A machine can produce a nail every 2.4 seconds. If the machine keeps running for 3 days without stop, how many nails can be produced?

The situation in which a function behaves differently over different parts of its domain is modeled by considering it to be a piecewise function.

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable

Such a situation can be explained through an example:

f(x) =   { x, for x > 0

        {     1, for x = 0

        { -x, for x < 0

now, when we take x value less than 0, say x= -1

   thus, f(x)= f(-1)= -(-1) = 1 , here we used f(x) given x<0

now, when we take x value more than 0, say x= 1

   thus, f(x)= f(1)= (1) = 1, here we used f(x) given x>0

now, when we take x =  0,

   thus, f(x)= f(0)= 1, here we used f(x) given x=0

this is how we model piecewise function, we  use f(x) as per the value of x. Following image shows plotted answer for this example.

Since inequalities given are exclusive of 0, we leave the dot at the origin unfilled. Now, for x = 0. Since the value is constant at f(x) =1, we pointed a point at (0,1)

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The amount that should be put into account is $6171.88

The formula for the compounded continuously is

              [tex]A = P(1 + {r}/{n})^{tn}[/tex]        (1)

    where , A  = future amount or the final amount

                  P = principal amount to be invested

                 r = annual interest rate

                 t = time

                 n = number of compounding in a year

According to the question we have been given that

              A = $8000

              r = 0.052

               t = 5

              n = 12

putting the required values in equation (1) we get

     8000 = P(1 + 0.052/12)^(5*12)

     8000 = P (1.004)^60

     8000 = P*1.27

            P = 8000/1.27

            P = $6171.88

Thus the amount that should be put into account is $6171.88

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After evaluating the logarithm log₂ 2⁵, we get the result as 5.

The common logarithm is also known as the base 10 logarithm. It is represented by log10 or simply log.

For example, the common logarithm of 1000 is written as log(1000). The common logarithm defines how many times we need to multiply by 10 to get the required output.  The natural logarithm is called the logarithm of base e. The natural logarithm is represented by ln or loge. Here, "e" stands for Euler's constant which is approximately equal to 2.71828.

For example, the natural logarithm of 78 is written as ln 78. The natural logarithm determines how much we need to multiply "e" to get the required output.

We need to evaluate log₂ 2⁵Using the property logₐ (mⁿ) = n logₐ m log₂ 2⁵ can be written as

log₂ 2⁵ = 5 log₂ 2

We know that logₐ a = 15 log₂ 2= 5

Therefore, after evaluating the logarithm log₂ 2⁵, we get the result as 5.

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Answer: I believe it is ZERO

Step-by-step explanation:

Answer:

No Solution

Source: cymath.com

Step-by-step explanation:

Answer:

#9 has 8 vertices

# 10 has 5 vertices

Step-by-step explanation:

A vertex is is a point where two or more curves, lines, or edges meet.  The word "vertices" is the plural of the word "vertex."

The result of simplifying each number 64²/₃ 64²/₃  using the exponent rules is 256

To solve this exercise we have to resolve algebraic operations following the exponent rules.

64²/₃ * 64²/₃

The base number 64 is the same that: 4³, then we get:

(4)³ ⁽²/₃⁾ * (4)³ ⁽²/₃⁾

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

4⁽³*²/³⁾ * 4⁽³*²/³⁾

4⁽⁶/³⁾ * 4⁽⁶/³⁾

(4)² * (4)²

Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:

4⁽²⁺²⁾

4⁴

4*4*4*4

256

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.

Given: 2 log (x + 1) = 5

=> log (x + 1) = [tex]\frac{5}{2}[/tex]

Raising both sides by 10, in order to remove the logarithm:

=> [tex]10^{log_{10}(x+1)} = 10^{2.5}[/tex]

=> x + 1 = 316.22 ( as [tex]a^{log_a(x)} = x[/tex])

=> x = 315.22

Hence, 2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.

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According to the box-and-whisker plot,

5)The 25th quartile = 60

6)The 75th quartile = 100

7)The range = 40

Box-and-whisker plot allows us to determine the mean, the largest or the lowest number in the data set as well as the quartiles in the data.

In this case, from the given figure,

Median is equal to = 80,

The range is equal to = 110-40

We can subtract the value,

So we can write,

The range is equal to = 70.

The 25th quartile is equal to = 60

The 75th quartile is equal to = 100.

The range is equal to = 100-60

We can subtract the value,

So we can write,

The range is equal to = 40. 

So,

Then,

The median=80

The range=70

Therefore,

According to the box-and-whisker plot,

5)The 25th quartile = 60

6)The 75th quartile = 100

7)The range = 40.

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Each logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 8}{log \\3}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression is,

[tex]log_38[/tex]

as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]

therefore ,

[tex]log_38[/tex] =  [tex]\frac{log \ 8}{log \ 3}[/tex]

Hence,  logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 8}{log \\3}[/tex]

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we get f(-4)= -52 and f(3)=4

suppose f(x)= -2x^2+6x+4

we have to compute f( -4)  and  f(3)

The value of f(-4) is found by substituting -4 into the equation per variable, solving and simplifying as needed, to get the answer.

f(x)= -2x^2+6x+4

we have to compute f( -4)  

then f( -4)= -2(-4)^2+6(-4) +4

               = -32-24+4

               = -52

similarly ,The value of f(3) is found by substituting 3 into the equation per variable, solving and simplifying as needed, to get the answer.

f(x)= -2x^2+6x+4

we have to compute f( 3)  

then f( 3)= -2(3)^2+6(3) +4

               = -18+18+4

               =4

Hence we get f(-4)= -52 and f(3)=4

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Answer:

$92

Step-by-step explanation:

32+4x where x is 15

32+(4*15)=?

32+60=92

The solution for the given logarithmic expression log₂4+3 log₂9 as a single logarithm is log₂ (2916).

A logarithmic equation is one that includes a logarithm in the variable x.

An exponential formula is one where the variable is represented by an exponent. To answer exponential equations, first determine whether both sides of the equation can be written as powers of the exact number. If you can't, take the common logarithm from both of the equation's sides and use property 7 to solve the problem.

Now, as per the stated condition in question;

The expressed equation is;

= log₂4+3 log₂9

Using the Power Rule in the second term.

= log₂4+log₂9³

=  log₂4+log₂729

As, the base of each log term is 2. We can use product rule to simplify the equation.

= log₂(4×729)

= log₂ (2916) [As a single log function]

Therefore, the simplification of the given logarithmic expression as the single logarithm is log₂ (2916).

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The solution for the radical equation 2√x =√(x+1) is x=1/3

The phrase "algebraic expression" refers to any arrangement of terms that have undergone operations like addition, subtraction, multiplication, division, etc. (or variable expression).. Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.

Eliminate the radical on the both sides by squaring on both sides-

Both sides must be raised to the second power

(2√x)²=(√x+1)²

After squaring we get 4x=x+1

Solving the equation-

We get rearranged equation as 4x=x+1

3x=1    x=1/3

Check if the  solution is correct by putting it in original equation-putting x=1/3 in the equation 2√x =√(x+1)

2×√1/3=√1/3+1

4/3=4/3

Therefore, the solution for the radical equation 2√x =√(x+1) is x=1/3.

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The biggest weight the person can be based on the recommendation by the doctor is 90 pounds.

From the information, it was stated that doctors recommend us to eat between 3 to 8 percent of our bodyweight each day and that one day someone eats 7.2 pounds.

It should be noted that based on the information given, the highest percentage which is 8% will be used for the calculation.

Therefore, the biggest weight the person can be will be:

8% of x <= 7.2

0.08x <= 7.2

x <= 7.2/0.08

x <= 90 pounds

Therefore, the biggest weight the person can be based on the recommendation by the doctor is 90 pounds.

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Answer:

Step-by-step explanation:

hi

Answer:

undefined

Step-by-step explanation:

4x-32=4x+2

-4x

-32=2

undefined

The simplified form of the expression is 6⁶

From the question, we are to simplify the given expression

The given expression is

6^5 * 2^3 * 6^4 / 12^3

That is,

6⁵ × 2³ × 6⁴ / 12³

Simplifying

6⁵ × 2³ × 6⁴ / 12³

6⁵ × 6⁴ × 2³ / 12³

Applying the exponents rule

6⁵ ⁺ ⁴ × 2³ / 12³

6⁹ × 2³ / 12³

Expanding 12³, we get

6⁹ × 2³ / 6³ × 2³

= 6⁹ / 6³

= 6⁹ ⁻ ³

= 6⁶

Hence, the simplified form of the expression is 6⁶

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The two pages the boys are reading are pages 31, and 30. I'm not sure which is which. (would depend on who is reading the odd number page).

Josiah is reading page 31. The page he is reading is an odd-numbered page is 31 by factorizing number.

Step 1: Determine the factors of 930.

The factors of 930 are 1, 2, 3, 5, 6, 10, 15, 31, 62, 93, 155, 186, 310, 465, and 930.

Step 2: Identify the factors that correspond to odd-numbered pages in the book.

Since Josiah is reading an odd-numbered page,  eliminate the even factors.

This leaves  with the odd factors:

1, 3, 5, 15, 31, 93, 155, and 465.

Step 3: Determine which odd factor corresponds to a page number within the range of the book.

Since the book has 50 pages,  eliminate the odd factors greater than 50. This leaves us with the odd factors: 1, 3, 5, 15, and 31.

Step 4: Identify the odd factor that, when multiplied by its complement, equals 930, that is:

31 × 30 = 930,

so Josiah is reading page 31.

Therefore, Josiah is reading page 31 of the book.

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The number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.

We are given that;

a represents the number of drinks purchased.

y represents the number of tacos purchased

He must buy a minimum of 11 drinks and tacos altogether. Thus, the inequality that describes this is;

2a + 4y ≤ 40

a + y ≥ 11

The inequality graph that represent the given system of inequalities is as shown in the atatched file.

From the given inequality graph, we can tell that one possible solution is; (a, y) = (2, 9)

Thus, the number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.

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Answer:

see explanation

Step-by-step explanation:

substitute the values of x, situated inside the parenthesis into f(x)

f(- 1) = - 1 - 5 = - 6

f(0) = 0 - 5 = - 5

f(1) = 1 - 5 = - 4

f(2) = 2 - 5 = - 3

f(5) = 5 - 5 = 0

f(8) = 8 - 5 = 3

1) Substitute x = -1 into f(x) = x - 5

2) Substitute x = 0 into f(x) = x - 5

3) Substitute x = 1 into f(x) = x - 5

4) Substitute x = 2 into f(x) = x - 5

5) Substitute x = 5 into f(x) = x - 5

6) Substitute x = 8 into f(x) = x - 5

The expression of the mathematical statement given as "The perimeter of a rectangle is equal to two times the length plus twice the width" is P = 2l + 2w

The mathematical statement is given as

The perimeter of a rectangle is equal to two times the length plus twice the width

Represent the perimeter with P

So, we have

P is equal to two times the length plus twice the width

Represent the length and the width with l and w

So, we have

P is equal to two times l plus twice w

So, we have

P = 2l + 2w

Hence, the expression of the mathematical statement given as "The perimeter of a rectangle is equal to two times the length plus twice the width" is P = 2l + 2w

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Answer: Option D is correct.

Step-by-step explanation:

Given: 7 and 11

We need to find the geometric mean of 7 and 11.

Geometric series whose common ratio is equal.

The geometric mean of two numbers is the square root of the product of two numbers.

If a, b and c are in GP then the geometric mean is b

The geometric mean of any two numbers a and b is

The given numbers are 7 and 11

Geometric mean is [tex]\sqrt 7x11\\[/tex]

Geometric mean: [tex]\sqrt{x} 77[/tex]

Answer: 21

Step-by-step explanation:

When it comes to finding the range, you must take the biggest number and subtract it from the smaller number, therefore in your question the answer is

25 - 4 = 21

Hope it helped :D

[tex]\large\bf\implies{infinitely \:many\: solutions}[/tex]

Alternate forms :

[tex] \large \bf \implies{x \in ( - \infty \: , \infty)}[/tex]

[tex] \bf \longrightarrow{3(2x - 2) = 6(x - 1)}[/tex]

[tex] \bf \longrightarrow{6x - 6 = 6x - 6}[/tex]

[tex] \bf \longrightarrow{6x - 6x = - 6 + 6}[/tex]

[tex] \bf \longrightarrow{0 = 0}[/tex]

[tex]\bf \longrightarrow{infinitely \:many\: solutions}[/tex]

Answer:

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