What are the 7 properties of logarithms?

Answer:

Step-by-step explanation:

1 7.3

2 33.3

3 21.3

4 31.9

5 25.6

6 11

7 41.8

8 64.2

9 12.8

10 51.3

11 24.4

12 35.1

couldn’t do 13 and 14 i’m doing same lesson with rizz but 15 is 44.6inches 16 78.8

Better-than-average illusion is the propensity to assume that one is superior to the majority within a certain group.

The disparity between the parameter's actual value and its expected value is known as bias. Anything that causes a systematic discrepancy between the statistics used to estimate the parameters of a population and their true parameters is considered statistical bias.

Truth is warped by bias. It is a flaw in the system that we don't frequently notice since it is wrapped up in our humanity. The definition of bias is as basic as "unconscious preference," yet it can be benign or evil. Whatever form they take, though, the biases we have prevent us from seeing the world as it really is.

Better-than-average illusion is the propensity to think that one is superior to the majority in a specific group.

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Logarithms can be calculated using the log function in a calculator or the formula loga(x) = y, where a is the base and x is the number you want to find the logarithm of.Inverse logarithms can be calculated using the 10x key on a calculator or the formula 10^y=x, where y is the logarithm and x is the number you want to find the inverse logarithm of.

Logarithms:

To calculate the logarithm of a number, use the log function in your calculator, or use the formula loga(x) = y, where a is the base and x is the number you want to find the logarithm of.

Inverse Logarithms:

To calculate the inverse logarithm of a number, use the 10x key on your calculator, or use the formula 10^y=x, where y is the logarithm and x is the number you want to find the inverse logarithm of.

Logarithms can be calculated using the log function in a calculator or the formula loga(x) = y, where a is the base and x is the number you want to find the logarithm of. Inverse logarithms can be calculated using the 10x key on a calculator or the formula 10^y=x, where y is the logarithm and x is the number you want to find the inverse logarithm of.

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Sarah and Joshua both use correct trigonometry expressions to find out the height of garage wall.

Sarah and Joshua serving to estimate the height of a parking garage using a 50 yards-long rope.

Joshua is in the floor while Sarah stands on the top of garage. Each holds an end of the rope. Joshua walks away until the rope is completely tense,

making an angle of 30° with the floor and an angle 60° with the top.

Joshua determined the height of the wall is 25 yards with the help of trigonometry expression for Sin, and Sarah determined by Cos.

So, let us examine whose approach is correct,

We have length of rope is 50 yards and the angle with floor is 30 and angle with top is 60°

first examine the approach of Joshua,

according to trigonometry, we have

[tex]Sin\theta=\frac{perpendicular}{hypotenuse}[/tex]

[tex]Sin30=\frac{h}{50}[/tex]

[tex]\frac{1}{2} =\frac{h}{50}[/tex]

thus, h =25 yards,

now come on the approach of Sarah

[tex]cos\theta=\frac{base}{hypotenuse}[/tex]

[tex]cos60=\frac{h}{50}[/tex]

thus, h=25 yards.

According to our examination both Joshua and Sarah have corrected approaches.

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An inequality depicts the relationship between two values in an algebraic statement that are not equal.

Inequality, a declaration of the relation of greater, greater than or equal to, smaller, or less than or equal to between two numbers or algebraic expressions.

An inequality is a claim that demonstrates the connection between two (or more) expressions that have one of the following five signs:,, >,,. Similar to an equation, an inequality can be true or untrue. A true statement is: 34 - 12 > 5 + 2. An incorrect statement is 1 + 3 6 - 2.

When two values in an algebraic expression are not equal, an inequality illustrates their relationship. One of the two variables on the two sides of the inequality can be represented by an inequality sign as greater than, greater than or equal to, less than, or equal to another value.

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Answer:

4x - 10

Step-by-step explanation:

3(x-2)2 - 2(x - 1)

(3x - 6)2 -2(x -1)

6x - 12 - 2x + 2

4x - 10

The factor of negative 1 will be -1

Now, According to the question:

What is factor?

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.

Hence, Every negative number can be thought of as having some positive factors and exactly one negative factor, -1. When a positive number and a negative number are multiplied, the product has that one -1, so it's negative.

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Answer:

108

Step-by-step explanation:

Answer:108

Step-by-step:180/100×6=180080180×6=

The mistake made is the error in finding the value of the slope, m, of the line.

The error can be corrected by plugging in m = 6/3 = 2 in the equation; y = m·x + b

The slope of a line is the ratio of the rise to run of the points on the graph of the line.

The points on the graph of the line are; (0, -2), and (3, 4)

The slope of the line, m, can be found using the formula;

m = (y₂ - y₁)/(x₂ - x₁)

Where for the line in the question, we get;

Therefore;

Slope, m = (4 - (-2))/(3 - 0) = 6/3 = 2

The slope of the line = 2

The equation of the line in point-slope form is therefore;

(y - 4) = 2·(x - 3)

y = 2·x - 6 + 4 = 2·x - 2

y = 2·x - 2

The equation can also be found using the x-intercept as follows;

At the x-intercept, x = 0. The x-intercept is therefore, the point (0, -2)

The equation of the line in the slope-intercept form is, y = m·x + b, where b is the y-value at the x-intercept is therefore;

y = -2, when x = 0

-2 = 2×0 + b

b = -2

y = m·x + b, therefore; y = 2·x - 2

The mistake of the student is therefore;

y = m·x + b

4 = 2·(3) + b

4 = 6 + b

-6 [tex]{}[/tex]  -6

-2 = b

y = 2·x - 2

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Answer: 24 3/25

Step-by-step explanation:

Divide 600 by 25, giving you 24. The rest goes into the fraction part.

The true interpretation of the situation is, The population is the total number of people who go to the movie theater and the sample is the first 150 people at the theater.

The complete set of items from which you collect data for a statistical investigation is known as the population in statistics. It could be a collection of things, a gathering of people, etc. It serves as the study's data set.

A sample is characterized as a more manageable and compact version of a bigger group. a smaller population that possesses the traits of a bigger group. When the population size is too big to include all individuals or observations in the test, a sample is utilized in statistical analysis.

Given, The first 150 people who entered the theater were asked about their favorite type of movie.

Therefore, The correct description of the statement is,

The population is the total number of people in the movie theater and the sample is the first 150 people surveyed.

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Answer:

Out of the 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 total students, 4 + 3 = 7 are freshmen so the answer is 7 / 30 * 100 = 23%.

Step-by-step explanation:

The measure of angle m ∠C is 24°.

Congruent triangles have both the same shape and the same size.

Given is that △DSJ ≅ △RCW and m ∠D = 114 and m ∠J = 42.

Since △DSJ ≅ △RCW, we can write -

m ∠S = m ∠C

Now, in △DSJ, we can write -

m ∠D + m ∠S + m ∠J = 180

m ∠S = 180 - 156

m ∠S = 24 = m ∠C

Therefore, the measure of angle m ∠C is 24°.

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Answer:

a. y=4x-3

b. y=x+3

c. y=3/2x+6

d. y=-2/3x+2

Step-by-step explanation:

a. y-4x=-3

  +4x     +4x

y=4x+3

b. 3y-3x=9

÷3           ÷3

y-x=3

y=x+3

c. 3x+2y=12

2y=3x+12

y=3/2x+6

d.

2(x-3)+3y=0

2x-6+3y=0

3y=-2x+6

y=-2/3x+2

The standard equation of a parabola takes the form ( y^2 = ± 4ax ).

In mathematics, a parabola is defined as a plane curve that is approximately U-shaped and mirror-symmetrical. Simply a parabola refers to a set of points that lie equidistant from the focus and the directrix.

In real life, the parabola has several important applications, from a parabolic antenna or parabolic microphone to the design of ballistic missiles and automobile headlight reflectors. It is frequently used in physics, engineering, and various other areas.

The standard equation of a parabola opening upwards or downwards is y^2 = ± 4ax.

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The pair of linear equations 3x + 4y + 5 = 0 and 12x + 16y + 15 = 0 has no solution.

To find the number of solutions that a pair of linear equations will have, we can use the concept of the ratio of coefficients.

For the pair of linear equations:

3x + 4y + 5 = 0

12x + 16y + 15 = 0

We can find the ratio of the coefficients of x in both equations.

In the first equation, the coefficient of x is 3 and in the second equation, the coefficient of x is 12. The ratio of these coefficients is

3/12 = 1/4

We can also find the ratio of the coefficients of y in both equations.

In the first equation, the coefficient of y is 4 and in the second equation, the coefficient of y is 16. The ratio of these coefficients is

4/16 = 1/4

As both ratio are equal, let us check ratio of constants.

5/15 = 1/3

So the ratio of constants is not equal, so there is no solution for this system of linear equations.

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The nearest ten of 555 is 550.

The number system or the numeral system is the system of naming or representing numbers. We know that a number is a mathematical value that helps to count or measure objects and it helps in performing various mathematical calculations.

In mathematics, there are various number systems such as the decimal number system, binary number system, octal number system, and hexadecimal number system.

Round the number to the nearest ten. 555 is between 550 and 560.

Looking at the 1 in the one's place. It's equal to 5, so round down to either 550 or 560. In this case, either one can be correct.

Thus, the nearest ten of 555 is 550.

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Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation

y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

Every point on the graph in red is 1/2 away from the x-axis as that of the equivalent position on the graph in black.

Therefore, the vertically scale factor is equal to 1/2:

=> y = (1/2)f(x)

This problem can be solved by multiplying it by two and yields the following solution:

=> 2y = f(x)

thus , option c is correct

Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

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Answer:

Step-by-step explanation:

P = 2l = 2w

P - 2l = 2w

P - 2l / 2 = w

W = P - 2l /2

The rational expression that is equal to 4(x-1)/(x-1)(x+5) is 4/(x+5).

What are rational expressions ?

Rational expressions represent the relationship between two polynomials. It signifies that the numerator and denominator are both polynomials in it. It is an algebraic expression ratio with an unknown variable, similar to a fraction. We may, however, simplify this type of equation with the aid of a calculator.

Addition and subtraction: When adding or subtracting rational expressions with the same (or similar/common) denominator, keep the denominator alone. If possible, reduce the remaining expression.

If the rational expressions have different denominators, then LCM is applied first. Change each rational expression to its equivalent by changing the denominator exactly. Finally, combine or delete similar phrases. If feasible, reduce the remaining expression.

Multiplication: Factor the polynomial numerators and denominators (if any exist); then reduce wherever possible. Reduced form is obtained by multiplying the remaining numerators and denominators independently.

Division: Invert the denominator (or divisor) and multiply it with the first rational expression (i.e. dividend or numerator) since reduction can only be done simply after changing the division into multiplication, as with fractions. As previously demonstrated, further simplification is equivalent to multiplication.

Now ,

Given rational expression is =4(x-1)/(x-1)(x+5)

=4/(x+5)                   ( x-1 is same in numerator and denominator so cut it)

Final Rational expression = 4/(x+5)

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The scale factor is 2. Then the perimeter of the triangle ΔCBF will be 64 units.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The perimeter of the triangle is determined by adding together all of its sides.

Triangle DEF ~ triangle CBE. Then the scale factor is given as,

Scale factor = 16 / 8

Scale factor = 2

The perimeter of the triangle ΔDEF is 32 units. Then the perimeter of the triangle ΔCBF will be given as,

P = (Scale factor) x (Perimeter of triangle ΔDEF)

P = 2 x 32

P = 64 units

The perimeter of the triangle ΔCBF will be 64 units.

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Evaluate f(3)

f(3) = 4(3)-2 = 12 - 2 = 10

f(3) = 10

f(x) = 6 = 4x- 2

4x=8

x = 2

The minimum number of $5-notes she has 32/3

Now, According to the question:

Siti opened her money box to find 50 pieces of $5-notes and $2-notes.

If the total value of all the notes is more than $132.

To find the minimum number of $5-notes she has

Based on the given condition:

= 2 × (50 - x) + 5x = 132

Apply Multiplicative Distributive law:

100 - 2x + 5x = 132

Rearrange the unknown terms on left sides of the equation:
-2x + 5x = 132 - 100

Combine like terms:

3x = 132 - 100

Calculate the sum or difference:

3x = 32

Divide the both sides of the equation by the coefficient of the variable:

x = 32 ÷ 3

Rewrite as fraction :

x = 32/3

Hence,  the minimum number of $5-notes she has 32/3

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Answer: 3=5, 6=10

Step-by-step explanation:

Basic Logic)

Three times two equals six, therefore the correspondent must also double itself.

Five times two equals ten.

Alternate Logic)

Three plus two-thirds of itself is five(3+2=5)

Six plus two-thirds of itself is four(6+4=10)

Answer:

10

Step-by-step explanation:

3=5

3+2

3x2= 6

2x2=4

6+4=10

Answer:

[tex]6^{5}[/tex]

Answer: If Zendaya invests $70 in an account paying a simple interest of 7.3% per year, and no money will be added or removed from the investment, she will have $75.11 in one year.

To calculate the amount of interest earned, you can use the formula:

Interest = Principal x Rate x Time

where

Principal = $70

Rate = 7.3/100 (expressed as a decimal)

Time = 1 year

So the interest earned is:

$70 x 0.073 x 1 = $5.11

To find the total amount at the end of the year, you add the interest to the original principal:

$70 + $5.11 = $75.11

Step-by-step explanation: