Answer:
a. 0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish
b. 0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL
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 establishes 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.
Mean 18 mL and standard deviation 0.6 mL.
This means that [tex]\mu = 18, \sigma = 0.6[/tex]
a. What is the probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish?
This is the p-value of Z when X = 17.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{0.6}[/tex]
[tex]Z = -0.83[/tex]
[tex]Z = -0.83[/tex] has a p-value of 0.2033
0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish.
b. What is the probability that the average fill of the twelve bottles is more than 17.5mL?
Twelve bottles, so now [tex]n = 12, s = \frac{0.6}{\sqrt{12}}[/tex]
The probability is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.5 - 18}{\frac{0.6}{\sqrt{12}}}[/tex]
[tex]Z = -2.89[/tex]
[tex]Z = -2.89[/tex] has a p-value of 0.0019
0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL
Which expression is equivalent to:
-(4a-4b)
-4a-4b
-8a+4b
-8ab
-4a+4b
Step-by-step explanation:
-4a+4b is equivalent to -(4a-4b).hope it helpsstay safe healthy and happy..Write the equation of the line that passes through the points (6,-6)
and (7,-4) Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
9514 1404 393
Answer:
y +6 = 2(x -6)
Step-by-step explanation:
The slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-4 -(-6))/(7 -6) = 2/1 = 2
The point-slope equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Using the slope we found and the first point, the equation is ...
y +6 = 2(x -6)
Suppose that next year the U.S. will be in one of the following economic conditions: Boom, Moderate Growth, Recession, or Depression. The probability that each economic condition will occur, and that a jewelry store will earn profits within that broader economic condition are listed below:
Economic Condition Probability. Jewelry Store Profits
Boom 0.40 $400,000
Moderate Growth 0.30 $300,000
Recession 0.20 $100,000
Depression 0.10 -$500,000
The standard deviation of the jewelry store's profits next year is
The mid point of the line segment joining the points A(4,7) and B(2,5)
Answer:
hope it helps you.......
It May Help You
Thank You:)
Mrs. Brown, Mrs. White, and Mrs. Gray are a teacher, a doctor, and a lawyer, not necessarily in that order. Each has a horse. One horse is white, one is brown, and one is gray. From the following clues, determine the occupation of each woman and the color of her horse. No one’s name is the same as the color of her horse. The teacher owns a brown horse. Mrs. Gray is a doctor.
Answers:
Mrs. Brown ( lawyer ) owns the gray horse.Mrs. White ( teacher ) owns the brown horseMrs Gray ( doctor ) owns the white horse===========================================================
Explanation:
We're given these three clues
Clue 1: No one's name is the same as the color of her horseClue 2: The teacher owns a brown horseClue 3: Mrs. Gray is a doctor.Clue 3 is what we'll start with. Since Mrs. Gray is a doctor, this means that the doctor owns either a white horse or a brown horse. The doctor can't own a gray horse because the names can't match up (eg: the last name Gray with gray horse), due to clue 1.
If Mrs. Gray owned a brown horse, then she'd be a teacher (clue 2). But clue 3 says she's a doctor. We have a contradiction if Mrs. Gray owns the brown horse. Therefore, Mrs. Gray owns the white horse.
----------------
After we concluded the last section, we now know the following:
The horses that are left are the brown and gray horse.The professions left are the teacher and lawyer.The people left are Mrs. Brown and Mrs. White.In short, we've just crossed "Mrs. Gray", "doctor", and "white horse" from the list.
Based on clue 1, we know that Mrs. Brown cannot possibly own the brown horse. Therefore, she must own the gray horse. So Mrs. White must own the brown horse.
Since Mrs. White owns the brown horse, she must be the teacher (clue 2). That leaves "lawyer" as the last profession, and that's assigned to Mrs. Brown.
----------------
Side note: I apologize for being a bit wordy, but I wanted to be very careful in the logical sense as to approach this problem. There's probably a much quicker efficient way to do this.
Which row of the table reveals the y-intercept of function f?
Answer:
No solution is possible from the informatin provided.
Step-by-step explanation:
You didn't include the table,
Answer:
y intercept is found from the pair that has a 0 for the x variable.
Step-by-step explanation:
if a choice was (0,2) this would be the point where the line intercepts the y axis.
x=0 is the position of the vertical line, and 2 is how high up the graph the line passes through the y-axis
Consider the following conditional statement. Determine the contrapositive
of the statement and then determine if the contrapositive is true or false.
If two angles are not complements, then their measures do not add up to 180°.
The contrapositive of the statement is true.
The contrapositve of the statement is false.
Answer:
The contrapositive of the statement is true.
Step-by-step explanation:
For a general statement:
p ⇒ q
The contrapositive statement is:
¬q ⇒ ¬p
where:
¬q is the negation of the proposition q.
Here we have the statement:
If two angles are not complements, then their measures do not add up to 180°
So we have:
p = two angles are not complements
q = their measures do not add up to 180°
Then the negations are:
¬p = two angles are complements
¬q = their measures do add up to 180°
The contrapositive statement is:
"if for two angles their measures do add up to 180°, then the two angles are complements"
This is true, if for two angles the sum of their measures is equal to 180°, then these angles are complementary.
Then: The contrapositive of the statement is true.
help pls i'll mark brainliest.. state the length of the line segment shown.
Answer:
i believe its 3 but i could be wrong
Step-by-step explanation:
sorry if i am..
Show A and Show B are two of the most popular television shows of all time. The number of episodes of each show are consecutive even integers whose sum is 570. If there are more episodes of Show A, how many episodes of each were there?
Answer:
A = 286 episodes
B = 284 episodes
Step-by-step explanation:
Let n = the [tex]\text{number of episodes}[/tex] of show B
n + 2 = the [tex]\text{number of episodes}[/tex] of show A
Therefore, according to the question,
The sum of the number of the episodes of each show are consecutive even integers = 570
Therefore,
n + n + 2 = 570
2n + 2 = 570
2n = 568
n = 284
Therefore, the number of episodes for B = 284
The number of episodes for A = n + 2 = 284 + 2
= 286
C. Directions: Complete the table ( Area of a Circle).
Radius Diameter Area
16. _____ 7.5cm _______
17. 10cm _______ _______
18. 21cm ________ _______
pasagot po plss bukas na po pasahan ko
Answer:
3.75cm 44.16cm²
20cm 314cm²
42cm 1384.74cm²
Step-by-step explanation:
Area of a circle = πr²
Where : = π = pi = 3.14
R = radius
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
16. Radius = 7.5 / 2 = 3.75
Area = 3.14 x 3.75² = 44.16
17. Diameter = 10 x 2 = 20
Area = 10² x 3.14 = 314
18. Diameter = 21 x 2 = 42
Area = 21² x 3.14 = 1384.74
6.
40 x 6+ (9+21)
I need help ASAP please due tomorrow show work
GIVING OUT BRAINLIEST PLEASE HELP ME!!
Answer: B (0,0) r=4
Step-by-step explanation:
In a sale, Ali buys a television for $195.80.
The original price was $220.
Calculate the percentage reduction on the original price.
11%
Hope this helps! :)
______________
Answer:
[tex] \frac{195.80}{220} \times 100 \% \\ = 0.89\%[/tex]
(a+b)2=??? hihihihihihii
PLS HELP
the simplest form of this product has a numerator of
x + 2
x - 2
( x - 2 ) ( x - 2 )
( x + 2 ) ( x - 2 )
and a denominator of
x - 5
( x - 5 ) ( x - 1 )
x - 1
( x + 5 ) ( x + 1 )
the expression has an excluded value of x
- 5
2
-1
5
(x+2)(x-2) / (x-1)(x-5) this is the simplified form of the expression.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.
x²-3x-10/x²-6x+5 • x-2/x-5
We can factor the numerator and denominator of the first fraction as follows: (x-5)(x+2) / (x-5)(x-1)
Notice that there's a common factor of x-5 in both the numerator and denominator. We can cancel them out, leaving: (x+2) / (x-1)
Now let's simplify the second fraction:
x-2 / x-5
We can't simplify this fraction any further, so we leave it as is.
Putting it all together, we get:
(x+2) / (x-1) * (x-2) / (x-5)
Multiplying the two fractions, we get:
(x+2)(x-2) / (x-1)(x-5)
This is the simplified form of the expression.
To learn more about fraction from the given link:
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five times the sum of the digits of a two digit number is 9 less than the number formed by reversing its digits . if four times the value of the digit at ones place is equal to half of the place value of the digit at tens place, find the numbers
9514 1404 393
Answer:
45
Step-by-step explanation:
Let x and y represent the tens and ones digits, respectively. The 5 times the sum of digits is 5(x+y). The value of the digit-reversed number is (10y+x), so the required relation is ...
5(x +y) = (10y +x) -9
The other relationship between the digits is given as ...
4y = 1/2(10x)
A graphing calculator shows the solution to these equations is (x, y) = (4, 5).
The two-digit number is 45.
__
Additional comment
You can solve these equations in any of a variety of ways. Using a graphing calculator to find integer solutions is fast and easy, so is one of my favorites. Here, the coefficients on one equation are not easy multiples of those in the other, so substitution and/or elimination can get messy. In this situation, I like to use the "cross-multiplication" method, which starts with the equations in general form:
4x -5y +9 = 05x -4y +0 = 0From the coefficients of these equations, differences of cross products are formed:
d1 = 4(-4) -(5)(-5) = 9d2 = -5(0) -(-4)(9) = 36d3 = 9(5) -0(4) = 45Then the solutions are the solutions to 1/d1 = x/d2 = y/d3:
x = d2/d1 = 36/9 = 4y= d3/d1 = 45/9 = 5(x, y) = (4, 5) ⇒ the number is 45.
__
This method is one of several variations of Cramer's Rule, the general solution of systems of linear equations using matrix methods.
d= (r+c)t
how do i solve for t?
Answer:
[tex] { \tt{d = (r + c)t}}[/tex]
Divide ( r+c ) on both sides:
[tex]{ \tt{t = { \frac{d}{(r + c)} }}}[/tex]
Answer:
d / ( r + c) = t
Step-by-step explanation:
d = ( r + c ) t
Divide each side by ( r + c)
d / (r + c ) = ( r + c ) t / ( r + c)
d / ( r + c) = t
In a mathematics each correct answer gains 5 marks - However, 1 mark is deducted for each incorrect answer. Mary answered 30 questions for a total of 78 marks Determine the number of correct and incorrect questions Mary answered.
Answer:
Correct answers= 18
Incorrect answers=30-18= 12 answers
Step-by-step explanation:
total questions=30
correct answers= x
incorrect answers= 30-x
given: 5 marks for each correct answer
therefore, marks for correct answers = 5*x = 5x
Given: 1 mark deducted for every incorrect answer
therefore, marks deducted = 1(30-x) = 30-x
Total marks scored= 78
★ The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78
5x- (30-x) =78
5x-30+x=78
5x+x=78+30
6x= 108
x=108/6 = 18
Correct answers= 18
Incorrect answers=30-18= 12 answers
Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 21 cups of coffee, using 294 ounces of coffee, while collecting a total of $24.35. How many cups of each size did Kyle fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ 20-oz cup(s).
Kyle filled 6 10-oz cup(s), 11 14-oz cup(s), and 4 20-oz cup(s).
Let's define the variables:
x = number of 10-oz cups of coffee sold.
y = number of 14-oz cups of coffee sold.
z = number of 20-oz cups of coffee sold.
We know that:
Kyle served 21 cups of coffee, then:
x + y + z = 21
He used 294 ounces of coffee, then:
x*10 oz + y*14 oz + z*20 oz = 294 oz
He collected a total of $24.35, then:
x*($0.95) + y*($1.15) + z*($1.50) = $24.35
Then we have a system of 3 equations:
x + y + z = 21
x*10 oz + y*14 oz + z*20 oz = 294 oz
x*($0.95) + y*($1.15) + z*($1.50) = $24.35
To solve this, the first thing we need to do is isolate one of the variables in one of the equations, let's isolate x in the first one.
x = 21 - y - z
Now we can replace this in the other two equations to get:
(21 - y - z)*10 oz + y*14 oz + z*20 oz = 294 oz
(21 - y - z)*($0.95) + y*($1.15) + z*($1.50) = $24.35
Now we can simplify these two equations:
y*4 oz + z*10 oz = 294 oz - 210oz = 84 oz
y*($0.20) + z*($0.55) = $24.35 - $19.94 = $4.40
Now we need to do the same thing, we need to isolate one of the variables in one of the equations, we can isolate z in the first one:
z*10 oz = 84oz - y*4 oz
z = (84oz - y*4 oz)/10oz
z = 8.4 - y*0.4
Now we can replace this in the other equation:
y*($0.20) + ( 8.4 - y*0.4)*($0.55) = $4.40
Now we can solve this for y.
y*($0.20) + $4.62 - y*$0.22 = $4.40
y*$0.02 = $4.40 - $4.62 = $0.22
y = $0.22/$0.02 = 11
Now that we know the value of y, we can use:
z = 8.4 - y*0.4
z = 8.4 - 11*0.4 = 4
Now that we know the value of z and y we can use:
x = 21 - y - z
x = 21 - 11 - 4 = 6
Then we found:
x = 6
y = 11
z = 4
this means that:
Kyle filled 6 10-oz cup(s), 11 14-oz cup(s), and 4 20-oz cup(s).
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/20067450
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
A. In 2 - In x
B. In 1 + In 2 - ln x
C. 1 + In 2 - In x
D. In 2 + ln x
Answer:c
Step-by-step explanation:
The equivalent expression is 1 + In 2 - In x.
How to estimate an equivalent to the given expression?Given:
[tex]$\ln \left(\frac{2 e}{x}\right)$[/tex]
Apply log rule:
[tex]$$\log _{C}\left(\frac{a}{b}\right)=\log _{c}(a)-\log _{c}(b)$[/tex]
[tex]$&\ln \left(\frac{2 e}{x}\right)=\ln (2 e)-\ln (x) \\[/tex]
= ln (2e) - ln (x)
Apply log rule:
[tex]$\log _{c}(a b)=\log _{c}(a)+\log _{c}(b)$[/tex]
ln (2e) = ln (2) + ln (e)
= ln (2) + ln (e) - ln (x)
Apply log rule:
[tex]$\log _{a}(a)=1$[/tex]
= ln (2)+1-ln (x)
Therefore, the correct answer is option C. 1 + In 2 - In x.
To learn more about log rule
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HW HELP ASAP PLZZZZZ
Answer:
last step is (2x + 5)(2x + 1)
Step-by-step explanation:
4x^2 + 12x + 5
4x^2 + (10 + 2)x + 5
4x^2 + 10x + 2x + 5
2x(2x + 5) +1(2x + 5)
(2x + 5)(2x + 1)
Which statement best describes the areas and perimeters of the figures?
Answer:
The last one!
Step-by-step explanation:
2 units
5
2 units
2 units
8 units
2 units
2 units
2 units
6 units
The area of the figure is
square units.
Can someone help me simplify it more?
Answer:
8[tex]v^{-3}[/tex]z - [tex]\frac{5}{3}[/tex] vz
Step-by-step explanation:
!pls help!
Use a net to find the surface area
Answer:
336 square inches
Step-by-step explanation:
Nets are the spreaded out version/outline of 3d figures. It shows the faces of the figure. The figure in this case is actually a triangular prism.
find the area of each shape in the net:
Triangle A (1/2 x base x height)
1/2 • 8 x 6 = 24 square inches
Rectangle B (length x width):
6 x 12 = 72 square inches
Rectangle C:
8 x 12 = 96 square inches
Rectangle D:
10 x 12 = 120 square inches
Triangle E:
1/2 x 6 x 8 = 24 square inches
Add up all the areas of all shapes:
24 + 24 + 120 + 72 + 96 = 336
Surface area is measured in square inches
(Inches in this case)
Hope this helps
Use the diagram to solve. What is 135% of 280?
Step-by-step explanation:
[tex] \frac{135}{100} \times \frac{280}{1} = 378[/tex]
How much is six dimes, 8 nickels, and three one-dollar bills? *
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{Guide}\downarrow[/tex]
[tex]\large\textsf{Penny: 1 cent} \\\large\textsf{Nickel: 5 cents}\\\large\textsf{Dime: 10 cents}\\\large\textsf{Quarter: 25 cents}\\\large\textsf{Half dollar: 50 cents}\\\large\textsf{1 bill = 1 dollar}[/tex]
[tex]\large\textsf{6 dimes:}\downarrow[/tex]
[tex]\large\textsf{= 10 + 10 + 10 + 10 + 10 + 10}[/tex]
[tex]\large\textsf{= 20 + 20 + 20}[/tex]
[tex]\large\textsf{= 40 + 20}[/tex]
[tex]\large\textsf{= \bf 60}[/tex]
[tex]\large\textsf{6 dimes = \bf 60 cents}[/tex]
[tex]\large\textsf{8 nickels}[/tex]
[tex]\large\textsf{= 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5}[/tex]
[tex]\large\textsf{= 10 + 10 + 10 + 10}[/tex]
[tex]\mathsf{= 20 + 20}[/tex]
[tex]\large\textsf{= \bf 40}[/tex]
[tex]\large\textsf{8 nickels = \bf 40 cents}[/tex]
[tex]\large\textsf{3 one dollar bills}[/tex]
[tex]\large\textsf{= 1 + 1 + 1}[/tex]
[tex]\large\textsf{= 2 + 1 }[/tex]
[tex]\large\textsf{= \bf 3}[/tex]
[tex]\large\textsf{3 one dollar bills = \bf 3 dollars}[/tex]
[tex]\large\textsf{NOW LETS SOLVE FOR YOUR EQUATION}[/tex]
[tex]\large\textsf{3.00 + 0.60 + 0.40}[/tex]
[tex]\large\textsf{= 3.60 + 0.40 }[/tex]
[tex]\large\textsf{= \bf \$4}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore, your answer is: \huge \bf \$4}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
By how much is the sum of 3 2/3 and 2 1/5 less than 7
Step-by-step explanation:
32/3+21/5÷7
14.87÷7
2.124
Antiderivative of Acceleration is???
Answer:
Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.
Step-by-step explanation:
Answer:
Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.
A shopkeeper bought bycicle for rs 3520 and a mobile for rs 4690 . he sold both the items for rs 8650 calculate how much money did he gain
Answer:
Rs 440
Step-by-step explanation:
Price of bicycle = 3520
Price of mobile = 4690
Cost Price of both mobile and bicycle = 3520 + 4690
=> 8210
Selling price of both mobile and bicycle = 8650
Profit = selling price - cost price
= 8650 - 8210
= 440
Therefore he gained Rs 440
