2.quality style manufactures self-assembling furniture. to reduce the cost of returned orders, the manager of its quality control department inspects the final packages each day using randomly selected samples. the defects include wrong parts, missing connection parts, parts with apparent painting problems, and parts with rough surfaces. the average defect rate is four per day. owhich type of control chart should be used? construct a control chart with 3-sigma control limits.
Answers
The type of control chart should be used here is equals to C-chart. So, the right answer is option (c). The upper and lower control limits are 10 and 0 respectively.
We have a quality style manufactures self-assembling furniture.
Average Defect rate = 4 per day
Now, here we are checking the number of defective packages per day which is independent day to day and have a mean or average of 4 per day. So, we use here the C- chart one of type of control chart. Also, we have to draw control chart with 3-sigma control limits. Average defect Rate, c' = 4
We determine the control limits,
CL = 3 ( 3-sigma )
The upper control limit , UCL = c' + 3 √c'
= 4 + 3 √4 = 10
The lower limit, LCL= max ( 0, c' - 3 √c')
c' - 3 √c' = 4 - 3√4 = -2, as it is less than zero, So, lower control limit, LCL= 0.00.
The construction of control chart always consists,
First, we have to determine the mean of the observed data.Secondly, we have to determine the variance of the set.Third, calculate the standard deviation, which means the square root of the variance.Fourth, we have to determine the three-sigma, which means three standard deviations above the mean. a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit.For more information about Control chart , refer :
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Complete question:
quality style manufactures self-assembling furniture. to reduce the cost of returned orders, the manager of its quality control department inspects the final packages each day using randomly selected samples. the defects include wrong parts, missing connection parts, parts with apparent painting problems, and parts with rough surfaces. the average defect rate is four per day. owhich type of control chart should be used?
i) R chart
ii) p chart
iii) c chart
construct a control chart with 3-sigma control limits.
Related Questions
Simplify the expression using basic identities Cosu - cosu sin^2u
Answers
Cos u - cos u sin²u simplifies to cos³(u). We can solve it in the following manner.
Starting with the expression Cos u - cos u sin²u, we can factor out cos(u) to get:
Cos u - cos u sin²u = cos(u) (1 - sin²(u))
Using the identity sin²(u) + cos²(u) = 1, we can substitute cos²(u) for 1 - sin²(u):
cos(u) (1 - sin²(u)) = cos(u) cos²(u) = cos³(u)
Therefore, Cos u - cos u sin²u simplifies to cos³(u).
In mathematics, a factor refers to a number, algebraic expression, or function that divides or multiplies with another number, algebraic expression, or function without leaving a remainder. For example, in the expression 12x, 12 is a factor of the expression because it can be divided evenly by 12.
In algebra, factoring is the process of finding the factors of an algebraic expression, which means breaking it down into simpler parts that can be multiplied together to get the original expression. Factoring is an important skill in algebra, as it allows us to simplify and solve equations, identify common factors, and manipulate expressions more easily.
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Find the value of x. 69° to 38°
Answers
Answer:
What kind of shape is it? a triangle???
Step-by-step explanation:
please provide the shape so i can help you
A data set contains student test scores. • The median test score is 75 points. The third quartile value is 85 points. The range of the test scores is 40 points. Which statement about the test scores in the data set is most likely true?
A The lowest test score is 45 points.
B About 25% of the test scores are between 75 and 85 points
C The highest test score is 95 points.
D About 25% of the test scores are less than 55 points
Answers
Answer:
The answer to your problem is, A. D.
Step-by-step explanation:
Median: 75
Quartile Value: 85
Range: 40
We can use this info to make some inferences about the test scores in our dataset.
Firstly, the range of the test scores, is 40 points, so the lowest test score must be 75 - 20 = 55 points, and the highest test score must be 75 + 20 = 95 points. Therefore the highest test score is 95
The third quartile value is 85 points, which means that 75% of the test scores are less than or equal to 85 points. Since the median test score is 75 points, we can infer that 50% of the test scores are less than or equal to 75 points. Therefore, the remaining 25% of the test scores must be between 75 and 85 points. Thus, about 25% of test scores are in between 75 and 85. The third option is incorrect, as the lowest possible test score is 55 points, which is greater than 50 points.
He used the scale 1 inch : 2 yards. A soccer field in the park is 35 inches wide in the drawing. How wide is the actual field?
Answers
The actual width of the soccer field will be around 70 yards.
We are given that the width of the soccer field in the drawing is 35 inches. To find the actual width of the soccer field, we need to use the scale provided. We can set up a proportion to relate the dimensions in the drawing to the actual dimensions:
1 inch ÷ 2 yards = 35 inches ÷ x
where x is the actual width of the soccer field in yards.
To solve for x, we can cross-multiply:
1 inch × x = 35 inches × 2 yards
Simplifying, we get:
x = (35 inches × 2 yards) ÷ 1 inch
x = 70 yards
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Write the name of the quartite which divides Continuous data he low 25%
Answers
Answer:
The first quartile ([tex]Q_{1}[/tex]) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower or 25th empirical quartile, as 25% of the data is below this point.
Answer:
The first quartile (Q1) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower or 25th empirical quartile, as 25% of the data is below this point.
Step-by-step explanation:
i need help with an ixl. i dont understand it at all. please help !!
Answers
The value of m∠U in the circle is 168 degrees
How to find the tangent of a circle?The tangent of a circle is the line that touches the circle at only one point.
The tangent to a circle is always perpendicular to the radius. Therefore, it forms a right angle.
Therefore, let's use the theorem to find the angle m∠U
Hence,
m∠STU = 90 degrees
m∠UTV = 90 - 84 = 6 degrees
Therefore, the triangle STV is an isosceles triangle. This means the base angle is congruent .
Hence,
m∠SVT = 84 degrees
Therefore,
m∠U = 180 - 6 - 6
m∠U = 180 - 12
m∠U = 168 degrees
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Mrs. Hinojosa, the student council sponsor, is planning an end-of-year field trip for the 72 student council members. Mrs. Hinojosa misplaced the survey data, but
she found some of her notes from the data, including a partially completed two-way table.
Notes:
• The number of students who like bowling, but do not like ice skating is triple the number of students who like ice skating, but do not like bowling.
• 50% of the students like one, but not both activities.
of the students like bowling.
Student Council Field Trip Survey
Do Not Like
Bowling
Like
Ice Skating
Do Not Like
Ice Skating
Like
Bowling
(9 students)
?
Total
Total 663% 33¹%
100%
(72 students)
How many of the 72 student council members like neither bowling nor ice skating?
A 12
B 21
C
15
O
24
Answers
The number of student council members who like neither bowling nor ice skating is 27.
How to solveLet's denote the following:
a = number of students who do not like either activity (bowling or ice skating)b = number of students who like ice skating but do not like bowlingc = number of students who like bowling but do not like ice skatingd = number of students who like both activitiesWe are given the following information:
c = 3 * b (number of students who like bowling but not ice skating is triple the number who like ice skating but not bowling)
50% of students like one but not both activities, so (b+c)/72 = 0.5
9 students like both activities, so d = 9
The total number of students is 72.
Let's solve for a, b, and c:
From (2), we have b + c = 36.
From (1), we can rewrite c as c = 3b.
Substituting this into the equation from (2), we get:
b + 3b = 36
4b = 36
b = 9
Now, we can find the value of c:
c = 3b = 3 * 9 = 27
Finally, we can find the value of a.
We know that a + b + c + d = 72:
a + 9 + 27 + 9 = 72
a + 45 = 72
a = 27
Therefore, the number of student council members who like neither bowling nor ice skating is 27.
The correct answer is not among the options provided.
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Based on the measures shown, could the figure be a parallelogram?
Yes, one pair of opposite sides could measure
10 in., and the other pair could measure 13 in.
Yes, one pair of opposite sides could measure
10 in., and the other pair could measure 8 in.
No, there are three different values for x when each expression is set equal to 10.
No, the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.
Answers
The measures shown, could the figure be a parallelogram: Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in.
What is parallelogram?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. This indicates that a parallelogram's opposing sides are parallel and congruent (the same length). Moreover, a parallelogram's opposing angles are congruent (have the same measure).
The following are some characteristics of parallelograms:
A parallelogram's opposing sides are parallel and congruent.
A parallelogram's opposing angles are congruent.
The parallelogram's subsequent angles are additional (their sum is 180 degrees).
A parallelogram's diagonals split each other in half (cut each other in half).
For the given quadrilateral to be a parallelogram the opposite sides need to be congruent.
Thus,
10 = x + 2
x = 8
Also,
2x - 3 = x + 5
2x - x = 5 + 3
x = 8
Hence, the measures shown, could the figure be a parallelogram: Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in.
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Cool-Down The background of this graph is the same coordinate grid from the previous screen. Both the x- and y-axes run from negative 8 to 8.Line "g" is graphed. Line "g" goes through the points ( negative 4 , 4 ) and ( 4 , negative 2 ). Here is a line on a coordinate grid. Write an equation for the line.
Answers
The equation of line "g" is y = (-3/4)x + 1. To find the equation of line "g" that goes through the points (-4, 4) and (4, -2), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we can find the slope of the line by using the slope formula, which is:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the two points given, we have:
m = (-2 - 4) / (4 - (-4)) = -6 / 8 = -3 / 4
Next, we can use the slope-intercept form and one of the two points to find the y-intercept, b. Using the point (-4, 4), we have:
4 = (-3/4)(-4) + b
4 = 3 + b
b = 1
Finally, we can substitute the values of m and b into the slope-intercept form to get the equation of line "g":
y = (-3/4)x + 1
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for what values of t can 10x^2+tx+8 be written as the product of two binomials
I NEED ASAP
Answers
We can write the quadratic expression 10x^2 + tx + 8 as:
10x^2 + tx + 8 = 10x^2 + (a+b)x + ab
where a and b are constants that we want to determine, and (a+b)x is the middle term in the quadratic expression.
We can factor 10 as 25 and 8 as 22*2, so we have:
10x^2 + tx + 8 = (2x + c)(5x + d)
where c and d are the constants that we need to determine.
Expanding the right-hand side of this equation, we get:
(2x + c)(5x + d) = 10x^2 + (2d+5c)x + cd
Comparing this to the original expression, we see that:
2d + 5c = t
cd = 8
We can use these equations to solve for c and d in terms of t:
c = (t - 2d)/5
d = 8/c
Substituting d in terms of c in the first equation, we get:
2(8/c) + 5c = t
Multiplying through by c, we get a quadratic equation in c:
16 + 5c^2 = tc
We want this equation to have real solutions for c, so the discriminant must be non-negative:
25t^2 - 80 >= 0
Solving this inequality for t, we get:
t <= -8/5 or t >= 8/5
Therefore, the quadratic expression 10x^2 + tx + 8 can be written as the product of two binomials for all values of t less than or equal to -8/5 or greater than or equal to 8/5.
Suppose a savings and loan pays a nominal rate of 3.1% on savings deposits. Find the effective annual yield if interest is compounded annually.
Question content area bottom
Part 1
The effective annual yield is enter your response here%.
(Type an integer or a decimal rounded to the nearest thousandth as needed.)
Answers
The effective annual yield is approximately 3.164%.
I need some help better understanding Area Volume/Differential Equations, as ive been stuck on this single string of questions in my workbook for some time now, any and all help would be appreciated.
"Let R be the region in quadrant 1 bounded by y=3sin(2x) and y=e^x "
1) Find the area of R
2) Let S be the solid generated by rotating R around the x-axis. Find the volume of S.
3) Let Q be the solid generated by rotating R around the horizontal line y=5. Find the volume of Q
4) Let P be the solid whose base is R and whose cross sections perpendicular to the x-axis are semicircles. Find the volume of P.
Answers
Answer: Sure, I'd be happy to help you with these questions! Here are the solutions:
To find the area of R, we need to find the points of intersection between the two curves.
Setting y = 3sin(2x) and y = e^x equal to each other, we get:
3sin(2x) = e^x
Taking the natural logarithm of both sides, we get:
ln(3sin(2x)) = x
Now, we can find the x-coordinates of the intersection points by graphing the two curves or using a numerical method, such as a graphing calculator or Newton's method. The intersection points are approximately x = 0.306 and x = 2.313.
To find the area of R, we can integrate the difference between the two curves with respect to x:
A = ∫(e^x - 3sin(2x)) dx from x = 0.306 to x = 2.313
This integral can be evaluated using integration by substitution or a numerical method, such as a calculator or computer software. The area of R is approximately 2.828 square units.
To find the volume of S, we can use the formula for the volume of a solid of revolution:
V = ∫πy^2 dx from x = 0.306 to x = 2.313
Here, y = e^x - 3sin(2x) is the radius of the cross sections of the solid generated by rotating R around the x-axis.
This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of S is approximately 41.201 cubic units.
To find the volume of Q, we can use the formula for the volume of a solid of revolution around a horizontal line:
V = ∫π(y - 5)^2 dx from x = 0.306 to x = 2.313
Here, y = e^x - 3sin(2x) is the distance from the horizontal line y = 5 to the cross sections of the solid generated by rotating R around the line y = 5.
This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of Q is approximately 14.503 cubic units.
To find the volume of P, we can use the formula for the volume of a solid with known cross-sectional area:
V = ∫A(x) dx from x = 0.306 to x = 2.313
Here, the cross sections of P are semicircles perpendicular to the x-axis. The radius of each semicircle is given by:
r = (1/2)(e^x - 3sin(2x))
So the area of each semicircle is:
A = (1/2)πr^2 = (1/8)π(e^x - 3sin(2x))^2
Therefore, the volume of P is:
V = ∫(1/8)π(e^x - 3sin(2x))^2 dx from x = 0.306 to x = 2.313
This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of P is approximately 5.654 cubic units.
I hope this helps! Let me know if you have any further questions.
Step-by-step explanation:
this is due tomorrow please help
Randall buys 3 tickets for a concert for $14.50 each. He gives the cashier a $50 bill. how much change does he get? weite equations to show your work.
Answers
next 50.00 - 43.5= 6.5
The amount of change he gets is $6.5
Answer the question below sorry making this again
Answers
Answer: 20
Step-by-step explanation:
First, we put the data values in order from least to greatest.
10 13 14 19 20 23 31 33 39
Next, we will find the middle value of this list.
10 13 14 19 20 23 31 33 39
--- 13 14 19 20 23 31 33 ---
--- --- 14 19 20 23 31 --- ---
--- --- --- 19 20 23 --- --- ---
--- --- --- --- 20 --- --- --- ---
The median is 20.
What are the coordinates of x pre algebra
Answers
Answer:
( -1, -1)
Step-by-step explanation:
We see on the graph, point x is located at (-1,-1)
Chau wants to rent a boat and spend less than $53. The boat costs $7 per hour, and Chau has a discount coupon for $3 off. What are the possible numbers of hours Chau could rent the boat?
Answers
Chau could rent the boat for 1, 2, 3, 4, 5, 6, or 7 hours and still spend less than $53.
To find out the possible number of hours Chau could rent the boat, follow these steps:
Apply the discount coupon: Chau has a $3 discount, so subtract that from the total amount he wants to spend, which is $53.
$53 - $3 = $50
Determine the maximum number of hours Chau can rent the boat:
The boat costs $7 per hour, so divide the adjusted total amount by the cost per hour.
$50 ÷ $7 ≈ 7.14 hours
Since Chau can't rent the boat for a fraction of an hour, he can rent it for a maximum of 7 hours.
List the possible number of hours: Starting from 1 hour (assuming Chau wants to rent the boat for at least an hour), list all the whole numbers up to the maximum number of hours determined.
Possible number of hours: 1, 2, 3, 4, 5, 6, 7.
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7. Groceries Galore sells bags of chips from two different companies., The mean absolute deviation of the number of chips in each bag from Company A is higher than the mean absolute deviation of the number of chips in each bag from Company B. Heather believes this means that Company A tends to sell more chips in each bag. Do you agree? Explain why or why not. CHIPS
Answers
Answer:
Always need to do research to improve your studies
The mean absolute deviation (MAD) is a measure of the variability of a dataset. It measures how spread out the data is by calculating the average distance between each data point and the mean of the dataset. So, if the MAD of the number of chips in each bag from Company A is higher than the MAD of the number of chips in each bag from Company B, it means that the data points in the dataset of Company A are more spread out than those in the dataset of Company B.
However, the MAD alone cannot tell us whether Company A tends to sell more chips in each bag than Company B. To determine this, we would need to look at other measures such as the mean, median, or mode of the datasets.
For example, if the mean number of chips in each bag from Company A is higher than the mean number of chips in each bag from Company B, then Heather's belief would be supported. On the other hand, if the mean number of chips in each bag from Company A is lower than the mean number of chips in each bag from Company B, then her belief would be contradicted.
In conclusion, the MAD alone cannot tell us whether Company A tends to sell more chips in each bag than Company B. We would need to look at other measures of central tendency to determine this.
Brenda went to the store with her dad toy buy snacks. They bought a box of 16 snack-size bangs of chips for $7.84 and a box of 24 snack-size of pretzels for $12.48.How much more do pretzels cost pero bag than chips?
Answers
Answer:
$0.03 pretzels cost more than cost of bag of chips.
Step-by-step explanation:
price of 16 snack- size bags of chips = 7.84
Cost of 1 bag of chip = 7.84 /16 = $0.49
Price of 24 snack-size bags of pretzels = 12.48
Cost of 1 snack-size bags of pretzels = 12.48 / 24 = 0.52
$0.03 pretzels cost more than cost of bag of chips.
Mr. Smith keeps track of his students' homework completion. He keeps track of how many boys and
girls do not complete their homework. He puts students who don't complete their homework into two categories: first-time offenders and repeat offenders. He uses a table to keep track of the results.
Boys-Girls-Total-First-Time Offenders & Repeat Offenders
a. In one month 36 girls and 12 boys did not do their homework for the first time. 12 girls and 30
boys did not do their homework again. Put these figures in your table.
b.How many students did not complete all of their homework assignments this month?
c. What percentage of the students who did not complete their homework were boys who were
First-Time Offenders?
d. Are boys or girls more likely to not complete their homework? Explain your reasoning.
Answers
Answer:
The question seems to be incomplete. It mentions that Mr. Smith keeps track of his students' homework completion and how many boys and girls do not complete their homework. It also mentions that he puts students who don't complete their homework into two categories: first-time offenders and repeat offenders, and uses a table to keep track of the results[1][2]. However, it does not provide enough information to answer a specific question.
If you have a specific question related to this topic, please provide more details so that I can assist you better.
Mrs. Myrtle wants to buy this plastic toy for Willow. How much plastic would it take to construct the following toy? [Assume toy is solid plastic]
9m
13 m
Radius: type your answer...
type your answer...
Height of the Cone: type your answer....
; Total: type your answer...
Cone: type your answer...
; Hemisphere:
Answers
Answer:
Step-by-step explanation:
6
what does 56 3/4 ( 1 3/8 + 1 1/5) equal
Answers
Answer:
23,381/160 or 146 21/160
Step-by-step explanation:
56 3/4 = 227/4
1 3/8 = 11/8
1 1/5 = 6/5
227/4( 11/8 + 6/5)
227/4(55/40 + 48/40)
227/4( 103/40) = 23,381/160 or 146 21/160
The data given represents the height of basketball players, in inches, on two different girls' teams.
Allstars
73 62 60
63 72 65
69 68 71
66 70 67
60 70 71
Champs
62 69 65
68 60 70
70 58 67
66 75 70
69 67 60
Compare the data and use the correct measure of center to determine which team typically has the tallest players. Explain your answer.
The Allstars, with a mean of about 67.1 inches
The Champs, with a mean of about 66.4 inches
The Allstars, with a median of about 68 inches
The Champs, with a median of about 67 inches
Answers
To determine which team typically has the tallest players, we need to compare the measures of center for each team. Since the data sets have outliers, it's better to use the median as a measure of center.
Calculating the median for each team:
Allstars: arrange the heights in order from smallest to largest: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73. The median is the middle value, which is 68 inches.
Champs: arrange the heights in order from smallest to largest: 58, 60, 60, 65, 67, 67, 68, 69, 70, 70, 75. The median is the middle value, which is also 68 inches.
Since both teams have the same median height of 68 inches, we can't say that one team typically has taller players than the other based on this measure alone. Therefore, neither option (C) nor (D) is correct. Instead, we need to choose between options (A) and (B) based on the mean height for each team.
Calculating the mean for each team:
Allstars: add up all the heights and divide by the total number of players: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 1006/15 ≈ 67.1 inches.
Champs: add up all the heights and divide by the total number of players: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 996/15 ≈ 66.4 inches.
Thus, the team with the higher mean height is the Allstars, so the correct answer is option (A): "The Allstars, with a mean of about 67.1 inches."
Pre-Algebra Question is an image Below. and Please do Part b also because people don't usually do it
Answers
Answer:
A.) w=P/2-l
Step-by-step explanation:
Part A.)
P=2(l+w)
P/2= l+w
P/2-l= w
w=P/2-l
Part B.) In order to get (l+w) by itself, so I could subtract l, I had to divide both sides by two. Then I was able to subtract l from both sides to get just w on the right.
why does the vertical line test tell us whether the graph of a relation represents a function? when a vertical line intersects the graph of a relation more than once, it indicates that for that input there is more than one output, which means the relation is not a function. when a vertical line intersects the graph of a function more than once, it indicates that for that output there is more than one input, which means the function is not a relation. when a vertical line intersects the graph of a function more than once, it indicates that for that input there is more than one output, which means the function is not a relation. when a vertical line intersects the graph of a relation more than once, it indicates that for that output there is more than one input, which means the relation is not a function.
Answers
When a vertical line intersects the graph of a function more than once, it indicates that for that output there is more than one input, which means the function is not a relation. (option b).
In mathematics, functions are an essential concept used to describe relationships between sets of numbers. A function is a set of ordered pairs, where each input corresponds to exactly one output.
Conversely, if every vertical line intersects the graph at most once, then the graph represents a function. This is because there is only one output for each input, satisfying the definition of a function.
It's important to note that not all relations are functions. A relation is a set of ordered pairs, while a function is a relation where each input corresponds to exactly one output.
Therefore, if a vertical line intersects a graph more than once, it indicates that there is more than one output for that particular input, and the relationship is not a function.
Hence the option (b) is correct.
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the lifetime of lightbulbs that are advertised to last for 4100 hours are normally distributed with a mean of 4400 hours and a standard deviation of 300 hours. what is the probability that a bulb lasts longer than the advertised figure?
Answers
the probability that a bulb lasts longer than the advertised figure of 4100 hours is approximately 0.8413 or 84.13%.
The probability that a bulb lasts longer than the advertised figure can be found using the normal distribution formula. In this case, we have a mean of 4400 hours and a standard deviation of 300 hours. The advertised lifetime is 4100 hours. We will calculate the z-score and then use the standard normal distribution table to find the probability. Here's the step-by-step explanation:
Calculate the z-score: The z-score is a measure of how many standard deviations away from the mean a data point is. To calculate the z-score for the advertised lifetime (4100 hours), use the formula:
z = (X - μ) / σ
where X is the advertised lifetime (4100 hours), μ is the mean (4400 hours), and σ is the standard deviation (300 hours).
z = (4100 - 4400) / 300
z = -300 / 300
z = -1
Use the standard normal distribution table: Now that we have the z-score (-1), we can use the standard normal distribution table to find the probability that a bulb lasts longer than the advertised figure. Look for the value corresponding to -1 in the table, which is 0.1587.
Calculate the probability: The value we found in the standard normal distribution table (0.1587) represents the probability that a bulb lasts less than the advertised figure (4100 hours). To find the probability that a bulb lasts longer, we need to subtract this value from 1:
Probability (bulb lasts longer than advertised figure) = 1 - 0.1587
Probability (bulb lasts longer than advertised figure) = 0.8413
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according to a study published by a group of university of massachusetts sociologists, approximately 60% of the valium users in the state of massachusetts first took valium for psychological problems. find the probability that among the next 8 users from this state who are interviewed
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the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is 60% is 0.03456.
As per the given information, 60% of the valium users in Massachusetts first took it for psychological problems. Now, we are supposed to find the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is: 60%.
What is Valium?
Valium is a prescription medicine that is used to treat the symptoms of anxiety, alcohol withdrawal, and muscle spasm. The use of Valium can lead to addiction, especially if it is not taken as prescribed by the doctor.The probability of the first 6 users first took it for psychological problems is 60%. Hence, the probability that the first user did not take it for psychological problems is: 40%.
Probability of first user did not take Valium for psychological problems = P(A) = 0.40
Probability of first user took Valium for psychological problems = P(B) = 0.60
Now, we are supposed to find the probability that among the next 8 users from this state who are interviewed, the first 6 users first took it for psychological problems is: 60%.Probability of the first 6 users first took it for psychological problems is:
Probability of the next 5 users took it for psychological problems = P(B) × P(B) × P(B) × P(B) × P(B) = (0.60)⁵
Probability of the next 2 users did not take it for psychological problems = P(A) × P(A) = (0.40)²
Thus, the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is 60%, is:(0.60)⁵ × (0.40)²= 0.03456 (rounded to five decimal places)
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Pls answer this correctly!
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After 60 minutes in the refrigeration, the can of soda will be approximately 42°F.
What is refrigeration?
We are given the following information:
[tex]T_{a}[/tex] = 35°F (temperature of the refrigerator)
To = 73°F (initial temperature of the can of soda)
T = 58°F (temperature of the can of soda after 10 minutes)
We can use these values to find the decay constant k:
T = [tex]T_{a}[/tex] + (To - [tex]T_{a}[/tex])[tex]e^{-kt}[/tex]
58 = 35 + (73 - 35)[tex]e^{-10k}[/tex]
23 = 38[tex]e^{(-10k)}[/tex]
ln(23/38) = -10k
k ≈ 0.0725 (rounded to the nearest thousandth)
Now we can use this value of k to find the temperature of the can of soda after 60 minutes:
T = [tex]T_{a}[/tex] + (To - [tex]T_{a}[/tex])[tex]e^{-kt}[/tex]
T = 35 + (73 - 35)[tex]e^{(-0.0725*60x^{2} )}[/tex]
T ≈ 42°F (rounded to the nearest degree)
Therefore, after 60 minutes in the refrigerator, the can of soda will be approximately 42°F.
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Please help me!!!!!!
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The rotation that we need to apply to CD is of 270° clockwise.
Which should be the angle of rotation?We want a clockwise rotation that maps CD in E'F'.
Remember that a rotation of 90° will move the figure from one quadrant to the previous one. We can see that E'F' is on the third quadrant. while CD is on the second qudrant, then we need to go from.
Second to first quadrant ---> 90°
First to fourth quadrant ---> 90°
Fourth to third quadrant ---> 90°
Adding these 3 we get.
90° + 90° + 90° = 270°
So we need to applly a rotation of 270° clockwise to CD.
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help asap assignment closes soon!
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The approximate surface area of the cone is equal to 35 ft²
How to calculate surface area of a cone?In Mathematics, the surface area (SA) of a cone can be calculated by using this mathematical expression:
Surface area (SA) of a cone = πr(l + r)
Where:
l represents the slant height of the cone.r represents the radius of the cone.Note: Radius = diameter/2 = 2/2 = 1 feet.
By substituting the given parameters into the formula for the surface area (SA) of a cone, we have the following;
Surface area (SA) of a cone = 3.14 × (1 + 10)
Surface area (SA) of a cone = 3.14 × (11)
Surface area (SA) of a cone = 34.54 ≈ 35 ft²
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I need help with this one quick !
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If Julian wrote the last term as -3x⁴ instead of -3x², then the first term of the polynomial in standard form would be:
3x⁴ + 6y⁴ + 5x²y² - 10xy³ + 9x³y - 214. The correct option is B.
How to calculate the valueIt should be noted that to simplify the polynomial and write it in standard form, we need to combine like terms and arrange them in descending order of their exponents.
First, we can combine the like terms of x²y²
4x²y² + x^2y² = 5x²y²
Next, we can combine the like terms of xy³:
-8xy³ - 2xy³ = -10xy³
Then, we have the following terms left:
9x³y, 6y⁴, -3x² -214
To write this polynomial in standard form, we need to arrange the terms in descending order of their exponents:
6y⁴ + 5x²y² - 10xy³ + 9x³y - 3x² - 214
If Julian wrote the last term as -3x^4 instead of -3x^2, then the first term of the polynomial in standard form would be:
3x⁴ + 6y⁴ + 5x²y² - 10xy³ + 9x³y - 214
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