 6 pages each.

Now we are asked to find how many albums will be needed to fill each page with her coins.

As we know that 1 album has 6 pages.

1 page can hold=5 coins.

So, 1 album can old=6×5=30 coins.

Now 46-30=16 coins are left

So we will need one ore album so that these 16 coins could be placed in it.

Hence, kaitlin will need 2 albums if she fills each page with her coins.

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Bingel [31]
Assuming the series is

\displaystyle\sum_{n\ge1}\frac{x^n}{2n-1}

The series will converge if

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|

We have

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|

So the series will certainly converge if -1, but we also need to check the endpoints of the interval.

If x=1, then the series is a scaled harmonic series, which we know diverges.

On the other hand, if x=-1, by the alternating series test we can show that the series converges, since

\left|\dfrac{(-1)^n}{2n-1}\right|=\dfrac1{2n-1}\to0

and is strictly decreasing.

So, the interval of convergence for the series is -1\le x.
6 0
3 years ago
The stock price for International Business Machines (IBM) historically has followed an approximately normal distribution (when a
olganol [36]

Answer:

0.494 is the probability that on a selected day the stock price is between $186.26 and $192.47.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $188.876

Standard Deviation, σ = $4.6412

We are given that the distribution of stock price is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(stock price is between $186.26 and $192.47)

P(186.26 \leq x \leq 192.47) = P(\displaystyle\frac{186.26 - 188.876}{4.6412} \leq z \leq \displaystyle\frac{192.47-188.876}{4.6412}) = P(-0.5636 \leq z \leq 0.7743)\\\\= P(z \leq 0.7743) - P(z < -0.5636)\\= 0.781 - 0.287 = 0.494 = 49.4\%

P(186.26 \leq x \leq 192.47) = 49.4\%

0.494 is the probability that on a selected day the stock price is between $186.26 and $192.47.

5 0
3 years ago
Please help with my last question.
Bas_tet [7]

Answer:

x = 8.3

y = 20.3

Step-by-step explanation:

21-\frac{2}{3} = 20\frac{1}{3} or 20.3

9-\frac{2}{3} = 8\frac{1}{3} or 8.3

6 0
2 years ago
An acrobat is on a platform that is 25 feet in the air. She jumps down in the initial velocity of 4 feet/seconds . Write the qua
Alenkasestr [34]

Answer:

a) h(t) = -16t²+ 4t + 25

b) Therefore it would take her 1.25 seconds to land safely in the net.

Step-by-step explanation:

The equation to be used is given as

h(t) = –gt²+ vt + S(t)

where g = force of gravity and because our question is in feet's = 16

V= Initial velocity

h = height

S = distance

a) The quadratic function for the above question

Using the formula

v = Initial velocity in the question = 4ft/s

S(t) = 25ft in the air

Hence the Quadratic function is

h(t) = –gt²+ vt + S(t)

h(t) = -16t²+ 4t + 25

b) If the safety net is placed 5 feet above the ground, how long will it take her to land safely in the net?

We are to find the time(t)

We can calculate this by using the quadratic function we derived in question (a)

The quadratic function is

h(t) = -16t²+ 4t + 25

Where, the height (h) = 5 feet above the ground

5= -16t² + 4t + 25

-16t² + 4t + 25 -5 = 0

-16t² + 4t + 20 = 0

Using the quadratic equation formula of

x = -b ± √b² -4ac /2a

where the quadratic equation =

ax² + bx + c = 0

a = -16 , b = 4 , c = 20

x = -16 ± √4² - 4×-16×20 / 2×-16

x = -1 or ,1.25

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3 years ago
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egoroff_w [7]

Answer:

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3(b+5)+b+2=

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4b+17

5 0
2 years ago
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