Given the above function:
a) Note that the number of people that need to sign up for a tour in order for the profit to be at least $108 is:
b) The number of people that need to sign up for a tour in order for the profit to be more than $144 is:
c) Yes, it is possible to make a negative profit on the tour in which case they would have made a loss.
What is the calculation justifying the above?a) To find out the number of people that need to sign up for the profit to be at least $108 where the function y = - x7 + 24x, models profit in y,
we must equate the function to $108 and solve for x.
Thus:
- x7 + 24x = 108
resolve like terms
17x = 108
x = 108/17
x = 6.35294117647
x [tex]\approx[/tex] 6. 4
Plug x back into the formula, and we have:
-(6.4) * 7 + 24 (6.4) = 108.8 this shows that our calculation is correct. Since you can have 6.4 persons, the best number to aim for is 7.
b) The number of people that need to sign up for the project to turn a profit of $144 is:
- x7 + 24x = 144
resolve like terms
17x = 144
x = 144/17
x = 8.4705882353
Let's impute back 8.5 into the equation:
-(8.5)7 + 24(8.5)
= 144.5.
This shows that our calculation is correct. However since you cannot have 8.5 persons, the number to budget for would be 9 persons.
c) for the tour guide to lose money, the amount made, that is revenue, would have to be less than the amount invested.
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Joshua goes to a store an buys an item that costs x dollars. He has a coupon for 5% off, and then a 6% tax is added to the discounted price. Write an expression in terms of x that represents the total amount that Joshua paid at the register
The expression representing the total amount paid by Joshua at the register is 1.007x dollars.
We have,
To represent the total amount that Joshua paid at the register, we need to account for the following steps:
- Applying the 5% discount to the original price x:
Discount = 5% of x = 0.05x
Calculating the price after the discount:
Price after discount = x - Discount = x - 0.05x = 0.95 x
Adding the 6% tax to the discounted price:
Tax = 6% of the discounted price = 0.06 x (0.95x)
The expression for the total amount that Joshua paid at the register:
Total amount paid
= Price after discount + Tax
= 0.95 x + 0.06 (0.95 * x)
Simplifying the expression:
Total amount paid = 0.95x + 0.057x
Total amount paid = 1.007x
Thus,
The expression representing the total amount paid by Joshua at the register is 1.007x dollars.
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A student went on a two-day hike. • On day one, the student hiked 11 kilometers. On day two, the student hiked at a rate of 2 kilometers per hour for x hours. Which of the following graphs represents y, the total distance, in kilometers, the student hiked over both days after hiking for x hours on day two?
The slope is 2, which equals the distance travelled each hour. The total distance hiked at the start of the second day is represented by the y-intercept, which is 4, which is also the y-value. intercept's
Explain about the Slope?We locate the rise/run before calculating the slope. Since the line increases by 2 between each point, the rise is 2. It travels over 1 between the points, hence the run is 1. The slope is now 2/1, or 2.
Given that it is rise/run, this gives us miles/hours, which indicates the number of miles she treks per hour.
The line's crossing of the y-axis is known as the y-intercept. At four, this is.
The fact that the y-value at this time is 4 and the x-value at this point is 0 tells us that she has trekked 4 miles in the 0 hours since the start of the second day, which is the distance she has covered so far.
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The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.
This ratio is the same in Mandy’s science class, in which there are 20 girls. How many boys are there in Mandy’s science class? Show your work
Number of boys in Mandy’s science class is 5.
Now, According to the question:
The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.
This ratio is the same in Mandy’s science class,
There are 20 girls.
To find the how many boys are there in Mandy’s science class?
Based on the given condition:
Let the ratio be 3x and 12x
Now, According to the statement:
12x = 20
x = 20/12
x = 5/3
So, Number of boys = 3 × 5/3 = 5
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Identify the number of terms and then the resend themselves for each algebraic expression
The number of terms in the algebraic expressions are:
6y + 14 ⇒ 2 terms3x³ + 7x² + x - 5 ⇒ 4 termsHow to determine the number of terms in the algebraic expressionsFrom the question, we have the following parameters that can be used in our computation:
6y + 14 and 3x³ + 7x² + x - 5
Consider an expression given as
ax + b
The number of terms in the expression is 2 and the terms are ax and b
Using the above as a guide, we have the following:
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Complete question
Identify the number of terms and then the resend themselves for each algebraic expression
6y + 14 and 3x³ + 7x² + x - 5
In right triangle ABC, ZC is a right angle, m ZA = 52, AC = 10. 01, and AB = c.
sin 52° 0. 788
cos 52° 0. 616
tan 52° 1. 280
What is the measurement of AB?
If necessary, round your answer to two decimal places, like this: 42. 53
The length of side AB rounded to two decimal places is 16.25.
In a right angle triangle, the side on the base of the angle in question is divided by the hypotenuse. In this case, we can use the cosine ratio to find the length of AB.
We are provided with the following information,
C is the right angle, C= 90°
A= 52°
AC = 10. 01
sin 52° = 0. 788
cos 52° = 0. 616
tan 52° = 1. 280
Now,
since angle C is the right angle, AB is the hypotenuse.
Therefore, with respect to Angle A, AC will be the base and BC will be the perpendicular.
We know, cos x= base/hypotenuse
In this case, cos A = AC / AB
cos 52° = 10. 01/ AB
AB = 10. 01 / 0. 616
AB = 16.25
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Consider this series.
16+32/3 +64/9 +128/27 +...
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
The series Choose... You know this because the series is
Choose....
The series converges to 16 * 3 = 48
What is a series?A number series is a continues chain of number identical of non-identical depending on the logic behind the series. It can contain letters, number, variable, fraction, and numbers with power or exponents.
How to find the series coverage?The series converges.
This series is in the form of 16 * (1 + 1/3 + 1/9 + 1/27 + ...)
The series 1 + 1/3 + 1/9 + 1/27 + ... is a geometric series with a common ratio of 1/3.
A geometric series converges if |r| < 1, where r is the common ratio. In this case, |1/3| < 1, so the series converges to lim (1/(1-1/3)) = 3.
So the series converges to 16 * 3 = 48
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Some people took part in a game. The frequency shows information about their scores.ScoreFrequency - 758 - 10811 - 15916 - 201521 - 351636 - 5013Estimate the mean.Give your answer rounded to 2 decimal places.
The estimated mean score is given as follows:
19.12.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
For each score, we consider it to be the mean of each interval in the frequency table, hence the sum of all scores is given as follows:
4 x 19 + 9 x 14 + 13 x 15 + 18 x 28 + 28 x 10 + 43 x 13 = 1740.
The total number of scores is of:
19 + 14 + 15 + 20 + 10 + 13 = 91.
Hence the mean score is obtained as follows:
1740/91 = 19.12.
Missing InformationThe frequency distribution for this problem is given as follows:
1-7:19
8-10:14
11-15:15
16-20:20
21-35:10
36-50:13
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To be a member at Sal's gym, there is a one-time sign-up fee plus a monthly fee for each month of membership. The table shows the total cost to be a member of the gym for different numbers of months.
Number of Months Total Cost
3 $53. 97
6 $77. 94
12 $125. 88
Create a function that gives the total cost,
C
C
, in dollars, to be a member of the gym given the number of months,
m
m
, of membership.
Enter your function in the space provided
A function that gives the total cost, C in dollars, to be a member of the gym given the number of months, m is C = 7.99m + 30
The table that shows the total cost to be a member of the gym for different numbers of months is:
Number of Months Total Cost
3 $53. 97
6 $77. 94
12 $125. 88
The rate of change of total cost per month would be,
m = [tex]\frac{77. 94-53. 97}{6-3}\\\\[/tex]
m = 7.99
so, the function for the total cost would be,
C = 7.99m + d .......(1)
where d is the fixed cost of the gym
For m = 3, C = 53.97
53. 97 = 7.99m + d
53. 97 = 7.99(3) + d
d = 30
So, function (1) would be,
C = 7.99m + 30
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1. If mA = 3x° and
m
what is the value
of x?
Answer: I'm sorry, but the information provided is not enough to determine the value of x. The statement "mA = 3x°" does not provide enough context to understand what "mA" and "x" represent, and what the relationship between them is. Additionally, the statement "m" does not provide any information that can help determine the value of x. Can you please provide more information or context?
Step-by-step explanation:
Carmela's gross pay is $784.25. Her deductions total is $191.17. What percent of her gross pay is take-home pay?
The percent of Carmela's gross pay that is her take-home pay is 75%
How to calculate the percent of Carmela's gross pay that is her take-home pay?
Carmela's gross pay is $784.25
Her total deductions is $191.17
Therefore the percent of her gross pay can be calculated as follows
The first step is to subtract the deductions from the gross pay
784.25 - 191.17
= 593.08
The percent of the gross pay that is take-home pay is
593.08/784.24 × 100
= 0.75 × 100
= 75%
Hence 75% of her gross pay is take-home pay
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At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
HELP ASAP !! :80 POINTS
How long is the shortest route from Ellport to Union Falls using the roads shown?
If necessary, round your answer to the nearest tenth.
The shortest route from Ellport to Union Falls using road is 18 miles
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Pythagoras theorem is used to determine the measure of the sides of a right angled triangle. It is given by:
(hypotenuse side)² = (adjacent side)² + (opposite side)²
The distance from Larksville to Smithfield = 9 + 9 + 6 = 24 miles
The distance from Larksville to Union Falls = 19.5 + 6.5 = 26 miles
Let x represent the distance from Smithfield to Union falls, using Pythaoras:
26² = 24² + x²
x² = 100
x = 10 miles
the distance from Smithfield to Union falls is 10 miles.
Let y be the shortest route from Ellport to Union Falls, using Pythagoras:
y² = 10² + (9 + 6)²
y² = 10² + 15²
y² = 325
y = 18 miles
The distance from Ellport to Union Falls is 18 miles
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Nasim is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 28 degrees
. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Step-by-step explanation:
this creates a right-angled triangle 2.5 ft above the ground.
the string is the Hypotenuse (the side opposite to the 90° angle). the air distance to the height of the kite is one leg, and the height of the kite minus the 2.5 ft is leg 2.
in the trigonometric triangle the up/down side is sine (multiplied by the Hypotenuse or radius of the circle) of the angle at the center of the circle. and the left/right side is cosine (again multiplied by the Hypotenuse or radius) of the angle.
so, the height of the kite above ground is
105×sin(28°) + 2.5 = 51.79451409... ≈ 51.79 ft.
A line includes the points (0, -8) and (3, 3).
Find the rate of change of the line. (1 point)
uy =
When the line passes through two points as shown, the slope is 11/3.
What is slope?The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.
Here,
m=3
m=(y2-y1)/(x2-x1)
3=(y+5)/(-3+(2))
-3=y+5
y=-8
The value of slope is 11/3 when the line is passing through 2 points as given.
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Does the point (0, 0) satisfy the equation y = x?
Answer:
yes
Step-by-step explanation:
when y equals 0, x equals 0 also
y = x will produce a straight line passing through the point of origin (0,0)
Write two expressions that could be used to determine what 340 increased by 19% is
The new value = 340 + (19% × 340)
The actual change = The new value - 340
"Information available from the question"
340 increased by 19%
To write in mathematically:
The value of the percentage increase = 19% × 340
The new value = 340 + The value of the percentage increase
The new value = 340 + The value of the percentage increase
= 340 + (19% × 340)
= 340 + 19% × 340
= (1 + 19%) × 340
= (100% + 19%) × 340
= 119% × 340
= 119 ÷ 100 × 340
= 119 × 340 ÷ 100
= 40,460 ÷ 100
= 404.6
The actual change = The new value - 340
= 404.6 - 340
= 64.6
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What is the greatest common factor shared by 39 and 15
Answer:
3
Step-by-step explanation:
15 is divisible by 3, 3 × 5 = 15. Then of course 1 and 15 no other ones. 1,3,5,15
39 is divisible by 3, 3× 13 = 39, then 1 and 39. 1,3,13,39
The only common factors are 1 and 3, and since 3 is greater that is the greatest common factor.
Hope that helps! Let me know if you have any further questions.
The greatest common factor shared by numbers 39 and 15 is 3.
Given two numbers, 39 and 15.
The greatest common factor can be defined as the factor which is common to both 39 and 15 and is the greatest of all those common factors of 39 and 15.
First, list out the factors of 39 and 15.
Factors of 39 = 1, 3, 13, 39
Factors of 15 = 1, 3, 5, 15
The only factor which is common to both 39 and 15 is 3.
So, the greatest common factor of both is 3.
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2. Amy has a room that is 6 feet by 10 feet. She bought tiles
that are 8 inches by 6 inches. How many tiles will she
need to cover the floor?
A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
Because we are dealing with different units here, we first would need to know how many inches are in one foot.
1 foot = 12 inches
Now that we know how many inches are in a foot, we can convert the length and width of the room from feet to inches.
6 feet = 72 inches
10 feet = 120 inches
Taking these numbers, we now need to figure out the area of the floor.
72 × 120 = 8640
Now, find the area of each tile.
6 × 8 = 48
Taking 8640, we can now divide that by 48 to get the number of tiles needed.
8640 ÷ 48 = 180
Therefore, 180 tiles are needed to cover the floor.
Select the linear function that describes the relationship between the domain and range in the table below.
x f(x)
−1 5
0 3
1 1
The linear function that describes the relationship is y = -2x + 3
How to determine the linear functionFrom the question, we have the following parameters that can be used in our computation:
x f(x)
−1 5
0 3
1 1
A linear function is represented as
y = mx + c
Where
c = y when x = 0
This means thar
c = 3
So, we have
y = mx + 3
From the table, we can see that
As x increases by 1, y decrease by 2
This means that
m = -2
So, we have
y = -2x + 3
Hence, the equation is y = -2x + 3
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how do i find the missing angles?! please help this is due today! please and thxx!
The measure of each angle are
<1 =46<2=164<3= 46<5= 46<6= 164<7= 46<8= 134What are Parallel lines?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
<4 = 134
So, <4 = <2 = 134 (Vertical opposite angle)
<4= <8= 134 (Corresponding Angle)
<1 + <4 = 180 (Linear Pair)
<1 = 180-134
<1 = 46
<1 = <3= 46 (Vertical opposite angle)
<2= <6= 164 (Corresponding Angle)
<3= <7 (Corresponding Angle)
<1= <5 (Corresponding Angle)
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The function W
gives the temperature, in degrees Fahrenheit, of a pot of water on a stove t
minutes after the stove is turned on.
After 30 minutes, the pot is taken off the stove.
The graph of the function is shown.
Describe the range of the function.
The range would be; [75,212] and the greatest one is around 212.5. .5] a domain and a range.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
Recall this by saying "DoLaR RiBiT," where "DoLaR" stands for "domain," "L" and "R" stand for "left to right," "R" stands for "range," and "B" and "T" stand for "bottom to top," and "R" stands for "range."
Since we can see that the function doesn't approach 250, in the graph, 250 is not inside the range.
Between the minimum and greatest value are the numbers that make up the range. The range would be; [75,212] because the lowest Y value is 75 and the greatest one is around 212.5. .5] a domain and a range.
The collection of values that can be substitute into a function's domain are called its parameters.
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The area of a circle is 64π cm2, and the area of a sector of the circle is 32π cm2. What is the degree measure of that sector? (Just type the number of degrees. )
The degree measure of the sector is θ = 180°
We know that the area of a sector is nothing but the area inside the section of the circle created by two radii and an arc.
The formula for the area of a sector of the circle is:
area of a sector = [tex]\frac{\theta}{360} \times \pi \times r^2[/tex]
where θ is the central angle measure in degrees
And πr² is the area of the circle
Here, the area of a sector of the circle A = 32π cm²
and the area of a circle (πr²) = 64π cm²
Using above formula of the area of a sector of the circle,
[tex]A=\frac{\theta}{360} \times \pi \times r^2\\\\32\pi=\frac{\theta}{360} \times \pi \times r^2\\\\32\pi=\frac{\theta}{360} \times 64\times \pi\\\\\theta=\frac{360}{2}\\\\ \theta=180^{\circ}[/tex]
Therefore, the central angle associated to that sector is 180°
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the sum of the cube of a number and the product of the number and twelve is equal to seven times the square of the number. find the number.
Answer:
4 or 3
Step-by-step explanation:
X³+12X=7X²
X³-7X²+12X=0
X(X²-7X+12)=0
SOLVING THE QUADRATIC EQUATION
you have X=3 or X=4
Some animal become endangered and a trict law ha to be
implemented to protect them. What will you do to protect and help
them?
One of the most important things to do to protect endangered animals is to reduce the amount of habitat destruction caused by human activities.
This can be done by creating protected areas and limiting or banning activities like logging, mining, or development in sensitive areas. Additionally, it is important to reduce over-hunting and poaching of these animals. This can be accomplished by establishing quotas and strict regulations on allowable hunting and fishing, as well as increasing enforcement efforts to catch violators. It is also important to understand the life cycles and behaviors of the threatened species so that we can better protect them. This can be done through field research, monitoring, and analyzing population trends. Finally, it is important to develop conservation plans and strategies to protect the species. These could include habitat restoration, reintroduction programs, captive breeding, and other measures to ensure their survival.
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since the mode is the most frequently occurring data value, . a. it can never be larger than the mean b. it is always larger than the median c. it is always larger than the mean d. more than one mode can exist
The distribution of the mean, median, and mode values will depend on how skewed the distribution is. As a result, mean or mode may be larger than or less than mode.
correct answer is D.
Different measures of the center in a set of numerical data include mean, median, and mode. They each attempt to condense a dataset into a single number that may be used to represent a "typical" data point.
The "mean" value is obtained by summing all the data points and dividing the result by the total number of data points.
The middle number, or median, is obtained by placing all data points in order and choosing the middle one (or, if there are two middle numbers, the mean of those two figures).
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A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. What is the surface area in square centimeters if the height is 2 centimeters?
60
120
180
240
*answer is 180. How?
The surface area of the triangular prism is 120[tex]cm^2[/tex]
Now, According to the question:
A triangular prism is a polyhedron with a triangle for a base, thus it is a three-sided prism. Given that the triangle has three sides and a height of h, the surface area would be A = Ph + ab where P is the perimeter of the triangle.
We have :
A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters.
Now,
Hypotenuse = 13
a = 5 cm
b = 12 cm
h = 2 cm
The perimeter of the triangle is the sum of all the sides or:
P = 13 + 5 + 12
P = 30 cm
To get the surface area, substitute the values in the formula below:
A = Ph + ab
A = (30)(2) + (5)(12)
A = 60 + 60
A = 120
Hence, The surface area of the triangular prism is 120[tex]cm^2[/tex]
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What are the table of values for y=x^2+2x-3
By factoring the preceding quadratic equation and then inserting the values of "x," which are -3, -2, -1, 0, 1, 2, 3, 4, 5, the values of "y," which are 12, 5, 0, -3, -4, 3, 0, 5, 12, may be found.
How to find the Calculation?First, factorize the given quadratic equation before completing the table.
Now, the values of "x" according to the given table are:
x = -3, -2, -1, 0, 1, 2, 3, 4, 5
Add the expression x=-3 to the equation (1).
y = (-3-3)(-3+1)
y = 12
Add the expression x=-2 to the equation (1).
y = (-2-3)(-2+1)
y = 5
Put x=-1 as a value in the equation (1).
y = (-1-3)(-1+1)
y = 0
Put x=0 as the value in the equation (1).
y = (0-3)(0+1)
y = -3
Put x=1 as the value in the equation (1).
y = (1-3)(1+1)
y = -4
Put x=2 as a value in the equation (1).
y = (2-3)(2+1)
y = -3
Add the expression x=3 to the equation (1).
y = (3-3)(3+1)
y = 0
Add the expression x=4 to the equation (1).
y = (4-3)(4+1)
y = 5
Add the expression x=5 to the equation (1).
y = (5-3)(5+1) y = 12
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which inequality represents the graph??
Answer:
C
Step-by-step explanation:
Mock June 22 1F Overview Question Progress Exam Paper Progress 42/80 Marks 10 Eric throws a biased coin 10 times. He gets 3 Tails. Sue throws the same coin 50 times. She gets 20 Tails. 10 Grade For This Paper U 3 Aadi is going to throw the coin once. (i) Which one of the following statements is correct about the probability of Aadi getting Tails? 2/5 (ii) Use Eric's and Sue's results to work out an estimate for the probability that Aadi will get Tails. Write your fraction in the form a/b 13 A Sue's estimate is best because she throws it 50 times. B Sue's estimate is best because she gets more Tails. C Sue's estimate is best because she throws it more times than Eric (1) (1) 15 Total marks: 2 16 17
The best estimate for the probability of getting tails is given as follows:
C Sue's estimate is best because she throws it more times than Eric.
How to obtain the probabilities?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
For this problem we calculate an experimental probability, as the outcomes are obtained from the previous trials of Eric and Sue.
The higher the number of trials, the closer the experimental probability is to the theoretical probability, meaning that the correct option is given by option C.
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For integers a, b, and c, define a*b*c to mean ab-bc+ca then 1*-1*2 equals
Options;
A; -4
B; -2
C; 0
D; 2
E; 4
The operation of 1 * (-1) * 2 equals option D. 2.
What are Binary Operations?Binary operations are the operations which are performed on a specific set.
If the operation is defined on a set X, then binary operation can be defined as,
* : X * X → X.
Addition, subtraction, ... are some of the binary operations.
The given binary operation is defined as,
a * b * c = [tex]a^b-b^c+c^a[/tex]
We have to find the value of 1 * (-1) * 2.
By the definition,
1 * (-1) * 2 = [tex]1^{-1}-(-1)^{2}+2^1[/tex]
= 1 - 1 + 2
= 2
Hence the correct option is D.
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