Given data: Outcome 0 1 2 Probability 0.26 0.35 0.39a)
The mean of the distribution is given by: Mean = $\sum x P(x)$The distribution can be represented as follows:
Outcome(x) Probability(P(x)) x P(x) 0 0.26 0 1 0.35 0.35 2 0.39 0.78 $\sum x P(x)=0+0.35+0.78=1.13$
Therefore, Mean = $\frac {\sum xP(x)}{n}=\frac {1.13}{3} =0.3767 ≈ 0.377$ (rounded to three decimal places)
b) The formula for standard deviation is given as: $$\sigma =\sqrt{\sum(x-\mu) ^2P(x)} $$where $\mu$ is the mean of the distribution
Substituting the given values in the above formula, we get:
\begin{align*}\sigma &=\sqrt{\sum(x-\mu) ^2P(x)} \\\sigma &=\sqrt{\sum(x-0.377) ^2P(x)} \end{align*} Outcome(x) Probability(P(x)) $x-μ$ $P(x)(x-μ)^2$ 0 0.26 -0.37746 0.03665 1 0.35 -0.02746 0.00076 2 0.39 1.01254 0.15709 Total 1 0.19450$$\sigma =\sqrt {0.1945}=0.441 ≈ 0.441$$
Therefore, the standard deviation of the distribution is approximately equal to 0.441 (rounded to three decimal places).
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Solve the following recurrence relations (a) [6pts] an = 3an-2, Q1 = 1, 42 = 2. b) [6pts] an = an-1 + 2n – 1,01 = 1, using induction (Hint: compute the first few terms, = pattern, then verify it).
a) an = 3(n-2) if n is even and an = 3(n-3) if n is odd
b) It is proved that an = n².
a)Given recurrence relation is an = 3an-2, Q1 = 1, Q2 = 2.
We have to find an in terms of n.
Step 1: Finding the pattern
Let us find the values of a1, a2, a3 and a4 a1 = Q1 = 1, a2 = Q2 = 2, a3 = 3, a1 = 3, a4 = 3a2 = 3 x 2 = 6
Let us represent it as a table
Step 2: Writing the general expression
The sequence obtained is an = 1, 2, 6, 18, 54, …We can see that an = 3an-2
If n is even, then an = 3(n-2)
If n is odd, then an = 3(n-3)
Step 3: Writing the final expression
The general expression of an is as follows:
an = 3(n-2) if n is even and an = 3(n-3) if n is odd
b) Given recurrence relation is an = an-1 + 2n – 1, a1 = 1, using induction
Let us prove that an = n² by induction
Step 1: Verification of base case
When n = 1an = a1 = 1
We have to prove that a1 = 12 an = n2 = 1
Therefore, the base case is verified.
Step 2: Let us assume that an = n2 is true for some k such that k > 0i.e., ak = k² (Inductive Hypothesis)
Step 3: Let us verify that an = n2 is true for n = k+1i.e., prove that ak+1 = (k+1)²
Using the recurrence relation given, we haveak+1 = ak + 2k+1 – 1 = k2 + 2k + 1 = (k+1)²
Therefore, the proof is complete. It is proved that an = n².
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Two numbers are randomly selected from the following set without replacement.
{3, 16, 2, 11, 15, 6, 14, 7, 10, 1}
a. What is the probability that they are both even?
b. What is the probability that they are both prime? Note: 1 is not prime.
c. What is the probability of the sum of the two numbers being even?
d. What is the probability of the product of the two numbers being odd?
The last two problems are based on a single draw from the set.
e What is the probability that a prime number was drawn from the set, given that it
is an odd number.
f. What is the probabilityselected from the set. that a prime number was drawn from
the set, given that it is an even number.
Answer:
I dot know good luck
Step-by-step explanation:
The mass of a sheep is about 6X10^1 kg. The mass of an ant is about 3X10^-3 kg. About how many times more mass does a sheep have than an ant?
Answer:
Given that average mass of an ant grams.
Given that average mass of a giraffe Kilograms.
Now we have to find about how many times more mass does a giraffe have than an ant. Before carring out any comparision, we must make both units equal.
Like convert kilogram into gram or gram into kilogram.
I'm going to convert kilogram into gram using formula
1 Kg = 1000 g
So the average mass of a giraffe grams.
Now we just need to divide mass of giraffe by mass of ant to find the answer.
=666666666.667
Hence final answer is which is approx 666666666.667.
Hope this Helps!
Write the following permutation as a product of disjoint cycles and thereafter as a product of transpositions 1 2 3 4 5 6 7 8 8 2 6 3 7 4 5 1 (62848X)
The given permutation (62848X) can be expressed as the product of disjoint cycles as (1 6 2 8 4) and as the product of transpositions as (1 6)(6 2)(2 8)(8 4).
To express the given permutation (62848X) as a product of disjoint cycles, we start by examining each element and its corresponding image under the permutation.
1 maps to 6.
6 maps to 2.
2 maps to 8.
8 maps to 4.
4 maps to 8 (since X represents a fixed point, meaning it remains unchanged).
Now, let's write these mappings as disjoint cycles:
(1 6 2 8 4)
The cycle notation indicates that 1 maps to 6, 6 maps to 2, 2 maps to 8, 8 maps to 4, and 4 maps back to 1.
Next, we'll express this permutation as a product of transpositions. A transposition swaps two elements.
We can achieve this by breaking down the cycle (1 6 2 8 4) into transpositions:
(1 6)(6 2)(2 8)(8 4)
Each pair of adjacent elements within the cycle forms a transposition. For example, (1 6) represents the transposition that swaps 1 and 6, (6 2) swaps 6 and 2, and so on.
Thus, the given permutation (62848X) can be expressed as the product of disjoint cycles as (1 6 2 8 4) and as the product of transpositions as (1 6)(6 2)(2 8)(8 4).
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Pls help me guysss !!!!
Answer:
First answer choice
Step-by-step explanation:
Answer:
The answer would be A
Step-by-step explanation:
Need help with this question thank you!
Answer:
Step-by-step explanation:
(5,3) should be your slope. Start from the bottom of the line and go up. Use the X axis slope 1st because of the x1 y1 coordinates.
Answer:
(5,-1)
(-4,0)
Step-by-step explanation:
5 is in the X axis
-1 is in the Y axis
-4 is in the Y axis
0 is in the X axis
According to the central limit theorem, which of the following statements is true?
a. The distribution of the sum (or average) of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution.
b. The center of a distribution is limited to move no more than 1.5 standard deviations (also known as the 1.5 sigma shift).
c. The center of dispersion of a sample (
) is limited by the size of the sample.
d. The central tendency of a distribution is limited by common-cause variation.
The central limit theorem,option (A) is correct
According to the central limit theorem, the following statement is correct:
a. Regardless of the underlying distribution, the distribution of the sum (or average) of a large number of independent variables with identical distributions will be approximately normal.
Regardless of the original distribution's shape, the central limit theorem states that independent and identically distributed variables tend to approximate a normal distribution when added together or averaged. We are able to draw conclusions about the parameters of the population based on the statistics of the sample because this is one of the fundamental principles of statistical inference.
The central limit theorem is unrelated to the other statements (b, c, and d). Statements b, c, and d all refer to common-cause variation rather than the central limit theorem, while statement d does not accurately describe the central limit theorem.
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Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: , where "h" is the height in feet and "x" is the horizontal distance in feet from the diving board. 1) How high is the diving board? 2) How deep does the diver dive into the water? 3) At what horizontal distance from the board does the diver enter the water? 4) At what horizontal distance from the board does the diver come to the surface of the water after the dive?
Answer:
1. 6 feet
2. 6.25 feet
3. 1 feet
4. 6 feet
Step-by-step explanation:
The equation is : [tex]$h(x)=x^2-7x+6$[/tex]
1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.
So, substituting x = 0 in the equation, we get
[tex]$h(0)=0^2-7(0)+6$[/tex]
[tex]$=0-0+6$[/tex]
[tex]$=6$[/tex]
So, the diving board is 6 feet above the surface of the water.
2. From the equation, we known that it is a parabola and the vertex is minimum.
It is the minimum height which represents the depth Kendra dives into the water.
So the [tex]$x$[/tex] coordinate of the vertex is = [tex]$\frac{-b}{2a}$[/tex]
Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,
a = 1 and b = -7
∴ x coordinate = [tex]$\frac{-(-7)}{2 \times 1} $[/tex]
[tex]$\frac{7}{2}=3.5$[/tex]
Now substituting to find f(x),
[tex]$h(3.5)=(3.5)^2-7(3.5)+6$[/tex]
= -6.25
Therefore, the diver dives 6.25 feet below the water surface.
3. The horizontal distance from the board the diver enters into the water.
This is the y-intercept and it is the value of x when h(x)=0.
∴ [tex]$0=x^2-7x+6$[/tex]
Factorizing, we get [tex]$(x-1)(x-6)=0$[/tex]
∴ [tex]$x=1 \text{ or}\ x=6$[/tex]
So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.
4. We know that the equation given has [tex]$\text{two}$[/tex] x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height [tex]$h(x)=0$[/tex]. The height is the water surface level.
The first x intercept represents the points where Kendra dives into the water.
And the second x intercept is the point where Kendra comes out of the water surface. This this is [tex]$x=6$[/tex] for [tex]$h(x)=0$[/tex].
Thus Kendra dives out of the water surface at 6 feet from the board.
i just don’t understand
Answer:
the answer is 9
Step-by-step explanation:
An analyst studied the average savings of recent college graduates. The results of the study reveal the following: n=40, sample mean = $16,000, sample standard deviation = $5,000. The probability that a randomly selected recent graduate has savings of $18,000 or more is closet to Hint: You need to calculate a z-score and remember to use the standard error in your calculations more than 5% less than 1% about 95% about 68%.
If The results of the study reveal that n=40, sample mean = $16,000, and sample standard deviation = $5,000 then the probability is about 65.54%.
To calculate the probability that a randomly selected recent graduate has savings of $18,000 or more, we first need to calculate the z-score using the formula z = (x - μ) / σ, where x is the value we're interested in, μ is the mean, and σ is the standard deviation. In this case, x = $18,000, μ = $16,000, and σ = $5,000.
Substituting these values into the formula, we get z = (18,000 - 16,000) / 5,000 = 0.4.
Next, we can use a z-table or calculator to find the corresponding probability.
Looking up the z-score of 0.4 in the z-table, we find that the probability is approximately 0.6554, or about 65.54%.
Therefore, the probability that a randomly selected recent graduate has savings of $18,000 or more is approximately 65.54%.
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express the magnitude of the average induced electric field, e , induced in the loop in terms of δφ , r and δt .
The magnitude of the average induced electric field, e, in a loop can be expressed in terms of δφ, r, and δt.
When a magnetic field changes within a loop, it induces an electric field according to Faraday's law of electromagnetic induction. The magnitude of the average induced electric field, e, can be determined by the change in magnetic flux δφ, the radius of the loop r, and the change in time δt. The magnetic flux is a measure of the total magnetic field passing through the loop and is given by the product of the magnetic field strength and the area of the loop. As the magnetic field changes, the magnetic flux through the loop changes, leading to an induced electric field. The magnitude of this induced electric field is directly proportional to the rate of change of the magnetic flux, which is δφ/δt. Additionally, the magnitude of the induced electric field is inversely proportional to the radius of the loop, meaning a smaller radius will result in a stronger induced electric field. Therefore, the magnitude of the average induced electric field, e, can be expressed as e = (δφ/δt) / r.
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Write an equation in point slope form that is parallel to AB with endpoints A (2, -1) and B (4, 5) that goes through the point (1.5, 4)
Answer:
[tex]y = 3x - 0.5[/tex]
Step-by-step explanation:
Given
Goes through
[tex]C = (1.5,4)[/tex]
Parallel to AB
[tex]A = (2,-1)[/tex]
[tex]B = (4,5)[/tex]
Required
Determine the line equation
First, calculate the slope of AB
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{5--1}{4-2}[/tex]
[tex]m = \frac{6}{2}[/tex]
[tex]m = 3[/tex]
The line is said to be parallel to AB. This implies that their slopes are equal.
The equation of the line is then calculated as:
[tex]y = m(x - x_1) + y_2[/tex]
Where:
[tex](x_1,y_1) = (1.5,4)[/tex]
So:
[tex]y = 3*(x - 1.5) + 4[/tex]
[tex]y = 3x - 4.5 + 4[/tex]
[tex]y = 3x - 0.5[/tex]
Find the parametric equations for the circle with radius 4 and centered at (-3,4) circle traced clockwise starting at (-3,0). include the domain.
The parametric equations for the circle with radius 4 and centered at (-3,4), traced clockwise starting at (-3,0), are x = -3 + 4cos(t) and y = 4 + 4sin(t), where t is the parameter representing the angle of rotation. The domain for these equations is 0 ≤ t ≤ 2π.
To obtain the parametric equations for the circle, we start by considering the general equation of a circle centered at (h,k) with radius r:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
In this case, the circle is centered at (-3,4) and has a radius of 4, so the equation becomes:
[tex](x + 3)^2 + (y - 4)^2 = 16[/tex]
To represent the circle parametrically, we can use the trigonometric functions cosine and sine to describe the x and y coordinates, respectively. We can rewrite the equation as:
(x + 3) = 4cos(t)
(y - 4) = 4sin(t)
Simplifying, we obtain:
x = -3 + 4cos(t)
y = 4 + 4sin(t)
These equations describe the x and y coordinates of points on the circle as a function of the angle t. The parameter t represents the angle of rotation around the circle. To trace the circle clockwise, we need to assign decreasing values to t. The domain for t is 0 ≤ t ≤ 2π, which corresponds to a full revolution around the circle.
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List three examples of aa variable costs
Answer:
utility cost, direct labor costs, cost of raw materials used in production
researcher created three groups based on participants BMI: normal weight, overweight and obese. The hypothesis being tested is that the three groups differ in the mean number of artificially sweetened drinks consumed weekly. Which statistical test might the researcher use, assuming a reasonable normal distribution of values?
A repeated measures ANOVA
An independent group t test
One way ANOVA
A chi-squared test
To test the hypothesis of mean differences in artificially sweetened drink consumption among BMI groups, assuming a normal distribution, the researcher might use a one-way ANOVA.
The one-way ANOVA compares the means of three or more independent groups and determines if there are statistically significant differences among them. In this case, the BMI groups (normal weight, overweight, and obese) represent the independent groups, and the number of artificially sweetened drinks consumed is the dependent variable. By conducting a one-way ANOVA, the researcher can assess if there are significant differences in mean consumption among the BMI groups and draw conclusions regarding their hypothesis.
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Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
[tex]15c - 1[/tex]
Step-by-step explanation:
[tex]3(5c + 3) - 10[/tex]
Apply the distributive property.
[tex]3(5c) + 3 \times 3 - 10[/tex]
Multiply 5 by 3.
[tex]15c + 3 \times 3 - 10[/tex]
Multiply 3 by 3.
[tex]15c + 9 - 10[/tex]
Subtract 10 from 9.
[tex]15c - 1[/tex]
Hope it is helpful....Which measurements are less than 475 inches?
Consider the set F of continuous functions f with the property that f'(2) = 0. a. Name a larger real vector space we've studied this semester that F is a subset of. b. Prove whether F is a subspace of the vector space you named in part a. C. We learned this semester that if something is a subset of a known vector space, we only need to check two axioms instead of 10. Explain why we can get away with not checking the other 8 axioms. Don't just quote the rule we learned-try to explain the logic behind it. d. Why was it not ok to only check the two subspace axioms on problem 8 from exam 2? Why wasn't it a subspace?
The set in problem 8 was not a subspace because one of the subspace axioms requires that the zero vector, which is the additive identity element, is included in the set. In the given problem, the zero vector was not part of the set, so it failed to satisfy this axiom
a. The set F is a subset of the vector space of continuous functions on some interval, which we have studied this semester.
b. To prove whether F is a subspace of the vector space of continuous functions, we need to check if F satisfies the three subspace axioms: closure under addition, closure under scalar multiplication, and the zero vector property.
Let f and g be two functions in F, and let c be a scalar. To show closure under addition, we need to prove that f + g is also in F. Since both f and g have the property that f'(2) = 0 and g'(2) = 0, their sum (f + g) will also have the property that (f + g)'(2) = f'(2) + g'(2) = 0 + 0 = 0. Therefore, f + g is in F.
To show closure under scalar multiplication, we need to prove that cf is also in F. Again, since f has the property that f'(2) = 0, multiplying f by any scalar c will not change the derivative at 2. Therefore, (cf)'(2) = c × f'(2) = c × 0 = 0, and cf is in F.
Finally, the zero vector property states that the zero function, denoted as 0, must be in F. The zero function has the property that its derivative is always zero, including at 2. Therefore, 0'(2) = 0, and the zero function is in F.
Since F satisfies all three subspace axioms, we can conclude that F is a subspace of the vector space of continuous functions.
c. We can get away with not checking the other eight axioms (associativity, commutativity, distributivity, etc.) because F is a subset of a known vector space. By being a subset of a vector space, F inherits those axioms from the larger vector space. The other eight axioms are properties of vector spaces that hold true for all vectors in the larger vector space, including the vectors in F. Therefore, if F satisfies the subspace axioms, it automatically satisfies the other eight axioms by virtue of being a subset of a vector space.
d. It was not okay to only check the two subspace axioms on problem 8 from exam 2 because the set in that problem did not satisfy the zero vector property. One of the subspace axioms requires that the zero vector, which is the additive identity element, is included in the set. In the given problem, the zero vector was not part of the set, so it failed to satisfy this axiom. As a result, the set in problem 8 was not a subspace.
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Which null distribution is used for a hypothesis test of a single population proportion? Select one: O a. t-distribution with df = n - 1 O b. standard normal distribution O c. t-distribution with df = n1 + n2 – 2
The null distribution used for a hypothesis test of a single population proportion is the standard normal distribution. The correct answer is b).
When conducting a hypothesis test for a single population proportion, we use the standard normal distribution as the null distribution. This is based on the assumption that the sampling distribution of the sample proportion follows a normal distribution when the sample size is sufficiently large.
The hypothesis test for a single population proportion involves comparing the observed sample proportion to the hypothesized population proportion. We calculate the test statistic, which is the standard error of the sample proportion under the null hypothesis, divided by its standard deviation.
Since the test statistic follows a normal distribution under the null hypothesis, we compare it to critical values from the standard normal distribution to determine the p-value and make a decision regarding the null hypothesis.
Therefore, correct option is B.
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an object is traveling on a circle with a radius of 5 cm. if in 20 seconds a central angle of 1/3 radian is swept out, what is the angular speed of the object? what is the linear speed?
arrange into ascending order 1/3,3/4,1/2
Answer:
1/3, 1/2, 3/4
Step-by-step explanation:
Mr. Johnson drove 4 1/3 miles on Monday and 5 1/2 miles on Tuesday, How many miles did Mr. Johnson drive altogether?
Answer:
9 [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Find the slope of the line
Help ASAP ASAP please please help ASAP ASAP please please help please
Answer:
XY = 9
Step-by-step explanation:
Similar polygons have corresponding sides with proportional lengths.
WX/AB = XY/BC
12/8 = XY/6
8XY = 12 * 6
8XY = 72
XY = 9
Can someone please help
okay sorry
Step-by-step explanation:
i just wanted point
simplify this number 27:81
Answer:
I believe the simplified form of this ratio is 1:3
*The common factor to both numbers is 27.
27÷27=1 and 81÷27=3
So, that's where the 1:3 came from
Angle 5 Has what angle
A.alternate interior angle
B.alternate exterior angle
C.same side interior angle
wildlife biologists believe that the weights of adult trout can be described by a normal model with a standard deviation of 1.2 pounds. if only 7% of adult trout weigh more than 5 pounds what is the mean weight (in pounds) of adult trout?
The mean weight of adult trout is 3.224 pounds is the answer.
Given, A normal model is used to describe the weights of adult trout, with a standard deviation of 1.2 pounds. It is known that only 7% of adult trout weigh more than 5 pounds.
To calculate the mean weight (in pounds) of adult trout, the following steps need to be followed:
Step 1: Find the z-score for the given percentage value.
The z-score formula is given by: z = (x - μ) / σ where x is the value of the variable, μ is the mean, and σ is the standard deviation.
Step 2: Once we have the z-score, we can find the corresponding value of x using the z-score table.
We need to find the z-score corresponding to the 93rd percentile as only 7% of the trout weigh more than 5 pounds.z = (x - μ) / σ
For a one-tailed distribution with α = 0.07, the z-score is 1.48, approximately.
Therefore, we have1.48 = (5 - μ) / 1.2Multiplying both sides by 1.2, we get1.776 = 5 - μ
Subtracting 5 from both sides, we getμ = 5 - 1.776μ = 3.224
Therefore, the mean weight of adult trout is 3.224 pounds.
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Mr. White is renting an oversized truck for one week and a few additional days d. He does not have to pay a per mile fee. Evaluate the expression 325+100d to find how much he will pay for a 13-day rental. Each day = $100
Answer:
$1,625
Step-by-step explanation:
Given:
Total cost = 325 + 100d
Where,
325 = fixed cost
100 = cost per day
d = number of days
Find the total cost when d = 13 days
Total cost = 325 + 100d
= 325 + 100d
= 325 + 100(13)
= 325 + 1,300
= 1,625
Total cost = $1,625
What is the domain and range of this graph?
(Pls don’t answer if you don’t know I rly need help<3 )
Answer:
Domain is all real numbers. Range is [36- negative infinity]