Samuel is going to invest in an account paying an interest rate of 5% compounded
continuously. How much would Samuel need to invest, to the nearest dollar, for the
value of the account to reach $77,000 in 9 years?

Answer:

50 , or , 10 ...................

Answer:  Hundredth- thousandths

Step-by-step explanation:

Expand  8.156 million

 8.156 =  8,156, 000    

As you can see 5 is at the hundredth- thousands place

Answer:

Step-by-step explanation:

(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]

Suppose [tex]5x^4 + 1 = f[/tex]

by differentiation;

[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]

Suppose n = 3

Then, the integral

[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]

[tex]= \int e^f \ \dfrac{df}{20}[/tex]

[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]

[tex]= \dfrac{1}{20} e^f + C[/tex]

recall that [tex]f = 5x^4 + 1[/tex]

Then;

[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]

(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]

suppose; [tex]\dfrac{1}{x^3} = f[/tex]

[tex]x^3 = f[/tex]

[tex]\implies -3x^{-4} \ dx = df[/tex]

[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]

If n = u, then the integration is:

[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]

[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]

Since;  [tex]x^3 = f[/tex]

Then;

[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]

(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]

Suppose  [tex]x^2 + 8x - 4 = f[/tex]

Then, by differentiation of both sides

[tex](2x + 8) \ dx = df[/tex]

[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]

Suppose n = 4 in integration, then:

[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]

By substitution;

[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]

[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]

[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]

The suitable substitutions of n are 3,4,4 respectively.

The process of finding integrals is called integration.

a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

Suppose

[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]

So, we need n=3 for easy integration.

[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]

[tex]I=\frac{e^{t} }{20}[/tex]

[tex]I = e^{5x^{4}+1 }/20 +c[/tex]

b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]

n=4 is needed for easy integration.

I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]

c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]

n=4 is needed for easy integration.

[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]

Hence, the suitable substitutions of n are 3,4,4 respectively.

To get more about integration visit:

https://brainly.com/question/2633548





Answer:

x=-3

Step-by-step explanation:

rearrange terms

distribute

subtract the numbers

subtract 1 from both sides of the equation

simplify

Answer:

Step-by-step explanation:

Here you go mate

Step 1

7(1-8x)-6=169  Equation/Question

Step 2

7(1-8x)-6=169  Simplify

-56x+1=169

Step 3

-56x+1=169  Subtract 1

-56x=168

Step 4

-56x=168  Divide both sides

Answer

x=-3

Answer

how much more is the cost of tickets than the cost of parking pass

Step-by-step explanation:\

i think, sorry if im wrong but its kinda hard to understand what you typed.

Answer:

A: No the tickets won't cost more than $1500.

B: 90 more dollars.

6 season tickets cost $720

D: 2 parking tickets will cost $60

Answer:

4

Step-by-step explanation:

25÷2= 12.50

So it would be 4 because you are trying to find the price (p) for the boots (b)

Answer:

c is correct answer is yes then please

Step-by-step explanation:

parallel

8g - 3 = 25

8g = 25 + 3

8g = 28

g = 28/8

g = 14/4

f + 30 + 72 = 180 (straight angle = 180°)

f = 180 - 30 - 72

= 78

Answer:

n=5, m = 4

Step-by-step explanation:

It is a parallelogram so m+8 = 3m and 2n-1 = 9

Answer:

the anser is 22.10

Step-by-step explanation:

you have to round to the nearest ten. here is a tip 4 or down round down 5 or up round up now you are good to go! and also to find me if you need help

Answer:

I think its true but im not sure

Step-by-step explanation:

9514 1404 393

Answer:

  it is less expensive to purchase a new car

Step-by-step explanation:

The expected cost of gas, insurance, and repairs for the old car are ...

  Total miles in 5 years = (325 mi/wk)(52 wk/yr)(5 yr) = 84,500 mi

Old car

  Gas cost in 5 years = (84,500 mi)/(14 mi/gal)($3.50/gal) = $21,125

  Insurance cost in 5 years = (5 yr)($600/yr) = $3,000

  Repair cost in 5 years = ($1500/yr)(5 yr) = $7,500

  Total operating cost in 5 years = $21125 +3000 +7500 = $31,625

__

New Car

  Gas cost in 5 years = (84,500 mi)/(47 mi/gal)($3.50/gal) ≈ $6,293

  Insurance cost in 5 years = (5 yr)($1000/yr) = $5,000

  Repair cost in 5 years = (0)(5 yr) = 0

  Total operating cost in 5 years = $6293 +5000 = 11,293

__

Difference in operating costs is $31,625 -11,293 = $20,332.

It is less expensive to purchase a new car for any price less than $20,300. If the new car costs only $16,000, it is the less-expensive option.

Purchase of a new car is the least-expensive option.

__

Additional comments

The cost of financing, annual license fees, and resale value of the new car may also come into play. In addition, the relative non-economic values of consumption of new materials, adding old materials to the scrap heap, and environmental pollution may figure in the decision. While the car dealer may pay for maintenance costs of a new car, it seems likely that at least one set of tires will be required in 5 years (85000 miles). (Assuming wheel alignment is not an issue for tire wear, that cost may balance out for the two cars.)

Answer:

$455 for seven nights

Step-by-step explanation:

260/4= 65

65 is the cost for 1 night

65*7=455

Answer:

$455

Step-by-step explanation:

260 divided by 4 will give you how much for one night so then multiply that answer by 7 and you have your answer.

Answer:

You can make infinite 3-digit number using the digits 6,7 and 8. Hope it helps :)

Answer:

it's easier if you use the scan & solve. that brainly provided for you

Step-by-step explanation:

Ryan's garden=1.3 yards wides

We know that,

1 yard=0.914 meters

so,

1.3 yards=0.914×1.3=1.1882=1.9

So,

Ryan's garden is 1.9 meters wide.

Answer:

someone game me that same question but sadly i wasn't able to get the answer sorry for the inconvience

Step-by-step explanation:

Answer:

3. 2nd degree. Leading term:

[tex] {3x}^{2} [/tex]

Leading coefficient: 3x

Part 1:

[tex] {2x}^{2} + 11x + 15[/tex]

Part 2:

[tex] {3x}^{2} - x - 2[/tex]

Part 3:

[tex] - {x}^{2} + 12x + 17[/tex]

(Part 3 should be correct, double check it, I think it cancels out the minuses in the part 2 equation?)

P.S. I forgot to solve the equations on this and the first page, don't forget that and I can leave another answer for those if you need!

Answer:

154.8 is you answer

Step-by-step explanation:

Answer:

um well i can do part A

Step-by-step explanation:

its 6/24 which equals 1/4 yards

Answer:

34 lies in between 5 and 6

5^2=25, 6^2=36, so sqrt(34) lies between 5 and 6

Answer:

59.58333

Step-by-step explanation:

715/12

write in long division format ( which u did )

divide 71 by 12 to get 5

multiply 71 by 12 = 5

subtract 60 by 71

bring down the next number

115/12 =9

multiply 12 by 9

subtract 180 by 115

add a decimal on the top and bring down zero

divide 70 by 12 = 5

multiply 5 by 12

subtract 60 - 70

bring down a zero

divide 100 by 12 = 8

multiply 12 by 8

subtract 96 by 100

bring down zero

divide 40 by 12 = 3

anddd u get the point

sorry it took so long

Step-by-step explanation:

Sum of interior angles in a polygon

= 180°(n - 2), where n is the number of sides.

Hence a convex polygon with 6 sides

=> 180°(6 - 2) = 720°.

Answer:

Step-by-step explanation:

We are given a circle with a partially shaded region. First, we need to determine the area of the whole circle. To do this, we need the measurement of the radius of the circle:

Use the Pythagorean theorem to solve for the other leg of the right triangle inside the circle:

5^2 = 3^2 + x^2

x = 4

The radius is 4 + 1 cm = 5 cm

So the area of the circle is A = pi*r^2

A = 3.14 * (5)^2  

A = 25pi cm^2

To solve for the area of the shaded region:

Ashaded = Acircle - Atriangles

we need to solve for the area of the triangles:

A = 1/2 *b*h

A = 1/2 *6 * 5

A = 15 cm^2

Atriangles = 2 * 15  

Atriangles = 30 cm^2

Ashaded = 25pi - 30

Answer:

The answer to that question is c. y = x

Answer:

Mean y = 19 ; SD y = 10

Step-by-step explanation:

Given that:

No of customers : __ 0 ____ 1 _____ 2 ___ 3

P(x) : ___________0.10 __ 0.20 __0.30 _0.40

Fuel cost =$1 (constant)

Amount paid per customer =$10

Number of customers = x

σx = 1 ; μx = 2

σ^2 = 1^2 = 1

Mean of Y

μy = E(Y)

= E(10x - 1)

= 10(Ex) - 1

E(x) = 2

= 10(2) - 1

= 20 - 1

= 19

σY = SD(y)

SD(10x - 1)

10*SD(x) - 1

SD(x) = 1

10(1) - 0

Note : SD of a constant = 0

10 - 0

= 10

The mean of Y is 19 and the standard deviation of Y is 10 and this can be determined by using the given data.

Given :

The mean of Y can be calculated as given below:

[tex]\rm \mu(Y)=E(Y)[/tex]

[tex]\rm \mu(Y)=E(10x - 1)[/tex]

[tex]\rm \mu(Y) = 10E(x) - 1[/tex]

According to the given data, the value of E(x) is 2. Substitute the value of E(x) in the above expression.

[tex]\rm \mu(Y) = 10(2) - 1[/tex]

[tex]\rm \mu(Y) = 19[/tex]

Now, the standard deviation of Y can be calculated as:

[tex]\rm \sigma_Y=SD(Y)[/tex]

[tex]\rm \sigma_Y=SD(10x-1)[/tex]

[tex]\rm \sigma_Y=10SD(x)-SD(1)[/tex]

The value of SD for a constant is zero.

[tex]\rm \sigma_Y=10(1)-0[/tex]

[tex]\rm \sigma_Y = 10[/tex]

For more information, refer to the link given below:

https://brainly.com/question/12402189

Answer:

Step-by-step explanation:

The two base angles in each triangle are equal. (The triangle is isoceles and the property used is angles opposite equal sides are equal).

Now the tricky part. The peak angles are also equal. That's because both peak angles are made equal by Peak angle + 2*base angle = 180

Peak angle = 180 - 2*base angle

Therefore the triangles are congruent by SAS.  

I suppose you could get them equal by taking one of the base angles (all 4 are equal to each other) and the peak angles and claim equality by ASA, but it seems a little bit tortuous to me.

Answer:

171.38 - 15% plus tax= 171.23

Hope this helped!

Answer:

i really dont know

Step-by-step explanation:

i just dont

Answer:

yes they are Similar

Answer:

x≤24

Step-by-step explanation:

4(x+5)≤116

x+5≤29

x≤29-5

x≤24