Use the four-step procedure to solve the following problem. How much water must be added to a gallon of 10% saline solution to create a 2% solution?

A quantitative variable with a countable number of values is known as a discrete variable, which includes whole number counts such as the number of yellow M&Ms or total M&Ms in a sample

A quantitative variable that has a finite or countable number of values is called a discrete variable. Quantitative discrete data such as the number of phone calls received each day can only take certain numerical values, which are typically integers like zero, one, two, or three. This is different from continuous data, which can take any value within a certain range, like weight or percentage values that can include fractions and decimals.

For example, in the case of counting M&Ms, the number of yellow M&Ms and the total number of M&Ms would be discrete data because they can only be whole numbers. In contrast, the weight of the M&Ms in ounces and the percentage that are red are examples of continuous data because these can take on any value, including fractions, within the range.

The distinction between discrete and continuous data is important for selecting appropriate statistical methods for analysis, as certain methods are more suitable for discrete data, while others are better for continuous data

The amount of space between two points on a line is a distance.

In Mathematics and Geometry, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

[tex]Distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

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If quadrilateral ABCD is an isosceles trapezoid

The true statements among the given options  are written below

BC || AD

So option (1) is correct.

AB ≅ DC  

So option (3) is correct

∠CBA ≅ ∠BCD

So option (5) is correct.

In an isosceles trapezoid there is one pair of  legs of equal length and a pair of parallel  lines.

Given that quadrilateral ABCD is a isosceles trapezoid.

We have to check that out of the given options hold good for the isosceles trapezoid

[] BC ∥ AD

[] BD ⊥ AC

[] BA ≅ CD

[] BE ≅ ED

[] ∠CBA ≅ ∠BCD

In the given trapezoid ABCD

BC || AD ( pair of parallel sides )

So option (1) is correct.

AB ≅ DC  ( For an isosceles trapezoid legs are equal)

So option (3) is correct

∠CBA ≅ ∠BCD (According to  the property of isosceles  trapezoid )

So option (5) is correct.

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The algebraic expression 5xy has three factors: the number 5 and the variables x and y. Factors are the multiplicative components of an expression, and factoring involves breaking down expressions into these components.

The algebraic expression 5xy has three factors: the number 5, the variable x, and the variable y. A factor is a number, variable, or a product/quotient of numbers and/or variables separated by + or - signs.

When we are factoring, we are essentially reversing the distributive law and turning the expression into its multiple components, which can also be termed as factors or multiples. For instance, expressions like 5px, 5py, or similar expressions are all made up of factors that, when multiplied together, produce the value of the expression.

When addressing expressions that can be factored, such as ax² +2hxy+by² = 0, we look for expressions that, when evaluated, produce the same value. In this particular example, it can be factored into two linear factors and represents two straight lines intersecting at the origin.

Answer:

The algebraic expression [tex]\(5xy\)[/tex] has [tex]\(8\)[/tex] factors.

Explanation:

The algebraic expression [tex]\(5xy\)[/tex] can be factored as [tex]\(5 \times x \times y\)[/tex]. To find the number of factors, we count all the unique combinations of its prime factors:

- For the factor [tex]\(5\)[/tex], we have [tex]\(2\)[/tex] options: [tex]\(5\) or \(1\).[/tex]

- For the factor [tex]\(x\)[/tex], we have [tex]\(2\)[/tex] options: [tex]\(x\) or \(1\).[/tex]

- For the factor [tex]\(y\)[/tex], we have [tex]\(2\)[/tex] options: [tex]\(y\) or \(1\).[/tex]

Therefore, the total number of factors is the product of the options for each factor, which is [tex]\(2 \times 2 \times 2 = 8\)[/tex]. So, the algebraic expression [tex]\(5xy\)[/tex] has [tex]\(8\)[/tex] factors.

The total number of tests that the student has taken in the course will be 7.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

In a chemistry course, a student scored 99 on one test, 98 on another test, and 88 on each of the other tests.

Let 'x' be the total number of tests in which he scored 88. Then the equation is given as,

(99 + 98 + 88x) / (2 + x) = 91

197 + 88x = 182 + 91x

91x - 88x = 197 - 182

3x = 15

x = 5

The total number of tests is given as,

Total tests = 2 + 5

Total tests = 7

The total number of tests that the student has taken in the course will be 7.

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we know that

The line passing through the origin [tex](0,0)[/tex] and the point [tex](2,4)[/tex]

If the equation of the line passes through the origin

then

the equation of the line represent a direct variation

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

The constant k is equal to the slope m

with the point [tex](2,4)[/tex] find the constant of proportionality k

[tex]y/x=k[/tex]

substitute

[tex]4/2=k[/tex]

[tex]k=2[/tex]

The linear equation is equal to

[tex]y=2x[/tex]

therefore

the answer is

[tex]y=2x[/tex]

The required equation of the line passing through the origin and point (2, 4) is y = 2x.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at

x = 0.

Given, a line passes through origin (0, 0) and point (2, 4).

So slope is = (y₂ - y₁)/(x₂ - x₁) = (4 - 0)/(2 - 0) = 2.

Let the required equation of the line be y = mx + b.

∴ 4 = 2×2 + b.

b = 0.

So, the equation is y = 2x + 0 ⇒ y = 2x.

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5 x 4 x 3 x 2 x 1 = 120

120 different ways

Answer:

[tex]p(x)=-5x-x^2[/tex]

C is correct

Step-by-step explanation:

Quadratic function: A polynomial whose degree is 2 called quadratic function.

Degree = It is highest power of the polynomial.

We have to check the degree of each option.

Option 1: [tex]c(x)=6x+3x^3[/tex]

Degree = 3

Option 2: [tex]d(x)=x-8x^4[/tex]

Degree = 4

Option 3: [tex]p(x)=-5x-x^2[/tex]

Degree = 2

Option 4: [tex]k(x)=2x^2+9x^4[/tex]

Hence, [tex]p(x)=-5x-x^2[/tex] has degree 2. It would be quadratic function.

Follow below steps;

The student is asking how many adult tickets were sold for a school play if a total of 308 tickets were sold and the number of student tickets sold was three times the number of adult tickets sold. To solve this problem, we will use algebra to set up an equation.

Let's define x as the number of adult tickets sold. Since the number of student tickets is three times that amount, we can say that 3x represents the number of student tickets sold. The total number of tickets sold is the sum of adult and student tickets, which is given by the equation x + 3x = 308.

To find the value of x, we combine like terms:

Therefore, the number of adult tickets sold was 77.

Answer:

35x>400  can be used to find the value of x

Step-by-step explanation:

Here, we have given the information employee works for 35 hours a week

Let, x be the number of hours employee can work

Here it will become 35 x since, he is working for 35 hours

Employee is earning more than $400 per week

The inequality is formed from the given information as below:

35x>400

x>80/7

Therefore, 35x>400 can be used to find the value of x which is giving value of x>80/7

To convert 6.666666667 into an improper fraction, identify the whole number part and the repeating decimal part, which correspond to 18/3 and 2/3 respectively. Adding these together results in the improper fraction 20/3.

The questions asks how to express the decimal number 6.666666667 as an improper fraction. To convert a decimal to a fraction, we can identify the repeating part of the decimal, which in this case is '666...'. We know that repeating '6' corresponds to '2/3' in fraction form. To write it as an improper fraction, we first write the non-repeating part which is '6' as '6/1'. Then we add the repeating fraction '2/3' to it after converting '6/1' to have a common denominator of '3' which becomes '18/3'. Adding these gives us '20/3' which is the desired improper fraction.

To put this process into steps:

The average of all integers from 11 to 35 is determined by summing the first and last integers and dividing by 2. The calculation is (11 + 35) / 2, which equals to 23.

Calculating the Average of Integers

To calculate the average of all integers from 11 to 35, you sum up all the integers and then divide by the number of integers. Since the numbers form an arithmetic sequence, we can use the formula for the average, which is: (first term + last term) / 2. Therefore, the average is (11 + 35) / 2.

The calculation would then be 46 / 2, which equals 23. This value represents the mean or average of the integer set from 11 to 35. The concept of finding the average is a fundamental aspect of statistics and general mathematics that is commonly applied in various practical scenarios.

The average of all integers from 11 to 35 is 46.

To find the average of all integers from 11 to 35, we first calculate the sum of all the integers from 11 to 35. Then, we divide the sum by the total number of integers (i.e., 35 - 11 + 1 = 25). The sum of the integers from 11 to 35 is (11 + 12 + 13 + ... + 35). We can simplify this sum by using the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term. Plugging in the values, we get Sn = (25/2)(11 + 35) = 25(46) = 1150. Now, we can find the average by dividing the sum by the total number of integers: Average = 1150/25 = 46. Therefore, the average of all integers from 11 to 35 is 46.

Average tax rate out of Mr. Johnsons earning is equals to $3500.

" Tax rate is the process of finding the percentage of amount of earnings to be taxed."

According to the question,

Given,

Total money earned by Mr. Johnson per year = $100,000

Every year amount he spend = $70,000

Every year amount he saved = $30,000

Percentage of sales tax on his spending paid by Mr. Johnson = 5%

Average tax rate = 70,000 × ( 5 / 100)

                           = $3,500

Hence, average tax rate out of Mr. Johnsons earning is equals to $3500.

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