The solutions to the system of equations f(x) = g(x) are given as follows:
x = 0 and x = 1.
The reason for these solutions is that f(x) and g(x) have the same numeric value at x = 0 and at x = 1.
How to interpret the solution of a system of equations?A system of equations is composed by multiple equations.
The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.
The x-values for which the numeric values of f(x) and g(x) are the same are given as follows:
x = 0 and x = 1.
Which are the solutions to the system of equations.
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# 1 Use the relationships and patterns in the tabel to identify the missing
value from the ordered pair. Type the missing value in the answer space
provided.
X
y
2
25
(2,25)
(3,__)
(4, 100)
(5, 125)
3
4
100
5
125
The missing value in the space provided is given as follows:
75.
How to model the proportional relationship?A proportional relationship is modeled as follows:
y = kx.
In which k is the constant of proportionality.
The constant for the relationship in this problem is given as follows:
k = 125/5 = 100/4 = 25/1 = 25.
Hence the relationship is given as follows:
y = 25x.
The missing value is the output when x = 3, hence:
y = 25(3)
y = 75.
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3. What are the three inequalities which define the in shaded region
The three inequalities that define the shaded region are given as follows:
y < 2.y > 2x.y ≤ -x - 2.How to define the inequalities?The inequality that defines the values below the vertical line y = 2 is given as follows:
y < 2.
(open interval as the line is dashed).
The increasing line has an intercept of 0 and slope of 2, with values to the right being shaded and the line being dashed, hence the inequality is given as follows:
y > 2x.
The decreasing line has an intercept of -2 and a slope of -1, with values to the left being shaded, with a closed interval, as the line is shaded, hence the inequality is given as follows:
y ≤ -x - 2.
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(a) Draw the graph of y=x²+x-5 for values of x ranging from -4 to +3. Use a scale of 1cm to 1 unit on both axes. (b) On the same graph draw the line y = 2(x-1). From your graph: (c) find the roots of the equation x²+x-5=0 (d) deduce the roots of the equation x²+x-7=0 (e) deduce the roots of the equation x²+x-5=2(x-1) (f) state the minimum value of x2+x-5.
We must first plot the given linear equation before we can draw the graph for it. Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.
How do you deduce roots?link the points that lie on it to form a straight line.
Y = 2x - 1 is the first equation.
Calculate the corresponding values of y by substituting various values of x into the equation.
X Y = 2x-1 point (x, y)
0 -1 (0, -1)
2 3 (2, 3)
4 7 (4, 7)
-1 -3 (-1, -3)
-3 -7 (-3, -7)
On the graph paper, place these points and draw a straight line connecting them.
Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.
In order to determine the critical point, we will set the first derivative of the function to zero and solve for x. We may determine whether this point will be a maximum or minimum by taking the second derivative, or f"(x). It will be a minimal value if the second derivative is positive.
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Suppose 0 is an angle in the standard position whose terminal side is in quadrant IV and cot 0 = -9/18. Find values of five remaining trigonometric functions of 0.
The values of five remaining trigonometric functions of θ.
sinθ = 1/√5, cosθ = 2/√5, tanθ = 2, secθ = √5/2, cosecθ = √5
We have to determine values of five remaining trigonometric functions of θ. Suppose θ is an angle in the standard position whose terminal side is in quadrant IV and cot θ = -9/18.
The ratio of trigonometry is:
sinθ = Perpendicular/Hypotenuse
cosθ = Adjacent Side/Hypotenuse
tanθ = Perpendicular/Adjacent Side
cotθ = Adjacent Side/Perpendicular
sec = Hypotenuse/Adjacent Side
cosec = Hypotenuse/Perpendicular
We know that;
Adjacent Side = 9, Perpendicular = 18
Now finding the value of Hypotenuse using the Pythagorean Theorem
(Hypotenuse)^2 = (Adjacent Side)^2 + (Perpendicular)^2
(Hypotenuse)^2 = (9)^2 + (18)^2
(Hypotenuse)^2 = 81 + 324
(Hypotenuse)^2 = 405
Taking square root on both side, we get
Hypotenuse = 9√5
Now finding the other trigonometry ratio:
sinθ = Perpendicular/Hypotenuse
sinθ = 9/9√5
sinθ = 1/√5
cosθ = Adjacent Side/Hypotenuse
cosθ = 18/9√5
cosθ = 2/√5
tanθ = Perpendicular/Adjacent Side
tanθ = 18/9
tanθ = 2
secθ = Hypotenuse/Adjacent Side
secθ = 9√5/18
secθ = √5/2
cosecθ = Hypotenuse/Perpendicular
cosecθ = 9√5/9
cosecθ = √5
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In 1957 an earthquake in Alaska measured about 9.0 on the Richter scale. An earthquake with magnitude 6.0 occurred in Japan in early 2007.
How many times more intense was the earthquake in Alaska than the one in Japan?
The number of times more intense that the earthquake in Alaska was than the one in Japan was 1, 000 times more intense.
How does the Richter Scale work ?The Richter magnitude is determined by measuring the height of the greatest wave that has ever been seen at a given distance from the seismic source.
Each order of magnitude is 10 times more intense than the previous one since the Richter scale is a base-10 logarithmic scale. To put it another way, a two is ten times as intense as a one, and a three is one hundred times stronger.
This means that the number of times more intense that the earthquake in Alaska was than the one in Japan was:
= 10 x 10 x 10
= 1, 000 times
Note : Alaska and Japan earthquake difference:
= 9 - 6
= 3
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After making several scale drawings, Joseph
decides on the best placement for a new grill on
his deck. He uses a scale of 2 cm for every 5 in.
What is the actual area of the space for Joseph's
new grill in square inches?
Answer: 50
Step-by-step explanation:
i don't know how i got this but yeah its 50
Fraction A pet store that sells birds has 12 male birds for every day 9 female birds write the ratio of female birds
The ratio of female birds is 3/7.
Explain ratio.One way to express something as a percentage of another is to use a ratio, which is a mathematical concept.
How are ratios determined?By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B). You are multiplying information A by information B, as indicated by this. For instance, if A is 5 and B is 10, your ratio will be 5/10.
The pet store has 12 male birds for every 9 female birds.
total birds = 12 + 9 = 21 birds.
So, the ratio of female birds = female birds / total birds
= 9/21
= 3/7
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two runners on an east-west highway are 421.2 feet apart heading east. a hot air balloon is flying ahead of them. the angle of elevation to the balloon of the runner closet to the balloon is 24.5o. if the hot air balloon is 1500 feet directly above a point on the highway east of both runners, what is the angle of elevation to the balloon of the runner the greatest distance from the balloon?
The angle of elevation to the balloon of the runner the greatest distance from the balloon is 83.13 degrees.
The concept used in this problem is Trigonometry. Specifically, the problem uses the tangent function, which is one of the three main trigonometric ratios (sine, cosine, and tangent) used to relate the angles and sides of a right triangle.
To solve this problem, we can use the tangent function of trigonometry, which relates the opposite side (the distance from the runner to the balloon) to the adjacent side (the distance from the runner to the point on the highway) and the hypotenuse (the distance from the point on the highway to the balloon).
Let's call the angle of elevation of the runner closest to the balloon as angle A and the angle of elevation of the runner farthest from the balloon as angle B.
tan(A) = opposite / adjacent = (1500 - 421.2) / 421.2 = 878.8 / 421.2
tan(B) = opposite / adjacent = (1500 + 421.2) / 421.2 = 1921.2 / 421.2
We can use the inverse tangent function (arctan) to find the angle of elevation of the runner the greatest distance from the balloon.
B = arctan(1921.2 / 421.2)
The result is in radians, to convert the angle from radians to degrees, we can use the conversion factor of 180/pi.
B = arctan(1921.2 / 421.2) = arctan(4.5536) = 83.13 degrees (approx)
so, the angle of elevation to the balloon of the runner the greatest distance from the balloon is 83.13 degrees.
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Lance and 7 other friends go to an activity center together. They each pay $5. 95 for dinner, 84 for laser tag, $3. 60 for bowling
shoes, and $2. 25 for video games. The total amount they spent is 8 (5. 95) +8 (4) +8 (3. 60) +8 (2. 25).
Part A
Rewrite the expression so that it only has one multiplication operation
Enter the correct answer in the box
The correct expression that will form with one multiplication operation is 8 × (5.95 + 84 + 3.60 + 2.25).
Firstly rewriting the correct expression according to the amount spent by each person on different entities. The expression will be -
Total amount spent by 8 people = number of people × (amount spent on dinner + laser tag + bowling shoes + video games)
Now keeping the values in formula to find the total amount spent by eight people in desired format.
Total amount spent by eight people = 8 × (5.95 + 84 + 3.60 + 2.25)
Performing addition to simplify the expression is -
Total amount spent by eight people = 8 × 95.8
Thus, the correct simplified expression will be 8×95.8.
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WILL MAKE BRAINIEST!!
Identify a 30 year mortgage
O. A mortgage that will be paid off in 15 years?
O. A mortgage that has the same interest rate and same monthly payment for 30 years.
O. A mortgage that fluctuates interest rates
O.None of the above
Because a 30-year mortgage has a longer term, your monthly payments will be lower and your interest rate on the loan will be higher.
What is the term for a 30-year mortgage?A 30-year fixed-rate mortgage is commonly used to refer to conventional loans. Conventional loans are not backed by the government; however, a 30-year fixed FHA, USDA, or VA loan that is insured by the government is available. Rocket Mortgage® does not currently provide USDA loans.
A 30-year fixed-rate mortgage is a house loan with a 30-year repayment period and an interest rate that remains constant during the loan’s duration. When you take for a 30-year fixed-rate home loan, the amount you make each month remains the same until the loan is paid off.
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Jeff wants to purchase a television for his first apartmentThe television costs 750. He can get a zerointerest loan for the television if he pays $100 per month. At the same time, he puts away $200 per month in savings. To figure out when his savings will equal the remaining amount he owes on the television , he starts writing a system of equations :
The correct equation for Jeff after every cost will be y = 750 -100x
Cost of the television = $750
Loan amount paid per month = $100
Amount put in savings = $200
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Since the amount of $200 is being saved, this means that it is not going away or is being spent. Now, as per the question, the initial remaining balance with Jeff is 750. The balance decreases by the loan amount of 100 per month.
This means that the amount is reduced by = 100x.
Therefore, the equation describing the scenario is -
y = 750 -100x
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What is the length of every median in an equilateral triangle whose side length is 5?
Answer:
√18.75 ≈ 4.33
Step-by-step explanation:
The median joins a vertex and the opposite side's midpoint.
side = 5
half side = 2.5
a² + b² = c²
2.5² + b² = 5²
b² = 18.75
b = √18.75
b = 4.33
The length of every median in an equilateral triangle whose side length is 5 is 4.330127018922193.
An equilateral triangle is one in which the angles and all three sides are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees. Due to its equal sides and angles, the equilateral triangle is regarded as a regular polygon or triangle.
In an equilateral triangle, all three medians have the same length.
The length of a median in an equilateral triangle can be found using the formula:
median length = (side length * sqrt(3))/2.
Therefore, in an equilateral triangle with a side length of 5, the length of each median would be,
[tex]=5*\sqrt{3}/2 \\=2.5*\sqrt{3}\\= 4.330127018922193[/tex].
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In the last three years, Frederico's basketball team won 50 more games than they lost. If they won 140 games, what was the ratio of wins to losses? Write the ratio in all three forms.
Answer:
Step-by-step explanation:
won 140
lost 140-50=90
Ratio wins to losses: 14:9
they charge $3.89 per square foot for materials and $122.42 per day of labor. chance spent $2882.48 on the renovation. if the number of square feet is 189 more than the number of days it took for the renovation, how long did the renovation take
Let's call the number of days of labor x, and the number of square feet y.
From the information provided, we can set up the following equation:
What does a math equation mean?
A mathematical statement that shows the equality of two mathematical expressions is the definition of an equation in algebra. As an illustration, the two equations 3x + 5 and 14 are joined by the equal sign to get the equation 3x + 5 = 14.
3.89y + 122.42x = 2882.48
We also know that y = x + 189
We can substitute the second equation into the first equation:
3.89(x + 189) + 122.42x = 2882.48
Expanding and simplifying:
3.89x + 730.91 + 122.42x = 2882.48
x = (2882.48 - 730.91) / (3.89 + 122.42) = 22.98 days
So the renovation took 22.98 days.
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11. Angel made 1 1/3pounds of trail mix for a
hike. Is there a way Angel can break up
the trail mix into four bags? Explain.
let's firstly convert the mixed fraction to an improper fraction.
[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{trail mix}}{\cfrac{4}{3}}\div \stackrel{bags}{4}\implies \cfrac{4}{3}\div \cfrac{4}{1}\implies \cfrac{4}{3}\cdot \cfrac{1}{4}\implies \cfrac{4}{4}\cdot \cfrac{1}{3}\implies \stackrel{per~bag}{\cfrac{1}{3}}[/tex]
621900 house cost 5.4 mortgage interest rate how  much do you have to pay monthly over 5 years
Over a period of 5 years, the amount that you would have to pay monthly is given as $3,201.37
How to solve for the mortgageTo calculate the monthly mortgage payment for a house that costs $621,900 with an interest rate of 5.4% over 5 years, you can use the following formula:
P = (r(1 + r)^n) / (((1 + r)^n) - 1) * L
Where:
P = monthly payment
r = monthly interest rate (5.4%/12 = 0.0045)
n = total number of payments (5 years x 12 = 60)
L = the loan amount ($621,900)
Plugging in the values, we get:
P = (0.0045(1 + 0.0045)^60) / (((1 + 0.0045)^60) - 1) * 621,900
P = $3,201.37
So you have to pay $3,201.37 monthly over 5 years.
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HELPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!
UR AMAZING
Answer:
1/
Step-by-step explanation:
1/3+1/2=5/6
1-5/6=1/6
1/
Any ideas?
In concave equilateral pentagon ABCDE, angle A = angle B = 108 degrees. What is the degree measure of angle E?
Answer:
In an equilateral pentagon, all angles have equal degree measures, so to find the degree measure of one angle, we need to find the sum of the degree measures of the interior angles and then divide by the number of angles.
Step 1: Find the sum of the degree measures of the interior angles of the pentagon:
180 * (5 - 2) = 540 degrees
Step 2: Divide the sum by the number of angles:
540 degrees / 5 angles = 108 degrees
The degree measure of angle E is 108 degrees.
The degree measure of angle E is 108°.
We can use interior angels theorm.
The sum of the interior angles of a pentagon can be calculated using the formula:
Interior angle sum = (n - 2) × 180
where n is the number of sides of the polygon.
In this case, n = 5, so the sum of the interior angles of the pentagon is (5 - 2) × 180 = 540°.
Since angle A and angle B are both equal to 108°, we can say that:
angle A + angle B = 2 × 108 = 216°.
So, the sum of the remaining three interior angles (angles C, D, and E) is:
540 - 216 = 324°
Since each of these three angles is equal, the measure of each angle must be 324° divided by 3, or:
324 ÷ 3 = 108°
So, the degree measure of angle E is also 108°.
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Choose the items that complete the sentence about the key features of f(x) = 8x. The y-intercept is , the asymptote is y = , and the range is y >
According to the following graph, the y intercept is 0, the asymptote is ∞ and the range is (-∞, ∞)
In math the term called graph is defined as a pictorial representation or a diagram that represents data or values in an organized manner and the points on the graph often represent the relationship between two or more things.
Here we know that the function is f(x) = 8x.
When we plot the function then we get the graph like the following.
While we looking into plotted graph, then we have identified that the y-intercept is 0.
And the horizontal asymptote is the limit as x goes to ∞.
And the range is the set of values above the horizontal asymptote (-∞, ∞).
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What is the quotient of 154,504 divided by 28 with long division?
How do you solve for x?
Step-by-step explanation:
please attached for details
log₂ 3+ log₂ (x-4)= 4
Answer:
In Explanation
Step-by-step explanation:
To solve for x in the equation log₂ 3+ log₂ (x-4)= 4, we can first use the logarithm identity: log₂ a + log₂ b = log₂ (ab)
So, we can rewrite the equation as:
log₂ (3(x-4)) = 4
Then we can use the definition of logarithm to find the value of x:
2^4 = (3(x-4)) = 3x-12
16 = 3x - 12
28 = 3x
x = 9 + 4 = 9
Therefore, x = 9 is the solution of the equation log₂ 3+ log₂ (x-4)= 4
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. people are given a blind taste test for bottled water and tap water. they cannot differentiate properly. what are the odds that at least 8 out of 9 people will guess the water type correctly?
The binomial distribution is a discrete probability distribution used in probability theory and statistics to explain the number of successes in a set number of trials, where each trial can only result in success or failure. The probability mass function (PMF) shown below defines the binomial distribution as follows:
P(a) = ⁿСₐ * p^a* (1-p)^(n-a)
Where:
a: the number of successes in n trials
n: the total number of trials
p: the probability of success in one trial
ⁿСₐ : n! / (a! * (n-a)!)
the binomial coefficient, which shows how many different ways there are to select k successes from n trials.
A variety of phenomena, including coin tossing, die rolling, and other tests with a set number of trials and only two possible outcomes, can be usefully modelled using the binomial distribution.
In a blind tasting test, if participants are unable to distinguish between bottled and tap water, we can assume that their guesses are random. The probability of accurately predicting the type of water in this situation is 50%.
The likelihood that 8 out of 9 people will properly predict their water type is
(1/2)^8 * (1/2)^1 = (1/2)^9 = 1/512
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I really need help on this!
Can someone help with problem 1 and 2
To find the sum of interior angles of a polygon, multiply the number of triangles formed inside the polygon to 180 degrees.
How to find the sum of interior angles ?
The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.Each interior angle of a regular hexagon has a measure of 120°. Because the sum of these angles will always be 360°, then each exterior angle would be 60° (360° ÷ 6 = 60°). If each exterior angle is 60°, then each interior angle is 120° (180° − 60° = 120°).The angles that lie inside a shape, are said to be interior angles, or the angles that lie in the area bounded between two parallel lines that are intersected by a transversal are also called interior angles.
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In a multicellular organism such as a dog or cat which structures listed would present the greatest in number?
In a multicellular organism such as a dog or cat have tens of trillions of cells and 60 to 80 million cells respectively. So we can say that dog have greatest number of cells
Organisms with many cell types and specialized cells that are gathered together to perform specific duties are known as multicellular organisms. An example of a multicellular organism with organization is a tree or a cat, which have tissues, organs, and organ systems.
Although we are unsure of the actual number of cells in a typical dog, we can estimate it roughly. We may apply this number to dogs, which have in the tens of trillions of cells, as some sources give a ballpark estimate of about fifty trillion cells within a human body. 60 to 80 million cells make up a cat.
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What are the answers they are due next period
Helppp
Answer:A.½ B.-½ C.2⁷/20
Step-by-step explanation:A. 5¾+(-¼) =23/4 - ¼ =22/
=5½
B. -⅔+⅙ = (-4+1)/6=-½
C. -8/5-¾= (-32-15)/20 =47/20 =2⁷/
Brandon invested $11,000 in an account paying an interest rate of 1% compounded
quarterly. Robert invested $11,000 in an account paying an interest rate of 13/%
compounded monthly. After 20 years, how much more money would Robert have in
his account than Brandon, to the nearest dollar?
Answer: $4,914
Step-by-step explanation:
To calculate the final balance in Brandon's account, we need to use the formula for compound interest: A = P(1 + r/n)^(nt)
where A is the final balance, P is the initial investment, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have:
P = $11,000
r = 1% = 0.01
n = 4 (because the interest is compounded quarterly)
t = 20
so, A = $11,000(1 + 0.01/4)^(4*20) = $11,000(1.0025)^80 = $22,817.20
To calculate the final balance in Robert's account, we need to use the same formula, but with different values for r, n, and t.
In this case, we have:
P = $11,000
r = 13/100 = 0.13
n = 12 (because the interest is compounded monthly)
t = 20
so, A = $11,000(1 + 0.13/12)^(12*20) = $11,000(1.01083333)^240 = $27,731.34
To find the difference in the final balances, we subtract the final balance in Brandon's account from the final balance in Robert's account:
$27,731.34 - $22,817.20 = $4,914.14
To the nearest dollar, the difference is $4,914.
Answer:391
Step-by-step explanation:
a truck is moving at the rate of 50 miles per hour, and the diameter of each wheel is 3 feet. what is the angualr speed of the wheels in raidans per minute
The angular speed of the wheels is approximately 1480 / π radians per minute.
We can start by converting the velocity of the truck from miles per hour to feet per minute, since the diameter of the wheels is given in feet.
50 miles/hour = 50 x 5280 feet/hour = 264,000 feet/hour
264,000 feet/hour / 60 minutes/hour = 4,400 feet/minute
Next, we can find the circumference of the wheel and then divide it by the velocity of the truck to find the angular velocity in radians per minute:
Circumference = 2 * π * r = 2 * π * (diameter/2) = 2 * π * (3 feet / 2) = 3π feet
Angular velocity (ω) = velocity / circumference = 4,400 feet/minute / (3π feet) = 1480 / π radians/minute
So the angular speed of the wheels is approximately 1480 / π radians per minute.
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the sum of the relative frequencies for all classes will always equal group of answer choices the sample size. the number of classes. one. any value l
The sum of the relative frequencies for all classes will always equal option (C) 1 i.e. when all relative frequencies on a set of values are added it is always equal to one.
A relative frequency tells us the number of times a particular value for a data item has been perceived to occur in relation as compared to the total number of values for that set of data items.
It is calculated by dividing the absolute frequency by the total number of values for the set of data items. It is used to express proportions, ratios, percentages, etc.
Absolute frequency is a mathematical term used in statistics to calculate the number of times a value occurs in a trial set of values. It is used to calculate relative frequency, and display a graph to give a visual representation.
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