Answer:
A).4m^(+5)
B).2m^ (+7)
Step-by-step explanation:
First let me convert the expression to words for easy simplification and evaluation.
2m squared times 2m to the power 3.
= 2m² * 2m³
m to the power 4 times 2m to the power 3
= m⁴ * 2m³
So to evaluate.
We just multiply and get our answer.
For 2m² * 2m³
= (2*2)(m²*m³)
= 4(m(²+³))
= 4m^(+5)
For m⁴ * 2m³
= 2(m⁴*m³)
= 2m(⁴+³)
= 2m^ (+7)
A population of values has a normal distribution with μ = 247 and σ = 62.2. You intend to draw a random sample of size n = 16. (a) Find the probability that a single randomly selected value is greater than 295.2. (b) Find the probability that a sample of size n= 16 is randomly selected with a mean greater than 295.2. Give your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Answer:
a) [tex] z = \frac{295.2-247}{62.2}=0.772[/tex]
And using the normal distribution table or excel we got:
[tex] P(Z>0.772) = 1-P(Z<0.772) = 1-0.77994= 0.22006[/tex]
b) [tex] z = \frac{295.5 -247}{\frac{62.2}{\sqrt{16}}}= 3.119[/tex]
And we can use the normal standard table or excel in order to find the probability and we got:
[tex] P(z>3.119) =1-P(Z<3.119)= 1- 0.999093=0.000907[/tex]
Step-by-step explanation:
For this case we know that the random variable of interest is normally distributed with the following parameters:
[tex] X \sim N (\mu = 247, \sigma =62.2)[/tex]
Part a
We want to find this probability:
[tex] P(X>295.2)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{X-\mu}{\sigma}[/tex]
Replacing we got:
[tex] z = \frac{295.2-247}{62.2}=0.772[/tex]
And using the normal distribution table or excel we got:
[tex] P(Z>0.772) = 1-P(Z<0.772) = 1-0.77994= 0.22006[/tex]
Part b
We select a random sample of size n = 16 and we try to find this probability:
[tex] P(\bar X >295.2)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z = \frac{295.5 -247}{\frac{62.2}{\sqrt{16}}}= 3.119[/tex]
And we can use the normal standard table or excel in order to find the probability and we got:
[tex] P(z>3.119) =1-P(Z<3.119)= 1- 0.999093=0.000907[/tex]
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
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%
How to solve? What are the rules in BODMAS
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...
What is the area of a circle with a radius of 6 inches?
9. in.
O 125 in.
O 36in 2
81 in 2
Answer:
A = 36pi in^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi 6^2
A = 36pi in^2
Radius(r)=6 inches
Area of circle=?
Now,
Area of circle=pi r ^2
=pi (6)^2
36 pi inches^2
So the right answer is 36 pi inches^2
Hope it helps
Seja a função real dada por f(x)=4x-9. Calcule f(6) - f(5). ( ) 4 ( ) 1 ( ) 2 ( ) -4 ( ) -1
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
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).
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
Please help! Correct answer only, please! Consider the matrix shown below: Find the inverse of the matrix A: (i.e Find A^-1).
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
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?
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
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?
Answer:
Step-by-step explanation:
36 inches, 20 inches, and 24 inches. What type of triangle did Rosa draw?
Answer:
Scalene triangle
Step-by-step explanation:
Please answer this correctly I want genius or expert people to answer this correctly.
Answer:
18.84mm^2
Step-by-step explanation:
Surface area of a cylinder can be found with the following formula:
2πrh+2πr^2
r is radius
h is height
Plug our values in
2π1(2)+2π(1)^2
2π(2)+2π(1)
4π+2π
6π
6(3.14)
18.84
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?
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.
if the perimeter of a square gardern is 84feet . what is the area of the qardern
Answer:
441
Step-by-step explanation:
84 / 4 = 21
21 x 21 = 441
Answer:
441
Step-by-step explanation:
84/2=42
Choose a reasonable estimate for the amount of water a cup would hold.
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
Please answer this question !! Thank you !! Will give brainliest !! Really important !!
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
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.
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
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
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
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.
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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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.
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
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.
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.
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.
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
Using the graph as your guide, complete the following statement.
The discriminant of the function is
O A. negative
OB zero
O C positive
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
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Keep gettin those wrong. Please help!!!
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]
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.
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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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.
*
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!!!
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.
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.
prove
cos A /(1- sin A) = (1 + sin A)/cos A
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
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?
Answer:
98.57
Step-by-step explanation:
3.5% over 100% X 102=3.43
102-3.43= 98.57
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)}
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.
Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 32 mpg with a standard deviation of 6 mpg. Thirty-one non-hybrid sedans get a mean of 21 mpg with a standard deviation of three mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test at the 5% level to evaluate the manufacturers claim. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Answer:
There is enough evidence to support the claim of the manufacturers that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
The significance level is 0.05.
The sample 1 (hybrid), of size n1=21 has a mean of 32 and a standard deviation of 6.
The sample 2 (non-hybrid), of size n2=31 has a mean of 21 and a standard deviation of 3.
The difference between sample means is Md=11.
[tex]M_d=M_1-M_2=32-21=11[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{6^2}{21}+\dfrac{3^2}{31}}\\\\\\s_{M_d}=\sqrt{1.714+0.29}=\sqrt{2.005}=1.4158[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{11-0}{1.4158}=\dfrac{11}{1.4158}=7.77[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=21+31-2=50[/tex]
This test is a right-tailed test, with 50 degrees of freedom and t=7.77, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>7.77)=0.0000000002[/tex]
As the P-value is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.