An archaeologist locates a fossil of an early human skeleton. To determine the age of the fossil, the archaeologist utilizes a technique called carbon dating, where the relative amount of carbon-14 can help determine the age of the fossil. Carbon-14 has a half-life of about 5700 years. He finds that the fossil contains 15% of the amount of carbon-14 anticipated when compared to a living femur of the same size. The decay of carbon-14 can be calculated as shown below, where N0 is original amount of carbon-14, t is the time of decay, in years, r represents the rate of decay, and N(t) represents the amount of carbon-14 remaining. Rounded to the nearest year, the skeleton is approximately years old.
Answers
Answer:
The skeleton is approximately 18970 years old.
Step-by-step explanation:
The amount of Carbon-14 remaining after t years is given by the following equation:
[tex]N(t) = N(0)(1-r)^{t}[/tex]
In which N(0) is the initial amount and r is the decay rate, as a decimal.
Carbon-14 has a half-life of about 5700 years.
This means that [tex]N(5700) = 0.5N(0)[/tex]
So
[tex]N(t) = N(0)(1-r)^{t}[/tex]
[tex]0.5N(0) = N(0)(1-r)^{5700}[/tex]
[tex](1-r)^{5700} = 0.5[/tex]
[tex]\sqrt[5700]{(1-r)^{5700}} = \sqrt[5700]{0.5}[/tex]
[tex]1-r = 0.9999[/tex]
[tex]r = 1 - 0.9999[/tex]
[tex]r = 0.0001[/tex]
So
[tex]N(t) = N(0)(1-r)^{t}[/tex]
[tex]N(t) = N(0)(0.9999)^{t}[/tex]
He finds that the fossil contains 15% of the amount of carbon-14 anticipated when compared to a living femur of the same size.
The age is t for which N(t) = 0.15N(0). So
[tex]N(t) = N(0)(0.9999)^{t}[/tex]
[tex]0.15N(0) = N(0)(0.9999)^{t}[/tex]
[tex](0.9999)^{t} = 0.15[/tex]
[tex]\log{(0.9999)^{t}} = \log{0.15}[/tex]
[tex]t\log{0.9999} = \log{0.15}[/tex]
[tex]t = \frac{\log{0.15}}{\log{0.9999}}[/tex]
[tex]t = 18970.25[/tex]
Rounding to the nearest year.
The skeleton is approximately 18970 years old.
Answer:
Mark as Brainliest Please :)
Step-by-step explanation:
Related Questions
Suppose a random variable, x, follows a Poisson distribution. Let μ = 2.5 every minute, find the P(X ≥ 125) over an hour. Round answer to 4 decimal places.
Answers
Answer:
P(X ≥ 125) = 0.9812
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the normal distribution.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.
Normal distribution:
When the distribution is normal, we use 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.
The Poisson can be approximated to the normal, with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]
Let μ = 2.5 every minute
This is the mean of the Poisson, so [tex]\lambda = 2.5n[/tex], in which n is the number of minutes.
P(X ≥ 125) over an hour
An hour has 60 minutes, so [tex]n = 60, \lambda = 2.5*60 = 150, \sigma = \sqrt{150} = 12.25[/tex]
Using continuity correction, this is [tex]P(X \geq 125 - 0.5) = P(X \geq 124.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 124.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{124.5 - 150}{12.25}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a pvalue of 0.0188
1 - 0.0188 = 0.9812
So
P(X ≥ 125) = 0.9812
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 400 gram setting. It is believed that the machine is underfilling the bags. A 9 bag sample had a mean of 397 grams with a standard deviation of 25. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answers
Answer:
Reject [tex]H_o[/tex] if [tex]t < -2.306[/tex]
Step-by-step explanation:
The decision rule for rejecting the null hypothesis is shown below:-
The machine is thought to be underfilling so that the test is left tailed.
Now the Degrees of freedom is
= 9 - 1
= 8
Critical left tailed value t for meaning level [tex]8 \ df[/tex] and 0.025 = -2.306
Therefore Decision rule will be in the following way:
Reject [tex]H_o[/tex] if [tex]t < -2.306[/tex]
Represent the relationship between the total cost and the number of items, if total cost t is proportional to the number n of items purchased at a constant price p.
Answers
Answer:
t = pn
Step-by-step explanation:
We are to find the relationship between total cost and the number of items.
First we would represent the relationship between total cost and number of items with variables
Let the total cost = t
and the number of items = n
Total cost t is proportional to the number n of items:
t ∝ n
t = kn
where k is constant
Since it is purchased at a constant price p, the constant of proportionality would be p. the k would be replaced with p
t = pn
Choose a reasonable estimate for the amount of water a cup would hold.
Answers
Answer:
A cup of water can hold a cup of water (or about 250 mL)
Step-by-step explanation:
anything between 1 and 4 cups should be an acceptable answer
If this helps, please consider giving me brainliest
Answer:
I'm gonna go with 250 ML
Step-by-step explanation:
One liter is a little more than 1 quart.
250 mL = 0.25 L
1. (a) The life time of a certain brand of bulbs produced by a company is normally distributed, with mean 210 hours and standard deviation 56 hours. What is the probability that a bulb picked at random from this company’s products will have a life time of:
(i) at least 300 hours,
(ii) at most 100 hours,
(iii) between 150 and 250 hours.
(b) In a contest, two friends, Kofi and Mensah were asked to solve a problem. The
probability that Kofi will solve it correctly is ' and the probability that Mensah
(
will solve it correctly is ) . Find the probability that neither of them solved it correctly.
*
Answers
Answer:
1a) (i) 0.0537
(ii) 0.0250
(iii) 0.6188
1b) The probability that neither Kofi nor Mensah solves the problem correctly = (9/20) = 0.45
Step-by-step explanation:
The complete Question is presented in the attached image to this answer.
1a) This is a normal distribution problem with
Mean lifetime of bulbs = μ = 210 hours
Standard deviation = σ = 56 hours
(i) at least 300 hours, P(x ≥ 300)
We first standardize 300 hours
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (300 - 210)/56 = 1.61
To determine the required probability
P(x ≥ 300) = P(z ≥ 1.61)
We'll use data from the normal probability table for these probabilities
P(x ≥ 300) = P(z ≥ 1.61) = 1 - P(z < 1.61)
= 1 - 0.94630 = 0.0537
(ii) at most 100 hours, P(x ≤ 100)
We first standardize 100 hours
z = (x - μ)/σ = (100 - 210)/56 = -1.96
To determine the required probability
P(x ≤ 100) = P(z ≤ -1.96)
We'll use data from the normal probability table for these probabilities
P(x ≤ 100) = P(z ≤ -1.96) = 0.0250
(iii) between 150 and 250 hours.
P(150 < x < 250)
We first standardize 150 and 250 hours
For 150 hours
z = (x - μ)/σ = (150 - 210)/56 = -1.07
For 250 hours
z = (x - μ)/σ = (250 - 210)/56 = 0.71
To determined the required probability
P(150 < x < 250) = P(-1.07 < z < 0.71)
We'll use data from the normal probability table for these probabilities
P(150 < x < 250) = P(-1.07 < z < 0.71)
= P(z < 0.71) - P(z < -1.07)
= 0.76115 - 0.14231
= 0.61884 = 0.6188 to 4 d.p.
1b) Probability that Kofi solves the problem correctly = P(K) = (1/4)
Probability that Mensah solves the problem correctly = P(M) = (2/5)
Probability that Kofi does NOT solve the problem correctly = P(K') = 1 - P(K) = 1 - (1/4) = (3/4)
Probability that Mensah does NOT solve the problem correctly = P(M') = 1 - P(M) = 1 - (2/5) = (3/5)
To find the probability that neither of them solves the problem correctly, we first make the logical assumption that the probabilities of either of them solving the problem are independent of each other.
Hence, the probability that neither of them solves the problem correctly = P(K' n M')
P(K' n M') = P(K') × P(M') = (3/4) × (3/5) = (9/20) = 0.45
Hope this Helps!!!
The temperature outside when Colin went to bed was -4°F. When he woke up the next
morning, it was -11°F outside. Describe the change in temperature by completing the
statements.
Answers
Step-by-step explanation:
The temperature outside when Colin went to bed was -4°F. When he woke up the next morning, it was -11°F outside
To find the change in the temperature , find the difference in temperature
Change in temperature = temperature in morning - temperature at night
change in temperature = [tex]-11 -(-4)= -7[/tex]
temperature changed by -7 °F
So the temperature is dropped by 7°F
Answer:
the temperature is dropped by 7°F
The temperature change when he woke up the next morning given the data was –7 °F.
Data obtained from the questionFrom the question given above , the following data were obtained:
Temperature at night (T₁) = –4 °F Temperature in the morning (T₂) = –11 °F Change in temperature (ΔT) =? How to determine the change in the temperatureThe temperature change when Colin woke up can be obtained by taking the difference in the temperature at night and morning. This is illustrated as follow:
ΔT = T₂ – T₁
ΔT = –11 – (–4)
ΔT = –11 + 4
ΔT = –7 °F
Thus, from the calculation made above, we can conclude that there was a temperature drop of –7 °F when he woke up the next morning
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prove
cos A /(1- sin A) = (1 + sin A)/cos A
Answers
Answer:
answer is in exaplation
Step-by-step explanation:
cosA
+
cosA
1+sinA
=2secA
Step-by-step explanation:
\begin{lgathered}LHS = \frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=\frac{cos^{2}A+(1+sinA)^{2}}{(1+sinA)cosA}\\=\frac{cos^{2}A+1^{2}+sin^{2}A+2sinA}{(1+sinA)cosA}\\=\frac{(cos^{2}A+sin^{2}A)+1+2sinA}{(1+sinA)cosA}\\=\frac{1+1+2sinA}{(1+sinA)cosA}\end{lgathered}
LHS=
1+sinA
cosA
+
cosA
1+sinA
=
(1+sinA)cosA
cos
2
A+(1+sinA)
2
=
(1+sinA)cosA
cos
2
A+1
2
+sin
2
A+2sinA
=
(1+sinA)cosA
(cos
2
A+sin
2
A)+1+2sinA
=
(1+sinA)cosA
1+1+2sinA
/* By Trigonometric identity:
cos² A+ sin² A = 1 */
\begin{lgathered}=\frac{2+2sinA}{(1+sinA)cosA}\\=\frac{2(1+sinA)}{(1+sinA)cosA}\\\end{lgathered}
=
(1+sinA)cosA
2+2sinA
=
(1+sinA)cosA
2(1+sinA)
After cancellation,we get
\begin{lgathered}= \frac{2}{cosA}\\=2secA\\=RHS\end{lgathered}
=
cosA
2
=2secA
=RHS
Therefore,
\begin{lgathered}\frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=2secA\end{lgathered}
1+sinA
cosA
+
cosA
1+sinA
=2secA
Mr. Collins and Ms. LaPointe are saving money to buy a new motorcycle. The total amount of money Mr. Collins will save is given by the function p(x) = 62 + 5x. The total amount of money Ms. LaPointe will save is given by the function a(x) = x2 + 38. After how many months, x, will they have the same amount of money saved?
Answers
We have been given that Mr. Collins and Ms. LaPointe are saving money to buy a new motorcycle. The total amount of money Mr. Collins will save is given by the function [tex]p(x) = 62+5x[/tex]. The total amount of money Ms. LaPointe will save is given by the function [tex]a(x) = x^2+38[/tex]. We are asked to find number of months when they have the same amount of money saved.
To solve our given problem, we will equate both equations as:
[tex]x^2+38=62+5x[/tex]
[tex]x^2-5x+38=62+5x-5x[/tex]
[tex]x^2-5x+38=62[/tex]
[tex]x^2-5x+38-62=62-62[/tex]
[tex]x^2-5x-24=0[/tex]
[tex]x^2-8x+3x-24=0[/tex]
[tex]x(x-8)+3(x-8)=0[/tex]
[tex](x-8)(x+3)=0[/tex]
[tex](x-8)=0,(x+3)=0[/tex]
[tex]x=8,x=-3[/tex]
Since time cannot be negative, therefore, after 8 months they will have the same amount of money saved.
Lines a and b are parallel.
Parallel lines a and b are cut by transversals s and t. The angles formed by the intersection of lines a, s, and t, clockwise from top left are (7 x) degrees, blank; formed by lines b and s are blank, blank, blank, (11 x) degrees; formed by lines b and t are 90 degrees,
What is the value of x?
5
10
35
55
If you answer correctly, we will name the brainiest!
This is a challenge question, you have 5 minutes.
Answers
Answer:
The answer is x=5.
Step-by-step explanation:
11x + 7x + 90 = 180
18x + 90 = 180
-90 -90
= 18x = 90
x = 5
x is 5!
Value of x is 10°.
Correct option is B.
What is angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”.
Given,
a || b
cut by transversal s and t
lines b and t have angle = 90°
The first top left angle between a, s, t = 7x
The last bottom angle between s and b = 11x
a || b, so a and t will also have angle = 90°
by the figure,
180° - 11x + 90° - 7x + 90° = 180°
360° - 18x = 180°
18x = 180°
x = 10°
Hence, 10° is value of x.
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if the perimeter of a square gardern is 84feet . what is the area of the qardern
Answers
Answer:
441
Step-by-step explanation:
84 / 4 = 21
21 x 21 = 441
Answer:
441
Step-by-step explanation:
84/2=42
Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. In a study of a gender selection method used to increase the likelihood of a baby being born a girl, 1961 users of the method gave birth to 961 boys and 1000 girls. There is about a 20% chance of getting that many girls if the method had no effect. 1. Does the weight loss program have statistical significance?A. Yes, the program is statistically significant because the results are unlikely to occur by chance.B. Yes, the program is statistically significant because the results are likely to occur by chance.C. No, the program is not statistically significant because the results are likely to occur by chance.D. No, the program is not statistically significant because the results are unlikely to occur by chance.2. Does the weight loss program have practical significance?A. Yes, the program is practically significant because the results are too unlikely to occur by chance.B. No, the program is not practically significant because the results are likely to occur even if the weight loss program has no effect.C. No, the program is not practically significant because the amount of weight lost is trivial.D. Yes, the program is practically significant because the amount of lost weight is large enough to be considered practically significant.
Answers
Answer:
C. No, the program is not statistically significant because the results are likely to occur by chance.
Step-by-step explanation:
At a significance level that is smaller than 0.2, the effect is not significant.
We have a P-value of 20%, which means that we have 20% chances of getting this sample given that the method has no effect.
We then can conclude that there is not enough evidence to support the claim that the method is effective.
2. 4 masks and 1 pack of gloves costs $18. Three packs of gloves and 4 masks costs $22. What is the cost of one pack of gloves and one mask?
Answers
Answer:
One mask=$4
One pack of glove=$2
Step-by-step explanation:
Let mask=m
Let glove=g
4m+g=18 (1)
4m+3g=22 (2)
From (1)
g=18-4m
Substitute g=18-4m into equation (2)
4m+3g=22
4m+3(18-4m)=22
4m+54-12m=22
4m-12m=22-54
-8m=-32
Divide both sides by -8
m=4
Substitute m=4 into equation (1)
4m+g=18
4(4)+g=18
16+g=18
g=18-16
g=2
One mask=$4
One pack of glove=$2
A customer will be charged extra if the weight of their suitcase is above 48 pounds.
Write an inequality to represent w, the weight of the suitcase in pounds, that will have an extra charge.
Enter your answer by clicking and using the expression evaluator.
Answers
Answer:
[tex]w>48[/tex] pounds
Step-by-step explanation:
The customer will be charged extra if the weight of their suitcase is above 48 pounds.
Let the weight of the suitcase = w (in pounds)
Therefore, w above (greater than) 48 pounds is written mathematically as:
[tex]w>48[/tex] pounds
This is the inequality that represents w, the weight of the suitcase in pounds, that will have an extra charge.
1 point
4. A tin can in the shape of the cylinder shown is filled with coconut oil. If
coconut oil costs $0.01 per cubic centimeter, what is the cost of filling the
tin can with coconut oil?
8 cm
O
A. $603.10
B. $12.06
O ooo
c. $6.03
O
D. $1.92
Answers
Answer:
$6.03
Step-by-step explanation:
Let's begin by listing out the given variables:
height (h) = 12 cm, diameter (d) = 8 cm, r = d ÷ 2 ⇒ r = 4 cm, cost of coconut oil (c) = $0.01 /cm³
The formula of cylinder is given by:
V = πr²h = π * 4² * 12 = 603.1858 cm³
cost of filling the tin can with coconut oil = cost of coconut oil * Volume of cylinder
Cost = c * V = 0.01 * 603.1858
Cost = $6.03
How to solve? What are the rules in BODMAS
Answers
Answer:
18/35
Step-by-step explanation:
1 1/5 ÷ 2 1/3
Change from mixed numbers to improper fractions
1 1/5 = (5*1+1)/5 = 6/5
2 1/3 = (3*2+1)/3 = 7/3
6/5÷ 7/3
Copy dot flip
6/5* 3/7
18/35
Answer:
Step-by-step explanation:
I don't say you must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me my friend...
Please help! Correct answer only, please! Consider the matrix shown below: Find the inverse of the matrix A: (i.e Find A^-1).
Answers
Answer: A
Step-by-step explanation:
Formula for inverse of a matrix is:
[tex]A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\qquad \rightarrow \qquad A^{-1}=\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]
[tex]A=\left[\begin{array}{cc}2&5\\3&8\end{array}\right] \qquad \rightarrow \qquad A^{-1}=\dfrac{1}{2(8)-5(3)}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\dfrac{1}{1}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right][/tex]
We have that Option A is the correct option as its the correct in verse of the Matrix A
From the question we are told that:
[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]
Inverse of a Matrix
The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is A^{-1}, and A.A^{-1} = I.
Therefore the inverse of the Matrix A is
[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]
Giving
[tex]A^{-1}= \begin{vmatrix}8 & -5 \\-3 & -2\end{vmatrix}[/tex]
In conclusion
The correct Option is Option A as its the correct in verse of the Matrix A
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In conclusion
If the ratio of similarity between two similar polygons is 4:3.2, this ratio converts to
1:8.
8:1.
4:5.
5:4.
Answers
Answer:
5 : 4
Step-by-step explanation:
4: 3.2
Multiply by 10 to get rid of the decimal
4*10 : 3.2* 10
40 : 32
Divide each side by 8 to simplify
40/8 : 32/ 8
5 : 4
PPPLLLLLEEAAASSSEEE HELP!!!!!!!!!
Consider the following situation, which involves two options. Determine which option is less expensive. Are there unstated factors that might affect your decision?
You currently drive 275 miles per week in a car that gets 16 miles per gallon of gas. You are considering buying a new fuel-efficient car for $18 comma 000 (after trade-in on your current car) that gets 44 miles per gallon. Insurance premiums for the new and old car are $1000 and $600 per year, respectively. You anticipate spending $1100 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 per gallon. Over a five-year period, is it less expensive to keep your old car or buy the new car?
Over a five-year period, the cost of the old car is $____ and the cost of the new car is $_____
Thus, over a five-year period, it is less expensive to keep the old car or buy the new car?
Answers
Answer:
Step-by-step explanation:
Seja a função real dada por f(x)=4x-9. Calcule f(6) - f(5). ( ) 4 ( ) 1 ( ) 2 ( ) -4 ( ) -1
Answers
Answer:
4
Step-by-step explanation:
A função em questão, f(x), é:
[tex]f(x)=4x-9[/tex]
Primeiramente calcule os valores das funções para x=5 e x=6:
[tex]f(5)=4*5-9\\f(5)=11\\f(6)=4*6-9\\f(6)=15[/tex]
Em seguida, subtraia f(5) de f(6):
[tex]f(6)-f(5) = 15-11\\f(6)-f(5) = 4[/tex]
A resposta para o problema é 4
Please answer this question !! Thank you !! Will give brainliest !! Really important !!
Answers
Answer:
0 = 3x -2y -6
Step-by-step explanation:
The general form of the equation of a line is 0 = Ax + By + C
y = 3/2x -3
Subtract y from each side
0 = 3/2x -y -3
Multiply each side by 2
0 = 3x -2y -6
QUALITY CONTROL1)Specifications for a part for a DVD player state that the part should weigh between 24.6 and 25.6 ounces. The process that produces the parts has a mean of 25.1 ounces and a standard deviation of .26 ounce. The distribution of output is normal. a)What control chart will you use and why?b)With a 2-sigma confidence, what are the upper and lower control limitsif sample of n = 11are taken and the process is in control (random)?c)Is the process in control
Answers
Answer:
Step-by-step explanation:
Given that,
μ = 25.1
σ = 0.26
a) since standard deviation is ideal measure of dispersion , a combination of control chart for mean x and standard deviation known as
[tex]\bar x \\\text {and}\\\mu[/tex]
Chart is more appropriate than [tex]\bar x[/tex] and R - chart for controlling process average and variability
so we use
[tex]\bar x \\\text {and}\\\mu[/tex]charts
b)
n = 11
we have use 2 σ confidence
so, control unit for [tex]\bar x[/tex] chart are
upper control limit = [tex]\mu +2\times\frac{ \sigma}{\sqrt{n} }[/tex]
lower control limit = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]
control limit = μ
μ = 25.1
upper control limit =
[tex]25.1+2\times \frac{0.26}{\sqrt{11} } \\\\=25.2567[/tex]
lower control limit =
[tex]25.1-2\times \frac{0.26}{\sqrt{11} } \\\\=24.9432[/tex]
Upper control limit and lower control limit are in between the specification limits , that is in between 24.9 and 25.6
so, process is in control
c) if we use 3 sigma limit with n = 11
then
upper control limit = [tex]\mu +3\times\frac{ \sigma}{\sqrt{n} }[/tex]
[tex]25.1+3\times\frac{0.26}{\sqrt{11} } \\\\=25.3351[/tex]
lower control limit = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]
[tex]25.1-3\times\frac{0.26}{\sqrt{11} } \\\\=24.8648[/tex]
control limit is 25.1
Then, process is in control since upper control limit and lower control limit lies between specification limit
So, process is in control
Which of these relations on the set {0, 1, 2, 3} are equivalence relations? If not, please give reasons why. (In other words, if a relation is not an equivalence relation, please list each property that is missing and the reason why it is missing.) (1) {(0,0), (1,1), (2,2), (3,3)} (2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)} (3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)} (4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}
Answers
Answer:
(1)Equivalence Relation
(2)Not Transitive, (0,3) is missing
(3)Equivalence Relation
(4)Not symmetric and Not Transitive, (2,1) is not in the set
Step-by-step explanation:
A set is said to be an equivalence relation if it satisfies the following conditions:
Reflexivity: If [tex]\forall x \in A, x \rightarrow x[/tex]Symmetry: [tex]\forall x,y \in A, $if x \rightarrow y,$ then y \rightarrow x[/tex]Transitivity: [tex]\forall x,y,z \in A, $if x \rightarrow y,$ and y \rightarrow z, $ then x \rightarrow z[/tex](1) {(0,0), (1,1), (2,2), (3,3)}
(3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)}
The relations in 1 and 3 are Reflexive, Symmetric and Transitive. Therefore (1) and (3) are equivalence relation.
(2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)}
In (2), (0,2) and (2,3) are in the set but (0,3) is not in the set.
Therefore, It is not transitive.
As a result, the set (2) is not an equivalence relation.
(4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}
(1,2) is in the set but (2,1) is not in the set, therefore it is not symmetric
Also, (2,0) and (0,1) is in the set, but (2,1) is not, rendering the condition for transitivity invalid.
36 inches, 20 inches, and 24 inches. What type of triangle did Rosa draw?
Answers
Answer:
Scalene triangle
Step-by-step explanation:
Tags are placed to the left leg and right leg of a bear in a forest. Let A1 be the event that the left leg tag is lost and the event that the A2 right leg tag is lost. Suppose these two events are independent and P(A1)=P(A2)=0.4. Find the probability that exactly one tag is lost, given that at least one tag is lost (write it up to second decimal place).
Answers
Answer:
0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost
Step-by-step explanation:
Independent events:
If two events, A and B, are independent, then:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
Conditional probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: At least one tag is lost
Event B: Exactly one tag is lost.
Each tag has a 40% = 0.4 probability of being lost.
Probability of at least one tag is lost:
Either no tags are lost, or at least one is. The sum of the probabilities of these events is 1. Then
[tex]p + P(A) = 1[/tex]
p is the probability none are lost. Each one has a 60% = 0.6 probability of not being lost, and they are independent. So
p = 0.6*0.6 = 0.36
Then
[tex]P(A) = 1 - p = 1 - 0.36 = 0.64[/tex]
Intersection:
The intersection between at least one lost(A) and exactly one lost(B) is exactly one lost.
Then
Probability at least one lost:
First lost(0.4 probability) and second not lost(0.6 probability)
Or
First not lost(0.6 probability) and second lost(0.4 probability)
So
[tex]P(A \cap B) = 0.4*0.6 + 0.6*0.4 = 0.48[/tex]
Find the probability that exactly one tag is lost, given that at least one tag is lost (write it up to second decimal place).
[tex]P(B|A) = \frac{0.48}{0.64} = 0.75[/tex]
0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost
Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of data, then compare the variation. Bank A (single line): 6.5 nbsp 6.7 nbsp 6.7 nbsp 6.8 nbsp 7.1 nbsp 7.3 nbsp 7.4 nbsp 7.7 nbsp 7.7 nbsp 7.7 Bank B (individual lines): 4.3 nbsp 5.4
Answers
Complete Question
1. Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of data, then compare the variation.
Bank A (single lines): 6.5, 6.6, 6.7, 6.8, 7.2, 7.3, 7.4, 7.6, 7.6, 7.7
Bank B (individual lines): 4.1, 5.4, 5.8, 6.3, 6.8, 7.8, 7.8, 8.6, 9.3, 9.7
- The coefficient of variation for the waiting times at Bank A is ----- %?
- The coefficient of variation for the waiting times at the Bank B is ----- %?
- Is there a difference in variation between the two data sets?
Answer:
a
The coefficient of variation for the waiting times at Bank A is [tex]l =[/tex]6.3%
b
The coefficient of variation for the waiting times at Bank B is [tex]l_1 =[/tex]25.116%
c
The waiting time of Bank B has a considerable higher variation than that of Bank A
Step-by-step explanation:
From the question we are told that
For Bank A : 6.5, 6.6, 6.7, 6.8, 7.2, 7.3, 7.4, 7.6, 7.6, 7.7
For Bank B : 4.1, 5.4, 5.8, 6.3, 6.8, 7.8, 7.8, 8.6, 9.3, 9.7
The sample size is n =10
The mean for Bank A is
[tex]\mu_A = \frac{6.5+ 6.6+ 6.7+ 6.8+ 7.2+ 7.3+ 7.4+ 7.6+ 7.6+ 7.7}{10}[/tex]
[tex]\mu_A = 7.14[/tex]
The standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum|x- \mu|}{n} }[/tex]
[tex]k = \sum |x- \mu | ^2 = 6.5 -7.14|^2 + |6.6-7.14|^2+ |6.7-7.14|^2+ |6.8-7.14|^2 + |7.2-7.14|^2+ |7.3-7.14|^2, |7.4-7.14|^2+ |7.6-7.14|^2+|7.6-7.14|^2+|7.7-7.14|^2[/tex]
[tex]k = 2.42655[/tex]
[tex]\sigma = \sqrt{\frac{2.42655}{10} }[/tex]
[tex]\sigma = 0.493[/tex]
The coefficient of variation for the waiting times at Bank A is mathematically represented as
[tex]l = \frac{\sigma}{\mu} *100[/tex]
[tex]l = \frac{0.493}{7.14} *100[/tex]
[tex]l =[/tex]6.3%
Considering Bank B
The mean for Bank B is
[tex]\mu_1 = \frac{4.1+ 5.4+ 5.8+ 6.3+6.8+ 7.8+ 7.8+ 8.6+ 9.3+ 9.7}{10}[/tex]
[tex]\mu_1 = 7.16[/tex]
The standard deviation is mathematically represented as
[tex]\sigma_1 = \sqrt{\frac{\sum|x- \mu_1|}{n} }[/tex]
[tex]\sum |x- \mu_1 | ^2 =4.1-7.16|^2 +| 5.4-7.16|^2+ |5.8-7.16|^2 + | 6.3-7.16|^2 + |6.8-7.16|^2 + | 7.8-7.16|^2 +|7.8-7.16|^2 +|8.6-7.16|^2 + |9.3-7.16|^2 +|9.7-7.16|^2[/tex]
[tex]\sum |x- \mu_1 | ^2 =32.34[/tex]
[tex]\sigma_1 = \sqrt{\frac{32.34}{10} }[/tex]
[tex]\sigma_1 = 1.7983[/tex]
The coefficient of variation for the waiting times at Bank B is mathematically represented as
[tex]l_1 = \frac{\sigma }{\mu} *100[/tex]
[tex]l_1 = \frac{1.7983 }{7.16} *100[/tex]
[tex]l_1 =[/tex]25.116%
The price of oil, in dollars per barrel, declined last week by 3.5%. If it started the week at 102.00 per barrel, at what per barrel price did it end the week?
Answers
Answer:
98.57
Step-by-step explanation:
3.5% over 100% X 102=3.43
102-3.43= 98.57
Using the graph as your guide, complete the following statement.
The discriminant of the function is
O A. negative
OB zero
O C positive
Answers
Answer:it’s ZERO
Step-by-step explanation:
The discriminant of the function is zero
What is a function?A relation is a function if it has only One y-value for each x-value.
The discriminant tells you where the graph of the parabola goes through the x-axis, if at all.
If the discriminant is negative there are no real zeros and the parabola does not cross or touch the x-axis;
if the discriminant is positive the parabola will go through the x axis in 2 places;
if the discriminant is 0 the parabola will touch the x-axis in 1 place.
Our discriminant is 0 since the parabola only touches the x-axis but does not go through.
Hence, the discriminant of the function is zero
To learn more on Functions click:
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Keep gettin those wrong. Please help!!!
Answers
Answer: About 14.14 in^3
Step-by-step explanation:
We know that the circumference of a sphere is C=2πr. We are given that the circumference is 9.42 in. We can find the radius to get our volume.
[tex]9.42=2\pi r[/tex]
[tex]4.71=\pi r[/tex]
[tex]r=1.5\\[/tex]
Now that we know radius, we can find our volume.
[tex]V=\frac{4}{3} \pi r^3[/tex]
[tex]V=\frac{4}{3} \pi (1.5)^3[/tex]
[tex]V=14.14in^3[/tex]
There are 4, 6, and 7 points on three lines. How many quadrilaterals is it possible to create with given points as vertices?
Answers
Answer:
1707
Step-by-step explanation:
Let's designate the three sets of collinear points, A, B, C, having 4, 6, 7 points, respectively.
Since there are 3 sets of collinear points, exactly two of the vertices must come from the same set.
For two vertices from set A, the remaining two must come from the 13 members of sets B and C. There are a total of (4C2)(13C2) = 468 such quadrilaterals.
For two vertices from set B, we have already counted the quadrilaterals that result when the remaining two are from set A. There are 4·7 = 28 ways to have one each from sets A and C, and 7C2 = 21 ways to have two from set C. Thus, the additional number of quadrilaterals having 2 vertices in set B is ...
(6C2)(28 +21) = 735
For two vertices from set C, we have already counted the cases where two are from A or two are from B. There are 4·6 = 24 ways to have one each of the remaining vertices from sets A and B. Then the number of additional quadrilaterals having two points from set C is ...
(7C2)(4)(6) = 504
So, the total number of unique quadrilaterals is ...
468 +735 +504 = 1707
__
nCk means "the number of ways to choose k from n"
nCk = n!/(k!(n-k)!)
Given that circle Q has a radius of 5 and a center of (1,4), which point lies on the perimeter of circle Q?
Answers
Answer:
(x-1)^2 + (y-4)^2 = 5^2
Step-by-step explanation:
In order to find the points that lie on the perimeter of the circle, you find the algebraic equation of the circle.
The general equation for a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex] (1)
The last is a circle centered at the point (h,k) and with radius r.
In this case you have a circle with a radius of r = 5, and the circle is centered at (1,4). Then, you have:
h = 1
k = 4
r = 5
You replace the values of h, k and r in the equation (1):
[tex](x-1)^2+(y-4)^2=5^2[/tex]
All point that lies on the curve of the last equation, are point that lie on the perimeter of the circle
