Answer:
Volume ≈ 153.93804 cm^3
Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.
Step-by-step explanation:
Robert has some nickels and some dimes. He has a maximum of 29 coins worth no less than $2.20 combined. If Robert has 10 nickels, determine all possible values for the number of dimes that he could have. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Robert's dimes are anywhere between 17 and 19.
Explanation:Nickels
are worth 5 cents, and
dimes
are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.
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Label the triangle sides, assuming the angle of interest is the 30-degree angle:
solve for
The side with x is the
blank side.
The side with y is the
NO SPAM I WILL REPORT YOU
blank side.
The side with 17 is the blank side
Check the picture below.
A bucket contains 4 green, 3 yellow, 6 red, and 4 blue marbles. Jessi removes 2 marbles, without replacement, from the bucket shown in the image. What is the probability that Jessi removes 1 red marble on her first try and 1 green marble on her second try?
A.
8.8%
B.
3.7%
C.
62.5%
D.
58.9%
Answer: A
Step-by-step explanation:
Which of the following represents the equation of the trigonometry function graphed below?
The equation of the trigonometric function graphed is A) f(x) = 3 sin (x) - 2.
Given a graph of the trigonometric function.
We have to find the equation of the trigonometric function.
For x = π/2, y = 1
Also, when x = 3π/2, y = -5
A) If the function is,
f(x) = 3 sin (x) - 2,
When x = π/2
f(x) = 3 sin (π/2) - 2
= 3(1) - 2
= 1
When x = 5π/2
f(x) = 3 sin (5π/2) - 2
= 3 (-1) - 2
= -5
Hence the correct option is A.
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The line r represents f ( x ) = x − 4 3 . Therefore, the line that represents f - 1 is and f - 1 ( x ) = x + .
Given statement solution is :- The Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.
To find the inverse function of f(x) = (x - 4)/3, we need to swap the roles of x and y and solve for y. Let's start by writing the equation with y instead of f(x):
y = (x - 4)/3
Now, let's interchange x and y:
x = (y - 4)/3
To solve for y, we can isolate it by multiplying both sides of the equation by 3:
3x = y - 4
Next, let's add 4 to both sides:
3x + 4 = y
Finally, we can write the inverse function as:
[tex]f^(-1)(x)[/tex] = 3x + 4
So, the Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A)19.0
B)10.0
Step-by-step explanation:
Using [tex]\frac{1}{2} * absin(C)[/tex]
This is used when you have an angle between two sides
Kindly check the attached image for the solution
What is the answer to this question? Having a hard time completing and finding answer
(x−5.2)
2
+(y+3.7)
2
=49left parenthesis, x, minus, 5, point, 2, right parenthesis, squared, plus, left parenthesis, y, plus, 3, point, 7, right parenthesis, squared, equals, 49
What is its center?
What is its radius?
Step-by-step explanation:
This is the equation for a circle in the form :
(x-h)^2 + (y-k)^2 = r^2 where h,k is the center and r is the radius
center = 5.2,-3.7 and radius = sqrt (49) = 7
JOSON Ortiz Budgeting Basics with Autumn Autumn is 22 years old and works as a checker at a local grocery store. Autumn lives in an apartment she shares with two other roommates. Autumn's take-home pay from her job is $1275.00 per month. Add this amount to her bank registry below. Here is a list of how Autumn will be budgeting her money this month. Move the expenses over to the bank registry and deduct them from the balance. Rent - $400.00 Utilities- $75.00 Cell Phone - $80.00 Subway Pass - $120.00 Groceries - $200.00 Work Clothes- $100.00 Entertainment $100.00 Savings $200.00 Transaction Paycheck Withdrawal Deposit Ending Balance Balance
Autumn's bank registry will be :
Transaction Amount Balance
Paycheck $1275.00 $1275.00
Rent $400.00 $875.00
Utilities $75.00 $800.00
Cell Phone $80.00 $720.00
Subway Pass $120.00 $600.00
Groceries $200.00 $400.00
Work Clothes $100.00 $300.00
Entertainment $100.00 $200.00
Savings $200.00 $0.00
How to explain the informationAs you can see, Autumn has $0.00 left over at the end of the month. This means that she is spending more money than she is earning. In order to create a budget that works for her, Autumn will need to find ways to cut back on her expenses. Some possible areas where she could cut back include:
Autumn could look for a cheaper apartment or move in with more roommates. Autumn could turn off lights and appliances when she's not using them and seal up any cracks or holes in her apartment to keep the heat in during the winter and the cool air in during the summer.
By cutting back on her expenses, Autumn can create a budget that works for her and save money for the future.
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Nicole and her 3 friends bought 8 pounds of candy and shared them equally. How many pounds
of candy
?
3
Answer:
Each person will get 2 pounds of candy
Step-by-step explanation:
Nicole + 3 friends = 4 total
8 pounds of candy = total
total candy / total people
8/4 = 2
Please help i will give brainliest
The value of measure of angle 1, angle 2, and angle 3 are,
⇒ ∠1 = 106 degree
⇒ ∠2 = 74°
⇒ ∠3 = 74°
We have to given that;
Angle in figure is,
⇒ 74°
Since, From figure,
angle 1 is,
⇒ ∠1 = 180 - 74
⇒ ∠1 = 106 degree
Hence, We get;
Measure of angle 2 is,
⇒ ∠2 = 180 - 106
⇒ ∠2 = 74°
And, Measure of angle 3 is,
⇒ ∠ 3 = ∠ 2
By definition of alternate interior angle.
⇒ ∠3 = 74°
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The measure of ∠1 is 106 because it is a straight angle with 74° angles.
The measure of ∠2 is 74 because it is a vertical angle with 74° angles.
The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.
We have,
The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
Now,
∠1 + 74 = 180
∠1 = 180 - 74
∠1 = 106
And,
∠2 and 74 are vertical angles.
So,
∠2 = 74
And,
∠3 and 74 are corresponding angles.
So,
∠3 = 74
Thus,
The measure of ∠1 is 106 because it is a straight angle with 74° angles.
The measure of ∠2 is 74 because it is a vertical angle with 74° angles.
The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.
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Find x to the nearest hundredth.
16
X
40°
O A x = 24.89
O
OB. x = 13.43
O C. x 10.28
D. x = 12.26
Option C is correct, the value of x in the triangle is 10.28 units.
The given triangle is right angled triangle.
We know that the sine function is a ratio of opposite side and hypotenuse.
To the angle 40 degrees the opposite side is x.
The hypotenuse is 16.
Sin 40 degrees=x/16
0.6428=x/16
Apply cross multiplication:
x=16×0.6428
x=10.28
Hence, the value of x in the triangle is 10.28 units.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
This is a simple one.
All you need to do is find the scale factor of the shapes. (How much has it decreased by?)
Wecan find this by doing 15 ÷ 20 (not the other way round because we want to find the scale factor for the bigger rectangle to the smaller)
15 ÷ 20 = 0.75
So to find the area all you need to do is times the area with the scale factor which is 0.75
500 x 0.75 = 375cm²
So the answer is
(A) 375cm²
By definition, theoretical probability is equal to:
A. No. of favorable outcomes/ total no. of possible outcomes ✅️
B. No. of total outcomes/ total no. of impossible outcomes
C. No. of possible outcomes/ total no. of favorable outcomes
D. No. of total outcomes/ total no. of possible outcomes
Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, making option A the correct answer.
The correct answer is A. Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. It represents the likelihood of an event occurring based on mathematical calculations and assumptions.
To provide a detailed explanation, let's break down the components of the definition:
Favorable outcomes: These are the outcomes that meet the desired criteria or event you are interested in. For example, if you are rolling a fair six-sided die and you want to find the probability of rolling a 3, the favorable outcome would be a single outcome where the die shows a 3.
Total number of possible outcomes: This refers to the complete set of all possible outcomes in the given situation. In the case of the fair six-sided die, there are six possible outcomes (numbers 1 to 6) since each face of the die represents a different number.
Theoretical probability is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This ratio provides an estimate of the probability of the event occurring under ideal, theoretical conditions. It assumes that each outcome is equally likely to occur.
It's worth noting that theoretical probability is based on mathematical calculations and assumptions, and it may not always reflect the actual probability observed in real-world scenarios. However, it serves as a foundation for understanding and analyzing probabilities in various contexts, such as in mathematics, statistics, and decision-making processes.
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see image see image see image see image see image
Using the bearing and trigonometry in the problem, the distance of the waterfall from the lake is 7.94km
How far away is the waterfall from the lake?To determine the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the distance in a south direction.
To find the distance between the waterfall and the lake, we can use the concept of right triangles and trigonometric functions.
Since the bearing is given as 236°, we can subtract this angle from 180° to find the angle formed by the south direction and the line connecting the lake and the waterfall:
180° - 236° = -56°
Now, we can consider the south direction as the reference direction (0°) and the line connecting the lake and the waterfall as the hypotenuse of a right triangle.
Using the cosine function, we can calculate the length of the side adjacent to the angle (-56°), which represents the distance between the waterfall and the lake:
cos θ = adjacent / hypothenuse
Adjacent = Hypotenuse * cosθ
Let's substitute the values into the formula:
Adjacent = 14.2 km * cos(-56°)
To calculate the cosine of -56°, we can use the fact that the cosine function is an even function:
cos(-56°) = cos(56°)
Adjacent side = 14.2 cos(56)
Adjacent side = 7.94km
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Answer:
The waterfall is approximately 8.91 km away from the lake
Step-by-step explanation:
To find the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the southward direction.
Since the waterfall is 14.2 km south of the lake, the line connecting the waterfall and the lake forms a right triangle with the south direction being the adjacent side, the distance between them being the hypotenuse, and the angle formed between them being the bearing of 236°.
To find the distance between the waterfall and the lake, we can use the cosine function, which relates the adjacent side, hypotenuse, and angle:
cos(236°) = adjacent side / hypotenuse
Let's denote the distance between the waterfall and the lake as "d." The adjacent side represents the southward direction.
cos(236°) = d / 14.2 km
Solving for "d":
d = cos(236°) * 14.2 km
Using a calculator:
d ≈ -8.91 km
Since distance cannot be negative, we take the absolute value:
|d| ≈ 8.91 km
Therefore, the waterfall is approximately 8.91 km away from the lake.
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Here, S.P. = . 1,61, 680 D%= 6%. M.P. = ?
The marked price (M.P.) is 1,72,000 when the selling price is 1,61,680 with discount of 6%.
To find the marked price (M.P.), we can use the formula:
M.P. = S.P. / (1 - D%)
Given:
S.P. = 1,61,680
D% = 6%
First, we need to convert the discount percentage to decimal form by dividing it by 100:
D% = 6/100 = 0.06
Now, we can substitute the values into the formula:
M.P. = 1,61,680 / (1 - 0.06)
M.P. = 1,61,680 / 0.94
M.P. = 1,72,000
Therefore, the marked price (M.P.) is approximately 1,72,000.
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Explain where the hands of an analog clock point at 1:27.
The hands of an analog clock point at 1:27 is at 1o'clock position
How to determine the pointAt 1:27 on an analog clock, the hour hand focuses straightforwardly at the numeral "1" on the clock confront, demonstrating that it is within the 1 o'clock position.
The miniature hand, on the other hand, focuses between the numerals "2" and "3" on the clock confront, roughly midway between them.
Since there are 60 minutes in an hour and the diminutive hand moves around the clock confront at a consistent rate, it shows that 27 minutes have passed since the hour started.
Hence, the miniature hand is closer to the numeral "3" but not however at it. The moment hand may be anyplace on the clock confront, because it moves persistently.
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Please help me solve this
There is 90% confidence that the population mean number of books people read is between 11.55 and 13.25.
To construct a 90% confidence interval for the mean number of books people read, we can use the following formula:
Confidence Interval = x ± (Z * (s / √n))
Where:
x = sample mean (12.4 books)
s = sample standard deviation (16.6 books)
n = sample size (1017)
Z = Z-score
Since the sample size is large (n > 30), we can assume the sampling distribution is approximately normal.
We can use the standard normal distribution to find the Z-score for a 90% confidence level.
The Z-score for a 90% confidence level is approximately 1.645.
Now we can calculate the confidence interval:
Confidence Interval = 12.4 ± (1.645 (16.6 / √1017))
Confidence Interval ≈ 12.4 ± (1.645 (16.6 / √1017))
Confidence Interval ≈ 12.4 ± (1.645 (16.6 / 31.95))
Confidence Interval ≈ 12.4 ± (1.645 x 0.518)
Confidence Interval ≈ 12.4 ± 0.85
There is 90% confidence that the population mean number of books people read is between 11.55 and 13.25.
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Any idea.???????
Here are four shapes
Rhombus and equilateral triangle will fit in regular circle and rectangle will fit in quadrilateral circle.
A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.
Here, rhombus and equilateral triangle are regular, and rectangle and triangle are not regular.
Therefore, rhombus and equilateral triangle will fit in regular circle and rectangle will fit in quadrilateral circle.
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Question no 59
Need solution
The area of the shaded region is 104 cm²
How to determine the areaFirst, we need to know that the area of a circle is calculated using the formula;
A = πr²
Such that the parameters of the formula are;
A is the area of the circler is the radiusFirst, let us find the area of the small circle
Area = 3.14 × 4²
Find the square value and multiply, we have;
Area = 50.24cm²
Area of the large circle = 3.14 × 7²
Find the square value and multiply
Area = 153. 86cm²
Area of the shaded region = Area of large circle - area of small circle
= 153.86 - 50.24
= 104 cm²
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The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 43
minutes of calls is $19.41, and the remaining credit after 56 minutes of calls is $17.72. What is the remaining credit after 65 minutes of calls?
The remaining credit after 65 minutes of calls is approximately $15.45.
To find the remaining credit after 65 minutes of calls, we can use the given information to determine the linear function that relates the remaining credit to the total calling time.
Let's assume the total calling time in minutes is represented by the variable "x," and the remaining credit in dollars is represented by the variable "y."
We are given two data points:
When x = 43, y = $19.41.
When x = 56, y = $17.72.
We can use these data points to form a system of linear equations.
Let's solve it to find the equation of the linear function.
Using the point-slope form of a linear equation:
y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values:
For the first data point:
x1 = 43
y1 = 19.41
Using the second data point:
x2 = 56
y2 = 17.72
The slope (m) can be calculated as:
m = (y2 - y1) / (x2 - x1)
m = (17.72 - 19.41) / (56 - 43)
m = -1.69 / 13
m ≈ -0.13
Now, we can use the point-slope form with one of the data points to find the equation of the linear function:
Using (x1, y1) = (43, 19.41):
y - 19.41 = -0.13(x - 43)
Simplifying the equation:
y - 19.41 = -0.13x + 5.59
y = -0.13x + 24
Now that we have the equation of the linear function, we can substitute x = 65 to find the remaining credit after 65 minutes:
y = -0.13(65) + 24
y ≈ $15.45
Therefore, the remaining credit after 65 minutes of calls is approximately $15.45.
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I have 7/4 green counters, and 24 yellow counter, so how much green counters will i have
Answer: the question doesn't give that much information but you would have 7/4 or 1.75 green counters.
Step-by-step explanation: 7/4 as a decimal is 1.75
7x 2/9 what the answer
Answer:
1.55
Step-by-step explanation:
2/9=0.22 x 7 =1.55
i hope this helps!
PLEASE HELP ONLY QUESTION 8 PLEASE !! :)
Answer:
150
Step-by-step explanation:
A passenger train leaves depot 2 hours after a freight train leaves the same depot. The freight train is traveling 18 mph slower than the freight train find the rate of each train if the passenger train over, takes the freight train in 3 hours
Answer:
The passenger train is traveling at 45 mph, and the freight train is traveling at 27 mph.
Step-by-step explanation:
Let's assume the speed of the passenger train is represented by x mph.
According to the given information, the freight train leaves the depot 2 hours before the passenger train. Therefore, when the passenger train starts, the freight train has already been traveling for 2 hours.
Let's represent the speed of the freight train as (x - 18) mph, which is 18 mph slower than the passenger train.
Now, we know that the passenger train overtakes the freight train in 3 hours. This means that the passenger train traveled for 3 hours, while the freight train traveled for 3 + 2 = 5 hours.
Since speed = distance/time, we can set up the following equation based on the distances covered by each train:
Distance covered by passenger train = Distance covered by freight train
Using the formula, distance = speed × time, we get:
x × 3 = (x - 18) × 5
Simplifying the equation:
3x = 5x - 90
90 = 5x - 3x
90 = 2x
Dividing both sides by 2:
45 = x
So, the speed of the passenger train is 45 mph.
The speed of the freight train is 45 - 18 = 27 mph.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x in triangle STU is given as follows:
b) 8.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.Applying the Pythagorean Theorem for this problem, the value of x is obtained as follows:
x² + 15² = 17²
x² = 17² - 15²
x² = 64.
x = 8.
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I have 12 teams that will play each other once, but have activities that each team will only play once. How many weeks and activities do I need.
==============================================
Explanation:
The formula to use is n*(n-1)/2
Plug in n = 12 to get 12*(12-1)/2 = 12*11/2 = 132/2 = 66
That formula is from the nCr combination formula when r = 2.
---------------------
Here's a visual way to see why that rule works.
Imagine there are only 4 teams. We'll make a table that has 4 rows and 4 columns. The team names are A,B,C,D.
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & & & & \\\cline{1-5}B & & & & \\\cline{1-5}C & & & & \\\cline{1-5}D & & & & \\\cline{1-5}\end{array}[/tex]
In the table, cross out the cells where one team pairs up with itself. That's along the main diagonal pointing to the northwest (or southeast).
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & & X & & \\\cline{1-5}C & & & X & \\\cline{1-5}D & & & & X\\\cline{1-5}\end{array}[/tex]
Let's also cross out any cell below the main diagonal.
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & X & X & & \\\cline{1-5}C & X & X & X & \\\cline{1-5}D & X & X & X & X\\\cline{1-5}\end{array}[/tex]
We do this because a mirrored copy is found above the diagonal.
We started with 4*4 = 16 cells. Then subtracted off the diagonal to get 16-4 = 12 cells left over. Then divide in half because we crossed off the lower half to get 12/2 = 6 different matchups among the 4 teams.
Those 6 matchups are:
A vs BA vs CA vs DB vs CB vs DC vs DThe order doesn't matter. A matchup like "A vs B" is the same as "B vs A".
We'll take this concept to extend it to n teams. We have n*n = n^2 cells to start with. Subtract off the n cells along the diagonal to get n^2-n = n(n-1) cells remaining.
Then we split that in half to get the formula n(n-1)/2.
Multiply out
5x(3x-2)=
The solution is the multiplication is: 5x × (3x-2) = 15x² - 10x.
Here, we have,
given that,
the expression is:
5x(3x-2)
now, we have to Multiply out
so, we have,
5x × (3x-2)
= 5x×3x - 5x×2
=15x² - 10x
Hence, The solution is the multiplication is: 5x × (3x-2) = 15x² - 10x.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
100°
Step-by-step explanation:
tThe sum of all arc measures that make up that circle is 360 degrees.
QS + RQ + RS = 360
QS = 360 - 120 - 140 = 100
An arc angle is the degree measurement of that angle inside the circle, opposite the arc
m∠R = arc QS = 100°
Answer:
∠ R = 50°
Step-by-step explanation:
the inscribed angle R is half the measure of its intercepted arc QS
the sum of the arcs on a circle is 360° , that is
RQ + QS + SR = 360°
120° + QS + 140° = 360°
QS + 260° = 360° ( subtract 260° from both sides )
QS = 100°
Then
∠ R = [tex]\frac{1}{2}[/tex] × 100° = 50°
On an exam students are asked to list 5 historical events in the order in which they occurred. A student randomly orders the events. what is the probability that the
The probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.
How to solveIf the student randomly orders the events, there is only one correct order out of all possible permutations.
Hence, the likelihood of selecting the accurate sequence is equal to 1 over the total count of potential arrangements.
As there are 5 occurrences, the overall count of conceivable sequences is equivalent to 5 factorial (5!), amounting to 120.
Therefore, the probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.
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On an exam, students are asked to list 5 historical events in the order in which they occurred. A student randomly orders the events. What is the probability that the student chooses the correct order?