Answer:
10
Step-by-step explanation:
180-140=20
20÷2=10
×=10
y=10
Can someone please solve this.
The correct option is the root of auxiliary equation are 0 and6
What is differential equation?A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable. For example, dy/dx = 5x.General Differential Equations. Consider the equation y′=3x2, which is an example of a differential equation because it includes a derivative. There is a relationship between the variables x and y:y is an unknown function of x. Furthermore, the left-hand side of the equation is the derivative of y.Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts. Also, in medical terms, they are used to check the growth of diseases in graphical representationTo learn more about differential equation refers to:
brainly.com/question/1164377
#SPJ1
What number must be multiplied to the vector <-4,2,-3> so it is normalized
A. [tex]\frac{1}{\sqrt{29} }[/tex]
B. -[tex]-\sqrt{29}[/tex]
C. [tex]-\frac{1}{\sqrt{29} }[/tex]
D. [tex]\sqrt{29}[/tex]
What is the measure of angle d1
What is the tangent ratio of angle C2
100 POINTS!!!
Answer:
[tex]\sf \tan\left(c_2\right)=\dfrac{OD}{OC}=\dfrac{2\sqrt{66}}{19}[/tex]
Step-by-step explanation:
**Please note that if the segment AO = 3.8 cm then the 50° angle on the given rhombus is incorrect. It should be 49.46° (2 d.p.)**
In a rhombus, all four sides are equal in length. Therefore:
CD = AB = 5cmDiagonals bisect each other at 90°. Therefore:
OC = AO = 3.8 cmm∠COD = 90°Therefore, triangle COD is a right triangle.
To find the tangent ratio of angle c₂, first find the length of OD using Pythagoras Theorem:
[tex]\implies OC^2+OD^2=CD^2[/tex]
[tex]\implies 3.8^2+OD^2=5^2[/tex]
[tex]\implies 14.44+OD^2=25[/tex]
[tex]\implies OD^2=10.56[/tex]
[tex]\implies OD^2=\dfrac{1056}{100}[/tex]
[tex]\implies OD^2=\dfrac{1056 \div 4}{100 \div 4}[/tex]
[tex]\implies OD^2=\dfrac{264}{25}[/tex]
[tex]\implies OD^2=\dfrac{4 \cdot 66}{25}[/tex]
[tex]\implies OD=\sqrt{\dfrac{4 \cdot 66}{25}}[/tex]
[tex]\implies OD=\dfrac{\sqrt{4 \cdot 66}}{\sqrt{25}}[/tex]
[tex]\implies OD=\dfrac{2\sqrt{66}}{5}[/tex]
[tex]\boxed{\begin{minipage}{6 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]
Given:
θ = c₂O = ODA = OCSubstitute the values into the tan ratio:
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{OD}{OC}[/tex]
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{3.8}[/tex]
Rewrite 3.8 as 19/5:
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{\frac{19}{5}}[/tex]
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{2\sqrt{66}}{19}[/tex]
Please help me step by step pls
there is no question!
PLEASE HELP ASAP WILL GIVE BRAINLIEST
Which linear graph represents a proportional relationship?
If a quantity increases or decreases as per the increase or decrease in other quantity, the two quantities are said to be in a proportional relationship.
And here, the graph representing the proportional relationship is the one with positive slope (2nd graph)
Solve the following inequality algebraically.
x + 2 >\ 13
X+2 is greater than 13
Answer:
[tex]x > 11[/tex]
Step-by-step explanation:
Greetings!!
Given equation
[tex]x + 2 > 13[/tex]
subtract 2 from both sides
[tex]x + 2 - 2 > 13 - 2[/tex]
simplify
[tex]x > 11[/tex]
[tex]solution \: \: x > 11 \\ interval \: notation \: (11, \infty )[/tex]
Hope it helps!!
Which value of x is in the domain of f(x)=√x - 8?
OA. x = 0
OB. x=7
OC. x = -8
OD. x = 10
SUBMIT
Answer: OC. x = -8 is not in the domain of the function f(x) = √x - 8 because the square root of a negative number is not a real number. Therefore, the only value of x that is in the domain of the function is x ≥ 0.
Step-by-step explanation:
Starsky and Hutch shared their profits in the ratio 3:1. If Starsky got £606, how much did hutch get?
Answer:
£202
Step-by-step explanation:
It is import that you read ratios from left to right - the subjects/names and the ratio itself. In this case the "subjects" are Starksy and Hutch. So Starsky = 3, Hutch = 1.
Use cross multiplication:
S(Starksy):H(Hutch)
3 : 1
606. : ?
(606 * 1) divided by 3 = your answer = 202
Reply if you are unfamiliar with the cross multiplication method
Answer:
202
Step-by-step explanation:
Ratios
Starsky : Hutch
3 : 1
Starsky has 606 so divide 606 by 3
606/3 = 202
Multiply each term by 202
Starsky : Hutch
3*202 : 1*202
Starsky : Hutch
606 : 202
Please help asap giving 50 points for it!!!
The inequality that can be used to find the number of windows is d + r ≤ 235 and 250r + 220d ≥ 55000
What is an equation?An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic
Inequalities are used to show the nonequal comparison of two or more numbers and variables
Let r represent the regular price and let d represent the discounted price.
Gerald company has an inventory of 235 windows, hence:
d + r ≤ 235 (1)
Also, the regular price is $250 and the discounted price is $220. The sales goal is $55000, hence:
250r + 220d ≥ 55000 (2)
The inequality is d + r ≤ 235 and 250r + 220d ≥ 55000
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Rider and Caleb bought 5 gallons of juice for a classroom party. The cost was $25.55. What is the cost per pint of juice? (Round your answer to the nearest cent.)
The cost per pint of juice $0.63875.
What is division?
Division, or the process by which two or more numbers are joined together to generate a new number, is one of the four basic arithmetic operations. Addition, subtraction, and multiplication make up the remaining operations.
Weight of juice for a classroom party is 5 gallons.
Total price is $25.55.
We know that 1 US liquid pint = 0.125 US liquid Gallon
=> 0.125 US liquid Gallon = 1 US liquid pint
Therefore, 5 US liquid Gallon = 5/0.125 US liquid pint
=> 5 US liquid Gallon = 8*5 US liquid pint
=> 5 US liquid Gallon = 40 US liquid pint
Now, the required price is 25.55/40 = $0.63875
Hence, the cost per pint of juice $0.63875.
To learn more about division from the given link
https://brainly.com/question/28119824
#SPJ1
Find the sums of the interior angles and the sum of the measures of the exterior angles of the polygon. Please answer 1, 2, and 3, 30 points!!!!!!!!!!!!!!!!!!!!!!!!
The sum of the internal angles of the polygons are
a) The sum is A = 540°
b) The sum is A = 360°
c) The sum is A = 1800°
What is the sum of the interior angles of a polygon?The sum of the interior angles of a polygon is given by the formula
Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
where n is the number of sides
θ = angle in degrees
Given data ,
Let the sum of the internal angles of a polygon be represented as A
Now , the value of A is
The sum of exterior angle of n polygon is = 360°
Now ,
a)
The number of sides of the polygon = 5 sides
So , Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
Substituting the value of n = 5 in the equation , we get
nθ = 180° ( 5 - 2 )
nθ = 180° x 3
nθ = 540°
b)
The number of sides of the polygon = 4 sides
So , Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
Substituting the value of n = 4 in the equation , we get
nθ = 180° ( 4 - 2 )
nθ = 180° x 2
nθ = 360°
c)
The number of sides of the polygon = 12 sides
So , Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
Substituting the value of n = 12 in the equation , we get
nθ = 180° ( 12 - 2 )
nθ = 180° x 10
nθ = 1800°
Hence , the sum of the internal angles of the polygon is solved
To learn more about sum of internal angles of polygons click :
https://brainly.com/question/14611583
#SPJ1
Which step is missing in the proof?
We can see here that the missing proof is option D: ΔBPQ ∼ ΔDRS Reason: SSA.
What is a proof?A proof is a logical argument that demonstrates the truth of a statement or theorem. In mathematics, a proof is a sequence of logical steps that shows that a statement is true by using a combination of logical reasoning, definitions, established facts, and accepted rules of inference.
In other fields, such as computer science, a proof may refer to a demonstration that a program or algorithm is correct or that a system has a certain property.
We see here that the option selected above is actually the missing step in the proof.
Learn more about triangles on https://brainly.com/question/29969150
#SPJ1
12. rotation 270° counterclockwise about the origin
سال
-> J'(,
)
J (2,-5)
K(-1, -3) --------> K'C
)
L (-4, 5) --------->', )
Answer:
A (x,y) becomes A'(y,-x)
Step-by-step explanation:
this means we switch x and y to make x a negative
The critical F value with 8 nurerator degrees of freedom and 29 denominator degrees of freedom at a 0.01 Is 2.28 -2.28 A value Greater than 2.28 A value less than -2,20
Critical F value with 8 numerator and 29 denominator degree of freedom at α = 0.01 is 3.20
The critical F value with 8 numerator degrees of freedom (also known as the numerator degrees of freedom or the numerator df) and 29 denominator degrees of freedom (also known as the denominator degrees of freedom or the denominator df) at a significance level of 0.01 can be found using a table of F-distribution values or by using a calculator or a software that can compute the F-distribution function.
The critical F value with 8 numerator degrees of freedom (df1) and 29 denominator degrees of freedom (df2) at a significance level of 0.01 can be found using the following formula:
F_critical = F(1 - alpha, df1, df2)
where F(1 - alpha, df1, df2) is the inverse of the cumulative distribution function (CDF) of the F-distribution, alpha is the significance level (0.01 in this case), and df1 and df2 are the numerator and denominator degrees of freedom, respectively.
For this case, the critical F value can be found using the inverse cumulative distribution function with 1- alpha = 0.99, df1 = 8 and df2 = 29
F(0.99,8,29) = 3.17
Read more about Cumulative Distribution:
https://brainly.com/question/15689447
#SPJ4
Which is the rate of change for the interval between –6 and –3 on the x-axis?
The rate of change for the interval between –6 and –3 on the x-axis is; 2
How to find the rate of change of the graph?To find the rate of change for the interval between –6 and –3 on the x-axis, the first step is to locate the ordered pairs at those two points. Locating the two ordered pairs from the graph is seen to be (3, -2) and (6, 4).
Applying the slope formula with those two points, we can find the rate of change as;
slope; m = (y₂ - y₁)/(x₂ - x₁)
m = (4 + 2)/(6 - 3)
m = 6/3
m = 2
This value of m represents the rate of change
Read more about rate of change at; https://brainly.com/question/8728504
#SPJ1
please need help asap 28, and 29
The length of the mid-segment of the trapezoid for these problems is given as follows:
28. n + 12 = 17.
29. 2n + 11 = 27.
How to obtain the length of the mid-segment of a trapezoid?The length of the mid-segment of a trapezoid is half the sum of the lengths of the bases.
Hence the value of n for item 28 is given as follows:
n + 12 = 1/2(2n - 2 + 4n + 6)
n + 12 = 0.5(6n + 4)
n + 12 = 3n + 2
2n = 10
n = 5.
Hence the length of the mid-segment is of:
n + 12 = 5 + 12 = 17.
The value of n for item 29 is given as follows:
2n + 11 = 1/2(5n - 2 + n + 8)
2n + 11 = 0.5(6n + 6)
2n + 11 = 3n + 3
n = 8.
Hence the length of the mid-segment is of:
2n + 11 = 16 + 11 = 27.
(replacing n = 8 into 2n + 11).
More can be learned about the mid-segment of a trapezoid at https://brainly.com/question/17116949
#SPJ1
find the length of the curve. r(t) = 6t i + 8t3/2 j + 6t2 k, 0 ≤ t ≤ 1
The length of the curve is given by the integral of the magnitude of the velocity vector, which is the derivative of the position vector. Taking the derivative of the position vector, we get the velocity vector as follows:
v(t) = 6i + 24t1/2j + 12tk
The magnitude of this vector is
√(6²+ 24²t + 12²t²)
= √(36 + 576t + 144t²).
To find the length of the curve, we need to integrate this magnitude from t=0 to t=1. This is given by the integral:
L = ∫0² √(36 + 576t + 144t²)dt
This evaluates to L = 18.75. Therefore, the length of the curve is 18.75.
Learn more about vectors:
https://brainly.com/question/28047791
#SPJ4
find the perimeter of the triangle with the vertices $(0,\ 1),\ (3,\ 6)$ , and $(4,\ 1)$ . if necessary, round your answer to the nearest hundredth.
The perimeter of the triangle having vertices (0,1),(3,6), and (4,1) will be 10.83 units.
Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.
Any polygon's perimeter is equal to the sum of its side lengths. Considering a triangle
The sum of the three sides equals the perimeter.
Units are always a part of the ultimate response. The final solution should be given in centimeters if the triangle's sides are in that unit.
Because the y values between U and V differ, the distance is equal to the x value difference.
Because the x values of V and W differ, the distance equals the difference between their y values.
The hypotenuse of a right triangle, or U to W, equals sqr (sum of squares on the other two sides)
Perimeter = sum of the 3 sides
[tex]= \sqrt{34} + \sqrt{26}+ \sqrt{16}= 5.83 + 5.1 + 4 = 10.83\:units[/tex]
As the value of 34 is 5.83 squared, 26 is 5.1 squared, 16 is about 4 squared.
To know more about the perimeter of triangle:
https://brainly.com/question/17394545
#SPJ4
The total distances add up to the triangle's perimeter is 10.00
The triangle's perimeter may be calculated by summing the distances between its three vertices. Use the distance formula to calculate the separation between the points:
d = √((x2 - x1)2 + (y2 - y1)2)
The distances between the points are as a result for the triangle with vertices (0,1), (3,6), and (4,1)
Utilizing the distance formula, determine the separation between (0,1) and (3,6):
d = √((x2 - x1) 2 + (y2 - y1) 2) = √((3-0) 2 + (6-1) 2) = √(32 + 52) = √45
Utilizing the distance formula, determine the separation between (3,6) and (4,1):
d = √((x2 - x1) 2 + (y2 - y1) 2) = √((4-3) 2 + (1-6) 2) = √(12 + 52) = √25
Utilizing the distance formula, determine the separation between (4,1) and (0,1):
d = √((x2 - x1) 2 + (y2 - y1)2) = √((0-4) 2 + (1-1) 2) = √(42 + 02) = √16
The triangle's perimeter is calculated by adding the three distances together:
Perimeter = √45 + √25 + √16 = 10.00.
Hence, the perimeter of the triangle is 10.00, rounded to the closest hundredth.
To learn more about perimeter visit:
https://brainly.com/question/345835
#SPJ4
convert to tons 2,600 pounds
2600 pounds are equal to 1.3 tons.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.
Given,
2,600 pounds to tons
1 US ton = 2000 pound
1 pound = 1/2000 US tons
2,600 pound = 2600/2000 US tons
2600 pound = 1.3 US tons.
Hence, 1.3 US tons are there in 26000 pounds.
Learn more about unit conversion here:
https://brainly.com/question/19420601
#SPJ1
please help me with this thank you
Answer:
3rd one is 100.6⁰F I think... not sure
Answer: B
Step-by-step explanation: 100.7 is current. In the past, it was lower so we have to subtract. We know how much we subtract (2.5). In B, if we subtract 2.5 we are taking 2.5 away from his current temp to get yesterday's temp.
Rashad had ducks and cows on his farm. These 14 animals had a total of 40 legs. How many cows and ducks were there?
The solution to the system of equations is
The number of ducks D = 8 ducks
The number of cows C = 6 cows
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of ducks be D
Let the number of cows be C
Now , the total number of animals = 14
So , D + C = 14 be equation (1)
And , the total number of legs = 40
Number of legs for ducks = 2 legs
Number of legs for cows = 4 legs
And , the total number of legs = 2D + 4C = 40
So , 2D + 4C = 40 be equation (2)
On simplifying the equations , we get
Multiply equation (1) by 2 , we get
2D + 2C = 28 be equation (3)
Subtracting equation (3) from equation (2) , we get
2C = 40 - 28
2C = 12
Divide by 12 on both sides of the equation , we get
C = 6 cows
Substituting the value of C in equation (1) , we get
D = 14 - 6
D = 8 ducks
Therefore , the value of C and D is 6 and 8 respectively
Hence , the number of cows is 6 and number of ducks is 8
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
Consider the following equation, known as the Arrhenius Equation Two-point form.
Solve for:
a)
b)
c)
d)
It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1
What is the Arrhenius Equation?
The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction and the temperature (T) of the reaction. The equation was first proposed by Svante Arrhenius in 1889 and it states that the rate constant of a chemical reaction is directly proportional to the exponential of the negative activation energy (Ea) of the reaction, divided by the gas constant (R) and the absolute temperature (T). The equation can be written as:
K = A * e^(-Ea / (R*T))
The Arrhenius Equation Two-point form is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction, the activation energy (Ea) of the reaction, the universal gas constant (R), and the temperature (T) of the reaction.
Given the equation K2/K1 = Ea / R (1/T1 - 1/T2)
a. To solve for K2, we can multiply both sides of the equation by
K1: K2 = K1 * Ea / R (1/T1 - 1/T2)
b. To solve for K1, we can divide both sides of the equation by
Ea / R (1/T1 - 1/T2): K1 = K2 / Ea / R (1/T1 - 1/T2)
c. To solve for Ea, we can multiply both sides of the equation by
R (1/T1 - 1/T2): Ea = K2/K1 * R (1/T1 - 1/T2)
d. To solve for T2, we can use the equation 1/T2= 1/T1 - Ea/R * K1/K2
It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1.
To learn more about Arrhenius Equation, visit
https://brainly.com/question/13467424
#SPJ1
NO LINKS!! Part 1
Find an exponential function in y = ab^x form that satisfies the given information :
a. Has y-int (0, 2) and has a multiplier of 0.8
b. passes through the points (0, 3.5) and (2, 31.5)
Answer:
A) y = 2*0.8ˣB) y = 3.5*3ˣ-----------------------------------------
Part AUse the coordinates to determine the function.
Point (0, 2):
2 = a*b⁰ ⇒ 2 = aThe function becomes:
y = 2bˣIt has a multiplier of 0.8, so b = 0.8, so the function is:
y = 2*0.8ˣPart BUse the first point:
3.5 = a*b⁰ ⇒ 3.5 = aUse the second point:
31.5 = 3.5*b²9 = b²b = √9b = 3The function is:
y = 3.5*3ˣAnswer:
[tex]\textsf{a)} \quad y=2(0.8)^x[/tex]
[tex]\text{b)} \quad y=3.5(3)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Question (a)Given:
y-intercept = (0, 2) ⇒ a = 2multiplier = 0.8 ⇒ b = 0.8Substitute the values of a and b into the exponential function formula:
[tex]\implies y=2(0.8)^x[/tex]
Question (b)The y-intercept is when x = 0. Therefore, given the function passes through point (0, 3.5), the y-intercept is 0.35 ⇒ a = 3.5.
Substitute the found value of a and given point (2, 31.5) into the exponential function formula and solve for b:
[tex]\implies 31.5=3.5b^2[/tex]
[tex]\implies b^2=9[/tex]
[tex]\implies b=3[/tex]
Substitute the values of a and b into the exponential function formula:
[tex]\implies y=3.5(3)^x[/tex]
Statins are used to keep cholesterol in check and are a top-selling drug in the
U.S. The equation:
S - 1.5x = 4.9
gives the amount of sales (S) of statin in billions of dollars a years after 1998.
According to this equation, how much will/did people in the U.S. spend on
statins in the year 2010?
Answer: People in the U.S. will spend ??
Billion dollars on statins in 2010.
Answer: 87
Step-by-step explanation:
-4x+5y=-19
-x-2y=5
Solve the system of linear equations
The solution for the system of linear equations is (1,-3)
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: -4x+5y=-19
-x-2y=5
Solving for x we get y equal to -3
Thus putting y=-3 in equation 1 we get x=1
Hence, The solution for the system of linear equations is (1,-3)
Learn more about linear equations here:
https://brainly.com/question/29739212
#SPJ1
Solve 6x - 7y= 18 for y
To solve the equation 6x - 7y = 18 for y, you can start by isolating y on one side of the equation. To do this, you can add 7y to both sides of the equation:
6x - 7y + 7y = 18 + 7y
6x = 18 + 7y
Next, divide both sides of the equation by 7:
6x/7 = 18/7 + 7y/7
x = 3 + y
So the solution is y = 3 - x
This is the final solution for y in the equation 6x - 7y = 18
While playing basketball, Ava’s heartbeat `is 80` times in `30` seconds. While running, her heartbeat `was 60` times in `20` seconds. Which activity made Ava’s heart beat faster? Basketball, running, or they were the same.
Running made Ava’s heart beat faster.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
While playing basketball, Ava’s heartbeat is 80 times in 30 seconds.
And, While running, her heartbeat was 60 times in 20 seconds.
Clearly, Ava's heartbeat is faster when he was running.
So, Running made Ava’s heart beat faster.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Suppose that the number of hours that it takes for a student to finish an inquiry has density
f(x) =
{ 2/5(x + 1) if 1 < x < 2
{ 0 otherwise.
a) Find the probability that the student finishes the inquiry in less than 1.5 hours.
b) Find the mean and standard deviation of the number of hours it takes to finish the inquiry.
The probability that the student finishes the inquiry in less than 1.5 hours is 0.45.
Mean= 4/3 and standard deviation= √(11/90)
a) To find the probability that the student finishes the inquiry in less than 1.5 hours, we need to find the area under the probability density function (PDF) of f(x) between the lower limit of 1 and the upper limit of 1.5.
This is given by the definite integral of f(x) from 1 to 1.5:
∫f(x)dx from 1 to 1.5
= ∫(2/5(x + 1))dx from 1 to 1.5
= (2/5)∫(x + 1)dx from 1 to 1.5
= (2/5)[x^2/2 + x] from 1 to 1.5
= (2/5)[(1.5)^2/2 + 1.5 - (1)^2/2 - 1]
= (2/5)[2.25/2 + 1.5 - 1/2 - 1]
=(2/5)[2.25/2]
=0.45
b) To find the mean, we need to use the formula:
Mean = ∫x*f(x)dx from a to b
In this case:
Mean = ∫x*(2/5(x + 1))dx from 1 to 2
= (2/5)∫x(x + 1)dx from 1 to 2
= (2/5)[x^3/3 + x^2/2] from 1 to 2
=(2/5)[(2)^3/3 + (2)^2/2 - (1)^3/3 - (1)^2/2]
= (2/5)[8/3 + 4/2 - 1/3 - 1/2]
=(2/5)[7/3 + 3/2]
=(2/5)[(20)/6]
=4/3
=1.333
To find the standard deviation, we need to use the formula:
Standard deviation^2 =(∫(x-μ)^2*f(x)dx) from a to b
Where μ is the mean
In this case,
Standard Deviation ^2= ∫(x-μ)^2(2/5)(x+1) dx from 1 to 2
=(2/5)∫(x-μ)^2(x+1) dx from 1 to 2
Simplifying, we get,
(x-μ)^3*(3x+μ+4)/30 from 1 to 2
=[(2-μ)^3*(6+μ+4)-(1-μ)^3*(3+μ+4)]/30
=[(2-μ)^3*(10+μ)-(1-μ)^3*(7+μ)]/30
Substituting the value of μ,
=[(2-4/3)^3*(10+4/3)-(1-4/3)^3*(7+4/3)]/30
=11/90
Therefore, Standard Deviation= √(11/90)
Read more about Probability Density Function:
https://brainly.com/question/14410995
#SPJ4
Can someone verify this?
The diagram that shows the C intercept D would be = diagram B. That is option B.
What is a universal set?A universal set is defined as the set that contains all the values that makes up a data.
The universal set contains the following:
A = ( yellow corn)
B = ( yellow corn with variety kernel)
C = ( white corn)
D= ( white corn with variety butter and sugar).
The C intercept means the contents that are in C that can be found in D. The diagram that represents this form is diagram B.
Learn more about universal set here:
https://brainly.com/question/29478291
#SPJ1
Fill the boxes with appropriate denominator /numerator
Answer:
the first box is 3 and the second box is 25
Step-by-step explanation:
Answer: Box 1: 3 Box 2: 25
Step-by-step explanation:
Box 1:
Since the top is divided by 3, you have to do the same to the bottom
9 / 3 = 3
Box 2:
The bottom is multiplied by 1 ⅔, so you do the same to the bottom
1 ⅔ x 15 = 25