Answer:
a) 0.9938 = 99.38% probability that the boxes will end up with at least 1 pound of cereal
b) 16.121 ounces.
c) 16.0664 ounces.
d) Between 16.0342 and 16.1658 ounces.
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 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.
Mean of 16.1 ounces, standard deviation of 0.04 ounces. So
[tex]\mu = 16.1, \sigma = 0.04[/tex]
(a) What is the probability of the boxes will end up with at least 1 pound of cereal?
One pound is 16 ounces, so this is 1 subtracted by the pvalue of Z when X = 16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 16.1}{0.04}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
1 - 0.0062 = 0.9938
0.9938 = 99.38% probability that the boxes will end up with at least 1 pound of cereal.
(b) The seventy percent of the boxes will contain less than what number of ounces?
Less than the 70th percentile, which is X when Z has a pvalue of 0.7. So X when Z = 0.525.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.525 = \frac{X - 16.1}{0.04}[/tex]
[tex]X - 16.1 = 0.525*0.04[/tex]
[tex]X = 16.121[/tex]
16.121 ounces.
(c) Eighty percent of the boxes will contain more than what number of ounces?
More than the 100 - 80 = 20th percentile, which is X when Z has a pvalue of 0.2. So X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 16.1}{0.04}[/tex]
[tex]X - 16.1 = -0.84*0.04[/tex]
[tex]X = 16.0664[/tex]
16.0664 ounces.
(d) The middle 90% of the boxes will be between what two weights?
Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile.
5th percentile:
X when Z has a pvalue of 0.05, so X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 16.1}{0.04}[/tex]
[tex]X - 16.1 = -1.645*0.04[/tex]
[tex]X = 16.0342[/tex]
95th percentile:
X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 16.1}{0.04}[/tex]
[tex]X - 16.1 = 1.645*0.04[/tex]
[tex]X = 16.1658[/tex]
Between 16.0342 and 16.1658 ounces.
It can be deduced that the probability of the boxes ending up with at least 1 pound of cereal will be 99.38%.
How to calculate the probabilityThe Z score based on the information will be:
Z = (16 - 16.1) / 0.04
Z = -2.5
Therefore, the p value is 0.0062. The probability will be:
= 1 - 0.0062
= 0.9938
The seventy percent of the boxes will contain less than 16 ounces. The ounces that will be contained in the eighty percent will be:
= -0.84 = (X - 16.1) / 0.04
X = 16
Lastly, the middle 90% of the boxes will be between 16.03 ounces 16.17 ounces.
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2. Give vector v=< 3,-6 > and w is a vector with a magnitude of 36 and direction 155 degrees.
a. Write the vector v in i, j component form.
b. Find the magnitude and direction of vector v.
c. Find the i, j vector form of w.
d. Find the resultant vector of v+w. This includes its component form, magnitude and direction.
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Answer:
a) v = 3i -6j
b) v ≈ 6.708∠-63.43°
c) w = -32.627i +15.214j
d) v+w = -29.627i +9.214j = 31.027∠162.72°
Step-by-step explanation:
Most graphing calculators and many scientific calculators can do arithmetic with vectors, often in the form of complex numbers or arrays. Of course, the usual conversions can be used:
(r; α) ⇒ (r·cos(α), r·sin(α))
(x, y) ⇒ (√(x²+y²); atan2(x, y))
where atan2(x, y) is arctan(y/x) quadrant-adjusted for the signs of x and y
__
a) v = 3i -6j
b) v ≈ 6.708∠-63.43°
c) w = -32.627i +15.214j
d) v+w = -29.627i +9.214j = 31.027∠162.72°
__
The first attachment shows the vectors and their sum in component form as complex numbers. For your purpose, the translation is ...
a +bi ⇒ ai +bj
The second attachment shows the vectors and their sum in polar form (magnitude and direction). I like the A∠B format. You may translate it to whatever form you need, for example, (A; B), A·cis(B), A(cos(B)i +sin(B)j), Ae^(iB), or any other. (The "semicolon format" is used by at least one app to distinguish between rectangular coordinates (a, b) and polar coordinates (A; B).) The angles here are in degrees (not radians), matching the form in the problem statement.
The sales tax for an item was $13.60 and it cost $340 before tax.
Find the sales tax rate. Write your answer as a percentage.
Answer:
4%
Step-by-step explanation:
13.60/340=.04 or 4%
A fair die is rolled four times. Calculate the probability of obtaining exactly two 4s.
Answer:
The probability of getting two 4s is 5.55%.
Step-by-step explanation:
Since fair says is rolled four times, to calculate the probability of obtaining exactly two 4s the following calculations must be performed:
100/6 = 16.6666
0.166666 x 0.166666 = X
0.02777 = X
1 = 100
0.02777 = X
0.02777 x 100 = X
2.77 = X
2.77 x 2 = 5.55
Therefore, the probability of getting two 4s is 5.55%.
Ixlllllllllllllllllllllllll
Answer:
am afraid am going to do a cooked method.this is the only way I can help please forgive me.
Step-by-step explanation:
answer is 5.9
Parker randomly pulled out a sock that was black form
his drawer. Without replacement, what is the
probability that Parker will randomly pull out a white
sock on his second pull?
Answer:
[tex]Probability\ that\ Parker'd\ pull\ off\ a\ White\ Sock(\ On\ His\ Second\ Pull)=\frac{6}{11}[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\Total\ number\ of\ Black\ Socks=7\\Total\ number\ of\ White\ Socks=12\\Total\ number\ of\ Navy\ Socks=4\\Hence,\\Total\ number\ of\ Socks\ Parker\ has=12+4+7=23\\We\ know\ that,\\The\ Random\ experiment\ here,\ is\ pulling\ out\ a\ white\ sock,\ after\ pulling\\ a\ black\ sock.\\Hence,\\Since\ the\ Black\ Sock\ had\ been\ removed\ from\ his\ drawer,\ the\\ number\ of\ 'Socks'\ that\ remain\ in\ his\ drawer=23-1=22\\[/tex]
[tex]Hence,\\Total\ elementary\ events\ for\ this\ random\ experiment=22\\Now,\\We\ just\ need\ to\ find\ out\ the\ probability\ of\ pulling\ out\ a\ 'White\ Sock'.\\Hence,\\Number\ of\ White\ socks=12\\Hence,\\Favorable\ number\ of\ elementary\ events\ for\ the\ Random\ Experiment=12[/tex]
[tex]We\ also\ know\ that,\\Probability\ for\ an\ Event\ A=\frac{Favorable\ No.\ of\ Elementary\ Events}{Total\ no.\ of\ elementary\ events}[/tex]
[tex]Hence,\\Probability\ that\ Parker\ would\ pull\ off\ a\ white\ sock\ on\ his\\ second\ pull=\frac{12}{22}=\frac{6}{11}[/tex]
I need help with this.
Answer:
9x2 and 9x2
Step-by-step explanation:
Help? ill give 10 points.
Answer:
it is the first one
Step-by-step explanation:
Solve the system of equations
If you flip three fair coins, what is the probability that you'll get all three tails?
Answer:
50%
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation:
trust me :D
write your answer as a mix number 8 1/2 + 7 2/3 add
Answer:
[tex]15\frac{13}{21}[/tex]
Step-by-step explanation:
[tex]answer[/tex]
Equalizing the denominator
Likening retailers can be done by calculating the frequency from numbered fractions. Based on examples calculated by pec from 4/3 and 5/3 = 34/4
#semogamembantu
Jade bought an airplane ticket to New York for $600. Her brother bought a ticket later that same week for $618. The price increase by what percent?
Answer:
the answer to the question is 3%
WILL GIVE BRAINLIEST ONLY IF RIGHT! Isabella grows several varieties of pepper plants. The following dot plots show the numbers of peppers, rounded to the nearest 5, per plant for different varieties. Each dot represents a different plant.
Order the varieties from least to greatest the typical number of peppers per plant.
Put the graph with the least typical value on top.
Answer:
In photo
Step-by-step explanation:
Answer:
Step-by-step explanation:
At a restaurant, a meal gives a choice between 4 entrees: Steak, Chicken, Fish or Lamb chops, two sides: potato, or rice and three vegetables: broccoli, spinach, or cauliflower. Find the probability of the customer requires either a meal with potato and/or spinach?
There's a 25% chance that this would occur because there is 4 dishes and that divided by the full 100% is 25 so your answer is 25%
The length of a rectangle is 11 units more than its width. The perimeter of the
rectangle is 182 units. Solve for the dimensions of the rectangle. What is the
area of the rectangle?
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Answer:
width: 40 unitslength: 51 unitsarea: 2040 square unitsStep-by-step explanation:
Let w represent the width of the rectangle. Then w+11 is the length. The perimeter is given by ...
P = 2(L +W)
182 = 2((w+11) +w)
182 = 4w +22 . . . . . simplify
160 = 4w . . . . . . . . . subtract 22
40 = w . . . . . . . . . . . divide by 4
40 +11 = length = 51 . . . . determine length
The dimensions of the rectangle are 40 × 51 units.
__
The area of the rectangle is ...
A = LW
A = (51)(40) = 2040 . . . . square units
The area is 2040 square units.
_____
Additional comment
The perimeter of a rectangle is double the sum of length and width, so that sum is 182/2 = 91 units. Now, this is a "sum and difference" problem, where the sum of length and width is 91, and the difference is 11. The solutions to such a problem are half the sum and half the difference of these numbers. Above, we found the smaller dimension (width) first: (91-11)/2 = 40. We could have found the length as (91+11)/2 = 51. The knowledge of the general solution to "sum and difference" problems often lets you work them with mental arithmetic.
Calculate the area.
Answer:
d. 91.61 cm^2
Step-by-step explanation:
have a nice day :)
Answer:
area of circle=πr²=π×5.4²=91.6cm²
what is the unit rate
Step-by-step explanation:
person above is . it's 5
Colin asked some of his classmates how many minutes they spent working on their math homework last night. He created a dot plot to show his results.
What is the range of the data Colin collected?
20
11
25
5
Answer:
If you can attach it i would be happy to help.
Step-by-step explanation:
*answer will be updated if shown*
Answer:
Step-by-step explanation:
5
Write an equation that can be used to find the nth term of the sequence, an.
80, 105, 130, 155, 180, ...
Enter your answer by filling in the boxes.
an = n +
Answer:
an=105-25n is the answer
The filling in the boxes an is equal to 105-25n.
We have given that,
Write an equation that can be used to find the nth term of the sequence, an.
What is the sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence.
The sequence is 80, 105, 130, 155, 180.
We have to determine an term.
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(b) In summer, the zoo increases the prices.
An Adult ticket increases by 20%.
A Child ticket increases by 15%.
How much more does it cost the family to visit in the summer than in the winter?
Please help me!! Determine whether the function shown below is or is not periodic. If it is, find the period.
Answer:
I believe it is not periodic but I am not 100%
Decide whether the equation describes a function.
y= 4x - 5
What is the domain and range?
Answer: The domain is in the picture
Step-by-step explanation:
An arena is hosting a concert. At the most, the arena can hold 8,500 people. If tickets have already been sold to 6,900 people, what is the highest number of tickets that can still be sold?
Answer:
Subtract 6,900 from 8,500 to get the highest number of tickets that can still be sold which is 1,600.
Find the measure of < 3
t
43
90°
K
43 = [?]
Enter
Answer:
Solution given:
<3+90=180[co interior angle ]
<3=180-90=90°
is your answer
A process that is in control has a mean of 12.5 and a standard deviation of 1.1.
a. Construct the control chart for this process if samples of size are to be used (to 1 decimal).
For N=4
Find the UCL
Find the LCL
b. Repeat part (a) for samples of size and (to 2 decimals).
For N=10
Find the UCL
Find the LCL
For N=15
Find the UCL
Find the LCL
c. What happens to the limits of the control chart as the sample size is increased? Discuss why this is reasonable. and become - Select your answer (closerfarther) together as n increases. If the process is in control, the larger samples should have less variance and should fall - Select your answer (closerfarther) to 12.5
Answer:
1a) UCL = 14.2
LCL = 10.9
b) UCL = 15.63
LCL = 9.37
c) UCL = 16.48
LCL = 8.52
2) The difference between the limits falls close together as n increases
and the difference between the limits falls farther away from 12.5
Step-by-step explanation:
mean ( μ ) = 12.5
std ( б ) = 1.1
UCL = μ + ( n - 1 ) б / √n
LCL = μ - ( n - 1 ) б / √n
1) a) Given n = 4
UCL = 12.5 + ( 3 ) * 1.1 / 2
= 12.5 + 3.3/2 = 14.15 ≈ 14.2
LCL = 12.5 - 3.3/2 = 10.85 ≈ 10.9
b) Given n = 10
UCL = 12.5 + ( 9 ) * 1.1 /√10
= 12.5 + 3.13 = 15.63
LCL = 12.5 - 3.13 = 9.37
c) Given n = 15
UCL = 12.5 + 14 * 1.1 / √15
= 12.5 + 3.98 = 16.48
LCL = 12.5 - 3.98 = 8.52
2) As the sample size increases the difference between the limits of the control chart decreases
Hence the difference falls close together as n increases
and the difference between the limits falls farther away from 12.5
What angle maximizes the area of the triangle below?
Answer:
90°
Step-by-step explanation:
Area of triangle with sides a and b and included angle Θ:
A = (1/2)ab * sin Θ
dA/dx = (1/2)ab cos Θ
(1/2)ab cos Θ = 0
cos Θ = 0
Θ = 90°
Find the simplified product: 2 square root 5x^3
Answer:
x Square root 5x
Step-by-step explanation:
1+1-1+1-1 Will choose brainly
Answer:
1
Step-by-step explanation:
9 divided by 8 is equal to 9 multiplied by _
Answer:
1/8.
Step-by-step explanation:
9/8 = 9x
Cross multiply:
9x * 8 = 9
72x = 9
x = 9/72 = 1/8.
CHECK the answer:
9/8 = 9 * 1/8 = 9/8.
Checks OK.
how many fluid ounces are equal to 26 quartz? i will give brainliest answer.
3. Find the values of the constants in each of the following:
(1) f(x) = ax + b, a and b are constants, f2) = 7,f(1) = -1
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Answer:
a = 8; b = -9
Step-by-step explanation:
Filling in the given values gives you two equations.
7 = a(2) +b
-1 = a(1) +b
Subtracting the second equation from the first gives ...
(7) -(-1) = (2a +b) -(a +b)
8 = a . . . . . simplify
Using this value in the first equation gives ...
7 = (8)(2) +b
b = 7 -16 = -9
The constants are a = 8, b = -9.