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3 years ago

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Bill wants to attend a college with a current tuition of $10,000 a year. He will graduate from high school in five years. Roughl

y how much will Bill need to save for one-year’s tuition to account for an annual rate of inflation of 3%?
A. $638.30
B. $667.50
C. $656.50
D. $633.30

1 answer:

Harlamova29_29 [7]3 years ago

5 0

Answer:

I think the anser is 667.50

Step-by-step explanation:

You might be interested in

Graph the linear equation y=7x+1

Kay [80]

Answer:

See attached graph.

Step-by-step explanation:

To graph the equation, use its form y = mx+b to guide you.

Since y = 7x + 1 then m = 7 and b=1. Start on the y-axis at 1. Plot this points. From this point go up 7 units and over 1 units. Plot this point (1,8). Connect the points.

5 0

4 years ago

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

A rectangular prism is 4 units by 2 1/2 units by 1 1/2 units. How many cubes with a side length of 1/2 unit will completely fill

Keith_Richards [23]

V prism = 4 × (5/2) × (3/2) = 15 units^3;
V cube = (1/2)^3 = 1/8 units^3;
15 ÷ (1/8) = 15 × 8 = 120 cubes;

3 0

3 years ago

Simplify 12 +3 [5+(4-2)]

horrorfan [7]

12 + 3 [5 + (4-2)] =
12 + 3 [ 5 + 2 ] =
12 + 3 [ 7] =
12 + 21 =
33 <===

7 0

3 years ago

Will give brainliest answer

Ann [662]

Answer:

not equivalent

equivalent

not equivalent

Step-by-step explanation:

25 is by itself already 5²

therefore

${25}^{m} = {5}^{2m}$

when we divide one time by 5, we simply take away 1 from the power making it

${5}^{2m - 1}$

the other options are wrong

${25}^{m - 1}$

would be right, if we have

${25}^{m} \div 25$

but we don't.

and

${25}^{2m - 1}$

would even square

${25}^{m}$

and then divide by 25. no, the original excision is nothing like that.

7 0

3 years ago