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marin [14]
3 years ago
10

The temperature in buffalo, New York, one Saturday was 68F. The temperature that following Monday was 80F. Write an equation tha

t shows the change in temperature when X represents the number of degrees the temperature increased. Then show how many degrees did the temperature increase
Mathematics
2 answers:
Zanzabum3 years ago
4 0
The equationnIS 80 f-68 f. I dont know about the increse tho.

Ugo [173]3 years ago
3 0
 the answer is 80F-68F=x

x=12
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If X is a r.v. such that E(X^n)=n! Find the m.g.f. of X,Mx(t). Also find the ch.f. of X,and from this deduce the distribution of
astraxan [27]
M_X(t)=\mathbb E(e^{Xt})
M_X(t)=\mathbb E\left(1+Xt+\dfrac{t^2}{2!}X^2+\dfrac{t^3}{3!}X^3+\cdots\right)
M_X(t)=\mathbb E(1)+t\mathbb E(X)+\dfrac{t^2}{2!}\mathbb E(X^2)+\dfrac{t^3}{3!}\mathbb E(X^3)+\cdots
M_X(t)=1+t+t^2+t^3+\cdots
M_X(t)=\displaystyle\sum_{k\ge0}t^k=\frac1{1-t}

provided that |t|.

Similarly,

\varphi_X(t)=\mathbb E(e^{iXt})
\varphi_X(t)=1+it+(it)^2+(it)^3+\cdots
\varphi_X(t)=(1-t^2+t^4-t^6+\cdots)+it(1-t^2+t^4-t^6+\cdots)
\varphi_X(t)=(1+it)(1-t^2+t^4-t^6+\cdots)
\varphi_X(t)=\dfrac{1+it}{1+t^2}=\dfrac1{1-it}

You can find the CDF/PDF using any of the various inversion formulas. One way would be to compute

F_X(x)=\displaystyle\frac12+\frac1{2\pi}\int_0^\infty\frac{e^{itx}\varphi_X(-t)-e^{-itx}\varphi_X(t)}{it}\,\mathrm dt

The integral can be rewritten as

\displaystyle\int_0^\infty\frac{2i\sin(tx)-2it\cos(tx)}{it(1+t^2)}\,\mathrm dt

so that

F_X(x)=\displaystyle\frac12+\frac1{2\pi}\int_0^\infty\frac{\sin(tx)-t\cos(tx)}{t(1+t^2)}\,\mathrm dt

There are lots of ways to compute this integral. For instance, you can take the Laplace transform with respect to x, which gives

\displaystyle\mathcal L_s\left\{\int_0^\infty\frac{\sin(tx)-t\cos(tx)}{t(1+t^2)}\,\mathrm dt\right\}=\int_0^\infty\frac{1-s}{(1+t^2)(s^2+t^2)}\,\mathrm dt
=\displaystyle\frac{\pi(1-s)}{2s(1+s)}

and taking the inverse transform returns

F_X(x)=\dfrac12+\dfrac1\pi\left(\dfrac\pi2-\pi e^{-x}\right)=1-e^{-x}

which describes an exponential distribution with parameter \lambda=1.
6 0
3 years ago
you are making beaded bracelets for your for your friends. you want to use 30 beads for each bracelet want to use no more than 1
Softa [21]

30(x)<=145 and yes she would be able to make 4 bracelets because 30 x 4 = 120 and that is less than 145

5 0
3 years ago
Can somebody help me with this? I'm bad at this stuff &lt;.
Sladkaya [172]

Answer:

Prime numbers are whole numbers that has factors of 1 and itself.

Example: 2 is a prime because there is no way you could factor it except 1 and 2.

Composite numbers have more factors which also include 1 and itself.

Example: 50 is composite because it has factors more than 1 and itself.

5 is a factor of 50; 10 is a factor of 50.

So let's begin sorting.

<em>Prime: 7, 11, 31.</em>

Composite: 4, 8, 10, 27.

Hope this helps! :)

6 0
3 years ago
Read 2 more answers
Please help me with this question.
Gelneren [198K]

Answer 1/4

Step-by-step explanation:

3/12 divided by 3 is 1/4

7 0
3 years ago
Read 2 more answers
1
tester [92]

Answer:

B. 4.5

Step-by-step explanation:

108 divided by 2 = 54

54 feet into inches is 4.5

4 0
3 years ago
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