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Ivahew [28]
3 years ago
6

Garrett has many annuity that pays $2,460 at the beginning of each year. If the economy grows at a rate of 2.35% semiannually, w

hat is the value of the annuity if he received it in a lump sum now rather than over a period of nine years?
Mathematics
1 answer:
mezya [45]3 years ago
7 0
FV value of the amount using future value annuity will be:
FV=P[(1+r)^n-1]/r
FV=2460[(1+0.01175)^18-1]/(0.01175)
FV=48,992.23

The present value of this amount will be:
PV=pe^(-rt)
PV=48992.23e^(-0.0235*9)
PV=39,652.81
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Which equations are equivalent to the expression below ? Check all that apply
taurus [48]

It looks like selections A and C are identical. (Neither is equivalent to 9^x.)

If B is supposed to be 3^(2x), it is equivalent to F and D and to the given expression.

Of course, D evaluates to 9^x, so is equivalent.

Choice E evaluates to 3^(x+2), which is not equivalent to 3^(2x).

The applicable choices appear to be

... B. 3^(2x)

... D. (3*3)^x

... F. (3^x)*(3^x)

7 0
4 years ago
You walk around a circle which has a diameter of 9 m, how far have you walked?
Snezhnost [94]

Answer:

C =28.26m

Step-by-step explanation:

We are walking around a circle, which means we are finding the perimeter.  The perimeter of a circle is called the circumference.

We find the circumference by

C = pi *d  where d is the diameter

C = 3.14 * 9

C =28.26m

6 0
3 years ago
Read 2 more answers
Classify the random variables below according to whether they are discrete or continuous.a. The number of people in a restaurant
Murrr4er [49]

Answer:

a) Discrete

b) Continuous

c) Continuous

d) Discrete

e)Discrete

Step-by-step explanation:

Continuous:

Real numbers, can be integer, decimal, etc.

Discrete:

Only integer(countable values). So can be 0,1,2...

a. The number of people in a restaurant that has a capacity of 100.

You cannot have half a person, for example.

The possible number of people in the restaurant are 0, 1, 2,..., 100. So this variable is discrete.

b. The height of a randomly selected giraffe.

The giraffe can have half a meter, for example. That is, the height can be a decimal number. So this variable is continuous

c. The square footage of a house.

You can have half a square, for example. So this variable is continuous.

d. The number of light bulbs that burn out in the next week in a room with 10 bulbs.

Possible values: 0 bulbs, 1 bulb, ..., 10 bulbs

Only countable values.

So discrete

e. The number of points scored during a basketball game.

0 points, 1 point, 2 points, 10 points, ...

There are no half points in basketball.

So discrete

8 0
3 years ago
F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 3)j + zk. find the flux of f across s, the part of the paraboloid x2 + y2 + z = 18 that l
Cerrena [4.2K]
\mathbf F(x,y,z)=z\tan^{-1}(y^2)\,\mathbf i+z^3\ln(x^2+3)\,\mathbf j+z\,\mathbf k
\implies\mathrm{div}\mathbf F(x,y,z)=0+0+1=1

By the divergence theorem, the flux of \mathbf F across the *closed* surface \mathcal S combined with the plane z=2 is given by a volume integral over the closed region:

\displaystyle\iint_{\mathcal S}\mathbf F\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}\nabla\cdot\mathbf F\,\mathrm dV

So in fact, to find the flux over \mathcal S alone, we'll need to subtract the flux of \mathbf F over the planar portion, oriented outward. First, compute the volume integral by converting to cylindrical coordinates:

x^2+y^2+z=18
z=2\implies x^2+y^2=16\implies r^2=16\implies r=4

\displaystyle\iiint_{\mathcal R}\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=4}\int_{z=2}^{z=18-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=128\pi

If the surface does actually contain z=2, then you can stop here; otherwise, continue.

Now, parameterize the part of the *closed* surface in z=2 by

\mathbf s(r,\theta)=r\cos\theta\,\mathbf i+r\sin\theta\,\mathbf j+2\,\mathbf k

where 0\le r\le4 and 0\le\theta\le2\pi. We get a surface element

\mathrm d\mathbf S=(\mathbf s_r\times\mathbf s_\theta)\,\mathrm dr\,\mathrm d\theta=(r\,\mathbf k)\,\mathrm dr\,\mathrm d\theta

We don't need to worry about the first two components of

and so the surface integral over this region is

\displaystyle\iint_{z=2\,\land\,x^2+y^2\le16}\mathbf F\cdot\mathrm d\mathbf S=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=4}2r\,\mathrm dr\,\mathrm d\theta=32\pi

Then the total flux over \mathcal S alone is (128-32)\pi=96\pi.
4 0
3 years ago
What is the difference when −2 is subtracted from 2?
lions [1.4K]

Answer:

4

Step-by-step explanation:

2-(-2)=2+2=4

6 0
2 years ago
Read 2 more answers
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