Answer:
4 gallons of water should be added in 10% saline solution.
Step-by-step explanation:
Let x gallon of water is added in one gallon of 10% saline solution.
Therefore total volume of 10% saline solution will become (1 + x) gallons
Since concentration of water is 0% so equation will be
0.10(1) + 0(x) = .02(1 + x)
0.10 = 0.02(1 + x)
1 + x = [tex]\frac{0.10}{0.02}[/tex]
x + 1 = 5
x = 5 - 1
x = 4 gallons
Therefore, 4 gallons of water should be added to 10% saline solution to create 2% solution.
Shyam invested money in the stock market
Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p.m. and walks at 50 steps per minute. Malory leaves her house at 12:20 p.m. and walks at 90 steps per minute.
At what time will Malory's steps catch up to Dori's steps?
If quadrilateral ABCD is an isosceles trapezoid, which statements must be true? Check all that apply. (Pick more than one)
[] BC ∥ AD
[] BD ⊥ AC
[] BA ≅ CD
[] BE ≅ ED
[] ∠CBA ≅ ∠BCD
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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Algebraic expression of 25 more than a number n
How do you rewrite y+4=-2(x-1) in slope-intercept form
What is the length of BC¯¯¯¯¯
Simplify 7a+(-10)-2a+1
The measure of a and the measure of b are complementary. the measure of a is 8 times the measure of
b. find the measurement of each angle.
How many factors does the algebraic expression 5xy have?
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.
What is the average of all integers from 11 to 35?
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.
Explanation: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.
Explanation: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.
14+3x−7=7x+7−4x14+3x-7=7x+7-4x is always, sometimes or never true.
What is the value of x?
A. 68°
B. 62°
C. 112°
D. 124
Write this number using digits: four million, ninety-eight thousand, seven hundred sixty-two
ana made 12 rainbow loom bracelets in 3 hours. how many can she make in 15 hours
-10x+5y=0 -4x-6y=54 find the solution of this system of equations
What is the amount of space between two points on a line. It is always expressed as a nonnegative number
The amount of space between two points on a line is a distance.
What is a line segment?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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A total of 308 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was three times the number of adult tickets sold. how many adult tickets were sold?
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:
x + 3x = 4x4x = 308x = 308 \/ 4x = 77Therefore, the number of adult tickets sold was 77.
What equation do you use to find average speed?
Mr. johnson earns $100,000 per year. each year he spends $70,000 and saves $30,000. he pays a 5 percent sales tax on all of his spending. assuming this is the only tax he pays, his average tax rate out of his income is
Average tax rate out of Mr. Johnsons earning is equals to $3500.
What is tax rate?
" 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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Write each expression in radical form
a. (10n)3/2
b. a6/5
3/2 and 6/5 are all exponents
PLEASE HELP! What is the equation of this line? y = 2x y=−12x y=12x y=−2x Graph of a line passing through the origin and the point begin ordered pair 2 comma 4 end ordered pair
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.
What are lines and their slopes?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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How do you solve 1650÷55
In a chemistry course, a student scored 99 on one test, 98 on another test, and 88 on each of the other tests. the student’s test average for the course, where each test is weighted equally, is exactly 91. what is the total number of tests that the student has taken in the course?
The total number of tests that the student has taken in the course will be 7.
What is Mean?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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What is 6.666666667 as a improper fraction?
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:
Identify 6 as the whole number part, which is equivalent to 6/1 or 18/3.Recognize that the repeating decimal .666... is equivalent to 2/3.Add 18/3 and 2/3 to get 20/3, which is the improper fraction form of 6.666666667.Explain how to compare 0.7 and 5/8.
Which function is a quadratic function
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.
A quantitative variable that has a finite or countable number of values is called
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 store employee works 35 hours per week,which inequality can be used to find the dollar value x, of weekly sales that the employee must make to earn more than $400 per week
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
There are 5 participants in a potato sack race. find the number of orders in which the participants can finish
5 x 4 x 3 x 2 x 1 = 120
120 different ways
Is the function g(x)= - 6x– 5 6 linear or nonlinear?