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3 years ago

9

Suppose you purchase a raffle ticket for $1.00. First prize is $5,000, second prize is $1,000, and third prize is $500. If 500 t

ickets are sold, what should you expect to win or lose? Round the answer to the nearest cent.
$0.99 loss

$13.00 loss

$10.00 gain

$12.00 gain

1 answer:

Keith_Richards [23]3 years ago

8 0

You should expect to gain 12$

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If a linear system has more unknowns than equations, then the system can-not have a unique solution. True or False

Oduvanchick [21]

Answer:

The statement is true.

Step-by-step explanation:

If a linear system has more unknowns than equations, then the system can-not have a unique solution. This is true.

When more unknowns are there than equations, then the system of polynomial equations is said to be under determined.

This means that if any solutions exist, it will not be unique.

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3 years ago

9^x=1/3<br><br> How much is x?

kumpel [21]

Answer:

x = -1/2

Step-by-step explanation:

This question can be solved by applying the laws of indices

In a^n, a - base

n - index

Given

9^x = 1/3

According to the laws of indices, a/b = b^(-a)

Hence we can write, 1/3 = 3^(-1)

9^x = 3^(2x)

Again according to the laws of indices,

a^b = a^n can be written as;

b = n

That is, if in an equation the bases are the same, the indices are also equal.

So we can write,

3^(2x) = 3^(-1)

2x = -1

Divide both sides of the equation by 2, the coefficient of x

2x/2 = -1/2

x = -1/2

6 0

3 years ago

A Walgreens purchase comes to $28. Find the total cost if a 2% sales tax is included.

OverLord2011 [107]

Answer:

The answer is $28.56

Step-by-step explanation:

To find the 2% sales tax, you need to multiply the 2% or 0.02 by 28.

Doing this will give you 0.56.

Then you add 0.56 to 28 to get 28.56, hence, $28.56 is the total cost.

Hope it helps!

4 0

3 years ago

Suppose that \nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}. if f(0,0,0) = 2, find f(1,1,1).

lesya [120]

The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted $C$ , which we can parameterize by the vector-valued function,

$\mathbf r(t)=(1-t)(\mathbf i+\mathbf j+\mathbf k)$

for $0\le t\le1$ , which has differential

$\mathrm d\mathbf r=-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

Then with $x(t)=y(t)=z(t)=1-t$ , we have

$\displaystyle\int_{\mathcal C}\nabla f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\nabla f(x(t),y(t),z(t))\cdot\mathrm d\mathbf r$

$=\displaystyle\int_{t=0}^{t=1}\left(2(1-t)^3e^{(1-t)^2}\,\mathbf i+(1-t)e^{(1-t)^2}\,\mathbf j+(1-t)e^{(1-t)^2}\,\mathbf k\right)\cdot-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)(t^2-2t+2)\,\mathrm dt$

Complete the square in the quadratic term of the integrand: $t^2-2t+2=(t-1)^2+1=(1-t)^2+1$ , then in the integral we substitute $u=1-t$ :

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)((1-t)^2+1)\,\mathrm dt$

$\displaystyle=-2\int_{u=0}^{u=1}e^{u^2}u(u^2+1)\,\mathrm du$

Make another substitution of $v=u^2$ :

$\displaystyle=-\int_{v=0}^{v=1}e^v(v+1)\,\mathrm dv$

Integrate by parts, taking

$r=v+1\implies\mathrm dr=\mathrm dv$

$\mathrm ds=e^v\,\mathrm dv\implies s=e^v$

$\displaystyle=-e^v(v+1)\bigg|_{v=0}^{v=1}+\int_{v=0}^{v=1}e^v\,\mathrm dv$

$\displaystyle=-(2e-1)+(e-1)=-e$

So, we have by the fundamental theorem of calculus that

$\displaystyle\int_C\nabla f(x,y,z)\cdot\mathrm d\mathbf r=f(1,1,1)-f(0,0,0)$

$\implies-e=f(1,1,1)-2$

$\implies f(1,1,1)=2-e$

3 0

3 years ago

Can someone help with this pls it’s due today

KiRa [710]

D, hope this is right! :)

7 0

3 years ago