Please help me Im confused on this problem

Answer:

12.16 years

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 5000=2500e^{0.0570t}[/tex]

[tex]\sf \implies \dfrac{5000}{2500}=\dfrac{2500e^{0.0570t}}{2500}[/tex]

[tex]\sf \implies 2=e^{0.0570t}[/tex]

Take natural logs of both sides:

[tex]\sf \implies \ln 2=\ln e^{0.0570t}[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\sf \implies \ln 2=0.0570t\ln e[/tex]

As ln e = 1:

[tex]\sf \implies \ln 2=0.0570t[/tex]

[tex]\sf \implies \dfrac{\ln 2}{0.0570}=\dfrac{0.0570t}{0.0570}[/tex]

[tex]\sf \implies t=\dfrac{ \ln 2}{0.0570}[/tex]

[tex]\implies \sf t=12.16047685...[/tex]

Therefore, the time required for the amount to double is 12.16 years (2 d.p.).

Learn more about continuous compounding interest here:

https://brainly.com/question/28004698

https://brainly.com/question/27355680

Answer:

The area of the shaded polygon is 31 square units.

Step-by-step explanation:

The procedure to calculate the area of the shaded irregular polygon is described below:

1) Calculate the area of the initial rectangle.

2) Calculate the areas of the four triangles.

3) Subtract the areas of the four triangles from the initial triangle.

[tex]A = (9)\cdot (6) - \frac{1}{2}\cdot (4)^{2} - \frac{1}{2}\cdot (5)\cdot (2) - \frac{1}{2}\cdot (2)^{2} - \frac{1}{2}\cdot (4)^{2}[/tex]

[tex]A = 31[/tex]

The area of the shaded polygon is 31 square units.

Answer:

The given triangle is right.

Step-by-step explanation:

The Pythagorean converse theorem states the following: if one can substitute the sides of a triangle into the following formula:

[tex]a^2+b^2=c^2[/tex]

If the equation formed is a true statement, then the triangle is right, if it is not, then the triangle is not right. In this case, one is not given the angle that has the right angle, however, the hypotenuse is the longest side in a right triangle. Therefore, if the triangle is right, then the hypotenuse is the longest, then side (c) is the longest side in the given triangle. Then side (a) and (b) are the legs, the sides adjacent to the right angle. It doesn't matter which sides one substitutes for these parameters.

Substitute in the given values and solve to prove the triangle is right,

[tex]a^2+b^2=c^2\\[/tex]

Substitute,

[tex](9.6)^2+(12.8)^2=(16)^2[/tex]

Simplify,

[tex]92.16+163.84=256[/tex]

[tex]256=256[/tex]

The given triangle is right since its sides follow the Pythagorean converse theorem.

Answer:

18.266

Step-by-step explanation:

Since these are right triangles, we can use Pythagorean Theorem.

Pythagorean Theorem: a^2 + b^2 = c^2

50^2 + 20^2 = c^2

2500 + 400 = c^2

2900 = c^2

c = sqrt[ 100 * 29]

c = 10 sqrt[29]

In the boxes, a = 10, b = 29.

Hope this helps!! :)

Answer:

[tex]x = \frac{12}{ \tan(60 \degree) } \\ x = \frac{12}{ \sqrt{3} } \\ x = 4 \sqrt{3} \: cm[/tex]

[tex]y = \frac{12}{ \sin (60 \degree) } \\ y = \frac{12 \times 2}{ \sqrt{3} } \\ y = \frac{24}{ \sqrt{3} } \\ y = 8 \sqrt{3} \: cm[/tex]

Answer:

A standard hexagonal pencil is approximately 7.5 inches in lenght. This is 19 centimeters when converted.

The question says to the nearest inch. Therefore we have to approximate to to a whole number.

7.5, when rounded up to the nearest number, is 8 inches.

Hence, the answer is 8 inches or 19 centinmeters.

Cheers

Answer:

C. -5

Step-by-step explanation:

If the two lines are parallel, they have the same slope. Therefore the slope of AB is -5.

Slope of line AB parallel to CD is -5

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

Given,

AB is parallel to CD

Slope of CD m = -5

When two lines are parallel

their slopes are same

m' is slope of AB

then

m' = m

m' = -5

Slope of AB is -5.

Hence, -5 is slope of line AB.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ7

Answer:

V = 267.95 cm^3

Dominic forgot to multiply by the approximation for pi

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

V = 4/3 ( 3.14) (4)^3

V = 267.946666666

Rounding to the nearest hundredth

V = 267.95 cm^3

If you do not multiply by the approximation for pi

V = 85.3333333pi cm^3

Dominic forgot to multiply by the approximation for pi

Answer:

Here is Your answer!!!!

Answer:

Option B is correct

Step-by-step explanation:

The triangle if rotated by 75 degrees in the counter clock wise direction will have C vertices in the second quadrant , A vertices also in the second quadrant and B vertices in the third quadrant.

Hence, option B is correct

Answer:

The responses to the given can be defined as follows:

Step-by-step explanation:

For point a:

fixing probability vector that is [tex]W = [a b c][/tex]

[tex]\therefore[/tex]

relation: [tex]WT =W[/tex]

[tex]\to 0.5a+0.3b+0.2c=a ..................(1)\\\\ \to 0.4a+0.4b+0.3c=b..............(2)\\\\ \to 0.1a+0.3b+0.5c=c.................(3)[/tex]

solving the value:

[tex]a=0.3387 \\\\ b=0.3710\\\\ c=0.2903[/tex]

Therefore the stationary distribution [tex]\pi =[0.3387 \ 0.3710\ 0.2903][/tex]

For point b:

[tex]\pi[/tex] will be limiting distribution if [tex]\pi_j=\lin_{n\to \infity} (X_n=\frac{j}{X_0}=i) \Sigma_{\sqrt{j}} n_j=1[/tex]

[tex]\pi[/tex] satisfies the above condition so, it is limiting the distribution.

Answer:

[tex]x = 0 \: \text{or} \: x = - 4.[/tex]

Step-by-step explanation:

[tex]6 {x}^{2} + 24x = 0 \\ \text{then} \: 6x(x + 4) = 0 \\ \text{hence} \: x = 0 \: \text{or} \: x + 4 = 0 \\\text{therefore} \: x = 0 \: \text{or} \: x = - 4.[/tex]

Answer:

23.31 ft

Step-by-step explanation:

Tan y= opposite÷adjacent

tan 47= 25÷ x

tan 47 • x = 25

x= 25÷ tan 47

x= 23.31 ft

HOPE THIS HELPS!

The area of the base of the first sandbox is 64 square feet

Area is the measure of the amount of surface that a two-dimensional figure or shape covers. It is typically expressed in square units, such as square inches or square meters.

The area of a shape can be calculated by multiplying the length of its base by its height or by using specific area formulas for different shapes, such as the area of a circle or the area of a triangle.

The area of a square is given by the formula: A = s², where s is the length of one side of the square.

In this case, the sandbox has a square base with a side length of 8 feet. Therefore, the area of the base of the first sandbox is:

A = 8² = 64 square feet.

So, the area of the base of the first sandbox is 64 square feet

To know more about an area follow

https://brainly.com/question/29204021

#SPJ2

Answer:

A) 16

Step-by-step explanation:

∠PQR and ∠TQS are vertical, meaning they equal each other

set up your formula as

3x+18=66

3x=66-18

3x=48

x=48/3

x=16

Answer:

9:11

Step-by-step explanation:

subtract the amount of girls to get the amount of boys then put it in ratio form in the order it is asked so it is 9:11

Answer:

Step-by-step explanation:

Numbers that is less than 5 like 4,3,2,1,0

Answer:

1>x>-2   or -2<x<1

Step-by-step explanation:

2<3-x<5   (minus 3)

-1<-x<2     (devide by -1)

1>x>-2

Answer:

You S,tupid

Step-by-step explanation:

A =?

P= 9456

r = 6% = 0.06

t = 5 yrs

Formula

A= P(1+r)^t

A= 9456×1.06⁵

A = 12646.23

the total amount that he had to pay was 12646 rs

Given:

The data set is:

25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24

To find:

The box plot for the given data set.

Solution:

We have,

25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24

Arrange the data in ascending order.

18, 19, 20, 21, 24, 25, 26, 27, 30, 31, 32, 33, 36, 36, 38

Divide the data in two equal parts.

(18, 19, 20, 21, 24, 25, 26), 27, (30, 31, 32, 33, 36, 36, 38)

Divide each parenthesis in two equal parts.

(18, 19, 20), 21, (24, 25, 26), 27, (30, 31, 32), 33, (36, 36, 38)

Now, the five number summary of the given data set is:

Minimum value = 18

First quartile = 21

Median = 27

Third quartile = 33

Maximum value = 38

Therefore, the required box plot for the given data set is shown below.

Answer:

(25m^4n^1/12)(m^1n^1/12)

Step-by-step explanation:

Re-order terms to the left.  

(5*5m^4/3 * n^1/4) (m^1/3*2n^1/8)

Combine terms

(5*5m^4n^1/3/4)     2m^1n^1/3/3/8    

Multiply

(25m^4n^1/3/4)       2m^1n^1/3/3/8    

(25m^4n^1/3 * 4)    2m^1n^1/3/3*8    

(25m^4n^1/12).        2m^1n^1/3/24

cancel common terms in both num and denominator

Final - (25m^4n^1/12) (2m^1n^1/12).

Answer:

18 inches

Step-by-step explanation:

Given

[tex]r = 15in[/tex] --- radius

[tex]h = 12in[/tex] --- distance between chord and the center of the circle

Required

The chord length

See attachment for illustration

First, calculate distance AX using Pythagoras theorem.

[tex]AO^2 = AX^2 + OX^2[/tex]

This gives:

[tex]15^2 = AX^2 + 12^2[/tex]

[tex]225 = AX^2 + 144[/tex]

Collect like terms

[tex]AX^2 = 225 - 144[/tex]

[tex]AX^2 = 81[/tex]

Take square roots of both sides

[tex]AX = 9[/tex]

AB is then calculated as:

[tex]AB= AX + XB[/tex]

Where:

[tex]AX=XB =9[/tex]

So:

[tex]AB = 9 + 9[/tex]

[tex]AB = 18[/tex]

Answer:

It's 46

Step-by-step explanation:

Because 90-44 it's 46

Answer:

Difference= $25.28

Step-by-step explanation:

Giving the following information:

She took $48.95 with her to spend. She spent $23.57 at one store.

To calculate the money she has left, we need to use the following formula:

Difference= total amount of money - money spent

Difference= 48.95 - 23.57

Difference= $25.28

Answer: j=8

Step-by-step explanation: first, add 5 to both sides. You now have 9j = 72. Then divide each side by 9. You now have j=8

Answer:

C) there are no solutions

Step-by-step explanation:

3x-6<3x+13

3x<3x+19

0<19