Question 3.13R:
Which of the following are equivalent exponential function(s) to f(x)=(4/7)^−x

There is 10.

28+5= 33

10+18+5=33

The equations 66 ÷ 10  = 6.6, 660 ÷ 10 = 66, 0.66 ÷ 10 = 0.066, and 6 ÷ 100 = 0.06 are true. which is the correct answer would be options (A), (B), (D), and (E).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

A. 66 ÷ 10  = 6.6

66/10 = 6.6

This is the true equation.

B. 660 ÷ 10 = 66

660/10 = 66

This is the true equation.

C. 6,600 ÷ 1,000 = 0.66

This is not the true equation.

D. 0.66 ÷ 10 = 0.066

This is the true equation.

E. 6 ÷ 100 = 0.06

This is the true equation.

Thus, the equations 66 ÷ 10  = 6.6, 660 ÷ 10 = 66, 0.66 ÷ 10 = 0.066, and 6 ÷ 100 = 0.06 are true.

Hence, the correct answer would be options (A), (B), (D), and (E).

Learn more about the equation here:

brainly.com/question/10413253

#SPJ1

Kevin needs to read 57 novels in 19 months.

Given,

The number of novels Kevin needs to read in a month = 3

N = Number of novels Kevin needs to read in M months.

Write an equation with M and N.

That is,

Kevin needs to read 3 novels in one month.

So, number of novels, N Kevin reads in M months,  3M = N

The equation is;

3M = N

Now,

The number of months Kevin needs to read the novels = 19

Then,

The number of novels Kevin reads in 19 months;

3M = N

3 × 19 = 57

That is,

Kevin needs to read 57 novels in 19 months.

Learn more about number of novels here;

https://brainly.com/question/29374029

#SPJ1

Answer: 9

Step-by-step explanation:

Each input is multiplied by 5. This means to get x, we need to divide 45 by 5, which is 9.

The time taken for the rocket to reach its maximum height by virtue of the information given is; 2.25 seconds.

The maximum height reached by the toy rocket is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

Read more on maximum height;

https://brainly.com/question/82347

#SPJ1

Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                   Depreciation        B.O.Y         Expense      Depreciation   Value

                        B.O.Y                                                               E.O.Y       E.O.Y

1    $29,000          $0           $29,000         $11,600            $11,600   $17,400

2   $29,000    $11,600          $17,400          $6,960           $18,560  $10,440

3   $29,000   $18,560          $10,440           $4,176           $22,736   $6,264

What is the double-declining-balance method?

The double-declining-balance method is one of the depreciation methods in use, but it allocates more cost to the earlier years of the asset's life.

This depreciation method uses twice the straight-line rate, which is computed as the product of 100/estimated useful life multiplied by 2.

For each year's depreciation expense, the double rate is applied at the end of the year's balance.

For the last year, the difference between the previous year's ending balance and the residual value is taken as the depreciation expense.

Auto  = $29,000

Estimated useful life = 5 years

Residual = $2,000

Depreciable amount = $27,000 ($29,000 - $2,000)

Straight-line depreciation rate = 20% (100/5)

Double-declining depreciation rate = 40% (20% x 2)

Depreciation Expense:

1st year = $11,600 ($29,000 x 40%)

2nd year = $6,960 ($17,400 x 40%)

3rd year =  $4,176 ($10,440 x 40%)

4th year = $2,506 ($6,264  x 40%)

5th year = $1,758 ($3,758 - $2,000)

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                  Depreciation        B.O.Y         Expense     Depreciation   Value

                        B.O.Y                                                               E.O.Y       E.O.Y

1    $29,000          $0           $29,000         $11,600            $11,600   $17,400

2   $29,000    $11,600          $17,400          $6,960           $18,560  $10,440

3   $29,000   $18,560          $10,440           $4,176           $22,736   $6,264

4   $29,000  $22,736           $6,264          $2,506           $25,242   $3,758

5  $29,000  $25,242            $3,758           $1,758           $27,000  $2,000

Learn more about the double-declining-balance depreciation method here;

https://brainly.com/question/29335025

#SPJ1

The function that can represent the graph is the option;

f(x) = x²·(x - a)²·(x - b)⁴·(x - c)

A function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation is referred to as a polynomial function.

As, the graph touches the at x axis by 3 points.

So, the graph has an even multiplicity at three points as x², (x - a)², and  (x - b)⁴ .

Now, The function has a single zero or factor such as (x - c) in the first equation

So, The function that could represent the graph is the function

f(x) = x²·(x - a)²·(x - b)⁴·(x - c)

Learn more about polynomial function graphs here:

brainly.com/question/11325213

#SPJ5

f(x) can be written as y

y=6x/8

make x the subject

8y=6x

x= 8y/6

replace y with x and x with f(x)

answer:

f(x)-1 = 8x/6

The value of x for the given equation (2x+5)=(17x-14) will be 19/15.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(2x+5)=(17x-14)

We have to rearrange the equation by applying the arithmetic operation for the like term, the terms which are similar, and we can perform arithmetic operations on it like addition and subtraction.

17x-2x=5+14

15x=19

x=19/15

Thus, the value of x for the given equation (2x+5)=(17x-14) will be 19/15.

The question is incomplete, the complete question is"solve the value of x for the given equation,

(2x+5)=(17x-14)

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ1

The positive solution of the given condition is 7.

What is a quadratic equation?

A second-order polynomial equation with a single variable, x, is known as a quadratic equation.

i.e. [tex]ax^{2} +bx+c=0[/tex]

Let '[tex]x[/tex]' be a number, then

The six-times a number= [tex]6x[/tex]

&, the square of a number= [tex]x^{2}[/tex]

Now, according to the question,

or,  [tex]6x = x^{2} -7[/tex]

or, [tex]x^{2} -6x-7=0[/tex]

or, [tex]x^{2} -7x+x-7=0[/tex]

or, [tex]x(x -7)+1(x-7)=0[/tex]

or, [tex](x -7)(x+1)=0[/tex]

Either, [tex](x -7)=0[/tex]            or, [tex](x+1)=0[/tex]

            [tex]x=7[/tex]                            [tex]x=-1[/tex]

Therefore, the positive solution is x = 7.

To learn more about quadratic equations

https://brainly.com/question/1214333

#SPJ1

Answer:

Triangle

Step-by-step explanation:

It has three side unlike the others can't have three sides

answer: 3

simply add 1 apple from Jeff and 2 apples from Jessica

(1+3) = ?

Thus, the answer is 3 apples all together

Solutions for the given equalities:

m < - 2

y > 5

b > -4

What is inequality in mathematics?

An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.

The given inequalities are

1)              m - 1 < -3

    Adding 3 on both sides, we get

             m - 1 + 3 < -3 + 3

               m + 2 < 0

    Subtracting 2 from both the side, we get

               m + 2 - 2 < 0 - 2

               m < - 2

The graph of this inequality is shown below

2)             -4y < -20

     Dividing by -4, we get

             y > 5

The graph of this inequality is shown below

3)       5 + b > 1

    Subtracting 1 from both the side, we get

           b + 4 > 0

            b > -4

The graph of this inequality is shown below

4)      y = -18

This is a point on a number line, and it can be shown as

To learn more about inequalities, visit:

brainly.com/question/24372553

#SPJ1

The number of turns the wheel makes is 1.93 ≈ 2.

What is Turns?

This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.

formular for calculating Turns:

Turns =         Lenght

              Circumference

Circumference of a circle, C= πD

Where,

Diameter=D

            π =22/7

Calculating Circumference;

C= 22  * 66

            7

    =207.4

From the question:

D= 66cm

L  =400m

Calculating Turns:

Turns =  Lenght

              Circumference

          =   400m

               207.4

      Turns =1.93

Turns =1.93≈ 2

Learn more about Turns on

https://brainly.com/question/28638630

#SPJ1

In the graphs given, only graph F has two x - intercepts and a < 0 i.e the graph is facing downwards or opens downwards

The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.

In this question, we have to find the graph of a function f(x) that a < 0 and has two intercepts.

The easy features of this graph are

In the options given, only graph F has such features and it is the answer to the question.

Learn more on graph of quadratic function here;

https://brainly.com/question/9028052

#SPJ1

Answer:

Their Divider

Step-by-step explanation:

1-->1/2+1/2-->1/4+1/4+1/4+1/4-->etc.

Answer: 300%

Step-by-step explanation:

Multiplying something by 3 is the same as 300% of that number

20 x 3 = 60

60 = 300% x 20

If the required reserve ratio is 10 percent, currency in circulation is $1,200 billion, checkable deposits are $1,600 billion, and excess reserves total $2,500 billion

Given that

Reserve ratio is 10 percent

Currency in circulation is $1,200 billion

Checkable deposits are $1,600 billion

Excess reserves total $2,500 billion

Here we are calculating M1 measure of money supply

C: Currency in circulation

D: Checkable Deposits

M1=C+D = 1200+1600= 2800

C: Currency in circulation

D: Checkable Deposits

Currency Deposit Ratio= C/D = 1200/1600 = 0.75

ER: Excess Reserves

CD: Checkable Deposits

Excess Reserve Ratio= ER/CD= 2500/1600 = 1.56

The formula for the M1 money multiplier is:

M1 money multiplier= M1/MB

M1 money multiplier= C+D / R+C

M1 money multiplier= C+D / q∗D+ER+C

M1 money multiplier= (1,200+1,600) / (0.1∗1,600+2,500+1,200)

M1 money multiplier= 0.73

To learn more about money multiplier, click here https://brainly.com/question/14182201

#SPJ4

If a company’s stock was selling at 35$ a share a month later it was selling at 14$ a share the percentage loss is 60%

The company's initial share price = $35 per share

The company's new share price = $14 per share

Therefore the share price decreased from $35 to $14,  we have to find the percentage loss

The percentage loss = [(The company's initial share price - The company's new share price) / The company's initial share price ] × 100

Substitute the values in the equation

The percentage loss = [(35-14) / 35] × 100

= (21/35)×100

= 0.6 × 100

= 60%

Hence, if a company’s stock was selling at 35$ a share a month later it was selling at 14$ a share the percentage loss is 60%

Learn more about percentage loss here

brainly.com/question/22882138

#SPJ1

The perimeter of the given figure is 19 cm and area is 20 cm².

What is perimeter?

A perimeter could be a closed path that encompasses, surrounds, or outlines either a 2 dimensional form or a one-dimensional length. The perimeter of a circle or an oval is termed its circumference.

Main body:

to find the perimeter we need the measurement of each side.

so length of DE side

DE = A F - BC

DE = 6-2

DE = 4 cm

so perimeter = 6+4+2+4+3

                     = 19 cm

area of figure =  area of rectangle ABCG + GDEF

area = 4*3 + 4*2

area of figure = 12+8

Hence area is 20 cm².

To know more about perimeter click on the link below

https://brainly.com/question/19819849

#SPJ1

Answer:

0.08%

Step-by-step explanation:

The exponential function for the given graph having points (2, 16) is f(x) = [tex]4^{x}[/tex].

The exponential function is a type of mathematical function that can be used to determine whether something is increasing or decreasing exponentially, such as population, money, or price. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base.

Exponents are used in exponential functions, as the name indicates.

The given point on the graph is (2, 16).

The given function is f(x) = [tex]a^{x}[/tex]

From graph, (x, y) = (2, 16)

Put the value of (x, y) = (2, 16) in f(x) = [tex]a^{x}[/tex]

16 = a²

a = √16

a = 4

So, the function is

f(x) = [tex]4^{x}[/tex]

To know more about exponential function, visit:

https://brainly.com/question/11154952

#SPJ13

Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

Answer:

1 and 3 equal 126 (vertical angle)

2 and 4 equal 54 (supplemental angles 180-126)

Step-by-step explanation:

Answer:

angle 2: 54 degrees

Angle 3: 126 degrees

Angle 4: 54 degrees

Step-by-step explanation:

since angle 1 is 126 degrees we can find angle 2 since it’s right next to it like that the 2 angles added equal 180 degrees so we just subtract from 180

180-126

Angle 2 is 54 degrees

Since angle 3 is across angle 1 they are equivalent so angle 3 is 126 degrees

Since angle 4 is across angle 2 they are equivalent so angle 4 is 54 degrees

Hopes this helps please mark brainliest

The probability that exactly 6 of the selected adults believe in reincarnation is 0.055

This will be a binomial distribution with parameters:

n = 7, p = 0.50

Hence,

a) P (Exactly 6)

= ⁷C₆(0.50)⁶ (0.50)¹

= 0.055

To learn more about binomial distribution, refer to

https://brainly.com/question/9325204

#SPJ1

In terms of trigonometric ratios, x is 6 sin∅ and y is 6 cos∅.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others. Circular trigonometric functions are another name for them. The ratios of an angle in a triangle are a straightforward definition of a function. This means that these trig functions provide the relationship between the angles and sides of a triangle.

Given,

Expressing x and y in terms of trigonometric ratios,

Base = 6

x = Opposite

y = Hypotenuse

x = 6 sin∅

y = 6 cos∅

To learn more about trigonometric ratios, visit:

https://brainly.com/question/25122825

#SPJ13

Answer:

B

Step-by-step explanation:

The domain is the set of x-coordinates.

The range is the set of y-coordinates.

In B, x is only 2 and 3.

In B, y is only 5 and 8.

The solution to the x/-3≤ 3 inequality is x ≤ -9.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.

Given,

Inequality:

x/-3 ≤ 3

Cross multiplying:

x ≤ 3× -3

x ≤ -9

The solution to the x/-3≤ 3 inequality is x ≤ -9.

To learn more about inequality, visit:

https://brainly.com/question/15064057

#SPJ13