a child who is 44.39 inches tall is one standaer deviation above the mean. what percent of children are between 41.25 aand 44.29 inches tall?
Answers
A child who is 44.39 inches tall is one standard deviation above the mean. Approximately 50.58% of children are between 41.25 and 44.29 inches tall.
To find the percentage of children between 41.25 and 44.29 inches tall, we need to calculate the area under the normal distribution curve within this range.
Given that the child's height of 44.39 inches is one standard deviation above the mean, we can infer that the mean height is 44.39 - 1 = 43.39 inches.
Next, we need to determine the standard deviation. Since the child's height of 44.39 inches is one standard deviation above the mean, we know that the difference between the mean and 41.25 inches is also one standard deviation.
Let's denote the standard deviation as σ. We have:
43.39 - 41.25 = σ
Simplifying the equation:
σ = 2.14
Now, we can calculate the percentage of children between 41.25 and 44.29 inches tall using the z-scores.
The z-score formula is given by:
z = (x - μ) / σ
For the lower bound, x = 41.25 inches:
z₁ = (41.25 - 43.39) / 2.14 = -0.997
For the upper bound, x = 44.29 inches:
z₂ = (44.29 - 43.39) / 2.14 = 0.421
We need to find the area under the normal distribution curve between z₁ and z₂. Using a standard normal distribution table or a calculator, we can find the corresponding probabilities.
Let P₁ be the probability associated with z₁, and P₂ be the probability associated with z₂. Then, the percentage of children between 41.25 and 44.29 inches tall is given by:
Percentage = (P₂ - P₁) * 100
Using the z-score table or a calculator, we find that P₁ ≈ 0.1587 and P₂ ≈ 0.6645.
Substituting these values into the formula:
Percentage = (0.6645 - 0.1587) * 100 ≈ 50.58%
Therefore, approximately 50.58% of children are between 41.25 and 44.29 inches tall.
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Related Questions
Verify the geometrical representation ofI) (a+b+c)^2
Answers
Presumably you're talking about a geometrical interpretation of the identity,
(a + b + c)² = a ² + b ² + c ² + 2 (ab + ac + bc)
See the attached sketch for a visual "proof" of it.
Find the curvature of the plane curve y=−2t^4 at the point t=1.
K(1)=?
Answers
To find curvature of a plane curve at a given point, we need to calculate radius of curvature of curve at that point. The formula for the radius of curvature is given by: R =\([(1 + (dy/dx)^2)^(3/2)]/|d^2y/dx^2|\). The curvature of curve \(y=-2t^4\) at point t=1 is K(1) = 1/R = 2/17.
where dy/dx is the slope of the tangent to the curve at the point, and \(d^2y/dx^2\)is the second derivative of y with respect to x. In this case, we have\(y = -2t^4\), so \(dy/dx = -8t^3\) and \(d^2y/dx^2 = -24t^2.\) At t=1, we have dy/dx = -8 and\(d^2y/dx^2 = -24.\) Substituting these values into the formula for R, we get: \(R = [(1 + (-8)^2)^(3/2)]/|-24| = 17/2,\) Therefore, the curvature of the curve\(y=-2t^4\) at the point t=1 is K(1) = 1/R = 2/17.
The curvature of a curve measures the rate at which the direction of the tangent to the curve changes as we move along the curve. A higher curvature indicates a sharper turn, while a lower curvature indicates a more gradual curve. In this case, the curvature is quite small, indicating a relatively gentle curve at the point t=1.
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(4) Read questions carefully and to pay close attention to the meaning of a statement to ensure when rules can and cannot be applied. 1. If f(x) = log x - 4, g(x) = (x + 5)² and h(x) = (f • g)(x).
Answers
The intersection of the domains of f(x) and g(x) is {x > 0}. We can now examine the product of f(x) and g(x) on this domain:(f • g)(x) = f(g(x)) = f((x + 5)²) = log((x + 5)²) - 4= 2 log(x + 5) - 4Since log(x + 5) is only defined for x > -5.
When we analyze the statement, we realize that we are dealing with the composition of functions. We can determine the value of h(x) by taking the product of f(x) and g(x) after determining the domain of the composite function. In this problem, we must first examine the domain of f(x).Since f(x) is equal to log x - 4.
The domain of f(x) is {x > 0}.The domain of g(x) is the set of all real numbers. This means that the product of f(x) and g(x) is only defined for values of x that satisfy the domains of both functions. As a result, we must first examine the intersection of the domains of f(x) and g(x). We must be cautious when applying rules to problems and not blindly use rules without first determining whether the domain allows for their application.
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Hii can someone who is really good at math please help me with these 2 math questions. I'm struggling with them!!
Answers
Could someone help me fix my errors please
Answers
The statements, reasons, situations that proves the congruence of the triangles are presented as follows;
1. 5. ∠POM ≅ ∠NOM \({}\) 5. Definition of angle bisector
6. ΔPMO ≅ ΔNMO \({}\) 6. SAS Congruence theorem
2. C. III only
3. SAS congruence rule
What are congruent triangles?Triangles are congruent if they have that same size and shape.
The completed two column method to prove the congruence of the triangles can be presented as follows;
Statements \({}\) Reasons
1. \(\overrightarrow{MO}\) bisects ∠PMN \({}\) 1. Given
2. ∠PMO ≅ ∠NMO \({}\) 2. Definition of angle bisector
3. \(\overline{MO}\) ≅ \(\overline{MO}\) \({}\) 3. Reflexive property
4. \(\overrightarrow{OM}\) bisects ∠PON 4. Given
5. ∠POM ≅ ∠NOM \({}\) 5. Definition of angle bisector
6. ΔPMO ≅ ΔNMO \({}\) 6. SAS congruence theorem
2. The leg HL Theorem states that the if the hypotenuse and a leg in one triangle are congruent to a leg and an hypotenuse side in another triangle, then the two triangles are congruent.
The specified dimensions of the triangle that indicates that the hypotenuse of the two triangles are congruent is the option III
The correct option is; C. III Only
3. The three angles in triangle ΔFDG are congruent to the three angles in triangle ΔFDE.
The reflexive property of congruence indicates; The side FD is congruent to itself (reflexive property of congruence)
The triangle ΔFDG is congruent to the triangle ΔFDE by the ASA congruence rule
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what is the inferential objective (parameter(s) of interest) of a paired t-test? question 7select one: a. a single population mean b. the difference of two population means c. the ratio of two population means d. comparison of the variances of two populations e. the population mean of the differences between two variables
Answers
The inferential objective of a paired t-test is the population mean of the differences between two variables.
The inferential objective of a paired t-test is to estimate the mean difference between two related variables, which can be thought of as the population mean of the differences between the two variables. In other words, the paired t-test is used to determine whether the mean difference between two variables is statistically significant, which can provide insight into the relationship between the two variables.
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Write the equations in cylindrical coordinates.
(a) 2x^(2) − 4x + 2y^(2) + z^(2) = 9
(b) z = 5x^(2) − 5y^(2)
Answers
The following parts can be answered by the concept of Cylindrical equation.
a. Cylindrical equation for (a) is: 2r² × cos²(θ) - 4r × cos(θ) + 2r² × sin²(θ) + z² = 9.
b. Cylindrical equation for (b) is: z = 5r² × cos²(θ) - 5r² × sin²(θ).
the given Cartesian equations to cylindrical coordinates.
(a) To convert 2x² − 4x + 2y² + z² = 9 to cylindrical coordinates, we use the following relationships:
x = r × cos(θ)
y = r × sin(θ)
z = z
Substituting these relationships into the equation, we get:
2(r × cos(θ))² - 4(r × cos(θ)) + 2(r × sin(θ))² + z² = 9
Simplifying the equation, we get:
2r² × cos²(θ) - 4r × cos(θ) + 2r² × sin²(θ) + z² = 9
Your cylindrical equation for (a) is: 2r² × cos²(θ) - 4r × cos(θ) + 2r² × sin²(θ) + z² = 9.
(b) To convert z = 5x² − 5y² to cylindrical coordinates, we use the same relationships as before. Substituting them into the equation, we get:
z = 5(r × cos(θ))² - 5(r × sin(θ))²
Simplifying the equation, we get:
z = 5r² × cos²(θ) - 5r² × sin²(θ).
Your cylindrical equation for (b) is: z = 5r² × cos²(θ) - 5r² × sin²(θ).
Therefore,
a. Cylindrical equation for (a) is: 2r² × cos²(θ) - 4r × cos(θ) + 2r² × sin²(θ) + z² = 9.
b. Cylindrical equation for (b) is: z = 5r² × cos²(θ) - 5r² × sin²(θ).
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The following parts can be answered by the concept of Cylindrical equation.
a. Cylindrical equation for (a) is: 2r² × cos²(θ) - 4r × cos(θ) + 2r² × sin²(θ) + z² = 9.
b. Cylindrical equation for (b) is: z = 5r² × cos²(θ) - 5r² × sin²(θ).
the given Cartesian equations to cylindrical coordinates.
(a) To convert 2x² − 4x + 2y² + z² = 9 to cylindrical coordinates, we use the following relationships:
x = r × cos(θ)
y = r × sin(θ)
z = z
Substituting these relationships into the equation, we get:
2(r × cos(θ))² - 4(r × cos(θ)) + 2(r × sin(θ))² + z² = 9
Simplifying the equation, we get:
2r² × cos²(θ) - 4r × cos(θ) + 2r² × sin²(θ) + z² = 9
Your cylindrical equation for (a) is: 2r² × cos²(θ) - 4r × cos(θ) + 2r² × sin²(θ) + z² = 9.
(b) To convert z = 5x² − 5y² to cylindrical coordinates, we use the same relationships as before. Substituting them into the equation, we get:
z = 5(r × cos(θ))² - 5(r × sin(θ))²
Simplifying the equation, we get:
z = 5r² × cos²(θ) - 5r² × sin²(θ).
Your cylindrical equation for (b) is: z = 5r² × cos²(θ) - 5r² × sin²(θ).
Therefore,
a. Cylindrical equation for (a) is: 2r² × cos²(θ) - 4r × cos(θ) + 2r² × sin²(θ) + z² = 9.
b. Cylindrical equation for (b) is: z = 5r² × cos²(θ) - 5r² × sin²(θ).
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Between 11 P.M. and 8:10 A.M., the water level in a swimming pool decreased by 5/24 in. Assuming that the water decreased at a constant rate, how much did the water drop each hour?
Answers
Answer:
1/44 inches per hour
Step-by-step explanation:
there are 9 hours and 10 minutes during which water decreased by 5/24"
9 hrs, 10 min can be converted to 9 1/6 hours (10 min is 1/6 of 60 min)
5/24 ÷ 9 1/6 = 5/24 x 55/6
5/24 x 6/55 = 1/44
The radius of a circle is 6mm. What is the area of the shaded portion of the circle.
Answers
The area of the shaded portion of the circle is \(\frac{29\pi}{3} \ mm^{2}\). The correct option is b) 29 π mm² got to station 3
Area of a sectorFrom the question, we are to determine the area of the shaded portion.
The shaded portion in the circle is the major sector.
The area of a sector is given by the formula,
\(A = \frac{\theta}{360 ^\circ} \times 2\pi r\)
Where \(\theta\) is the angle subtended by the sector
and r is the radius of the circle.
From the given information,
r = 6 mm
and \(\theta\) is the angle subtended by the major sector
Therefore
\(\theta = 360^\circ - 70^\circ\)
\(\theta = 290^\circ\)
Putting the parameters into the formula, we get
\(A = \frac{290^\circ}{360 ^\circ} \times 2\pi \times 6\)
Simplifying
\(A = \frac{29}{3} \tim\pi \ mm^{2}\)
Hence, the area of the shaded portion of the circle is \(\frac{29\pi}{3} \ mm^{2}\). The correct option is b) 29 π mm² got to station 3
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Evaluate the integral by making an appropriate change of variables.
∫∫R 5 sin(81x² +81y² ) dA, where R is the region in the first quadrant bounded by the ellipse 81x² +81y² = 1
......
Answers
To evaluate the integral ∫∫R 5 sin(81x² + 81y²) dA over the region R bounded by the ellipse 81x² + 81y² = 1 in the first quadrant, we can make the appropriate change of variables by using polar coordinates.
Since the equation of the ellipse 81x² + 81y² = 1 suggests a radial symmetry, it is natural to introduce polar coordinates. We make the following change of variables: x = rcosθ and y = rsinθ. The region R in the first quadrant corresponds to the values of r and θ that satisfy 0 ≤ r ≤ 1/9 and 0 ≤ θ ≤ π/2.
To perform the change of variables, we need to express the differential element dA in terms of polar coordinates. The area element in Cartesian coordinates, dA = dxdy, can be expressed as dA = rdrdθ in polar coordinates. Substituting these variables and the expression for x and y into the integral, we have ∫∫R 5 sin(81x² + 81y²) dA = ∫∫R 5 sin(81r²) rdrdθ.
The limits of integration for r and θ are 0 to 1/9 and 0 to π/2, respectively. Evaluating the integral, we obtain ∫∫R 5 sin(81x² + 81y²) dA = 5∫[0 to π/2]∫[0 to 1/9] rr sin(81r²) drdθ. This double integral can be evaluated using standard techniques of integration, such as integration by parts or substitution, to obtain the final result.
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Which are true and which are false?
Answers
The correct statement is: the volume of the cylinder is 8 cubic inches more than that of the cone.
What is the Volume of a Cone and Volume of a Cylinder?The volume of cone (V) = 1/3 * πr²h
Volume of cylinder (V) = πr²h
Where, r is the radius of their bases.
The base area formula for the cone = πr²
Calculate the area of the base of the cone that has a radius (r) of 2.5 in:
Area of the base of the cone = π(2.5)² ≈ 19.6
The volume of the cone (V) = 1/3 * πr²h = 1/3 * π * 2.5² * 6.5
≈ 42.5 cubic inches
Volume of cylinder (V) = πr²h = π * 2² * 4
≈ 50.3 cubic inches
The difference in volume = 50.3 - 42.5
= 7.8 ≈ 8 cubic inches
Therefore, the only statement that is true is: the volume of the cylinder is 8 cubic inches more than that of the cone.
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help me asp please with this answer
Answers
Option B) If the sum of the squares of the two short sides equals the square of the longest side
It is because if we apply Pythagoras Theorem which is\( {hypotenuous}^{2} = {base}^{2} + {perpendicuar}^{2} \)If the left side (hyp^2) is equal to the right side (base^2 + per^2) then the triangle is right angled triangle.Hypotenuse is the longest side And base and height are the other two sidesJerome found the lengths of each side of triangle QRS as shown, but did not simplify his answers. Simplify the lengths of each side to answer the question Which statement about triangle QRS is true?
Answers
Answer:
\(QR = 6.0033\)
\(QS = 8.22\)
\(RS = 6.0033\)
QRS is isosceles
Step-by-step explanation:
Given
See attachment for complete question
From the attachment, we have the following parameters\(QR = \sqrt{(-3-0)^2+(-5.2-0)^2}\)
\(QR = \sqrt{9+27.04}\)
\(QS = \sqrt{(-3-5)^2+(-5.2-(-3.322))^2}\)
\(QS = \sqrt{64+3.53} = \sqrt{67.53\)
\(RS = \sqrt{(0-5)^2 + (0 - (-3.322))^2}\)
\(RS = \sqrt{(25 + 11.04}\)
Solving further, we have:
\(QR = \sqrt{9+27.04}\)
\(QR = \sqrt{36.04}\)
\(QR = 6.0033\)
\(QS = \sqrt{64+3.53} = \sqrt{67.53}\)
\(QS = 8.22\)
\(RS = \sqrt{25 + 11.04}\)
\(RS = \sqrt{36.04}\)
\(RS = 6.0033\)
From the calculations;
\(RS = QR = 6.0033\)
This means that: QRS is isosceles
Answer:
the answer is D
Step-by-step explanation:
Which of the following are real numbers?
A.86/49
B.√77
C.69
D. 7 1/2
PLEASE HELP!! I have trouble with these types of questions
Answers
All the numbers in the list of options are real numbers
How to determine the real numbers?The numbers in the options represent the given parameter
As a general rule;
Real number consists of the following types of numbers
Rational number: Integers, whole numbers, terminating decimalIrrational numbers: Non terminating decimalsAny number other than this is a complex number
And it is denoted by the letter i
There are no complex number in the list of options
This means that 86/49, √77, 69 and 7 1/2 are all real numbers
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find the value of y in the solution to the system of equations shown.
y=5x+3
2y=18x−10
Answers
The value of y in the solution to the system of equations is 13
y = 5x + 3
2y = 18x - 10
Rearranging the equation, the combined equation is as follows;
Combined Equationy - 5x = 3
2y - 18x = -10
multiply equation(i) by 2
2y - 10x = 6
2y - 18x = -10
8x = 16
x = 16 /8
x = 2
y = 5(2) + 3
y = 10 + 3
y = 13
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Answer:
y=13
Step-by-step explanation:
Given the following diagram, find the missing measure 2 m_2 = 2x°, m _3 = 5x, m 1 = 0 2x + 5% 5x - 2x 180 - 5x 180 - 7x
Answers
We know 3 angles sum to 180 degrees {in a triangle]. Thus, we can write:
\(\angle1+\angle2+\angle3=180\degree\)We are given Angles 2 and 3 and are told to find Angle 1. We substitute and do a bit algebra to figure Angle 1 out. The steps are shown below:
\(\begin{gathered} \angle1+\angle2+\angle3=180\degree \\ \angle1+2x+5x=180 \\ \angle1+7x=180 \\ \angle1=180-7x \end{gathered}\)The last answer choice is correct.
Which statistical process would be most helpful in determining critical variables in a student’s success in statistic class?
Group of answer choices
regression with success in statistics class as the dependent variable
hypothesis testing with a null hypothesis that student success is less than or equal to the current average in the course
use a confidence interval with the success in statistics class as the mean
hypothesis testing with a null hypothesis that student success is more than the current average
regression with success in statistics class as an independent variable
Answers
Option A is correct i.e., Regression with class performance as the dependent variable would be the most beneficial statistical procedure for identifying key factors in a student's success in statistics class.
Using this strategy, you may pinpoint the crucial independent factors that are most closely linked to academic achievement and gauge the degree and direction of those associations.
Contrarily, using the success in statistics class as an independent variable would prevent you from identifying the additional factors that affect class success, while confidence intervals and hypothesis testing would not reveal information on the particular independent variables that are most crucial.
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A farm has 6 chickens, 4 ducks, 2 pigs and 4 cows. If an animal is chosen at random, find P(Cow U C-name).
a.) 1
b.) 3/5
c.) 5/8
d.) 2/5
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Draw the graph of f(x)=3x^4+4x^3−12x^2+12 and enter all extreme points. Also state whether they are minimum or maximum points.please show a figure and detailed answer
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The draw is:
Now, to find the extreme points we need to calculate the derivative and solve it for equal zero.
\(\begin{gathered} f(x)=3x^4+4x^3−12x^2+12 \\ f^{\prime}(x)=12x^3+12x^2−24x \end{gathered}\)Let's solve = 0:
\(\begin{gathered} f^{\prime}(x)=12x^3+12x^2−24x^=0 \\ 12x^3+12x^2−24x=0 \\ 12x(x^2+x-2)=0 \\ x^2+x-2=0 \\ (x+2)(x-1)=0 \\ x=-2 \\ x=1 \\ x=0 \end{gathered}\)We have the extreme points: x= -2, x=1, x=0. To compute what point is minimal or maximal we have to evaluate each point. For x= -2
\(\begin{gathered} f(x)=3x^4+4x^3−12x^2+12 \\ f(-2)=3(-2)^4+4(-2)^3−12(-2)^2+12 \\ f(-2)=48-32-48+12=-20 \end{gathered}\)Now for x=1:
\(f(1)=3(1)^4+4(1)^3-12*1^2+12=3+4-12+12=7\)Now for x=0:
\(f(0)=3*0+4*0-12*0+12=12\)Comparing these 3 points, we have local minimals at -2 and 1, and a local maximal at 0.
what are the lengths of SV and QT? no links.
Answers
ok so we see that TR is 17 units, so RV is the same amount
3x+2 so 3x=15 so divide both sides by 3 we get x=5
now we know x=5 4x+1=21 and 9x-4=41
*drops microphone*
Answer:
TR = 12
=> 3x + 2 =17
=> x = 5
We have QT = QV (because QTV is an isosceles triangle)
=> QT = 4x+1=4x5+1=21 units
We have TS = SV (because TSV is an isosceles triangle)
=>SV = 9x-4= 9x5-4=41 units
what i 5 + 5
ok
ok
ko
Answers
Answer:
haha The answer is 10!(::
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
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plz helpppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
d.....hope this will help u:))
If you were a truck driver on the highway, for how many more miles would you expect to see camels, wombats, and kangaroos?
Answers
Answer:
30 miles
Step-by-step explanation:
An aeroplane flies 500km in one hour. How long does it take to f a distance of 10925km? for class 4
Answers
Answer:
It will take 22 hours
Step-by-step explanation:
10925 ÷ 500 = 21.9 = 22 hours
HELP NEED THIS NOW
A laptop has a listed price of $804.99 before tax. If the sales tax rate is 7.75%, find the total cost of the laptop with sales tax included.
Round your answer to the nearest cent, as necessary.
Answers
Answer:
$867.37Step-by-step explanation:
tax rate = 7.75%sale prize = $804.99tax = (804.99 × 7.75) / 100 = 62.38amount with tax = $804.99 + $62.38 = $867.37MARK ME AS BRAINLIST31 9. To fence a shamba it requires 3 Men Working 8 hource a day for 5 days. How long will if take Working 6 hours a day if they work at (3MKS) the same rate ?
Answers
It will take approximately 6.67 days for the 3 men to fence the shamba if they work 6 hours a day at the same rate.
Let's first understand the given information:
3 men work for 8 hours a day
They work for 5 days to complete the fencing
We need to find out how long it will take if they work 6 hours a day at the same rate
Calculate the total man-hours needed to complete the fencing.
Total man-hours = (Number of men) x (Hours per day) x (Days)
Total man-hours = 3 men x 8 hours/day x 5 days = 120 man-hours
Calculate the number of man-hours completed per day when working 6 hours a day.
Man-hours per day = (Number of men) x (Hours per day)
Man-hours per day = 3 men x 6 hours/day = 18 man-hours/day
Determine how many days it will take to complete the fencing while working 6 hours a day.
Days = (Total man-hours) / (Man-hours per day)
Days = 120 man-hours / 18 man-hours/day = 6.67 days
So, it will take approximately 6.67 days for the 3 men to fence the shamba if they work 6 hours a day at the same rate.
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1. Identify the shape of the Cross section that is sliced vertically.
A)Rectangle
B)Triangle
C)Square
D)Circle
Answers
Answer:
triangle
Step-by-step explanation:
If X~x^2 (m, mu^2) find the corresponding (a) mgf and (b) characteristic function.
Answers
Given X ~ x² (m, μ²), to find the corresponding MGF and characteristic function, we have;The probability density function (PDF) is;\(`f(x) = 1/(sqrt(2*pi)*sigma)*e^(-(x-mu)^2/2sigma^2)`\) Here, \(m = μ², σ² = E(X²) - m = 2μ⁴ - μ⁴ = μ⁴\)
The moment generating function\((MGF) is;`M(t) = E(e^(tX))``M(t) = E(e^(tX))``M(t)\)=\(∫-∞ ∞ e^(tx) * 1/σsqrt(2π) * e^-(x-μ)²/2σ² dx`\) We can rewrite the exponent of the exponential function in the integral as shown;\(`(tx - μ²t²/2σ²) + μt²/2σ²``M(t) = e^(μt²/2σ²) ∫-∞ ∞ e^-(x - μ)²/2σ² * e^(tx - μ²t²/2σ²)\)\(dx`\)We know that the integral above is the same as the integral of the standard normal PDF with\(`μ' = 0` and `σ' = sqrt(σ²)`.\) Therefore, we can write the above integral as shown below;\(`M(t) = e^(μt²/2σ²) * 1/√(1-2tσ²) * e^(μt²/2(1-2tσ²))`\) Simplifying the above equation, we obtain\(;`M(t) = 1/√(1-2tμ²\))`, which is the MGF of the given distribution.To find the characteristic function (CF), we substitute jx for t in the MGF, then we have;\(`ϕ(t) = E(e^(jtx))``ϕ(t) = E(e^(jtx))``ϕ(t) = ∫-∞ ∞ e^(jtx) * 1/σsqrt(2π) * e^-(x-μ)²/2σ² dx`\)Similar to the derivation for MGF, we can rewrite the exponent of the exponential function in the integral as shown below\(;`(jtx - μ²t²/2σ²) + μt²/2σ²``ϕ(t) = e^(μt²/2σ²) ∫-∞ ∞ e^-(x - μ)²/2σ² * e^(jtx - μ²t²/2σ²) dx`\)We know that the integral above is the same as the integral of the standard normal PDF with \(`μ' = 0` and `σ' = sqrt(σ²)\)`. Therefore, we can write the above integral as shown below;\(`ϕ(t) = e^(μt²/2σ²) * e^(-σ²t²/2)`\)Simplifying the above equation, we obtain;\(`ϕ(t) = e^(-μ²t²/2)`\) , which is the characteristic function of the given distribution.Therefore, the MGF is\(`1/√(1-2tμ²)`\) and the characteristic function is `e^(-μ²t²/2)`. Answering the question in 100 words:The moment generating function (MGF) and characteristic function can be found by using the given probability density function (PDF). First, substitute the given values for m and μ into the PDF to obtain the standard form.
From there, derive the MGF and characteristic function by integrating the standard form, rewriting the exponent in the integral, and simplifying the final expression. The MGF and characteristic function of \(X ~ x² (m, μ²)\) are\(1/√(1-2tμ²)\)and \(1/√(1-2tμ²) )\), respectively.
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A volleyball tournament starts out with 32 teams . After each round , half of the teams are eliminated after 4 rounds , how many teams are left ?
A. 4 teams
B. 16 teams
C 1 team
D2 teams
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Answer:
8 Teams would be remaining.
Step-by-step explanation:
32 divided by 4 equals 8.
Find the unit rate
93 push-ups in 3 days = push-ups per day
Answers
Answer: 31 push-ups per day
Step-by-step explanation: 93/3 = 31 because 90/3=30 and 3/3 = 1 so 30 + 1 = 31.
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