I need help with this pleaseee!!

Given:

Rate of interest = 8% compounded continuously.

Amount = 100,000

Time = 25 years

To find:

The principal value.

Solution:

Formula for amount after continuous compound interest:

[tex]A=Pe^{rt}[/tex]

Where, A is amount, P is principal, r is the rate of interest and t is the number of years.

Putting [tex]A=100000, r=0.08, t=25[/tex] in the above formula, we get

[tex]100000=Pe^{0.08(25)}[/tex]

[tex]100000=Pe^{2}[/tex]

[tex]\dfrac{100000}{e^{2}}=P[/tex]

[tex]\dfrac{100000}{7.389056}=P[/tex]

On further simplification, we get

[tex]P\approx 13533.528[/tex]

Therefore, the amount 13533.528 is invested.

Answer:

y = 5/4x-15

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 5/4x+b

Substitute the point into the equation and solve for b

-5 = 5/4(8)+b

-5 = 10+b

Subtract 10 from each side

-5-10 = b

-15 = b

y = 5/4x-15

Step-by-step explanation:

y-y'=m(x-x')

y-(-5)=5/4(x-8)

y+5=5x/4-10

4(y+5)=4(5x/4)-10(4)

4y+20=5x-40

4y-5x=-40-20

4y-5x=-60

5x-4y-60=0

y=5x/4-15

Thank You! Hope it helps! Please mark me brainliest!

Answer:  Choice A

Explanation:

Notice how the numerators (2,4,6,8) are multiples of 2. So we can say that they are of the form 2k, where k is a whole number from 1 to 4.

If k = 1, then 2k = 2*1 = 2

If k = 2, then 2k = 2*2 = 4

and so on until we reach k = 4 and 2k = 8.

Similarly, the denominators are also multiples of 2. We shift things 1 spot to the right. So we start with 4 instead of 2. So we need to add on 2

If k = 1, then 2k+2 = 2*1+2 = 4

If k = 2, then 2k+2 = 2*2+2 = 6

and so on.

[tex]\displaystyle \sum_{k=1}^{4}\frac{2k}{2k+2} = \frac{2}{4}+\frac{4}{6}+\frac{6}{8}+\frac{8}{10}[/tex]

Answer:

I say it's the fourth option

Answer:

9

Step-by-step explanation:

KL + KJ = 17

2 + 3x + 5x - 1 = 17 add like terms

8x + 1 = 17 subtract 1 from both sides

8x = 16 divide both sides by 8

x = 2

KL = 5x - 1 replace x with 2

5*2 - 1 = 9

Step-by-step explanation:

8 . 9 + 3x = 6

3x =6 - 9

3x = -3

x =. -1

9 . 9 (x - 1) - 4( 7 - x ) ≤ 10x - ( 2x +1 ) -6

9x -9 - 28 - 4x ≤ 10x - 2x + 1 - 6

C. L. T.

9x - 4x - 10x + 2x ≤ 1 - 6 + 28 + 9

- 3x ≥ 32

x ≥ - 32/3

x ≥ 10⅔

10 b/ 22 =. 16/ 88

cross multiply

88b = 352

b = 4

11. x- 10 / x+2 = 1/5

cross multiply

5x - 50 = x + 2

4x = 52

x = 13

Answer:

Step-by-step explanation:

Answer:

it appears to be  FALSE....

f(g(x) = 3(13-2x) -7 = 39 - 6x - 7 = 32 - 6x

h(32-5x) = 6(32-6x)

= 192 - 36x

Step-by-step explanation:

Answer:

22+g=65

Step-by-step explanation:

take the 22 add (sum) to g (the variable) and have them = 65

Answer:

The height of first tree is

[ 5.5+18tan(50 degrees) ] ft. This is approximately 26.95 ft.

Angle of elevation from Jimmy's eyes to top of tree is arctan([20+18tan(50 degrees)] /18). This is approximately 66.53 degrees.

Step-by-step explanation:

It would help you to draw a picture for both of these.

You have a person whose height is 5.5 ft and from there horizontal gaze they see a bird from a 50 degree angle of elevation. He is standing 18ft ftom the tree.

So we will first want to find the distance from his eyesight level to the top of the tree. We can do this using the tangent ratio since we have the opposite and adjacent measurements.

Let the distance from eyesight level to the top of the tree be r.

tan(50)=r/18

Multiply both sides by 18:

18tan(50)=r

Now the height of the tree is

[5.5+18tan(50 degrees)] ft.

Now if he is the middle of two trees, then he 18 ft from the 2nd tree.

Since he says the height is 20ft taller than the first tree then it's height is

[20+5.5+18tan(50 degrees)] ft.

Now since we want to find his angle of elevation to the top of the 2nd tree we need to take out his height given us the distance from his eyesight level to the top of the tree which is

[20+18tan(50 degrees)] ft..

So again we are using the tangent ratio.

Let this angle if elevation be P.

tan(P)=[20+18tan(50 degrees)] /18

Take arctan() of both sides:

P=arctan([20+18tan(50 degrees)] /18)

Taking into account the total amount of money spent on the games and the money that Tyrell had left after he bought the video games, Tyrell started with $541.

First you must know the total amount of money spent on the games. For that Tyrell bought 6 video games this summer and each game cost 27 dollars.

So to calculate the amount spent, the number of games purchased must be multiplied by the price of each one:

6 video games* 27 dollars each game= 162 dollars

So Tyrell spends 162 dollars.

On the other hand, you know that Tyrell had 379 dollars left after he bought the video games.

This indicates that after spending $ 162 on video games, there were $ 379 left over.

To know the amount of money that Tyrell had, you must add the amount spent on games and the money that was left over:

162 dollars + 379 dollars= 541 dollars

So, Tyrell started with $541.

Learn more with this similar examples:

Tyrell started with 541 $

There are two actions in the question.

First Tyrell bought 6 video games, each game cost 27 $.

Spent

According to that Tyrell spent

6 * 27 = 162 $

Keeps

The second fact is that after shopping Tyrell keeps 379 $.

If Tyrell spent 162 $ and still keeps 379 $, that means that the total amount of money Tyrell had is the sum of the money he spent plus the money he has

Now if we call "x" the quantity of money Tyrrel started with: Then

x  =  the money Tyrell spent on video games  plus the remaining 379 $

Then

x  =  162  + 379

x = 541 $

Answer:

y = -2x -3

Step-by-step explanation:

- the altitude trough F is a perpendicular line to the line DE

- find slope of line DE

D ( x2 = -5, y2 = -1); E (x1 = 3, y1 = 3)

slope m = (y2-y1) / (x2-x1) = (-1-3) / (-5-3) = -4/ -8 = 1/2

-find equation of the altitude trough F

lines that are perpendicular have the slope negative reciprocal (negative reciprocal of 1/2 is -2)

y= -2x +b , for point F(1, -5)

-5 = -2*1 +b, add 2 to both sides

-5 +2 = b, combine like terms

-3 =b

equation of the altitude trough F is y = -2x -3

Answer:

9(5+8)

Step-by-step explanation:

Answer:

5:05

6

10

Step-by-step explanation:

3:30 + 1 hour = 4:30

4:30 + 35 mins = 5:05 pm

5 days per 1 gallon, 30 days for :

30/5 = 6

500/50 = 10

Answer:

gradient = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Calculate the gradient m using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (3, 1) ← 2 points on the line

m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex]

Answer:

To find the greatest common factor of two monomials, first find the prime factorization of each monomial, including all the variables (and a – 1 factor if necessary). Then take the product of all common factors. First, find the prime factorization of each monomial. So, the GCF is 3p2r3 .

Step-by-step explanation:

Answer:

x ≥ -30

Step-by-step explanation:

The equation is 3 - x / 2 ≤ 18.

First, subtract 3 on both sides:

- x / 2 ≤ 15.

Multiply by -2 on both sides and swap the less than or equal to sign:

x ≥ -30

Hope this helps!

Answer:

Slope=[tex]\frac{11}{-4}[/tex]

Step-by-step explanation:

Answer:

5 inches

Step-by-step explanation:

To find the area of a square the formula is A = bh which with a square is essentially one side squared. We know this because every side of a square is the same. We also know that 5 squared is 25 meaning the answer is 5 inches(You could also use the formula A = bh : A = 5 x 5 : A = 25).

Answer:

The side is 5 square inches.

Step-by-step explanation:

Area of square formula:

A = s x s or [tex]s^2[/tex]

To figure out the sides, we use this formula:

A = 25 ÷ s = s

But to figure out s = side, think of factors of 25 like this:

25: 1,5,25

Now let's plug in the factors of 25 to figure out the missing side length.

A = 25 ÷ 1 = 25

This is not true.

A = 25 ÷ 5 = 5

This is true.

A = 25 ÷ 25 = 1

This is not true.

So our answer is 5 square inches on each side.

Answer:

Area= 2000 feet^2

Step-by-step explanation:

Know how to find the perimeter and the area of a rectangle

area=length*width

perimeter= 2*length + 2*width

Draw a rectangle

The question states that the pasture is 50 feet long

So the length of the rectangle pasture should be 50. We can label the 2 lengths of the rectangle to be 50 feet long

Since the farmer only has 160 feet of fence, we can say that because the pasture is a rectangle, we can label the width as 40 because 2*50+2*40=160

Now that we know the length and width, we can find the area by multiplying those 2 values together to get 2000

Answer:

D

Step-by-step explanation:

He needs to buy 6 items

6 bags of chips

6*2.25= $13.5 so not possible

6 candy bars

6*1.5= $9 so possible

These statements knock out B and C because the dark gray needs to be able to include 6 on the y-axis to show that he could buy 6 candy bars leaving D and A. However, in D it shows that he could actually buy more than 6 candy bars and buy 8 which leaves him with 0 dollars left

8*1.5=$12

Answer:

Step-by-step explanation:

Answer:

x = 18

Step-by-step explanation:

Since BD bisects ∠ ABC , then

∠ ABD = ∠ DBC = 79°

∠ ABC = ∠ ABD + ∠ DBC , that is

9x - 4 = 79 + 79 = 158 ( add 4 to both sides )

9x = 162 ( divide both sides by 9 )

x = 18

Answer:

r = 3 ft

Step-by-step explanation:

Area = 9π

So, πr²=9π where r is the radius

so, r²=9

or, r=√9

or, r=3, since r can't be negative

Answered by GAUTHMATH

Answer:

a. 35 Kilometres.

b. 60 litres.

c. 8150 sweets.

Step-by-step explanation:

Given the following data;

a. To find how many kilometres he traveled in one day;

770 km = 22 days

X km = 1 day

Cross-multiplying, we have;

22X = 770

X = 770/22

X = 35 Kilometres.

b. To find how many litres he would need to go 840 km;

1 litre = 14 kilometres

X litres = 840

Cross-multiplying, we have;

14X = 840

X = 840/14

X = 60 litres.

c. To find how many sweets are there in his car;

Number of sweet box, Ns = 326 boxes

Number of sweets in each box, Sw = 25 sweets

Total number of sweets = Ns * Sw

Total number of sweets = 326 * 25

Total number of sweets = 8150 sweets.

Answer:

[tex]\boxed{\sf Distance_{AB}= 8.24 \ units }[/tex]

Step-by-step explanation:

Here two points are given to us and we need to find the distance between the two points . The given points are , A(0,0) and B(8,2) . The distance between the two points can be found out using the Distance Formula , which is ,

Distance Formula:-

[tex]\sf\implies \green{ Distance =\sqrt{ (x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

Therefore on substituting the respective values ,we can find the Distance as ,

[tex]\sf\longrightarrow Distance = \sqrt{ ( 0 - 8)^2 + (0-2)^2} [/tex]

Simplify the brackets ,

[tex]\sf\longrightarrow Distance =\sqrt{ (-8)^2+(-2)^2}[/tex]

Square the numbers inside the squareroot ,

[tex]\sf\longrightarrow Distance =\sqrt{ 64 + 4} [/tex]

Add the numbers inside the squareroot ,

[tex]\sf\longrightarrow Distance = \sqrt{68} [/tex]

Find the value of squareroot,

[tex]\sf\longrightarrow \boxed{\blue{\sf Distance = 8.24 \ units }}[/tex]

Hence the distance between the two points is 8.24 units .

Answer:

This gives us a pair of simple equations:

100percent =150(1). xpercent =114(2).

therefore, 114 is 76percent of 150

Step-by-step explanat:

Answer:  Choice A

x = 19, RZ = 49, and RT = 98

====================================================

How to get that answer:

Z is the midpoint of RT. This midpoint splits segment RT into two equal pieces RZ and ZT

RZ = ZT

4x-27 = 49

4x = 49+27

4x = 76

x = 76/4

x = 19

So far, we can see that the answer is either choice A or choice D.

------------------

If x = 19, then

RZ = 4x-27

RZ = 4*19-27

RZ = 76 - 27

RZ = 49

Which points us to Choice A as the final answer

-------------------

We could skip the second section entirely because we initially set RZ equal to ZT, and ZT was 49. However, I showed that section to help confirm that we had the correct x value.

Also,

RT = RZ + ZT

RT = 49 + 49

RT = 98