The answer of the given question based on circle is we have shown that XY = WZ, since both line segments are equal to XM.
What is Pythagorean theorem?The Pythagorean theorem is fundamental concept in mathematics that relates to sides of right triangle. It states that square of the length of hypotenuse (the side opposite the right angle) is equal to sum of the squares of lengths of the other two sides (the legs).
To prove that XY = WZ, we will use the fact that the line segment connecting the center of a circle to the midpoint of a chord is perpendicular to the chord.
Let M be the midpoint of XY, and N be the midpoint of WZ. Since X = Z, we know that XM is parallel to ZN, and therefore MZNX is a parallelogram.
Let O be center of circle k(O). Then, by the perpendicularity property mentioned above, we know that OM is perpendicular to XY, and ON is perpendicular to WZ.
Since M and N are midpoints of XY and WZ respectively, we have:
XM = MY, and ZN = NW
Therefore, by the Pythagorean theorem, we have:
OX² = OM² + MX², and OZ² = ON² + NZ²
Adding these two equations gives:
OX² + OZ² = OM² + MX² + ON² + NZ²
Since MZNX is a parallelogram, we know that OM = ON, and MX = NZ. Substituting these values gives:
OX² + OZ² = 2OM² + 2MX²
But since OM is perpendicular to XY and ON is perpendicular to WZ, we have:
OM² + MX² = XM²/4, and ON² + NZ² = ZN²/4
Substituting these values gives:
OX² + OZ² = XM²/2 + ZN²/2
But since MZNX is a parallelogram, we know that XM = ZN. Therefore:
OX² + OZ² = XM²
Thus, we have shown that XY = WZ, since both line segments are equal to XM.
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in a class of c children there are 16 boys what fraction of the class are boys
Answer:
16/c
Step-by-step explanation:
hope this helps <3
The authors of the firsthand and secondhand accounts use different language to describe the pony's arrival. Which BEST states the difference between the authors' language styles? READ IT! Trail Mail! READ IT! The Sacramento Bee
Answer: The answer is The secondhand account is more formal.
Step-by-step explanation:
Answer:
The secondhand account is more formal.
Step-by-step explanation:
For the graph, name the parent function and write an equation of the graph.
This is a transformation of the parent square root function, and it can be written as:
f(x) = √(-x + 4) - 2
Which is the parent function graphed?
It is ratter easy to identify the shape of the general square root function:
f(x) = √x
The only difference is that now it opens to the left, and it starts at the point (4, -2)
Then:
The sign of the x must be negative.
And with the known vertex we can write the equation:
f(x) = √(-x + 4) - 2
That is the graphed function.
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Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?
The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
--------------------------------------------------------------------------------------------------------------------------
The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Simplify: −2[−3(x − 2y) + 4y].
thanks!
Answer:
6x − 20y
Step-by-step explanation:
−2[−3(x − 2y) + 4y] =
= −2[−3x + 6y + 4y]
= −2[−3x + 10y]
= 6x − 20y
Answer:
Step-by-step explanation:
Here you go mate
PEDMAS:
Parenthesis
Exponent
Multiplication
Addition
Subtraction
Step 1
−2[−3(x − 2y) + 4y] Equation
Step 2
-2[-3(x -2y) + 4y] simplify
(-2)(-3(x-2y))+(-2)(4y)
Step 3
(-2)(-3(x-2y))+(-2)(4y) Add,Subtract And Remove parenthesis
6x-12y-8y
answer
6x-20y
I don't need help but I am giving the answer to everyone :) hope it helps
The number of cannonballs in illustration is 506.
What is illustration?Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.
The number of cannonballs in the first layer = 1² = 1
Number of cannonballs in the second layer = 2² = 4
Number of cannonballs in the third layer = 3² = 9
So, the generalized formula to count the balls is given as
= n(n + 1) (2n + 1)/ 6
Here, n= the total number of layers
Put n =11
11(11 + 1)(2(11) + 1) / 6
= 11(12)(23)/6
= 3036/6
= 506
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What is the range of f?
Choose 1 answer:
(A) -4 < f(x) < 5
(B) The f(x)-values -4, -3, 1, and 5
(C) -6 < f(x) < 7
(D) The f(x)-values -6, 0, 2, 4, and 7
Answer:
B
Step-by-step explanation:
The range of a function f, would contain outputs that the function can output, or in other words, y-values.
Generally we use inequalities to describe functions that are continuous (not always the case) over a certain interval because using inequalities, doesn't just mean that the inequality has some outputs, but rather every value that satisfies the given inequality, should be an output.
For example if the function f(x) only outputs: 1, 2, 3, 4
It would be invalid to say the range is: \(1\le f(x)\le 4\)
because saying this is the range, would imply that all values between 1 and 4 (including 1 and 4), are in the range. Meaning that 1.2, 1.3, 1.4, etc... are also in this range, but they're not since the function doesn't output these y-values.
Now looking onto the graph provided, we only want to focus on the outputs aka y-values.
Looking at the graph, we can see that the y-values are: 1, -4, 5, -3, and -3.
Notice that we actually have a duplicate y-value, and whenever we have this, we don't state it "twice" in the range, since the range is just telling us of y-values the function can output, and not how many times it occurs.
Thus the range is: -4, -3, 1, and 5
So "b" would be the correct option.
Note: "D" would be the correct choice for the domain of this function (like the range, except it deals with x-values)
Writing On a number line, between which two consecutive whole numbers would √221 be located? Use pencil and paper Explain why it might be used to approximate the value rather than use the exact value.
Answer:
√221 is between 14 and 15.
√221 ≈ 14.86
Step-by-step explanation:
Perfect square: A number made by squaring a whole number.
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, ...
To find an approximate value of a square root, find the perfect squares above and below the number:
⇒ 196 < 221 < 225
Therefore:
\(\implies \sf \sqrt{196} < \sqrt{221} < \sqrt{225}\)
\(\implies \sf \sqrt{14^2} < \sqrt{221} < \sqrt{15^2}\)
\(\implies \sf 14 < \sqrt{221} < 15\)
Therefore, √221 is between 14 and 15 on a number line.
Drawing the number line
Draw a number line from 196 to 225.Place 14 below 196 and 15 below 225.Divide the space between 14 and 15 into 10 equal increments.(see attachment 1)
Locate 221 on the number line. We can see that it is between 14.8 and 14.9. Place a marker halfway between 14.8 and 14.9, then divide the second half into 5 equal increments (see attachment 2).
Therefore, an approx value of √221 is 14.86.
A= -(-9x+10)(4x-3)-(4x-9)
The simplified equation of the function A= -(-9x+10)(4x-3)-(4x-9) is A= 36x² - 17x + 39
How to determine simplify the equation for A in the function?From the question, we have the following equation that can be used in our computation:
A= -(-9x+10)(4x-3)-(4x-9)
To make the equation legible, we need to rewrite it
So, we have the following representation
A= -(-9x + 10)(4x - 3) - (4x - 9)
Next, we expand the brackets
This gives
A= -(-36x² - 27x + 40x - 30) - (4x - 9)
Next, we open the brackets
So, we have the following representation
A= 36x² + 27x - 40x + 30 - 4x + 9
Solving further, we collect the like terms
A= 36x² + 27x - 40x - 4x + 30 + 9
Solving further, we evaluate the like terms
A= 36x² - 17x + 39
Hence, the equation is A= 36x² - 17x + 39
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What is the square root of 12
Answer:
144 3.464
Step-by-step explanation:
Answer:
the square root of 12 is 2 square root of three but if your looking for a decimal answer it's 3.5
Step-by-step explanation:
Write 15*15*15*15 using an exponent
Answer:
15^4
Step-by-step explanation:
An exponent refers to the number of times a number is multiplied by itself,
so 15 multiplied 3 more times by itself (15 * 15 * 15 * 15) its 15^4.
\(15^{4} .\)
Step-by-step explanation:1. General concept about exponents.When working with positive non fractional exponents, we state that a number A elevated to the n power is that number A in a multiplication of itself n times. For example, when we write \(7^{3}\) we're stating that the seven is being multiplied 3 times: \(7*7*7\).
2. Use the rule to rewrite the expression.As you may see, the expression "15*15*15*15" is just the number 15 being multiplied by itself four times. Hence, we could say that the number 15 to the power of 4. Thus, we can rewrite it as:
\(15^{4} .\)
When you calculate (In) 7, you would be finding the
value of which of the following expressions?
O log10 7
O log, 10
O log, e
O log 7
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
what is logarithm?In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).
When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).
As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
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A certain truck traveled 7,605 miles in 15 days. What is the average number of miles traveled per day?
If the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.
What is average?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
It is given that, a certain truck traveled 7,605 miles in 15 days.
The average number of miles traveled per day is obtained by dividing the total distance traveled by the total time taken as,
Suppose the average number of miles traveled per day is x,
x=76015 / 15
x=507 miles per day.
Thus, if the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.
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A biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road. How much more does he need to travel? (distance)
The biker needs to travel 45 km more to complete his journey.
Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,
Let the total distance of the road be x,
So,
2x/5 - 5 = 3x/8
2x/5 - 3x/8 = 5
Solving for x,
Multiply by 40 to both sides,
16x-15x = 200
x = 200
Therefore, the total distance of the road is 200 km.
Since, he travelled =
200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km
Therefore, he needs to travel 200-155 = 45 km more.
Hence, the biker needs to travel 45 km more to complete his journey.
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Question in the image will give brainlyy
David watches Maria and Alma race electric trains around a track. Maria's train goes around the track in 10 seconds. Alma's train goes around the track in 12 seconds.
How long will it take for both trains to cross the finish line together the first time?
Answer:
60 seconds
Step-by-step explanation:
The LCM of 10 and 12 is
10 = 2 × 5
12 = 2² × 3
LCM = 2² × 3 × 5 = 60
Answer: 60 seconds
the anwser is 60 seconds
An engineer designs a 65-foot cellular telephone tower. Find the angle of elevation to the top of the tower at a point on level ground 40 feet from its base. (Round your answer to one decimal place.)
Answer:
the angle of elevation is 58.4°
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
let ∅ be the angle of elevation;
Opposite (AC) = 65 ft
Adjacent (CB) = 40 ft
we know that; from SOH CAH TOA
TOA
tan∅ = Opposite / Adjacent
so;
tan∅ = 65 / 40
tan∅ = 1.625
∅ = tan⁻¹ ( 1.625 )
∅ = 58.3924 ≈ 58.4°
Therefore, the angle of elevation is 58.4°
3. A bowling alley charges $1.50 for bowing shoes and $3.75 for each game. Paul and
Brandon each have $15 to spend at the bowling alley.
a Paul brings his own bowling shoes. How many games can he bowi?
b. Brandon needs to pay for bowling shoes. How many games can he bowl? Round
your answer down to the nearest whole number.
c. Both Paul and Brandon decide to bowl the number of games that Brandon can
afford to bowl. Does Paul have enough money to buy a slice of pizza and a soda
that cost a total of $3.25? Explain your reasoning.
Answer:
A. Paul can bowl 4 games.
B. Brandon can bowl 3 games.
C. Yes, Paul can have a pizza and a soda. Paul, with his bowling shoes, can afford exactly four games. When playing three games, Paul has a remained of $3.75
Alesha went to the movies. A popcorn is $3 more than a soda. She purchased 1 popcorn and 2 sodas. She spent $21. How much is a popcorn?
Answer: a popcorn is $9
Step-by-step explanation:
soda is $6
What is 2/3 divided 1/6? Explain or show your reasoning?
we have that
2/3 divided 1/6 is equal to
\(\frac{2}{3}\colon\frac{1}{6}=\frac{2\cdot6}{1.3}=\frac{12}{3}=4\)that means
the number 2/3 is 4 times the number 1/6
see the figure below
4/6 and 2/3 are equivalent fractions
because
4/6=2/3
4*3=2*6
12=12 ----> is ok
If you divided 2/3 into 4 equal parts, each part is equal to 1/6
If you divided 2/3 by 1/6, the result is 4 parts
At an arcade, a book of 20 tickets costs $5, a book of 30 tickets costs $7, and a book of 50 tickets costs $10. Would a graph of the relationship between price and number of tickets in a book be a straight line? Explain.
Answer:
yes
Step-by-step explanation:
Jeff Ryan bought 200 shares of BUI for $19.50. Eight weeks later he sold the stock for $20.75. Assuming a 3% commission, his bottom line was a gain of:
Multiple Choice
$250.00
$374.50
$8.50
$257.50
His bottom line was a gain from selling and 3% commission is $257.50.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
The cost price of 200 shares of BUI is (19.50×200) = $3900.
The selling price of 200 shares of BUI is (20.75×200) = $4150.
The net gain is (4150 - 3900) = $250 and with 3% commission it is,
= (103/100)×250.
= $257.50.
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About 217,000 high school students took the AP Statistics exam in 2017. The free-response section of the exam consisted of five open-ended problems and an investigative task. Each free-response question is scored on a 0 to 4 scale (with 4 being the best). For one of the problems, a random sample of 30 student papers yielded a mean score of x =1.267 and a standard deviation of 1.230. a. Find and interpret the standard error of the mean. b. Construct and interpret a 90% confidence interval to estimate the true mean score on this question.
The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.
What is a confidence interval?The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
The confidence interval formula is \(\bar x\pm t\frac{s}{\sqrt{n}}\).
Where, \(\bar x\) is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.
Here,
\(\bar x\) =1.267, s=1.23, n=30
The standard error is Se= 1.23/√30
= 0.2246
Item a:
The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.
Item b:
Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.
\(\bar x\pm tS_c\)
\(\bar x+ tS_c\) =1.267-2.7564(0.2246) =0.6479
\(\bar x- tS_c\) =1.267+2.7564(0.2246) =1.8861
Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.
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PLS HELP I HAVE AN ASSIGNMENT DUE!!
Karl needs 3 1/2 square yards of fabric to make 1 patio chair cover. What is the total amount of fabric needed to make 6 patio chairs?
Answer:
1.71428571
Step-by-step explanation:
1.71428571
Answer:
21 square yards
Step-by-step explanation:
I'm not too sure, but I just did 3 1/2 square yards of fabric and multiplied it by 6 patio chairs. Hope that helps, sorry if it didn't!
Please help geometry question Pythagorean theorem
Therefore , the solution of the given problem of triangle comes out to be L = 3(√(h²) + ((w/2²))) + 3h .
What is a triangle exactly?A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular.
Here,
Given the height and breadth of the top of the frame, we can use the Pythagorean theorem to determine the length of each side of the triangle.
Let's assume the height is h feet and the width of the top of the frame is w feet. The triangle's side lengths can then be calculated as follows:
=> s =√((h²) + ((w/2)²))
We must add up the lengths of all the pipe segments that will be used to build the frame in order to determine the total quantity of steel pipe required.
The following formula can be used to determine how much steel tubing is required:
=> L = 3s + 3h
where h is the height of the frame and s is the length of each edge of the triangle.
Using the method instead of s, we obtain:
=> L = 3(√(h²) + ((w/2²))) + 3h
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Solve and graph. |3x+6/9|>=2
The solution to the inequality expression is -8/9 ≤ x ≥ 4/9
How to solve and graph the inequality expressionFrom the question, we have the following parameters that can be used in our computation:
|3x + 6/9| ≥ 2
Expand the inequality expression
So, we have
-2 ≤ 3x + 6/9 ≥ 2
Subtract 6/9 from both sides
So, we have
-24/9 ≤ 3x ≥ 12/9
Divide through the equation by 3
-8/9 ≤ x ≥ 4/9
Hence, the solution to the inequality expression is -8/9 ≤ x ≥ 4/9
The graph is attached
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PLEASE HELP
You have$1400, how long would it take to DOUBLE your money in an account that paid 6% interest per year? Round to the nearest year.
Answer:
12 years roughly ends in $2,817.08
Step-by-step explanation:
Help pls it’s urgent
Answer:
d. -2
Step-by-step explanation:
they're telling you those lines are parallel there are specific knowns about the angles
since it's urgent I won't go into it, but PLS look it up it's super simple and makes sense
nonetheless this means angle 1 and angle 5 are the same value so we can set them equal
3x + 24 = 7x + 32
substract 32 from both sides
3x - 8 = 7x
substract 3x from both sides
-8 = 4x
divide 4 from both sides
-2 = x
Evaluate the following expression,
5x [7+ (10-2) + 4)
Answer: 95x
Step-by-step explanation: Remove parentheses. 5x(7+10-2+4)
Add 7 and 10.
5x(17-2+4)
Add 15 and 4.
5x multiped by 19
Multiply 19 by 5
95x
1/2-1/6
Jzjzhhzhzhzhhz
Answer:
ummm the answer is very simple
The answer is 0/6
Step-by-step explanation:
\( \frac{1}{2 \times 3} - \frac{1}{6} \)
\( \frac{1}{6} - \frac{1}{6} \)
\(1 - 1 = \frac{0}{6} \)