By solving a simple equation, we will see that Avelina earns $62.50
How much did Avelina earn?Here we know that Avelina earns half as much as Gus, then if we define the variables:
A = amount that Avelina earns.
G = amount that Gus earns.
Then we can write the equation:
A = G/2
That says that Avelina earns half as much as Gus.
We know that Gus earns $125. then we can replace that in the equation above:
A = $125/2
A = $62.50
Avelina earns 62.50 dollars.
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In general F^-1(f(x))=f(f^-1(x))
In general F^-1(f(x))=f(f^-1(x)) wherein f^-1(x) is the inverse of f(x).
What is function?Function is a process or activity that fulfills a specific purpose or set of requirements. It is a building block of programming and can be used to create various types of applications. Functions allow coders to modularize their code and make it easier to debug and maintain. Functions can also be used to process data, perform calculations, and display outputs.
It is a mathematical law which states that if a function f(x) has an inverse function then the composition of the function with its inverse should be equal to the original function. This law is also known as the Involution Law or the Composition Law of Inverse Functions.
The Involution law or the Composition law of inverse functions is a fundamental law of mathematics. This law states that for any function f(x) which has an inverse function, f^-1(x), the composition of the function with its inverse should be equal to the original function. That is, F^-1(f(x))=f(f^-1(x)). This law is important as it helps to understand the relationship between the original function and its inverse. This law is useful in solving various mathematical problems and in understanding various mathematical concepts such as differentiation and integration.
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A certain volcano has an elevation of 13,741 feet. A nearly oceanic trench has an elevation of 21,151 feet below sea level. Find the difference in elevation between those two points.
The difference in elevation between the two points is
What is an elevation?An elevation can be defined as the height or depth of a point using the sea level as the reference point. Thus when an object is above the sea level, its elevation or altitude can be determined. But if the object is below the sea level, its depth can be determined.
The sea level is taken to be zero, while elevation is positive. but depth is taken as negative.
Therefore, the difference in elevation between the volcano and oceanic trench can be determined by taking the sea level as 0.
elevation between the two points = elevation - depth
= 13741 - (-21151)
= 13741 + 21151
= 34892
elevation between the two points = 34892 feet.
The difference in elevation between the two points is 34892 feet.
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round 202.2 to the nearest whole number
Answer:
it can't be rounded so the answer is just 202
Step-by-step explanation:
Add. What is the answer
(5b^2-3b+2)+(2b-4)
Heya! Quick answer/step by step:
Add like terms. 5b^2 is not a like term, no other numbers finish in "b^2". -3b + 2b = -1b or -b, either one is correct. 2 - 4 = -2. So you would get...
5b^2 + (- b) + (- 2)
Hope that helps!
PLEASE HELP NEED ANSWER AND STEPS
The expected answer is AD.
Parts of a segment.A segment has a unique property of having two end points such that it can be differentiated from a ray or line. A given segment can be divided into a required number of parts, so that addition or subtraction operations can be performed on some or all parts of the segment.
In the given question, we have;
AE = AB + BC + CD + DE
AC = AB + AC
CE = CD + DE
BD = BC + CD
BE = BD + DE etc.
Therefore, the appropriate answer after showing the steps is;
AC + CD = AD
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Mr. Thornton moves horses from one stable to another using a trailer. The trailer can
hold no more than four horses, and it can support no more than a total of 4500
pounds.
Mr. Thornton loads his trailer with three horses that weigh 890 pounds, 1250 pounds,
and 940 pounds. He wants to load a fourth horse in his trailer.
Using w to represent the weight of the fourth horse, write an inequality to express
how many pounds the fourth horse could weigh. Use a number line to show all the
possible solutions in this real-world situation.
Explain in detail how you determined the possible weights of the fourth horse.
The inequality is 3,080 + w <= 4500. and we have explained the possible weights of the fourth horse.
What is inequality?
Inequality is a mathematical statement that compares two values or expressions and shows the relationship between them. It is used to express that one value is either greater than, less than, greater than or equal to, or less than or equal to another value. Inequalities can be represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to).
We know that Mr. Thornton has already loaded three horses into his trailer with the following weights: 890 pounds, 1250 pounds, and 940 pounds. To load a fourth horse, we need to know the total weight of the trailer and the horses.
Total weight of the trailer = 890 + 1250 + 940 = 3,080 pounds
The trailer can support no more than 4500 pounds, so we need to make sure that the total weight of the trailer and the fourth horse does not exceed 4500 pounds.
Therefore, we can write the inequality:
3,080 + w <= 4500
This inequality tells us that the total weight of the trailer and the fourth horse (3,080 + w) must be less than or equal to 4500 pounds.
To graph the solutions of this inequality on a number line, we can start by plotting point 4500 on the number line. Since the inequality contains the "less than or equal to" sign, we need to shade everything to the left of 4500, including 4500.
The solutions to this inequality are all possible weights of the fourth horse that would not cause the total weight of the trailer and the horses to exceed 4500 pounds. The solutions are all real numbers between 0 and 420.
It's worth mentioning that the solution set is an interval [0,420] and it includes 0, but not 420. It means that the horse can weight 0 pounds (which is not possible) but it can't weight 420 pounds since it would exceed the maximum weight that the trailer can support.
Hence, the inequality is 3,080 + w <= 4500. and we have explained the possible weights of the fourth horse.
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What is the domain and range of x³?
Domain of function [tex]x^3[/tex] is R(Real number) and range of function is also R.
Let's know about domain: the domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The domain is indicated by the fact that the fraction's denominator is not equal to zero and by the fact that the digit under the square root bracket is positive.
Range: the range of a function is the set of all possible values for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.
[tex]x^3[/tex]is a polynomial, which means that R is its domain, and in this case, R is also its range because the sole root that [tex]x^3[/tex] possesses.
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A skateboarding ramp is 20 in. high and rises at an angle of 14°.
How long is the base of the ramp?
Round to the nearest inch
The length of the base to the nearest inch is 37 inches
What are Angle of elevation and depression?Between the horizontal line and the line of sight, an angle called the angle of elevation is created. When the line of sight is upward from the horizontal line, an angle of elevation is created. In order to get the angle of elevation for an object at a distance of 10 units from the horizontal line (y=10) and 12 units from the observer w.r.t. the horizontal line (x=12), for instance, we write tan = 10/12, which can be simplified to tan = 5/6. The value of so obtained is tan-1 (5/6).Given the following parameters from the questions:
Height of the ramp = 10in
angle of elevation = 15degrees
Using the SOH CAH TOA identity
tan 15 = opp/adj
tan 15 = 10/B
B = 10/tan15
B = 10/0.2679
B = 37 inches
Hence the length of the base to the nearest inch is 37 inches.
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scott solves the equation when he checks his work he realizes that he made a mistake identify scotts error and find the correct solution
y-(-9)= -2 check: 7 (-9) = -2. 16= -2
y- (-9) + 9 = -2+9
y=7
Based on the given task content; Scott error was adding 9 to both sides of the equation and the correct solution is y = -11
How to correctly solve an equation?Scott solution:
y-(-9)= -2
check:
7 (-9) = -2.
16= -2
y- (-9) + 9 = -2+9
y=7
Correct solution:
y-(-9)= -2
y + 9 = -2
Subtract 9 from both sides
y = -2 - 9
y = -11
Check:
y-(-9)= -2
-11 - (-9) = -2
-11 + 9 = -2
-2 = -2
In conclusion, the solution to Scott's equation is y = 11
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What is 2 over 3 times 5 over 8?
31 over 24
16 over 15
7 over 11
5 over 12
The statement 2 over 3 times 5 over 8 is [2/(3×5)]/8 which is equal
to 16 over 15.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A fraction [2/(3×5)]/8 which is,
= {2/(3×5)/8}.
= {2/(15)/8}.
Now, Numerator 8 will multiply to numerator 2 which is,
= (2×8)/15.
= 16/15.
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A city has a cone shaped building for storing salt and sand for icy roads. Each building has radius of 25 feet and height of 18 feet. Find the volume of the building. Use 3.14 for the pie
.
(A) 471 ft3
(B) 35, 325 ft3
(c) 11, 775 ft3
(D) 1413 ft 3
Answer: The volume of a cone is given by the formula: V = (1/3) * π * r^2 * h
Where:
V is the volume
π is 3.14
r is the radius
h is the height
So in this case, using the given values:
V = (1/3) * 3.14 * (25^2) * 18
V = (1/3) * 3.14 * 625 * 18
V = (625 * 18 * 3.14) / 3
V = 35,325 ft^3
So the answer is (B) 35,325 ft3
Step-by-step explanation:
8+(2x3)-6 divided by 2
Answer:
4
Step-by-step explanation:
8+(2x3)-6=8
8/2=4
Answer: Correct Answer Is:11
Step-by-step explanation: I Use Calculator To Help
What is the elapsed time between 10:50 a.m. and 3:45 p.m.?
Answer: 4 Hours & 55 Minutes
Step-by-step explanation:
10:50 to 11:50 (1 hour)
11:50 to 12:50 (1 hour)
12:50 to 1:50 (1 hour)
1:50 to 2:50 (1 hour)
2:50 to 3:50 = 1 hour
1 hour = 60 minutes
3:45 to 3:50 is five minute difference
60 - 5 = 55
Therefore, it would be 4 hours and 55 minutes.
Solve for c 89=8c+25
Answer: c is 8
Step-by-step explanation: c has to multiply 8 into 89-25 which is 64. 64/8 equals 8
Answer:
c=8
Step-by-step explanation:
i hope this helps have a good day!
FOLLOW UP #3 (STILL UNIT-6 LIKE THE PREVIOUS OTHER 2!) 8-11 questions (HELP it'a due tomorrow i'm getting a head start today!) (QUESTIONS 12-15 WILL BE POSTED SO LOOK AT MY POST TO HELP ME PLEASE :) !) (it would help out a lot<3)
The range of the given graph of the function is y ≤ 0. The correct option is A.
What are a domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
The range of the function will be the y value of the function. here in the graph, the y value is varying from 0 to negative infinite value which means that the y value will ranges from 0 and less than zero.
y ≤ 0
The correct option would be A.
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what is 20x (to power -4) / 27y² divide 8x ( to power -3) / 15y ( to power -5 )
Answer:25/18y^7x
Step-by-step explanation:(Multiply the numerator by the reciprocal of the denominator.)
20x^-4/27y^2*15y^-5/8x^-3
then simplify
20*15/27y^7(8x)
cancel the common factor and you will get the answer
What is the average speed of the car if it covers 300 km in 5 hours?
An object's average speed is a measurement of how quickly it moves over a predetermined amount of time. The calculation is done by dividing the overall distance travelled by the overall travel time. In other words, it reveals the average amount of distance an object has travelled per unit of time.
In the case provided, we can apply the following calculation to get the average speed of the car:
average speed = total distance / total time
In this instance, a total of 300 kilometers was travelled while 5 hours were expended.
so, average speed = 300 km / 5 hours
= 60 km/h.
This indicates that the car travels at an average speed of 60 kilometers per hour. This represents the average speed of the car's five-hour journey. Although the car may have gone faster or slower at various points throughout the course of the five hours, on average, it was moving at a speed of 60 kilometers per hour.
Therefore, the average speed of the car is 60km/h .
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can somebody answer this question pls
The irregular polygon has an area of 39 square units.
How to determine the area of an irregular polygon
In this question we find the case of an irregular pentagon, that is a polygon with five sides with different lengths and five different central angles. The area of any polygon can be found by summing the areas of rectangles and right triangles. The area formulas for rectangles and right triangles are shown below:
Rectangle
A = w · l
Right triangle
A = 0.5 · w · l
Where:
w - Width, in units.l - Length, in units.A - Area, in square units.Now we proceed to determine the area of the irregular polygon:
A = 0.5 · 3 · 1 + 0.5 · 5 · 3 + 5 · 6
A = 1.5 + 7.5 + 30
A = 39
The area of the irregular polygon is equal to 39 square units.
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The Description method of the word "SINIGANG"
Answer: In mathematics, the method of polynomial interpolation is a method for constructing a polynomial function that passes through a given set of points. The polynomial function constructed in this way is called an interpolating polynomial. It is used to approximate a function when it is known only at a few discrete points, and the goal is to find a smooth curve that fits the data as closely as possible.
The method of polynomial interpolation involves finding the polynomial of the lowest degree that passes through a given set of points. This is done by setting up a system of equations using the coordinates of the points, and then solving for the coefficients of the polynomial. Once the coefficients are known, the polynomial function can be evaluated at any point within the domain of the data points.
There are several different techniques that can be used to find the interpolating polynomial, such as the Lagrange interpolation, Newton's divided differences method and the least-squares method. The choice of method will depend on the specific problem and the desired properties of the interpolating polynomial.
In summary, the method of polynomial interpolation is a technique used to construct a polynomial function that passes through a given set of points. It is used to approximate a function when it is known only at a few discrete points and aims to find a smooth curve that fits the data as closely as possible.
Step-by-step explanation:
PLEASE HURRY WILL GIVE BRAINLIEST TO THE 1ST PERSON TO ANSWER
How is the volume of a solid object measured?
Responses
Cubic units
Watt
Length
Square meter
The state of Colorado is 4 centimeters long and 2 centimeters wide on a map. A cartographer wants to use a scale factor of 3.5 to enlarge the map. What is the area of the enlarged map?
98 cm2
42 cm2
28 cm2
8 cm2
The area of the enlarged map of the state of Colorado, based on the scale factor of 3.5, is A. 98 cm².
What is a scale factor?The scale factor refers to the ratio or size by which the shape is enlarged or reduced.
When a shape is scaled down, the scale factor is used to divide the given size or dimensions of the object.
On the other hand, when a shape or object is scaled up, the scale factor multiplies the given size or dimensions to determine the new scale size.
Original dimensions:Length = 4 cm
Width = 2 cm
Area = 8 cm² (4 x 2)
Scale factor = 3.5
New dimensions:Length = 14 cm (4 x 3.5)
Width = 7 cm (2 x 3.5)
Area = 98 cm² (14 x 7)
Thus, the enlarged map's area is Option A. 98 cm².
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Answer: B: 42 cm2.
Step-by-step explanation:
"Oh
Mark was trying to open his gym locker and forgot the combination
noll I need my gym clothes! He was in a panic. He remembered a
clue that he'd left himself to remember the combination, though. The combination to
his lock is based on the prime factors of 315. (HINT: prime factors = prime numbers
that are factors of that number).
Answer:
357
Step-by-step explanation:
Since the prime factors of 315 are 3, 5, 7.
angles formed by a transversal worksheet answer key
A transversal is a third line that crosses two other lines.
Lines on a plane that do not intersect are considered parallel lines in geometry. It is referred to as being parallel when two straight lines in a plane do not cross at any point.
Eight distinct angles may be obtained by drawing two parallel lines, a line across them, and then another line through that.
A key mathematical ability that calls for conceptual comprehension and clarity is the angles form. Worksheets on angles generated by parallel lines and transversals provide a variety of activities and problems based on angles that can aid students in learning about angles.
Correct question: What is the angles formed by a transversal called?
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Research suggests that depression significantly increases the risk of developing dementia later in life. Suppose that in a study involving 949 elderly persons, it was found that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression. Choose the relevant population and the sample.a. The sample consists of 949 elderly people. b. The population is all elderly people. c. The sample consists of 949 younger people. d. The population is all younger people.
The sample consists of 949 elderly people and the population is all elderly people.
A sample is a random group chosen to represent the complete population. Based on the characteristics of the sample, conclusions about the population are drawn in statistical analysis. The complete collection of people or objects of interest is referred to as a population. It is the collection of all components or individuals who share a characteristic, such as all seniors or all depressed individuals. Usually, the sample size is larger than the population size.
According to research, depression considerably raises the risk of dementia in a given situation. Consider the possibility that research of 949 senior people found that 22% of those who experienced depression went on to develop dementia, compared to only 17% of those who did not. As a result, the population is made up entirely of the elderly, and the sample consists of 949 of them.
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For what value of k are the roots of the quadratic equation are real and equal?
The value of k for which the roots of the equation are real and equal is k = b^2/4a.
What is quadratic equation?A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x represents an unknown. It is a type of polynomial equation, with the degree of the polynomial being 2. The solutions to a quadratic equation can be found using the quadratic formula, which involves taking the square root of the coefficient of x^2 and then subtracting the coefficient of x from both sides of the equation. Quadratic equations are commonly used in science, engineering, and mathematics.
The roots of any quadratic equation ax^2 + bx + c = 0 are real and equal when the discriminant, b^2 - 4ac, is equal to zero. This can be written as b^2 = 4ac, or b^2/4a = c. Therefore, the value of k for which the roots of the equation are real and equal is k = b^2/4a.
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What is the y-intercept of y =- 3 7xy − 3 − 7x?
The given expressions y =- 3+7x and y= − 3 − 7x are compared with the general form of slope y=mx+c. And the y-intercept of both is found to be -3.
A line's slope, often known as its gradient, is a numerical value that represents the line's steepness and direction. This slope provides the ratio of the rise in y when x rises by a specific amount. Therefore, this may be calculated using the basic formula y=mx+c, where c stands for the y-intercept and m for the slope.
Given the expressions are y = -3+7x and y= -3-7x. Compare these two expressions one by one with the general form of the slope. By comparing the first expression we get, the slope as 7 and the y-intercept as -3. Similarly, comparing the second expression we get, the slope is -7 and the y-intercept is -3.
Therefore, the required answers are -3 and -3.
The complete question is -
What is the y-intercept of y =- 3+7x and y= − 3 − 7x?
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Is the line y 3x 7 parallel or perpendicular to 3x 9y 9 explain your answer?
The slopes 3 and -1/3 are the opposites of one another. So the line y = 3x - 7 is perpendicular to line 3x + 9y = 9.
In the given question, we have to explain the line y = 3x - 7 is either parallel or perpendicular to 3x + 9y = 9.
The given equation is y = 3x - 7.
y = mx+ c is the line's equation in the slope-intercept form.
By comparing this to the preceding equation, we can determine that this line's slope is 3 and its y-intercept is -7.
Lines with equal slopes are said to be parallel. Lines that are perpendicular will have a slope product of -1.
3x + 9y = 9
We can write this equation as
9y = -3x + 9
Divide by 9 on both side, we get
y = -3/9 x + 9/9
y = -1/3 x + 1
Now the slope is -1/3 and y-intercept is 1.
Hence, the slopes 3 and -1/3 are the opposites of one another. So the line y = 3x - 7 is perpendicular to line 3x + 9y = 9.
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The complete question is:
Is the line y = 3x - 7 parallel or perpendicular to 3x + 9y = 9? Explain your answer.
What is an equation of the line that passes through the point (- 1/4 and is parallel to the line 2x y 1?
The equation of line passing through (-1, 4) and parallel to y = 2x + 1 is y = 2x + 6.
In the given equation, we have to find the equation of the line passing through (-1, 4) and parallel to y = 2x + 1.
The given equation of line is y = 2x + 1.
The given points (x(1), y(1)) = (-1, 4)
The equation of line in the slope intercept form is y = mx + c, where m is the slope of the line and c is the y-intercept of the line.
The slope of the given line y = 2x + 1 is m = 2, on comparing to the general equation of the line.
The equation of the line that passes through the point (x(1), y(1)) is:
y - y(1) = m(x - x(1))
Now putting the value in the formula
y - 4 = 2(x - (-1))
Now simplifying the equation,
y - 4 = 2(x + 1)
Using distributive property to simplify the equation
y - 4 = 2x + 2
Add 4 on both side, we get
y = 2x + 6
Hence, the equation of the line passing through (-1, 4) and parallel to y = 2x + 1 is y = 2x + 6.
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The complete question is:
What is the equation of the line passing through (-1,4) and parallel to y=2x+1 ?
Need help using supplementary and vertical angles. Pt.2
The following are the measures of the vertical angles:
m∠EBF = 30°m∠ABC = 80°m∠DBE = 65°m∠ABG = 125°How to evaluate for the vertical anglesm∠EBF = m∠ABC = (3x + 15)° {vertical angles}
(3x + 15)° + (20x - 10)° + 60° = 180° {supplementary angles}
23x + 65° = 180°
x = (180° - 65)/23 {make x the subject}
x = 5
so;
m∠EBF = 3(5) + 15 = 30°
m∠ABC = m∠DBE = (2x + 14)° {vertical angles}
(2x + 14)° + (3x - 1)° = 180° {supplementary angles}
5x + 15° = 180°
x = (180° - 15)/5 {make x the subject}
x = 33°
so;
m∠ABC = 2(33) + 14° = 80°
m∠DBE = m∠CBG = (5x + 5)° {vertical angles}
(5x + 5)° + (x + 48)° + 55° = 180° {supplementary angles}
6x + 108° = 180°
x = (180° - 108°)/6 {make x the subject}
x = 12
so;
m∠EBF = 5(12) + 5 = 65°
m∠ABG = m∠EBG = (137 - 2x)° {vertical angles}
(137 - 2x)° + (5x)° + 25° = 180° {supplementary angles}
3x + 162° = 180°
x = (180° - 162)/3 {make x the subject}
x = 6
so;
m∠EBF = 137 - 2(6) = 125°
Therefore, the vertical angles m∠EBF, m∠ABC, m∠DBE, and m∠ABG have the measures 30°, 80°, 65°, and 125° respectively.
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how many ounces of pure chocolate must be added to 100 oz of chocolate topping that is 50% chocolate to make a topping that is 75% chocolate?
100 ounces of pure chocolate is required to be included in 100 ounces of chocolate topping that is 50% chocolate to prepare a topping that is 75% chocolate.
Using the given equation to determine the number of ounces needed:
0.50 . 100 + 1.00x = 0.75(100 + x)
50 + 1.00x = 75 + 0.75x
50 - 75 = 0.75x - 1.00x
- 25= -0.25x
or
0.25x= 25
x= 25/0.25
x= (25. 100)/25
x = 100.
Thus, 100 ounces of pure chocolate is required to be included in 100 ounces of chocolate topping that is 50% chocolate to prepare a topping that is 75% chocolate.
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