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Vsevolod [243]
2 years ago
11

Two number cubes each have sides labeled 1 to 6. Ann rolls both number cubes. On the first roll, the sum of the numbers was equa

l to 8. On the second roll, the sum of the numbers was equal to 6. Is one of these sums more likely to occur?
Mathematics
2 answers:
ad-work [718]2 years ago
5 0

Answer:

yes.

Step-by-step explanation:

because i know

Sladkaya [172]2 years ago
3 0

Answer:

No.

Step-by-step explanation:

The table shows the possible sums of rolling the two dies. There are 5 combinations for both the sum of 6 and 8. Therefore, neither 6 nor 8 are more likely to occur.

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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
Michelle needs to rent storage space for some of her belongings. She paid a one-
Lerok [7]

Answer:

c

Step-by-step explanation:

she pays a one-time fee of 50, and 15$ per month

7 0
2 years ago
Please someone help me I'm stuck on my homework for at least a hour
miss Akunina [59]

Pi is 3.14

1st # is 3.13

2nd # is 3.15

These numbers are irrational because pi=infinity

( I am not exactly sure if this is right so don't blame me if you get this wrong, I just tried to help.....) :T

6 0
3 years ago
Which function has a greater y-intercept?
Natali5045456 [20]

Answer:

Option C, both functions have an y-intersect equal to 2.

Step-by-step explanation:

When we have a function f(x), the y-intercept is the value f(0). This is the point where the graph of the function intersects the y-axis.

Then, for f(x) = -x^2 + 5*x + 2

The y-intercept is:

f(0) = -0^2 + 5*0 + 2 = 2

f(0) = 2

And for g(x) we do not have the equation, but we have the graph, so we can just look at which value of y does the graph intersects the y-axis.

We can see that the graph intersects the graph at y = 2

Then the y-intersect is: g(0) = 2

So both functions have the same y-intersect. Then the correct option is C.

4 0
2 years ago
PLEASE HELP I WILL MARK
lys-0071 [83]

Answer: 37 pieces of candy

Step-by-step explanation:

24-8.50 is 15.50 she wants to save 6.25, so, 15.50-6.25 is 9.25. 9.25 divided by the cost of each candy (0.25) is 37

6 0
2 years ago
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