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aleksley [76]
3 years ago
9

I have a bag of 4 cotton candy lollipops 3 cherry 6 butterscotch and 1 orange what is the probability of randomly choosing a cot

ton candy or orange lilipop
Mathematics
1 answer:
lorasvet [3.4K]3 years ago
4 0

Answer:

= 1/2

Step-by-step explanation:

From the question: 1 bag contains

4 cotton candy lollipops

3 cherry lollipops

6 butterscotch lollipops

1 orange lollipops

Total number of possible outcomes =

14

The probability of randomly choosing a cotton candy or orange lollipops is calculated as:

P(Cotton candy) + P(Orange)

= 4/14 + 3/14

= 7/14

= 1/2

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Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7
Zolol [24]
f(x)=\begin{cases}1&\text{for }-7

The Fourier series expansion of f(x) is given by

\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7

where we have

a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx
a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)
a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2

The coefficients of the cosine series are

a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx
a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)
a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}
a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}

When n is even, the numerator vanishes, so we consider odd n, i.e. n=2k-1 for k\in\mathbb N, leaving us with

a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}

Meanwhile, the coefficients of the sine series are given by

b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx
b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)
b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}
b_n=\dfrac{7(-1)^{n+1}}{n\pi}

So the Fourier series expansion for f(x) is

f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7
3 0
2 years ago
Brian deposits $7000 into an account that pays simple interest at an annual rate of 3%. He does not make any more deposits. He m
Andre45 [30]

Answer:

A)1050

B)8050

Step-by-step explanation:

to find interest we use the formula A= P(1+rt) where P is the initial investment, r is the rate percent, and t is the time interval

for this question we have A=7000(1+3(5)) which gives 8,050 dollars which is the answer to part B

for part A we simply subtract the answer from B from the initial investment so 8050 - 7000 = 1050 made from interest

4 0
2 years ago
10% of the 150 students in sixth grade are on the student council. How many sixth graders are on the student council?
Vinil7 [7]

Answer:

The answer is 15.

Step-by-step explanation:

10% of 150 is 15. (you can take away the zero)

8 0
2 years ago
Read 2 more answers
Can someone help me please
Tasya [4]

Answer:

  Square

Step-by-step explanation:

The length of AB is (a+b)-a = b. The length of BC is b-0 = b. So, adjacent sides are the same length. AB has a constant y-value, so is horizontal. BC has a constant x-value, so is vertical.

A figure with horizontal and vertical sides of the same length is a square.

7 0
3 years ago
A survey shower that 82% of adults need correction for their eyesight. If 18 adults are randomly selected, find the probability
Ksju [112]

Answer: yes.

Step-by-step explanation:

18 people × .82 percent = 14.76

4 0
3 years ago
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