There is significant evidence at 0.100 significance level that the die is fair or not using the given data of the number of times each value has been obtained over 32 rolls.
we can follow the steps given below:
Step 1: Define null and alternate hypotheses
The null hypothesis states that the die is fair and has an equal probability of landing on each value. Therefore, the null hypothesis is:
H0: The die is fair, i.e. P(1) = P(2) = P(3) = P(4) = P(5) = P(6)
The alternate hypothesis states that the die is not fair and does not have an equal probability of landing on each value. Therefore, the alternate hypothesis is:
H1: The die is not fair, i.e. P(1) ≠ P(2) ≠ P(3) ≠ P(4) ≠ P(5) ≠ P(6)
Step 2: Calculate the expected number of counts under the null hypothesis
To calculate the expected number of counts under the null hypothesis, we assume that the die is fair and has an equal probability of landing on each value. Therefore, the expected count of each value is 32/6 = 5.33. Then, the expected number of counts for each value is calculated as follows:
Value Count Expected count (under H0)
1 11 5.33
2 4 15.33
3 7 15.33
4 2 5.33
5 3 15.33
6 5 15.33
Step 3: Calculate the test statistic
To calculate the test statistic, we use the formula given below:
χ2 = ∑(O − E)2/E
where, O = Observed count, E = Expected count
Using the given data, we can calculate the test statistic as follows:
Value Count Expected count (under H0) Observed count (O)
1 11 5.33 11
2 4 5.33 4
3 7 5.33 7
4 2 15.33 2
5 3 15.33 3
6 5 15.33 5
χ2 = ∑(O − E)2/E = (11 − 5.33)2/5.33 + (4 − 5.33)2/5.33 + (7 − 5.33)2/5.33 + (2 − 5.33)2/5.33 + (3 − 5.33)2/5.33 + (5 − 5.33)2/5.33 = 9.01 (approx.)
Step 4: Determine the p-value
We can use the chi-square distribution table or a calculator to determine the p-value corresponding to the test statistic. The degrees of freedom for the chi-square distribution is (6 - 1) = 5, as there are 6 possible values of the die. Using the chi-square distribution table, we find that the p-value for a chi-square statistic of 9.01 with 5 degrees of freedom is between 0.1 and 0.05. Since this is a two-tailed test, we double the p-value to get:
p-value = 2 × 0.05 = 0.10
Step 5: Compare the p-value with the significance level
Since the p-value.
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what is the answer for 23/4 + -23/4 - -15/4 + 9/4
Answer:
\(-\frac{6}{4}\)
Step-by-step explanation:
The first 2 numbers cancel, and -15/4+9/4 is the same as 9/4 - 15/4
Please mark me as brainliest if I am correct
Answer:
6
Step-by-step explanation:
In the equation, \(\frac{23}{4} + -\frac{23}{4} --\frac{15}{4} + \frac{9}{4}\), we can see that \(\frac{23}{4} + -\frac{23}{4}\) cancel each other out
This leaves us with \(--\frac{15}{4} + \frac{9}{4}\). The negatives "negate" themselves giving us \(\frac{15}{4} + \frac{9}{4} = \frac{24}{4}\) or \(6\)
Hopefully (some part of) this explanation makes sense (or at least somewhat). If this doesn't make sense, please tell me and I will try to make it more understandable as soon as possible.
It would help if you marked my answer as Brainliest, if I'm correct, so I can help even more people! (I would really appreciate it!)
Simplify give ur answer in index form.
\( \frac{( {j}^{4} \: \times \: {j}^{8}) ^{3} }{( {j}^{9} \: \div \: {j}^{2}) ^{2} } \)
First we calculate the product of the denominator.\( \frac{( {j}^{12}) ^{3} }{( {j}^{9} \: \div \: {j}^{2}) ^{2} } \)
Then we calculate the quotient of the numerator.\( \frac{( {j}^{12}) ^{3} }{( {j}^{7}) ^{2} } \)
We multiply the exponents of the expression.\( \frac{ {j}^{36} }{ {j}^{14} } \)
We divide.\( \boxed{ \bold{ {j}^{22} }}\)
MissSpanishI NEED HELP PLEASE I NEED TO KNOW HOW U GOT THE ANSWER PLEASE
Linear is basically a straight line. It can be increasing or decreasing.
Decreasing is when on the graph, when x increases, y decreases.
On the graph, there are two parts that are decreasing. Between -2 and 0, and Between 2 and 4. Let's look at these two.
- For between -2 and 0, the line is not straight. Therefore, it is decreasing and nonlinear. We can check if this is the right answer.
- For between 2 and 4, the line is decreasing. However, the line is straight, which means it is decreasing but linear.
Your final answer is B.
). a lottery offers one $1000 prize, one $500 prize, and two $50 prizes. one thousand tickets are sold at $4.00 each. find the expectation of winning amount if a person buys one ticket. create a probability distribution as part of your answer.
Expectation = ($1 + $0.50 + $0.40) x $4.00 = $7.40
The expectation of winning amount if a person buys one ticket is $7.40. This can be calculated using the probability distribution below.
Lottery Prize: | Probability: | Win Amount: | Probability x Win Amount:
$1000 | 1/1000 | $1000 | 1/1000 x $1000 = $1
$500 | 1/1000 | $500 | 1/1000 x $500 = $0.50
$50 | 2/1000 | $50 | 2/1000 x $50 = $0.40
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hi answer for this if your a genius
Answer:
1/6 Is your answer
Hope it helps!!!
Answer:
2/6
Step-by-step explanation:
can also be 1/3 depending on choices
What is the image point of (-2, 10) after the transformation R270° 0 D₁?
f(x)= {x+4 if x<5
{8 if 5 < or equal to x<7
{2x-1 if 7 < or equal to x < or equal to 10
for f(x), evaluate the following:
A. f(0)
B. f(6)
show all of your work.
Answer:
A. f(0) = 4
B. f(6) = 8
Step-by-step explanation:
When evaluating a piecewise function, the fist step is to determine the applicable domain. Then the function defined for that domain is the one that is used for the evaluation.
A.x = 0 is in the domain x < 5, so the applicable function is f(x) = x+4.
f(0) = 0 +4 = 4
__
B.x = 6 is in the domain 5 ≤ x < 7, so the applicable function is f(x) = 8.
f(6) = 8
The sum of two numbers is 53 The larger number is 11 more than the smaller number. What are the numbers?
Answer:
21 and 32 are the numbers
Step-by-step explanation:
Let assume that the the two numbers are X and Y and that X is the large number.
According to the question,
X + Y = 53 .................. Equation 1
then, X = 11 + Y........... Equation 2
Substitute equation 2 into equation 1.
[11 + Y] + Y = 53
11 + 2Y = 53
2Y = 53 - 11 = 42
2Y = 42
Y = 42 / 2 = 21,
Therefore, Y = 21 [Small number].
According to equation 1,
X +Y = 53
X + 21 = 53
X = 53 - 21 = 32.
Therefore, X = 32 [Big number]
Evaluate 7 with an exponent of -2
Answer:
7 x -7 = -49
Step-by-step explanation:
To solve 7 to the power of -2 we multiply 7 by -7.
(っ◔◡◔)っ ♥ Hope It Helps ♥
The value of 7 with an exponent of -2 is 1/49 .
Given,
7 with an exponent of -2.
Now,
Let us simplify the given statement.
\(7^{-2}\) = 1/7²
Value of 7² is 49.
Thus the value of 7 with an exponent of -2 is 1/49 .
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HELP ME PLEASE FOR BRAINLESTT!!
Answer:
The solution of a system of linear equations is:
D. The values of the variables that satisfy both equations.
Answer:
See below.
Step-by-step explanation:
The answer is D. The solution is when the two lines intersect, or are satisfied.
-hope it helps
Results from the Family Lifestyles Project indicate that children raised by counterculture parents are different from children raised by parents with more traditional values in that
The results from the Family Lifestyles Project suggest that children raised by counterculture parents differ from those raised by parents with more traditional values.
The Family Lifestyles Project conducted research to explore the differences between children raised by counterculture parents and those raised by parents with more traditional values. The findings indicate that these two groups of children exhibit distinct characteristics and behaviors.
Children raised by counterculture parents, who embrace non-conventional or alternative lifestyles, may experience different socialization processes and environments compared to children raised by parents with traditional values. These children may have been exposed to unique belief systems, values, and practices that deviate from societal norms.
As a result, the study suggests that children raised by counterculture parents may demonstrate variations in their attitudes, beliefs, behaviors, and lifestyle choices. This could manifest in different educational preferences, career aspirations, social interactions, and perspectives on various social issues.
Overall, the research highlights the influence of parental values and lifestyles on child development and emphasizes the potential impact of counterculture parenting on shaping children's identities and behaviors.
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Claim: Fewer than 93% of adults have a cell phone. In a reputable poll of 1232 adults, 87% said that they have a cell phone. Find the value of the test statistic. Question content area bottom
The value of the test statistic is -8.2542.
We have,
p'= 0.87, p= 0.93 and n= 1232
We know, the equation for the Test statistic for a population proportion is mathematically given as
z = (p' - p)/ √p(1-p)/ n
So, z= (0.87 - 0.93)/ √0.93(1-0.93)/ 1232
z = (-0.06) / 0.007269
z = -8.2542
So, the value of the test statistic is -8.2542.
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Jeremiah makes 25% of the three-point shots he attempts. For a warm up, Jeremiah likes to shoot three-point
shots until he makes one. Let M be the number of shots it takes Jeremiah to make his first three-point shot.
Assume that the results of each shot are independent.
Find the probability that it takes Jeremiah fewer than 4 attempts to make his first shot.
You may round your answer to the nearest hundredth.
P(M < 4) =
The probability will be "0.578".
Given values,
p = 25%or,
= 0.25
q = 1-p= 1-0.25
= 0.75
To find the probability that it takes Jeremiah fever than 4 attempts is given by,
→ \(P(M<4) = P(1-P)^{M-1}\)
M = 1, 2, 3
→ \(= P[(1-P)^{1-1}+(1-P)^{2-1}+(1-P)^{3-1}]\)
→ \(= P[1+(1-P)+(1-P)^2]\)
→ \(= 0.25[1+0.75+0.75^2]\)
→ \(= 0.25\times 2.3125\)
→ \(= 0.578125\)
or,
→ \(= 0.578\)
Thus the above answer is right.
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The Maclaurin series for f(x) is given by 1 + (x)/2! +x2/3! + x3/4! + . . . + xn/(n +1)! + . . .
a) Find f '(0) and f(17) (0).
b) For what values of x does the given series converge? Showyour reasoning.
c) Let g(x) = xf(x). Write the Maclaurin series for g(x),showing the first three nonzero terms and the generalterm.
d) Write g(x) in terms of a familiar function withoutusing series. Then, write f(x) in terms of the same familiarfunction.
a) f'(0) = 1/2 and f(17) (0)= 1/18 b) the series converges for all values of x c) The three nonzero terms are x, x^2/2!, and x^3/3!, and the general term is x^(n+1)/(n+1)!. d) f(x) in terms of the same familiar function is e^x
The Maclaurin series for f(x) is given by 1 + (x)/2! + x^2/3! + x^3/4! + ... + x^n/(n + 1)! + ...
a) To find f'(0), we take the derivative of the Maclaurin series and plug in x = 0:
f'(x) = 1/2! + 2x/3! + 3x^2/4! + ... + n*x^(n-1)/(n+1)! + ...
f'(0) = 1/2! = 1/2
To find f(17)(0), we take the 17th derivative of the Maclaurin series and plug in x = 0:
f(17)(x) = 17!/(n+1)! + ...
f(17)(0) = 17!/(17+1)! = 1/18
b) The given series converges for all values of x. This can be shown using the ratio test:
lim (n -> infinity) |(x^(n+1)/(n+2)!)/(x^n/(n+1)!)| = lim (n -> infinity) |x/(n+2)| = 0
Since the limit is less than 1, the series converges for all values of x.
c) To find the Maclaurin series for g(x), we multiply the Maclaurin series for f(x) by x:
g(x) = x*f(x) = x*(1 + (x)/2! + x^2/3! + ... + x^n/(n+1)! + ...)
= x + x^2/2! + x^3/3! + ... + x^(n+1)/(n+1)! + ...
The first three nonzero terms are x, x^2/2!, and x^3/3!, and the general term is x^(n+1)/(n+1)!.
d) To write g(x) in terms of a familiar function without using series, we can use the fact that the Maclaurin series for e^x is 1 + x/1! + x^2/2! + x^3/3! + ...:
g(x) = x + x^2/2! + x^3/3! + ... = x*(1 + x/1! + x^2/2! + x^3/3! + ...) = x*e^x
Then, we can write f(x) in terms of the same familiar function by dividing both sides of the equation by x:
f(x) = g(x)/x = (x*e^x)/x = e^x
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Toby picks a 6-digit number.
It is larger than 599,999 and it is a multiple of 5.
How many different numbers could he have picked?
Answer:
80,000 numbers.
Step-by-step explanation:
Since the number is 6-digits and is larger than 599,999, it would be between 600,000 and 999,999.
Between those two numbers (included), there are \(999999 - 600000 = 399999\) numbers.
In addition, we know that the number is a multiple of 5. Therefore, we should divide this number by 5 to find how many of the numbers in that group are divisible by 5.
Since it's difficult dividing 399,999 by 5, I would divide 400,000 by 5, as we must also include 600,000.
\(\frac{400000}5 = 80000\)
Which graph best represents y=-4(x+3)-2
The graph of equation y=-4(x+3) - 2 is as shown below.
In this question we have been given an equation y=-4(x+3) - 2
We need to graph an equation y=-4(x+3) - 2
For x = 0,
y = -4(0+3) - 2
y = -14
For x = 1,
y = -4(1+3) - 2
y = -18
For x = -1,
y = -4(-1+3) - 2
y = -10
The line y=-4(x+3) - 2 passes through points (0, -14), (1, -18) and (-1, -10)
The graph of equation y=-4(x+3) - 2 is as shown below.
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(A) Use contour integration to evaluate the integral cos20 -do, [. a²+6²-2abcose where b> a > 0.
Answer: The final answer is:\(`I = -2π / [ab (a² + b² - 2abcos(t))^(1/2)]`\)
Explanation: We have to use contour integration to evaluate the integral cos20 -do, [. a²+6²-2abcose where b> a > 0.
Let \(f(z) = cos(20 - z) / [a² + b² - 2abcos(z - 6)] .\)
The denominator in the integral looks like\(cos(z - 6) = Re(e^(i(z-6)) ).\)
Therefore, we have \(cos(20 - z) = Re(e^(i(20 - z)))\)
Thus, we can write the integral as follows: `I = ∮ |z|=1 f(z) dz `
By Cauchy's Residue Theorem, the integral of f(z) over any closed curve in the complex plane is equal to `2πi` times the sum of residues of f(z) at its poles within the curve.
If we use the parametrization \(`z = 6 + b/a + re^(it)`\) with `0 <= t <= 2π`, then the integral becomes:
\(`I = -i ∫ 0^{2π} dt (a² + b² - 2abcos(t) ) / [ a² + b² - 2abcos(t) + 2ib(asin((r/a)sin(t-θ))]`\)
This integral can be computed using the residue theorem. If we define
\(`g(z) = 1 / [ a² + b² - 2abcos(t) + 2ib(asin((r/a)sin(t-θ))]`,\)
then the residue of g(z) at `z = 6 + b/a + i(asin((r/a)sin(t-θ))` is given by:
\(`Res(g, z) = lim_{z->6+b/a+i(asin((r/a)sin(t-θ)))} (z - (6 + b/a + i(asin((r/a)sin(t-θ))))) g(z) / [a² + b² - 2abcos(t)]`\)
We can compute this residue using L'Hopital's Rule.
After some algebraic manipulation, we can show that the residue is:\(`Res(g, z) = -1 / [ab (a² + b² - 2abcos(t))^(1/2)]`\)
Hence, by the residue theorem, we have: \(`I = -2πi / [ab (a² + b² - 2abcos(t))^(1/2)]`\)
Therefore, the final answer is:\(`I = -2π / [ab (a² + b² - 2abcos(t))^(1/2)]`\)
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what is the domain of the graph in set Notation?
a) Calculate the size of angle x in the diagram
below.
b) Work out the bearing of A from B.
The angle x in the diagram is 98 degrees.
How to find the angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.
Therefore, let's find the angle of x using the angle relationships as follows:
The size of the angle x can be found as follows:
82 + x = 180(same side interior angles)
Same side interior angles are supplementary.
Hence,
82 + x = 180
x = 180 - 82
x = 98 degrees
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PLEASE HURRY
You have already planted 6 trees today. You plant another t trees.
Which expression represents total trees planted by you?
1. 6t
2. t - 6
3. t + 6
HELP? is this easy or am i ?? HELP
Answer:
6960
Step-by-step explanation:
A teacher has a bag of marbles. there are 10 red, 10 blue, 8 green, 8 purple, and 8
yellow marbles in the bag. as the students enter the classroom, they draw a marble
and keep it. if the first student in the room draws a red, and the second draws a red,
what is the probability that the third student will draw a red?
17%
21%
15%
19%
The probability that the third student will draw a red marble is approximately 19%.
The probability of an event occurring is the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, we are looking for the probability that the third student will draw a red marble given that the first two students drew red marbles.
Initially, there were 10 red marbles out of a total of 44 marbles (10 red + 10 blue + 8 green + 8 purple + 8 yellow). After the first two students drew red marbles, there are now 8 red marbles remaining, and the total number of marbles in the bag has decreased to 42.
To find the probability of the third student drawing a red marble, we will calculate the ratio of red marbles to the total number of marbles:
Probability = (Number of red marbles) / (Total number of marbles) = 8/42 ≈ 0.1905
Multiplying this result by 100 gives us the probability as a percentage:
Probability ≈ 0.1905 * 100 = 19.05%
So, the probability that the third student will draw a red marble is approximately 19%.
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of the 75 entries in a costume contest, 31 entrants were dressed as heroes and 31 entrants were wearing a mask. if 15 entrants were dressed as heroes wearing a mask, how many entrants were neither dressed as heroes nor wearing a mask?
The 75 entries in a costume contest, 31 entrants were dressed as heroes and 31 entrants were wearing a mask. 8: No masks or costumes were worn by contestants .
What is Probability?The possibility of an event occurring is described by the concept of probability. In real life, we frequently have to make predictions about the future. We might know about the result of an occasion.
We declare that there is a possibility that the event will take place when this occurs.
In conclusion, probability can be used in a lot of great ways in business, entertainment, and this new area of artificial intelligence.
By simply dividing the total number of possible outcomes by the favorable number, the probability of an event can be calculated using the probability formula.
n(A)=31 and n(B) = 20 and n(AB) =9
50-42 = 8
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how is the answer 4??
Answer:
see below
Step-by-step explanation:
log sqrt5 (25) = y
we know that loga (b) = c can be rewritten as a^c = b
sqrt(5) ^ y = 25
Rewriting sqrt(5) as 5^1/2 and 25 as 5^2
5^1/2 ^ y = 5^2
we know a^b^c = a^ (b*c)
5 ^ 1/2y = 5^2
1/2y = 2
y = 4
Which expression is equivalent to square root of 80
Answer: 2nd one down
Step-by-step explanation:
how do i solve for x?
Answer:
x = 15°
Step-by-step explanation:
angle S is 90° (right-angle) since RS is tangent to circle and S is a point on the circle.
angles in triangle add up to 180°.
so angle x must be 180 - 90 - 75 = 15°.
a(n) is an unusually small or unusually large data value. a. z-score b. median c. sample statistic d. outlier
The answer is outlier. a value in a set of data that "lies outside" (is much smaller or greater than) the majority of the other values.
what is sample statistic?Any figure derived from your sample data is referred to as a sample statistic (or simply a statistic). The sample mean, median, sample SD, and percentiles are a few examples. A statistic is a random variable since it is based on information gained by random sampling, which is a random experiment.
How come we employ sample statistics?A sample is a statistical term for a population that has been analytically subset. As a result of the usage of samples, investigations may be completed faster and with more manageable data.
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The correct equation of the line that passes through ( -8.5) and is perpendicular to y = 4x + 2 is...
Answer:
u need to substitute (-8,5) in the equation because the line passses through that point
Plssss help me :( ASAP
Mariah is planting a rectangular rose garden. In the center of the garden, she puts a smaller rectangular patch of grass. The grass is 2 feet by 3 feet. What is the area of the rose garden?
The area of the rose garden is 129 sq. ft.
Consider the following diagram.
The dimensions of the rectangular garden:
length = 15 ft and width = 9 ft
Using the formula for the area of rectangle,
The area of the rectanguler garden would be,
A₁ = 15 × 9
A₁ = 135 ft²
In the center of the garden, she puts a smaller rectangular patch of grass. And the dimensions of the grass is 2 feet by 3 feet.
The area of rectangular patch is:
A₂ = 2 × 3
A₂ = 6 ft²
So, the area of the rose garden would be,
A = A₁ - A₂
A = 135 - 6
A = 129 ft²
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