What is the domain?
ху
1
1
32
5 3
73
22
O {1, 2, 3, 4, 5, 6, 7}
O {1,2,3,5,7)
O {1,3,5,7)
O {1,2,3}

Evaluate f(3)

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

f(3) = 10

f(x) = 6 = 4x- 2

4x=8

x = 2

Therefore , the solution of the given problem of percentage comes out to be 61.29% .

A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100.

Here,

We recognize that the number is 77 in the provided table. consisting solely of seventh and eighth grade

There are 31 students in eighth grade.

Total number of 7th graders

=> (77-31) = 46

There are 46 kids in the 7th grade who use social media on average in this grade, depending on whether they spend more or less time on it.

In seventh grade, there were 19 students who spent more than an hour on a task.

38 pupils in all, including 7th and 8th graders, spend less than an hour on social media.

Total 8th graders using social media for less than an hour is (38- 19) = 19

Thus,  percentage of 8th grades is

=> 19/31 * 100

=> 61.29%

Therefore , the solution of the given problem of percentage comes out to be 61.29% .

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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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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:

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 volume of the cylinder will be 90π cm^3 i.e. D.

What is volume of a cylinder?

The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another. The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula,   πr^2h,

where r is the radius of the circular base and

h is the height of the cylinder. The material could be a liquid quantity or any substance which can be filled in the cylinder uniformly.

Therefore,

Volume of a cylinder = πr^2h

height of cylinder=10cm

radius=diameter/2=6/2=3cm

=π *3*3*10

Volume of a cylinder=90π cm^3

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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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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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Answer:

108

Step-by-step explanation:

Answer:108

Step-by-step:180/100×6=180080180×6=

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:

To solve the inequality 7x - 1 <= -50, we'll start by isolating x on one side of the inequality.

Add 1 to both sides: 7x <= -49

Divide both sides by 7: x <= -7

So the solution to the inequality is x <= -7.

This means that x can be any value less than or equal to -7. For example, -7, -8, -9, -10, etc. It is also possible to express this as an interval notation, which is (-∞, -7].

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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Answer:

Step-by-step explanation:

P = 2l = 2w

P - 2l = 2w

P - 2l / 2 = w

W = P - 2l /2

To translate a graph down and right, you would take each point on the graph and move it down and to the right by a given number of units. To be more specific, you would add the given number of units to the x-coordinate and add the given number of units to the y-coordinate.

A graph can be translated down and right by taking each point on the graph and moving it down and to the right by a given number of units. This means that for each point on the graph, the x-coordinate will be increased by the given number of units and the y-coordinate will be increased by the same number of units. This type of translation is often used to move a graph from one position to another on the coordinate plane. It can also be used to create a graph that is shifted from its original position. This shifting of the graph can be used to compare two different graphs or to move a graph to the origin. In either case, translating the graph down and right will move each point on the graph in the same direction and by the same number of units.

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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 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 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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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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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:

T < E

E < M

M > E

Step-by-step explanation:

The fraction 1/18 has the following decimal expansion :[tex]$0.0556=\frac{0}{10}+\frac{5}{100}+\frac{5}{1000}+\frac{6}{10000}$[/tex] . The fraction 1/18 is 0.05 .

The fraction 1/18 has the following decimal expansion:

[tex]$0.0556=\frac{0}{10}+\frac{5}{100}+\frac{5}{1000}+\frac{6}{10000}$[/tex]

A number's representation in base-10 is known as its decimal expansion (i.e., in the decimal system). Each "decimal place" in this system is made up of a digit from 0 to 9, arranged so that each digit is multiplied by a power of 10, decreasing from left to right, and with a decimal place designating the s place.

The real or inferred decimal point of a number is represented in its expanded form, or decimal form. 10.2 and 0.0084 are examples of decimal values that have actual decimal places. The entire number 17, which is really represented by the decimal point 17.000000000000, is an illustration of a number with inferred decimal points. It is a number in algebra that is irrational.

Therefore the correct answer is option C ) 0.05 .

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The number/word combination that best estimates each number is.

(a) 87,300,000:

(i) 8. 73 million

(ii) 87.3 million

(b) 2,670,000,000,000

(i) 2.7 trillion

(iv) 2700 billion

Note: In (a) option (ii) & (iv) are not correct, as 8.73 billion is 873000000000 and 87.3 billion is 87.3*1000000000 = 873000000000. In (b) option (ii) & (iii) are not correct, as 2.7 billion is 2700000000 and 2700 million is 270000000000.

I chose option (iii) for (a) because 87,300,000 is closest to 87.3 million. 87.3 million is also the correct way to express this number in the millions.

I chose option (i) for (b) because 2,670,000,000,000 is closest to 2.7 trillion. 2.7 trillion is also the correct way to express this number in trillions.

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Factoring or root extraction are not always effective ways to solve quadratic equations. The problem [tex]x^2[/tex]+x-1=0, for instance, cannot be solved by factoring since the expression [tex]x^2[/tex]+x-1 cannot be factored. Factoring other equations could be challenging.

The quadratic equation's standard form is a[tex]x^2[/tex] + bx + c = 0, where 'a' is the leading coefficient and a non-zero real number. Due to the word "quad" meaning "square," this equation, whose degree is 2, is referred to as "quadratic."

No. Every quadratic equation has two solutions, and they can all be factored, however as the difficulty increases, dividing may become more difficult, and people may start to apply the quadratic formula.

The basic theorem of algebra states that a polynomial of degree n has n solutions. There are always always two solutions to a quadratic problem. One method to resolve such an equation is through factorization.

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5, H is an element in the sample space for first rolling a number cube (with sides numbered 1-6) and then tossing a coin (with heads or tails outcomes).

Option (B) is correct.

What is the sample space in probability?

In probability, the sample space is the set of all possible outcomes of a random experiment. It is the set of all possible results of a random variable. For example, if you roll a die, the sample space would be the set {1, 2, 3, 4, 5, 6}. If you flip a coin, the sample space would be the set {heads, tails}. In more complex experiments, the sample space may be a combination of multiple outcomes from different processes.

B) 5,H is an element in the sample space for first rolling a number cube (with sides numbered 1-6) and then tossing a coin (with heads or tails outcomes).

Hence, 5, H is an element in the sample space for first rolling a number cube (with sides numbered 1-6) and then tossing a coin (with heads or tails outcomes).

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For many students, algebra is intimidating since it is the first math course they take where they are forced to deal with variables, abstract ideas, and original problem-solving techniques.

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the Answer is 1  so ya

The answer is 1.

Structure of the sequence is.

S = 1/2³, 1/2², 1/2¹, ......

The next term in our sequence should be,

= 1/2⁰ = 1/1 = 1

The sequence would continue,

= 1/2⁰, 1/2⁻¹, 1/2⁻², .... = ...., 1, 2, 4, .......

Therefore, the answer is.

∴ 1/8, 1/4, 1/2, 1 ....

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