The scale of a model train is 1.5 to 2 yards if the real train has an engine car that is 20, what is the length in inches of the model engine car ?

The logarithm function can be used to calculate the log values. So the value of log 3 is 0.4771.

Logarithmic functions, also referred to as log functions, are the opposite of exponentiation. According to its definition, a logarithm is a measurement that depicts the degree to which a base (fixed number) is raised to generate a specific number.

The logarithmic function is typically expressed as:

f(x) = [tex]log_ax[/tex]

[tex]log_an=x[/tex] can be expressed as an exponential function in accordance with the definition of the logarithm function:

[tex]a_x = n[/tex]

In general, there are two types of logarithmic functions, namely:

1. Frequently Used Logarithmic Function

2. Natural Logarithmic Function

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Answer: A

Step-by-step explanation:

The relationship between two equal amounts is described by the characteristics of equality

The relationship between two equal amounts is described by the characteristics of equality. To maintain balance, each mathematical operation that is done to one side of an equation must also be applied to the opposing side.

a = 2b, then a-c = 2b - c

This is Subtraction Property of Equality

According to the Subtraction Property of Equality, if two equal things have an equal value subtracted from them or deleted, the outcome is a new equal quantity. When two equivalent sides of a mathematical statement are separated by an equal sign, an equation is being expressed. The subtraction property has the expression if a = b, then a - c = b - c.

X = X

This represents the Reflexive Property

In algebra, a number is always equal to itself according to the reflexive property of equality.

3(p-7) = 3p - 21

This represent distributive property.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

-7k = -42 then k= 6

This is Division Property of Equality

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

m + n = 15 and n = 2, then m + 2 = 15

This represent Substitution Property

x/4 = -5 then x = -20

This is Multiplication Property of Equality

w² = 2x and 2x = y, then w² = y

This is Transitive Property

c-9 = -1, then c = 8

This is Addition Property of Equality

n = -3, then -3 = n

This is Symmetric Property

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Answer:

$40. If she bought 3 for $30, then each shirt must be equal to $10 each.

4 times 10 = 40

Step-by-step explanation:

Hope it helps you! =D

Answer:

B

Step-by-step explanation:

B.B.B.B.B.B.BB.B.B.B.B.B.B.B.B

The total length of wood in meters is 9.65m .

To convert mm to meter

There are 1000mm per meter so divide number of mm by 1000 to convert to meters

The sizes of the pieces of wood are

Add the number of pieces of wood:

1.5m + 2.5m + 0.85m + 4.8m = 9.65m

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units (SI) system.

Most people understand length to refer to an object's longest dimension. However, depending on the object's position, this is not always the case.

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The equation can be solved by breaking it down into two separate absolute value equations:

||2x + 5|= 13 and |—3|= 10.

The first equation has two possible solutions: x = 4 or x = -8.

The second equation has one possible solution: -3 = 10.

Since both equations must be true for the original equation to be true, there is only one possible solution to the original equation: x = 4.

Therefore, the original equation has one possible solution.

Answer:

x - 75 ≥ 420

Step-by-step explanation:

Answer: 14

Step-by-step explanation:

7 * 2 = 14

Answer:

Sum = 14

Step-by-step explanation:

The sum refers to addition. Quotient refers to division.

The sum of 4 and 3 is written as 4+3. The quotient of 4 and 2 is written as 4/2.

4 + 3 = 7

4 / 2 = 2

Multiply 7 by 2

7 * 2 = 14

The sum of 4 and 3 multiplied by the quotient of 4 and 2 is 14.

Answer:

B) m × 3 = 27

Step-by-step explanation:

Explanation:

m = 27 ÷ 3 = 9

E) q ÷ 3 = 27

Explanation:

q = 27 × 3 = 81

So, the equations with 9 as a solution are B and E.

It could be challenging to remove blocks from the middle and bottom of the pile in order to draw a basic random sample. Take 10 blocks off the top of the pile to represent convenience as an example.

A non-probability sampling technique called convenience sampling includes selecting a sample from the nearest area of the population. Pilot testing makes the most use of this kind of sampling. Convenience sampling enables researchers to acquire data that would not otherwise be possible in the absence of a sample frame.

Convenience sampling can assist you in collecting data for exploratory research that can be utilised to develop a compelling hypothesis or research topic. Convenience sampling has several benefits, but its main benefits are that it is affordable, effective, and straightforward to use. The main drawback of convenience sampling is the sample's unclear generalizability.

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The statement angle 8=85, because 180-115=65 , 180-(65+30)=85 is true.

A triangle is a three-sided polygon that consists of three edges and three vertices.

In the given triangle one measure is given which is 30 degrees.

The angle 7 we calculate because the other side angle is 115 degrees.

The sum should be 180 degrees

115+angle 7=180

angle 7=180-115

angle 7=65 degrees

Now we know that the sum of interior angles of a triangle are 180 degrees.

65+30+angle 8=180

95+angle 8=180

Angle 8=85

Hence, the statement angle 8=85, because 180-115=65 , 180-(65+30)=85 is true.

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Therefore , the solution of the given problem of circle comes out to be

n =4 for the length of chord.

Each spot that is a certain distance from that other point in the plane forms a circle (center). As a result, it is a curve composed of vertices that are isolated from one another in the plane by a specific distance. Furthermore, it is axis of rotation symmetric about the center at all angles. The circle's enclosed, two-dimensional plane has every pair of endpoints uniformly separated from the "center." Draw a line thru the circle to create a circular symmetry line. Additionally, at every angle, it rotates equally about the center.

Here,

Given :

2 cords AB & CD can intersect at point P,

according to the following theorem:

|AP| |PB| = |CP| |PD|

We obtain

=>(n-2) x 16 = 8x (n+8)

using the theory of intersection between two cords.

Use the following formula:

=>16n+32 = 8n +64

=>8n -32 = 0

=>8n=32.

8 divided by both sides.

n = 32/8

n = 4

Consequently, n has a value of 4.

Therefore , the solution of the given problem of circle comes out to be

n =4 for the length of chord.

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Answer:

16/52

8/26

4/13

As 13 cards are one suit or are hearts, and in that suit, there is one king, I just add 3 more cards for the other king cards as well and you get 16/52

Step-by-step explanation:

The domain of the function f(x) = (3 - 2x)/(9 - 4x) is equal to (-∞, 9/4) U (9/4, ∞) or (-∞, 2.25) U (2.25, ∞).

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined.

In order to determine the domain of this rational function, we would use an online graphing calculator to plot it and then write its domain in interval notation based on the values on the x-coordinate of the graph as follows:

Domain = (-∞, 9/4) U (9/4, ∞) or (-∞, 2.25) U (2.25, ∞)

By using set builder notation, the domain of this rational function f(x) = (3 - 2x)/(9 - 4x) can be re-written as follows;

Domain = {x|x ≠ 9/4} or {x|x ≠ 2.25}.

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Mountain View received at least 4000 visits 66.67% of the time during their busy season.

Calculating the percentage of times Mountain View received at least 4000 visitors is the task at hand in this exercise. According to the data plot, we can see that they had no visitors the first weekend, 2000 the following weekend, 4,000 the third week, 6,000 the fourth, 8,000 the following week, and 10,000 the last week of their busy season. We can see that starting in week 3, they had more than 4,000 visits, making the total number of weeks within our 6-week study period that had more than 4,000 views equal to 4 weeks. Therefore, (4/6)*100, or about, 66.67% represents the percentage of visitors of at least 4,000 at Mountain View.

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It will take 3750 minutes (62.5 hours) time for all the water to flow out of the tank.

1. Calculate the total volume of the tank: 4500 litres

2. Calculate the rate of flow: 1.2 litres per second

3. Calculate the total time it will take for all the water to flow out: 4500 / 1.2 = 3750 minutes (62.5 hours)

The tank contains 4500 litres of water and is flowing out of the tank at a rate of 1.2 litres per second. This means it will take 3750 minutes (62.5 hours) for all the water to flow out of the tank. To calculate this, we first had to determine the total volume of the tank which was 4500 litres. Then, we had to calculate the rate of flow which was 1.2 litres per second. Finally, using the total volume of water and the rate of flow, we were able to calculate that it would take 3750 minutes (62.5 hours) time for all the water to flow out of the tank.

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Although the examples referenced are note given, the subject or principle of Quadratic Equations and the Quadratic formula are universal principles and hold true regardless of what examples are used.

Thus, two tings that one can learn about solving quadratic equations by using the Quadratic formula are:

In mathematics, almost every student encounters the quadratic formula, which is a popular method for determining the roots of a quadratic problem. In practice, the quadratic formula may be used to calculate the size of a place, the speed of a moving item, the value of profit earned on a product, and other things.

We've shown that a quadratic equation is a degree 2 equation. A quadratic has the standard form y = ax² + bx + c, where a, b, and c are integers and a cannot be zero. All quadratic equations graph into some form of curve. All quadratics have two solutions, although not all of them are real.

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The required value of k will the system of linear equations has infinite number of solutions is -9.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We know that

2x+3y13=0. ..........(1)

6x−ky−39=0 ..........(2)

Because there are infinity many solutions to linear equations.

[tex]\frac{a_{1}}{a_{2}} =\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}[/tex]

⇒ 2/6 = -3/k = -13/-39

-3/k = 1/3

k = -9

Thus,required value of k is -9.

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Answer: The simplest ratio of squares to circles would be 3:4.

The simplest ratio of squares to circles would be 3:4. To get this ratio, we need to simplify the ratio of 12 squares to 16 circles. We can divide both 12 and 16 by 4, which is their greatest common factor. This gives us 12/4 = 3 and 16/4 = 4. So, the ratio of squares to circles is 3:4. This ratio can also be written as 3/4.

Step-by-step explanation:

hope this helps!

The given line segment which is divided into the ratio 3 : 4  shows line is divided into 7  parts.

As given in the question,

Let us consider the given line segment be PQ .

And take point R between the given points AB such that it get divided in the ratio 3 : 4.

From the given ratio PR is divided into 3 equal parts.

And RQ  is divided into 4 equal parts.

Total number of parts PQ  is divided is given by

= PR + RQ

= 3 + 4

= 7  parts  which are equal to each other.

Therefore,  the given ratio 3 : 4 represents that the line segment is divided into 7 equal parts.

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Therefore , the solution of the given problem of inequality comes out to be x<6 and x>9.

A connection of linear solutions or integers in mathematics that lacks an equal sign is known as an inequality. Inequity so follows an imbalance. There exists an inequality between two numerical values when they are not equal. Differences exist between equality and inequality. I've used the most typical symbol in cases where the variables aren't comparable or equal (). Regardless of how little or large the values are, there are numerous inequities that can be used to compare them. A variety of fundamental inequality issues can be solved by switching the two sides until variables represent everything that is left. There are numerous variables that could lead to inequality, including the conjunction or division of low values on both sides. Alternating sides

Here,

Given : 5x + 2 < 32

=> 5x < 32-2

=>5x < 30

=>x < 6

thus,

=> x-7>2

=> x>9

Therefore , the solution of the given problem of inequality comes out to be x<6 and x>9.

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The required  temperature of the oven 17 and t minutes after being turned on are 245º and 75º + 17t.

The formula R = D/T, or rate of change equals the distance travelled divided by the time required to do so, can be used to approach rate of change problems in general.

The initial temperature of the oven is 75º and temperature will increase at a rate of 10° per minute after being turned on.

Total temperature after 17 minutes,

75º  + 17(10º )

75º + 170º

245º

And

Temperature after oven t minutes after being turned on

75º + 17t

Thus, required temperature of oven is 245º and 75º + 17t.

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Between these two integers the square roots lie

a)√ 56=7 < √56 < 8

b)-√78= 8 < -√78 < 9

c) -√43=-7 < -√43 < -6

d)√99= 9 < √99 < 10

Find the square of the two integers that are immediately adjacent to the square root. For instance, we would discover the square of 7 and 8, which is 49 and 64, respectively, for 56.

The surd should be compared to the square of the adjacent numbers. The surd is said to be between two integers if it is bigger than the square of the lower integer and less than the square of the higher integer.

This approach allows us to see that √56 is between 7 and 8 as 49 < √56 < 64.

Similarly,

b) -√78 lies between 8 and 9 because 64 < -√78 < 81

c) -√43 lies between -7 and -6 because 49 > -√43 > 36

d) √99 lies between 9 and 10 because 81 < √99 < 100

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Inverse of logarithm function is exponential function, undoing the effect of logarithm.

What is logarithm ?

A logarithm is a mathematical function that calculates the power to which a given number (the base) must be raised to produce a certain value. Commonly, logarithms are written with the notation log base b (x), where b is the base and x is the value for which we want to find the power. It can also be written as log x.

The reverse or inverse of a logarithm function is the exponential function. If f(x) = log_b x, then the inverse function, denoted as f^-1(x), is the exponential function with base b, denoted as b^x. This is because log_b (b^x) = x, and b^(log_b x) = x. The logarithm and the exponential function are inverse of each other, meaning that applying the logarithm function "undoes" the effect of the exponential function, and applying the exponential function "undoes" the effect of the logarithm function.

Inverse of logarithm function is exponential function, undoing the effect of logarithm.

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Answer:

the answer is in the picture

Answer:

21 - 20i

Step-by-step explanation:

Simplify the following:

(-2 i + 5)^2

(-2 i + 5)^2 = 25 - 10 i - 10 i - 4 = 21 - 20 i:

Answer: -20i +21 = 21 - 20i

The inverse of the logarithmic function 3 is 1000 for base 10.

The index or power to which the base must be raised in order to reach the given number is represented by the logarithm of any positive number, whose base is a number that is larger than zero but not equal to one.

mathematical form: [tex]log_ab=x[/tex].

Here for inverse of given function is derived by given formula.

[tex]a^x=b[/tex]

There are two types of logarithm function:

Natural Logarithm and common logarithm.

[tex]log_{a}b=x\\log_{10}b=3\\a^x=b\\10^3=b\\b=1000[/tex]

So inverse of logarithmic function 3 is 1000.

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His total profit is  13130. Your remaining cash balance (also known as your net profit) is the sum of all your business expenses.

The answer is given below :

Sum = Rs 40000

We know that,

Interest = (Sum × Time × Rate)/100

So, for the 1st year when profit is 5%,

Interest

= Rs (40000 × 1 × 5)100

= Rs 2000

So, according to the question,

Rs (40000 + 2000) = Rs 42000 be the Sum for the 2nd year.

So, for the 2nd year, when profit is 10%,

Interest

= Rs (42000 × 1 × 10)/100

= Rs 4200

Again, for the 3rd year, Sum

= Rs (42000 + 4200)

= Rs 46200

Thus, for the third year, when profit is 15%,

Interest

= Rs (46200 × 1 × 15)/100

= Rs 6930

So, now amount is total

= Rs (46200 + 6930)

= Rs 53130

Hence, total profit

= Rs (53130 - 40000)

= Rs 13130

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The value of constant of proportionality is, 9,400

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The local dam lets 75,200 gallons pass through it over the course of 8 hours on Wednesday.

And, On Thursday, the dam lets 141,000 gallons pass through it over the course of 15 hours.

Now, We know that;

By the definition of proportionality,

⇒ y = kx

Where, k is constant of proportionality.

Let y represent the number of gallons and x represent the number of hours.

So, We get;

For The local dam lets 75,200 gallons pass through it over the course of 8 hours on Wednesday.

⇒ y = kx

⇒ 75,200 = k × 8

⇒ k = 9,400

And, On Thursday, the dam lets 141,000 gallons pass through it over the course of 15 hours.

⇒ y = kx

⇒ 141,000= k × 15

⇒ k = 9,400

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