Find the values of the variables.

Total amount of money in the account in the first bank after 3 years will be given by the function: P[tex]e^{0.07}[/tex].

The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously after t years is-

A = P[tex]e^{rt}[/tex]

Here, we are given that there are 2 financial institutions-

1st financial institution:

interest rate =  3% for the first year

and interest rate for next two years = 2%

2nd Financial institution:

interest rate = 2.49% for three years

Let the principal amount deposited be P

We assume that the interest is compounded continuously.

Then for the 1st year-Amount = P[tex]e^{0.03}[/tex]

Since, there are no withdrawals or deposits,

The Amount of the 1st year will become the principal for the second year-Amount = (P[tex]e^{0.03}[/tex]) [tex]e^{0.02 * 2}[/tex]

= P × [tex]e^{0.03}[/tex] × [tex]e^{0.04}[/tex]

= P[tex]e^{(0.03 + 0.04)}[/tex]

= P[tex]e^{0.07}[/tex]

Thus, the total amount of money in the account in the first bank after 3 years will be- P[tex]e^{0.07}[/tex].

Learn more about compound interest here- brainly.com/question/24274034

#SPJ4

The ratio of time inside to time eating lunch Ratio: 3:2

The ratio of time eating lunch to time watching television Ratio: 10:3

The ratio of time reading to time drawing Ratio: 3:2

What is the ratio?

A ratio is a mathematical comparison between two numbers that indicates how many times one value is contained within the other.

Description: The ratio of time inside to time eating lunch

Ratio: 3:2

Description: The ratio of time eating lunch to time watching television

Ratio: 10:3

Description: The ratio of time reading to time drawing

Ratio: 3:2

To learn more about ratio, Visit

https://brainly.com/question/12024093

#SPJ1

Answer:

the ratio of time inside to time eating lunch 10: 3

the ratio of time eating lunch to time watching television 3:2

the ratio of time reading to time drawing 2:1

Step-by-step explanation:

I got it wrong following the other person this is what Khan academy says is correct.

Answer:

=15p+60-24q-48=15p-24q+12

it's the first one

The equivalent form of the given expression will be 15p - 24q +8. Hence, the first option is correct.

In mathematics, expressions are assertions that must contain at least two words with variables or terms with numbers in them, or both, and connect them with an operator. It is possible for the mathematical operators to be addition, subtraction, multiplication, or division.

For instance, the equation (x+y) has the terms x and y with an addition operator in between. Numerical expressions, which just contain numbers, and algebraic expressions, which also include variables, are the two types of expressions used in mathematics.

The given expression in the question,

15(p + 4) - 12(2q + 4)

15p + 60 - 24q - 48

15p - 24q + 12.

Hence, it is proved that the equivalent form of the expression is 15p - 24q + 12.

To get more information about Expression :

https://brainly.com/question/14083225

#SPJ5

The number 8 is a solution to the equation 3m + 7 = 31

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

3m + 7 = 31

Subtracting 7 from both sides of the equation:

3m + 7 - 7 = 31 - 7

3m = 24

Dividing both sides of the equation by 3:

3m/3 = 24/3

m = 8

The number 8 is a solution to the equation 3m + 7 = 31

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

Answer:

2

Step-by-step explanation:

The logarithmic form of the exponential equation 2³=8 is (D) log₂ 8=3 .

In mathematics, the inverse function of an exponent is a logarithm. This means that the logarithm of a fixed number, such as a, at base b, is used to represent the exponent to which the fixed number must be raised in order to create the number x.

The general properties of logarithm for a fixed base are:

The given exponential equation is  2³=8.

To convert the above equation to logarithmic form we have to take logarithm to the base 2 on both sides of the equation.

Taking log₂ on both sides of the equation we get:

log₂(2³)=log₂(8)

Now we know from the properties of logarithms

logₐxⁿ=n logₐx

therefore:

3×log₂(2)=log₂8

Now logₐa=1, so

3×1=log₂8

or, log₂ 8 = 3

Therefore the required logarithmic equation is log₂ 8 = 3.

To learn more about logarithms visit:

https://brainly.com/question/28346542

#SPJ4

I did it with a calculator and got 63

V 26

1

 <  

24

5

Step-by-step explanation:

The value of x for a given logarithmic expression is 2 or -4.

What is a logarithmic function?

Logarithmic function is the inverse of an exponential function. It is denoted by using the word, log. For example log 10 = 1.

Solving the given equation: log ₂ ( x² + 2x ) = 3

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

Now, the equation becomes,

log ( x² + 2x ) / log 2 = 3

log ( x² + 2x ) = 3 × log 2

log ( x² + 2x ) = log 2³

log ( x² + 2x ) = log 8

Applying exponent both the sides, we get,

e^[log ( x² + 2x )] = e^[log 8]

x² + 2x = 8

x² + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = 2 or -4

Hence, the value of x for a given logarithmic expression is 2 or -4.

To learn more about the logarithmic functions, visit here:

brainly.com/question/13473114

#SPJ4

Answer:Isolate the g

w = 7 - √g

Do the opposite of PEMDAS, first subtract 7 from both sides

w (-7) = -√g + 7 (-7)

w - 7 = -√g

multiply -1 (as -√g is the same as -1√g) to both sides

-1(w - 7) = √g

-1w + 7 = √g

to get rid of the square root, you must square both sides

Note: -1w is the same as -w

Note: you are squaring all the terms on the other side, not just one.

(-w + 7)² = (√g)²

g = (-w + 7)²

g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or                                            g = (-w + 7)²    )

Use the FOIL method (First, Outside, Inside, Last)

(-w)(-w) = w²

(-w)(7) = -7w

(7)(-w) = -7w

(7)(7) = 49

g = w² - 7w - 7w + 49

simplify (combine all like terms)

g =w² - 7w - 7w + 49

g = w² - 14w + 49

g = w² - 14w + 49 is your answer

hope this helps

Step-by-step explanation:

We need to know about inequality to solve the given problem. The double inequality to represent the possible length of a gymnastics routine is given by 3≤b≤7.

Inequality is a realtion which makes comparison between numbers or other expressions. Double inequality means when two or more inequalities are joined together. Here in this question we know that each gymnastic routine is at least 3 minutes long. We assume that the length of a gymnastic routine is b, then we can say from the given information 3≤b. It is also said that no gymnastic routine is longer than 7 minutes, so maximum length of any gymnastic routine is 7 minutes, we can write it as, b≤7. Joining these two inequalities we get the double inequality which describes the possible length of a gymnastic routine.

3≤b≤7

Therefore using the concept of inequality we found the double inequality for possible length of gymnastic routine which is 3≤b≤7.

Learn more about inequality from here:

https://brainly.com/question/14361489

#SPJ9

Answer:

-11

Step-by-step explanation:

2x - 3y - z

2(-2) - 3(3) - (-2)

-4 -9 +2

-13+2

-11

Answer:

-11

Step-by-step explanation:

What we are solving for: 2x - 3y - z

x = -2

y = 3

z = -2

We can just plug in the variables.

[tex](2*-2) - (3*3) - (-2)[/tex]

[tex]-4-9+2[/tex]

Therefore, the answer is -11.

Hope this helped!!

Answer:

The water level drop in temperature per hour is 40 °C per hour

Unit rate

   Hours between 10 P.M. and 7:36 A.M = 9 hours 36 minutes

= 9.6 hours

   The total decrease in temperature = 6/25

The unit rate of decrease in temperature per hour = Hours between 10 P.M. and 7:36 A.M ÷ Total drop in temperature

= 9.6 ÷ 6/25

= 9.6 × 25/6

= 240/6

= 40 °C per hour

Therefore, the water level drop in temperature per hour is 40 °C.

The values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C

Complementary angles are defined as angles that sum up to 90 degrees.

Example:

If x and y are complementary angles, then;

x + y = 90°

From the information given, we have the angles;

since they are complementary, then;

2x - 7 + 3x + 2 = 90

collect like terms

2x + 3x = 90 + 5

Add like terms

5x = 95

Make 'x' the subject of formula

x = 95/5

x = 19

But;

m∠WYX = (2x − 7) = ( 2(19) - 7) = 38 - 7 = 31°

m∠WYZ = (3x + 2)° = (3(19) + 2) = 57 + 2 = 59°

Thus, the values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C

Learn more about complementary angles here:

https://brainly.com/question/16281260

#SPJ1

The mean or the average height of all the corn plants is 43.8 inches.

There are various mean types in mathematics, especially in statistics.

The average of the frequency distribution is given by the mean of the data set .

Hence the statement here indicates that the average height of all the plants combined is 43.8 inches

To learn more about mean visit:

https://brainly.com/question/28670966

#SPJ1

Answer:

Don't cheat, there is your answer.

Step-by-step explanation:

The volume of the cube is determined as 27 unit³.

The volume is calculated using the formula V = s³, in which "s" is the length of a square box's side.

The cube's side length is 3 units.

The volume of a cube = 3³ unit³.

= 3×3×3

= 27

Thus, the volume of the cube is estimated as 27  unit³.

To know more about the volume of the cube, here

https://brainly.com/question/1972490

#SPJ9

The percentage error of the candidate is 38.1%.

So, the percentage error:

Now,

He ought to have received x-15 = 120-15 = 105.

Therefore, the percentage error of the candidate is 38.1%.

Know more about percentages here:

https://brainly.com/question/24304697

#SPJ9

The diagonal of the new screen is approximately 21.21 inches.

The diagonal is a straight line that joins two opposite sides of a quadrilateral(polygon with 4 sides).

The length of the diagonal of the square is given as d=5/6√3A where A is the area of the square.

Now when diagonal d=15 cm then we substitute the value of d=15 to calculate area A of the square.

15=5/6√(3A)

or, 3A=15²×6²÷5² (squaring both sides)

or, A=108 square inches

The new monitor has an area of twice the old monitor.

Area of the new monitor =2×108 square inches=216 square inches.

Now we use the value of A=216 to calculate the value of diagonal d for the new monitor.

d=5/6√(3×216)

d=21.213.. inches

Therefore the diagonal of the new screen is approximately 21.21 inches.

To learn more about diagonal of a square visit:

https://brainly.com/question/3417399

#SPJ4

Julian factored the expression of [tex]2x^{4} +2x^{3} -x^{2} -x[/tex], then the

step 2 ( [tex]x(2x^{2} +1)) -1(x-1)[/tex]) statement is wrong statement.

Julian should have factored (2*2-1) as a difference of squares.

Julian incorrectly factored -1 from the second group of terms.

Julian should have factored 2x from all terms instead of x

Julian incorrectly factored 2*2 from the first group of terms

The expression is,  [tex]2x^{4} +2x^{3} -x^{2} -x[/tex]

Factors greatest  common factors out,

= [tex]x(2x^{3} +2x^{2} -x-1)[/tex]

Regroup terms into two proportional parts,

= [tex]x((2x^{3} +2x^{2} )+(-x-1))[/tex]

Factor the expression,

= [tex]x(2x^{2} (x+1)+(-x-1))[/tex]

= [tex]x(2x^{2} (x+1)-(x+1))[/tex]

= [tex]x(x+1)(2x^{2} -1)[/tex]

Hence, we can write,

= [tex]2x^{4} +2x^{3} -x^{2} -x[/tex]

= [tex]x(2x^{3}+2x^{2} -x-1)[/tex]

So step 1 is correct.

= [tex]x(2x^{2} (x+1)-(x+1))[/tex]

Then, step 2 is wrong.

Therefore, the expression of [tex]2x^{4} +2x^{3} -x^{2} -x[/tex], then the

step 2 ( [tex]x(2x^{2} +1)) -1(x-1)[/tex] )statement is wrong statement.

To learn more about visit Factorization :

brainly.com/question/3057890

#SPJ1

Answer:

Julian should have factored (2x^2-1) as a difference of squares.

Step-by-step explanation:

The solution for the variable y according to the one-variable equation given in the task content is; y = -7.5.

It follows from the task content that the equation which is given in the task content and from which the variable y is to be determined is;

−140 = 18 + 20y − 8.

Hence, the equation can be solved as follows;

−140=18+20y−8

Evaluate each side of the equation;

-140 = 10 + 20y

Subtract 10 from both sides;

-150 = 20y

Divide through by 20; we have;

-7.5 = y.

Ultimately, the solution for the variable y as required in the task content is; y = -7.5.

Read more on one-variable equation;

https://brainly.com/question/10839449

#SPJ1

Answer:

  7

Step-by-step explanation:

You want the value of the expression ||-2|-|3-12||.

Inner groups are evaluated first:

  ||-2|-|3-12|| = |2 -|-9||

  = |2 -9|

  = |-7| = 7

The value of the expression is 7.

__

Additional comment

The absolute value function changes negative signs to positive:

  |-2| = 2

It has no effect on positive signs.

  |2| = 2

The value of x and y from the given angles 6x - 25, y  and 4x + 15 will be x = 20 and y = 85 degrees.

The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

The angles are given that 6x - 25, y  and 4x + 15

WE can see that the angles 6x - 25 and 4x + 15 are  vertically opposite angle, then

6x - 25 = 4x + 15

6x - 4x = 25 + 15

2x = 40

x = 20

Now by linear pair we get

y + 4x + 15 = 180

y + 4(20) + 15 = 180

y = 180 - 80 - 15

y = 100 - 15

y = 85

Therefore, the value of x and y from the given angles 6x - 25, y  and 4x + 15 will be x = 20 and y = 85 degrees.

Learn more about vertically opposite angles;

https://brainly.com/question/18045519

#SPJ1

Using the factored form of a polynomial for the given zeros, we can see that option A is the correct one, the function is:

F(x) = x*(x + 1)*(x - 2)

For a polynomial with the zeros:

x₁, x₂, x₃, ..., xₙ

The polynomial can be written as:

y = (x - x₁)*(x - x₂)*...*(x - xₙ)

In this case, the zeros are:

0, -1, and 2

Then we can write the polynomial as:

y = (x - 0)*(x + 1)*(x - 2)

If we simplify this, we get:y = x*(x + 1)*(x - 2)Which is the one we can see in option A, so we conclude that option A is the correct one.F(x) = x*(x + 1)*(x - 2)

Learn more about polynomials:

https://brainly.com/question/4142886

#SPJ1

The number of outcomes in the sample space is 25

First time taking the tile out of urn and marking it down, the possibilities are 1,2,3,4,5

After replacement of the tile, once again there are 5 tiles in the urn.

Second time taking the tile and marking it down, the possibilities are 1,2,3,4,5

The sample space is set of all possibilities, which is

S = {(1,1),(1,2),(1,3),(1,4),(1,5),(2,1),(2,2),(2,3),(2,4),(2,5),(3,1),(3,2),(3,3),(3,4),(3,5),(4,1),(4,2),(4,3),(4,4),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5)}

S=25

The number of outcomes in the sample space is 25

Learn more about probabilities here:

https://brainly.com/question/28735434

#SPJ4

Answer:

x/5 - 4

Step-by-step explanation: