Step-by-step explanation:
multiply 2 with the bracket numbers
6x+16=0
6x= - 16
x=-16/6
x= - 8/3
A manager at a shipping company will purchase boxes in the shape of right rectangular prisms. He wants the volume of each box to be exactly 98 cubic feet. Which figure shows a box with the dimensions, in feet, that the manager will purchase?
The manager needs to select dimensions for a right rectangular prism that when multiplied together equal 98 to achieve a volume of 98 cubic feet. Possible dimensions could be 7 feet by 7 feet by 2 feet, or 14 feet by 7 feet by 1 foot.
The question pertains to calculating the volume of right rectangular prisms (boxes) and understanding the relationship between their dimensions and volume. To find a box with a volume of 98 cubic feet, one can use the formula for the volume of a right rectangular prism, which is Volume = length * width * height. The manager needs to identify the dimensions that, when multiplied together, equal 98. For instance, if a box has dimensions of 7 feet, 7 feet, and 2 feet, the volume would be 7 * 7 * 2 = 98 cubic feet, as required. Other possible dimensions could be 14 feet by 7 feet by 1 foot, as 14 * 7 * 1 also gives 98 cubic feet.
What is the value of this expression when a=3 and b=-1?
Answer:
1/4
Step-by-step explanation:
[tex](\dfrac{3(3)^{-2}(-1)^6}{2(3)^{-1}(-1)^5})^2=[/tex]
[tex](\dfrac{\frac{1}{3}}{-\frac{2}{3}})^2=[/tex]
[tex](-\dfrac{1}{2})^2=[/tex]
[tex]\frac{1}{4}[/tex]
Hope this helps!
Which of the following is equivalent to tan(x) * csc(x) when simplified?
O
O
O
sec(x)
cos(x)
sin(x)
csc(x)
O
cot(x) + 1
Answer:
Sec(x)
Step-by-step explanation:
Tan(x) = Sin(x)/Cos(x)
Csc(x) = 1/Sin(x)
Sin(x) 1
--------- . ---------
Cos(x) Sin(x)
Sin(x) cancel
1
--------- =
Cos(x)
Sec(x)
The simplified expression is,
⇒ sec x
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ tan x × csc x
Now,
We can simplify as;
⇒ tan x × csc x
⇒ ( sin x/ cos x ) × (1 / sin x)
⇒ 1 / cos x
⇒ sec x
Thus, The simplified expression is,
⇒ sec x
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One of the more famous anecdotes in the field of statistics is known as the "Lady Tasting Tea" and involves the renowned statistician Sir Ronald Aylmer Fisher. A woman claimed to be able to tell the difference in a cup of tea depending on whether or not the milk or tea was poured first. You have chosen to recreate this experience with a classmate and have fixed 40 cups of tea, of which your classmate correctly identifies 12. How large a sample n would you need to estimate p with margin of error 0.01 with 95% confidence? Use the guess p = 0.30 as the value for p. n = 42 n = 81 n = 4116 n = 8068
Answer:
[tex]n=\frac{0.3(1-0.3)}{(\frac{0.01}{1.96})^2}=8067.36[/tex]
And rounded up we have that n=8068
Step-by-step explanation:
The margin of error for the proportion interval is given by this:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
We want for this case a 95% of confidence desired, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The margin of error for this case is [tex]ME =\pm 0.01[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
The estimated proportion for this case is [tex]\hat p=0.3[/tex]. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.3(1-0.3)}{(\frac{0.01}{1.96})^2}=8067.36[/tex]
And rounded up we have that n=8068
The Cartesian coordinates of a point are given.(a) (6, −6)(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.(r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π.(r, θ) = (b) (−1, 3)(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.(r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π.(r, θ) =
To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the equations (r, θ) = (√(x² + y²), atan2(y, x)).
Explanation:To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the following equations:
(r, θ) = (√(x² + y²), atan2(y, x))
(a)(i) For the Cartesian coordinates (6, -6),
(r, θ) = (√(6² + (-6)²), atan2(-6, 6))
(r, θ) = (√(36 + 36), atan2(-6, 6))
(r, θ) = (6√2, -45°)
(a)(ii) For the Cartesian coordinates (6, -6),
(r, θ) = (-√(6² + (-6)²), atan2(-6, 6) + π)
(r, θ) = (-6√2, -45° + π)
(b)(i) For the Cartesian coordinates (-1, 3),
(r, θ) = (√((-1)² + 3²), atan2(3, -1))
(r, θ) = (√(1 + 9), atan2(3, -1))
(r, θ) = (√10, 116.57°)
(b)(ii) For the Cartesian coordinates (-1, 3),
(r, θ) = (-√((-1)² + 3²), atan2(3, -1) + π)
(r, θ) = (-√10, 116.57° + π)
What percent is 7 out of 40?
Answer:
17.5%
Step-by-step explanation:
Convert fraction (ratio) 7 / 40 Answer: 17.5%
Answer:
17.5
Step-by-step explanation:
7/40 = 17.5
Hope this helps! Please mark brainliest :)
Spanky, Alfalfa, and Buckwheat sit down to take a geography test that has 12 multiple-choice questions. Each question has three possible answers, of which only one is correct. Alfalfa, as usual, has been spending too much time daydreaming about Darla and has not properly studied for the exam. After looking it over, he discovers that he knows the answers to just five of the questions. So, he answers those questions correctly and randomly guesses on the remaining seven. Afterward, as Miss Crabtree is grading Alfalfa’s exam, she selects one question at random and finds that he answered it correctly. What is the exact probability that Alfalfa actually knew the answer to this question? Answer this question by completing the following parts:a. Carefully construct a correct tree diagram using the letters K for the event that he knows the answer to a question, N for the event that he doesn’t know the answer to a question, and C for the event that he answers a question correctly. Also, label each edge with its exact probability (as either a fraction or a whole number).b. Use the definition of conditional probability to compute the exact value of P(K|C), writing your answer as a fraction in simplified form.
Will give brainliest please explain how
Answer:
x = 5/4
Step-by-step explanation:
√2+√2+√2+√2 = 2^x
4√2 = 2^x
4√2 = [tex]2^{\frac{5}{2} }[/tex] = [tex]2^{x}[/tex]
x = 5/2
Answer:
x = 5/4
Step-by-step explanation:
√2+√2+√2+√2 = 2^x
4√2 = 2^x
4√2 = =
x = 5/2
If f(x) = 2x – 1 and g(x) = 3x + 5, then (f o g)(x) is equal to
Answer:
(f◦g)(x) = 6x +9
Step-by-step explanation:
Use g(x) as the argument to f(x) and simplify.
(f◦g)(x) = f(g(x)) = f(3x +5) = 2(3x +5) -1
(f◦g)(x) = 6x +9
Translate the triangle left 1 units and up 5 units. What are the coordinates of point C after the translation?
Answer:
b++nfr
Step-by-step explanation:
jjkiki
If the area of a circle is 121 pi square units, what is its diameter
Answer:22
Step-by-step explanation:
diameter=d
Area=121π
area of circle=π x (d/2)^2
121π=π x d^2/4
121π=πd^2/4
Cross multiplying we get
121π x4=πd^2
484π=πd^2
Divide both sides by π
484π/π=πd^2/π
d^2=484
Taking the square roots of both sides we get
d=√(484)
d=22 diameter=22
In a random sample of 125 highway bridges around the country, 75 were in need of repair.
What is the sample proportion (point estimate) of highway bridges that need repaired? (Only type ONE decimal place)
Answer:
The sample proportion of highway bridges that need repaired is 0.6.
Step-by-step explanation:
The sample proportion of highway bridges that need repaired is the number of bridges in need of repair divided by the number of bridges around the country.
In this question:
75 bridges in need of repair, out of 125. So
75/125 = 0.6
The sample proportion of highway bridges that need repaired is 0.6.
How can you isolate the variable x-3=7
to get the variable alone you need to add three to both sides
x-3=7
+3 +3
-----------------
x= 10
Answer:
Step 1: Bring like terms together Step 2: Add variable to both sides Step 3: Simplify Step 4: Add the constant to both sides Step 5: Simplify Step 6: Divide by the coefficient Step 7: Solve Step 8: Test your solution Answer: 10
Step-by-step explanation:
What function do you use to find the angle of a vector, when you know its components?
Answer:
[tex]\theta = tan^{-1}(\frac{y}{x})[/tex]
Step-by-step explanation:
If we are given components of a vector then we can find the angle between them.
Suppose we are given a vector v
[tex]v = (x, y)[/tex]
Where x is the horizontal component and y is the vertical component.
The angle can be found by using
[tex]tan(\theta)=\frac{y}{x}\\\\\theta = tan^{-1}(\frac{y}{x})[/tex]
The magnitude of the vector v can be found using
[tex]v = \sqrt{x^{2}+y^{2}}[/tex]
Example:
Lets do a quick example:
[tex]v = (2, 4)[/tex]
The angle of the vector is
[tex]tan(\theta)=\frac{4}{2}\\\\\theta = tan^{-1}(\frac{4}{2})\\\\\theta = 63.43^{\circ}[/tex]
The magnitude of the vector is
[tex]v = \sqrt{x^{2}+y^{2}}\\\\v = \sqrt{2^{2}+4^{2}}\\\\v = \sqrt{4+16}\\\\v = \sqrt{20}\\\\v = 4.47[/tex]
Simon walks a total of 45.55 miles in March and 35.7 miles in April.
How many miles does Simon walk in all in March and April?
Enter your answer
Answer:
81.25
Step-by-step explanation:
45.55 + 35.7
Answer:I hope that helps
Step-by-step explanation:
On the Red Trail, the distance between point A and point B is 7.3 kilometers. You walked this distance back and forth. What is the distance you walked in meters?
Answer:
[tex]d = 14,600\,km[/tex]
Step-by-step explanation:
The distanced travelled is equal to twice the distance between points A and B. The distance that was walked in meters is:
[tex]d = 2\cdot (7.3\,km)\cdot \left(\frac{1000\,m}{1\,km} \right)[/tex]
[tex]d = 14,600\,km[/tex]
Final answer:
The total distance walked on the Red Trail, back and forth, when converted from kilometers to meters, is 14,600 meters.
Explanation:
The question asks for the total distance walked in meters if a person walks from point A to point B and back on the Red Trail, where the distance between point A and point B is 7.3 kilometers.
Firstly, we know that 1 kilometer equals 1,000 meters. Therefore, to find the distance in meters for a single trip from point A to point B, we multiply 7.3 kilometers by 1,000:
7.3 km × 1,000 = 7,300 metersSince the trip was made back and forth, the total distance covered is twice the distance of a single trip:
Total distance = 2 × 7,300 meters = 14,600 metersTherefore, the total distance walked back and forth on the Red Trail, in meters, is 14,600 meters.
Plot the point (3 comma StartFraction 7 pi Over 4 EndFraction ), given in polar coordinates, and find other polar coordinates (r comma theta )of the point for which the following are true. (a) r greater than 0 comma negative 2 pi less than or equals theta less than 0 (b) r less than 0 comma 0 less than or equals theta less than 2 pi (c) r greater than 0 comma 2 pi less than or equals theta less than 4 pi
Answer:
See explaination
Step-by-step explanation:
Please kindly check attachment for the step by step solution of the given problem.
The attached file have the solved problem.
Answer: B
Step-by-step explanation:
just did it
the height of the two triangular faces is 5.2 centimeters. the surface area of the triangular prism is ____ square centimeters.
The surface area of the triangular prism is 171.2 square centimeters.
From the given triangular prism,
Area of base (rectangle) = Length×Breadth
= 8×6=48 square centimeter
So, area of 3 congruent rectangles = 3×48
= 144 square centimeter
Here, area of a triangle = 1/2 × Base × Height
= 1/2 ×6×5.2
= 15.6 square centimeter
So, area of 2 congruent triangles= 2×15.6
= 31.2 square centimeter
Total surface area = 144+31.2
= 171.2 square centimeter
Therefore, the surface area of the triangular prism is 171.2 square centimeters.
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Wich shapes can the the shaded area be divided into to find the area
Answer:
A. a rectangle and a triangle
Answer:
a) rectangle and triangle, then add both to fin the total area.
Step-by-step explanation:
Do political science classes require less writing than history classes? The 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages. The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages. What can be concluded at the α = 0.01 level of significance?
Answer:
We conclude that political science classes require less writing time than history classes at 0.01 level of significance.
Step-by-step explanation:
We are given that the 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.
The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages.
Let [tex]\mu_1[/tex] = average writing time required by political science classes.
[tex]\mu_2[/tex] = average writing time required by history classes.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1\geq\mu_2[/tex] {means that political science classes require more or equal writing time than history classes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex] {means that political science classes require less writing time than history classes}
The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_-_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample average pages of essay writing for political science classes = 16.3 pages
[tex]\bar X_2[/tex] = sample average pages of essay writing for history classes = 18.9 pages
[tex]s_1[/tex] = sample standard deviation for political science classes = 4.8 pages
[tex]s_2[/tex] = sample standard deviation for history classes = 5 pages
[tex]n_1[/tex] = sample of political science classes = 55
[tex]n_2[/tex] = sample of history classes = 54
Also, [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(55-1)\times 4.8^{2}+(54-1)\times 5^{2} }{55+54-2} }[/tex] = 4.90
So, test statistics = [tex]\frac{(16.3-18.9)-(0)}{4.9 \sqrt{\frac{1}{55}+\frac{1}{54} } }[/tex] ~ [tex]t_1_0_7[/tex]
= -2.77
The value of t test statistics is -2.77.
Now, at 0.01 significance level the t table gives critical value of -2.365 at 107 degree of freedom for left-tailed test.
Since our test statistics is less than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that political science classes require less writing time than history classes.
How do I write the exponent expression below in numbers
Three to the sixth power all divided by two
Answer:
(3^6)/2
Step-by-step explanation:
make sure everything as the numerator is in parenthesis
"If a method produces a random error for each measurement of 4%, but a percent error of equal to or less than 1% is required for this value for later analysis, what is the minimum number of measurements that must be collected and averaged? You will need to solve equation 1 for the value of n that meets the criterion of a 1% error in the average."
Answer:
N = 16 measurements
Step-by-step explanation:
A method produces a random error for each measurement of 4%
A percent error of equal to or less than 1% is required.
We want to find out the minimum number of measurements that must be collected.
The standard error is given by
[tex]SE = \frac{S}{\sqrt{N} } \\[/tex]
Where s is the standard deviation and N is the number of measurements.
We are given standard deviation equal to 4% and SE equal to 1%
So re-arranging the above equation for N
[tex]\sqrt{N} = \frac{S}{SE} \\N = (\frac{S}{SE})^{2}\\N = (\frac{0.04}{0.01})^{2}\\N = 16[/tex]
Therefore, a minimum 16 number of measurements are needed.
14/10 divided by blank equals seven
Answer:
14/10=1.4
7/1.4=5
1.4x5=7
Step-by-step explanation:
In the given equation 14/10 divided by a certain number equals seven, the missing number is 0.2
Explanation:The subject of this question is Mathematics and it appears to be suitable for a Middle School grade level. You're asking for a number that, when 14/10 or 1.4 is divided by it, the result is seven.
To solve it, one can set it up as an equation in the form of 1.4 / x = 7. To find 'x', multiply both sides by 'x' to get rid of 'x' on the denominator of the left side, so the equation becomes 1.4 = 7x. The next step is to isolate 'x' by dividing both sides of the equation by 7. Solving this equation gives x = 1.4/7 = 0.2.So, 14/10 divided by 0.2 equals seven.
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Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court judges consist of 24 men and 3 women. (Enter your probabilities as fractions.) (a) Find the probability that both appointees are men. (b) Find the probability that one man and one woman are appointed. (c) Find the probability that at least one woman is appointed.
Answer:
[tex](a)\dfrac{92}{117}[/tex]
[tex](b)\dfrac{8}{39}[/tex]
[tex](c)\dfrac{25}{117}[/tex]
Step-by-step explanation:
Number of Men, n(M)=24
Number of Women, n(W)=3
Total Sample, n(S)=24+3=27
Since you cannot appoint the same person twice, the probabilities are without replacement.
(a)Probability that both appointees are men.
[tex]P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}[/tex]
(b)Probability that one man and one woman are appointed.
To find the probability that one man and one woman are appointed, this could happen in two ways.
A man is appointed first and a woman is appointed next.A woman is appointed first and a man is appointed next.P(One man and one woman are appointed)[tex]=P(MW)+P(WM)[/tex]
[tex]=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}[/tex]
(c)Probability that at least one woman is appointed.
The probability that at least one woman is appointed can occur in three ways.
A man is appointed first and a woman is appointed next.A woman is appointed first and a man is appointed next.Two women are appointedP(at least one woman is appointed)[tex]=P(MW)+P(WM)+P(WW)[/tex]
[tex]P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}[/tex]
In Part B, [tex]P(MW)+P(WM)=\frac{8}{39}[/tex]
Therefore:
[tex]P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}[/tex]
Maria and her friends went on a bike ride. The start and end times are shown below how long did they Ride
Start time: 1:09
End time: 2:05
Maria and her friends rides for 56 minutes
Duration of timeDuration is defined as the length of time that something lasts. Eg. When a film lasts for two hours, this is an example of a time when the film has a two hour durationHow to solve the problem?GivenStart time = 01:09
End time = 02:05
From start and end time we can see that there is 4 minutes to complete 1 hoursSo to find total time we need to subtract 4 minutes from 1 hours i.e 60 minutes∴ Ride Time = 60-4
∴ Ride Time = 56 minutes
Therefore the total ride time that Maria and her friend rode is 56 minutes
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The radial spokes of a bicycle tire are 13 inches long. What is the diameter of the tire?
Answer:
the answer is 5
Step-by-step explanation:
the
87 1/3% into a fraction
Final answer:
87 1/3% is approximately 17433/10000 as a fraction after converting 87.33% to a fraction with a denominator of 100 and simplifying.
Explanation:
To convert 87 1/3% into a fraction, we first recognize that 1/3% is equal to 0.33% (approximately), so 87 1/3% is approximately 87.33%. Next, we write this percent as a fraction with a denominator of 100 to represent the percent: 87.33/100.
To simplify further, we can convert the decimal to a fraction, where 0.33 is approximately 33/100, and add this to 87 to get:
8733/10000 + 8700/10000 = 17433/10000Thus, 87 1/3% is approximately 17433/10000 when expressed as a fraction.
(1) Saad had a box that is 15cm by 20cm by 22cm. What is the volume of the box?
(2) jake is redoing her kitchen. It measures 18ft by 19 ft. If wallpaper costs $1.29 per foot, how much will it cost her to wallpaper the kitchen?
Answer:
Question1:volume=6600cm^3
Question2:cost=$441.18
Step-by-step explanation:
Question 1:
volume=length x width x height
Volume=15 x 20 x 22
Volume=6600cm^3
Question 2:
area of kitchen=length x width
Area of kitchen=18 x 19
Area of kitchen=342ft^2
$1.29 for 1ft^2
$b for 342ft^2
$b=342 x1.29
$b=$441.18
HURRY PLEASE
morgan poured 3/4 gallon of punch into each of 6 bottles. how many gallons of punch did she pour in all
Answer:
gallons of punch in all = 4.5 gallons
Step-by-step explanation:
Morgan poured 3/4 gallons of punch into each of 6 bottles . This means Morgan poured 3/4 gallons of punch in each of the available 6 bottle .
He pours 3/4 gallons of punch in 1 bottle . For 6 bottles the gallons of punch poured is calculated below
1 bottle = 3/4 gallons of punch
6 bottles = ? gallons of punch
cross multiply
gallons of punch in all = 3/4 × 6
gallons of punch in all = 18/4
gallons of punch in all = 9/2 gallons
gallons of punch in all = 4.5 gallons
After getting trounced by your little brother in a children's game, you suspect the die he gave you to roll may be unfair. To check, you roll it 48 times, recording the number of times each face appears. Do these results cast doubt on the die is fairness
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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