Answer:
The mean and standard devaition of W are 6 and 31 respectively.
Step-by-step explanation:
Given that:
W = 7 + 2X
Variance (W) = Variance(7 + 2X)
For a term constant term, the variance is zero.
So;
[tex]W = Var (2X)[/tex]
W = 4 × Var(X)
W = 4 × (SD (X))²
W = 4 × (3)²
W = 4 × 9
W = 36
Thus, Variance (W) = 36
The standard deviation of W = [tex]\sqrt{variance}[/tex]
W = [tex]\sqrt{36}[/tex]
W = 6
Also;
E(W) = E(7 +2 X)
E(W) = 7 + 2 × E(X)
where;
mean X = 12
E(W) = 7 + 2(12)
E(W) = 31
Thus, the mean and standard devaition of W are 6 and 31 respectively.
The mean and the standard deviation of W are 31 and 6 respectively.
The given parameters are:
[tex]\mathbf{\bar x_x = 12}[/tex]
[tex]\mathbf{\sigma_x = 3}[/tex]
The definition of W is given as:
[tex]\mathbf{W = 7 + 2X}[/tex]
This means that:
[tex]\mathbf{Var(W) = Var(7) + Var(2X)}[/tex]
So, we have:
[tex]\mathbf{Var(W) = 0 + Var(2X)}[/tex] --- the variance of a constant term is 0
[tex]\mathbf{Var(W) = Var(2X)}[/tex]
This gives
[tex]\mathbf{Var(W) = 2^2 \times Var(X)}[/tex]
We have:
[tex]\mathbf{Var(X) = \sigma^2_x}[/tex]
So, the equation becomes
[tex]\mathbf{Var(W) = 2^2 \times \sigma^2_x}[/tex]
[tex]\mathbf{Var(W) = 2^2 \times 3^2}[/tex]
[tex]\mathbf{Var(W) = 36}[/tex]
The standard deviation is then calculated as:
[tex]\mathbf{\sigma_W = \sqrt{Var(W)}}[/tex]
[tex]\mathbf{\sigma_W = \sqrt{36}}[/tex]
[tex]\mathbf{\sigma_W = 6}[/tex]
The mean is then calculated as:
[tex]\mathbf{E(W) = E(7 + 2X)}[/tex]
This gives
[tex]\mathbf{E(W) = 7 + 2E(X)}[/tex]
So, we have:
[tex]\mathbf{E(W) = 7 + 2 \times 12}[/tex]
[tex]\mathbf{E(W) = 31}[/tex]
Hence, the mean and the standard deviation of W are 31 and 6 respectively.
Read more about mean and standard deviation at:
https://brainly.com/question/10729938
Four students simplified the expression.
410
45
Camilla added the exponents: 410 + 5 = 415
Bentley divided the exponents: 410 + 5 = 42
Mira multiplied the exponents: 410.5 = 450
Regan subtracted the exponents: 410 - 5 = 45
Which student correctly simplified the expression?
Answer:
camilaaaaaaaaaaaaaaa
Answer:
Regan subtracted the exponents: 410 − 5 = 45
PLZ HELP!
Ramon earns $1,820 each month and pays $53.20 on electricity. To the nearest tenth of a percent, what percent of Ramon's earnings are spent on electricity each month?
Step-by-step explanation:
2.6% b/c 1820×2.6/100
Mrs . Smith has 4 tables for her students. Each table can seat 5 students,
How many students can sit at all the tables?
A. 8
B. 9
C. 16
D. 20
E. 25
Answer:
D.20
Step-by-step explanation:
4*5=20
the sum of three consecutive integers is 261 , which equation could be used to find the integer .
Answer:
You got it wrong, its the first option
Step-by-step explanation:
Since its not asking for a consectuive EVEN or ODD integer its not
X + X+2 + X+4...
Instead its just the normal way
X + X+1 + X+2 + X+3....
SO thats the correct answer.
Marcy concludes that the following system of equations has one solution.
y = 3x + 6
y = -2x + 10
Which characteristic of the equations did she use to reach this conclusion?
A. They have different slopes.
B. They have the same two variables.
C. They have y on the same side of the equation.
D. They have the same slope, but different y-intercepts.
Answer:
A
Step-by-step explanation:
took test on edge
Answer:
A
Step-by-step explanation:
Just took the test
John has $10 in his bank account when he gets a job. He begins making $120 a day. A student found that
the equation that represents this situation is y = 10x + 120.
What is wrong with the student's equation? Complete the explanation and correct the student's error.
Answer:
The answer is switched.
Step-by-step explanation:
Given that John's bank account is $10 which is a constant (fixed) amount and he make $120 per day.
In the equation, x act as number of days so if you wants to find how much he earn after few days, you have to multiply $120 with the number of days.
The correct equation will be y = 120x + 10, 120 is the slope value and 10 is the y-intercept.
Please help me???? Transition math
A water tank already contains 55 gallons of water when John begins to fillet water flows into the tank at a rate of 8 gallons per minute write a linear equation to model the situation find the volume of the water tank in 25 minutes after John begins filling the tank.
Answer:
y= 8x + 55
After 25 minutes the tank will have 255 gallons
Step-by-step explanation:
A sheet of 28 stickers has star and heart stickers. There are 16 heart stickers. How many heart stickers does a pack of 140 stickers have? Choose equivalent ratios to show your reasoning. __ heart stickers; __ = __ fractions and numbers to drag: 60, 80, 12/28, 60/140, 80/140, 16/28, and 12
Answer:
80 heart stickers does a pack of 140 stickers
Step-by-step explanation:
The number of heart stickers in a pack of 140 stickers is 60.
Given that, a sheet of 28 stickers has star and heart stickers.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, the number of star stickers in a sheet
= 28-16 =12
The ratio of star and heart stickers
= 12:16
= 3:4
Now, 3+4=7
Number of heart stickers = 3/7 ×140
= 60
Therefore, the number of heart stickers in a pack of 140 stickers is 60.
To learn more about the ratio visit:
brainly.com/question/13419413.
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You go shopping and spend $264 on shirts and shorts. You purchase a total of 9 items. Each shirt costs $24 and each pair of shorts cost $32. How many of each did you buy?
Answer:
3 shirts, 6 shorts
Step-by-step explanation:
A total of $264 is spent during shopping on shirts and shorts
Each shirt costs $24
Each shorts cost $32
Therefore the quantity of shirts and shorts bought can be calculated as follows
24× 3= 72
32×6= 192
192+72= 264
Hence 3 shirts and 6 shorts were bought
Emma is making two different kinds of cookies for a cookie party she will be attending. She needs 2 and 2/3 cups of sugar for the first recipe and 1 and 1/4 cups of sugar for the second recipe. Emma thinks she will have enough sugar but she isn't quite sure. She knows that her full 2 pound bag of sugar says it contains 4 and 1/2 cups of sugar. Determine the exact difference between the amount of sugar Emma has and the amount of sugar she needs for the recipes.) Emma's mom brought home another 2 pound bag of sugar (4 and 1/2 cups) and wants to make fudge to take to work. Her mom will need 2 and 1/6 cups of sugar. Write a numerical expression that could be used to determine exactly how much sugar will be left over from the two bags of sugar after Emma bakes cookies and her mom makes fudge
Answer:
Step-by-step explanation:
Emma is making two different kinds of cookies for a cookie party she will be attending. She needs 2 and 2/3 cups of sugar for the first recipe and 1 and 1/4 cups of sugar for the second recipe. Emma thinks she will have enough sugar but she isn't quite sure. She knows that her full 2 pound bag of sugar says it contains 4 and 1/2 cups of sugar. Determine the exact difference between the amount of sugar Emma has and the amount of sugar she needs for the recipes.) Emma's mom brought home another 2 pound bag of sugar (4 and 1/2 cups) and wants to make fudge to take to work. Her mom will need 2 and 1/6 cups of sugar. Write a numerical expression that could be used to determine exactly how much sugar will be left over from the two bags of sugar after Emma bakes cookies and her mom makes fudge
Please Help!!! Find the slope of the line that passes through (63, 77) and (-10, -2).
Answer:
y=79/73x+644/73
theres the equation, enjoy <3
8.
Last week, Janet used 4 cups of flour to make pizza dough. This week, she uses 3/8
the amount of flour as last week. Which statement is true about the amount of
flour Janet uses this week?
Janet uses more than 4 cups of flour because 4 is greater than 1.
Janet uses more than 4 cups of flour because 4 is greater than 3/8.
Janet uses less than 4 cups of flour because is less than 1.
Janet uses less than 4 cups of flour because is less than 4.
As
Answer:
Janet uses less than 4 cups of flour because is less than 4.
Step-by-step explanation:
She is using 3/8 of 4 so less than. Then you use 4 not 1 because there is 4 cups.
Answer:
She uses less than four cups because 3/8 (1.5) is less than 4.
Step-by-step explanation:
If x-2 is one of the factors of x^4-kx^2+4, find the value of k.
Step-by-step explanation:
Given expression is x⁴-kx²+4 =0
x−2 is a factor of the given expression.
So, x=2
Substitute in the equation, we get
2⁴-k(2)²+4
⇒16+4k+4=0
⇒4k=−20
⇒k=−5
Work out the value of x.
4X - 57
3x + 25
3x + 15
2x - 3
4x
The diagram is not drawn to scale
Clue: I am 0.02 units away from -3.8. Where am I?
Answer:
-3.82
Step-by-step explanation:
You are going up the line of negative numbers so you have to add o.o2 to 3.8 (3.80).
Every day, Isabella practices the piano for 0.75 hour and the flute for 1.4 hours. What is the total number of hours that she practiced in April? (Reminder: April has 30 days
Answer:
She practiced a total of 64.5 hours
Step-by-step explanation:
Here, we need to know the number of hours practiced on both per day
Mathematically, that will be;
0.75 + 1.4 = 2.15 hours per day
So in 30 days ; the total number of hours will be
30 * 2.15 = 64.5 hours
4 Tan A/1-Tan^4=Tan2A + Sin2A
tan(2A) + sin(2A) = sin(2A)/cos(2A) + sin(2A)
• rewrite tan = sin/cos
… = 1/cos(2A) (sin(2A) + sin(2A) cos(2A))
• expand the functions of 2A using the double angle identities
… = 2/(2 cos²(A) - 1) (sin(A) cos(A) + sin(A) cos(A) (cos²(A) - sin²(A)))
• factor out sin(A) cos(A)
… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (1 + cos²(A) - sin²(A))
• simplify the last factor using the Pythagorean identity, 1 - sin²(A) = cos²(A)
… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (2 cos²(A))
• rearrange terms in the product
… = 2 sin(A) cos(A) (2 cos²(A))/(2 cos²(A) - 1)
• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(A)
… = 4 sin(A) cos(A) / (2 - 1/cos²(A))
• rewrite cos = 1/sec, i.e. sec = 1/cos
… = 4 sin(A) cos(A) / (2 - sec²(A))
• divide through again by cos²(A)
… = (4 sin(A)/cos(A)) / (2/cos²(A) - sec²(A)/cos²(A))
• rewrite sin/cos = tan and 1/cos = sec
… = 4 tan(A) / (2 sec²(A) - sec⁴(A))
• factor out sec²(A) in the denominator
… = 4 tan(A) / (sec²(A) (2 - sec²(A)))
• rewrite using the Pythagorean identity, sec²(A) = 1 + tan²(A)
… = 4 tan(A) / ((1 + tan²(A)) (2 - (1 + tan²(A))))
• simplify
… = 4 tan(A) / ((1 + tan²(A)) (1 - tan²(A)))
• condense the denominator as the difference of squares
… = 4 tan(A) / (1 - tan⁴(A))
(Note that some of these steps are optional or can be done simultaneously)
given that f(x)=2x/3 evaluate f^-1(6)
Answer:
9
Step-by-step explanation:
we know by definition that
[tex]f^{-1}(f(x))=x\\\\f^{-1}(\frac{2x}{3})=x\\\\f^{-1}(x)=ax\\\\f^{-1}(\frac{2x}{3})=a(\frac{2x}{3})=x\\\\f^{-1}(x)=\frac{3x}{2}[/tex]
so now we evaluate
[tex]f^{-1}(6)=\frac{3*6}{2}\\\\=3*3\\\\f^{-1}(6)=9[/tex]
and if we want to do an extra step
[tex]f^{-1}(f(6))=6\\\\f^{-1}(\frac{2*6}{3})=f^{-1}(4)=\frac{3*4}{2}=6[/tex]
which works.
A linear function is a function in which the dependent variable changes at a constant rate relative to the independent variable. Based on this assumption, determine whether each relationship below can be modeled by a linear function. Select Yes or No for each situation. Yes No The total number of tires, T, on c cars. C The cost, C. in dollars, of p pounds of tangerines 0 O The temperature, F, after m minutes of a pie taken out of the oven. The value, V, in dollars, of a bank account eaming compound interest after t years. OO
yes
no
no
yes
hope it help!!!
Yes, no, no, yes I believe
Help please. This is due at midnight
Answer:
Yes, he got the correct quotient
Step-by-step explanation:
1.5 divided by 1/3 is 4.5, and 4.5 is equal to 4 1/2
Answer:
Sage did it right.
your work:
1 1/2 ÷ 1/3
3/2 ÷ 1/3
3/2 × 3/1
9/2
4 1/2
Step-by-step explanation:
first convert 1 1/2 into an improper fraction:
multiply the 2 and 1, you get 2, than add that to the current numerator to get a new one. You get 3/2 as your improper fraction
you now have: 3/2 ÷ 1/3
then turn the division sign into a multiplication sign by flipping the divisor:
you get 3/2 × 3/1
solve this:
multiply the numerators together, you get 9 as a new numerator
multiply your denominators, you get 2 as your new denominator
so now you have 9/2
next turn this into a mixed fraction, you get 4 1/2
so Sage did it right.
Susan bought 12 ounces of candy. How many pounds did she buy?
Show the proportions needed
Answer:
If Susan bought 12 ounces that would equal to .75 pounds
Step-by-step explanation:
Write an equation of the line in slope-intercept form.
f(0)=9, f(2)=4
Answer:
f(x)=-[tex]\frac{5}{2}\\[/tex]x+9
Step-by-step explanation:
Use the slope formula and slope intercept formula form y=mx + b to find the equation
need help with this
Answer:
ΔABD is an obtuse triangle
Step-by-step explanation:
The type of a triangle according to its angle measures
The acute triangle ⇒ it has 3 acute anglesThe right triangle ⇒ it has 1 right angle and 2 acute anglesThe obtuse triangle ⇒ it has 1 obtuse angle and 2 acute angles0° < acute angle < 90°right angle = 90°90° < obtuse angle < 180°In triangle ABD
∵ m∠ABD = 100°
∵ m∠BAD = 50°
→ The sum of the interior angles of a triangle is 180°
∴ m∠ABD + m∠BAD + m∠BDA = 180°
∴ 100 + 50 + m∠BDA = 180
∴ 150 + m∠BDA = 180
→ Subtract 150 from both sides
∴ m∠BDA = 30°
∵ m∠ABD = 100°
∴ ∠ABD is an obtuse angle
∵ m∠BAD = 50° and m∠BDA = 30°
∴ ∠BAD and ∠BDA are acute angles
∵ ΔABD has 1 obtuse angle and 2 acute angles
∴ ΔABD is an obtuse triangle
FIRST TO GET IT RIGHT GETS BRAINLIEST PLSSS HELPPWhat type of function does the equation below represent?
y = -8x
O A. inversely proportional
OB. directly proportional
OC.
not a function
OD
neither directly nor inversely proportional
Answer:
The type of function the equation represents is "directly proportional" ⇒ B
Step-by-step explanation:
The equation of the directly proportional is y = kx, where k is the constant of proportionality, k is a real number that could be positive or negativeThe equation of the inversely proportional is xy = k or y = [tex]\frac{k}{x}[/tex] , where k is the constant of proportionality, k is a real number that could be positive or negativeLet us solve the question using the rules above
∵ The equation of the function is y = -8x
→ Compare it with the two forms above
∵ The equation is in the form of y = kx, where k = -8
∴ The equation represents directly proportional
∴ The type of function the equation represents is "directly proportional"
6 ft
5 ft
5 ft
4 ft
10 ft
SHAPE 1
SHAPE 2
NAME
Trapezoid
NA
FORMULA
PLUG IN VALUES
xG
Bx
AREA
pov you scrolling through brainly looking for a bots post
smh
Answer:
HoW diD yOu KnOw ?? :/
Step-by-step explanation:
:D have a blessed day <3
Answer:
no just trying to see who I can help
A^n =16 + (N - 1) (-0.5), 15th term
Find the indicated term of the arithmetic sequence.
Answer:
9
Step-by-step explanation:
we just replace n with 15
A(n) =16 + (N - 1) (-0.5)
=16 + (15 - 1) (-0.5)
=16-7.5+0.5
=9
hope it helps
Helpppppplpppo! Hurry hurry
Answer:
I hurried wat
Step-by-step explanation:
wAT
Determining Points on a Line Given a Direct Variation
y
x
y
What other points are on the line of direct variation through
(5, 12)? Check all that apply.
(0,0)
(2.5, 6)
36
32
28
24
(3, 10)
(7.5, 18)
20
18
(12.5, 24)
12
00
(15, 36)
x
Draw
8
12
10
Click or tap the graph to plot a point.
Tone
Answer:
Step-by-step explanationAl final de esta lección, debes ser capaz de:
Reconocer una relación de variación directa
Encontrar la fórmula de una relación de variación directa
Resolver problemas verbales asociados con variaciones directas
Introducción
x = Horas Trabajadas 0 1 2 3 4
y = Dólares Ganados 0 3 6 9 12
La tabla anterior muestra la relación entre las horas trabajadas y el dinero en dólares, que obtuvo Juan trabajando a razón de $3.00 por hora. En esta tabla, podemos ver que el dinero ganado es igual al producto de las horas trabajadas por 3. Otra manera de decir eso es que la constante de variación o proporción es igual o 3. También se puede observar que cada vez que x aumenta en un 1, la variable y aumenta en 3. Otra manera de decir eso es que la razón de cambio es igual a 3.
En la aplicación de abajo, mueve el botón de la barra “constante de variación” a 3. Observa que los puntos de la gráfica coinciden con los valores en la tabla, y que con cada aumento de 1 en x, la variable y aumenta 3 y que la relación entre las variables es y = 3 × x .
Lo sentimos, pero la GeoGebra Applet no se pudo iniciar. Por favor, asegzrese de que Java 1.4.2 (o posterior) esta instalado y activo en su navegador ( Haga clic aqum para instalar Java ahora )
Cajas de Leche 0 1 2 3 4
Botellas de Leche 0 4 8 12 16
Si cada caja de leche contiene 4 botellas, la tabla anterior muestra la relación entre el número de cajas de leche y el número de botellas que contienen. En esta tabla, podemos ver que el número de botellas de leche se obtiene multiplicando el número de cajas de leche por 4.
En la aplicación de arriba, mueve el botón de la barra constante de variación a 4. Observa que los puntos de la gráfica coinciden con los valores en la tabla, y que con cada aumento de 1 en x, y aumenta 4 y que la relación entre las variables es y = 4 × x.
.
Cantidad de dólares 0 1 2 3 4
Cantidad de galletas que se puede comprar 0 2 4 6 8
Si una galleta cuesta 50 centavos, la tabla anterior muestra la relación entre la cantidad de dólares y la cantidad de galletas que se puede comprar. En esta tabla, podemos ver que la cantidad de galletas se obtiene multiplicando la cantidad de dólares por 2.
En la aplicación de arriba, mueve el botón de la barra constante de variación a 2. Observa que los puntos de la gráfica coinciden con los valores en la tabla, y que con cada aumento de 1 en x, la variable y aumenta en 2 y que la relación entre las variables es y = 2 × x
.
En todas estas relaciones de los ejemplos anteriores, una variable es igual a otra variable multiplicada por una constante distinta de cero. Estas relaciones se conocen como proporciones directas o variaciones directas.
Definición
Dadas dos variables x y y, los enunciados:
y varía directamente como x,
y es directamente proporcional a x y
y es proporcional a x
todos significan que y = kx, para algún número real fijo k.
Al número k se le llama la constante de variación o constante de proporcionalidad. El valor de k también representa la razón de cambio de la relación. Es decir, cada aumento de 1 en x va a corresponder a un aumento de k en y.
Pasos para hallar la Fórmula para Relaciones de Variación Directa
Las relaciones de variación directa tienen la forma y = kx donde x y y son variables y k es una constante distinta de cero. La fórmula para una relación de variación directa se puede hallar mediante los siguientes pasos:
Paso 1: Traducir el enunciado a una fórmula de variación directa.
y es directamente proporcional a x significa
y =k·x
Paso 2: Sustituir las variables conocidas para encontrar k.
Paso 3: Sustituir k y escribir la fórmula.
Ejemplos
Ejemplo 1
u es proporcional a v. Si u = 16 cuando v = 4, escribe la fórmula para la relación entre u y v.
Paso 1: Traducir el enunciado a una fórmula de variación directa.
u es proporcional a v significa
u =k·v
Paso 2: Sustituir valores conocidos para encontrar k.
16 = k· 4
k=164=4
Paso 3: Sustituir k y escribir la fórmula.
u =4v
Conclusión: la fórmula para expresar la relación entre u y v es u =4v
Ejemplo 2
p varía directamente como z. Si p = 210 cuando z = 200, escribe la fórmula para expresar la relación entre p y z .
Paso 1: Traducir el enunciado a una fórmula de variación directa.
p varía directamente como z significa
p = k·z
Paso 2: Sustituir valores conocidos para encontrar k.
210 = k· 200
k=210200=1.05
Paso 3: Sustituir k y escribir la fórmula.
p =1.05z:
Answer:
A, B, D, F On edge!
Step-by-step explanation:
Have a good day! :3