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kirill115 [55]
3 years ago
13

Sabena invests $250 in an account that earns 2.4% interest per year compounded continuously. How many years will it take the acc

ount to have a value of $300?
Mathematics
1 answer:
g100num [7]3 years ago
6 0

Answer:

It'll take 7.5967 years to have $300 on that account.

Step-by-step explanation:

This problem involves a compounded interest compounded continuously, so in order to solve it we must use the formula for those cases as shown below:

M = C*e^(i*t)

Where M is the final value, C is the initial capital, i is the interest rate and t is the total time. We have:

300 = 250*e^(0.024*t)

e^(0.024*t) = 300/250

e^(0.024*t) = 1.2

0.024*t = ln(1.2)

t = ln(1.2)/0.024 = 7.5967

It'll take 7.5967 years to have $300 on that account.

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 23 in. by 13 in. by
faltersainse [42]

Answer:

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is 361.19 in^3.

Step-by-step explanation:

Given that the dimensions of a cardboard is 23 in by 13 in.

Let the side of the square be x in.

Then the length of the box= (23-2x) in

and the width of the box =(13-2x) in

and height = x in.

The volume of the box is = length ×width × height

                                         =[(23-2x)(13-2x)x] in^3

                                         =(299x-72x² +4x^3) in^3

∴V=299x-72x² +4x³

Differentiating with respect x

V'= 299-144x+12x²

Again differentiating with respect x

V''= -144+24x

To find the dimensions, we set V'=0

∴299-144x+12x²=0

Applying Sridharacharya formula that is the solution of a quadratic equation ax²+bx+c is x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Here a=12, b=-144 , c=299

\therefore x=\frac{-(-144)\pm\sqrt{(-144)^2-4.12.299}}{2.12}

\Rightarrow x= 9.33, 2.67

If  we take x=9.33 in, then the width of the box [13-(2×9.33)] will negative.

∴x = 2.67 in

If at x = 2.67, V''<0 , then the volume of the box will be maximum or V''>0 then volume of the box will be minimum.

V''|_{x=2.67}=-144+(24\times 2.67)=-79.92

Therefore  at x = 2.67, the volume of the box maximum.

The length of the box =[23-(2×2.67)] in

                                    =17.66 in

The width of the box =[13-(2×2.67)] in

                                  =7.66 in

The height of the box= 2.67 in

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is =(17.66×7.66×2.67) in^3

                                                            =361.19 in^3

8 0
3 years ago
Iven 5 different letters, how many different ways can you arrange 3 of them (whether they spell a word or not)
nevsk [136]
Permutation so 5!/(5-3)!=5!/2!= 5 x 3 x 4= 60 ways.
4 0
3 years ago
he U.S. Bureau of Labor Statistics reports that the average annual expenditure on food and drink for all families is $5700. Assu
Papessa [141]

Answer:

87.08% percentage of families spend more than $4000 annually on food and drink

Step-by-step explanation:

Given -

average annual expenditure on food and drink for all families is $5700

Mean  (\nu) = 5700

standard deviation (\sigma ) = 1500

Let X be the no of families spend annually on food and drink

percentage of families spend more than $4000 annually on food and drink =

P(X > 4000)  = P(\frac{X - \nu }{\sigma }> \frac{ 4000 - 5700}{1500})

                      =  P(Z > - 1.13)     Using  (Z = \frac{X - \nu }{\sigma })

                      =  1 - P(Z

                      = 1 - .1292

                      = .8708

                       = 87.08%

7 0
3 years ago
Help me with this plz
Sergio [31]

Answer:

C) Similar-SAS

Step-by-step explanation:

Here,

BSE ~ TES

Now,

BS = TE (:• being corresponding side )

BSE = TES (:• Being Corresponding angle

SE = SE (:•Being corresponding side)

Therefore,

the given triangle is similar by

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6 0
3 years ago
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ANTONII [103]
B 216 because if you multiply pi with the answer you get 678.58
5 0
3 years ago
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