The random variable is 3×sigma²/4.
Since, X1, X2 & X3 are independent & identically distributed.
so we have,
var(X1) = var(X2) = var(X3) = \sigma².
And,[tex]cov(X1 , X2) = cov(X2 , X3) = cov(X1 , X3) = 0.[/tex]
Now, [tex]var(Y1) = var(X2 + X3) = var(X2) + var(X3) + 2.cov(X2 , X3) = \sigma² + \sigma² + 0 = 2.\sigma²[/tex]
[tex]var[(Y1 + Y2 + Y3)/2] = (1/4). [var(Y1) + var(Y2) + var(Y3) + 2.cov(Y1 , Y2) + 2.cov(Y1 , Y3) + 2.cov(Y2 , Y3)] = (1/4). (\sigma² + \sigma² + \sigma² + 0 + 0 + 0) = 3.\sigma²/4[/tex]
What is random variable and example?The collection of potential outcomes for a random event is referred to as the sample space, which is the domain of a random variable. When a coin is tossed, for instance, there are only two possible outcomes: heads or tails. Read Related Links as well. Probability.
Different from an algebraic variable is a random variable. An algebraic equation's variable is an unknowable but calculable value. The formula [tex]10 + x = 13[/tex] demonstrates that we can determine the precise value of x, which is [tex]3.[/tex] As seen in the example of the dice above, a random variable has a set of values, and any of those values could be the outcome.
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It takes 15 over 2 minutes to fill an empty aquarium to a depth of 3 over 5 meters. What is the unit rate in minutes per meter? Write your answer as a fraction or a mixed number in the simplest form. pls answer
The unit rate in minutes per meter is 12½ min./m if it takes 15 over 2 minutes to fill an empty aquarium to a depth of 3 over 5 meters.
It takes 15/2 mins to fill an empty aquarium to a depth of 3/5 meters.
In a situationism like this we can make a equation such as
15/2 = 3/5
Lets multiply 5 in both sides
15/2 × 5= 3/5 × 5
75/2 = 3
Now lets divide both sides with 3
(75/2)/3 =3/3
25/2 = 1
Thus, the unit rate in minutes per meter is 12½ min./m if it akes 15 over 2 minutes to fill an empty aquarium to a depth of 3 over 5 meters.
What is unit rate?Which car goes faster, a car that travels 42 miles in three hours or a car that travels 132 miles in seven hours? The solution is determined by the unit rate of each automobile. Rather than comparing the distances traveled in two or seven hours, compare how far each car drives in one hour.
A unit rate is just a ratio of two unit values, with the denominator always being one. This enables easy comparison of data values. To mention a few, common unit rates in the real world include miles per hour (MPH), price per unit, miles per gallon (MPG), revolutions per minute (RPM), and pay per year.
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Louis sets off a firework. The height of the firework at the time t seconds is given by h (t) 16t^2+128t.
Use the quadratic formula to estimate when into the trip the rocket is 64 feet high.
A
at about 0.4 seconds and about 7.6 seconds
B
at about 0.8 second and about 5.2 seconds
C
at about 1.1 seconds and about 6.8 seconds
D
at about 0.5 seconds and about 7.5 seconds
The option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.
What is a quadratic equation ?
A quadratic equation is an equation which contains a single variable of degree 2 and its general form is ax² + bx + c = 0.
The height of firework is represented by a quadratic equation which is 16t² + 128t.
Let's find out that at what time the rocket will be at height of 64 feet.
So,
16t² + 128t = 64 feet
or
16t² + 128t - 64 = 0
or
t² + 8t - 4 = 0
We know that quadratic equation is in form ax² + bx + c = 0.
Using the quadratic formula to find value of t :
[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
t = [ -8 ± √(8² - (4 × 1 × - 4))] / ( 2 × 1 )
t = [ - 8 ± 8.94 ] / 2
t = -4 ± 4.47
So , the value of t can be either -4 + 4.47 or -4 - 4.47 which is equal to 0.47 or - 8.47 seconds. Time can't be negative , so t = 0.47 or 0.5 seconds.
Therefore , the option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.
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What is P(AC)? I don’t know the answer to this
P(ac) means that it's 100%
How do we find the "rate of change"
Answer: To find the average rate of change, divide the change in y-values by the change in x-values
Step-by-step explanation:
W H A T I S T H E A W N S E R F O R 8 x 2/5 =
Answer:
3 1/5
Step-by-step explanation:
8×2/5 is 16/5= 3 1/5
because u multiple the top number
Margot purchased 13.5 cups of almond flour to make gluten-free muffins. each batch of muffins requires 3 1/2 cups of flour plus another 1/5 cup to coat the pan. how many batches of muffins can margot make?
Answer:
I don't know
Step-by-step explanation:
I don't know
if 5 out of 30 students scored an A on a quiz.what percent did not get an A on the quiz?Round to the nearest whole percent.
PLEASE SHOW WORK
Answer:
83 %
Step-by-step explanation:
If 5 out of 30 got an A, that means that
30 -5 = 25
25 out of 30 did not get and A
25/30 = .8333333 = 83.33333 %
Rounding to the nearest whole percent
83 %
What is the square root of m6?
m²
m³
m4
m5
Answer:
m³
Step-by-step explanation:
have a good night :)
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given that $a$ is an odd multiple of $7767$, find the greatest common divisor of $6a^2 49a 108$ and $2a 9$.
Odd Multiples of 7767 are 1, 3, 9, 863, 2589, 7767.The greatest common divisor of [tex]$6a^2 49a 108$[/tex] = 6×1×49×1×108= 31,752 and
2a9=2×1×9=18
What do you mean by Greatest Common Divisor?The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor (GCD) in mathematics. The greatest common divisor of two numbers x and y is shown for x and y. As an illustration, the GCD of 8 and 12 equals 4, or. The words "divisor" and "factor" can be swapped out in the name "largest common divisor" so that alternative names such as "highest common factor" (HCF), etc. can be used instead. In the past, the term biggest common measure has been used to refer to the same idea.
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In ΔUVW, w = 3 inches, ∠W=23° and ∠U=73°. Find the length of u, to the nearest 10th of an inch.
The length of u by using sine rule is 7.4 to the nearest 10th of an inch.
What is sine rule?In mathematics, sine rule is a trigonometric method which relates the angle and side of a triangle. We can say that by using the sine rule we can find the side of any triangle if we knows the angle and vice versa. This rule is also known as law of sines.
Formulas for sine rule:
If we have three sides a, b, c and angle say A, B and C respectively .Then sine rule is :
[tex]\frac{Sin A}{a} = \frac{Sin B}{ b} = \frac{Sin C}{c}[/tex]
In the given question,
Sine rule will be used to get the unknown side of the triangle.
According to the rule;
[tex]\frac{Sin U}{u} = \frac{Sin V}{ v} = \frac{Sin W}{w}[/tex]
Given w = 3 in, ∠W=23° and ∠U=73°, substitute into the equation above to get u we have;
we can write the eq. as
[tex]\frac{Sin U}{u} = \frac{Sin W}{w}[/tex]
[tex]= > u = \frac{w \ sinu}{sinw} \\\\= > u = \frac{3 sin73}{sin 23} \\\\= > u = \frac{2.87}{0.39}\\ \\= > u = 7.398 = 7.4[/tex]
Hence, length of u is 7.4 inches to the nearest 10th of an inch.
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1. A baseball pitch traveled 128 feet per second. During a golfer's drive, the club head
speed was 99 miles per hour. Was the baseball faster than the club head?
The baseball was faster than the club head will be incorrect.
What is conversion?Conversion means to convert the same thing into different units.
A baseball pitch traveled 128 feet per second. During a golfer's drive, the club head speed was 99 miles per hour.
We know that in one mile, there are 5280 feet. And in one hour, there are 3600 seconds.
Then the speed of the golfer's drive will be
⇒ 99 x 5280 feet / 3600 seconds
⇒ 145.2 feet per second
The speed of the club head is faster than the baseball.
The baseball was faster than the club head will be incorrect.
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16 divided by 200 times 100
[tex]16 : (200 \cdot 100) =[/tex]
[tex]16 : 20000 = 0.0008[/tex]
Answer:
8
Step-by-step explanation:
To solve this problem we use PEMDAS; Parenthesis, Exponents, Multiply, divide, add, subtract
Let's set up an equation:
16/200*100
Now let's solve:
16/200=0.08
Now we multiply 0.08 by 100
0.08*100=8
Thus, our answer is 8
Evaluate: b - a for a = 2 and b = 7
O -5
O 5
O 9
O 14
b - a = 5
Here we have to find the value of b-a,
Where, a = 2 and b =7
By putting the value of a and b we have,
b - a =7 - 2
= 5
Therefore b-a = 5 that is option b is the correct answer.
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A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator
descends 6 feet per second. The elevator for the miners descends 15 feet per second. One day, the equipment elevator begins to descend. After 33 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 12 seconds? At that time, which elevator is deeper?
i. The equipment elevator is at a depth of 270 feet (-270 feet), while the miners elevator is at a depth of 180 feet (-180 feet) below the surface.
ii. The equipment elevator is deeper than that of the miners elevator.
The speed of an object is the rate at which the object moves.
speed = distance / time.
Thus,
Speed of the equipment elevator = 6 feet per second
Speed of the miners elevator = 15 feet per second.
Time of descent of the equipment elevator = 33 + 12
= 45 seconds
So that, the distance of the elevator at this time is;
⇒ distance = speed x time
= 6 x 45
= 270 feet
distance = - 270 feet
The distance of the miners elevator after 12 seconds is:
⇒ distance = speed x time
= 15 x 12
= 180 feet
distance = - 180 feet
Thus after another 12 seconds, the equipment elevator is at a depth of 270 feet (-270 feet), while the miners elevator is at a depth of 180 feet (-180 feet) below the surface.
Therefore, the equipment elevator is deeper than that of the miners elevator.
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students no longer have to visit a physical store to buy course books because most course books can now be obtained .
Students no longer have to visit a physical store to buy course books because most course books can now be obtained online.
What should you try first if an online course is having technical issues?
If you have any questions or concerns about the material in your online course, don't be afraid to ask your teacher or a fellow student. You should speak with your teacher or Blackboard Help for Students if you are experiencing technical issues with Blackboard.What drawbacks exist with online learning?
The fact that much online learning is one-way communication presents one of the largest obstacles. There is no communication between the teacher and the student. The experience will be radically different, and for many students, the transition may be challenging. Motivation is the second issue with online learning.Learn more about online learning
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Triangle ABC has the following angle measures:
m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°
What is m∠A?
pleaseee help
The measure of angle A in the triangle is 18°
How to determine the measure of angle A?The angles in the triangle are given as:
m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°
The sum of angles in a triangle is 180
So, we have
m∠A + m∠B + m∠C = 180
Substitute the known values in the above equation
So, we have:
2x − 24 + x + 8 + 4x + 49 = 180
Evaluate the like terms
7x = 147
Divide both sides by 7
x = 21
Substitute x = 21 in m∠A = (2x − 24)°
m∠A = (2 * 21 − 24)°
Evaluate
m∠A = 18°
Hence, the measure of angle A in the triangle is 18°
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A gasoline pump fills an automobile tank at the rate of .7 gallon every 2 seconds. At this rate, how long would it take to fill a 28- gallon tank?
Help!!
Answer:
80 seconds
Step-by-step explanation:
rate x time = gallons
[tex]\frac{.7}{2}[/tex]t = 28 Multiply both sides by [tex]\frac{2}{.7}[/tex]
t = 80
A 10½ ounce bottle of apple juice costs $2.49. A 16 ounce bottle costs
$2.99. A 16 1/4 ounce bottle costs $2.99. Which bottle is the better buy per cost?
Answer:
3rd option
Step-by-step explanation:
find the cost of 1 ounce and see which one is the cheapest
h) Suppose that a cold drink costs R4,50 now but will cost double in eight years' time. What will the average inflation rate be?
average inflation rate of cold drink will be 100%
WHAT IS INFLATION RATE ?Inflation is the term used to describe an increase in the price of goods and services that households buy. It is determined by how quickly these prices fluctuate. Prices frequently rise with time, but they can also fall (a situation called deflation).
CALCULATIONYou will subtract the starting price (A) from the later price (B), and divide it by the starting date (A). Then multiply the result by 100 to get the inflation rate percentage.
FORMULA FOR FINDING AVERAGE INFLATION = ((B-A)/A)*100
plugging in the values =
∵ given in the question that cost will double in the next 8 years i.e.
= Rs. 4.50 * 2
= Rs.9.00
∴ when we plug in the values in the formula we get
= ((9-4.5)/4.5) * 100
= 100 % inflation rate
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If p and q are negative integers such that [tex]p^2 \ \textgreater \ q^2[/tex],
then [tex]p^3[/tex] ________ [tex]q^3\\[/tex].
a) >
b) <
c) =
d) none of these
By compatibility principle of inequalities we complete the following sentence:
If p and q are negative integers such that p² > q², then p³ < q³. (Correct choice: B)
What is the relationship between two distinct negative integers?
According to the statement, the elements p and q are negative integers such that p² > q². By the sign law, the product of two negative numbers is always equal to a positive number, then by compatibility principle:
p² > q² Given
p · p > q · q Definition of power
p < q Compatibility principle
p³ < q³ Compatibility principle / Result
Please notice that the inequality symbol, that is, from "<" to ">" and viceversa, changes when the compatibility principle is applied in the given inequality.
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Struggling with this assignment hoping to get some tips and an explanation also please put the answer and solution thank you
The price of an item has been reduced by $6.18. The new sale price is $30.55. What was the original price?
Answer:
30.55 + 6.18 = $36.73
Step-by-step explanation:
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Solve:
-567 divided by 7
Answer: -81
Hope this helps
Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of this function:
h(x) = (x − 1)2 − 9.
See attachment for the graph of the function and the features
How to use the drawing tool(s) to form the correct answer on the provided graph?The function is given as
h(x) =(x - 1)^2 - 9
The x-intercept
Set h(x) to 0
So, we have
(x - 1)^2 - 9 = 0
Add 9 to both sides
(x - 1)^2 = 9
Take the square root of both sides
x - 1 = ±3
This gives
x = 1 ± 3
Expand
x = (1 - 3, 1 + 3)
Evaluate
x = (-2, 4)
Hence, the x-intercepts are x =2 and x = 4
The y-intercept
Set x to 0
So, we have
h(0) = (0 - 1)^2 - 9
Evaluate
h(0) = -8
Hence, the y-intercept is h(x) =-8
The vertex
We have
h(x) =(x - 1)^2 - 9
Expand
h(x) = x^2 - 2x + 1 - 9
Differentiate
h'(x) = 2x - 2
Set to 0 and solve for x
2x - 2 = 0
This gives
x = 1 --- this represents the axis of symmetry
Substitute x = 1 in h(x) =(x - 1)^2 - 9
h(1) =(1 - 1)^2 - 9
Evaluate
h(1) = -9
Hence, the vertex of the function is (1, -9)
See attachment for the graph of the function and the features
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PLEASE HELP!! QUESTION IS BELOW!! :)
The two column proof that completes each statement is as shown below.
How to complete the two column proof?We are given that ∠ABD = 85°
We are also told that;
Statement 1: m∠ABC + m∠CBD = M∠ABD
Reason 1: Angle Addition Postulate
Statement 2; m∠ABC + x° = 85°
Reason 2; Substitution Property
Statement 3; m∠ABC + x° - x° = 85° - x°
Reason 3; Subtract x° from both sides.
Statement 4; m∠ABC = 85° - x°
Reason 4; Simplify
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find the circumference of a circle whose area is equal of 64 π centimeters square
The circumference of the given circle is: 16πcm.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Given: Area of a circle = 64π cm²
To find: Circumference of the circle.
Finding:
We know that the formula of the area of a circle = πr²,
On comparing it with the given value, we get:
πr² = π(64)
πr² = π(8)²
8² = r²
r = 8cm (as the side of a circle can never be negative).
Also, the formula of the circumference of a circle = 2πr
Thus, for the circle having radius 8 cm, circumference = 2π(8) = 16πcm.
Hence, The circumference of the given circle is: 16πcm.
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59263 dived by the power of 10 x843
59263 divided by a number raised to the power of 10 × 843 is presented as follows;
[tex] \frac{59263}{843}\times x^{-10} [/tex]
How can the given expression be simplified?The given number to be divided is 59263
Let x represent the number that is raised to the power of 10, we have;
The number by which 59263 is divided = x¹⁰ × 843
Therefore, we have;
59263/(x¹⁰ × 843)[tex] \frac{59263}{x^{10} \times 843} = \frac{59263}{843}\times x^{-10} [/tex]
The given expression expressed using the rules of indices is therefore;
[tex] \frac{59263}{843}\times x^{-10} [/tex]
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I need help with this question
Answer:
x= 32
Step-by-step explanation:
3x-2+3x-10= 180 (sum of angles in straight line)
6x-12=180
6x=192
6x/6= 192/ 6
x = 32
Step-by-step explanation:
3x - 2 ° + 3x - 10° = 180°
reason : being angle in linear pair ...
6x - 12 = 180°
6x = 180° + 12
6x = 192°
[tex] x = \frac{192}{6} \\ [/tex]
x = 32°
Now ,
3x - 2 °
= 3 × 32 - 2
= 96 - 2
= 94°
Again ,
= 3x - 10°
= 3 × 32 - 10°
= 86°
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89 degrees
Step-by-step explanation:Triangles will always have 180 degrees. This means that given 2 angles, we can find the missing measurement.
Setting Up an Equation
To help us solve for the unknown angle, a, we can set up an algebraic equation. To make this equation remember that all 3 internal angles sum to 180.
14 + 77 + a = 180This is only one equation that you could set up to represent this situation.
Solving For a
Now that we have an equation we can begin to solve it. First, combine like terms that are on the same side of the equation.
91 + a = 180Next, subtract 91 from both sides.
a = 89To check our answer we can plug it back into the original equation.
14 + 77 + 89 = 180180 = 180This means that the missing angle must be 89 degrees.
How much mustard, chili, and salt would you need for 5 batches of spice mix?
how much is in the spice mix? context is necessary