Answers
Answer:
90
Step-by-step explanation:
Related Questions
Solve for x
THANK YOU
Answers
Step-by-step explanation:
so, I read here
2/3 x + 3x/x = 4x/2 × (3x + 6)
that is
2/3 x + 3 = 4x/2 × (3x + 6)
2x/3 + 3 = 2x × (3x + 6)
2x + 9 = 6x × (3x + 6)
2x + 9 = 18x² + 36x
18x² + 34x - 9 = 0
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 18
b = 34
c = -9
x = (-34 ± sqrt(34² - 4×18×-9))/(2×18) =
= (-34 ± sqrt(1156 + 648))/36 =
= (-34 ± sqrt(1804))/36 =
= (-34 ± sqrt(4×11×41))/36 =
= (-34 ± 2×sqrt(451))/36
x1 = (-34 + 2×sqrt(451))/36 =
= 0.235375588...
x2 = (-34 - 2×sqrt(451))/36 =
= -2.124264477...
Answer:
\(x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}\)
Step-by-step explanation:
\(\textsf{Given equation}:\)
\(\dfrac{2}{3}x+\dfrac{3x}{x}=\dfrac{4x}{2}(3x+6)\)
\(\textsf{Cancel the common factor } x \textsf{ in }\dfrac{3x}{x}:\)
\(\implies \dfrac{2}{3}x+3=\dfrac{4x}{2}(3x+6)\)
\(\textsf{Simplify }\dfrac{4x}{2}\textsf{ by dividing the numbers}:\)
\(\implies \dfrac{2}{3}x+3=2x(3x+6)\)
\(\textsf{Apply the distributive law}\quad \:a\left(b+c\right)=ab+ac:\)
\(\implies \dfrac{2}{3}x+3=6x^2+12x\)
\(\textsf{Multiply both sides by 3 to cancel the denominator of }\dfrac{2}{3}:\)
\(\implies \dfrac{2}{3}x\cdot 3+3\cdot 3=6x^2\cdot 3+12x \cdot 3\)
\(\implies 2x+9=18x^2+36x\)
\(\textsf{Switch sides}:\)
\(\implies 18x^2+36x=2x+9\)
\(\textsf{Subtract }2x \textsf{ from both sides}:\)
\(\implies 18x^2+36x-2x=2x+9-2x\)
\(\implies 18x^2+34x=9\)
\(\textsf{Subtract 9 from both sides}:\)
\(\implies 18x^2+34x-9=9-9\)
\(\implies 18x^2+34x-9=0\)
Solve using the Quadratic Formula:
\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0\)
Define the variables:
\(\implies a=18, \quad b=34, \quad c=-9\)
Substitute the defined variables into the quadratic formula and solve for x:
\(\implies x=\dfrac{-34 \pm \sqrt{34^2-4(18)(-9)} }{2(18)}\)
\(\implies x=\dfrac{-34 \pm \sqrt{1156+648} }{36}\)
\(\implies x=\dfrac{-34 \pm \sqrt{1804} }{36}\)
\(\implies x=\dfrac{-34 \pm \sqrt{4 \cdot 451} }{36}\)
\(\implies x=\dfrac{-34 \pm \sqrt{4}\sqrt{451} }{36}\)
\(\implies x=\dfrac{-34 \pm 2\sqrt{451} }{36}\)
\(\implies x=\dfrac{-17 \pm \sqrt{451} }{18}\)
Therefore, the solutions to the given equation are:
\(x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}\)
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The cost for painting a shed is 8,00. If the dimensions of a similar shed are havled, what would the cost be for painting the reduced sized shed?
Answers
Answer:
4
Step-by-step explanation:
8/2=4
9+x=11 what is the value of x?
Answers
Answer: the answer to that problem is
X=2
Vhich graph represents a function?
Answers
Answer:
answer D or the 4th answer
The fourth graph represents the function.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A relation is a function if it has only One y-value for each x-value.
In the given graphs, the graph which represents the functions is the graph in which there is only one y value for the x value.
For each input there should be only one output.
In graph (1), the x value is same but the y values are changing which is not a function.
In graph (2), each x value has two different outputs so it it is not a function.
In fourth graph the x values are different but the y values are same, so it is a function.
Hence, the fourth graph represents the function.
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variable x and y and by the differentiation xdy/dx = 1-y^2 when x=2 ,y=0 solve the differential equation obtaining an expression for y in terms of x
Answers
The solution to the differential equation is y = √(2x/(1 + x))
What is the solution to the differential equation?We can solve this equation using separation of variables. First, we can divide both sides of the equation by x to get:
dy/dx = 1/x - y²/x
Now, we can separate the variables to get:
y*dy = (1 - y²) dx
We can then integrate both sides of the equation to get:
1/2*y² = x - x*y²/2 + C
where C is an arbitrary constant.
We are given that x=2 and y=0 when x=2. Plugging these values into the equation, we get:
1/2*0² = 2 - 2*0²/2 + C
C = 1
We can now substitute this value of C back into the equation to get:
1/2*y² = x - x*y²/2 + 1
y² = 2x - x*y²
y² + x*y² = 2x
y²(1+x) = 2x
y² = 2x/(1+x)
Therefore, the expression for y in terms of x is:
y = √(2x/(1 + x))
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Pls help with this question!!!!
Answers
There are 75 dimes in the box. This is because all of the pennies, nickels and quarters is 14.20$. So subtracting the full total 21.70 bu 14.20 gives us 7.50$. Which is 75 dimes.
Which strategies can be used to find the product of 1,587 x 1,000? Select two options
Answers
Answer:
Step-by-step explanation:
you can multiple and get 1,587,000]and then you divide to get 8 \(\sqrt{1587000\)Find the solutions of (x – 4)(x – 4) = 0.
Question 4 options:
A)
x = –4
B)
x = 4, –4
C)
x = 0
D)
x = 4
Answers
Answer:
Step-by-step explanation:
(x – 4)(x – 4) = 0.
So factor are x-4=0
X=4 (D) is the answer
please help me somebody!
Answers
Answer:
Blonde: 54 for mountains
Brunette: 100 for total
Red: 70 for total
Black: 41 for beach
Total: 162 for beach, 197 for mountains, 360 for total
Step-by-step explanation:
add and subtract as needed
a survey of 400 non-fatal accidents showed that 173 involved faulty equipment. find a point estimate for p, the population proportion of accidents that involved faulty equipment
Answers
Based on a survey of 400 non-fatal accidents, where 173 involved faulty equipment, the point estimate for the population proportion (p) of accidents that involved faulty equipment is 173/400 = 0.4325.
To calculate the point estimate for the population proportion, we divide the number of accidents involving faulty equipment (173) by the total number of accidents surveyed (400).
This gives us a ratio of 0.4325, which represents the estimated proportion of accidents involving faulty equipment in the population.
A point estimate is a single value that serves as an approximation or best guess for an unknown population parameter.
In this case, the population proportion (p) represents the proportion of all accidents that involved faulty equipment. The point estimate of 0.4325 suggests that approximately 43.25% of non-fatal accidents may involve faulty equipment based on the sample data.
It's important to note that this point estimate is subject to sampling variability and may not perfectly reflect the true population proportion. To obtain a more precise estimate with a measure of uncertainty, one would need to consider confidence intervals or conduct hypothesis testing using statistical methods.
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Find all angles between 0 and 2pi satisfying the condition.
Answers
Answer:
5π/6 and 7π/6
Explanation:
Using the inverse function of cosine, we get:
\(\begin{gathered} \text{cos x = }\frac{-\sqrt[]{3}}{2} \\ x=\cos ^{-1}(\frac{-\sqrt[]{3}}{2}) \\ x=\frac{5\pi}{6} \end{gathered}\)Then, cos(x) = cos(-x), so:
\(\cos (\frac{5\pi}{6})=\cos (\frac{-5\pi}{6})=\frac{-\sqrt[]{3}}{2}\)Finally, -5π/6 is also equivalent to 7π/6, because:
2π - 5π/6 = 7π/6
So, all the angles between o and 2π that satisfy the condition are:
5π/6 and 7π/6
If a man is removed from the data set, the correlation decreases only slightly from 0.83 to 0.81. Why do you think the change in the correlation is so small?
Answers
Answer:
So we always look for \(R^{2}\) to find a correlation. 0.81 is known as, Large Positive Linear Association. There are many variables, in this case, this "man" is part of other variables. So by removing HIM, the correlation goes from 8 to 9. It is still significant. However, it can be because of many reasons. Perhaps he has diabetes or cancer and was removed. *Hypothetically
Step-by-step explanation:
Define the domain of the following:
{-2, -1, 0, 2, 5}
{-2, -1, 0, 1, 2, 3, 4, 5}
All Real Numbers
{3, -1, 3, 1, 2}
Answers
The domain of the relation in the graph is:
{-2, -1, 0, 2, 5}
How to define the domain for the graph?A relation maps elements from one set (the domain) into elements from another set (the range).
Such that the domain is represented in the horizontal axis.
In the graph, we can see the points:
{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}
The domain is the set of the first values of these points, then the domain is:
{-2, -1, 0, 2, 5}
The correct option is the first one.
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Calculate the future value of a three year uneven cash flow given below, using 11% discount rate:
Year 0 Year 1 Year 2 Year 3
0 $600 $500 $400
Answers
Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.
To calculate the future value of a three-year uneven cash flow given below, using an 11% discount rate, we need to use the formula;
Future value of uneven cash flow = cash flow at year 1/(1+discount rate)¹ + cash flow at year 2/(1+discount rate)² + cash flow at year 3/(1+discount rate)³ + cash flow at year 4/(1+discount rate)⁴
Given the cash flows;
Year 0: $0
Year 1: $600
Year 2: $500
Year 3: $400
Then the Future value of uneven cash flow
= $600/(1+0.11)¹ + $500/(1+0.11)² + $400/(1+0.11)³
= $600/1.11 + $500/1.23 + $400/1.36
=$540.54 + $405.28 + $293.00
=$1,238.82
Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.
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Please give an explanation as well as an answer :)
Answers
You have to match the letters to the numbers.
0=P, 5=I, 8=A, 2=L, 3=C, 4=E
Once you have all that info you can figure out your answer by writing LACE and trying to match the numbers to those four letters.
Hope that helps :)
respectively Q 1
=160−10P 1
OR r 1
=16−0.1Q 1
aWD 1/P 6
=16 6
−2T −
Q 2
=200−20P 2
ORP 2
=10−0,050,…H1AP 2
=15−0:0% Saga's Total Cost function is: TC =120+4Q With third degree price discrimination, the condition for peofit marimizater is MR 1
=MR 2
=MR=MC Find P 1
,Q 1
,P 2
,Q 1
Total Revenue, Total Cost, and Total proft wit sree discrimination. Find P,Q,TR,TC&π In the absence of price discrimination. Marks: 7
Answers
In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.
Given the demand equations and the total cost function:
Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1
Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2
Total Cost: TC = 120 + 4Q
To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:
MR1 = MC:
16 - 0.2Q1 = 4
0.2Q1 = 12
Q1 = 60
MR2 = MC:
10 - 0.1Q2 = 4
0.1Q2 = 6
Q2 = 60
Substituting the quantities back into the demand equations, we find:
P1 = 16 - 0.1(60) = 10
P2 = 10 - 0.05(60) = 7
The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:
TR = P1 * Q1 + P2 * Q2
TR = (10 * 60) + (7 * 60)
TR = 600 + 420
TR = 1020
The total cost (TC) is given by the total cost function:
TC = 120 + 4Q
TC = 120 + 4(60 + 60)
TC = 120 + 480
TC = 600
Finally, the profit (π) can be calculated by subtracting total cost from total revenue:
π = TR - TC
π = 1020 - 600
π = 420
In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
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hiii please help i’ll give brainliest if you give a correct answer tysm!
Answers
Answer:
20
Step-by-step explanation:
The no. of people will be 2/3 of the pounds of turkey.
2/3 of 30 is 20.
Hope this helps!
Determine the intercepts of the line.
Do not round your answers.
3x+2y=5
Answers
Answer:
x intercept = 1.66666...
y intercept = 2.5
The x intercept is approximate. The 6's go on forever. The y intercept is exact without any rounding done to it.
======================================
Explanation:
Plug in y = 0. Then solve for x to get the x intercept.
3x+2y = 5
3x+2*0 = 5
3x = 5
x = 5/3
x = 1.66666...
The 6's go on forever.
------------------
Plug x = 0 into the equation and solve for y. This will get us the y intercept.
3x+2y = 5
3*0+2y = 5
0+2y = 5
2y = 5
y = 5/2
y = 2.5
This value is exact without any rounding
x = 5/3 or 1 2/3
y = 5/2 or 2 1/2
Step by step
To solve for x and y intercepts:
For x, sub 0 in for y and solve
For y, sub 0 in for x and solve
a store buys jackets for $49.99 . the markup on the jacket is $18.49.during the sales,the jacketsare sold for 57.99. what is the markup during the sales?
Answers
Step-by-step explanation:
$1,999 minds right Jitpur defective defective here note justice Jhapa Jhapa here's
Help Quick im gonna fail
Answers
Answer:
A
Step-by-step explanation:
I just want someone to proof-read these so that I have a good understanding of what I am doing (leave feedback)
Ok so these are the math questions I don't understand because they are trickily worded or just make no sense.
E.) Explain how you could write 60,000,000 as the product of a number greater than or equal to 1 that is multiplied by a power of 10.
I think the way to understand this is to focus just on how to understand it. This one is trickily worded so I'm going to have to try to find the main idea of the question so that I can figure it out.
It wants me to explain how to write 60,000,000 that much I understand, however, how it wants me to explain it is where I get lost. I get lost because it says "as the product of a number greater than or equal to 1 that is multiplied by a power of 10". I don't get what that means though.
It says that is has to be multiplied by a power of 10, meaning that this is dealing with Scientific Notation, and in Scientific Notation, you cannot have a number greater than or equal to 10, meaning that the number I am looking to put with a power of 10 has to be under a value of 10.
As trick as that may sound, all that means is that I cannot have a number above or equal to ten, but I have to find out which number between 1 and 9 that is.
Also it says "as a product" meaning that it has do deal with the number in which becomes the answer. 60,000,000 in scientific form would have to start out as a number such as 6.00, until it worked its way up to 60,000,000 by moving the decimal to the right. That means I have to find out how many place values the decimal was moved up, which would give me the expression I need to use as my answer.
If I moved the decimal point from 6.00 to the right 7 times, then I would get the number 60,000,000. The expression for this problem should be along the lines of 10^7. (That's just how you have to type it. What it stands for is 10 to the seventh power).
The answer to write is:
6.00 times 10^7
Okay so now another one (it also deals with Scientific Notation)
Write 63,120,000 is scientific notation.
It sounds simple but really it's more complex. If I connect my background knowledge into this, I know that the decimal has to go in between 6 and 3 in order for scientific notation to take form in this question. However that leaves me with 6.3120 as the original number. It doesn't feel right to say that because it seems like a number too large to be put through the process of scientific notation.
In order to find the answer to this question I need to pay attention to the amount of zeros on the endo of 63,120,000 and I know that there are four of them If I take the decimal and move it over 7 place values to the right, I end up with 63,120,000. Still it doesn't feel like the right answer. Even so I have to answer it so I'm going to say that the scientific notation for this problem would likely be 6.3120x10^7=63,120,000.
Another (still dealing with scientific notation)
Write 9.054 x 10^-6 in standard form.
According to what my teacher says (and also what the internet says) any base number with a negative exponent will have a positive product. So if I put that information into thought then I should be able to write the answer. However, I am asked to put this in standard form, meaning that I have to solve the problem to get the answer. The way it is already written is in Scientific Notation, so I have to find out what the product is, that way I can get my answer.
I have to move the decimal in 9.054 over 6 place values in the right direction to get my answer. I know that if I move the decimal over HALF of six times that I will get 9054, and if I move it over three more times, all I have to do is add 3 zeros.
That means that my answer is 9,054,000.
Answers
Yea it's good but make sure to check your answers to see if you did anything wrong.
Please help heres some points!
Answers
Answer:
tooth A
Step-by-step explanation:
0.23 = 0.230
0.230 > 0.195
Answer:
a
Step-by-step explanation:
Lauren has a bucket of sidewalk chalk. In the bucket there are 2 green, 8 red, 2 yellow, 4 blue and 4 pieces of white chalk. If she randomly pulls out 6 pieces of chalk, in how many ways can she pull out exactly 2 red chalks and 1 white chalk
Answers
Answer:
32 ways
Step-by-step explanation:
Since there are 8 red chalks and 4 white chalks.
Then number of ways to select exactly 2 red chalks is; 8C2 = 28 ways
Number of ways to select exactly 1 white chalk is; 4C1 = 4 ways
Total number of ways = 28 + 4 = 32 ways
Solve the system d.x = 7x - 6y dt dy dt = 9x - 8y with the initial value x(0) = 5 y(0) = 8 x(t) = = y(t) =
Answers
The solution to the given system of differential equations is x(t) = 5e^t + 2e^(-t) and y(t) = 3e^t + 4e^(-t), with initial conditions x(0) = 5 and y(0) = 8.
To solve the system of differential equations, we can use the method of separation of variables. First, let's solve for dx/dt:
d(x) = (7x - 6y) dt
dx/(7x - 6y) = dt
Integrating both sides with respect to x:
(1/7)ln|7x - 6y| = t + C1
Where C1 is the constant of integration. Exponentiating both sides:
e^(ln|7x - 6y|/7) = e^t e^(C1/7)
|7x - 6y|/7 = Ce^t
Where C = e^(C1/7). Taking the absolute value away:
7x - 6y = C e^t
Now let's solve for dy/dt:
dy/(9x - 8y) = dt
Integrating both sides with respect to y:
-(1/8)ln|9x - 8y| = t + C2
Where C2 is the constant of integration. Exponentiating both sides:
e^(-ln|9x - 8y|/8) = e^t e^(C2/8)
|9x - 8y|/8 = De^t
Where D = e^(C2/8). Taking the absolute value away:
9x - 8y = De^t
Now we have a system of two linear equations:
7x - 6y = C e^t ----(1)
9x - 8y = De^t ----(2)
We can solve this system using various methods, such as substitution or elimination. Solving for x and y, we obtain:
x(t) = (5C + 2D)e^t + (6y)/7 ----(3)
y(t) = (3C + 4D)e^t + (9x)/8 ----(4)
Applying the initial conditions x(0) = 5 and y(0) = 8, we can determine the values of C and D. Plugging these values back into equations (3) and (4), we find the final solutions for x(t) and y(t).
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use a venn diagram to illustrate the relationships a ⊂ b and a ⊂ c.
Answers
In a Venn diagram, we illustrate the relationships between sets a, b, and c, specifically the relationships a ⊂ b (a is a subset of b) and a ⊂ c (a is a subset of c).
A Venn diagram is a visual representation of sets using overlapping circles. In this case, we have three sets: a, b, and c. To illustrate the relationship a ⊂ b, we draw a circle representing set b and a smaller circle inside it representing set a. This indicates that every element in a is also an element of b, but b may contain additional elements that are not in a. The subset a is completely contained within set b. Similarly, to represent the relationship a ⊂ c, we draw a circle representing set c and a smaller circle inside it representing set a. This indicates that every element in a is also an element of c, but c may contain additional elements that are not in a. The subset a is completely contained within set c. By using the Venn diagram, we visually demonstrate the relationships between sets a, b, and c. The diagram clearly shows that a is a subset of both b and c, indicating that all elements of a are also elements of b and c. However, b and c may have additional elements that are not in a.
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Among 13 Eastern red-backed salamanders released into a controlled forest environment, six are the red-backed morphs, four are lead-backed, and three are erythristic. Find the number of possible orders in which these salamanders can be captured by predators. 7. In a production process, a product is selected by using four different independent parts (A,B,C,D). In order for the product to operate properly, each part must be free of defects. The probability of the parts being non - defectives are given by P(A)=0.8, P(B)=0.9,P(C)=0.6 and P(D)=0.7. What is the probability that all four parts are defective?
Answers
There are 171,600 possible orders in which the salamanders can be captured by predators and the probability that all four parts are defective is 0.024.
The number of possible orders in which the salamanders can be captured by predators can be found using the concept of permutations. Since all 13 salamanders are distinct (different morphs), we can calculate the number of possible orders by applying the permutation formula. The total number of salamanders is 13, with 6 red-backed, 4 lead-backed, and 3 erythristic salamanders. The number of possible orders is:
13! / (6! * 4! * 3!) = 171,600
Therefore, there are 171,600 possible orders in which the salamanders can be captured by predators.
The probability that all four parts are defective can be found by multiplying the probabilities of each part being defective. Since the parts are independent, we can multiply their individual probabilities of being defective:
P(all four parts are defective) = P(A is defective) * P(B is defective) * P(C is defective) * P(D is defective)
P(all four parts are defective) = (1 - P(A is non-defective)) * (1 - P(B is non-defective)) * (1 - P(C is non-defective)) * (1 - P(D is non-defective))
P(all four parts are defective) = (1 - 0.8) * (1 - 0.9) * (1 - 0.6) * (1 - 0.7)
P(all four parts are defective) = 0.2 * 0.1 * 0.4 * 0.3
P(all four parts are defective) = 0.024
Therefore, the probability that all four parts are defective is 0.024.
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Given f(x) = -2x and g(x) = 4x - 8, find h(x) = f(x) + g(x).
Answers
f(x) = -2x and g(x) = 4x - 8, find h(x) = f(x) + g(x).
Replace f(x) and g(x) with their given values:
h(x) = -2x + 4x -8
Combine like terms:
h(x) = 2x -8
which expression is equivalent to the expression shown below?
-1/2(-3/2x + 6x + 1) - 3x
A) 3/2x - 1/2
B) 6 3/4x - 1/2
C) -3/4x + 1/2
D) -5 1/4x - 1/2
Answers
Answer:
vcbnvjhgbvnhtrgbhj hy6tyuk
Step-by-step explanation:
The correct answer is: [D]: " (-5 )x − " .
_________________________________________________________
Explanation:
_________________________________________________________
" -1/2(-3/2x + 6x + 1) − 3x " ;
= (-1/2 * -3/2 x) + (-1/2 * 6x) + (-1/2 * 1) − 3x ;
= [ (-1 *-3) /(2*2)] x + (-3x) + (-1/2) ] − 3x ;
= [ (3/4)x − 3x − (1/2) ] − 3x ;
= (3/4)x − 3x − (1/2) − 3x ;
= ?? ; → Combine the "like terms" ;
→ "(3/4)x − 3x − 3x " = ?? ;
→ "(3/4)x − 3x = "(-9/4)x";
→ "(-9/4)x − 3x = "(-21/4)x " = " (-5 )x " ;
→ The answer is: " (-5 )x − " ;
___________________________________________________
→ which is:
___________________________________________________
→ Answer choice: [D]: " (-5 )x − " .
___________________________________________________
The length of a rectangle is 3 inches more than its width. The perimeter of the rectangle is 34 inches.
The length of the rectangle is ___ Inches, and its width is ___ inches.
Answers
Answer:7 and 10
Step-by-step explanation:
Trust I got it 100% right
Answer:
1
Step-by-step explanation:
a die is tossed 180 times with the following results: x 1 2 3 4 5 6 f 28 36 36 30 27 23 is this a balanced die? use a 0.01 level of significance
Answers
Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.
We have,
To determine if the die is balanced, we can perform a chi-square test of goodness of fit.
The null hypothesis is that the die is balanced, and the alternative hypothesis is that the die is not balanced.
First, let's calculate the expected frequencies for each outcome assuming the die is balanced. Since there are 180 tosses in total, each outcome is expected to have an equal probability of 1/6.
Expected frequency for each outcome
= (Total tosses) x (Probability of each outcome)
Expected frequency for each outcome = (180) x (1/6)
Expected frequency for each outcome = 30
Now, we can calculate the chi-square test statistic using the formula:
χ² = Σ [(Observed frequency - Expected frequency)² / Expected frequency]
Let's calculate the chi-square test statistic:
χ² = [(28 - 30)² / 30] + [(36 - 30)² / 30] + [(36 - 30)² / 30] + [(30 - 30)² / 30] + [(27 - 30)² / 30] + [(23 - 30)² / 30]
χ² = [(-2)² / 30] + [(6)² / 30] + [(6)² / 30] + [(0)² / 30] + [(-3)² / 30] + [(7)² / 30]
χ² = 4/30 + 36/30 + 36/30 + 0/30 + 9/30 + 49/30
χ² = 134/30
χ² ≈ 4.467
Next, we need to compare the calculated chi-square value to the critical chi-square value at a significance level of 0.01 and degrees of freedom equal to the number of outcomes minus 1 (6 - 1 = 5).
Looking up the critical chi-square value in a chi-square distribution table with 5 degrees of freedom and a significance level of 0.01, we find it to be approximately 15.086.
Since the calculated chi-square value (4.467) is less than the critical chi-square value (15.086), we fail to reject the null hypothesis.
Therefore, we do not have sufficient evidence to conclude that the die is not balanced at a 0.01 level of significance.
Thus,
Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.
Learn more about the chi-square test here:
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