Answer:
0.9544 = 95.44% probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Suppose the mean fill for the shipment is actually 50 gallons. Standard deviation of 0.6 gallons.
This means that [tex]\mu = 50, \sigma = 0.6[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{0.6}{\sqrt{100}} = 0.06[/tex]
What is the probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons?
This is the pvalue of Z when X = 50.12 subtracted by the pvalue of Z when X = 49.88. So
X = 50.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{50.12 - 50}{0.06}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 49.88
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{49.88 - 50}{0.06}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons.
Solve for x:
3-a/x-a=1/a
PLEASE HELP NEED ASAPPP WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWERRRR
a2 (exponent 2)
x= - _______
1 - 3a + a2 (exponent 2)
Mark brainliest please.
Please Help i need this done
Answer:
i think u add 2.5 everytime
Step-by-step explanation:
for example start with(0, 2.5) 0n the graph then add 2.5 to 2.5 then keep adding if im wrong srry
Solve the inequality. 4/5v < 7/15
Answer:
v < 7/12
Step-by-step explanation:
which scatterplot most likely has a line of best fit represented by y=-2x-1?
NO LINKS PLS
Answer:
The answer to your question is the letter C
Answer:
I think it is c
Step-by-step explanation:
the product of 5 and 6 reduced by t
Answer:
5(6-t)
Step-by-step explanation:
in math, product means the "sum" of the equation or the final answer
and in your case, that means 5*6, but then we also have to remember that we're "reducing" or subtracting 't'-
5(6-t)
good luck :)
i hope this helps
brainliest would be highly appreciated
have a nice day!
Solve the system of equations
There is a box of colored marbles on the counter top. There are 24 blue, 16 green, and 56 red.
Write the ratio of green marbles to red marbles. Don't forget to put your answer in simplest form.
Answer:
i think its 2:7
Step-by-step explanation:
heres why
16 and 56 both have a number that equals which it is 8
so u divide
16/8=2
56/8=7
16:56 in simplest form is 2:7
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 40 % salt and Solution B is 90 % salt. She wants to obtain 50 ounces of a mixture that is 80 % salt. How many ounces of each solution should she use?
Answer:
The scientist must use 10 ounces of Solution A and 40 ounces of Solution B.
Step-by-step explanation:
Since a scientist has two solutions, which she has labeled Solution A and Solution B, each containing salt, and she knows that Solution A is 40% salt and Solution B is 90% salt, and she wants to obtain 50 ounces of a mixture that is 80% salt, to determine how many ounces of each solution should she use the following calculation must be performed:
100 x 0.9 + 0 x 0.4 = 90
90 x 0.9 + 10 x 0.4 = 85
80 x 0.9 + 20 x 0.4 = 80
50 x 0.8 = 40
Therefore, the scientist must use 10 ounces of Solution A and 40 ounces of Solution B.
find the volume of 6✓2cm
Step-by-step explanation:
Complete Question :-
find the volume of a cube of side 6✓2cm .We know that the Volume of a cube is cube of side . So,
[tex]\implies Volume = side^3 \\\\\implies Volume = (6\sqrt2 \ cm)^3 \\\\\implies\boxed{\boxed{ Volume= 432\sqrt2\ cm^3}}[/tex]
Adrian is putting streamers across the ceiling of his dining room to decorate for his nephews birthday party. The ceiling is rectangular. Its area is 122,5 square feet, and its
width is 7 feet. How long should Adrian cut a streamer that will run the length of the ceiling?
Answer: 17.5 feet long.
A 50 foot ladder is set against the side of a house so that it reaches up 40 feet. If Aisha grabs the ladder at its base and pulls it 9 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 31 ft.) Round to the nearest tenth of a foot.
Answer: ~31.3
first use the pythagorean theorem. a^2+(40)^2=50^2.
simply. a+1600=2500. subtract 1600 from both sides. a^2=900.
square root both sides to get a= 30
then find how far the top of the ladder is from the ground once in its new position.
a^2+(39)^2=50^2.
simplify. a^2+1512=2500. subtract 1512 from both sides to get a^2=979.
square root both sides to get a=31.288975. round to the nearest tenth to get a=31.3
Answer:
Step-by-step explanation: iT'S 31.3
Which is the better definition of line of best fit?
A line of best fit guides a line through a scatter plot of data points that best describes the association between those points.
What is line of best fit?
A line of best fit guides a line through a scatter plot of data points that best describes the association between those points. Statisticians typically utilize the least squares approach to arrive at the geometric equation for the line, either through manual computations or regression analysis software.
A line of best fit can be approximately specified utilizing an eyeball the method by marking a straight line on a scatter plot so that the numeral of points above the line and below the line stands about equal (and the line passes via as many points as possible).
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Monica hizo galletas de dos tamaños como se muestra en la imagen. ¿Cuánto mide el lado Z de la galleta más grande?
A computer game was originally priced at $59.99. It was marked down 15%. Then it was moved to a clearance rack marked "Take an additional 50% off the lowest marked price." What was the final price of the computer game?
Answer:
25.50 is the final price
Step-by-step explanation:
First find the new price at 15% off
59.99 * 15%
59.99 * .15
9.00
Subtract 9 dollars from the price
59.99-9.00
50.99
Now take 50% off
50.99 * 50%
50.99*.50
25.50
50.99-25.50
25.50
I need help please don’t scam or no brainlist
find the value of x. Pregunta matemática
Answer:
Ejercicios Resueltos
ANGULOS
1. Si el complemento de ángulo x es 2x, ¿Cuál es el valor de x en
grados?
Solución:
2x x 90 += °
3x 90
x 90 / 3
x 30
= °
= °
= °
2. Si el suplemento del ángulo x es 5x, ¿Cuál es el valor de x?
Solución:
5x+x=180
6x=180
x=180 /6
x=30
°
°
°
°
3- Determínese los dos ángulos x e y, cuya suma es 90 y cuya
diferencia es 10 .
°
°
Solución:
-Planteamos el sistema de ecuaciones:
x y 90
x y 10
+= °
−= °
-Resolvemos el sistema. Mediante el método de suma y resta
obtenemos:
2x 100
x 100 / 2
x 50
= °
= °
= °
-Hacemos la sustitución del valor encontrado de x en la primera
ecuación: 50 y 90
y 90 50
y 40
°+ = °
= °−
= °
°
∴La solución al problema es x 50 , y 40 =°= °
°
4. Hállense dos ángulos complementarios tales que su diferencia sea
30° .
Solución:
-Planteamos el sistema de ecuaciones:
x y 90
x y 30
+= °
−= °
-Resolvemos el sistema. Mediante el método de suma y resta
obtenemos:
2x 120
x 120 / 2
x 60
= °
= °
= °
-Hacemos la sustitución del valor encontrado de x en la primera
ecuación:
60 y 90
y 90 60
y 30
°+ = °
= °−
= °
∴La solución al problema es x 60 , y 30 = °= °
°
5. Hállense dos ángulos suplementarios tales que el uno sea 20 mayor
que el otro.
°
Solución:
-Planteamos el sistema de ecuaciones:
x y 180
x y 20
+= °
=+ °
-Resolvemos el sistema:
(y 20 ) y 180
2y 180 20
2y 160
y 80
+ °+ =
= °− °
= °
= °
-Hacemos la sustitución del valor encontrado de y en la primera
ecuación: x 80 180
x 180 80
x 100
+ °=
= °−
= °
°
°
∴La solución al problema es:
x = °= ° 100 , y 180
TRIANGULOS
1.- ¿Cuánto miden cada uno de los ángulos interiores del siguiente
triángulo?
Solución:
Nota: La suma de los ángulos interiores de los triángulos es
180° .
((( A B C 180 ++= °
3x 5x 4x 180 ++ = °
12x 180 = °∴( ( (( A 22.5 , B 52.5 , C 30 , CBR 127.5 = ° = ° =° = °
x 15 = °
∴( ( A 45 , B 75 ,C 60 =° =°= °
°
°
°
°
°
°
2.- ¿Cuánto miden cada uno de los ángulos del siguiente triángulo?
Solución
a) Ángulo extendido
( ( B CBR 180 + = Esto debido a que son ángulos suplementarios
(B 15x 60 180 + − °=
(B 180 60 15x = °+ °−
(B 240 15x = °−
b) Suma de los ángulos interiores del triángulo
((( A B C 180 ++=
3x (240 15x) 4x 180 + °− + =
7x (240 15x) 180 + °− =
− + °= 8x 240 180− =− 8x 160°
x 7.5 =
∴( ( (( A 22.5 , B 52.5 , C 30 , CBR 127.5 = ° = ° =° = °
3.- Escribe la definición de bisectriz del triángulo.
Es la semirrecta que biseca el ángulo, es decir, divide el ángulo
en dos ángulos congruentes.
4.- ¿Qué es la mediatriz de un triángulo?
La mediatriz de un lado de un triángulo (y en general de un
segmento de recta), es la recta perpendicular a ese lado en su
punto medio.
5.- ¿Que es la mediana de un triángulo?
La mediana de un triángulo, es el segmento de la recta que une
un vértice con el punto medio del lado opuesto.
CUADRILATEROS
1.- ¿Qué cuadrilátero tiene las dos diagonales iguales y sus lados son
iguales dos a dos?
Rectángulo
2.- Si los ángulos de un cuadrilátero miden, respectivamente, 80º, 110º
y 70º, ¿Cuánto medirá el ángulo que falta?
100º
3.- ¿Cuál es el paralelogramo que tiene las diagonales perpendiculares?
Rombo
4.- ¿Cómo se llama el cuadrilátero que tiene dos lados paralelos?
Trapecio
5.- Encuentra el área del paralelogramo que tiene 5cm de base y 3 de
altura
A b*a
A 5*3
A 15
=
=
=
POLÍGONOS 1.- Cuatro ángulos interiores de un pentágono valen respectivamente
110°, 90°, 85° y 125°. ¿Cuánto vale el quinto ángulo?
Solución:
Si la suma de los ángulos interiores de un polígono es:
180°*(n-2)=180°*(5-2) = 540°, a lo que le se le resta los
valores de los ángulos que se dieron, consecuentemente, el
quinto ángulo vale 130°.
2.- ¿Cuántos lados tiene, en cada caso, el polígono cuyos ángulos
interiores suman respectivamente 1080°, 900°, 1260°?
Solución:
Despejando de la fórmula el valor de n, tenemos que:
. 2
180
suma angulos n = ° + , y esto aplicado a cada valor de la suma de los
ángulos internos, obtenemos que los valores de n son 8, 7 y 9
respectivamente.
3.- ¿Cuánto vale cada ángulo exterior de un octágono regular?
Solución:
Aplicando el teorema de que la suma de los ángulos exteriores
de un polígono es 360°, entonces cada ángulo exterior vale
360°/8 = 45°
4.- Calcular los ángulos exteriores de un triángulo rectángulo que tiene
un ángulo agudo doble del otro.
Solución:
Se tiene que la suma de los ángulos interiores es
180°*(n-2)= 180° y éste a su vez es igual a 90° + x + 2x,
despejando x de 3x = 90°, x= 30°, entonces los ángulos
interiores son 30°, 60° y 90°, teniendo como ángulos exteriores
150°, 120° y 90°.
Step-by-step explanation:
8 (6-4x) = 12
equation with parentheses
Answer:
x=9/8
Step-by-step explanation:
1. If x and y are vertical angles, then y _____ has the same measure as x.
2. If x and y are adjacent angles, then x and y are ____ acute
Fill in blank with (sometimes, never, always)
Someone please help me for brainliest and 30 points. Please DO NOT answer if u don’t know. And do not put in the comment here’s a link cause it leads to no where. Ty.
Answer: 1. Sometimes 2. Always
Step-by-step explanation:
I am pretty sure these are right.
Gina is shopping for a new bicycle. The price of the bicycle is $300 and there is an 8% sales tax. Gina wants to know the total price of the bicycle including soles tax. How much sales tax does Gina pay on the bicycle? Enter the amount in the table.
Answer:
24
Step-by-step explanation:
The person above me is incorrect . I got it right on the i-Ready Quiz!
ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP
Step-by-step explanation:
11.True
12.False
13.False
14.False
15.True
16.False
17.False
18.True
19.True
20.False
Answer:
here
Step-by-step explanation:
1.36 km is how many cm
Answer:
136000 cm
Step-by-step explanation:
I think it's helps you
1
Write the equation of a circle whose center is at (-11,–8) and whose radius is 4.
Answer:
Step-by-step explanation:
[tex](x_c,y_c)=(-11,-8) \quad r=4\\(x-x_c)^2+(y-y_c)^2=r^2 \quad (x+11)^2+(y+8)^2=4^2[/tex]
there were 125 customers at walmart. 64% paid with a credit card;the rest paid with cash. how many paid with cash?
Answer:
45
Step-by-step explanation:
100-64 is 36. 36% paid with cash 125×35%=45 or 125×.36=45
A woman decides to have children until she has her first girl or until she has five children; whichever happens first. Find the expected value and standard deviation of X. Let X represent the number of children she has. Assume that she is equally likely to give birth to a boy or a girl on each child, and that gender is independent between children.
(a) Write out and sketch the complete probability distribution function for X.
(b) Write out and sketch the complete cumulative distribution function for X.
(c) Find the expected value and standard deviation of X.
Answer:
E(X) = 1.9375
SD(X) = 1.20
Step-by-step explanation:
Let :
G = girl ; B = Boy
P(G) = 0.5 ; P(B) = 0.5
Sample space :
G, BG, BBG, BBBG, BBBBG, BBBBB
Using the multiplication rule of independence :
P(G) = 0.5
P(BG) = 0.5 * 0.5 = 0.25
P(BBG) = 0.5 * 0.5 * 0.5 = 0.125
P(BBBG) = 0.5 * 0.5 * 0.5 * 0.5 = 0.0625
P(BBBBG) = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125
P(BBBBB) = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125
Creating a probability distribution table :
X = 1, 2, 3, 4, 5
For X = 5 ;
P(BBBBG) + P(BBBBB) = 0.03125 + 0.03125 = 0.0625
X :___ 1 ____ 2 ____ 3 _____ 4 _____ 5
P(X) : 0.5 __ 0.25 _ 0.125 _0.0625 _0.0625
The expected value E(X) :
√(ΣX * P(X)) = (1*0.5)+(2*0.25)+(3*0.125)+(4*0.0625)+(5*0.0625) = 1.9375
The standard deviation SD(x) :
√(ΣX²*p(x) - E(X)²
√((1^2*0.5)+(2^2*0.25)+(3^2*0.125)+(4^2*0.0625)+(5^2*0.0625) - 1.9375^2)
√(5.1875 - 3.75390625)
√1.43359375
SD(X) = 1.197
SD(X) = 1.20
What happens to the volume of a sphere if its radius is multiplied by 6?
Answer:
216 times the original
Step-by-step explanation:
Volume 1 = 4/3 πr³
volume 2 = 4/3 π(6r)³
v 2 / v 1 = 6³ = 216
When the radius of a sphere is multiplied by 6, the volume is multiplied by 216
How to determine the volume?Let the radius of the sphere be r
The volume of a sphere of radius, r is calculated as:
v = 4/3 πr³
When multiplied by 6, the radius becomes:
R = 6r
The new volume is then calculated as:
V = 4/3 π(6r)³
Divide both volumes
V/v = 4/3 π(6r)³ / 4/3 πr³
Evaluate the quotient
V/v = 6³
V/v = 216
Hence, when the radius of a sphere is multiplied by 6, the volume is multiplied by 216
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THE TOPIC IS: AREA OF CIRCLES!! PLEASE HELP ME WITH THIS QUESTION!!! WHATS THE ANSWER?? I WILL GIVE YOU BRAINLIEST AND A THANKS!!! AND PLS PUT AN EXPLANATION!! THANK YOU GUYS SO MUCHHHH!!
Answer:
If you are finding area then the area is 254.34
Step-by-step explanation:
Area of a circle- 3.14 times radius squared
3.14 (pi) times 81 (9 squared)
-4x+3x<4 what is the awenswer to this equation
Answer:
X > -4
Step-by-step explanation:
Collect the like terms which literally leaves you with -x<4
Then just changes the signs, hence the answer.
Please mark brainliest!
Find the vertex and focus of
(x+3)^2 = 4 (y+2)
Answer: I don’t know how to solve x but look at the picture
Step-by-step explanation: Hope this help :D
55 times 4 and time 3 equals what?
Answer:
55 times 4 =220
220 times 3 =660
Leslie tunes a guitar with 6 strings and a piano with 37 times as many strings.
How many strings did the piano have?
Choose 1 answer:
(Choice A)
The piano has 422 strings, because 37×6=422.
(Choice B)
The piano has 222 strings, because 37×6=222.
(Choice C)
The piano has 6 strings, because 37÷6=6 remainder 1.