The Variance of (A +2B) is 12.6724.
What is Variance ?
Variability is measured by the variance. The average of the squared deviations from the mean is used to compute it. The degree of dispersion in your data collection is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.
Here we have to select two card out of 6 card. now suppose we take 2 card (1,2 ) out of six card (1,2,3,4,5,6) . so here A=1 and B=2 but it is also possible that A=2 and B =1 because it represent same two card . Therefore here order of card matter.
Hence the posible out come of selecting 2 card are (without replacement)
-- (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) -- (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) -- (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) -- (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) -- (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) --
Therefore A+2B of this outcome are
A B A+2B
1 2 5
1 3 7
1 4 9
1 5 11
1 6 13
2 1 4
2 3 8
2 4 10
2 5 12
2 6 14
3 1 5
3 2 7
3 4 11
3 5 13
3 6 15
4 1 6
4 2 8
4 3 10
4 5 14
4 6 16
5 1 7
5 2 9
5 3 11
5 4 13
5 6 17
6 1 8
6 2 10
6 3 12
6 4 14
6 5 16
therefore there variance of A +2B can be computed as follows
x x2
5 25
7 49
9 81
11 121
13 169
4 16
8 64
10 100
12 144
14 196
5 25
7 49
11 121
13 169
15 225
6 36
8 64
10 100
14 196
16 256
7 49
9 81
11 121
13 169
17 289
8 64
10 100
12 144
14 196
16 256
[tex]\Sigma x=315[/tex] [tex]\sum x^2=3675[/tex]
Therefore variance
[tex]$$\begin{aligned}& =\frac{\sum x^2-\frac{\left(\sum x\right)^2}{n}}{n-1} \\& =\frac{3675-\frac{(315)^2}{30}}{30-1} \\& =\frac{3675-3307.5}{29} \\& =12.6724\end{aligned}$$[/tex]
The Variance of (A +2B) is 12.6724.
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Please por favor someone help me out (;
The answers are 1) Distributive property 2) Combining like terms 3) Subtraction property of equality 4) Subtraction property of equality 5) Subtraction property of equality
What is mathematical identities?An identity is an equality that holds true regardless of the values chosen for its variables. They are used in simplifying or rearranging algebra expressions.
Given; 4x-2(3+2x) = 2x+11
1) 4x-6-4x = 2x+11 = Distributive property
2) 4x-4x-6 = 2x-11 = Combining like terms
3) -6 = 2x-11 = Subtraction property of equality
4) -17 = 2x = Subtraction property of equality
5) -8.5 = 2 = Subtraction property of equality
Hence, the answers are 1) Distributive property 2) Combining like terms 3) Subtraction property of equality 4) Subtraction property of equality 5) Subtraction property of equality
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Do you know the answer~?
then please help me!!!!!!!!!!!!!!
The amount of Chemical B needed is 1.6 g.
what is graph?This refers to a diagram that shows a series of one or more points, lines, line segments, curves, or areas that represents the variation of a variable when compared with that of one or more other variables.
The quantity of Chemical B is plotted against the quantity of Chemical A.
Chemical B is plotted on the vertical axis using the scale of 1 cm to represent 2 units. Chemical A is plotted on the horizontal axis using the scale of 1 cm to represent 1 unit.
Therefore, on the graph, the line passing through the origin of the graph shows that when 1.4 g of Chemical A is used 1.6 g of Chemical B is needed.
Calculations:Chemical B is plotted on the vertical axis using the scale of 1 cm to represent 2 units.
To get the amount of Chemical B is on vertical axis = 2 grams
5 boxes
=0.4 g
Tracing the mass of Chemical A used 1.4 g it meets the line passing through the center at 4th line (4th box).
To get the amount of Chemical B is on vertical axis = amount of Chemical B per box * the number of line (boxes).
To get the amount of Chemical B is on vertical axis = 0.4 g * 4 lines (boxes)
= 1.6 g
Hence The amount of Chemical B needed is 1.6 g.
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If (a + b + c)‐¹= a‐¹+ b‐¹ + c‐¹, show that (a + b + c)³ = a³ + b³ + c³.
Step-by-step explanation
:We have to prove that (a + b + c)³ - a³ - b³ - c³ = 3(a + b ) (b + c) (c + a).
Considering LHS,
LHS : (a + b + c)³ - a³ - b³ - c³
= [(a + b + c)³ - a³] - (b³ + c³)
Using the algebraic identity,
a³ - b³ = (a - b)(a² + b² + ab)
(a + b + c)³ - a³ = ((a + b + c) - a)((a + b + c)² + a² + (a + b + c)a)
Using the algebraic identity,
(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)
= (b + c)(a² + b² + c² + 2(ab + bc + ca) + a² + a² + ab + ac)
= (b + c)(3a² + b² + c² + 3ab + 2bc + 3ac)
Using the algebraic identity,
a³ + b³ = (a + b)(a² + b² - ab)
b³ + c³ = (b + c)(b² + c² - bc)
So, [(a + b + c)³ - a³] - (b³ + c³) = (b + c)(3a² + b² + c² + 3ab + 2bc + 3ac) - [(b + c)(b² + c² - bc)]
= (b + c)[3a² + b² + c² + 3ab + 2bc + 3ac - (b² + c² - bc)]
= (b + c)[3a² + b² + c² + 3ab + 2bc + 3ac - b² - c² + bc]
= (b + c)[3a² + 3ab + 3bc + 3ac]
= (b + c)[3(a² + ab + bc + ac)]
= (b + c)[3(a(a + b) + c(b + a)]
= (b + c)[3(a + c)(a + b)]
= 3(a + b)(b + c)(a + c)
= RHS
1. You made a decision that you are doing to take care of the animals for the Claus family so they can go to a
warmer climate for their vacation this year. They will be on vacation the months of January and February. You will
be in North Pole, Alaska caring for their Reindeer, dogs, and hanging out with some of the Elves that take care of
things.
The weather for January 2022 and February 2022 are files found with the TGA.
Find the change in temperature (from the high and low) for the first day and last day of each month. How would
you have to pack for this trip?
2. What was the hardest part for you? Explain why.
Considering the climate of the North Pole, Alaska, we have seen that the change in the Temperature is 13°F and 14 °F respectively on the 1st and last day of the month respectively.
How to calculate the change in temperature?
From records, we know that Alaska usually has an average low temperature of 9°F and an average high temperature of 22°F in January.
However In February, Alaska's temperature usually ranges from an average low temperature of 12°F to an average high temperature of 26°F.
Thus, we can find the change in Temperature:
On 1st day of January , the Change in temperature is;
ΔT = Highest Temperature - lowest temperature
ΔT = 22°F - 9°F
ΔT = 13°F
On the 1st day of February, and then the last day of January, the change in temperature is;
ΔT= Highest Temperature - lowest temperature
ΔT = 26°F - 12°F
ΔT = 14 °F.
The hardest part will be to take take care of the animals since most of the animals only require a warm, secure, as well as protected area to reside in addition to sufficient food, drink, and exercise.
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finding an irrational number between which given pair of numbers supports the idea that irrational numbers are dense in real numbers? math 3
If there is another element of the same set between any two members of a set, we can say that the set is dense.
We'll show that the first choice—3.14 and pi—is the right one.
To prove that the set of irrational numbers contains a lot of real numbers, we must first discover an irrational number that lies between two specified real numbers.
In order to extend this to the real set, which is the union of irrational numbers and rational numbers, we should be able to find an irrational number between a rational number and an irrational number (or between an irrational number and a rational number). This is because we know that irrational numbers are dense (between two irrational numbers we can find another irrational number).
The first option, which has one of each, will then be the right choice.
Pi is irrational, while 3.14 is rational.
Finding an irrational number between these two indicates that the real set contains many irrational numbers.
(Note that the third option likewise has an irrational and a rational number, but the first one, [tex]e^{2}[/tex], is larger than the second one[tex]\sqrt{54}[/tex], thus it is written wrongly; for this reason, we did not choose it.)
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Write 0.000000836 in scientific notation.
The decimal 0.000000836 in scientific notation is 8. 36 × 10^-7
What is scientific notation?Scientific notation can be defined as a way of expressing numbers too small or too large to be conveniently written in decimal form.
It is also referred to as standard index form, standard form and scientific form.
It is commonly used for complex calculations with lengthy numbers.
It is also described as a method of expressing numbers in the terms of a decimal number that is between 1 and 10, and not 10 itself multiplied by a power of 10.
Given the decimal;
0.000000836
In scientific notation, it is written as;
8. 36 × 10^-7
The power is negative because the zeros are counted towards the right side.
Hence, the value is 8. 36 × 10^-7
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solve for g:
3/4(4g+5)=6
Answer:
G = -32
Step-by-step explanation:
when there are three treatment groups and 300 participants, what is the degrees of freedom in the denominator of the f-statistic calculation?
The degrees of freedom in the denominator of the f-statistic calculation is 2.
Explain the term degrees of freedom?The number of distinct bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df.
It is determined by subtracting the number of constraints from the sample size.Normal reporting of the results of a statistical test includes the test statistic and the degrees of freedom in brackets.Its degrees of freedom refers to the quantity of independent data points utilized to generate the statistic.For the stated question-
degrees of freedom df = n - 1
n = 3 groups
df = 3 - 1
df = 2
Thus, the degrees of freedom in the denominator of the f-statistic calculation is 2.
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Mike's old graphing calculator had 96 pixels across the screen.
His new calculator has 144 pixels. Find the scale factor by
which he increased his screen size.
Thus, the scale factor by which he increased his screen size is 3:2
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Given, the pixel of Mike's old calculator = 96 pixel
His new calculator has pixels = 144 pixel
Scale by which it increased = New pixels/Old pixel
= 144p/96p
= 3:2
Thus, the scale factor by which he increased his screen size is 3:2
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(b) Each unit on the grid repreent 25 feet. Find the perimeter of the factory. Show your work
If each unit on the grid represent 25 feet, then the perimeter of the factory is 1000 feet
Each unit on the grid represent 25 feet
The length of the side w1 = 3 × 25
= 75 feet
The length of the side N1 = 13 × 25
= 325 feet
The length of the side E1 = 7 × 25
= 175 feet
The length of the side S1 = 5 × 25
= 125 feet
The length of the side W1 = 4 × 25
= 100 feet
The length of the side S2 = 8 × 25
= 200 feet
The perimeter of the factory = 75 + 325 + 175 + 125 + 100 + 200
Add the terms together
= 1000 feet
Therefore, the perimeter of the factory is 1000 feet
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pleaseeeeeeeeeeeeeee help whats da volume
Answer:
if you want the volume of the outer cube with the other cube in it, it would be 48. if you want it without the cube its 120. the inside cube is 72.
Step-by-step explanation:
Answer:
48 mm³
Step-by-step explanation:
Outer prism:
5 mm by 4 mm by 6 mm
V = LWH = 5 × 4 × 6 mm³ = 120 mm³
Inner prism:
4 mm by 3 mm by 6 mm
V = LWH = 4 × 3 × 6 mm³ = 72 mm³
Difference:
120 mm³ - 72 mm³ = 48 mm³
Jenna gets an iTunes gift card for her birthday and decides to buy some games and some music the music she likes costs $1.99 per song and the games costs $3.99 each if she buys a total of 12 items and spends $18.88 how many of each item did she buy
The number of songs and games Jenna bought is 9.5 and 2.5 respectively.
How many of each item did she buy?let
Number of songs bought = xNumber of games bought = yx + y = 12
1.99x + 3.99y = 18.88
From (1)
x = 12 - y
Substitute into (2)
1.99x + 3.99y = 18.88
1.99(12 - y) + 3.99y = 18.88
23.88 - 1.99y + 3.99y = 18.88
- 1.99y + 3.99y = 18.88 - 23.88
2y = -5
y = -5/2
y = 2.5
Substitute into (1)
x + y = 12
x + 2.5 = 12
x = 12 - 2.5
x = 9.5
Therefore, Jenna bought 9.5 songs and 2.5 games.
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What is the address of the element 0 ?
Gary is collecting stamps and wants to collect the same number of stamps each week. He currently has 520 stamps. He only has 6 more weeks to collect the remaining stamps that he needs for his collection. He needs a total of at least 1000 stamps before he is done. Graph the answer to the inequality.
Answer:
Step-by-step explanation:
1000-520=480
480/6=80
x+6+520=1000 (-6)
x+514=1000
x=486
A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad. The probability of drawing a bag with bad potatoes is less than 1. The probability of drawing a bag with good potatoes is greater than 0. What is the probability of drawing a bag with bad potatoes? what is the expected probability of the complement of the event?.
Probability of drawing bad potatoes = 0.1
The probability of drawing a bag with bad potatoes is less than 1.
The probability of drawing a bag with good potatoes is greater than 0
The probability of drawing a bag with bad potatoes as a decimal .
The probability is 20% which means 20 by hundred , which means there is a chance of being its ok.
probability of bad potatoes = 2/20
=1/10
=0.1
To find the probability of the outcomes = Number of favourable outcome / Number of total outcome.
Probability of event 1 and 2
probability of event 1 =Number of favourable outcome / Number of total outcome.
probability of event 2 = 1 -( probability of event 1)
probability of good potatoes = 1- ( probability of bad potatoes)
Probability of the given event( probability of the bad potatoes = 1-(0.1)
Thus,
Probability of the bad potatoes in the 2 of the bags are=0.9
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The winner of a 1000 mile race drove his car to victory at a
rate of 131.3009 mph. What was his time (to the nearest
thousandth of an hour)?
He took 7.616 hours for victory at the speed of 131.3009 and cover 1000 miles.
What is distance?
The distance between two sites is the length of the route. The metre is the SI unit for distance.
What is speed?
The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.
What is time?
The amount of time that something happens, goes through a process, or remains the same.
Speed= 131.3009 mph
Total distance= 1000 miles
Speed = distance/ time
time= distance/ speed
time= 1000/131.3009
(nearest thousandth means round off upto 3 decimal places)
time= 7.616 hours
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Theater tickets cost $2.50 for children and $3.50 for adults. The price for 9 tickets was $29.50. How many adult tickets were purchased?
Answer:
8 is the answer
First try was incorrect
Hercules ate 6 hot dogs every 16 minutes. At that rate, how long,
minutes, will it take to eat 18 hot dogs?
Answer:
48 minutes
Step-by-step explanation:
6 : 16 = 18 : x
x = 16 * 18 / 6
x = 16 * 3
x = 48
Solve for x: 1 < x + 3 < 4
© 4>x>7
O 4
® -2>x>1
O -2
Answer: -2 < x < 1
Step-by-step explanation:
A school staff meeting had 70 teachers in attendance, 40% of whom were first-year teachers. How many first-year teachers were in the meeting?
Answer: 28.
Step-by-step explanation:
If 40% of the teachers in attendance at the school staff meeting were first-year teachers, that means 28 of the teachers in the meeting were first-year teachers.
Answer:
28
Step-by-step explanation:
We first would need to figure out what %10 of 70 is.
%10 of 70 is equal to 7.
Now that we have this answer, we can multiply 7 by 4 to get the number of teachers.
7 × 4 = 28
28 first year teachers were in the meeting.
Giving Brainly to whoever helps! Thanks.
Answer:
140 hamburgers
Step-by-step explanation:
to find the answer we must first use a let statement and write an equation
let x = hamburgers
hamburgers * 2 is cheeseburgers and added together that is 420
so
x + 2x = 420
now solve
3x = 420
x = 140
140 hamburgers were sold
Answer:
Step-by-step explanation:
240 divided by 3= 80
80+80=160
160 hamburgers sold altogether on Wednesday.
An elevator in the Seattle Space Needle can rise 100 meters
in 50 seconds, Use a model to show the elevator's rate of travel in
meters per second and in seconds per meter. Describe each rate
in words.An elevator in the Seattle Space Needle can rise 100 meters
in 50 seconds. Use a model to show the elevator's rate of travel in
meters per second and in seconds per meter. Describe each rate
in words.
The elevator's rate of travel in meters per second is 2m/s and 1/2 s/m is in seconds per meter.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
An elevator in the Seattle Space Needle can rise 100 meters in 50 seconds,
We need to find the elevator's rate of travel in meters per second and in seconds per meter
To find in meter per second we just need to divide 100 by 50 seconds
100/50=2 m/s
To find in seconds per meter we just need to divide 50 by 100
50/100=1/2s/m
Hence, the elevator's rate of travel in meters per second is 2m/s and 1/2 s/m is in seconds per meter.
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what is 42 divided by 51,860
SHOW STEPS!!!!!
The given expression can be simplified using the arithmetic operation as 0.00080987.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The given problem can be written in terms of expression as,
42 ÷ 51860
It can be solved as follows,
The number of digits in 51860 is 5 and in 42 is 2.
In order to divide the two numbers, the dividend should be greater than the divisor.
Therefore, multiply both 42 and 51860 by 10000 to obtain,
(42 × 10000) ÷ (51860 × 10000)
⇒ 420000 ÷ (51860 × 10000)
Now, first divide 420000 by 51860 to get,
420000 ÷ 51860 = 8.0987
Then, divide 8.0987 by 10000 to get,
8.0987 ÷ 10000 = 0.00080987
Hence, the required result of the given expression is 0.00080987.
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The price (in dollars) of a stock tracked from noon to three on a given day is shown by the function f(t) = 0.1(t - 2)3 + 6 where t is in hours. Find the rate at which the stock price was changing at one o’ clock.
The rate of increase in stock price is $ 0.10 per hour.
Calculating the Rate of increase:To calculate the rate of increase we need to know the increased amount per given time period
In this problem, we will calculate the stock price per given hour from that will calculate the rate of increase in a given situation.
Here we have
The price (in dollars) of a stock tracked from noon to three on a given day is shown by the function f(t) = 0.1(t - 2)³ + 6 where t is in hours.
Take t = 1
=> f(1) = 0.1(1 - 2)³ + 6
= 0.1(-1)³ + 6
= 0.1(-1) + 6
= - 0.1 + 6
= 5.9
Take t = 2
=> f(2) = 0.1(2 - 2)³ + 6
= 0.1(0)³ + 6
= 6
Take t = 3
=> f(3) = 0.1(3 - 2)³ + 6
= 0.1(1)³ + 6
= 0.1 + 6
= 6.1
The rate rate of increase = f(3) - f(2) = 6.1 - 6 = 0.1 ≅ $ 0.10
Therefore,
The rate of increase in stock price is $ 0.10 per hour.
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What is the domain of the function of x graphed below?
(-6.-5)
A {xx>-1}
(-1.3)
Cx-5
B {x-6
D {xx<3}
Answer:
Step-by-step explanation:
B is the answer
Create a line from-6,-5 to the x axis to -6 and draw a line from -1,3 down to x axis because that is your domain. Make sure to look at your open circles or closed circles at end of the line, if closed there are block brackets, If open then it is parenthesis. If it is a coordinate it is curly brackets. So therefore the answer is B
Tell how you can ue mental math to find 45. 8 X 10 to the 3rd power and 45. 8 X 0. 1
The result of 45.8*10^3 is going to be 45800. Using mental math, 45.8*0.1 will be 4.58.
What is mental math?A set of abilities known as mental math enable people to perform calculations "in their heads" without the aid of paper and pencil or a calculator. Recalling math information, such as 8 x 5 = 40, is one of these abilities. Rounding numbers and estimating calculations are additional abilities. Mathematical calculations made solely with the human brain, without the aid of any materials or tools like a calculator, are referred to as mental calculations. When computing tools are not available, when mental calculation is quicker than other methods, or even in a competitive setting, people may use it.
Here,
45.8*10³=45800
45.8*0.1=4.58
The value of 45.8*10³ will be 45800. The value of 45.8*0.1 will be 4.58 using mental math.
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PLEASE HELP!! WILL GIVE BRAINLIEST AND 25 POINTS!!
Solve for x
A. 10
B. 100
C. 64
Answer: 4
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]3^2 + x^2 = 5^2\\\\9+x^2=25\\\\x^2=16\\\\x=4[/tex]
Reflect GLQ across the x-axis. (PLEASE HELP!)
Answer:
Q-(1,1) L-(1,-2) G-(4,-4)
Step-by-step explanation:
becuase
Calculate 30% of 100 km.
Answer:30,000 meters
Step-by-step explanation:
Answer:
30km
Step-by-step explanation:
to find 10% you divide 100km by 10= 10km
to find the full 30% simply divide 10% by 3 which will give you 30km.
Use the model to answer the question.
a 10 by 10 grid is shown. 5 columns and 1 row are shaded.
Choose the numbers to find the product shown by the model.
0.5 × ____ = _____
The complete model will be;
⇒ 0.5 × 0.1 = 0.05
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A 10 by 10 grid is shown.
And, 5 columns and 1 row are shaded.
Now,
Since, 5 columns and 1 row are shaded.
Hence, The complete model will be;
⇒ 0.5 × 0.1 = 0.05
Thus, The complete model will be;
⇒ 0.5 × 0.1 = 0.05
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