Answer:
The results are
Face Count Face Count
1 6 4 9
2 12 5 5
3 8 6 20
These results are not fair, because they clearly shows that the dice was tricked. We deduct this by observing that he obtained the face 6, 20 times out of 48, which represents 42% of chances to get that result.
Now, a fair dice must have equal probabilities per side, or an approximation to that at least. In this case, we don't have such equality.
So, next time your little brother roll the dice, we probably will get 6.
To check the fairness of a die, use statistical testing. Expect each face to appear equally in a fair die. Discrepancies suggest possible bias, but randomness can make results vary. Conduct a hypothesis test, like Chi-square, for a more statistically sound conclusion.
Explanation:To verify the fairness of the die, we need to conduct a hypothesis test. With a fair six-sided die, each face (numbered 1 to 6) should have an equal probability of appearing on any given roll. That means, if you roll the die 48 times, each face should theoretically appear about 8 times (48 rolls divided by 6 faces).
If the observed frequency of each face being rolled significantly varied from 8, it would suggest that the die might be biased. However, keep in mind that random chance can also result in each face not appearing exactly 8 times. Therefore, a hypothesis test would have more statistical power if more repetitions were performed.
Conduct the hypothesis testing by comparing your observed frequencies to the expected frequencies using a Chi-square test. This would provide a more quantitative and concrete conclusion about whether the die is biased or fair.
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A researcher is studying the monthly gross incomes of drivers for a ride sharing company. (Gross incomes represent the amount paid to drivers before accounting for the costs associated with driving.) The researcher obtains a list of all the drivers in San Francisco and randomly selects 200 of them to contact. The list of incomes in the sample has an average of $800 per month, with an SD of $1000. (a) Does the histogram of the sample incomes follow the normal curve? Explain why or why not.
Answer:
The histogram of the sample incomes will follow the normal curve.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
In this case the researches wants to determine the monthly gross incomes of drivers for a ride sharing company.
He selects a sample of n = 200 drivers and ask them their monthly salary.
As the sample selected is quite large, i.e. n = 200 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the Normal distribution.
Thus, the histogram of the sample incomes will follow the normal curve.
The domain of the following relation R {(6, −2), (1, 2), (−3, −4), (−3, 2)} is (1 point)
Answer:
Domain: { -3,1,6}
Step-by-step explanation:
The domain is the input values
Domain: { 6,1,-3,-3}
We usually put them in numerical order and we do not list the same value twice
Domain: { -3,1,6}
Find the sum of the first 10 terms if a(n) = n^2 - n +1
Answer: 36
Step-by-step explanation:
explicit
The large exhibit at the aquarium has a viewing window that is 22 feet long 58.25 feet high and 13 inches thick estimate its volume in cubic feet remember remember 12 inches equal 1 foot
Answer:
Step-by-step explanation: convert feet to inches then multiply all 3 numbers. 264 x 699x13 = 2398968. Then decide that by 12 the amount of inches in a foot and get 199,914 ft^3
Pls help me Idk what to do
Answer:
6
Step-by-step explanation:
The line in the middle of the box is the median
Wendy had 20 apples. If 1/4 of them were red, how many apples were red?
Answer:
5
Step-by-step explanation:
split 20 into 4 and find out how much is one portion the four
Plz mark brainliest
Four golfers are asked to play a round of golf each on two consecutive Saturday afternoons. During the first round, one of two club types is to be used. During the second round, another club type is to be used. The order in which a golfer uses each brand is determined randomly. Scores are recorded. The results are given below.
Golfer Brand 1 Brand 2
1 93 95
2 88 86
3 112 111
4 79 77
To determine if the mean scores differ by brand of club, we would use
a. the one-sample t test.
b. matched pairs t test.
c. two-sample t test.
d. Any of the above are valid. It is at the experimenter's discretion.
Answer:
c) Two sample t-test
Step-by-step explanation:
Given data
Golfer 1 2 3 4
Brand1 (x) 93 88 112 79
Brand 2 (y) 95 86 111 77
Mean of x =
[tex]\frac{93+88+112+79}{4} = 93[/tex]
x⁻ = 93
Mean of y
[tex]\frac{95+86+111+77}{4} = 92.25[/tex]
y ⁻ = 92.25
Given data
Brand1 (x) : 93 88 112 79
Brand 2 (y) : 95 86 111 77
x- x⁻ : 0 -5 19 -14
y -y ⁻ : 2.75 -6.25 18.75 -15.25
(x- x⁻)² : 0 25 361 196
( y -y ⁻ )² : 7.5625 39.0625 351.5625 232.5625
S² = [tex]\frac{sum((x- x^{-} )^{2} +sum (y- y^{-} )^{2} }{n_{1}+n_{2} -2 }[/tex]
[tex]S^{2} = \frac{582+630.75}{4+4-2} = 202.125[/tex]
S = 14.21706
Null hypothesis: H₀: There is no significant difference between the means
Alternative hypothesis: H₁: There is significant difference between the means
Student's t test for difference for means
The test statistic
[tex]t = \frac{x^{-} -y^{-} }{\sqrt{S^{2}(\frac{1}{n_{1} } +\frac{1}{n_{2} } } }[/tex]
[tex]t = \frac{93 -92.25}{\sqrt{202.125(\frac{1}{4 } +\frac{1}{4 } } }[/tex]
on calculation , we get
t = 0.0746
Degrees of freedom ν = n₁ +n₂ -2 = 4+4-2 =6
[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025} = 2.447[/tex]
The calculated value t = 0.0746 < 2.447 at 0.05 level of significance
null hypothesis is accepted
Conclusion:-
There is no significant difference between the means
Final answer:
The matched pairs t-test is the correct method for analyzing the difference in golfers' scores with two different brands of clubs, as each golfer serves as their control.
Explanation:
The appropriate test to determine if the mean scores differ by brand of club is b. matched pairs t-test. Since the data consists of scores from the same golfers using two different brands of clubs in a controlled setting (meaning, the same golfer's scores are paired with each type of golf club), the analysis compares two related samples. In matched pairs designs, we test the differences by subtracting one measurement from the other. The golfers serve as their controls, eliminating variations between different individuals' performances, which could affect the scores. This is a classic scenario of a paired sample t-test, where each golfer's scores with Brand 1 are paired with their scores with Brand 2, and the difference in scores is analyzed.
If "f" varies directly with "m," and f=-19 when m=14, what is "f" when m=2?if
Answer:-19/7
Step-by-step explanation:
f varies directly as m
f=k x m
When f=-19,m=14
-19=k x 14
k=-19/14
Relationship is f=-19m/14
When m is 2
f=(-19x2) ➗ 14
f=-38 ➗ 14
f=-19/7
Which graph represents the solution set for the inequality StartFraction one-half EndFraction x is less than or equal to 18.x ≤ 18?
Answer:
the answer is D
Step-by-step explanation:
i guessed until it gave me the answer yw
Answer:
D
Step-by-step explanation:
Check all the statements that are true: A. If a relation is symmetric, it cannot be anti-symmetric. B. The equality relation on the real numbers is an equivalence relation. C. If RR is a reflexive relation on a set S, then any two RR- related elements of S must also be R2R2 related. D. There are n2n2 relations from a set with n elements to itself. E. If a relation is anti-symmetric, it cannot be symmetric. F. The less than or equal relation on the real numbers fails to be an equivalence relation because it is reflexive and transitive but not symmetric. G. A relation from a set with n elements to itself can have up to n2n2 elements. H. If RR is an equivalence relation, then R2
Answer:
See explaination
Step-by-step explanation:
B. The equality relation on the real numbers is an equivalence relation.
This statement is true
C. If RR is a reflexive relation on a set S, then any two RR- related elements of S must also be R2R2 related.
This statement is true
F. The less than or equal relation on the real numbers fails to be an equivalence relation because it is reflexive and transitive but not symmetric
This statement is true
H. If RR is an equivalence relation, then R2
This statement is true
For the same signal emitted by a radio antenna,
Observer A measures its intensity to be 16 times the
intensity measured by Observer B. The distance of
Observer A from the radio antenna is what fraction
of the distance of Observer B from the radio
antenna?
Answer: The distance of Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?
It is 1/4.
Step-by-step explanation:
We know that the intensity of electromagnetic waves decreases with the radius squared, this means that we can write a simple relation as:
Intensity(r) = A/r^2
Observer A measures 16 the intensity of observer B.
if Ia is the intensity that observer A measures and Ib is the intensity that observer B measures, we have that:
Ia = 16Ib
A/(ra)^2 = 16*A/(rb)^2
1/(ra)^2 = 16/(rb)^2
rb^2 = 16*ra^2
and we know that 16 = 4*4 = 4^2
rb^2 = (4*ra)^2
then rb = 4*ra
this means that the distance between observer B and the antenna is equal to 4 times the distance between observer A and the antenna.
The fraction is ra = rb/4
The distance of
Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?
It is 1/4.
Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is 4 times the distance of Observer B.
Explanation:Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. Let's denote the distance of Observer A from the radio antenna as dA and the distance of Observer B as dB.
We can use the inverse square law to relate the intensity to the distance: Intensity is inversely proportional to the square of the distance.
So, we have:
IntensityA/IntensityB = (dA/dB)^2 = 16
Solving for dA/dB, we find:
dA/dB = sqrt(16) = 4
Therefore, the distance of Observer A from the radio antenna is 4 times the distance of Observer B.
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What is the height of the following triangle if the area is 60 square meters? Do not round your answer.
Answer:
The height of the triangle, h, is 8 m
Step-by-step explanation:
The formula for the area of a triangle of base b and height h is A = (1/2)(b)(h).
Here b = 15 m and A = 60 m^2. We want the measure of the height, h.
First we solve the area equation (above) for h: 2A = bh, or h = 2A/b,
and then substitute the given values for b and A:
2(60 m^2)
h = ------------------ = 8 m
15 m
The height of the triangle, h, is 8 m
Answer:
Answer is 8 because I did the quiz on my online school.
Hope it helps
A college entrance exam company determined that a score of 2323 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 150150 students who completed this core set of courses results in a mean math score of 23.423.4 on the college entrance exam with a standard deviation of 3.23.2. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 2323 on the math portion of the exam? Complete parts a) through d) below.
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]
c) Test statistic t=1.53
P-value=0.064
d) The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that students who complete the core curriculum are ready for college-level mathematics. That is that the true score for the group is not significantly higher than 23.
Step-by-step explanation:
The question is incomplete:
a) State the appropriate null and alternative hypotheses.
c) Use the P-value approach at the 0.05 level of significance to test the hypotheses in part (a). ldentify the test statistic. (Round to two decimal places as needed.) Identfy the P-value. P-value (Round to three decimal places as needed.)
d) Write a conclusion based on the results. Choose the correct answer below. ? the null hypothesis and claim that there ? sufficient evidence to conclude that the population mean is ? than 20.
This is a hypothesis test for the population mean.
The claim is that students who complete the core curriculum are ready for college-level mathematics.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=150.
The sample mean is M=23.4.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.2.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.2}{\sqrt{150}}=0.261[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{23.4-23}{0.261}=\dfrac{0.4}{0.261}=1.531[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=150-1=149[/tex]
This test is a right-tailed test, with 149 degrees of freedom and t=1.531, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>1.531)=0.064[/tex]
As the P-value (0.064) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that students who complete the core curriculum are ready for college-level mathematics.
Is 5/8 mile larger or less than 1 mile
Answer:
5/8 mile is less than 1 mile
Step-by-step explanation:
in this question, one could assume a mile is 8/8
5/8<8/8
What is the range of the data represented in the dot plot below?
Answer:
3
Step-by-step explanation:
Range is the difference between
For the graffiti cat sweater on page 9, Dodd knit
12 stitches to make 2 inches in width. The sweater is
9 inches wide from the left edge to the beginning of the
black smile. How many stitches wide is that?
Answer: 54 stitches
Step-by-step explanation:
12/2=6
6 stitches= 1 inch
X stitches=9 inches
X=54 stitches
40% is NOT equivalent to....?
A. 0.4
B.2/5
C.40/100
D. 0.04
E. None correct
Answer: D
A is correct because when you convert 40% into a decimal the results will be .40 or .4
B is correct because 2/5 as a percent is 40%. It's like having 5 questions on a quiz and you get 2 right and 3 wrong. That means your grade is 40%.
C is correct because 40/100 means the decimal will be .4. 40÷100 will equal .4 which means 40/100 is also 40%.
D is incorrect due to the fact when you convert it to a fraction it'll be 4/25. When converting it to a percent the result will be 16%.
The number 40% in not equivalent to 0.04.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The number is,
⇒ 40%
Now,
Since, The number is,
⇒ 40%
Hence, It can be written as;
⇒ 40% = 40/100
= 4/10
= 2/5
= 0.4
Thus, The number 40% in not equivalent to 0.04.
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Please answer this correctly
Answer:
n=9 10 11
Step-by-step explanation:
Answer: 10
Step-by-step explanation:
If 3/4 of a number minus 1/2 of the number is 4. What is the number?
Answer:
16
Step-by-step explanation:
Number = x
(3/4 of x) - (1/2 of x) = 4
3x/4 - x/2 = 4
3x - 2x / 4 = 4
x/4 = 4
x = 16
Can someone please help me with this question ?
Answer:
1350 square inches
Step-by-step explanation:
The area of the end trapezoid is ...
A = (1/2)(b1 +b2)h = (1/2)(12 +36)(5) = 120 . . . . . square inches
The perimeter of the end trapezoid is ...
P = 13 +12 +13 + 3×12 = 74 . . . . inches
so the total area of the rectangular surfaces (including the bottom) is ...
(74 in)(15 in) = 1110 in²
The total area of the ramp is this rectangular area plus the two trapezoidal ends:
total area = rectangle area + 2×trapezoid area
= 1110 in² +2×120 in²
total area = 1350 square inches
what is a way you can use a distributive property for 6x82
Answer:
Well all the distributive property is is just splitting up a number so you can distribute it to other numbers so you could do 2x(3x82)
Step-by-step explanation:
Which of the following is the correct interpretation of the p-value? A. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the mean number of partners. B. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is a difference in the mean number of partners. C. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the sample mean number of partners. D. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is a difference in the sample mean number of partners.
Answer:
The correct option is (A).
Step-by-step explanation:
The p-value is well defined as the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
From the provided options we can guess that the hypothesis was defined as follows:
H₀: There is no difference in the mean number of partners, i.e. μ₁ - μ₂ = 0.
Hₐ: There is difference in the mean number of partners, i.e. μ₁ - μ₂ ≠ 0.
The test is two tailed mean difference test.
A z-test or a t-test can be used to conclude the result.
In this case the p-value can be defined as the probability of obtaining a test statistic value equal to or more extreme that the results obtained from the sample, when the difference between the mean number of partners is 0.
Thus, the correct interpretation of the p-value is provided by statement (A).
The p-value represents the likelihood of obtaining a test statistic as extreme as our observed data, assuming the null hypothesis is true. The null hypothesis usually posits there's no difference or effect. A small p-value would suggest rejecting the null hypothesis in favor of the alternative hypothesis, indicating a significant effect or difference.
Explanation:The correct interpretation of the p-value is: The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the mean number of partners.
In other words, the p-value measures how likely you are to get the observed data if the null hypothesis is true. The null hypothesis typically represents a theory that there is no effect or no difference between the groups you're comparing. Hence, if there's no difference in the mean number of partners (which is our null hypothesis here), then the p-value tells how likely we are to observe a test statistic as extreme as our sample result.
For example, if the p-value is very small, it might be less than our significance level (commonly 0.05 or 5%). In such a case, we have evidence to reject our null hypothesis in favor of the alternative hypothesis. The alternative hypothesis generally represents a theory that there is an effect or a difference between the groups. So, in this case, a small p-value would indicate a statistically significant difference in the mean number of partners.
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Triangle D E F. Side D F is 6 inches, side F E is 10 inches, and side E D is question mark.
Which could be a possible length of side DE?
2 in.
3 in.
7 in.
16 in.
Answer:
7
Step-by-step explanation:
THe Triangle Inequality Theorem states that the sum of the two least sides of a triangle must be greater than the third side. In this case, 2 and 6 are less than 10, 3 and 6 are less than 10, 6 and 10 are greater than 16, so the only number left is 7. The sum of seven and six is greater than ten so seven would be the correct answer.
Question:
Triangle D E F. Side D F is 6 inches, side F E is 10 inches, and side E D is question mark.
Which could be a possible length of side DE?
2 in.
3 in.
7 in.
Answer:
C.) 7 in.
Step-by-step explanation:
To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c. Remember the formula for finding the perimeter of a triangle. For a triangle with sides a, b and c, the perimeter P is defined as: P = a + b + c. What this formula means in simpler terms is that to find the perimeter of a triangle, you just add together the lengths of each of its 3 sides. Since all the three sides of the triangle are of equal length, we can find the perimeter by multiplying the length of each side by 3. 20 + 20 + 20 = 3 × 20 = 60 cm. Thus, the perimeter of an equilateral triangle is 3 times the length of each side. Area of a two-dimensional shape is the space occupied by the shape.
Have a Nice day! <3
Problem 3: Sampling methods
Willy wants to find what percent of students at his school drink the milk after
they finish their cereal. He is considering the following sampling methods:
QUESTION
He selects every tenth person who enters the school. What type of sampling
is this?
Choose 1 answer:
Willy is using a systematic sampling method by selecting every tenth person entering the school to understand milk consumption habits after cereal.
Explanation:When Willy selects every tenth person who enters the school to determine what percent of students drink the milk after they finish their cereal, he is using a systematic sampling method. This type of sampling involves selecting subjects at regular intervals from an ordered list.
It's a form of probability sampling where the first unit is selected randomly and the subsequent units are selected using a fixed periodic interval.
In the context of the situation provided, this method could potentially provide a more representative sample compared to methods like convenience sampling, but there could be inherent biases if there are underlying patterns in the student arrivals at school that correlate with milk drinking habits after cereal.
what is the derivative of 66lnx +135
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{66}{x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 66 \ln x + 135[/tex]
Step 2: Differentiate
Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{d}{dx}[66 \ln x] + \frac{d}{dx}[135][/tex]Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = 66\frac{d}{dx}[\ln x] + \frac{d}{dx}[135][/tex]Logarithmic Differentiation: [tex]\displaystyle y' = \frac{66}{x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Which is the unit rate if 4 tuna cans are sold for $6
Answer:
$1.50 per can
Step-by-step explanation:
6/4 = 1.5
to check your answer, do 1.50*4, and you get $6
hope this helps :)
Answer:
The unit rate is $1.50 per can.
Step-by-step explanation:
Price: $6
Number of Cans Purchased at This Price: 4
$6/4 cans=$1.50 per can
graph the two lines y=2x + 5 and y= x -1 what is the the x-value of the point where they intersect
Answer:
x=-6
Step-by-step explanation:
y=2x + 5
y= x -1
Plug in the equation for y
x-1=2x+5
Combine like terms
-1=x+5
-6=x
Hope this helps! Please mark brainliest :)
the measure of two complementary angles are 7x + 17 and 3x - 20. find the measures of the angles.
The required measure of the complementary angles is 82.1° and 7.9°.
Given that,
The measure of two complementary angles is 7x + 17 and 3x - 20. To find the measures of the angles.
The angle can be defined as the one line inclined over another line.
Here,
the sum of the two complementary angles is equal to 90°. Implying
7x + 17 + 3x - 20 = 90
10x -3 = 90
10x = 93
x = 93 / 10
x = 9.3
Now,
The measure of angles
7x + 17 = 7 * 9.3 + 17
= 82.1°
3x - 20 = 3 * 9.3 - 20
= 7.9°
Thus, the required measure of the complementary angles is 82.1° and 7.9°.
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Sequence: 10, 21, 32, 43, 54, ... Find the 75th term.
Answer:
186
Step-by-step explanation:
definition: a_n = a_1 + f × (n-1)
Common difference is 11
The sum of all numbers up through the 17th: 1666
Answer: 824
Step-by-step explanation:
This is problem on progression.
Considering the series/ sequence,
10, 21, 32, 43, 54, ........
To find the 75th term, we first of all find which of the sequence is it, is it, Arithmetic or Geometric sequence .
Now fro this, it is an AP sequence because, when the first term us subtracted from the second term and the common difference added to the second term it produces the third term and so on, . Haven't gotten this, we now apply the formula for finding the number if terms in an AP.
Tn = a + (n - 1 )d, where n = number of terms we are computing for = 75, a = first term = 10, and d = 21 - 10 = 11.
Now substitute for those values in the formula above
T75 = 10 + ( 75 - 1 )11
= 10 + 74 × 11
= 10 + 814
= 824.
Which expression shows 20% of 60! Please give the right answer tryna pass
Answer:
1/5 - 60 or b
Step-by-step explanation:
The expression that shows 20% of 60 is 1/5 * 60
How to determine the correct expression?The expression is given as:
20% of 60
Express of as *
20% * 60
Express the percentage as fraction
20/100 * 60
Simplify the fraction
1/5 * 60
Hence, the expression that shows 20% of 60 is 1/5 * 60
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