Therefore , the solution of the given problem of inequality comes out to be ax - b > c, we get ax - b > c or ax - b < -c, which is the same as
|ax - b| > c.
What does inequality actually mean?A mathematical inequality is a relationship or group of values without the equal sign. Equity usually comes after equilibrium. When two parameters are not equal, inequality results. Between equality and inequality, there are differences. Because the numbers are not equal or variable it was chosen to use the most common symbol (). Any difference, no matter how little or significant, can be utilised to compare values.
Here,
One possible equivalent compound inequality is:
ax - b > c or ax - b < -c
To see why this is true, consider the two cases:
Case 1: ax - b > c
If we take the absolute value of both sides, we get |ax - b| > c, which is the original inequality.
Case 2: ax - b < -c
If we multiply both sides by -1, we get -ax + b > c.
Adding ax to both sides, we get b > ax + c. If we subtract this inequality from
=> ax - b < -c
=> -2b < -2c, or b > c.
Substituting b > c back into the inequality ax - b < -c, we get ax < 0. Multiplying both sides by -1 (since c >= 0),
we get
-ax > 0, or ax < 0.
Combining this with the inequality ax - b > c, we get ax - b > c or ax - b < -c, which is the same as |ax - b| > c.
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What is the value of x in this triangle?
The value of x in the triangle, given the angle measures of the other angles, is D. 100 degrees
How to find the value of x ?To find the value of x, you first need to find the value of the last interior angle in the triangle.
The sum of the interior angles of a triangle would add up to 180 degrees which means that the angle inside would be :
= 180 - 65 - 35
= 180 - 100
= 80 degrees
Angles on a straight line add up to 180 degrees so the value of x, which is on a straight line with 80 degrees, is :
= 180 - 80
= 100 degrees
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For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNA-based tests to detect TB that can be done in a couple of hours.
We have the following data on a DNA test for TB
· If a person does not have TB then the DNA test always is negative.
· If a person does have TB, then the DNA test will be positive 94% of the time.
Assume that we will use the test in Africa where the rate of incidence of TB is 450 per 100,000.
Has TB
Does not have TB
Row Totals
Test result: negative
Test result: positive
P
Column Totals
Q
100,000
What is the value of P?
· 100,000
· 99,550
· 450
· 423
For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNA-based tests to detect TB that can be done in a couple of hours. We have the following data on a DNA test for TB • If a person does not have TB then the DNA test always is negative. • If a person does have TB, then the DNA test will be positive 94% of the time. Assume that we will use the test in Africa where the rate of incidence of TB is 450 per 100,000. Has TB Does not have TB Row Totals Test result: negative Test result: positive P Column Totals Q 100,000 What is the value of P? • 100,000 • 99,550 • 450 • 423
The number of positive results for all persons with TB will be D. 423
How to calculate the value of PProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true
Rate of incidence of TB is 450 per 100,000
Column Totals of "Has TB" = (450 / 100,000) * Grand Total = (450 / 100,000) * 100,000 = 450
If a person does have TB, then the DNA test will be positive 94% of the time.
Therefore, P = Number of positive results for all persons with TB:
= 0.94 * 450
= 423
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A -foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is , and that the angle of depression to the bottom of the monument is. How far is the person from the monument? round the answer to the nearest hundredth.
The distance between the man and the monument is 1060.16 feet.
Here we have the angle of elevation to be 18°
and the angle of depression to be 3°
Let the distance between the man and the monument be x feet
Now for any angle a, tana = opposite angle / adjacent angle
Hence we can sum up the building's height to be
x tan18 + x tan3 = 400
or, x(tan18 + tan3) = 400
or, x(0.3249 + 0.0524) = 400
or, 0.3773x = 400
or, x = 400/0.3773
or, x = 1060.16
Hence the distance between the man and the monument is 1060.16 feet.
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Two trains start from towns 540 mi apart and travel towards each other on parallel track. They pass each other 4.5 hr later. If one train travels 20 mph faster than the other, find the rate of each train
- A commonly used fraction that helps you understand a different size or amount is called a
Answer:
A commonly used fraction that helps you understand a different size or amount is called a ratio.
Step-by-step explanation:
A ratio is a comparison of two or more quantities or measurements, expressed as a fraction or a colon. Ratios are commonly used to express the relationship between different amounts or sizes, and they can be used to help solve problems involving proportions, rates, and percentages. For example, if you are making a recipe that calls for two cups of flour and one cup of sugar, the ratio of flour to sugar is 2:1, or 2/1. Ratios can also be expressed in decimal or percentage form!
Which best describes the rate at which Mandy used up her bags of dog food?
OA. 6 bags per day
OB. 2/3 bags per day
OC. 4 bags per day
OD. 3/2 bags per day
The rate at which Mandy used up her bags of dog food is 2/3 bags per day
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Slope = change in y /change in x
Here, Slope = change in bags of food/ /change in days
form the graph = 4/6 = 4 bags per 6 days
4/6 simplifies to 2/3
=> 2/3 bags per day
The rate at which Mandy used up her bags of dog food is 2/3 bags per day
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What is 2 3/4 X 12 ????
Answer:
33
Step-by-step explanation:
Please brainliest, and Hope this helped you, I also answered first! :D
Answer: 33
Step-by-step explanation:
the coordinates of the endpoints of jk are j(5,19) and k(11,1). point l is on jk and divides it such that jl:kl is 5:1. what are the coordinates of l?
The coordinates of point l are (8,9).
What is coordinate?Numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.
To find this point, we must first calculate the midpoint between j and k. The midpoint can be found by taking the average of the x-coordinates and y-coordinates. The midpoint between j and k is (8,10). Since the ratio of jl:kl is 5:1, we can determine that l is 5 units away from j and 1 unit away from k. This means that l must be 5 units up and 1 unit to the right from the midpoint. Thus, the coordinates of l are (8,9).
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Need help, thanks!
Last question
The maximum total deduction that can be claimed is OE. $17,100.
What is deduction ?
Deduction refers to the process of subtracting or taking away something. In the context of taxes, a deduction is a specific amount of money that a taxpayer is allowed to subtract from their income before calculating their tax liability. Deductions are one way to reduce the amount of taxes owed and can help to lower a person's overall tax burden.
There are two main types of deductions in the U.S. tax system: standard deductions and itemized deductions. The standard deduction is a fixed amount that varies depending on the taxpayer's filing status, while itemized deductions are specific expenses that a taxpayer can deduct from their taxable income. Some common examples of itemized deductions include mortgage interest, charitable contributions, medical expenses, and state and local taxes.
It's important to note that not all deductions are available to all taxpayers, and there are specific rules and limits that apply to each type of deduction. It's also important to keep accurate records and documentation to support any deductions that are claimed on a tax return.
The maximum total deduction that can be claimed is OE. $17,100, because that is the sum of the deductible expenses and the standard deduction.
The question is asking for the maximum total deduction that can be claimed, given certain deductible expenses and a standard deduction.
The standard deduction for the tax year is $6,100, and the deductible expenses are $6,000 in mortgage interest and $5,000 in charitable contributions.
Since the deductible expenses ($6,000 + $5,000 = $11,000) are less than the standard deduction of $6,100, it makes sense to use the standard deduction instead of itemizing deductions.
Therefore, the maximum total deduction would be the sum of the deductible expenses and the standard deduction:
$11,000 + $6,100 = $17,100
So, the maximum total deduction that can be claimed is OE. $17,100.
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For the rotation 664°, find the coterminal angle from 0° ≤ 0 < 360°, the quadrant,
and the reference angle.
The coterminal angle is
of
°, which lies in Quadrant, with a reference angle
The coterminal angle is 304°, which lies in the fourth quadrant with a reference angle of 44°.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To find the coterminal angle of 664°, we can add or subtract any multiple of 360° to it.
664° - 360° = 304°
The coterminal angle of 664° is 304°.
To determine the quadrant that 664° lies in, we can divide it by 90° and take the quotient:
664° ÷ 90° = 7 with remainder 34
As remainder is 34 and it is less than 90, the angle lies in the fourth quadrant.
To find the reference angle of 664°
we can subtract the nearest multiple of 90°:
664° - 6(90°) = 44°
The reference angle of 664° is 44°.
Therefore, the coterminal angle is 304°, which lies in the fourth quadrant with a reference angle of 44°.
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If using the method of completing the square to solve the quadratic equation
2? + 7x + 27 = 0, which number would have to be added to "complete the
square"?
The number that completes the square is 12.25
How to determine the number that completes the squareFrom the question, we have the following parameters that can be used in our computation:
x^2 + 7x + 27 = 0
Take the coefficient of x
So, we have
k = 7
Divide by 2
k/2 = 3.5
Take the square of both sides
Square = 12.25
This means that the number to add is 12.25
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Find the terminal point
P(x, y)
on the unit circle determined by the given value of t.
t = −
4
3
The terminal point of p(x,y) on the unit circle is (-2, -1).
What is unit circle?The unit circle is a circle with a radius of 1, centered at the origin (0, 0) on a Cartesian coordinate system. It is used to illustrate relationships between angles and their corresponding trigonometric functions. The unit circle is also used to explain concepts in trigonometry such as the sine and cosine functions, the Pythagorean theorem, and the definitions of the six trigonometric functions. It is especially useful in solving problems involving angles, such as finding the values of trigonometric functions given the angle in radians.
Step 1: Find the angle t in its standard form.
t = -4π/3 + 2π = -2π/3
Step 2: Calculate the coordinates using the unit circle formula.
x = cos(-2π/3)
x = -1/2
y = sin(-2π/3)
y = -√3/2
Step 3: The terminal point of p(x,y) on the unit circle is (-2, -1).
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Use this table to answer the question. Round to 2 decimal places.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total are made up of Trains?
Trains make up approximately 49.04% of the total journeys across all modes of transportation.
We must divide the total number of train trips by the total number of trips made using all modes of transportation, then multiply the result by 100 to get the percentage that trains make up of the total.
There have been 2320 train trips overall, and there have been 4730 trips overall using all forms of transportation.
Trains therefore account for the following proportion of the total:
(2320 / 4730) x 100% = 49.04%
Train travel thus accounts for roughly 49.04 percent of all travels made using all modes of transportation.
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Tell whether the ratios are equivalent: 3 miles to 4 minutes and 9 miles to 12 miles. Show your work.
Answer:
they are
Step-by-step explanation:
divide 12*4=3
9*3=3
same ratio
What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x minus 2
1 over the quantity x plus 3 times the quantity x plus 4
1 over the quantity x plus 3 times the quantity x minus 2
1 over the quantity x plus 4 times the quantity x minus 2
1 over the quantity x plus 3 times the quantity x plus 1
Answer: To simplify the expression, we can start by rewriting it as the product of the first fraction and the reciprocal of the second fraction. Then, we can factor the denominators of each fraction and simplify as much as possible.
x + 1 / (x^2 + x - 6) ÷ (x^2 + 5x + 4) / (x - 2)
= (x + 1 / (x + 3)(x - 2)) ÷ ((x + 4)(x + 1) / (x + 4)(x - 1))
= (x + 1 / (x + 3)(x - 2)) * ((x + 4)(x - 1) / (x + 4)(x + 1)) (reciprocal of second fraction)
= (x + 1 / (x + 3)(x - 2)) * (x - 1 / (x + 1)) (cancel out (x + 4) and simplify)
= (x + 1) * (x - 1) / (x + 3)(x - 2)(x + 1) (multiply the numerators and simplify)
= (x - 1) / (x + 3)(x - 2) (cancel out (x + 1) in the numerator and denominator)
Therefore, the simplified form of the expression is 1 / ((x + 3)(x - 2) / (x - 1)). This can be further simplified to:
1 / ((x + 3)(x - 2) / (x - 1)) = (x - 1) / ((x + 3)(x - 2)) * (x - 1) / 1 = (x - 1)^2 / ((x + 3)(x - 2))
So the answer is: 1 over the quantity (x + 3) times the quantity (x - 2), all multiplied by the quantity (x - 1) squared.
Step-by-step explanation:
The simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
The given expression is:
[tex]\frac{x+1}{x^2+x-6} / \frac{x^2+5x+4}{x-2}[/tex]
When a fraction is in the denominator, we take the reciprocal of the fraction and multiply it with the numerator.
So the expression becomes,
[tex]\frac{x+1}{x^2+x-6} * \frac{x-2}{x^2+5x+4}[/tex]
We can factorize the expression x² + x - 6
x² + 3x - 2x - 6
= x(x+3) -2 ( x+3)
= (x-2) (x+3)
We can also factorize the expression x² +5 x +4
x² + 4x + x +4
= x(x+4) +1 ( x+4)
= (x+1) (x+4)
Substituting these values, the expression becomes as follows:
[tex]\frac{x+1}{(x-2)*(x+3)} * \frac{x-2}{(x+1)(x+4)} = \frac{1}{(x+3)(x+4)}[/tex]
Therefore the simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.
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6 In a school the ratio of teachers : male learners: female learners is 1 : 7:8. The total number of learners is 720. Find the number of teachers in the school.
Using the given ratio, we can see that there are 48 teachers.
How to find the number of teachers?Here we know that the ratio of teachers to male learners to female learners is:
1:7:8
So for each teacher there are 7 female learners and 8 male learners, for a total of 15.
So we can simplify this and say that there are 15 learners for each teacher.
Then if there are 720 learners, the number of teachers is:
720/15 = 48
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Let u and v be linearly independent unit vectors. Find the set of all possible values of u⋅v. Give your answer in interval notation.
If u and v be linearly independent unit vectors then the set of all possible values of u⋅v is zero.
What are Vectors?Vectors are used in science to describe anything that has both a direction and a magnitude.
Since u and v are unit vectors, their magnitudes are both 1.
|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v
= 1 + 2u⋅v + 1
= 2 + 2u⋅v.
On the other hand, we also have:
|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v = 2,
since u and v are linearly independent and hence orthogonal.
Equating the two expressions for |u + v|² we get:
2 + 2u⋅v = 2,
u⋅v = 0.
Therefore, the only possible value for u⋅v is 0.
Hence, u and v be linearly independent unit vectors then the set of all possible values of u⋅v is zero.
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need help with part b
The image of the polygon after the rotation is added as an attachment
How to determine the image of the polygonFrom the question, we have the following coordinates that can be used in our computation:
(1, 0), (2, 0), (0, 2) and (2, 2)
The location of point G is
G = (3, -1)
To rotate about point G, we start by subtracting the points from G
So, we have
[(1, 0), (2, 0), (0, 2) and (2, 2)] - (3, -1)
This gives
(-2, 1), (-1, 1), (-3, 3) and (-1, 3)
The rule is 90 degrees clockwise rotation
This is represented as
(x, y) ⇒ (y, -x)
So, we have
(-2, 1), (-1, 1), (-3, 3) and (-1, 3) ⇒ (1, 2), (1, 1), (3, 3) and (3, 1)
Next, we plot (1, 2), (1, 1), (3, 3) and (3, 1)
See attachment for the image of the transformation
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A group of students have been surveyed to determine if they prefer to work in groups or individually for projects. There are 8 students who prefer to work in groups for every 10 students who prefer to work individually. If there were 2,200 students who prefer to work in groups, how many students were surveyed in total?
The sum of the ages of Farhan and his cousin is 38. Seven years ago, Farhan was thrice as old as his cousin. Find Farhan's present age.
Answer:
25
Step-by-step explanation:
let farhan's age be x and his cousin's age be y
sum of ages = x + y = 38
7 years ago (so x-7 and y-7), farhan was thrice as old as his cousin, so 3 * his cousin's past age = farhan's past age= 3 *(y-7) = x-7
subtract y from both sides in the first equation to solve for x
x = 38-y
substitute this into the second equation
3 *(y-7) = 38-y-7
3y-21 = 31-y
add y to both sides to put all y values on one side
4y -21 = 31
add 21 to both sides to solve for y
4y = 52
y = 13
sum of ages = x + y = 38 = 13 + x so x = 25 = 38-13
Find the values of the sine, cosine, and tangent for LA-
A
4 m
B
3 m
с
Mark this and return
Save and Exit
Next
S
The sine, cosine and tangent are obtained applying the trigonometric ratios presented in this problem.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.The hypotenuse is the slanted segment connecting the horizontal and the vertical segment.
For the desired angle, you must identify the adjacent side(between the angle and the angle of 90º) and the opposite side.
Missing InformationThe problem is incomplete, hence the concepts needed to obtain the sine, cosine and tangent were presented.
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In Hillsdale, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 15 miles and the
distance between the courthouse and the city pool is 25 miles, how far is the library from the
community pool?
The library is 20 miles from the community pool as calculated after performing mathematical operations.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, In Hillsdale, the library is due south of the courthouse and due west of the community swimming pool.
Also given,
The distance between the library and the courthouse is 15 miles.
The distance between the courthouse and the city pool is 25 miles,
Using the Pythagorean theorem, we have:
x = 25² - 15²
x² = 625 - 225
x = 400
Taking the square root of both sides, we get:
x = 20
Therefore, the library is 20 miles from the community pool
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Solve for x.
Show work
Answer:
x=11.34
Step-by-step explanation:
Select all that have a value of 0. cos(pi)/2 cos 0 sin 0 sin3(pi)/2
cos(0) and sin(0) both have a value of 0, so they would be selected.
cos(pi)/2 is equal to -0.5, and sin(3(pi)/2) is equal to -1, so they would not be selected.
Answer:
1 | 3 | 5
Step-by-step explanation:
sin 0 sin 3pi/2 and tan pi
cos pi/2 is -.5
cos 0 is 1
Michelle is buying a 95,000 dollar home. She has been approved for a 4.95% APR, 30 year mortgage. She made a 15% down payment and will be closing on April 8th. How much should she expect to pay in prepaid interest at the closing
Answer:
b
Step-by-step explanation:
because u can tell
At the closing of her home purchase, Michelle should expect to pay prepaid interest of $6,934.50. This amount represents the interest accrued from April 8th to the end of the month.
The monthly payment for Michelle's mortgage is calculated as follows:
Principal and interest payment = (95,000 - 15,000) x 0.0495 / 12
This equals a monthly payment of $420.63.
Michelle's total interest over the life of the loan is $119,750. This amount is the sum of her prepaid interest and the total interest she pays over the life of the loan.
Kayden and his children went into a grocery store where they sell apples for $0.75 each and mangos for $2 each. Kayden has $20 to spend and must buy a minimum of 16 apples and mangos altogether. Also, he must buy no less than 16 apples. If x represents the number of apples purchased and y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.
If x represents the number of apples purchased and y represents the number of mangos we can set up the following:
Kayden has $20, so can spend up to this amount:
0.75x + 2y ≤ 20He must buy a minimum of 16 apples and mangos altogether:
x + y ≥ 16Also, he must buy no less than 16 apples:
x ≥ 16We also need to consider y can't be negative, hence add one more inequality:
y ≥ 0Plot all four inequalities and see what is the zone of intersection.
The solution is the set of whole coordinates for x and y within the triangle with vertices at (16, 0), (16, 4) and (26.67, 0).
One possible solution is (20, 2) another one (24, 1).
See attached.
A television manufacturer produces x sets per week so the total cost of production is given by relation C(x)=x²-195x² +66000x+15000 find how many television sets must be manufacturer per week to minimize the total cost.
We require x = 170 televisions to minimize total cost
What is the minimum of a function?The minimum of a function is the lowest value of that function.
How to find how many television sets must be manufacturer per week to minimize the total cost.?Given that a television manufacturer produces x sets per week so the total cost of production is given by relation C(x) = x² - 195x² + 66000x + 15000.
To find the minimum value, we differentiate C(x) with respect to x and equate to zero.
So, C(x) = x² - 195x² + 66000x + 15000
dC(x)/dx = d(x² - 195x² + 66000x + 15000)/dx
= dx²/dx - d195x²/dx + d66000x/dx + d15000/dx
= 2x - 195(2)x + 66000 + 0
= 2x - 390x + 66000
= -388x + 66000
Equating to zero, we have
dC(x)/dx = 0
-388x + 66000 = 0
-388x = -66000
x = -66000/-388
x = 170.1
x ≅ 170
So, we require x = 170 televisions to minimize total cost
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(a) The length of a rectangle is 6 cm more than its width, w cm. The perimeter of the rectangle is 37 cm. Form an equation in w and solve it to find the width of the rectangle.
The width of the rectangle whose perimeter is 37 cm is 6.25 cm.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The length of a rectangle is 6 cm more than its width, w cm.
So, the length = w + 6
The perimeter of the rectangle is 37 cm.
Then, Perimeter of the rectangle = 37
2(l+ w) = 37
2( w+ 6 +w )= 37
2(2w + 6)= 37
4w + 12 = 37
4w = 25
w = 6.25 cm
and, length = w+ 6 = 6 + 6.25 = 12.25 cm
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√2x = 3 solve for x?
Answer:
9/2
Step-by-step explanation:
g bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.truefalse
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
What are error bars?A confidence intervals bar chart (shown as red lines)
In graphs, error bars are used to graphically show data variability and to denote error or uncertainty in reported measurements. They provide a basic indication of a measurement's accuracy or, alternatively, how far the true (error-free) value may deviate from the reported value. The standard deviation of uncertainty, the standard error, or a specific confidence range (such a 95% interval) are frequently represented as error bars. Due to the fact that these values are not the same, the measure chosen needs to be specified clearly in the graph or supporting text.
According to the definition the statement is true.
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
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