Last year, Manuel deposited $7000 into an account that paid 11% interest per year and $1000 into an account that paid 5% interest per year. No withdrawals were made from the accounts. Answer the questions below. Do not do any rounding. (a) What was the total interest earned at the end of year? (b) What was the percent interest for the total deposited?

Answer:

22=4

Step-by-step explanation:

0977-=ytb

(3.1) … … …

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2x-y}{x-2y}[/tex]

Multiply the right side by x/x :

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2-\dfrac yx}{1-\dfrac{2y}x}[/tex]

Substitute y(x) = x v(x), so that dy/dx = x dv/dx + v :

[tex]x\dfrac{\mathrm dv}{\mathrm dx} + v = \dfrac{2-v}{1-2v}[/tex]

This DE is now separable. With some simplification, you get

[tex]x\dfrac{\mathrm dv}{\mathrm dx} = \dfrac{2-2v+2v^2}{1-2v}[/tex]

[tex]\dfrac{1-2v}{2-2v+2v^2}\,\mathrm dv = \dfrac{\mathrm dx}x[/tex]

Now you're ready to integrate both sides (on the left, the denominator makes for a smooth substitution), which gives

[tex]-\dfrac12\ln\left|2v^2-2v+2\right| = \ln|x| + C[/tex]

Solve for v, then for y (or leave the solution in implicit form):

[tex]\ln\left|2v^2-2v+2\right| = -2\ln|x| + C[/tex]

[tex]\ln(2) + \ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]

[tex]\ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]

[tex]v^2-v+1 = e^{\ln\left(1/x^2\right)+C}[/tex]

[tex]v^2-v+1 = \dfrac C{x^2}[/tex]

[tex]\boxed{\left(\dfrac yx\right)^2 - \dfrac yx+1 = \dfrac C{x^2}}[/tex]

(3.2) … … …

[tex]y' + \dfrac yx = \dfrac{y^{-3/4}}{x^4}[/tex]

It may help to recognize this as a Bernoulli equation. Multiply both sides by [tex]y^{\frac34}[/tex] :

[tex]y^{3/4}y' + \dfrac{y^{7/4}}x = \dfrac1{x^4}[/tex]

Substitute [tex]z(x)=y(x)^{\frac74}[/tex], so that [tex]z' = \frac74 y^{3/4}y'[/tex]. Then you get a linear equation in z, which I write here in standard form:

[tex]\dfrac47 z' + \dfrac zx = \dfrac1{x^4} \implies z' + \dfrac7{4x}z=\dfrac7{4x^4}[/tex]

Multiply both sides by an integrating factor, [tex]x^{\frac74}[/tex], which gives

[tex]x^{7/4}z'+\dfrac74 x^{3/4}z = \dfrac74 x^{-9/4}[/tex]

and lets us condense the left side into the derivative of a product,

[tex]\left(x^{7/4}z\right)' = \dfrac74 x^{-9/4}[/tex]

Integrate both sides:

[tex]x^{7/4}z=\dfrac74\left(-\dfrac45\right) x^{-5/4}+C[/tex]

[tex]z=-\dfrac75 x^{-3} + Cx^{-7/4}[/tex]

Solve in terms of y :

[tex]y^{4/7}=-\dfrac7{5x^3} + \dfrac C{x^{7/4}}[/tex]

[tex]\boxed{y=\left(\dfrac C{x^{7/4}} - \dfrac7{5x^3}\right)^{7/4}}[/tex]

(3.3) … … …

[tex](\cos(x) - 2xy)\,\mathrm dx + \left(e^y-x^2\right)\,\mathrm dy = 0[/tex]

This DE is exact, since

[tex]\dfrac{\partial(-2xy)}{\partial y} = -2x[/tex]

[tex]\dfrac{\partial\left(e^y-x^2\right)}{\partial x} = -2x[/tex]

are the same. Then the general solution is a function f(x, y) = C, such that

[tex]\dfrac{\partial f}{\partial x}=\cos(x)-2xy[/tex]

[tex]\dfrac{\partial f}{\partial y} = e^y-x^2[/tex]

Integrating both sides of the first equation with respect to x gives

[tex]f(x,y) = \sin(x) - x^2y + g(y)[/tex]

Differentiating this result with respect to y then gives

[tex]-x^2 + \dfrac{\mathrm dg}{\mathrm dy} = e^y - x^2[/tex]

[tex]\implies\dfrac{\mathrm dg}{\mathrm dy} = e^y \implies g(y) = e^y + C[/tex]

Then the general solution is

[tex]\sin(x) - x^2y + e^y = C[/tex]

Given that y (1) = 4, we find

[tex]C = \sin(1) - 4 + e^4[/tex]

so that the particular solution is

[tex]\boxed{\sin(x) - x^2y + e^y = \sin(1) - 4 + e^4}[/tex]

Answer:

Step-by-step explanation:

Total sales = x

Correct choice is C

Answer:

15 / 4

Step-by-step explanation:

1 kg = 1000 g

3 kg

= 3 x 1000

= 3000 g

3kg to 800g

= 3kg : 800g

= 3000 : 800

= 30 : 8

= 30 / 8

= 15 / 4

15/4 is the fraction representing the ratio of 3 kilograms to 800 grams.

To express the ratio of 3 kilograms to 800 grams as a fraction in its lowest terms.

we need to convert both the quantities to the same units. Since 1 kg is equal to 1000 g, we can convert 3 kg to grams as follows:

3 kg = 3 * 1000 g = 3000 g

Now, we have the quantities in the same unit, and the ratio becomes:

3000 g to 800 g

To express this ratio as a fraction, we place the quantities over each other:

3000 g

-------

800 g

Now, to simplify the fraction to its lowest terms, we find the greatest common divisor (GCD) of the two numbers (3000 and 800) and divide both the numerator and denominator by this GCD.

The GCD of 3000 and 800 is 200, so dividing both by 200 gives us:

3000 ÷ 200 = 15

800 ÷ 200 = 4

Therefore, the ratio 3 kg to 800 g expressed as a fraction in its lowest terms is 15/4.

In summary, we first converted the units to the same (grams) to make the ratio easier to handle. Then, we represented the ratio as a fraction and simplified it to its lowest terms using the GCD method. The final answer, 15/4, is the fraction representing the ratio of 3 kilograms to 800 grams.

To know more about Fraction here

https://brainly.com/question/32865816

#SPJ2

Answer:

-36m^3-21n^3+85mn^2+36m^2n

Step-by-step explanation:

That's what the calculator says:).

Answer:

g(x) = x^3 - 2

Step-by-step explanation:

As you can see on the graph, the line has been translated down 2 units.

If the graph of f has the same shape as the graph of g, then the slope remains the same. The y intercept (k) changes by -2 units, so the k value is -2

g(x) = x^3 - 2

Hope this helps!!

(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,

{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}

Integrate the joint density over this region:

[tex]P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}[/tex]

(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,

{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}

Integrate to get the probability:

[tex]P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}[/tex]

Y₁ and Y₂ are not independent because

P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)

To see this, compute the marginal densities of Y₁ and Y₂.

[tex]P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}[/tex]

but this clearly does not match the joint density.

Answer:

the anwer is B ( i mean second option)

And you can try it

you will find ;

[tex]y = \frac{x}{3} - 1[/tex]

HAVE A NİCE DAY

Step-by-step explanation:

GREETİNGS FROM TURKEY ツ

Answer:

1,108 in²

Step-by-step explanation:

SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)

+ (2×20×11)

= 240+320+108+440

= 1,108 in²

Answer:

The right answer is "0.3193".

Step-by-step explanation:

According to the question,

Mean,

[tex]\frac{1}{\lambda} = 13[/tex]

[tex]\lambda = \frac{1}{13}[/tex]

As we know,

The cumulative distributive function will be:

⇒ [tex]1-e^{-\lambda x}[/tex]

hence,

In the first 5 years, the probability of failure will be:

⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]

                    [tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]

                    [tex]=1-e^(-\frac{5}{13})[/tex]

                    [tex]=1-0.6807[/tex]

                    [tex]=0.3193[/tex]

Answer:

Step-by-step explanation:

B

Answer:

c. 1.29

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Andy 70578 60000 8200

This means that [tex]X = 70578, \mu = 60000, \sigma = 8200[/tex]

What is the z-score of Andy's salary?

This is Z, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70578 - 60000}{8200}[/tex]

[tex]Z = 1.29[/tex]

So the correct answer is given by option c.

Answer:

Step-by-step explanation:

356 * 80 = 28 480

275 * 60 = 16 500

369 * 45 = 16 605

sum = $ 61 585

Answer:

729π ft³

Step-by-step explanation:

Applying,

Volume of a cone

V = πr²h/3.............. Equation 1

Where r = radius of the base, h = height, π = pie

From the question,

Given: r = 9 ft, h = 27 ft

Substitite these values into equation 1

V = π(9²)(27)/3

V = 729π ft³

Hence the volume of the figure in terms of π is 729π ft³

Answer:

The probability that exactly 12 buyers would prefer green

=0.00555

Step-by-step explanation:

We are given that

p=50%=50/100=0.50

n=14

We have to find the probability that exactly 12 buyers would prefer green.

q=1-p

q=1-0.50=0.50

Using binomial distribution formula

[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]

[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]

[tex]P(x=12)=0.00555[/tex]

Hence, the probability that exactly 12 buyers would prefer green

=0.00555

6

+

4

−

8

Step-by-step explanation:

Please mark me as brain list and please like my answer and rate also

Answer:

hope this will help you more

Answer:

[tex]\mu = 5.2[/tex]

[tex]\sigma = 2.257[/tex]

Step-by-step explanation:

Given

[tex]n = 260[/tex] -- samples

[tex]p = \frac{1}{50}[/tex] --- one in 50

Solving (a): The mean

This is calculated as:

[tex]\mu = np[/tex]

[tex]\mu = 260 * \frac{1}{50}[/tex]

[tex]\mu = 5.2[/tex]

Solving (b): The standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\mu * (1-p)}[/tex]

[tex]\sigma = \sqrt{5.2 * (1-1/50)}[/tex]

[tex]\sigma = \sqrt{5.2 * 0.98}[/tex]

[tex]\sigma = \sqrt{5.096}[/tex]

[tex]\sigma = 2.257[/tex]

Answer:

Step-by-step explanation:

-2

Answer:

36 (maybe...)

Step-by-step explanation:

Technically there is no way to answer this question, it says that 120 ADULTS were surveyed and then asks how many STUDENTS rank themselves as introverts.  But if we a supposed to assume that all adults are students:

The ratio of 3:7 means that for every 3 introverts, there are 7 extroverts.

In other words for every 10 people (total introvert+extrovert) there are 3 introverts.

So to find the number of introverts in the group of 120, just multiply by 3/10 or 0.3

The answer would be 36

Answer:r=v^2/A

Step-by-step explanation: To solve for r means you have to isolate r on one side and put all the other terms on the other. To get r out from under the fraction, multiply both sides by r. This leaves:

A*r=v^2     so to isolate r, divide by A and get:

r=v^2/A.

Answer:

a) 0.0062 = 0.62% probability that the return will exceed 55%.

b) 0.3085 = 30.85% probability that the return will be less than 25%

c) 30%.

d) The 75th percentile of returns is 36.75%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 30% and standard deviation 10%.

This means that [tex]\mu = 30, \sigma = 10[/tex]

(a) Find the probability that the return will exceed 55%.

This is 1 subtracted by the p-value of Z when X = 55. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 30}{10}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a p-value of 0.9938

1 - 0.9938 = 0.0062

0.0062 = 0.62% probability that the return will exceed 55%.

(b) Find the probability that the return will be less than 25%

p-value of Z when X = 25. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{25 - 30}{10}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.3085

0.3085 = 30.85% probability that the return will be less than 25%.

(c) What is the expected value of the return?

The mean, that is, 30%.

(d) Find the 75th percentile of returns.

X when Z has a p-value of 0.75, so X when Z = 0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 30}{10}[/tex]

[tex]X - 30 = 0.675*10[/tex]

[tex]X = 36.75[/tex]

The 75th percentile of returns is 36.75%.

Answer:

Step-by-step explanation:

circumference = πd ≅ 250 ft

d ≅ 250/π ≅80 ft

Answer:

16?

Step-by-step explanation:

I'm not sure. I hope so.

10x-5

Answer:

5(2x-1)

5*2x 5*-1

10x-5

Hey there!

5(2x - 1)

= 5(2x) + 5(-1)

= 10x - 5

Therefore, your answer should be: 5x - 5

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

The answer is a

Step-by-step explanation:

Answer:

Step-by-step B represents the $14 John earned in the 2 hours he worked.

explanation:

Answer:

Step-by-step explanation:

We have similar triangles here.

The ratio of corresponding sides of similar triangles is same:

Take the similar triangles,

→ ∆ADE ≈ ∆ABC

Now we can find,

The height of the tree in meters,

→ BC/DE = AC/AE

In this equation BC is the height of tree,

→ BC/2 = 30/3

→ BC/2 = 10

→ BC = 10 × 2

→ BC = 20

Hence, the height of the tree is 20 m.

Answer:

option one is the correct answer

Answer:

1/625

Step-by-step explanation:

Answer:

7x+y=-3

Step-by-step explanation:

if m is the slope of a line, then the slope of its parallel line will have the same slope m,

in the given equation, y=-7x-8, the slope is -7

among the options, 1st option has a slope of -7, since,

7x+y=-3

or, y=-7x-3

Answered by GAUTHMATH

Answer:

1000

Step-by-step explanation: