Complete Question
The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected.
Required:
a) Find the probability that the drink is less than 11.9 fluid ounces
b) Find the probability that the drink is between 11.6 and 11.9 fluid ounces
c) Find the probability that the drink is more than 12.6 fluid ounces. Can this be considered an unusual event? Explain your reasoning.
Answer:
a
[tex] P(X < 11.9 ) = 0.25239 [/tex ]
b
[tex]P( 11.6 < X < 11.9 ) = 0.20463 [/tex]
c
[tex] P(X > 12.6 ) = 0.047757 [/tex ]
Yes It is an unusual event
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 12.1[/tex]
The standard deviation is [tex]\sigma =0.3[/tex]
Generally the probability that the drink is less than 11.9 fluid ounces is mathematically represented as
P(X < 11.9 ) = P(\frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} )
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex] P(X < 11.9 ) = P(Z< -0.667 ) [/tex ]
From the z table the area under the normal curve to the left corresponding to -0.667 is
P(Z< -0.667 ) = 0.25239
So
[tex] P(X < 11.9 ) = 0.25239 [/tex ]
Generally the probability that the drink is between 11.6 and 11.9 fluid ounces is mathematically represented as
[tex] P( 11.6 < X < 11.9 ) = P( \frac{11.6 -12.1}{0.3} < \frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} ) [/tex]
[tex]P( 11.6 < X < 11.9 ) = P( -1.667 < Z < -0.667 ) [/tex]
=> [tex]P( 11.6 < X < 11.9 ) = P( Z < -0.667) - P ( Z < -1.667 ) [/tex]
From the z table the area under the normal curve to the left corresponding to -1.667 is
P(Z< -1.667 ) = 0.047757
So
[tex]P( 11.6 < X < 11.9 ) = 0.25239 - 0.047757 [/tex]
=> [tex]P( 11.6 < X < 11.9 ) = 0.20463 [/tex]
Generally the probability that the drink is more than 12.6 fluid ounces is mathematically represented as
P(X > 12.6 ) = P(\frac{X -\mu}{\sigma } > \frac{12.6 - 12.1}{0.3} )
[tex] P(X >12.6 ) = P(Z> 1.667 ) [/tex ]
From the z table the area under the normal curve to the right corresponding to 1.667 is
P(Z> 1.667 ) = 0.047757
So
[tex] P(X > 12.6 ) = 0.047757 [/tex ]
Given that this probability is less than 0.05 , it mean it is an unusual event
Mrs canales class is selling pizza to earn money for a field trip. For every pizza sold the class makes $5.35. They have already earned $182.90 toward their $750 goal. How many more pizzas must they sell to earn $750 (algebraic approach) Thanks
Answer:
They still have to earn:
$750 - $182.9 = $567.1
and if they make $5.35 for every pizza sold:
$567.1 : $5.35 = 106
They must sell 106 pizzas more.
Step-by-step explanation:
You can buy 5 bananas for $4.25. What is the unit price per banana?
Answer: 85 cents
Step-by-step explanation:
Answer:
$0.85 per banana
Step-by-step explanation:
if you can get 5 bananas for $4.25 then you need to figure out how much you need to pay for 1. To do that you go 4.25 divided by 5 which is .85. so thats your answer, you can cha]eck it by going .85 times 5 which will get you 4.25
A fast food chain sells 4,500 hamburgers per hour worldwide. How many hamburgers does the fast food chain sell worldwide in 1 minute?
Answer:
75 hamburgers per minute
Step-by-step explanation:
We’ll it’s 4500 per hour, or every 60 minutes, to find 1 min, you can divide by 60.
4500/60 = 75
At the carnival, the ratio of people who won the ring toss game to lost it was 8 : 5. If 56
people won, how many people would have lost?
Answer:
The answer is 35
Step-by-step explanation:
First of all, note that 56 is the same as 56/1 since 56 divided by 1 is 56. Therefore, start by setting up the problem like this:
Step 1: 56/1 x 8/5 =
Step 2: Multiply the numerators together (56 x 8 = 448) and multiply the denominators together (1 x 5 = 5) and make it into one fraction like so 448/5 Step 3: Convert the improper fraction above to a mixed number to get the answer: 89 3/5
That's it! Now you know how to calculate 56 times 8:5.
Answer:
35
Step-by-step explanation:
There are 33 students in your class. Yesterday, 9 students were absent. What decimal represents the students were absent? *
Answer:
27.27% of the class was absent
Step-by-step explanation
Jason buys a jar of vitamins that contains 180 tablets. He
saves $5 by using a coupon. He pays $11.20. What is the cost
of each tablet for someone who does not have a coupon?
Write and solve an equation for this situation. Solve the
problem.
Answer: 11 cents
Step-by-step explanation:
add 11.20 +5=16.20, then dived by 180, which equals .11
Given 2x+4y=12 what is the x and y int
Write each parabola in the form y−k=a(x−h)^2 and determine its vertex: y=−4x^2+16x−19
Matt and Chris leave their uncle's house in Phoenix at the same time, Matt drives west on 1-60 at a speed of 79 miles per hour. Chris drives east on 1-60 at a speed of 83 miles per hour.
How many hours will it take them to be 64 miles apart
Two boats leave the same dock in Cairo at the same time. One heads north on the Mississippi River while the other heads south. The northbound boat travels five miles per hour. The
southbound boat goes seven miles per hour How many hours will it take them to be 66 miles apart?
he
Addit
Answer:
It will take them (Matt and Chris) 0.395 hours to be 64 miles apart
It will take 5.5 hours for the boats to be 66 miles apart
Step-by-step explanation:
We are to determine the time when Matt and Chris will be 64 miles apart, that is, when the total distance traveled by both of them will be 64 miles.
Let the time be t and
Let the distance covered by Matt be S₁ and the distance covered by Chris be S₂.
For Matt,
From the question, Matt drives at a speed of 79 miles per hour
From the formula
Distance = Speed × Time
S = v × t
∴ S₁ = 79×t
S₁ = 79t
For Chris,
From the question, Chris drives at a speed of 83 miles per hour
Using the same formula,
∴ S₂ = 83 × t
S₂ = 83t
To determine when they will be 64 miles apart, that is when S₁ + S₂ = 64 miles.
Hence,
S₁ + S₂ = 79t + 83t
∴64 = 79t + 83t
64 = 162t
t = 64/162
t = 0.395 hours
Hence, it will take them 0.395 hours to be 64 miles apart.
For the boats,
To determine how many hours it will take them to be 66 miles apart, that is when the total distance traveled by the two boats will be 66 miles.
Let the time be t and
Let the distance traveled by the northbound boat be S₁ and the distance traveled by the southbound both be S₂.
From the question,
The northbound boat travels five miles per hour
From the formula
Velocity = Distance / Time
Then, Distance = Velocity × Time
That is, S = v × t
Hence, for the northbound boat,
S = S₁
v = 5 miles per hour
∴ S₁ = 5t
Also from the question,
The southbound boat goes seven miles per hour
Hence, for the southbound boat
S = S₂
v = 7 miles per hour
∴ S₂ = 7t
To determine when the boats will be 66 miles apart, that is when S₁ + S₂ = 66 miles
Then,
S₁ + S₂ = 5t + 7t
Hence,
66 = 5t + 7t
66 = 12t
t = 66/12
t = 5.5 hours
Hence, it will take 5.5 hours for the boats to be 66 miles apart.
20+20 omg.please help :(
Answer:
40
Step-by-step explanation:
Complete the table of values for this equation:
y = 4x +30
Enter your answer by filling in the boxes
Answer:
42, 46, and 50.
Step-by-step explanation:
We need to plug in each x value to find the y values.
1) y = 4(3) + 30
y = 12 + 30
y = 42
2) y = 4(4) + 30
y = 16 + 30
y = 46
3) y = 4(5) + 30
y = 20 + 30
y = 50
Suppose a team is to be formed consisting of a head chef, sous chef, and dishwasher, in that order. What is the probability of forming such a team with 6 people?
Answer:
0.0083
Step-by-step explanation:
From the given information;
The total number of individual in the team = 3
The number of ways the team, which comprises of head chef, sous chef, and dishwasher can be arranged = [tex]^{6}P_3[/tex]
= (6×5×4×3!)/3!
= 6×5×4
= 120 ways
The probability of forming such a team with 6 people = 1/120
= 0.0083
Which of the following equations has only one solution?
X( x - 1) = 9
x2 - 6x + 9 = 0
x2 = 9
Answer:
x^2 - 6x + 9
Step-by-step explanation:
x(x - 1) = 9
x^2 - x - 9 = 0
x = 3.54 or x = -2.54 (using quadratic formula)
x^2 - 6x + 9 = 0
(x-3)^2 = 0
x = 3
x^2 = 9
x = ±√3 (any positive number square rooted always have 2 answers)
Help guyssssssssssssss
Answer:
1
Step-by-step explanation:
36/ BLANK= 12/ BLANK FILL IN THE BLANKS PLEASE
Answer:
All real numbers
Step-by-step explanation:
36/something1 = 12/something2
36/12=3
to get from something1 to something2 you divide by 3
36/3x=12/x
Cross multiply
36x=12*3x
36x=36x
x=x
Since each side of the equation is equal, the solution is all real numbers
I hope this helps :)
Does this equation have no solution, one solution, or infinite number of solutions x=y-3 2x-2y=-6
Answer:
Infinite amount of solutions
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesAlg I
Solving systems of equations by substitution/eliminationStep-by-step explanation:
Step 1: Define systems
x = y - 3
2x - 2y = -6
Step 2: Solve for y
Substitute: 2(y - 3) - 2y = -6Distribute 2: 2y - 6 - 2y = -6Combine like terms: -6 = -6Here we see that -6 does equal -6. Therefore, any value y would work as a solution. Hence, this systems of equations has an infinite amount of solutions.
Please help 30 points for a quick response!!
Find the equation of the line.
6
The line is parallel to y =--x + 1 and passes through the point (-7, -3).
7
The equation of the line is
Answer:
y = - x - 10
Step-by-step explanation:
y - (- 3) = - (x + 7)
y = - x - 10
What is the purpose of a pilot sample?
a. To help clarify how the sampling process will be performed.
b. To provide an idea of what the population standard deviation might be.
c. To save time and money instead of having to carry out a full sampling plan.
d. To provide a better idea of what the population mean will be.
Answer:
b. To provide an idea of what the population standard deviation might be
Step-by-step explanation:
Pilot sample can be regarded as the
small scale preliminary experiment whereby a smaller size of samples which is smaller compare to expected size is taken population of interest which gives the estimate for the population standard deviation.
The population standard mean is a parameter and it's been calculated from every entity of the population and
can be calculated using below formula
σ =√Σ (xi -μ)^2 /N
Where N= size of the population
σ= population standard mean
μ= population mean
Xi=each sample from the population
Which shows two expressions that are equivalent to (-8)(-12)(2)?
The solution is option C.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
(-8)(-12)(2)
=96*2
=192
so. we get,
It would be c because when you multiply 8 and 12 you get 96 and when you multiply 96x2 you get 192 .
so, therefore your answer is c.
To learn more on multiplication click:
brainly.com/question/5992872
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40 subtracted from five times a number is 8 more than the number write the equation
Answer (let x be the number):
5x - 40 = x + 8
I hope this helps!
The number in the equation 5n - 40 + 8 = n is 8.
What is a numerical expression ?A numerical expression is formed by numbers and their operation.A numerical expression can also be constructed from given statements.
We can also construct numerical expression form real life scenarios.
According to to the question statement 40 subtracted from five times a number is 8 more than the number and we have to form an numerical expression.
Let the number be 'n'.
∴ 5n - 40 + 8 = n
5n - n = 40 - 8.
4n = 32.
n = 32/4.
n = 8.
learn more about numerical expression here :
https://brainly.com/question/14642484
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OK THIS IS MAH 3rd QUESTION CAN SOMEONE PLS HELP MEH?
I REALLY NEED HELP PLS!
:3
Answer:
The earthquake was a magnitude 6.8, which describes the relative size of the earthquake at the spot where it occurred. Earthquakes with a magnitude larger than 6 tend to be severe and cause damage.
Step-by-step explanation:
Now that i wrote this passage you have to figure out which one it is
What is the measure of an angle if the measures of its two adjacent supplementary angles add up to 100°?
The answer is not 80 btw
Explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130
Answer:
130°
Step-by-step explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130
hey guys what is this type of equation/ question called 1 < x < 30
Answer:
2,3,4,5,6,7,8,9,10,...29
Step-by-step explanation:
put 1.12 2.10 3.11.40 4.10.48 5.10.95 6.10.72 7.11.53 in a number line
Answer:Add them up
Step-by-step explanation:
Write an algebra expression to represent each scenario:
“the sum of 6 and y”
Answer:
6+y
Step-by-step explanation:
simple:)
Helen had Php7500 for shopping money. When she got home, she had Php132.75 in her pocket. How much did she spend for shopping?
Answer:
Step-by-step explanation:
Helen had Php7500 for shopping money
she had Php132.75 in her pocket
she spend= 7500.00-132.75
=7367.25answer
HEEEEEEEEEEEELLLLLLPPPPPPPPP
what makes this number special 8549176230
Uhm hope this help (:
8,549,176,320 What makes this number unique? Answer: The said number has all the numbers from 0-9 exactly once and what is special is they are in lexicographical order of their English words.
how to find a inequality