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1 year ago

I'm a student at LUOA and, this is way too hard. Can someone help me, please?

Mathematics

1 answer:

puteri [66]1 year ago

6 0

The answer is the first one.

Knowing that population density is like a rate, people per a given area, you would take the amount of people and divide by the area.

3.11E7/7.69E6 = 4.02 people per km squared.

Also the “E” is another way to write times 10 to a power and I recommend using that notation when plugging it into a calculator.

You might be interested in

Radius of a circle is 5 cm

Vesnalui [34]

Answer:

the answer is (b.)41.7cm²

the workings;;

9.2cm×4cm+5cm=41.8 or 41.7cm²

7 0

2 years ago

What’s the answer???

Andreyy89

Answer:

Step-by-step explanation:

6 0

2 years ago

Two investments totaling $21,000 produce an annual income of $870. One investment yields 4% per year, while the other yields 10%

Citrus2011 [14]

Answer:

The amount invested at 4% is $20,500 and the amount invested at 10% is $500

Step-by-step explanation:

Let

x -----> the amount invested at 4%

(21,000 -x) ----> the amount invested at 10%

we know that

The interest of the amount invested at 4% plus the interest of the amount invested at 10% must be equal to $870

$4\%=4/100=0.04$

$10\%=10/100=0.10$

$0.04(x)+0.10(21,000-x)=870$

Solve for x

$0.04x+2,100-0.10x=870$

$0.10x-0.04x=2,100-870$

$0.06x=1,230$

$x=\$20,500$

$21,000-x=\$500$

therefore

The amount invested at 4% is $20,500 and the amount invested at 10% is $500

7 0

2 years ago

Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

9 months ago

A marketing consultant observed 40 consecutive shoppers to estimate the average money spent by shoppers in a supermarket store.

KonstantinChe [14]

Answer:

0.998 is the probability that the average money spent by a sample of 40 shoppers is within $10 of the actual population mean.

Step-by-step explanation:

We are given the following information in the question:

Standard Deviation, σ = $21.51

We are given that the distribution of average money spend is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

We have to find:

P( average money spent is within $10 of the actual population mean.)

$= P( z \leq \displaystyle\frac{10\times \sqrt{40}}{21.51}}) = P(z \leq 2.94)$

Calculation the value from standard normal z table, we have,

$P(z \leq 2.94) = 0.998$

6 0

2 years ago