Abigail invested $29,000 in an account paying an interest rate of 2. 1% compounded continuously. Assuming no deposits or withdrawals are made, how much money to the nearest dollar, would be in the account after 8 years?

Answer:

S₄₀ = 2780

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence, that is

14 - 11 = 17 - 14 = 3

this indicates the sequence is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 11 and d = 3 , then

S₄₀ = [tex]\frac{40}{2}[/tex] [ (2 × 11) + (39 × 3) ]

      = 20( 22 + 117)

      = 20 × 139

      = 2780

Answer: Amia is correct

Step-by-step explanation:

the total bill would be $46.82

Answer:

Approximating has always been an important process in the experimental sciences and engineering, in part because it is impossible to make perfectly accurate measurements. Approximation also arises because some numbers can never be expressed completely in decimal notation. In these cases approximations are used.

Answer:

Approximating has always been an important process in the experimental sciences and engineering, in part because it is impossible to make perfectly accurate measurements. Approximation also arises because some numbers can never be expressed completely in decimal notation. In these cases approximations are used.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A doesn't work because a square is not a rhombus

B is out of context

C is true

D makes the most sense to the original question

Answer:

$24.24

Step-by-step explanation:

0.41 x 36 = 14.76
36 - 14.76 =21.24
Hope this helps :)

Answer:

AC=18.1cm

Step-by-step explanation:

When we subtract 11-4=7cm  we get one cathetus of the right triangle a=7cm also we know hypotenuse which is c=16cm.

We will use Pythagorean theorem to find the second cathetus b

b=√16∧2-7∧2= √256-49= √207 ≈ 14.39cm =DC =>

AC =√(DC)∧2+(AD)∧2= √14.39∧2+11∧2= √207+121= √328= 18.1cm

AC=18.1cm

Answer:

it could be many answers but my guess is acute

Answer:

(3) We can also name an angle by placing any number or symbol at the vertex in the INTERIOR of the angle. So, angles can also be called angle 1 or angle 2 or angle 4, etc. Sides AB and AC of the given angle are actually rays.

Step-by-step explanation:

Answer:

the answer is 7/12..

thank u

Step-by-step explanation:

what do you mean by "the hard part" ?

anyway,

we need to sum the numbers in every column creating 5 sums.

then we need to multiply these 5 numbers (product) and divide the result by 16 (we need 1/16 of that product).

so, we have

5 + 1 = 6

1 + 6 + 4 + 8 = 19

2 + 1 + 3 = 6

2 + 5 = 7

1 + 0 + 7 = 8

6×19×6×7×8 = 38,304

38,304 / 16 = 2394

that is your code : 2394

Answer:

The U.S. won 101 medals.

Step-by-step explanation:

101

Hope it helped and have a great day!

Answer:

true false false

Step-by-step explanation:

3,4,5 is a common triangle (proof sqrt(3^2+4^2) = 5)

5,6,7 cant exist sqrt(5^2+6^2) doesnt equal 7

5,5,10 cant exist sqrt(5^2+5^2) doesnt equal 10

Answer:

1/4

Step-by-step explanation:

from 8 to 27, there are 5 number that are divisible by 6 or 7.

=>       12,14,18,21,24

=>       number of favourable outcomes = 5

=>       numer of possible outcomes = 20

probability = no. of favourable outcomes/ no. of possible outcomes

=>       probability = 5/20

=>       5/20 = 1/4

Answer: [tex]4\frac{4}{5}[/tex]

Step-by-step explanation:

To see how many [tex]\frac{1}{6}[/tex] pound servings are in [tex]\frac{4}{5}[/tex] of a pound of chicken we must divide [tex]\frac{4}{5}[/tex] by [tex]\frac{1}{6}[/tex]

[tex]\frac{4}{5}[/tex]÷[tex]\frac{1}{6}[/tex]

When dividing by a fraction you can take the reciprocal (flip the numerator and denominator) and you can multiply instead of dividing

[tex]\frac{4}{5}[/tex]×[tex]\frac{6}{1}[/tex]=[tex]\frac{24}{5}[/tex]=[tex]4 \frac{4}{5}[/tex]

Answer:

24/5, or 4.8, servings

Step-by-step explanation:

Let s represent the number of servings. We have:

[tex] \frac{1}{6} s = \frac{4}{5} [/tex]

[tex]s = \frac{24}{5} = 4.8[/tex]

Answer:

See below

Step-by-step explanation:

1. Two numbers that multiply to 17 and add to 18.

2. Two numbers that multiply to 36 and add to -20.

Answer:

9

It is 9 because 9 is the only number that multiplied by itself is 81.

Answer:

5.5

Step-by-step explanation:

We nned to divide to solve this!!

22/4 = 5.5

She is going 5.5 mph!!

Have an amazing day!!

Please rate and mark brainliest!!!!

y = 1

Step-by-step explanation:

X = 2y + 6

X³ - 8y³ - 36xy - 216 = 0

(subsitute)

(2y + 6)³ - 8y³ - 36(2y + 6)y -216 = 0

(concentrate on first part)

(2y + 6)(2y + 6)(2y + 6)

(4y² + 12y + 12y + 36)(2y + 6)

(4y² + 24y + 36)(2y + 6)

8y³ + 24y² + 48y² + 144y + 72y + 216

(back to full equation)

8y³ + 72y² + 216y + 216 - 8y³ - 36(2y + 6)y - 216 = 0

(factor the last part)

-36(2y + 6)y

y(-72y - 216)

-72y² - 216y

(back to main equation)

8y³ + 72y² + 216y + 216 - 8y³ - 72y² - 216y - 216 = 0

(start to cancel out)

8y³ and -8y³ cancel

72y² + 216y + 216 - 72y² - 216y - 216 = 0

72y² and -72y² cancel

216y + 216 - 216y - 216 = 0

216y and -216y cancel

216 - 216 = 0

those cancel

0y = 0

add 1 to both sides

y = 1.

(I hope this helped)

Answer:

[tex] \dfrac{x^5}{y^{10}} [/tex]

Step-by-step explanation:

[tex] \dfrac{x^2y^{-6}}{x^{-3}y^4} = [/tex]

[tex] = x^{2 - (-3)}y^{-6 - 4} [/tex]

[tex] = x^5y^{-10} [/tex]

[tex] = \dfrac{x^5}{y^{10}} [/tex]

Answer:

0.078125.

Step-by-step explanation:

This is a geometric sequence with first term a1 = 20 and common ratio r = 10/20 = 5/10 = 0.5.

nth term = a1 r^(n -1) so here:

9th term = 20(0.5)^(9-1)

= 20(0.5)^8

= 0.078125.

Answer:

1A.)The tip would be $18, thus meaning the total will shoot up to 108$.

1B.) Divide 3 by 18, and you get $6 per person.

Step-by-step explanation:

Hope this helps!~

The total bill with the tip will be $108.00. Considering this value each person will pay $36.00

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the example: [tex]\frac{20}{100}=\frac{1}{5}=0.2*100=20\%[/tex]

The question gives:

For solving this item you should sum the value of the total bill without the tip with the value equivalent to a 20% tip.

Tip=[tex]\frac{20*90}{100} =\frac{1800}{100}=18[/tex]

Total bill= 18+90=108

For solving this item you should divide the value of the total bill with the tip by 3 (friends).

Individual Payment= 108/3 = 36

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Answer:

145.1 m^2

Step-by-step explanation:

(8x15)+(3.14x8)

120+25.12

145.12

round

145.1

The volume of the stucture made from three rectangular prism is 4080 ft³

Volume is the amount of space occupied by a three dimensional shape or object.

The volume of the rectangular prism = length * width * height = 12 * 10 * 5 = 600 ft³

The volume of the other prism = length * width * height = 10 * 8 * 36 = 2880 ft³

Volume of the structure = 600 ft³ + 600 ft³ + 2880 ft³ = 4080 ft³

The volume of the stucture made from three rectangular prism is 4080 ft³

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Answer:

20

Step-by-step explanation:

3x=x+40

Because Vertical Angles

2x=40

x=20

Answer:

Step-by-step explanation:

This is a quadrilateral. A quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.

The interior angles of a simple quadrilateral ABCD add up to 360 degrees of arc.

Answer:

Angle x = 40°

Step-by-step explanation:

All angles of any quadrilateral sum up to 360°.

So here, already measure of 3 angles are given.

So if we add up all angles + Angle x then it sums up to 360°.

So, the following steps will lead you to the answer:

73° + 157° + 90° + Angle x = 360°

(Now add up the measure of the three given angles)

320° + Angle x = 360°

(Now, through transposition moves 320° to the RHS) (Remember when transposing the signs change)

Angle x = 360° - 320°

Finally,

Angle x = 40°

Hope it helps!!!

Answer:

x = amount invested in the 15% account

x*.15*3 + (500-x)*.1*3 = 200

x = 333.33

so, 500-333.33 = 166.67 at 10%

Step-by-step explanation:

Answer:

x = amount invested in the 15% account

x*.15*3 + (500-x)*.1*3 = 200

x = 333.33

so, 500-333.33 = 166.67 at 10%

Step-by-step explanation:

sorry if i did it wrong

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Area of a Parallelogram is ~

[tex]\qquad \sf  \dashrightarrow \:base \times height[/tex]

[tex]\qquad \sf  \dashrightarrow \:7 \times 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:35 \: {cm}^{2} [/tex]

Answer:

If

Hight = 6×base

And

Base = X

Then

Hight = 6 × X

Which is equivalent to

Hight = 6X

By working with percentages, we will see that there are 1,080 seats in the theater.

We know that the students filled 702 seats, leaving 35% vacant.

Then 702 seats represents the (100% - 35% = 65%) of the total number of seats.

So, if the total number of seats is S, we can write:

(65%/100%)*S as the 65% of S.

Then we solve:

(65%/100%)*S = 702

0.65*S = 702

S = 702/0.65 = 1,080

There are 1,080 seats in the theater.

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[tex]4x + x = 180[/tex]

[tex]5x = 180[/tex]

[tex]x = \frac{180}{5} = 36[/tex]

Answer:

36

Step-by-step explanation:

This is a Linear Pair. Adjacent (next to) angles that form a straight line. A good rule of thumb for 90% of Geometry, angle relationships are usually either supplementary or congruent. In this case, since they together form a straight line, they are supplementary.

x + 4x = 180

5x = 180

180/5 = 36

If you plug these numbers in, you have a 36 degree angle and a 144 degree angle (sum of 180). Easy way to check your work if ever unsure.

The Laplace transform of the non-homogeneous second order differential equation is [tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex].

A Laplace transform is a frequency-based algebraic substitution method used to determine the solutions of differential equations in a quick and efficient manner.

In this question we shall use the following Laplace transforms:

[tex]\mathcal {L} \{f(t) + g(t)\} = \mathcal {L} \{f(t)\} + \mathcal {L}\{g(t)\}[/tex]   (1)

[tex]\mathcal {L} \{\alpha\cdot f(t)\} = \alpha\cdot \mathcal {L} \{f(t)\}[/tex]   (2)

[tex]\mathcal{L} \left\{y^{(n)} \right\} = s^{n}\cdot \matcal {L}\{f(t)\}-s^{n-1}\cdot y(0) -...-y^{(n)}(0)[/tex]   (3)

[tex]\mathcal {L} \{e^{-a\cdot t}\} = \frac{1}{s+a}[/tex]   (4)

Now we proceed to derive an expression fo the Laplace transform of the solution of the differential equation:

[tex]y'' -5\cdot y' = 8\cdot e^{4\cdot t}-4\cdot e^{-t}[/tex]

[tex]s^{2}\cdot \mathcal {L}\{f(t)\}-5\cdot y(0) - y'(0) - 5\cdot s \cdot \mathcal {L} \{f(t)\} +5\cdot y(0) = \frac{8}{s-4}-\frac{4}{s+1}[/tex]

[tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex]

The Laplace transform of the non-homogeneous second order differential equation is [tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex]. [tex]\blacksquare[/tex]

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The Laplace transform Y'' − 5y' = 8e4t − 4e−t when y(0) = 1, y'(0) = −1 for f(t) = 8e4t − 4e−t would be  [tex]\frac{4(s+6)}{s.(s-4)(s+1).(s-5)} + \frac{1}{s} - \frac{1}{s.(s-5)}[/tex].

A Laplace transform is a frequency-based algebraic substitution method used to determine the solutions of differential equations quickly and efficiently.

The Laplace transform

L[ f(t) + g(t) ] = Lf(t) + Lg(t)

Also,

L [[tex]y^{n}[/tex]] = [tex]s^{n} . L[ f(t) ] - s^{n-1} .y(0) .....y^{n}(0)[/tex]

We have

Y'' − 5y' = 8 . e^4t − 4 . e−t

[tex]s^{2} . L[ f(t) ] - 5. y(0)- y'(0) .....y^{n}(0)[/tex]

y(0) = 1, y'(0) = −1  

for f(t) = 8e4t − 4e−t.

= [tex]\frac{8}{s-4} - \frac{4}{s+1}[/tex]

L [f(t)] = [tex]\frac{4(s+6)}{s.(s-4)(s+1).(s-5)} + \frac{1}{s} - \frac{1}{s.(s-5)}[/tex]

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