Answer:
1000/39
Step-by-step explanation:
What is the frequency of the sinusoidal graph?
The frequency shown in the given sinusoidal graph is:
f = 1/T (s⁻¹).
What is the frequency?Frequency means the rate at which something occurs or is repeated over a particular period of time or in a given sample.
A sinusoidal function is a periodic function because the basic shape repeats indefinitely in both the positive and negative directions. The frequency of a sine wave is defined as the number of cycles it completes in a given interval and is the reciprocal of the period.
In a mathematical language, this is written as:
f = 1/T
Where,
f = frequency,
T = Period
To get the period, just subtract the x-coordinates of two consecutive peaks, so:
T = п - 0
T = п (s)
Therefore, the frequency is:
f = 1/T (s⁻¹).
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Find the z-score for the value 93, when the mean is 100 and the standard deviation is 3.
The z-score for the value 93, when the mean is 100 and the standard deviation is 3 is solved to be
2.3How to solve for z scoreZ scores is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of the parameters
mean, μ = 100
standard deviation, σ = 3
sample score, X = 93
z score for the score of 93
z = (X - μ) / σ
substituting into the formula
z = (93 - 100) / 3
= -7 / 3
= -2.333
Hence we can say that the z score is 2.333
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find an equation of the plane. the plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1)
25x -15y -40z +45 =0 is the equation of the plane that passes through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1).
Let the given points be P(2 , 1 , 2) ,Q(3 , -8 , 6) and R(-2 , -3 ,1)
PQ = (3-2 , -8-1, 6-2)
=(1 , -9, 4)
PR = (-2 -2,-3-1 ,1-2)
=( -4 ,-4 ,-1 )
→PQ * →PR = [tex]\left[\begin{array}{ccc}i&j&k\\1&-9&4\\-4&-4&-1\end{array}\right][/tex]
=(9+16)i + (-16+1)j + (-4 -36)k
= 25i - 15j - 40k
Therefore , the normal vector to the plane is
→n = (25 , -15 ,-40)
Since , the plane passes through all the three points we can choose any point to find its equation .So,the equation of the plane through the point P(2,1,2) with normal vector
→n = (25,-15,-40) is
25(x-2) - 15(y-1) -40(z-2) =0
⇒25x - 50 -15y + 15-40z+80=0
⇒25x -15y -40z +45 =0
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When do scientists use math in an experiment? How do you know?
Scientists use math in experiments when they make measurements, analyze quantitative data, and make predictions based on this data.
This is known because Math is an integral part of Science which is why both subjects ( Science and Math ) are considered STEM subjects.
How do scientists use math ?Scientists use math in an experiment to make measurements, analyze data, and make predictions.
For example, scientists use math to make precise measurements of physical quantities such as length, weight, and temperature. They also use math to perform calculations such as determining the concentration of a substance in a solution or the rate of a chemical reaction.
Scientists also use mathematical models and statistical analysis to analyze data and make predictions about the outcome of an experiment. They use mathematical equations to describe the relationships between different variables and to test hypotheses. They also use statistical techniques to determine the significance of their results and to make inferences about a larger population from a smaller sample of data.
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let s denote the set of all (positive) divisors of 60^5 . the product of all the numbers in s equals 60^e for some integer e. what is the value of e?
As per the given divisor and product, the value of e is 5.
The term divisor in math is defined as a number which divides another number and it is a part of the division process.
Here we have given that let us consider that s denote the set of all positive divisors of 60⁵
Here we also know that the product of all the numbers in s equals 60ⁿ for some integer n.
As per the given condition, the terms are written as,
=> s = 60⁵
=> s = 60ⁿ
Here we have to compare the given values then we the expression like the following,
=> 60⁵ = 60ⁿ
As per the rule of exponent, the value of e = 5.
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5. The sum of two numbers is 15. The difference between five times the first number and Three times the second number is 19. Find the two numbers.
The first number will be 8 and the second number will be 7.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The sum of the two numbers is 15. The difference between five times the first number and Three times the second number is 19.
Let the first number be 'x' and the second number be 'y'. Then the equations are given as,
x + y = 15 ...1
5x - 3y = 19 ...2
From equations 1 and 2, then we have
5x - 3(15 - x) = 19
5x - 45 + 3x = 19
8x = 64
x = 8
Then the value of the variable 'y' is given as,
8 + y = 15
y = 15 - 8
y = 7
The first number will be 8 and the second number will be 7.
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a 95% confidence interval for the true proportion of math students who prefer to use a handheld calculator versus computer software for computations is (0.751, 0.863). is it reasonable to believe more than 75% of math students prefer to use a handheld calculator versus computer software for computations?
It is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.
To determine this:
A 95% confidence interval for a proportion gives us an estimate of the range of values where the true proportion is likely to fall. The interval (0.751, 0.863) means that we are 95% confident that the true proportion of math students who prefer to use a handheld calculator versus computer software for computations falls between 0.751 and 0.863.
Given this information, it is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.
In other words, based on the sample data and the construction of the confidence interval, there is strong evidence that the true proportion of math students who prefer to use a handheld calculator is above 75%.
It's important to note that the confidence interval is only an estimate of the true proportion, and it's possible that the true proportion is not exactly within this interval. However, the 95% confidence level means that if we were to repeat the study many times, in about 95% of the cases, the interval would contain the true proportion.
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What are the 2 types of ratios for grade 7?
Two common types of ratios we'll see are part to part and part to whole.
The ratio of trees to flowering plants in Marsha’s backyard is shown on the ratio table.
30 numbers complete the ratio table to make an equivalent ratio.
What is equivalent ratio?
When we compare two ratios, they are said to be equivalent. To determine if two or more ratios are comparable, they can be compared to one another.
Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you may get the corresponding ratio. Finding comparable fractions follows the same procedure.
Here in this case,
for trees: 2: 12 [ 2 to 12, 6 times more ]
for plants: 5: 30 [ 5 to 30, it is also 6 times more]
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Write the equation of the line that passes through (17,-7) and (34,27)
Answer:2
Step-by-step explanation:
how many standard drinks are in a mixed drink? choose an option below one to two three four or more it can vary
Depending on how many shots you add, a single mixed drink can be equivalent to more than one or two regular drinks. Keep in mind that a 1.25 oz. shot is equivalent to one normal drink.
What is a standard drink?
Approximately 14 grams of pure alcohol are present in one "normal" drink in the United States (or one alcoholic drink's equivalent).
This amount can be found in: 12 ounces of standard beer, which typically contains 5% alcohol. 12% alcohol in 5 ounces of wine is the normal amount. Approximately 40% alcohol is present in 1.5 ounces of distilled spirits.
What makes it a regular drink?
The amount of pure alcohol in various alcoholic beverages varies. Any alcoholic beverage with 10 grams of pure alcohol is referred to as a STANDARD DRINK. There are varying percentages of pure alcohol in various alcoholic beverages.
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The rental rate for a car at CarRus is either plan A: $70 a day with unlimited miles or plan B: $40 per day and $0.25 per mile. If you want to rent a car for 4 days and drives 300 miles how much would you save by choosing plan B?
Answer:
$45 would be the savings of option b
Step-by-step explanation:
A. $70*4=$280
B. $40*4=$160 + $0.25*300=$75
a-b =$45
Please see attached photo for better explanation
an automobile manufacturer claims that their van has a 28.228.2 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this van. after testing 2727 vans they found a mean mpg of 28.028.0 with a standard deviation of 2.62.6. is there sufficient evidence at the 0.010.01 level that the vans underperform the manufacturer's mpg rating? assume the population distribution is approximately normal.
The p-value is <0.01, reject the null hypothesis, vans underperform the manufacturer's mpg rating.
What is null hypothesis ?
The null hypothesis is a statement that there is no statistical significance between the results of an experiment and a certain theoretical prediction or postulate. It is usually denoted by H0 and it is a statement of "no effect" or "no difference".
The null hypothesis is that the mean mpg of the vans is equal to the manufacturer's rating of 28.228.2 mpg, and the alternative hypothesis is that the mean mpg of the vans is less than the manufacturer's rating.
We can use the t-test statistic to determine the probability of observing a sample mean as extreme or more extreme than the one computed from the data, assuming that the null hypothesis is true.
The t-test statistic is: (sample mean - population mean) / (standard deviation/sqrt(sample size)) = (28.028.0 - 28.228.2) / (2.62.6 / sqrt(2727)) = -3.34
The p-value is the probability of observing a t-value as extreme or more extreme than -3.34, assuming that the null hypothesis is true. With a sample size of 2727, we can use a t-distribution table to find that the p-value is less than 0.01.
The p-value is <0.01, reject the null hypothesis, vans underperform the manufacturer's mpg rating.
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The Cayman trough has an elevation of -7\dfrac{7}{10}−7
10
7
minus, 7, start fraction, 7, divided by, 10, end fraction kilometers. The Mariana trench has an elevation of -10\dfrac{9}{10}−10
10
9
minus, 10, start fraction, 9, divided by, 10, end fraction kilometers. Note that both places have negative elevations because they are below sea level.
Drag the white cards onto the gray rectangle to write an inequality that correctly compares the elevations.
The inequality that correctly compares the elevations is given as follows:
-7 and 7/10 > -10 and 9/10.
What are the inequality symbols?The four inequality symbols are given as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The elevations are given as follows:
Cayman through: -7 and 7/10.Mariana trench: -10 and 9/10.Those two elevations are given by mixed numbers, which are composed by both an integer part and a fractional part.
To compare which elevation is greater, we look at which one has the greater integer part. An integer part of -7 is greater than an integer part of -10, hence the inequality is given as follows:
-7 and 7/10 > -10 and 9/10.
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A study concluded that among people with a certain virus, 99.2% of tests conducted were (correctly) positive, while for people without the virus, 98.1% of the tests were (correctly) negative. If 29% of patients actually carry the virus, what's the probability that a patient testing negative is truly free of the virus?
If a study concluded that among people with a certain virus, 99.2% of tests conducted were (correctly) positive, while for people without the virus, 98.1% of the tests were (correctly) negative. the probability that a patient testing negative is truly free of the virus is 0.9967.
How to find the probability?Probability (testing negative is truly free of the virus) = (1- 0.29) (0.981) / (0.29) (1- 0.992) + (1- 0.29) (0.981)
Probability (testing negative is truly free of the virus) = (0.71) (0.981) / (0.29) (0.008) + (0.71) (0.981)
Probability (testing negative is truly free of the virus) = 0.69651 / 0.00232 + 0.69651
Probability (testing negative is truly free of the virus) = 0.69651/ 0.69883
Probability (testing negative is truly free of the virus) =0.9967
Therefore we can conclude that the probability (testing negative is truly free of the virus) is 0.9967.
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A square with sides 6 inches is shown. If $P$ is a point such that the segment $\overline{PA}$, $\overline{PB}$, $\overline{PC}$ are equal in length, and segment $\overline{PC}$ is perpendicular to segment $\overline{FD}$, what is the area, in square inches, of triangle $APB$
The area of the triangle APB is 6.75 square inches.
We know that PA=PB=PC and that PC is perpendicular to FD. Thus C will be the midpoint of FD.
Draw a perpendicular from P to AB, let the point of intersection be Q.
We know that CQ = DB = 6 inches
That is PC + PQ = 6 inches
PQ = (6 - PC) inches
Consider triangle APQ, it is a right angled triangle, right angled at Q. So using Pythagorean theorem
PA² = PQ² + AQ²
PA² = (6 - PC)² + (AB/2)²
PA² = (6 - PA)² + (6/2)²
PA² = 36 - 12PA + PA² + 9
12PA = 45
PA = 3.75
So PA = PB = PC = 3.75 inches
Also PQ = 6 - PC = 2.25 inches
The area of a triangle can be found by using the formula:
area = (base * height) / 2.
In this case, the base, AB is equal to the length of the side of the square, which is 6 inches, and the height is equal to PQ. So the area of triangle APB is
= (6*2.25)/2
= 6.75 square inches.
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some stores print multiple coupons and advertisements on their receipts, making the receipts unusually long. a curious shopper makes the same purchase at a random sample of 10 stores and measures the length of each receipt (in inches). here are the results: 8.25, 7.5, 5, 9.5, 12, 5.5, 9, 14, 11.5, 18 what is the value of the standard error of the mean?
The standard deviation of the mean was 1.256.
Now, in response to the question: We have given that, some stores print many coupons and advertisements on business receipts, resulting in exceptionally long receipts.
A curious customer makes the identical purchase at ten different stores and counts the length of the each receipt (in inches).
Here are the results,
8.25, 7.5, 5, 9.5, 12, 5.5, 9, 14, 11.5, 18.
Therefore, The value of the standard error of the mean is 1.256.
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Part C
What is the equation of the directrix of the parabola? If the value of a changed from - to, what would the equation of the directrix be?
If the value of 'a' changed from -a to +a , the equation of the directrix of the parabola is x= a
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
If parabola is y² = 4ax and the equation of the directrix of the parabola is x= -a
when parabola becomes y² = - 4ax and the equation of the directrix of the parabola is x= a
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help I didn't do this before
Answer:
5 4/9
Step-by-step explanation:
7/9 of 7
= 7/9 × 7
= 7/9 × 7/1
Multiply top×top and bottom×bottom
= 49/9
means 49÷9
9 goes into 49, 5 times. And 9 × 5 is 45. 49 - 45 is 4. So
49÷9 is 5 and 4 leftover.
49 ÷ 9
= 5 4/9
Sipho’s Mum wants him to learn to save his money. Sipho’s mum offers to add double the amount of money he saves in his bank account each month.
If x is the amount of money Sipho saves in the month and y is the total amount of money in Sipho’s bank account at the end of the month after his Mum’s deposit, write an equation to show the relationship between x and y. (Do not include any spaces in your answer)
The equation that shows the relationship b/w x and y is
y= 3x
What is the equation?Generally, An equation is a mathematical statement that demonstrates that two mathematical expressions have the same value. This is the most basic version of the definition of an equation in algebra. For example, the phrase "3x + 5" = 14 is an equation, in which the two expressions "3x + 5" and "14" are separated by the symbol for "equal."
A mathematical expression is considered to be an equation if it includes the equals sign (=). Equations often use algebraic notation. Mathematicians turn to algebra when they are unsure about the value of a certain number in a computation.
In mathematics, an equation is represented by the conjunction "=", which is placed between two expressions. The "left-hand side" and "right-hand side" of an equation refer to the expressions that are located on the left and right sides of the equals sign, respectively.
Since Sipho’s mum will double the amount saved
let the amount saved be x
Therefore the equation for the total amount will be
y=x+2x
simplfing
y=x(1+2)
Therefore
y = x + 2x
y= 3x
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does. Anyone get a and b please help I’ll mean a lot
Answer:
5x + 190 = 300
[tex]\frac{300-190}{5}[/tex]
Step-by-step explanation:
The equation
5x + 190 = 300 helps us to figure out how many minutes it will take for the tank to be empty.
5x + 190 = 300 Subtract 190 from both sides
5x + 190 - 190 = 300 - 190
5x = 110 Divide both sides by 5
[tex]\frac{5x}{5}[/tex] = [tex]\frac{110}{5}[/tex]
x = 22
It will take 22 minutes for the tank to be empty.
Your friend shows you a coin collection. In it, 44/50
of the coins are quarters. What percent of the coins are quarters?
Answer:
88% of the coins are quarters.
To find out, you can convert the fraction 44/50 to a percentage by multiplying it by 100.
(44/50) * 100 = 88%.
Using P.M.I , prove that 6^n - 1 is divisible by 5.
Therefore , the solution of the given problem of PMI comes out to be
6 ⁿ -1 is always divisible by 5.
What is the purpose of mathematical induction?A mathematical method known as mathematical induction is used to demonstrate that a claim, formula, or theorem holds true for every natural number. Step 1 (Base Step) demonstrates the truth of a statement for the starting value.
Here,
Given : 6 ⁿ -1 is divisible by 5
Let,
=> 6 ⁿ -1
=> 6 ¹ - 1
=>5
P(k) is divisible by 5
P(k+1)=6
k+1−1=6.6k−1
=(5+1).6k−1
=5×6 k+6k−1
=5×6k+5m
=5(6k+m)
P(k+1) is divisible by 5
Therefore , the solution of the given problem of PMI comes out to be
6 ⁿ -1 is always divisible by 5.
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carbon-14 decays continuously at a rate of 0.0121% a year. if a 5-gram sample currently weighs 3.2-grams, how old is the sample?
Show your work
Answer:
Step-by-step explanation:
if 1 = 2 than 3 is 4
A mechanic named Zeke plans to work a maximum of 12 hours tomorrow, and no more, doing tune-ups and oil changes. It takes 1 hour to perform a tune-up and 2 hours to perform an oil change.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
The inequality that models the situation is:
x + 2y ≥ 12
How to write the inequality that models this situation?We know that a Mecnahinc named Zeke plans to work a maximum of 12 hours (12 hours is an allowed value) tomorrow.
And we know that he works doing tune-ups and oil changes.
Let's define the variables:
x = number of tune-upsy = number of oil changes.We know that It takes 1 hour to perform a tune-up and 2 hours to perform an oil change.
Then the total number of hours worked by Zeke is given by the expression:
x*1 + y*2
And that must be equal to or smaller than 12, so we will get the inequality:
x + 2y ≥ 12
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Describe the rule for this sequence by completing this sentence. The number of black triangles in each stage is the number of triangles in the previous stage.
The rule can be described as The number of black triangles in each stage is the number of triangles in the previous stage multiplied by 2.
This can be interpreted as follows:
In each stage, the number of black triangles is determined by the number of triangles that were present in the previous stage. This suggests that the sequence may be formed by repeatedly adding a certain number of triangles to the previous stage, with the number of added triangles equal to the number of triangles present in that stage.
Therefore, the rule can be described as The number of black triangles in each stage is the number of triangles in the previous stage multiplied by 2.
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Answer: 3 times
Step-by-step explanation:
edge 2023
From a sample with n=36, the mean number of televisions per household is 2 with a standard deviation of 1
television. Using Chebychev's Theorem, determine at least how many of the households have between 0 and 4
televisions.
At least ____ of the households have between 0 and 4 televisions.
(Simplify your answer.)
Answer:
Chebyshev's Theorem states that for any dataset with a mean and standard deviation, at least 1 - (1/k^2) of the data will lie within k standard deviations of the mean.
In this case, we're looking for households that have between 0 and 4 televisions, which is 4 - 0 = 4 - 2 = 2 standard deviations from the mean of 2 televisions.
So, using Chebyshev's Theorem, we can calculate that at least 1 - (1/2^2) = 1 - (1/4) = 3/4 or 75% of the households have between 0 and 4 televisions.
At least 75% of the households have between 0 and 4 televisions.
Write and equation for a line through the points (8,13) and(-12,18)
The slope intercept from of equation exists y = -0.25x -19.5.
What is meant by slope?The relationship between how a line's y coordinate and x coordinate change determines the slope of that line. The net modifications to the y and x coordinates, respectively, are denoted by y and x. In light of this, it is possible to express the change in y coordinate in relation to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given: A line that passes through points (8, 13) and(-12, 18)
substituting the values, we get
m = ( 18 - 13)/ ( -12 - 8)
simplifying the above equation, we get
m = -0.25
Now, using slope intercept form
y - a = -0.25( x- b)
substitute the values in the above equation, we get
y - (13)= -0.25(x-(18))
y - 15= -0.25x-(-0.25 × 18))
simplifying the equation, we get
y = -0.25x - 4.5 -15
y = -0.25x -19.5
Therefore, the slope intercept from of equation exists y = -0.25x -19.5.
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If 10 2.29=195, find the value of log10 19.5
Answer:
log10 195 = 2.29
Answer:
I found this
To solve for the value of log10 19.5, we can use the property of logarithms that states:
loga(b^c) = c * loga(b)
In this case, we can express 19.5 as 10^2.29:
19.5 = 10^2.29
So, we can find the logarithm of 19.5 by solving for c:
log10(19.5) = log10(10^2.29)
By using the property of logarithms mentioned above, we can simplify the equation to:
log10(19.5) = 2.29 * log10(10)
Since log10(10) = 1, we can further simplify the equation to:
log10(19.5) = 2.29
Therefore, the value of log10 19.5 is 2.29.
Solve the equation.
12.5(3x-1)+132.4=(2.8-4x) 0.5
Will reward brainliest
Answer:First we need to simplify the left side of the equation:
12,5(3x-1)+132,4 = 12,5*3x - 12,5 + 132,4 = 37,5x + 120,9
Now we need to simplify the right side of the equation:
2,8-4x = 2,8 - 4x
Now we have to set the two sides equal:
37,5x + 120,9 = 2,8 - 4x
Now we have to move all the x terms to one side of the equation:
37,5x - 4x + 120,9 = 2,8
Next step is to combine like terms:
33,5x + 120,9 = 2,8
Subtracting 120.9 from both sides of the equation:
33,5x = -118.1
Dividing both sides by 33,5
x = -3,54
So the solution of the equation is x = -3,54
Step-by-step explanation:
in a pen-and-paper role-playing game, a 10-sided die is rolled. each side of the die is labeled with a number from 1 to 10. a player succeeds if a 9 or 10 is rolled, what is the probability of success?
The probability of success is 0.2. The result is obtained by adding the probability of getting 9 and the probability of getting 10.
How to calculate probability?Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceThe probability of A or B can be calculated by
P(A or B) = P(A + P(B)
A 10-sided die is rolled. Each side of the die is labeled with a number from 1 to 10. A number of 9 or 10 should be rolled to make a player succeed. Find the probability of success!
The number of each side of die are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
The probability of success is the probability of getting 9 or 10.
P(9) = 1/10
P(10) = 1/10
P(9 or 10) = P(9) + P(10)
P(9 or 10) = 1/10 + 1/10
P(9 or 10) = 2/10
P(9 or 10) = 1/5
P(9 or 10) = 0.2
Hence, the probability that a player would succeed is 0.2.
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