The (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² using difference of two squares.
What is the difference of two squaresConsidering two numbers a and b, the difference of their squares written as a² - b² is equal to the the product of the sum of the numbers and the difference of the numbers, that is (a + b)(a - b).
We have from the question two squares which are (a + b)² and (b + c)² and we shall express their difference as a product as follows:
(a + b)² - (b + c)² = [(a + b) + (b + c)][(a + b) - (b + c)]
open brackets and simplify;
(a + b)² - (b + c)² = (a + b + b + c)(a + b - b - c)
add and subtract like terms;
(a + b)² - (b + c)² = (a + 2b + c)(a + b - b - c)
(a + b)² - (b + c)² = (a + 2b + c)(a - c)
In conclusion, we have that (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² that is a difference of two squares.
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0=-25x+800 solve for x
-25x+800=0
-25x =-800
25x=800
x=32
Answer:
x = 32
Step-by-step explanation:
0=-25x+800
To solve for x, add 25x to each side
0+25x=-25x+800+25x
25x = 800
Divide each side by 25
25x/25 = 800/25
x = 32
Light travels at about 186,000 miles per second.
Which shows an equivalent speed?
(A)
(В)
O
D
1.86x103 miles per second
1.86x104 miles per second
1.86x105 miles per second
1.86x106 miles per second
Answer:
The answer is 1.86x10 6
Step-by-step explanation:
10x6 is 100k and the speed light travels is 186k so to get the answer you need to find the one that gets to 100k and then multiply it by 1.86
suppose that for a particular piece of machinery, the frequency distribution of monthly breakdowns is as follows: number of breakdowns prob. 0 0.50 1 0.25 2 0.10 3 0.10 4 0.05 the cost of a breakdown is $2,000, and the cost of a preventive maintenance program is $2,000 per month. if the preventive maintenance program is adopted, the probability of a machine breakdown is negligible. how much better off per month would the firm be if it adopted preventive maintenance? multiple choice $100 better off $2,000 better off $200 better off $100 worse off $200 worse off
$100 much better off per month would the firm be if it adopted preventive maintenance.
Given that,
We have to find how much more profitable would the company be each month if it implemented preventive maintenance.
We know that,
Number of Breakdowns are 0, 1, 2, 3, 4
The problems for the breakdowns are 0.50, 0.25, 0.10, 0.10, 0.05
Cost of a breakdown is $2,000
A monthly preventive maintenance programme costs $2,000
Expected probability of breakdown:
E(x) = Σ(X × p(x))
= (0×0.5) + (1×0.25) + (2×0.10) + (3×0.10) + (4×0.05)
= 0.95
E(x) ×cost of breakdown = (0.95 × 2000) = $1900
So, Difference between breakdown and preventive maintenance
1900 - 2000 = - $100
Therefore, $100 much better off per month would the firm be if it adopted preventive maintenance.
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Help finding the linear equation for this chart
The linear equation for the given chart is: y = -3x + 7.
How to Write a Linear Equation?From the chart given, we can use two pairs of values to find the slope (m) and the y-intercept (b), then plug in their values into the equation that is expressed in slope-intercept form as y = mx + b.
Using two points, (1, 4) and (3, -2), find the slope (m):
Slope (m) = change in y / change in x = (-2 - 4) / (3 - 1)
Slope (m) = -6/2
Slope (m) = -3
Find the y-intercept (b) by substituting m = -3 and (x, y) = (1, 4) into y = mx + b:
4 = -3(1) + b
4 = -3 + b
4 + 3 = b
7 = b
b = 7
To write the linear equation, substitute m = -3 and b = 7 into y = mx + b:
y = -3x + 7
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jerry graded seven standardized tests with the following scores: 60, 74, 41, 87, 94, 79, 57 which standardized test score represents the 50th percentile? 41 57 74 79
Answer: 74
Step-by-step explanation:
Answer:
74
Step-by-step explanation:
Got it right on the test.
Solve the given proportion 7/x 21/6 x = [?] Enter
Answer:
x=2
Step-by-step explanation:
7÷x=22÷6
cross multiply
7×6=21×x
21x=42
21x/21=42/21
x=2
a new vaccination is being used in a laboratory experiment to investigate whether it is effective. there are 273 subjects in the study. is there sufficient evidence to determine if vaccination and disease status are related?vaccination statusdiseasednot diseasedtotalvaccinated5762119not vaccinated8371154total140133273step 2 of 8: find the expected value for the number of subjects who are vaccinated and are diseased. round your answer to one decimal place.
The expected value for the number of subjects who are vaccinated and are diseased is 56.7
Since we are given the information that a new vaccination is being used in a laboratory experiment to investigate whether it is effective. there are 273 subjects in the study. We can calculate this by taking the total number of subjects who are vaccinated (119) and multiplying it by the proportion of subjects who are diseased
(47/273). 119 x (47/273) = 56.7
which is the expected value for the number of subjects who are vaccinated and are diseased
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Order these from least to greatest
Answer: -20, -19, -18, |-18|, |-22|, |30|
Step-by-step explanation:
A number with vertical lines on either side means the absolute value of that expression, i.e. how far it is from 0. An absolute value can be 0 or positive but never negative.
|-18| = 18
|-22| = 22
|30| = 30
Positive numbers are bigger, greater, or higher than zero. They are on the opposite side of zero from the negative numbers. Negative numbers get smaller the farther they are from zero. You can think of positive and negative numbers as being opposites because they are on opposite sides of the number line.
I hope this helps :)
Which of the following types of functions have inverse functions?
A.May-to-one
B.One-to-many
C.One-to-one
D.Many-to-many
One-to-one is the following types of functions have inverse functions.
What is a simple definition of a function?
As a set of inputs with one output for each, a function is defined as a relationship between them. In plain English, a function is an association between inputs in which each input is connected to precisely one output.
A function is a type of rule that produces one output for a single input. One function, many. function onto (Surjective Function) into: perform. Function of a polynomial.
What does function entail when it does not?
A function is a relationship between a domain and a range where every value in the domain only has one possible value in the range. This notion is violated by relations that are not functions.
They contain at least one value in the domain that relates to two or more values in the range.
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Need help answering this question
Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
The rate of change of the distance below the sea level with respect to time is 11 feet per second.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
The table has a linear relationship.
We can choose two data from the table.
At time = 15,
Distance below the sea level = 545 feet.
At time = 27,
Distance between the sea level = 677
Now,
The rate of change of the distance below the sea level with respect to time.
Slope:
= (677 - 545) / (27 - 15)
= 132 / 12
= 11 feet per second
Thus,
The rate of change of the distance below the sea level with respect to time is 11 feet per second.
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The rate of change of distance for the submarine is given by 11 feet/sec.
How to find the slope for two given points?In order to find the slope between two points (x₁, y₁) and (x₂, y₂), take the ratio of the difference of the respective coordinates as (y₂ - y₁)/(x₂ - x₁).
Given that,
The table for distance travelled versus time taken for a submarine.
In order to find the slope, take two values of distance and time from the given table as 380 feet at t = 0 and 545 feet at t = 15.
Now, the slope can be found as,
slope = (545 - 380)/(15 - 0)
= 165/15
= 11
Hence, the rate of change of distance below sea level with respect to time is given as 11 feet/sec.
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express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]
The limit as a definite integral on the interval [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π , 4π] is [tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex].
What is meant by definite integral?
A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.
Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.
If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.
Let the equation be
[tex]$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$[/tex]
substitute the values in the above equation, we get
= [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π, 4π],
simplifying the above equation
[tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex]
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Classify each proposition as simple or compound. Classify each compound proposition as i netton conjunction desunction conditional or biconditional 1. My friend took his master's degree in Spain.
2. Roses are red, but violets are blue. 3. You are entitled to a 30% discount if you are a member.
4. Boel was on time, but Tom was late,
5. Either he watches a niovie or dines with his friends.
6. If it is an acute angle, then it has less than 90
1. My friend took his master's degree in Spain :- Simple
2. Roses are red, but violets are blue. :- Compound
3. You are entitled to a 30% discount if you are a member.:- Compound
4. Boel was on time, but Tom was late.:- Compound
5. Either he watches a niovie or dines with his friends.:- Compound
6. If it is an acute angle, then it has less than 90.:- Simple
A simple sentence consists of just one clause. And it is consist of a subject and a verb.
A simple sentence has the most basic elements that make it a sentence: a subject, a verb, and a completes thought.
A compound sentence is made up of two or more independent clauses.
This compound sentence consist of two simple clauses connected by the coordinating conjunction 'and'.
Two independent clauses need to be connected with a coordinating conjunction or separated with a full stop or semicolon.
A simple sentence can also be refereed to as an independent clause.
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A drama class has a total of 39 students. The number of males is 17 more than the number of females. How many males and how many females are in the
class?
There are 28 males and 11 females in the class.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Let the number of males be x and the number of females be y. We know that x = y + 17 and x + y = 39.
Substituting the first equation into the second equation, we get:
y + y + 17 = 39
2y + 17 = 39
2y = 22
y = 11
The number of females is 11, and the number of males is x = y + 17 = 11 + 17 = 28.
Hence, there are 28 males and 11 females in the class.
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Use the table to write a proportion.
The proportion is 12 : 14 : : 18 : w and the value of w is 21
The number of shots in Game 2 is 21
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the 2 games be Game 1 and Game 2
Now , the equation will be
The number of points in Game 1 = 12
The number of shots in Game 1 = 14
And ,
The number of points in Game 2 = 18
The number of shots in Game 2 = w
So , the proportion equation is given as
Number of points in Game / number of shots in Game = number of points in Game / number of shots in Game 2
Substituting the values in the equation , we get
12 / 14 = 18 / w
Multiply by 14 on both sides of the equation we get
12 = ( 18 x 14 ) / w
Multiply by w on both sides of the equation , we get
12w = 18 x 14
Divide by 12 on both sides of the equation , we get
w = ( 18 x 14 ) / 12
On simplifying the equation , we get
w = 3 x 7
w = 21
Therefore , the value of w is 21
Hence , The proportion is 12 : 14 : : 18 : w and the value of w is 21
The number of shots in Game 2 is 21
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Help me please I don’t understand
The age of Michelle is 30 years old (option A).
What is Michelle's age?The mathematical operation that would be used to determine the required value is multiplication. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is ×.
The first step is to determine Fiona's age.
Fiona's age = Madeline's age x 2
Fiona's age = 5 x 2 = 10
The second step is to determine Michelle's age.
Michelle's age = Fiona's age x 3
Michelle's age = 10 x 3
Michelle's age = 30
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The map given shows the relationship between three streets. Suppose that m21.
+ m2=180.
Are Maple Street and Elm Street parallel? Explain.
Maple Street
Elm Street
River Drive
No because m1 and m42 are supplementary
Yes because m1 and m42 are supplementary
Yes because m1 and m2 are congruent.
No because m 21 and m22 are congruent.
-30
The correct statement regarding whether Maple Street and Elm Street are parallel lines is given as follows:
Yes, because angles 1 and 2 are supplementary.
How to define whether the lines are parallel?Parallel lines are two lines that do not intersect, or technically, intersect only at infinity.
In this problem, we have that angles 1 and 2 are supplementary angles, hence:
m<1 + m<2 = 180º
As the sum of the measures of supplementary angles is of 180º.
Then these two angles are classified as consecutive interior angles, meaning that Maple Street and Elm Street are parallel lines cut by the transversal River Drive.
Thus the second option is the correct option.
Missing InformationThe situation is represented by the image shown at the end of the answer.
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how to find equations of the lines that pass through given point and are parralell and perpendicular to the given line
We can find the equation of any line passing through a given point and parallel or perpendicular to a given line by finding the slope of the given line and using slope-intercept form.
Given, the line passing through a given point and parallel and perpendicular to a given line
we have to find the equation of the lines
Let l1 be a line passing through a point (p , q) and parallel to a line l2.
suppose the equation of the line l2 be,
y = mx + c
the line l2 has slope m
Now to find the equation of the line l1,
(y - q)/(x - p) = m
On cross-multiplying, we get
y - q = m(x - p)
y = mx - pm + q
So, the equation of the line l1 be,
y = mx + (q - pm)
Similarly, we can find the equation of any line passing through a point and parallel to a given line.
Hence, we can find the equation of any line with the slope.
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graph the line that has a slope of -3 and includes the point (1,5)
On solving the provided question, we got to know that - to plot the graph, required equation is 3x +y -8 = 0
What is an expression?a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples - 2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥
How do you write a mathematical expression?We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.
To plot the graph,
we need to find the equation first.
and to find the equation -
[tex](y - y1) = m(x - x1)\\here,\\x1 = 1\\y1 = 5\\m- ( -3 )[/tex]
equation -
(-3)(x-1) = y-5
-3x + 3 = y-5
3x - 3 = 5-y
3x +y -8 = 0
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HELP! I give Brainliest!!
A right rectangular prism is 3 in by 4.75 in by 20.5 in. What is the total surface area of the prism?
151.5 in²
173.125 in²
317.75 in²
346.25 in²
The rectangular prism that has the dimensions of 3 inches by 4.75 inches by 20.5 inches, has a total surface area, found by adding the surface areas of the six faces of 346.25 in²
What is the surface area of an object?The surface area of a solid three dimensional object is the area of the boundary surface of the object and its surroundings.
The dimensions of the rectangular prism in the question can be defined as follows;
Let the length of the rectangular prism = 3 inches
Let the width of the prism = 4.75 inches
Let the height of the prism = 20.5 inches
The surface area, A, of a rectangular prism can be found using the formula
A = 2 × Length × Width + 2 × Length × Height + 2 × Height × Width
Therefore, the surface area of the rectangular prism in the question is found as follows;
Area, A = 2 × 3 × 4.75 + 2 × 3 × 20.5 + 2 × 20.5 × 4.75 = 346.25
The total surface area of the rectangular prism is; 346.25 in²
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if the racetrack publishes that the odds in favor of a horse winning a race are 3 to 5, what is probability that the horse will not win the race? a) 0.3333 b) 0.3750 c) 0.2000 d) 0.6250 e) 0.0667 f) none of the above.
Probability that the horse will not win the race is d) 0.6250
What is a probability ?
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
odds in favour of winning a race of 3:5
thus, 3 chances of winning to every 5 chances of losing.
So, if the race were held 8 times, one would be expected to win 3 races and lose 5 races.
Thus, the probability of winning the race is 3/8.
Probability that the horse will not win the race is 1- 3/8 = 1 - 0.3750 = d) 0.6250
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a flight overbooked by 4 passengers
(Write an integer to represent the equation)
The integer the represent a flight overbooked by 4 passengers is y = x + 4
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given,
A flight overbooked by 4 passengers.
Let, x = Initial capacity of the flight to have passengers
and, y = Total capacity after adding all the passengers
so, the equation is
y = x + 4
Therefore, the integer the represent a flight overbooked by 4 passengers is y = x + 4.
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Question
Find the range of the function represented by the list of ordered pairs below.
((-9, 4). (-0,3). (-8,0). (-2, -4))
Answer: {4,3,0,-4}
Step-by-step explanation:
The range is the set of all the values of y
Range {4,3,0,-4}
a student's exponential model has smaller residuals than their quadratic model. what can you infer about their experiment?
You can infer that the exponential model is a better fit for the data in the experiment, as it has smaller residuals than the quadratic model.
Residuals are the difference between the actual data points and the predicted values generated by the model. They are a measure of how well a model fits the data, and a lower residual indicates a better fit. Therefore, if the student's exponential model has smaller residuals than their quadratic model, it can be concluded that the exponential model is a better fit for the experiment data.
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ASAP (GET LOTS OF POINTS) If ABCD is a parallelogram, find m∠D.
Answer:
∠D = 127°
Step-by-step explanation:
Let's define the properties of a parallelogram to understand how to solve for ∠D.
⭐The opposite angles in a parallelogram are congruent.
∠D = ∠B∠A = ∠C⭐The sum of the interior angles of a parallelogram is 360°.
∠A + ∠B + ∠C + ∠D = 360°or: 2(∠A) + 2(∠B) = 360°or: 2(∠D) + 2(∠C) = 360°First, let's solve for x knowing that the opposite angles are congruent.
∠A = ∠C
[tex]13x - 25 = 9x - 1[/tex]
[tex]13x - 9x = 25 - 1[/tex]
[tex]4x = 24[/tex]
[tex]x = 6[/tex]
∴ x = 6
Next, substitute x into ∠C.
∠C = 9x - 1
∠C = 9(6) - 1
∠C = 54 - 1
∴ ∠C = 53°
Finally, substitute ∠C into the equation 2(∠D) + 2(∠C) = 360° to solve for ∠D.
2(∠D) + 2(∠C) = 360°
2(∠D) + 2(53) = 360
2(∠D) + 106 = 360
2(∠D) = 254
∴ ∠D = 127°
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Which of the following is an example of discontinuous class?
(a) 10-15, 15-20 (b) 5-9, 10-14 (c) 0-5, 10-15
(d) none of these
The correct answer is (a) 10-15, 15-20. This is an example of a Discontinuous class.
In the context of statistical data and classification, a class is a group of observations or data points that share certain characteristics. Classes can be either continuous or discontinuous, depending on whether the values or categories they represent are continuous or not.
A discontinuous class is a set of values or categories that are not continuous, meaning there are gaps or breaks between them. In this case, the classes 10-15 and 15-20 are discontinuous because there is a gap between them at 15. In contrast, the classes 5-9 and 10-14 are continuous because there are no gaps between them, and 0-5 and 10-15 are also continuous because the lower bound of the second class is equal to the upper bound of the first class.
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Click and drag like terms onto each other to simplify fully.
66+3x+3x-6−6+4+4+5y+5y
Answer:
62 + 6x + 10y
Step-by-step explanation:
1. add the x's together
3x+3x = 6x
2. add the constants together
66-6-6+4+4 = 62
3. add the y's together
5y + 5y = 10y
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The required choice for inequality is Option 2.
What is inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.
Given, 3(8 – 4x) < 6(x – 5)
or, 24 - 12x < 6x - 30
or, 24 + 30 < 6x + 12x
or, 54 < 18x
or, 18x > 54
or, x > 3 means x is greater than positive 3 and pointing to the right.
Hence, the required choice for inequality is Option 2.
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Answer: b
Step-by-step explanation:
Is this Relation a Function?
{(0,2),(3,4),(-3,-2),(2,4)}
Answer:
Yes.
Step-by-step explanation:
In order for a relation to be a function, Each y value must have a unique x value. If there is any point where a vertical line hits the relation in two places, it is not a function. This relation follows the rules of being a function, and therefore is a function.
the length of a rectangle is less than double the width, and the area of the rectangle is . find the dimensions of the rectangle.
The dimensions of the rectangle are 6 and 3.5 ft.
Let the width of rectangle be x. So, the length of the rectangle will be 2x - 1. As per the known fact, the area of rectangle is given by the formula -
Area = length × breadth
Keep the values in formula to find the dimensions of the rectangle
x(2x - 1) = 21
Performing multiplication on Left Hand Side of the equation
2x² - x = 21
Rewriting the equation
2x² - x - 21 = 0
On factorizing we get, x = -3 and 3.5.
The dimensions of rectangle can not be negative, this, taking the value of x as 3.5. Now, the width of rectangle will be 3.5.
Length of rectangle = (2×3.5 - 1)
Length of rectangle = 7 - 1
Length of rectangle = 6
Thus, the length and width is 6 and 3.5 ft respectively.
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The complete question is -
the length of a rectangle 1ft less than double the width ,and the area of the rectangle is 21ft^2 find the dimensions
Look carefully at the triangle in the diagram.
The value of x is ___ °
Answer:
60 or 90 degrees
Step-by-step explanation:
if one angle is 30 the other has to be 60 or 90 as they are common múltiples due the cosine rule and pythogras therom (mind my spelling).
