Answer:
0.6892 = 68.92% of bottles are within specification.
Step-by-step explanation:
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
On average, each bottle contains 2.07 liters of soda, with a standard deviation of 0.06 liters.
This means that [tex]\mu = 2.07, \sigma = 0.06[/tex]
The plant’s quality manager wants to determine how well the process is operating.
To do this, we find the proportion of bottles within specification.
The specification limits for a bottle of soda are 2.1 liters and 1.9 liters
This is the pvalue of Z when X = 2.1 subtracted by the pvalue of Z when X = 1.9. So
X = 2.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.1 - 2.07}{0.06}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a pvalue of 0.6915.
X = 1.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.9 - 2.07}{0.06}[/tex]
[tex]Z = -2.83[/tex]
[tex]Z = -2.83[/tex] has a pvalue of 0.0023
0.6915 - 0.0023 = 0.6892
0.6892 = 68.92% of bottles are within specification.
wx=?
please i need help asap!
Answer:
24 because hsbs. hwhvw w Whelan has w hahaha
I will mark you brainalist
Answer:
1.25 since all prices are sam e
Step-by-step explanation:
help this is due today
Answer:
A
Step-by-step explanation:
Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal.) The results were as follows:
Duration of Exposure
< 1 1 to < 5 >= 5
Diseased 12 10 18
Sensitized 14 18 13
Normal 66 142 210
Required:
a. Compute the expected frequencies of diseased workers.
b. Compute the expected frequencies of sensitized workers.
c. How many degrees of freedom are there?
Answer:
1. Has been answered below
2. Degree of freedom is 4
Step-by-step explanation:
Row 1: 12+10+18 = 40
Row 2: 14+18+13 = 45
Row 3: 66+142+210 = 418
Grand total = 40+45+418 = 503
Column 1 : 12+14+66 = 92
Column 2: 10+18+142 = 170
Column 3: 18+13+210 = 241
Total = 92+170+241 = 503
Expected frequencies of diseased workers
92x40/503 = 7.316
170x40/503 = 13.52
241 x 40/503 = 19.165
Expected frequencies of sensitized workers
92x45/503 = 8.23
170x45/503 = 15.20
241x 45/503 = 21.56
2.
Degree of freedom
= (Number of row -1)(number of column - 1)
= 3-1 * 3-1
= 2x2
= 4
Antonio constructs a model of a moon orbiting a planet along an elliptical orbit. The equation StartFraction x squared Over 342.25 EndFraction + StartFraction y squared Over 324 EndFraction = 1, with units in inches, represents the shape of the orbit. If the planet is located at one of the foci, which phrase describes a possible location of the model planet relative to the center?
approximately 0.5 in. below the center
approximately 4.3 in. above the center
approximately 0.5 in. to the left of the center
approximately 4.3 in. to the right of the center
Answer:
D
Step-by-step explanation:
edge
D. approximately 4.3 in. to the right of the center
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the problem; determining, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a teacher may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Learn more about problem-solving here
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#SPJ2
PLEAS HELP THERE IS PIC drag the tiles to the correct boxes to complete the pairs. how many solutions does each equations have ?
Answer:
|2x+1|=0 has one solutions
2|x+1|=-2 has no solution
|x+21|=2 has two solution
Step-by-step explanation:
Part 1: Identify key features and graph a parabola from standard form.
Answer the following questions to determine the key features of the parabola based on the
equation shown, and then graph it.
12(x + 3) = (y - 2)^2
a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation.
(1 point)
b) What is the vertex of the parabola? (1 point)
c) What is the focus of the parabola? (2 points)
d) What is the directrix of the parabola? (2 points)
e) Sketch a graph of the parabola and label the vertex, focus, directrix, and axis of symmetry. (4 point
Answer:
a) The axis of symmetry is the line, y = 2
b) The vertex of a parabola is (-3, 2)
c) The focus of the parabola is (0, 2)
d) The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola
Step-by-step explanation:
a) The function for the parabola can be expressed as follows;
12·(x + 3) = (y - 2)²
The general form of the equation of the parabola is x = a·(y - k)² + h
The axis of symmetry is the line, y = k
By comparison, with the given equation of the parabola, we have;
12·(x + 3) = (y - 2)²
x = (1/12)·(y - 2)² - 3
Therefore;
a = (1/12), k = 2, h = -3
The axis of symmetry is y = k
∴ The axis of symmetry is the line, y = 2
b) The vertex of a parabola = (h, k)
∴ The vertex of a parabola = (-3, 2)
c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]
Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)
The focus of the parabola = (0, 2)
d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]
[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]
The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel
The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6
It is given that the parabola equation is [tex]\rm 12(x+3)=(y-2)^2[/tex]
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We know the standard form of a parabola is:
[tex]\rm x= a(y-k)^2+h[/tex] .........(1)
We have the equation of parabola:
[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)
a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.
By comparing the equation (1) and (2), we get:
Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.
b) Vertex of the parabola = (h,k): (-3, 2)
c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],
[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]
∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]
The focus of the parabola is (0, 2)
d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]
[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]
The directrix of a is x = -6
e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry
Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6
Know more about the parabola here:
brainly.com/question/8708520
two numbered cubes are rolled then a spinner with 4 different colors on it spun twice then two coins are flipped how many total possible outcomes are their(show you working out)
Answer: 12 possible outcomes in total
Step-by-step explanation:
If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.
Answer:
A' (-2,-4) B' (-3,-7) C' (-1,-8) D' (1,-6)
Step-by-step explanation:
Just take it one point at a time and move each point down 3 and 4 left. Prime notation just means to put this little sign ' so it indicates that this is the new coordinate. So A was (2,-1) and A' (the new one) is (-2,-4)
Please help me with this :)
Please help it’s pretty easy and ikr reward brainiest
Answer:
Choice 1 is correct: 8/3 x 1/4 = 2/3
Step-by-step explanation:
PLEASE ANSWER QUICK
The sum of the data values divided by the number of data values is a measure of ______ and is called the _____
FIRST BLANK'S OPTIONS = CENTER/SPREAD
SECOND BLANK'S OPTIONS = MEAN/MEAN ABSOLUTE DEVIATION/MEDIAN/RANGE
Answer:
Center... Mean
Step-by-step explanation:
The mean of a data set is the sum of the values divided by the number of values. The median of a data set is the middle value when the values are written in numerical order.
Fill in the blank so that the ordered pair is a solution of y = 22 – 9x.
( ,4)
What is the slope of the line below? If necessary, enter your answer as a
fraction in lowest terms, using the slash (/) as the fraction bar. Do not enter
your answer as a decimal number or an equation.
(5, 11)
(-5, -1)
9514 1404 393
Answer:
6/5
Step-by-step explanation:
The slope formula is useful for finding the slope.
m = (y2 -y1)/(x2 -x1)
m = (-1 -11)/(-5 -5) = -12/-10
m = 6/5
The slope of the line through the given points is 6/5.
Allison and Megan were at track practice. The track is 3/8 kilometers around.
- Allison ran 1 lap in 3 minutes.
- Megan ran 4 laps in 6 minutes.
How many minutes does it take Allison to run one kilometer?
Allison ran 3/8 km (0.375 km) in 3 minutes.
Set up a proportion to find how long it takes for her to run 1 km
[tex]\frac{0.375\textrm{km}}{3 \textrm{min}} = \frac{1\textrm{km}}{x \textrm{min}}[/tex]
Cross multiply to get:
[tex]3 = 0.375x[/tex]
Solve:
[tex]x = \frac{3}{0.375}[/tex]
x = 8 minutes
Please help!!!!!!!!!!!!
Answer:
a) 5 cm b) 12in c) 7yd
I think it's so simple. Anyways
This is your answer. If I'm right so,
Please mark me as brainliest. thanks!!!
Answer:
5 cm, 12in, 3.5 yrds
Step-by-step explanation:
to find the radius you divide the diamenter by 2.
b) The cost (x) for hiring and artist for a stage show for (y) hours is represente
as 2y + x = 20.
Draw the graph 2y + x = 20 on the grid below.
[4]
The easiest way is to transform this equation to intercept form of straight line.
[tex]\\[/tex]
Intercept form of straight line:
[tex]\dfrac{x}{a}+\dfrac{y}{b}=1[/tex]where [tex]a[/tex] is the x intercept - where the graph intersects the x axis, and [tex]b[/tex] is the y intercept - where the graph intersects the y axis.
[tex]\\[/tex]
Given that,
[tex]2y + x = 20[/tex]
[tex] \longrightarrow \: \dfrac{2}{20}y + \dfrac{x}{20} = 1[/tex]
[tex] \longrightarrow \: \dfrac{x}{20} + \dfrac{y}{10} = 1[/tex]
On comparing with [tex]\dfrac{x}{a}+\dfrac{y}{b}=1,[/tex] we get,
[tex]a=20[/tex][tex]b=10[/tex]Hence, the graph shall cut the x axis and y axis at 20 and 10 respectively. This information is enough to plot the graph.
[tex]\\[/tex]
Graph: Refer to the attachment.
Nadia bought tickets to attend a spaghetti supper fundraiser at her school. The equation can be used to find , the cost of each ticket in dollars. Which equation represents the cost of each ticket?
Calculate the area of this trapezium.
6 cm
4 cm
5 cm
8 cm
area=1/2(AB+0A)Ac=4cm
Answer:
28cm²
Step-by-step explanation:
Area of trapezium = 1/2×(6+8)×4
= 28cm²
If you don’t know I don’t answer (NO LINKS ) please helllllppppp
Answer:
Step-by-step explanation:
1. 6.96 in
2. 2.6 in
3. 8.1 in
4. 5.6 m
5. 1.89 cm
6. 6 in
A trawler caught 2/3 ton of fish on Monday and 1/2 on Tuesday. What was the total amount of fish caught?
Answer:
1 1/6 ton
Step-by-step explanation:
A market researcher analyzing the fast-food industry noticed the following: The historical average amount spent at an upscale restaurant was $150.30, with a standard deviation of $50. The researcher wishes to have a sampling error of $5 or less and be 95 percent confident of an estimate to be made about average amount spent at an upscale restaurant from a survey. What sample size should be used (round the number up)
Answer:
A sample size of 385 should be used.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
What sample size should be used (round the number up)
A sample of n should be used.
n is found when M = 5.
We have that [tex]\sigma = 50[/tex]
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5 = 1.96\frac{50}{\sqrt{n}}[/tex]
[tex]5\sqrt{n} = 1.96*50[/tex]
Simplifying by 10
[tex]\sqrt{n} = 1.96*10[/tex]
[tex]\sqrt{n} = 19.6[/tex]
[tex](\sqrt{n})^2 = (19.6)^2[/tex]
[tex]n = 384.16[/tex]
Rounding up
A sample size of 385 should be used.
Can someone help me please?
Answer:
uh i dont know lol im new how do i use this thing bahahaha
Step-by-step explanation:
On Triangle ABC, Angle A measures 30 degrees, Angle B measures 90 degrees, and Angle C measures 60 degrees. List the sides of Triangle ABC in order from shortest to longest.
Answer:
A=30 B=90 C=60
Step-by-step explanation:
A=30 C=60 B=90
A jar contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the
probability that the first jelly bean will be blue and the second will be blue as well?
(1.75)^2 in expanded form
Answer:
1.75 x 1.75
fillerfillerfiller
DONT answer if you don’t know
Answer:
c. 8 1/4 inches.
Step-by-step explanation:
The snail crawls 2 3/4 inches in 1 minute.
In 3 minutes, it can crawl 2 3/4 x 3 inches.
= 8 1/4 inches.
From the set {1, 4, 6}, use substitution to determine which value of x makes the equation true. 10 x + 8 = 48
Can someone please help me with this?
Jenny and Buddy collected 376 plastic bottles for recycling.
They recycled 131 bottles on Monday and 114 bottles on Tuesday.
How many bottles do they have left to recycle?
Complete the equations to solve. Enter your answers in the boxes.
Let
m
=
the number of bottles left to recycle after Monday.
Answer:
151
Step-by-step explanation:
114+131= 272 376-272=104