The coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.
A coefficient is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial. It is usually a number, but sometimes may be replaced by a letter in an expression. For example, in the expression: ax2 + bx + c, x is the variable and 'a' and 'b' are the coefficients.
coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable and written next to it. The variables which do not have a number with them are assumed to be having 1 as their coefficient.
Let [tex]$x$[/tex] denote the claim sizes
[tex]& x= \begin{cases}100 & ; p=0.05 \\200 & ; p=0.2 \\300 & ; p=0.5 \\400 & ; p=0.2 \\500 & ; p=0.05\end{cases}[/tex]
[tex]& \mu_1^{\prime}=\varepsilon(x)=\sum x^0 p(x=x)=300 \\\\& \mu_2{ }^{\prime}=\sum x^2 p(x)=98000 \\\\& \mu_3^{\prime}=\sum x^3 p(x)=342 \times 10^5 \\[/tex]
[tex]& \mu_4^{\prime}=\sum x^4 p(x)=1.262 \times 10^{10} \\\\& \mu_2=\mu_2^{\prime}-\left(\mu_1^{\prime}\right)^2=8000 \\\\& \mu_3=\mu_3^{\prime}-3 \mu_2^{\prime} \\\\\mu_1^{\prime}+2\left(\mu_1^{\prime}\right)^3=0 \\\\& \mu_4=\mu_4^{\prime}-4 \mu_3^{\prime} \mu_1^{\prime}+6[/tex]
[tex]\mu_2^{\prime} \mu_1^{\prime 2}-3 \mu_1^{\prime 4} \\& \mu_4=2 \times 10^8 \\\\& \beta_1=\frac{\mu_3{ }^2}{\mu_2^3}=0 \quad \Rightarrow y_1=0 \\\\& \beta_2=\frac{\mu_4}{\mu_2{ }^2}=\frac{2 \times 10^8}{64 \times 10^6}=3.125\\ \\& y_2=\beta_2-3=0.125 \\[/tex]
Therefore, coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.
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Three times the square of a number minus eight
The expression of the statement is 3x² - 8
How to determine the expression of the statementFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as
Three times the square of a number minus eight
Represent the number with x
So, we have
Three times the square of x minus eight
Express as squares and numbers
This gives
3 * x² minus 8
So, we have
3x² - 8
hence. the expression is 3x² - 8
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If SX=z, TW=6z–76, and UV=3z–24, what is the value of z?
The value of {z} is equivalent to 13.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that SX = z, TW = 6z - 76 and UV = 3z - 24.
We can write -
{z} + {6z - 76} = {3z - 24}
7z - 76 = 3z - 24
7z - 3z = - 24 + 76
4z = 52
z = 13
Therefore, the value of {z} is equivalent to 13.
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i need to explain how i got the answer also
The triangle proportionality theorem, used to evaluate the figures indicates that we get;
8. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]
9. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]
10. [tex]\overline{ST}[/tex] ∦ [tex]\overline{PR}[/tex]
11. x = 57.6
12. x = 27.3
13. x = 11
14. x = 10
15. x = 5
16. x = 17
What is the triangle proportionality theorem?The triangle proportionality theorem states that, in a triangle, a line drawn parallel to one of the sides of a triangle and intersects the other two sides at two different points, then the ratio in which the other two sides are divided by the line are the same.
8. The triangle proportionality theorem indicates, if [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel, [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get; QS/SP = QT/TR
QS/SP = 7/11.2 = 0.625
QT/TR = 10/16 = 0.625
Therefore, QS/SP = QT/TR = 0.625, [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel9. Where [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel, [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get;
PS/SQ = RT/TQ
PS = 102 - 45 = 57
PS/SQ = 57/45 = 1.2[tex]\overline{6}[/tex]
RT/TQ = 41.8/33 = 1.2[tex]\overline{6}[/tex]
PS/SQ = RT/TQ, therefore, [tex]\overline{ST}[/tex] is parallel to [tex]\overline{PR}[/tex]10. Where [tex]\overline{ST}[/tex] is parallel to [tex]\overline{PR}[/tex], we get;
QS/SP = QT/TR
QS/SP = 19/38 = 0.5
QT/TR = 24/52 = 6/13 ≠ 0.5
QS/SP ≠ QT/TR, therefore, [tex]\overline{ST}[/tex] ∦ [tex]\overline{PR}[/tex]11. The triangle proportionality theorem, indicates that we get;
48/25 = x/30
x/30 = 48/25
x = (48/25) × 30 = 57.6
12. Making use of the triangle triangle proportionality theorem, we get;
(49 - 28)/28 = x/36.4
x/36.4 = (49 - 28)/28
x = ((49 - 28)/28) × 36.4 = 27.3
x = 27.313. 32/60 = (2·x + 6)/52.5
(2·x + 6)/52.5 = 32/60
(2·x + 6) = (32/60) × 52.5 = 28
(2·x + 6) = 28
2·x = 28 - 6 = 22
x = 22/2 = 11
x = 1114. (x - 3)/21 = (x - 1)/27
27 × (x - 3)= 21 × (x - 1)
27·x - 27 × 3 = 21·x - 21
27·x - 21·x = -21 + 27 × 3 = 60
6·x = 60
x = 60/6 = 10
x = 1015. (7·x - 11)/(4·x - 2) = 20/(35 - 20)
(7·x - 11)/(4·x - 2) = 20/(35 - 20) = 20/15
(7·x - 11)/(4·x - 2) = 20/15
15 × (7·x - 11) = (4·x - 2) × 20
105·x - 165 = 80·x - 40
105·x - 80·x = 25·x = 165 - 40 = 125
25·x = 125
x = 125/25 = 5
x = 516. 35/(x - 3) = (x - 7)/4
35 × 4 = (x - 3) × (x - 7)
140 = x² - 10·x + 21
x² - 10·x + 21 - 140 = 0
x² - 10·x - 119 = 0
x² - 10·x - 7 × 17 = 0
x² + 7·x - 17·x - 17 × 7 = 0
x·(x + 7) - 17·(x + 7) = 0
(x + 7)·(x - 17) = 0
x = -7, or x = 17
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Mr Musk bought a £75000 car at the beginning of the year 2016.
Each year the value of the car decreased by 8%.
a) Calculate the value of the car at the beginning of the year 2020.
Give your answer correct to the nearest £100
Answer:
53700
Step-by-step explanation:
Depreciation of every year is 8%, 2016-2017-18-19-20 - 4 years
in the beginning of 2017 it'll be 0.92*75000
so it'll be (1-8%)^4 = 0.71639
multiply by 75000 = 53729. to the nearest 100 = 53700
Mr. Bernard needs to order boxes for his 18-inch diameter "Super Pizza. "
What is the approximate circumference of the Super Pizza? Use 3. 14 for π. Show your work.
What is the approximate area of the Super Pizza? Use 3. 14 for π. Show your work.
Please help and hurry!! Ty!!
The circumference of the Super Pizza is 56.52 inches and approximate area of the Super Pizza 253.34 inches2.
To calculate the circumference of the Super Pizza
Circumference = π x diameter
Circumference = 3.14 x 18
Circumference = 56.52 inches
To calculate the area of the Super Pizza
Area = π x radius2
Area = 3.14 x (18/2)2
Area = 3.14 x 81
Area = 253.34 inches2
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you will need a straightedge for this assessment. which table represents a proportional relationship
The table that represents the proportional relationship would be table A. Option A
What is a proportional relationship?In this table we can see that in option A, there is a constant for which the values of the y are gotten. This is common on all of the values in A
For instance 2² = 4
3² = 9
4² = 16
0² = 0
The power of 2 is the constant that when applied on the values it gives the corresponding solution.
This shows the constant proportional relationship that is in existence between the values in x and the y solution
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Can you write an Orginal Oratory speech on benefits of solar energy
Throughout the solar system, solar energy is continuously emitted by the sun. The Earth is warmed by solar energy, which also affects the weather, the wind, and the survival of plant and animal life. Electromagnetic radiation, which is a kind of energy, heat, and light, is released from the sun (EMR).
What is solar system?Anything produced by the sun is considered to be solar energy.Nuclear fusion that occurs in the sun is the source of solar energy. Hydrogen atom protons clash ferociously in the sun's core, where they fuse to form helium atoms, which is the process of fusion.An large quantity of energy is released during this process, which is sometimes referred to as a PP (proton-proton) chain reaction. Around 620 million metric tons of hydrogen are fused by the sun every second in its core. Other stars, similar in size to our sun, also experience the PP chain reaction, which supplies them with ongoing heat and energy. These stars have an average Kelvin temperature of 4 million degrees (about 4 million degrees Celsius, 7 million degrees Fahrenheit).The CNO cycle is responsible for energy production in stars that are around 1.3 times larger than the sun. Carbon, nitrogen, and oxygen (C, N, and O) are required for the CNO cycle to convert hydrogen to helium. As of right now, the CNO cycle produces less than 2% of solar energy.To Learn more About solar system, refer To:
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a newly employed nurse administrator wants to know more about the employees on the units the administrator supervises. the manager accesses the managerial database and gathers data about all of the current employees on the unit, including work shift, number of years employed, age, gender, educational preparation, certifications, work history, and professional accomplishments, analyzing the data statistically. what type of quantitative research is this?
This is an example of a descriptive quantitative research study.
Descriptive quantitative research involves collecting and analyzing data to describe the characteristics of a population or phenomenon. In this case, the nurse administrator is gathering and analyzing data about the employees on the units they supervise, such as work shift, number of years employed, age, gender, educational preparation, certifications, work history, and professional accomplishments. Statistical techniques such as mean, median, and mode are used to analyze the data, allowing the nurse administrator to compare the characteristics of the employees across various dimensions. This type of research is used to develop an understanding of a given population or phenomenon, allowing for informed decision-making.
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what is the surface area
Answer:
518.4 cm²
Step-by-step explanation:
We have two triangles so
2 × (9×10/2) = 90
We have a base so
14 × 10 = 140
We have two other rectangles so
2 × 14 × 10.3 = 288.2
Now we add it all together
288.4 + 140 + 90 = 518.4
Triangle ABC is dilated with the origin as the center of the
dilation. Which ordered pair could represent the image of
point C(5, 2) after the dilation?
0 (5,-2)
(-1,-4)
O (2.5, 1)
o (7.5, 4.5)
The ordered pair could represent the image of point C(5, 2) after the dilation is (2.5, 1)
Which ordered pair could represent the image after the dilation?If we have a general point (x, y) and we apply a dilation with the origin as the center of a scale factor k, then the coordinates of the image after the dilation is (k*x, k*y)
Here we want to see which point can be the image of (5, 2) after the dilation, it will must have the form (k*5, k*2)
The only point that has this form is the one on the third option, where we can write:
(2.5, 1) = (k*5, k*2)
Then we have two equations:
2.5 = k*5
1 = k*2
Solving these we should get the same value of k.
2.5/5 = k = 0.5
1/2 = k = 0.5
so that is the correct option.
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Penelope mixed 6 ounces of apple juice concentrate with 9 ounces of water.
Which ratio of apple juice to water will make the same recipe?
A 45:30
B 42.60
C 42:63
D 9:6
Ratio of apple juice to water will make the same recipe is 42.60
What is the ratio formula?Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.
Add the elements of the ratio together to get the total number of shares.
Subtract the total value from the total number of shares.
Multiply by the number of necessary shares.
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to one.
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Which is a correct solution for the following system of Inequalities
The solutions of the system of inequalities are the points on the purple region, one example of a solution is (-2, -2)
Which is a correct solution for the system of inequalities?When we have a system of inequalties (so we have 2 or more inequalities) the solutions are the points (x, y) that are solutions of both inequalities at the same time.
Here we can see the graph of a system, such that the solution set of one of the inequalities is represented by the red shaded area, and the solution set of the other inequality is represented by the blue shaded area.
The solution set of the system is represented by the intersection between the areas, which is the purple area.
So any point on that region is a solution to the system, for example, the point (-2, -2) is a solution.
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Can someone help me please? I know the answer but the equation. Thanks.
Answer:
Equation is x-5 = 37
Reason:
x = starting temperature
We start with x degrees, and decrease by 5 degrees.
We go from x to x-5
The x-5 is now 37 degrees
Therefore, we arrive at the equation x-5 = 37
To solve this equation, add 5 to both sides and you'll get x = 42
Nice work on getting the correct value of 42.
Go step by step to reduce the radical.
V 224
NOVO
try
The square root of 224 in long division is 14.96
The term square root in math is defined as a factor of a number that, when multiplied by itself, gives the original number
Here we know that we need to find the square root of √224.
In order to solve this one we have to do the following steps,
Here we have to start dividing the digits from the right side into pairs of two by drawing a line on top of them. In the case of 224, then we have two pairs 24 and 2.
And then we have to find a number(z) whose square is ≤ 2.
Then the value of z will be 1 as 1 × 1 = 1 ≤ 2.
Here we get the value of quotient and the remainder as 1 and now we have to add the divisor z with itself and get the new divisor 2z (2).
And then we have to drag down the next pair and find a number (n) such that 2n × n ≤ 124 here we have the value of n comes out to be 4.
Finally we have to add a decimal in the dividend (224) and quotient (14) simultaneously.
Here we have to add 2 pairs of zero in the dividend after the decimal and repeat the above step for the remaining three pairs of zero.
Complete Question:
Finale the square root of √224 and go step by step to reduce the radical.
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David took out a 20-year $70,000 loan from his bank in 2010. The quadratic equation that approximates the year/loan balance relationship is y = -98^2 - 1,531x + 69,718, where x is the number of years and y is the balance. In what year will his loan balance be $37,234?
A. 2022
B. 2023
C. 2024
D. 2025
his loan will be $37,234 in the year 2022.
What is a Quadratic equation?ax2+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given, David took out a 20-year $70,000 loan from his bank in 2010.
The quadratic equation that approximates the year/loan balance relationship is y = -98*x^2 - 1,531x + 69,718,
where x is the number of years and
y is the balance
Since the Loan balance is given $37,234.
Thus to calculate the year
$37,234 = -98*x^2 - 1,531x + 69,718,
98 x² + 1534x - 32484 = 0
Comparing with the general form of the quadratic equation.
ax² + bx + c = 0
The discriminant b² - 4ac > 0 thus it has Two real roots.
using the Quadratic Formula
x = [tex]\frac{-b +- \sqrt{b^{2} - 4ac } }{2a}[/tex]
x = -27.62
and
x = 12
Thus year = 2010 + 12 = 2022
Therefore, In the year 2022, his loan will be $37,234.
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Please help me do this
Answer:
1. 5 inches in 2 days
2. y = (5/2)x. where y is rainfall and x is days.
3. Yes
4. (5/2)
5. 2.5"/day
6. 37.5 Inches
Step-by-step explanation:
See attached worksheet
.
a president and vice-president for a sorority are chosen from six people. how many different president/vice-president combinations are possible?
Answer:
there is 30 ways
Step-by-step explanation:
There are 6 people who can be president x 5 other people who can be vice president. so there is 30 ways
Write the values of n such that -15<3n<6
The values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.
What are inequalities?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The given expression is:
-15< 3n < 6
Divide all the sides of the equation with 3 to isolate the value of n.
-15 / 3 < 3n/3 < 6/3
-5 < n < 2
Hence, the values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.
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does anyone know what 4/5 + 5/6 is and how to solve the problem
4/5 + 5/6
24+25/30
49/30
hope it will help you
can you talk with me?
Naudia rode her bike two miles south. Then, she went east for three miles to reach her destination. How far is she
from her starting point?
The distance of Naudia from starting point based on distance travelled is 13 miles.
The distance travelled by Naudia and distance from starting point will form right triangle. Distance between Naudia and her final destination is the straight line or hypotenuse.
So, the expression will be -
Distance of South² + distance of East² = Distance from starting point
Distance form starting point = 2² + 3²
Distance form starting point = 4 + 9
Distance form starting point = 13 miles
Thus, the required distance is 13 miles.
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A right rectangular prism measures 12 cm tall, 8 cm long, and 5 cm wide.
A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled?
Enter your answer, to the nearest tenth, in the box
Answer: Volume of a right prism = BH where B is the area of the base and H is its height.
So Volume = 16 × 12 = 192 cm^3
Step-by-step explanation:
would there be an ordered pair that is a sulution to both 4x + 3y < 12 and -x + 3y < = -3? explain
The ordered pair that is a solution of given two expressions is (3,0) .
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expressions,
4x + 3y < 12
-x + 3y < -3
First find where the 2 lines intersect
4x + 3y = 12
-x + 3y = -3
Subtract :
5x = 15
x = 3
and y = -3 + 3 / 3 = 0
So they intersect at the point (3,0).
Therefore , The ordered pair that is a solution of given two expressions is (3,0) .
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400 pounds equals how many tons?
Answer:
400 pounds equal to 0.2 tons
Find the equation of the perpendicular bisector of AB where A and B are the points (3,6) and (-3,4) respectively. Also find its point of intersection with (i) x-axis and (ii) y-axis.
The point of intersection with x - axis is (5/3,0) and the point of intersection with y - axis is (0,5).
Any point on AB's perpendicular bisector, P(x,y), shall be considered. Then, PA = PB.
√(x-3)²+(y-6)² = √(x+3)²+(y-4)²
(x-3)²+(y-6)² = (x+3)²+(y-4)²
x² -6x+ 9 + y²- 12y + 36 = x² +6x+ 9 + y²- 8y + 16
12x + 4y -20 = 0
3x+ y-5 =0 ---(1)
Consequently, 3x+y-5=0 is the equation for the perpendicular bisector of AB.
We know that the coordinates of any point on x-axis are of the form (x,0). In other words, any point on the x-axis has a y-coordinate of zero. Thus, if we enter y = 0 in (1), we get
3x -5 = 0
x = 5/3
Thus, the x-axis is cut by the perpendicular bisector of AB at (5/3, 0).
(ii) Any point's y-axis coordinates have the following format: (0,y). When we enter x = 0 in (1), we obtain
y − 5 = 0
⇒ y = 5
Thus, the y-axis is where the perpendicular bisector of AB intersects (0,5).
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A cylindrical rod measures 8 inches long and the circumference of one of its bases is 8π inches. The rod is cut into two equally-sized pieces and then all surfaces are painted.
What is the area that is painted?
Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
128π in.² ≈ 402.1 in.²
Step-by-step explanation:
The rod can be cut into two equal sized pieces in different ways, so there are different answers to this question. I assume the question is asking when the rod's length is cut in half, so now there are two rods, each one being a cylinder with 4 inch height.
We need the area of the original rod and then add two more base areas.
C = 8π in.
r = 4 in.
total surface area = lateral area + 4 × area of base
SA = 8 in. × 8π in. + 4 × π × (4 in.)²
SA = 64π in.² + 64π in.²
SA = 128π in.² ≈ 402.1 in.²
Answer:
401.9
Step-by-step explanation:
I got this question wrong on my quiz
1. Michael is replacing a rectangular wooden gate in his backyard. The prefabricated gate is measured in inches and is shown below. What is the length, in inches, of the diagonal support lumber (AC) in this gate? Round to the nearest TENTH
The length of the diagonal support lumber is given as follows:
161.5 inches.
How to obtain the length of the diagonal?The figure is a rectangle, hence the diagonals have equal measure, and thus the value of x can be obtained as follows:
15x + 13.25 = 17x + 4.5.
2x = 9
x = 4.5.
Hence the length of the diagonal support lumber is obtained as follows:
2 x (15 x 4.5 + 13.25) = 161.5 inches.
We multiply by 2 as we are given half the length of the diagonal.
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whats 4*4*5*10 equals the the fild of math
The expression 4× 4 × 5 × 10 = 800 in the field of math.
What is algebra?Algebra is a branch of mathematics that is used to manipulate symbols and equations in order to solve problems. Algebra helps to solve problems involving unknown quantities and to develop relationships between different variables. It is a powerful tool that can be used to solve and analyze a variety of mathematical problems and equations.
Algebra can be used to solve equations, simplify expressions, and find solutions to linear and quadratic equations. Through algebra, we can also find the slope of a line, the area of a triangle, and the volume of a cube. Algebra is an invaluable tool that is useful in many areas of mathematics and science.
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What kind of triangle is this please help me find the relationship and value please.
Answer: x=14°
Step-by-step explanation:
All angles of a triangle added together is 180°. So we can add the angles together.
7x-11+5x-2+2x-3=180 [combine like terms]
14x-16=180 [add both sides by 16]
14x=196 [divide both sides by 14]
x=14
Therefore, x=14°.
A rectangle pool is 11 feet wide and 12 feet long. The owner of the pool will create a rectangular walkway, 3 feet wide, around the pool. What is the area, in square feet, of the walkway?
The area of the walkway around swimming pool is 78 square feet.
The outer sides of the walkway will have a length of 12 feet and the breadth will be 11 feet.
The area of the pool along without the walkway will be 12 X 11 = 132 square feet.
The outer sides of the walkway will have a length of 15 feet and the breadth will be 14 feet after the owner create the walkway.
The area of the pool along with the walkway will be 15 X 14 = 210 square feet.
Therefore ,
area of the walkway will be:-
= 210 - 132
= 78 square feet.
so, the area of the walkway around swimming pool is 78 square feet.
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a spherical snowball is rolled in fresh snow causing it grow so fast that its radius increases at a rate of 2 in/sec. how fast is the volume of the snowball increasing when the radius is 9 in
The volume is increasing at a rate of 784 * pi cubic inches per second.
The volume of a sphere is given by the formula V = (4/3) * pi * r^3, where r is the radius of the sphere.
We can find the rate of change of the volume with respect to time by taking the derivative of V with respect to time.
dV/dt = (4/3) * pi * 3r^2 * dr/dt
Given that the radius is increasing at a rate of 2 in/sec, we can substitute this value into the equation and find the rate at which the volume is increasing:
dV/dt = (4/3) * pi * 3 * 9^2 * 2 in^3/sec = 784 * pi in^3/sec
So, when the radius of the snowball is 9 inches, the volume is increasing at a rate of 784 * pi cubic inches per second.
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