If [tex]X,Y[/tex] are independent, we have the properties for expectation and variance,
[tex]\Bbb E[aX + bY] = a\,\Bbb E[X] + b\,\Bbb E[Y][/tex]
[tex]\Bbb V[aX + bY] = a^2\,\Bbb V[X] + b^2\,\Bbb V[Y][/tex]
where [tex]a,b\in\Bbb R[/tex] are fixed.
Then
[tex]\Bbb E[R - S] = \Bbb E[R] - \Bbb E[S] = 10 - 7 = \boxed{3}[/tex]
and
[tex]\Bbb V[R - S] = \Bbb V[R] + (-1)^2\, \Bbb V[S] = 4^2 + 3^2 = \boxed{5}\,{}^2 = 25[/tex]
(recall that standard deviation = √(variance))
In the relationship y=3x, if x is reduced by 1/3, how will y change? Responses It will triple.
If x is reduced by 1/3, 3x will be reduced by 1/3 x 3 = 1
Because y = 3x, y will also be reduced by 1.
Convert the following angle to decimal degrees.
α = 27° 20' 21"
PLEASE HELP ME!
Answer:
27.33917°
Step-by-step explanation:
27° 20' 21"
= 27° + 20'/60 + 21"/3600
= 27.33917°
a souvenir of the eiffel tower is scaled 1/80 at inch to 1 foot. if the total height of the tower is 1,069 feet, the approximate height of the souvenir of the eiffel tower to the nearest tenth is
well, let's convert 1 foot to inches, that'd be 12 inches per foot.
so we know that the souvenir is 1/80 in, to the actual of 12 inches on the Eiffel Tower, if the Tower itself is 1069 feet high, namely (1069)(12) inches, how high is the souvenir?
[tex]\begin{array}{ccll} \stackrel{in}{souvenir}&\stackrel{in}{actual}\\ \cline{1-2} \frac{1}{80}&12\\[1em] x&(1069)(12) \end{array}\implies \cfrac{ ~~ \frac{1}{80} ~~ }{x}~~ = ~~\cfrac{12}{(1069)(12)}\implies \cfrac{ ~~ \frac{1}{80} ~~ }{\frac{x}{1}}~~ = ~~\cfrac{12}{12828} \\\\\\ \cfrac{1}{80}\cdot \cfrac{1}{x}=\cfrac{1}{1069}\implies \cfrac{1}{80x}=\cfrac{1}{1069}\implies 1069=80x\implies \cfrac{1069}{80}=x\implies 13.4\approx x[/tex]
If f, g, and h are all positive number which of the following is NEVER true?
Answer:
C) fgh = 0==================================
Since all numbers are positive, their sum or product can be a positive number but never negative or zero.
A) f + g = 2h, both sides are positive → trueB) fh = 1, both sides are positive → true C) fgh = 0, at least one of the numbers should be zero → never trueD) gh = 23, both sides are positive → trueAlejandro and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3.50 and a drink for $4. How much would it cost if they bought 3 bags of popcorn and 8 drinks? How much would it cost if they bought p bags of popcorn and d drinks?
Total cost, 3 bags of popcorn and 8 drinks:______
Total cost, p bags of popcorn and d drinks:______
Answer:
Step-by-step explanation:
Using a proportional relationship, the costs are given as follows:
3 bags of popcorn and 8 drinks: $42.05.p bags of popcorn and d drinks: C(p,d) = 3.35p + 4d.What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
A proportional relationship may also involve multiple variables, as is the case in this problem, in which the cost is a function of the number of bags of popcorn p and the number of drinks d.
The constants are the prices of each product, hence the function for the total cost of p bags of popcorn and d drinks is given by:
C(p,d) = 3.35p + 4d.
Hence, for 3 bags and 8 drinks, the cost is:
C(3,8) = 3.35(3) + 4(8) = $42.05.
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At lunch, Kira eats either a burrito containing 490 milligrams of sodium or a peanut butter sandwich containing 700 milligrams of sodium. Her doctor told her to reduce her sodium to no more than 4,000 milligrams per week. Which inequality represents x, the number of microwave burritos, and y, the number of peanut butter sandwiches, she can eat each week?
490x + 700y < 4000
490x + 700y ≤ 4000
490x + 700y > 4000
490x + 700y ≥ 4000
Answer: 490*x + 700*y ≤ 4000
Answer:
its b
Step-by-step explanation:
PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT
Answer:
Option 3
Step-by-step explanation:
When y is positive, there is always increase.
Eliminate options 1 and 2.When y is negative, there is always decrease.
Eliminate option 4.help me understand this
Answer:
2
Step-by-step explanation:
According to the table, when x changes 7 units, y will change 14 units
x y
-28 -54
-21. -40
-14 - 26
-7 - 12
0 2
y-intercept is where the line intersects y axis, which x = 0
so y-intercept is 2
18. Simplify the complex fraction.
Answer:
B.
4*2=8
5*3=15
Answer:
A is 3\5; B is 8\3; C is 3\8; D is 5\3
Step-by-step explanation:
divide or multiply
i don't know if these are right bc I didn't do them in a long time.
if pi is 3.142 what is the area of a circle of radius 3.5 cm
Answer:
38.4895cm²
Step-by-step explanation:
The area=3.142×(3.5cm)²=38.4895cm²
Answer:
The Area of circle is 34.49cm
Step-by-step explanation:
⟼ Area of a circle = [tex] \sf \pi {r}^{2} [/tex]
where,
π = 3.142r = radius = 3.5cm⟼ Area = (3.142)(3.5)(3.5)
⟼ Area = (3.142)(12.25)
⟼ Area = 38.4895cm
in a study reported in the news, "researchers found that adults who used headphones with a screen, for more than one hour per day were at a 13% higher risk for hearing loss compared to those who used headphones with their screens less than one hour. the research team randomly surveyed 3,506 people in california about their screen/headphone behaviors, as well as information about ear infections and other noises a person may encounter at work and in daily life. participants were also given physical check-ups, including a hearing test and a physical exam of the ears and eyes. the increased likelihood of hearing loss remained, even after the researchers adjusted for risk factors such as construction noise and inner ear anatomy. the researchers found no increased risk among people who used headphones with a screen less than one hour per day.
Headphones that go over your ears can also damage your hearing if you use them too long or play music too loudly.
What is decibel explain with examples?
A decibel is a unit used to measure how loud something is using a logarithmic formula. It is also used to describe the degree of loudness. This is an example of when you listen to your music at the loudest volume that your iPod will allow.If you use over-the-ear headphones for an extended period of time or listen to loud music, you could end up damaging your hearing. They simply pose less of a risk than earphones do: The level of a sound can be increased by 6 to 9 decibels when the source is inside your ear canal, which can result in some major issues.Learn more about decibel
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Graph the line with the equation y= - 1/2x + 7
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope: 1^2
y-intercept: (0,7)
(XY)
(07)
(28)
Does the ratio 5 1/2 : 1 1/2 has the unit rate of 3 2/3
Based on the ratio, 5¹/₂ : 1¹/₂, the unit rate can be found to be so the statement is TRUE.
How to find the unit rate?To find the unit rate of a ratio, you should divide the first number in the ratio by the second number in the ratio.
When given the ratio, 5¹/₂ : 1¹/₂, therefore, the unit rate is:
= 5¹/₂ ÷ 1¹/₂
= 11/2 ÷ 3/2
= 11/2 x 2/3
= 22 / 6
= 3.6667
= 3²/₃
In conclusion, the unit rate of 5¹/₂ : 1¹/₂ is 3²/₃.
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-2x + y = 0
5x + 3y = -11
The solution for equations can be determined by .
-2x + y = 0
5x + 3y = -11
Equating both the equations
-6x+5x = -11
x= 11
substitute x in any one of the equation to find y value.
-2(11) + y = 0
y = 22
What is an equation?A declaration that two mathematical expressions are equal. a phrase that uses chemical symbols to illustrate a chemical reaction.
Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.
Equation is a mathematical term for a scenario where numerous aspects need to be taken into account. It is commonly expressed as a mathematical expression with equal values on either side and is defined as the state of equality.
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Call bag contains six red tiles and 15 yellow towels. lelia removes two red towels how many yellow tiles should she remove so that the ratio of red tiles to yellow towels in the bag stays equivalent to 6:15
5 yellow tiles should be removed.
The original ratio of red tiles to yellow tiles as per the question :Ratio = 6:15. Now, after removal of red tiles, the numerator of ratio will become = 6 - 2. The numerator of new ratio will be 4. For yellow tiles, let the number of yellow tiles removed be x. So, the denominator or new number of yellow tiles will be 15 - x.
Now, relating the two ratio -
6:15 = 4:(15 - x)
Performing cross-multiplication to find the value of x.
6 × (15 - x) = 4 × 15
Performing multiplication on both the Left Hand Side and Right Hand Side
90 - 6x = 60
6x = 90 - 60
Performing subtraction to find the value of x
6x = 30
x = [tex]\frac{30}{6}[/tex]
Performing division to find the value of x
x = 5
So, the number of yellow tiles to be removed is 5.
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The complete question is -
A bag contains 6 red tiles and 15 yellow tiles. Lilia removes 2 red tiles. How many yellow tiles should she remove so that the ratio of red tiles to yellow tiles in the bag stays equivalent to 6 : 15?
The phone company A Fee and Fee has a monthly cellular plan where a customer pays a flat monthly fee
and then a certain amount of money per minute used on the phone. If a customer uses 360 minutes, the
monthly cost will be $86. If the customer uses 610 minutes, the monthly cost will be $123.5.
A) Find an equation in the form y = mx +b, where x is the number of monthly minutes used and y is
the total monthly of the A Fee and Fee plan.
Answer: y =
B) Use your equation to find the total monthly cost if 945 minutes are used.
Answer: If 945 minutes are used, the total cost will be
dollars.
The equation in the form y = mx +b, where x is the number of monthly minutes used and y is the total monthly of the A Fee and Fee plan is: y = (3/20)x + 32 and the total monthly cost is $173.75.
Equationa. Equation
Slope = ( $123.5-$86)/(610-360)
Slope=37.5/250
Slope= 3/20
y = mx + b
Solve for "b"
$123.5 = (3/20)610 + b
$123.5 = 91.5 + b
b=$123.5-$91.5
b = 32
Equation:
y = (3/20)x + 32
b. Total cost
Total cost= (3/20)945+32
Total cost= 141.75+32
Total cost= $173.75
Therefore the equation in the form y = mx +b, where x is the number of monthly minutes used and y is the total monthly of the A Fee and Fee plan is: y = (3/20)x + 32 and the total monthly cost is $173.75.
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Which is it… Please.
Answer:
No association
Step-by-step explanation:
This type of data is usually random; think about it, how could what gender person you are affect how you survive? Children may have a higher chance, but that's primarily based on health. Women is about 3/4 and men about 1/4.
Hope this helps.
Find the area of parallelogram ABCD given mA = 30 and the following measures. AB = 6ft ; AX = 3 [square root] 3, A = ?
The area of the given parallelogram is: 9√3 sq. feet.
What is a parallelogram?A parallelogram is a simple quadrilateral with two sets of parallel sides in Euclidean geometry. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
Area of a parallelogram = Base of the Parallelogram * Height
Now, given:
A parallelogram ABCD,
AB = 6 feet, AX = 3√3. Angle A = 30°
To find: Area of the Parallelogram ABCD.
Finding: Here, AB = 6 feet = base
For height,
Height = perpendicular distance from X to AB
= AX(sinA)
Height = 3√3 (sin30) = 3√3 / 2
Thus, area of the parallelogram = [tex]\frac{3\sqrt{3}}{2}\times6= 9\sqrt{3}sq. feet.[/tex]
Hence, The area of the given parallelogram is: 9√3 sq. feet.
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Write 5 600 000 in standard form.
Step-by-step explanation:
5.6 × 10⁶
hope it's helpful
Find the quotients. Answer as whole numbers or fractions.
2/5 ÷ 3/4 =
9/4 ÷ 3/4 =
5/7 ÷ (-1/-3) =
(whole fraction is negative)
-5/3 ÷ 1/6 =
if its only ‘-‘ at the numerator that means only the numerator is negative )
Answer:
ANSWERS
1st Question: 8/15
2nd Question: 3
3rd Question: -2 1/7
4th Question: -10
Used a Calculator :3 hope it helps
the u.s. census bureau needs to estimate the median income of males in the u.s., they collect incomes from 2500 males. state the individual, variable, population, sample, parameter, and statistic.
Individual : a male in the United States
Variable : income
Population : All males in the United States
Sample : 2500 males of which the information is collected
Parameter : Median income of males in the U.S
Statistic : Median income of the 2500 males sampled
Any satisfactory, quantity, or number that can be gauged or tallied qualifies as a variable. A records object is some other name for a variable.A sample is a subset of units selected to symbolize all the people in a population. due to the fact only a portion of the populace become counted, it is only a partial enumeration. To estimate the traits of the total populace of hobby, facts from the sampled devices is used.A statistic is a numerical illustration of a sample, whereas a parameter is a numerical illustration of the complete populace.To learn more about statistics, visit :
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What is the measure of the angle shown below?
Answer:57 degrees
Step-by-step explanation:
It is just below the 60-degree line. And it is less than 90 degrees.
25 points plus brainliest
Answer:
The answer is C.
(0,4) and (3,0)
Step-by-step explanation:
To find the x, substitute 0 to the y.
* 4x + 3(0) = 12
> 4x = 12
> x = 3 (3,0)
To the y, substitute 0 to the x.
* 4(0) + 3y = 12
> 3y = 12
> y = 4 (0,4)
I hope you get this right!
Answer:
(0,4) and (3,0)
Step-by-step explanation:
Hope this helps :D
Translate the sentence into an equation.
Seven times the sum of a number and 3 equals 2.
Use the variable b for the unknown number.
0-0
X
OXO
0+0
Ś
The translation of the given sentence into an equation is: 7(b + 3) = 1.
How to Translate a Sentence into an Equation?Variables can be used to represent an unknown quantity when translating statements into equation. The word "times" is represented as or means "×" (multiplication). "Sum" means addition as well.
Thus, the sentence given can be translated as shown below:
The unknown number is represented as variable b.
"The sum of a number (b) and 3" would be translated as: b + 3.
"Seven (7) times the sum of a number and 3 (b + 3)" would therefore be: 7(b + 3).
Therefore, translating the whole sentence into an equation, we would have:
7(b + 3) = 1.
Thus, the translation of the given sentence into an equation is: 7(b + 3) = 1.
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Question 4 (1 point)
Choose all the terms in the expression
5x⁴ - 7x³ + x + 2
(below are multiple choice options)
5
5x⁴
-7x³
1
X
2
Answer: there are 4 terms and they are 5x^4, -7x^3, x, and 2
Step-by-step explanation:
An article is advertised for 262.50$ inclusive of 5% gst. find the original price
Answer: If we are looking at percentages you want to find what 262.50 is 5% of what number using the percentage rates equation, the original price would be, $525.00! Hope this helps!
Build Understanding
1
The table shows how many ounces of salsa you get
when buying small jars of salsa.
8
64
12
16
96
24
MaR
Small jars of salsa 4
Ounces of salsa
32
. Describe a pattern you see in the rows of the table. Oraciones con esas tablas de númeracion
The rows of small jars of salsa are increased by 4 times.
The rows of ounces of salsa are increased by 32 times.
The pattern in the column of the table is
y = 8x
Therefore x = 4 then y = 8(4) = 32
x = 8 then y = 8(8) = 64
x = 12 then y = 8(12) = 96
x = 16 then y= 8(16) = 128.
x = 20 then y = 8(20) = 160.
The pattern in the column of the table is
y = 8x
Therefore x = 4 then y = 8(4) = 32
x = 8 then y = 8(8) = 64
x = 12 then y = 8(12) = 96
x = 16 then y= 8(16) = 128.
x = 20 then y = 8(20) = 160.
The relationship between ounces of salsa and small jars of salsa using a unit rate is
4 ounces = 1 serving
y = 4x
If x = 1 then y = 4
If x = 2 then y = 4(2) = 8
If x = 3 then y = 4(3) = 12
If x = 4 then y = 4(4) = 16
If x = 5 then y = 4(5) = 20
The relationship using the unit rate is
48 ounces = 4 medium jars of salsa.
For 1 medium jars of salsa = 48/4 = 12 ounces.
1 medium jar of salsa = 12 ounces.
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Phoebe, Andy and Polly share £270
Phoebe gets 3 times as much as Andy who gets twice as much as Polly
work out how much they get each?
Answer:
Phoebe=180
Andy=60
Polly=30
Step-by-step explanation:
let Polly be x
:Andy becomes 2x while Phoebe becomes 6x
therefore 6x+2x+x=270
9x=270
x=30
Hence: Phoebe=6x=180
Andy =2x=60
Polly=x=30
a swimming pool has two pipes coming in. one fills the pool in four hours, the other in six hours. an outlet pipe empties the pool in five hours. the outlet pipe is accidentally left open. in how many hours is the pool full?
The pool is full for 4 hrs.
Add the rates of filling of the 2 filling pipes and
subtract the rate of draining of the emptying pipe;
1st pipe's rate: ( 1 pool filled ) / ( 3 h);
2nd pipe's rate: ( 1 pool filled ) / ( 6 h );
3rd pipe's rate of emptying: ( 1 pool emptied ) / ( 4 h);
Let t = the time in hrs to fill the pool with all 3 pipes open
1/3+16-1/4 = 1/t;
Multiply both sides by 24t;
t = 4 hrs
volume is a measure of occupied three-dimensional space. it's miles frequently quantified numerically using SI derived units (consisting of the cubic meter and liter) or by way of diverse imperial devices (inclusive of the gallon, quart, cubic inch).
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0.82, 45/50 ,80%
14. The numbers ordered from lowest to highest are
Answer:
Step-by-step explanation:
0.82, 45/50 ,80%
14. The numbers ordered from lowest to highest are
0.82 = 0.82
45/50 = 0.9
80% = 4/5 = 0.8
80%0.8245/50