Calculation of p-value: area beyond the test statistic in tails of Gaussian distribution; two-tailed test needs both tails, one-tailed test needs only alternative hypothesis tail.
To derive an expression for computing the p-value for the test in terms of the standard Gaussian CDF, we first need to understand what a p-value represents. A p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the data, assuming the null hypothesis is true. For a two-tailed test, we can calculate the p-value as the area in the tails of the standard normal distribution beyond the absolute value of the test statistic. This can be expressed mathematically as:Learn More About Right Tailed Test: https://brainly.com/question/30465749
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2. sketch the final figure if you combine the first 100 figures. you do not need to draw every square. how many squares would you have drawn if you drew it like the others?
Drawing every single square may not be necessary, as you can use the pattern of the previous figures to predict the placement of the squares in the final figure. This can save time and effort, while still achieving the desired outcome.
To answer your question, if you were to combine the first 100 figures, you would end up with a much larger figure consisting of 100 squares in each row and column, resulting in a total of 10,000 squares. However, you do not need to draw every square to sketch the final figure.
To sketch the final figure, you would start by drawing a square grid of 100 squares in each row and column, similar to the previous figures. Then, you would need to fill in the squares based on the pattern of the previous figures.
Assuming you drew each square in the previous figures, combining the first 100 figures would result in drawing a total of 100 x 100 x 100 squares, which equals 1,000,000 squares. This is because each figure consists of 100 squares, and there are 100 figures being combined.
However, drawing every single square may not be necessary, as you can use the pattern of the previous figures to predict the placement of the squares in the final figure. This can save time and effort, while still achieving the desired outcome.
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find the area of the parallelogram determined by the points p(7, -5, 5), q(-7, 2, -2),r(10, 1, 3) and s(-4, 8, -4).
Area = 0.5 * |PQ x PR| = 0.5 * sqrt(12475) ≈ 55.93 square units.
To find the area of the parallelogram determined by these points, we need to find the cross product of the vectors formed by two adjacent sides of the parallelogram. Let's choose vectors PQ and PS:
Vector PQ = (-7 - 7, 2 - (-5), -2 - 5) = (-14, 7, -7)
Vector PS = (-4 - 7, 8 - (-5), -4 - 5) = (-11, 13, -9)
The cross product of these two vectors is:
(-7)(-9) - (-7)(13), (-2)(-9) - (-14)(-9), (-2)(13) - (-14)(-11)
= (-14, 126, -30)
The magnitude of this vector gives us the area of the parallelogram:
|(-14, 126, -30)| = sqrt(14^2 + 126^2 + (-30)^2) = sqrt(17308) ≈ 131.6
Therefore, the area of the parallelogram determined by the given points is approximately 131.6 square units.
To find the area of the parallelogram determined by the points P(7, -5, 5), Q(-7, 2, -2), R(10, 1, 3), and S(-4, 8, -4), we can use the cross product of the vectors PQ and PR.
First, let's find the vectors PQ and PR:
PQ = Q - P = (-7-7, 2-(-5), -2-5) = (-14, 7, -7)
PR = R - P = (10-7, 1-(-5), 3-5) = (3, 6, -2)
Next, find the cross product of PQ and PR:
PQ x PR = (7*(-7) - (-7)*6, (-14)*(-2) - 3*(-7), (-14)*6 - 7*3) = (-49+42, 28+21, -84-21) = (-7, 49, -105)
Now, calculate the magnitude of the cross product:
|PQ x PR| = sqrt((-7)^2 + 49^2 + (-105)^2) = sqrt(49 + 2401 + 11025) = sqrt(12475)
The area of the parallelogram is half the magnitude of the cross product:
Area = 0.5 * |PQ x PR| = 0.5 * sqrt(12475) ≈ 55.93 square units.
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A sequence in which the ratio between the subsequent terms is the same is called a geometric progression.
The general term of a G.P. is: a =arn-1 The sum of the infinite terms of a G.P. is:
The sum of the infinite terms of a G.P. is (aᵣ / (1 - r))
A geometric progression (G.P.) is a sequence where each term is obtained by multiplying the preceding term by a constant ratio. The general term of a G.P. is given by the formula aₙ = aᵣ(r)^(n-1), where aᵣ is the first term and r is the common ratio.
The sum of infinite terms of a G.P. can be calculated using the formula Sₙ = a(1 - rⁿ) / (1 - r), where Sₙ is the sum of the first n terms of the G.P., a is the first term, and r is the common ratio.
As n approaches infinity, rⁿ approaches zero if the value of r is less than one. Hence, we can write the formula for the sum of infinite terms of a G.P. as S = a / (1 - r), provided that the value of r is less than one.
Therefore, the main answer can be written as the sum of the infinite terms of a G.P. is (aᵣ / (1 - r)), where aᵣ is the first term, and r is the common ratio.
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[ 1 2 1 ]
Find the matrix E that converts A = [ 0 3 5 ] to triangular form EA = U.
[ 3 6 7 ]
The matrix E that converts A to triangular form EA = U is: [ 1 0 0 ] [ 3 -1 0 ] [ -5/2 7/2 -1/2 ]
To convert matrix A to triangular form, we need to perform row operations on A until we have a matrix U with all zeros below the diagonal. These row operations can be represented by an elementary matrix E. To find E, we perform the same row operations on the identity matrix I to get E.The first step is to subtract 3 times the first row from the second row to eliminate the 3 in the (2,1) position:Learn More About Matrix: https://brainly.com/question/11989522
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using any of the rules of natural deduction we’ve learned, prove that following argu- ment is valid: ¬g, ¬k ∴¬(k ∨g)
We have shown that the argument is valid and ¬g, ¬k entails ¬(k ∨ g) using natural deduction.
Here's one possible proof using natural deduction:
Assume k ∨ g
Assume k
The premise ¬k, derive a contradiction: ⊥
Assume g
Derive a contradiction: ⊥
Conclude from above equations, ¬(k ∨ g) by negation introduction
From the premise ¬g and ¬(k ∨ g), conclude ¬(k ∨ g) by modus tollens (¬g → ¬(k ∨ g))
From the premise ¬k and ¬(k ∨ g), conclude ¬(k ∨ g) by modus tollens (¬k → ¬(k ∨ g))
Now, from above, conclude ¬(k ∨ g) by conjunction introduction (¬g ∧ ¬k → ¬(k ∨ g))
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1) The distribution of sample means (for a specific sample size) consists of a. All the scores contained in the sample x b. All the scores contained in the population x C. All the samples means that could be obtained (for the specific sample size) d. The specific sample mean computed for the sample of scores
The distribution of sample means (for a specific sample size) consists of all the sample means that could be obtained (for the specific sample size).
This distribution is created by taking multiple random samples from the population and calculating the mean for each sample. The resulting distribution shows the range of possible sample means and how often they are likely to occur. It does not include all the scores contained in the population or in any one particular sample.
The distribution of sample means (for a specific sample size) consists of c. All the sample means that could be obtained (for the specific sample size). This concept is also known as the sampling distribution of the mean, which represents the distribution of all possible sample means for a given sample size from a population.
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The cylinder shown is sliced vertically through its center. What is the area of the cross-section?
Answer:
The cylinder shown is sliced vertically through its center. What is the area of the c
The area of the cross-section of the cylinder is 142.5 in.sq.
What does mean by a cross-section of any shape?
The cross-section is a mathematical depiction of an object's intersection with a plane along its axis. A cross-section is a shape that results from the cutting of a solid (such as a cone, cylinder, or sphere) by a plane.
For instance, if the base of a cylinder-shaped item is cut by a plane, the resulting cross-section will be a circle. The object has to come into contact with one another. This idea may be used for two-dimensional forms as well as three-dimensional ones, therefore the item need not be in three dimensions.
Given:
The length and radius of a cylinder are 19 inches and 7.5 inches respectively.
Now, the vertical cross-section of a cylinder is a rectangle.
Length = 19 in; Breadth = 7.5 in
Area of cross-section (rectangle) = length * breadth
= 19 * 7.5 ⇒ 142.5 in.sq
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5. In the diagram shown, parallelogram IMP is shown. Diagonal MP is drawn and contains points R and S' such that IR 1 MP and NS I MP. Prove that RM = SP
In parallelogram LMNP the side RM= SP. The proof of the question is given below.
Since LR || MP and NS || MP, we have ∠LMP = ∠RMP and ∠MNP = ∠SNP by alternate interior angles.
Also, since LMNP is a parallelogram, we have LM || NP and LP || MN.
Therefore, we have ∠MLN = ∠MNP and ∠PLN = ∠LMP by alternate interior angles.
Adding these two angles, we get:
∠MLN + ∠PLN = ∠MNP + ∠LMP
2∠PLN = 180° (since LMNP is a parallelogram)
∠PLN = 90°
Similarly, we can show that ∠MLN = 90°.
Therefore, LMNP is a rectangle.
Since MP is a diagonal of the rectangle, we have RM = SP by the property of diagonals of rectangles.
Hence, we have proved that RM = SP.
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The image of the correct question is given in the attachment.
let be the solution of the equation y''-5y' 6y=0 satisfying the conditions y(0)=1 and y'(0)=2 and . find ln(y(1))
The given differential equation y'' - 5y' + 6y = 0 can be factored as (D-2)(D-3)y = 0, where D denotes the derivative operator. Hence, the general solution is y = c1*e^(2x) + c2*e^(3x), where c1 and c2 are constants that depend on the initial conditions.
Using the given initial conditions, we can find c1 and c2 as follows:
y(0) = c1 + c2 = 1
y'(0) = 2c1 + 3c2 = 2
Solving this system of equations, we get c1 = -1 and c2 = 2. Therefore, the particular solution that satisfies the given initial conditions is:
y = -e^(2x) + 2*e^(3x)
To find ln(y(1)), we substitute x = 1 in the above expression:
y(1) = -e^2 + 2*e^3
Taking natural logarithm on both sides, we get:
ln(y(1)) = ln(-e^2 + 2*e^3)
Note that this is an exact value, which cannot be simplified further.
To find the solution of the given differential equation y'' - 5y' + 6y = 0 with initial conditions y(0) = 1 and y'(0) = 2, we will first find the complementary function and then apply the initial conditions to determine the constants.
The given equation is a second-order linear homogeneous differential equation with constant coefficients. We will start by finding the characteristic equation:
r^2 - 5r + 6 = 0
This can be factored as:
(r - 2)(r - 3) = 0
This gives us two roots, r1 = 2 and r2 = 3. Now, we can write the general solution for the differential equation as:
y(x) = C1 * e^(2x) + C2 * e^(3x)
Now, let's apply the initial conditions:
1. y(0) = 1:
C1 * e^(2*0) + C2 * e^(3*0) = 1
C1 + C2 = 1
2. y'(0) = 2:
The derivative of y(x) is:
y'(x) = 2C1 * e^(2x) + 3C2 * e^(3x)
y'(0) = 2C1 * e^(2*0) + 3C2 * e^(3*0) = 2
2C1 + 3C2 = 2
Solving this system of linear equations for C1 and C2, we get:
C1 = 1
C2 = 0
So, the particular solution is:
y(x) = e^(2x)
Now we need to find ln(y(1)):
ln(y(1)) = ln(e^(2*1)) = ln(e^2) = 2
So, ln(y(1)) = 2.
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The average cost for a company to produce x units of a product is given by the function A(x) = 12x+1250/x. Use A (x) to estimate the change in average cost as production goes from 250 units to 251 units. The change in average cost is approximately _____dollars.
The change in average cost is approximately 11.98 dollars.
To estimate the change in average cost as production goes from 250 units to 251 units, we need to calculate the difference between A(251) and A(250).
A(250) = 12(250) + 1250/250 = 300 + 5 = 305
A(251) = 12(251) + 1250/251 = 301.03
Therefore, the change in average cost is approximately:
A(251) - A(250) = 301.03 - 305 = -3.97 dollars (rounded to two decimal places)
So the change in average cost is approximately negative 3.97 dollars.
To estimate the change in average cost as production goes from 250 units to 251 units, we need to find the difference between the average cost at 251 units and the average cost at 250 units using the given function A(x) = 12x + 1250/x.
First, find the average cost for 250 units:
A(250) = 12(250) + 1250/250 = 3000 + 5 = 3005 dollars.
Next, find the average cost for 251 units:
A(251) = 12(251) + 1250/251 ≈ 3012 + 4.98 ≈ 3016.98 dollars.
Now, find the change in average cost:
Change = A(251) - A(250) ≈ 3016.98 - 3005 = 11.98 dollars.
The change in average cost is approximately 11.98 dollars.
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A
Find the slope.
y = 4x - 3
Remember: y = mx + b
m = −3
B
m = 4
C
m = 3
Answer:
4
Step-by-step explanation:
ik how to find slope and yeah
(X-7)(x+3) y intercept
Answer: coordinates of the y-intercept is (0, -21)
Step-by-step explanation:
I'm assuming that you are asking for the coordinates of the y-intercept of the function
f(x)=(x-7)(x+3).
Well the y-intercept occurs when x=0, so plugging this value into f(x) yields f(0)=(-7)(3)=-21.
if you want to be 99onfident of estimating the population mean to within a sampling error of ±3 and the standard deviation is assumed to be 13, what sample size is required?
The required sample size for a 99% confident of estimating the population mean to within a sampling error and the standard deviation are ± 3 and 13 respectively is equals to the 124.60.
We have, to be 99% confident of estimating the population mean. Sampling error = ±3
standard deviations= 13
Level of significance= 0.99
[tex] \frac{ \alpha }{2} = 0.005[/tex]
We have to determine the sample size. The standard error is calculated by dividing the standard deviation by the sample size's square root. It results the precision of a sample mean. Using the formula for 99% confident of estimating the population mean to within a sampling error is [tex]SE = z_{ \frac{ \alpha }{2}}\frac{\sigma}{\sqrt{n}} [/tex]
Using the Z-distribution table, value of Z for 99% confidence interval is 2.576.Plug the known values in above formula, 3 = 2.576(13/√n)
=> 3√n = 33.488
=> n = ( 11.162)² = 124.60
Hence, required size value is 124.60.
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Help I’m completely lost and I’m looking for help
We use a population parameter to make inferences about a sample statistic. True or false , please explain if it is false
False. We use a sample statistic to make inferences about a population parameter. True. We use a population parameter, which is a numerical value.
A parameter represents a characteristic of a population, while a statistic represents a characteristic of a sample drawn from the population. We gather sample data and calculate the statistic to estimate the true population parameter. True. We use a population parameter, which is a numerical value that describes a characteristic of a population, to make inferences about a sample statistic, which is a numerical value that describes a characteristic of a sample. This is the basis of statistical inference, where we use information from a sample to draw conclusions about the larger population from which it was drawn.
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How can you prove that p→(q^r) =(p→q) ^(p→r)?
We have proven that p→(q∧r) is equivalent to (p→q) ∧ (p→r).
How do you prove that p→(q∧r) is equivalent to (p→q) ∧ (p→r)?To Prove that p→(q∧r) is equivalent to (p→q) ∧ (p→r) using the terms you've provided.
Here is a step-by-step explanation:
1. Definition of Implication: We'll use the definition of implication, which states that a→b is equivalent to ¬a ∨ b.
2. Apply Definition to Original Expression: Replace the implications in the original expression p→(q∧r) with their equivalent ¬a ∨ b form:
¬p ∨ (q∧r)
3. Distributive Law: Use the distributive law to expand the expression:
(¬p ∨ q) ∧ (¬p ∨ r)
4. Apply Definition of Implication Backwards: Now, we'll reverse the definition of implication (¬a ∨ b is equivalent to a→b) to convert the expression back into implication form:
(p→q) ∧ (p→r)
So, we have proven that p→(q∧r) is equivalent to (p→q) ∧ (p→r).
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What is the perimeter, in units, of a rhombus if its area is 120 square units and one diagonal is 10 units?
The perimeter of the rhombus is 52 units.
What is Rhombus?A rhombus is a quadrilateral with equal sides in Euclidean plane geometry. A quadrilateral with equal-length sides is also referred to as a "equilateral triangle". A parallelogram has a different shape called a rhombus. A rhombus has equal and parallel opposing sides and angles. A rhombus has equal-length sides and a right angle that divides its diagonal in half.
Let's denote the diagonals of the rhombus as d₁ and d₂, and let's denote its side length as s. The area of the rhombus is given by the formula:
A = (d₁ x d₂) / 2
Since the area is given as 120 square units and one diagonal is 10 units, we can substitute these values into the formula and solve for the other diagonal:
120 = (10 x d₂) / 2
240 = 10 x d₂
d₂ = 24 units
Now we can use the Pythagorean theorem to find the length of the sides of the rhombus:
s = √[(d₁/2)² + (d₂/2)²]
s = √[(10/2)² + (24/2)²]
s = √[25 + 144]
s = 13 units
Since a rhombus has four congruent sides, the perimeter of the rhombus is:
P = 4s = 4 x 13 = 52 units
Therefore, the perimeter of the rhombus is 52 units.
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Use the definition of the Laplace transform to find L{f(t)}. (Write your answer as a function of s.) f(t) = te 6t L{f(t)} = (s > 6) x
The Laplace transform of f(t) = te^(6t) is:
L{f(t)} = ∫[0, ∞] te^(6t) e^(-st) dt
Using integration by parts, we can write:
L{f(t)} = [t * (-1/6) * e^(6t) * e^(-st)]∣[0,∞] + ∫[0, ∞] (1/6) * e^(6t) * e^(-st) dt
Simplifying, we get:
L{f(t)} = [-t/6 + (1/6) * 1/(s-6)]∣[0,∞]
Since the limit as t approaches infinity of t/6 is infinity, the first term in the expression above does not converge. Therefore, we have:
L{f(t)} = (1/6) * 1/(s-6) (for s > 6)
Given f(t) = te^(6t), we can use the definition of the Laplace transform to find L{f(t)}:
L{f(t)} = ∫(from 0 to ∞) f(t) * e^(-st) dt
In our case, f(t) = te^(6t), so the integral becomes:
L{f(t)} = ∫(from 0 to ∞) te^(6t) * e^(-st) dt
To solve this integral, we can combine the exponentials:
L{f(t)} = ∫(from 0 to ∞) te^(t(6-s)) dt
Now, we can use integration by parts to solve the integral:
Let u = t and dv = e^(t(6-s)) dt
Then, du = dt and v = ∫e^(t(6-s)) dt = (1/(6-s))e^(t(6-s))
Applying integration by parts:
L{f(t)} = uv |(from 0 to ∞) - ∫(from 0 to ∞) v du
L{f(t)} = (1/(6-s))te^(t(6-s)) |(from 0 to ∞) - (1/(6-s)) ∫(from 0 to ∞) e^(t(6-s)) dt
Now, we evaluate the limits and the integral:
L{f(t)} = (1/(6-s))[0 - (1/(6-s)) ∫(from 0 to ∞) e^(t(6-s)) dt]
The remaining integral is the Laplace transform of e^(t(6-s)), which is:
(1/(s-(6-s))) = (1/(2s-6))
So, L{f(t)} = (1/(6-s))[0 - (1/(2s-6))]
Finally, L{f(t)} = (1/((6-s)(2s-6)))
Thus, the Laplace transform of f(t) = te^(6t) is L{f(t)} = (1/((6-s)(2s-6))).
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Please help with this math problem!
[tex]x^2/9 + y^2/0 = 1[/tex] is the equation of a vertical line passing through (3,0) and (-3,0).
What is equation?
An equation is a mathematical statement that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
We know that the distance between the center and each focus is equal to c = 3 and the eccentricity is 1.
Let the distance between the center and each vertex be a. Since the eccentricity is given by e = c/a, we have e = 1 = 3/a, which implies a = 3.
Therefore, the semi-major axis is a = 3 and the distance between the center and each focus is c = 3. The semi-minor axis b can be found using the relationship [tex]b^2 = a^2 - c^2[/tex], so we have [tex]b^2 = 3^2 - 3^2 = 0[/tex], which implies b = 0.
Thus, the equation for the ellipse is:
[tex](x - 0)^2/3^2 + (y - 0)^2/0^2 = 1[/tex]
Simplifying this equation, we get:
[tex]x^2/9 + y^2/0 = 1[/tex]
or
[tex]x^2/9 = 1[/tex]
This is the equation of a vertical line passing through (3,0) and (-3,0). Note that since the semi-minor axis is zero, the ellipse is actually a line segment.
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A set of n = 25 pairs of scores (X and Y values) has a Pearson correlation of r = 0.80. How much of the variance for the Y scores is predicted by the relationship with X?Question 15 options:0.36 or 36%0.20 or 20%0.80 or 80%0.64 or 64%
The answer is 0.64 or 64%. The Pearson correlation (r) measures the strength and direction of the relationship between two variables, in this case, X and Y.
To determine the proportion of variance in Y that is predicted by the relationship with X, you need to square the correlation coefficient (r²). In this case, r = 0.80, so r² = 0.80 * 0.80 = 0.64 or 64%. Therefore, 64% of the variance in the Y scores is predicted by the relationship with X. To calculate the amount of variance in Y scores predicted by the relationship with X, we need to square the correlation coefficient (r) which gives us the coefficient of determination (r²).
r² = 0.80² = 0.64
This means that 64% of the variance in Y scores is predicted by the relationship with X.
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Answer:
The answer is 0.64 or 64%. The Pearson correlation (r) measures the strength and direction of the relationship between two variables, in this case, X and Y.
To determine the proportion of variance in Y that is predicted by the relationship with X, you need to square the correlation coefficient (r²). In this case, r = 0.80, so r² = 0.80 * 0.80 = 0.64 or 64%. Therefore, 64% of the variance in the Y scores is predicted by the relationship with X. To calculate the amount of variance in Y scores predicted by the relationship with X, we need to square the correlation coefficient (r) which gives us the coefficient of determination (r²).
r² = 0.80² = 0.64
This means that 64% of the variance in Y scores is predicted by the relationship with X.
Step-by-step explanation:
Evaluate the expression when x=3.
x^2+ 10*x + 24
81
60
86
63
Answer:
[tex]\huge\boxed{\sf 63}[/tex]
Step-by-step explanation:
Given expression:[tex]= x^2+10x + 24[/tex]
Put x = 3
= (3)² + 10(3) + 24
= 9 + 30 + 24
= 63
[tex]\rule[225]{225}{2}[/tex]
Answer:
Option D) 63 is the correct answer.
Step-by-step explanation:
Evaluate :x² + 10x + 24where :
x = 3Solution :[tex] \quad\sf{\dashrightarrow{{x}^{2} + 10x + 24}}[/tex]
Substituting the value of x :
[tex] \quad\sf{\dashrightarrow{{(3)}^{2} + 10 \times 3 + 24}}[/tex]
[tex] \quad\sf{\dashrightarrow{(3 \times 3) + 30 + 24}}[/tex]
[tex] \quad\sf{\dashrightarrow{(9) + 54}}[/tex]
[tex] \quad\sf{\dashrightarrow{9 + 54}}[/tex]
[tex] \quad\sf{\dashrightarrow{63}}[/tex]
[tex]\quad{\star{\underline{\boxed{\sf{\pink{63}}}}}}[/tex]
Hence, the answer is 63.
————————————————Jeremy is going to roll a fair
6
66-sided die
180
180180 times. What is the best prediction for the number of times that Jeremy will roll a number greater than
4
44?
The best prediction for the number of times Jeremy will roll a number greater than 444 is 60060060.
Since the die is fair, each number between 1 and 666 is equally likely to show up on any given roll. The probability of rolling a number greater than 444 is:
(666-444)/666 = 222/666 = 1/3
This means that out of every 3 rolls, we expect one to be greater than 444. Therefore, out of 180180180 rolls, we expect:
180180180/3 = 60060060
rolls to be greater than 444. Therefore, the best prediction for the number of times Jeremy will roll a number greater than 444 is 60060060.
Since the die is fair, each number between 1 and 666 is equally likely to show up on any given roll. The probability of rolling a number greater than 444 is:
(666-444)/666 = 222/666 = 1/3
This means that out of every 3 rolls, we expect one to be greater than 444. Therefore, out of 180180180 rolls, we expect:
180180180/3 = 60060060
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Evaluate the given expression and express the result using the usual format for writing numbers instead of scientific notation) 34^C3 34^C3= _____. Enter your answer in the answer box
I'm sorry, but I cannot provide an answer without more information about the value of "C3". Can you please provide that information?
To evaluate the given expression 34^C3, we need to find the number of combinations of choosing 3 items from a set of 34 items. This can be calculated using the formula:
C(n, r) = n! / (r!(n-r)!)
Here, n = 34 and r = 3. Plugging the values into the formula, we get:
34^C3 = C(34, 3) = 34! / (3!(34-3)!)
= 34! / (3! * 31!)
= (34 * 33 * 32) / (3 * 2 * 1)
= 5984
So, 34^C3 = 5984.
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a study examines the personal goals of children in grades 4, 5, and 6. a random sample of students was selected for each of the grades 4, 5, and 6 from schools in georgia. the students received a questionnaire regarding achievement of personal goals. they were asked what they would most like to do at school: make good grades, be good at sports, or be popular. results are presented in the following table by the sex of the child. boys girls make good grades 192 590 be popular 64 90 be good in sports 188 80 which hypotheses are being tested by the chi-square test? group of answer choices the null hypothesis is that personal goals and sex are independent, and the alternative is that they are dependent. the null hypothesis is that the mean personal goal is the same for boys and girls, and the alternative is that the means differ. the distribution of personal goals is different for boys and girls. the distribution of sex is different for the three different personal goals.
The hypotheses that are being tested by the chi-square test is the null hypothesis is that personal goals and sex are independent, and the alternative is that they are dependent. (option a).
The chi-square test involves formulating two hypotheses: a null hypothesis and an alternative hypothesis. The null hypothesis is the default assumption that there is no relationship between the two variables being studied, while the alternative hypothesis is the opposite of the null hypothesis.
Option a) states that the null hypothesis is that personal goals and sex are independent, and the alternative is that they are dependent. This means that the chi-square test is being used to test whether there is a relationship between the personal goals and the sex of the child.
If the null hypothesis is rejected, it means that there is a statistically significant relationship between the personal goals and the sex of the child.
In conclusion, the chi-square test is used in this study to test whether there is a relationship between the personal goals and the sex of the child. Option a) correctly states the hypotheses being tested.
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a website gets four hits every ten minutes, on average. use a poisson process to model the number of hits. (a) how many hits does the website get per hour, on average?
The website gets, on average, 24 hits per hour.
To answer this question using a Poisson process, we first need to find the average rate of hits per hour. Given that the website gets 4 hits every 10 minutes, we can calculate the average hits per hour by multiplying the hits per 10 minutes by 6 (since there are six 10-minute intervals in an hour).
So, 4 hits/10 minutes * 6 = 24 hits per hour. The Poisson process allows us to model the number of hits as a random variable with an average rate of 24 hits per hour, making it suitable for predicting the number of hits in different time intervals.
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I NEED THIS ASAP
4000KG EQUALS TO BLANK EQUALS TO BLANK TONES
4000 kg is equal to 4 metric tonnes or 4.4 short tons.
We need to convert 4000 kg to tonnes.
Identify the units you need to convert:
In this case, you want to convert 4000 kilograms (kg) to tonnes (t).
Determine the conversion factor:
To convert from kilograms to tonnes, you need to know the relationship between the two units.
1 tonne is equal to 1000 kilograms (1 t = 1000 kg).
Apply the conversion factor:
To convert 4000 kg to tonnes, divide the number of kilograms (4000 kg) by the conversion factor (1000 kg/t):
4000 kg ÷ 1000 kg/t = 4 t
Write the final result:
4000 kg is equal to 4 tonnes.
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laws for the given expression
A.1=A
A.0=0
The algebraic laws for the given expressions are Identity Law and Zero Law
Stating the laws for the expressionsThe algebraic laws for the given expressions are:
A.1 = A: (Identity Law)
This law states that any variable or expression multiplied by 1 remains unchanged. In this case, A multiplied by 1 is still A.
A.0 = 0 (Zero Law)
This law states that any variable or expression multiplied by 0 equals 0. In this case, A multiplied by 0 equals 0.
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Find the volume of the solid that lies under the plane z=x in the first octant that lies between the circles x^2+y^2= 4 and x^2+y^2= 2x. Sketch the solid and the region.
To find the volume of the solid that lies under the plane z=x in the first octant between the two circles [tex]x^2+y^2=4[/tex] and [tex]x^2+y^2=2x[/tex], we need to set up an integral in cylindrical coordinates and integrate over the appropriate region.
First, let's sketch the region in the first octant. The two circles can be represented in cylindrical coordinates as follows:
For the circle [tex]x^2+y^2=4:[/tex]
[tex]r^2 = 4 (since x^2 + y^2 = r^2[/tex] in cylindrical coordinates)
For the circle [tex]x^2+y^2=2x:[/tex]
[tex]r^2 = 2r cos(θ) (since x^2 + y^2 = r^2[/tex]and x = r cos(θ) in cylindrical coordinates)
Setting these two equations equal to each other, we get:
4 = 2r cos(θ)
Solving for r, we get:
r = 2 cos(θ)
This represents the boundary between the two circles in the first octant. The region enclosed between the two circles in the first octant can be represented as 0 ≤ r ≤ 2 cos(θ), 0 ≤ θ ≤ π/2.
Next, we set up the integral for the volume using cylindrical coordinates. The volume element in cylindrical coordinates is given by r dz dr dθ, where r is the radial distance, θ is the angle, and z is the height.
Since z = x in this case, we have z = r cos(θ).
The limits of integration for r and θ are 0 to 2 cos(θ) and 0 to π/2, respectively, as determined by the region we sketched earlier.
The integral for the volume becomes:
V = ∫∫∫ r dz dr dθ
= ∫∫∫ r (r cos(θ)) dr dθ from r=0 to 2cos(θ) and θ=0 to π/2
Now we can integrate with respect to r and θ accordingly:
∫∫∫ r (r cos(θ)) dr dθ
= ∫[0,π/2] ∫[0,2cos(θ)] r^2 cos(θ) dr dθ
Integrating with respect to r first:
= ∫[0,π/2] [tex][(r^3/3)[/tex] cos(θ)] from r=0 to 2cos(θ) dθ
= ∫[0,π/2] (8/3) cos^4(θ) dθ
Finally, integrating with respect to θ:
= (8/3) ∫[0,π/2] [tex]cos^4[/tex](θ) dθ
This integral can be evaluated using trigonometric identities or integration by parts. After evaluating the integral, the result will give us the volume of the solid that lies under the plane z=x in the first octant between the two circles [tex]x^2+y^2=4 and x^2+y^2=2x.[/tex]
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What is the measure?
The measure of the angle FNM is ∠FNM = 73°
How to find the measure?Here we want to find the measure of the angle FNM, and we know the measures of two angles, these are:
∠GNF = 60°
∠MNL = 47°
You can see that:
∠GNF + ∠FNM + ∠MNL = ∠GNL
And GNL is a plane angle, so its measure is 180°, then we can write tehe quation:_
60° + ∠FNM + 47° = 180°
We can solve that to get.
∠FNM = 180° - 60° - 47°
∠FNM = 73°
That is the measure of the angle.
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True or False? using chebyshev's theorem for standard deviation, calculate the percentage of data that lie within five standard deviations of the mean
Using Chebyshev's theorem, at least 96% of the data lies within five standard deviations of the mean.
Let's use Chebyshev's theorem for standard deviation to calculate the percentage of data that lie within five standard deviations of the mean.
Chebyshev's theorem states that at least [tex](1 - \frac{1}{k^2})[/tex] of the data will be within k standard deviations of the mean, where k is the number of standard deviations from the mean. In this case, k = 5.
Calculate the proportion using Chebyshev's theorem formula.
[tex](1 - \frac{1}{k^2}) = (1 - \frac{1}{5^2}) = (1 - \frac{1}{25})[/tex]
Simplify the expression to get the following:
(1 - 1/25) = 24/25
Convert the fraction to a percentage to get:
(24/25) × 100% = 96%
Using Chebyshev's theorem, at least 96% of the data lies within five standard deviations of the mean.
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