Answer:
a) Null hypothesis: [tex] \mu \geq 863[/tex]
Alternative hypothesis: [tex] \mu >863[/tex]
b) For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:
[tex] z_{\alpha}=-1.64[/tex]
And the rejection zone would be:
[tex] z<-1.64[/tex]
c) For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance
d) [tex] p_v = P(z<-2.17) =0.015[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided
Step-by-step explanation:
Part a
We want to test for this case if the true mean is significantly less than 863 calories so then the system of hypothesis are:
Null hypothesis: [tex] \mu \geq 863[/tex]
Alternative hypothesis: [tex] \mu >863[/tex]
Part b
For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:
[tex] z_{\alpha}=-1.64[/tex]
And the rejection zone would be:
[tex] z<-1.64[/tex]
Part c
For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance
Part d
For this case the p value would be given by:
[tex] p_v = P(z<-2.17) =0.015[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided
What is the value of sec(-45°)? there was no photo given or answer choices... sorry guys. thats why i asked on here lol
Answer:
It is about 1.41421356. (square root of 2)
Step-by-step explanation:
You can use a calculator to figure it out! Just enter the value (-45) and press the sec button! Hope this helps :)
sec (-45) = 1/ cos (-45) .
and cos (-45) = (sqrt 2)/2 is the answer to the question
What is the value of sec(-45°)? there was no photo given or answer choices... sorry guys. thats why i asked on here lol
What is the solution to the system of equations below?
x + 3y = 1
-3x - 3y = -15
Answer:
Step-by-step explanation:
x + 3y = 1
-3x - 3y = -15
-2x = -14
x = 7
7 + 3y = 1
3y = -6
y = -2
(7, -2)
Answer:
x =7 , y= -2
Step-by-step explanation:
x + 3y = 1
-3x - 3y = -15
Add the equations together to eliminate y
x + 3y = 1
-3x - 3y = -15
-------------------------
-2x = -14
Divide by -2
-2x/-2 = -14/-2
x = 7
Now we can find y
x+3y = 1
7 + 3y = 1
Subtract 7 from each side
7+3y-7 = 1-7
3y = -6
Divide by 3
3y/3 = -6/3
y = -2
5/8x + 4 = 3/8x + 12
Answer:
x = 32
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5/8*x+4-(3/8*x+12)=0
Step by step solution :
Step 1 :
3
Simplify —
8
Equation at the end of step 1 :
5 3
((—•x)+4)-((—•x)+12) = 0
8 8
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 8 as the denominator :
12 12 • 8
12 = —— = ——————
1 8
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3x + 12 • 8 3x + 96
——————————— = ———————
8 8
Equation at the end of step 2 :
5 (3x + 96)
((— • x) + 4) - ————————— = 0
8 8
Step 3 :
5
Simplify —
8
Equation at the end of step 3 :
5 (3x + 96)
((— • x) + 4) - ————————— = 0
8 8
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 8 as the denominator :
4 4 • 8
4 = — = —————
1 8
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
5x + 4 • 8 5x + 32
—————————— = ———————
8 8
Equation at the end of step 4 :
(5x + 32) (3x + 96)
————————— - ————————— = 0
8 8
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
3x + 96 = 3 • (x + 32)
Adding fractions which have a common denominator :
6.2 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(5x+32) - (3 • (x+32)) 2x - 64
—————————————————————— = ———————
8 8
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
2x - 64 = 2 • (x - 32)
Equation at the end of step 7 :
2 • (x - 32)
———————————— = 0
8
Step 8 :
When a fraction equals zero :
8.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
2•(x-32)
———————— • 8 = 0 • 8
8
Now, on the left hand side, the 8 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
2 • (x-32) = 0
Equations which are never true :
8.2 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
8.3 Solve : x-32 = 0
Add 32 to both sides of the equation :
x = 32
One solution was found :
x = 32
Step-by-step explanation:
Show the reflection of the given points.Locate the points of the reflection in their proper position around the x-axis
Answer: I believe this is it
The required reflection of the given points are A' = (5, -1), B' = (1, -3), C' = (-2, -2), D' = (-5, -4)
What is Reflection of point around x-axis?If we have any point say P(x, y) then their reflection around x -axis is
P'(x, -y)
Therefore around x-axis reflection only y coordinate changes
How to find reflection around x -axis?here we have the points
A = (5, 1), B = (1, 3), C = (-2, 2), D = (-5, 4)
Therefore the reflected points are
A' = (5, -1), B' = (1, -3), C' = (-2, -2), D' = (-5, -4)
The presentation is attached in the image
This is the conclusion to the answer.
Learn ore about reflection of the points here-
https://brainly.com/question/7243416
#SPJ2
Find the interval of converge to this series? Sum when n=1 and goes to infinity (x-2) ^n/ (n! .2^)
[tex] sum (x - 2)^{2} \ (ni.{2}^{n}) [/tex]
By the ratio test, the series converges if
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(x-2)^{n+1}}{(n+1)!2^{n+1}}}{\frac{(x-2)^n}{n!2^n}}\right|=|x-2|\lim_{n\to\infty}\frac{n!2^n}{(n+1)!2^{n+1}}[/tex]
[tex]=\displaystyle\frac{|x-2|}2\lim_{n\to\infty}\frac1{n+1}[/tex]
is less than 1. The limit itself is 0 < 1, so the series converges everywhere, i.e. on the entire real line [tex](-\infty,\infty)[/tex].
40% of a number is 44. Find the number
Answer:
110
Step-by-step explanation:
40% is the same as 40/100, which is equal to 0.4. Therefore, you can write the following equation:
0.4x=44
Divide both sides by 0.4 to isolate x:
x=44/0.4=110
Hope this helps!
Write the equation of the line that passes through the points (-2,-6) and (7,8).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answer:
y+6=14/9(x+2)
Step-by-step explanation:
Hope this helps
FIND THE CORRECT INTERCEPT OF THE LINE!
find the X and Y.
and please tell me how u got it. u know if u can
Answer:
see below
Step-by-step explanation:
The x intercept is where it crosses the x axis
It crosses at x = -7.5
(-7.5,0)
The y intercept is where it crosses the y axis
It crosses at y = 5.5
(0,5.5)
Jasmine found a wooden jewelry box shaped like a right rectangular prism. What is the volume of the jewelry box?
Answer:
The volume of the jewelry box will be given by,
[tex]\text{Volume}=\text{l}\times \text{w}\times\text{h}[/tex]
Step-by-step explanation:
It is provided that, Jasmine found a wooden jewelry box shaped like a right rectangular prism.
Consider the diagram below for the shape of a right rectangular prism.
The volume of a right rectangular prism is given by the formula:
[tex]\text{Volume}=\text{l}\times \text{w}\times\text{h}[/tex]
Here,
l = length of the rectangle
w = width of the rectangle
h = height of the rectangular prism
Thus, the volume of the jewelry box will be given by,
[tex]\text{Volume}=\text{l}\times \text{w}\times\text{h}[/tex]
Answer:
In the given problem, since it was stated that the dimension of the right rectangular prism is 8 by 6 by 14 cm. To solve the problem, you can use the formula for finding the volume. Therefore, the volume of the jewelry box is 672 cubic cm.
B
А
С
T
D
© 2016 Strong Mind. Created using GeoGebra.
In circle T, m AB = (3x + 9° and mCD = (11x – 71).
What is the measure of AB?
61°
37°
10°
39°
Answer:
D. 39°
Step-by-step explanation:
mAB = (3x + 9°)
mCD = (11x – 71)
From the diagram: |AB|=|CD|
Since arcs AB and CD are subtended by a chord of equal length.
mAB=mCD
3x + 9°=11x – 71°
Collect like terms to solve for x
11x-3x=9°+71°
8x=80°
x=10°
Therefore, the measure of AB:
mAB = (3x + 9°)
=3(10)+9
=30+9
=39°
The correct option is D.
how many pieces each 2 3/4 m long may be cut from a string 16 1/2 ?
Answer:
6
Step-by-step explanation:
2 3/4 = 2.75 & 16 1/2 = 16.5
No of pieces = 16.5/2.75 = 6
Answer:
6 pieces.
Step-by-step explanation:
16 1/2 / 2 3/4
= 33/2 / 11/4
= 33/2 * 4/11
= 132 / 22
= 6
Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200students in group 1 had a mean score of 24.5 with a standard deviation of 4.3, while the 200 students in group 2 had a mean score of 16.3 with a standard deviation of 3.1.Complete parts (a) and (b) below.(a) Determine the 90% confidence interval for the difference in scores, mu 1 minus mu 2.Interpret the interval. ( , ) (Round to three decimal places asneeded.)Interpret the interval. Choose the correct answer below.A.There is a 90% probability that the difference of the means is in the interval.B.The researchers are 90% confident that the difference of the means is in the interval.C.The researchers are 90% confident that the difference between randomly selected individuals will be in the interval.D.There is a 90% probability that the difference between randomly selected individuals will be in the interval.(b) What does this say about priming?A.Since the 90% confidence interval does not contain zero, the results suggest that priming does not have an effect on scores.B.Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.C.Since the 90% confidence interval contains zero, the results suggest that priming does have an effect on scores.D.Since the 90% confidence interval contains zero, the results suggest that priming does not have an effect on scores.
Answer:
Step-by-step explanation:
a) The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean of group 1
x2 = sample mean of group 2
s1 = sample standard deviation for data 1
s2 = sample standard deviation for data 2
For a 90% confidence interval, the z score is 1.645
From the information given,
x1 = 24.5
s1 = 4.3
n1 = 200
x2 = 16.3
s2 = 3.1
n2 = 200
x1 - x2 = 24.5 - 16.3 = 8.2
z√(s1²/n1 + s2²/n2) = 1.645√(4.3²/200 + 3.1²/200) = 1.645√0.1405
z = 0.62
Therefore, the 90% confidence interval is 8.2 ± 0.62
Interpretation:
B.The researchers are 90% confident that the difference of the means is in the interval.
b) B.Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.
The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 27 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.1 years and a sample variance of 36.0 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girlCalculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is SM______ . The t statistic is_________
Answer:
The estimated standard error is SM=1.1547 . The t statistic is 1.4722.
Step-by-step explanation:
We have to esimate the standard error and test statistic for a sample.
The sample has a size n=27.
The sample mean is M=17.7.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√36=6.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6}{\sqrt{27}}=1.1547[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.7-16}{1.1547}=\dfrac{1.7}{1.1547}=1.4722[/tex]
What is the value of Y?
Answer:
Finding the y value is easy if you know the slope of the line and the x coordinate. Review the equation for the slope of a line. The equation for finding the slope is: m = [y1 - y2] / [x1 - x2]. If you know x, you can solve for y to find the y value for the slope of the line.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer B
cause a full triangle degrees is 180 degrees and u just have to remove:
180-40-30= 110 degrees
a team won 8 of the 24 games it played in one season .what percentage of the games did it win
Answer:
The team won 33.33% of their games.
Step-by-step explanation:
Proportion and percentage of games won:
The proportion of games won is the number of games won divided by the total number of games.
The percentage of games won is the proportion multiplied by 100.
We have that:
8 wins in 24 games.
So
8/24 = 0.3333
0.3333*100 = 33.33%
The team won 33.33% of their games.
Solve for x in the diagram.
Answer:
x = 20
Step-by-step explanation:
x° + 2x° + (x+10)° = 90°
3x° + x° + 10° = 90°
4x° + 10° = 90°
4x° = 90°-10°
4x° = 80°
x = 80/4
x = 20
Answer:
20°
Step-by-step explanation:
The sum of all three angles combined is 90°. You can see this by the square at the corner. This means that you have to add all of the angles together and set it equal to 90° to solve for x.
x° + 2x° + (x + 10)° = 90°
3x° + (x + 10)° = 90°
4x° + 10° = 90°
4x° = 80°
x = 20°
Can someone solve this??
Answer:
see below
Step-by-step explanation:
There are a few relevant relations involved:
an inscribed angle is half the measure of the arc it interceptsan arc has the same measure as the central angle that intercepts itthe angle exterior to a circle where secants meet is half the difference of the intercepted arcs (near and far)the angle interior to a circle where secants meet is half the sum of the intercepted arcsthe angle where tangents meet is the supplement of the (near) arc interceptedan exterior angle of a triangle is equal to the sum of the remote interior anglesthe angle between a tangent and a radius is 90°the angle sum theoremAB is a diameter, so arcs AB are 180°.
a) BC is the supplement to arc AC: 180° -140° = 40°
b) BG is the supplement to AG: 180° -64° -38° = 78°
c) ∠1 has the measure of BC: 40°
d) ∠2 is inscribed in a semicircle, so has measure 180°/2 = 90°
e) ∠3 is half the measure of arc AE: 64°/2 = 32°
f) ∠4 is half the sum of arcs AG and BC: ((64°+38°) +40°)/2 = 71°
g) ∠5 is half the difference of arcs AC and EG: (140° -38°)/2 = 51°
h) ∠6 is half the sum of arcs EAC and BG: ((140°+64°) +78°)/2 = 141°
i) ∠7 is the difference of exterior angle 4 and interior angle 1: 71° -40° = 31°
j) ∠8 is the measure of arc AC: 140°
k) ∠9 is the supplement to arc AC: 180° -140° = 40°
l) ∠10 is the complement of angle 7: 90° -31° = 59°
How do you relate the points made by Professor Degraeve and the use of decision trees as a decision making tool?
In practice, do you feel that organizations focus more on outcomes or decisions?
Suggest at least one idea as to how an organization can make a cultural shift to focusing on the process associated with decision making as opposed to the outcomes.
Answer:
Organizations really focus more on early results, than on thinking carefully about the decisions they must make to achieve accurate and reliable results.
The diagram of the decision tree really helps to analyze all the possible associated variables that can contribute to a good result.
Step-by-step explanation:
We could think of an organization that has children's toys as its final product; At first this organization might think that it is best to make the most popular toys that are promoted by the advertising media, but making a decision diagram and really evaluating what is best at the moment and how this affects demand, it could be induced to look all the variables that could determine to what extent those "toys" to which the media advertise so much are so acceptable in the children's market; we could really be surprised.
plss help answer these qutions plss
Answer:
Step-by-step explanation:
[tex]V=whl=15*7*6=630ft^3(truck)[/tex]
[tex]V=whl=1.25*2.5*2=6.25ft^2(boxes)[/tex]
To determine how many boxes can go in each truck you have to divide the volumes with ach other so 630/6.25 which equals 100.8
So you could say 2 trucks because each truck can carry 100.8 boxes each
[tex]V=\frac{1}{4} h\sqrt{-a^4+2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4} \\V=\frac{1}{4} *7.1*\sqrt{-4^4+2*(4*5)^2+2*(4*4)^2-5^4+2*(5*4)^2-4^4} \\=55.42m^3\\(chalet)[/tex]
There is allowed 1 person per 15m^3 and there are 5 people. Only 3 people can stay in the chalet equalling 45m^3 leaving 10m^3 left thus, not allowing anymore people to stay in the chalet. So the family cant meet the fire safety standards with 5 people
Answer:
9) 630 ft^3; 6.25 ft^3; 2 trucks (3, if you consider space utilization)
10) 71 m^3; 4 persons; no
Step-by-step explanation:
9) The volume of the truck is the product of the dimensions:
V = LWH = (15 ft)(7 ft)(6 ft) = 630 ft^3 . . . truck V
Likewise, the volume of a storage box is the product of its dimensions:
V = LWH = (2 ft)(2.5 ft)(1.25 ft) = 6.25 ft^3 . . . box V
If the boxes pack well into the truck (they don't), then the number of boxes that would fit in the truck is the ratio of these volumes:
number of boxes = (630 ft^3)/(6.25 ft^3) = 100.8
This suggests that half of the 200 boxes will fit in one truck, so 2 trucks are needed.
__
Comment on space utilization
In the real world, not all of the truck's interior space can be utilized. This is because not all of the truck dimensions are integer multiples of the box dimensions. 96 is about the most boxes that can be placed in the truck. (Fitting more than 90 requires boxes be first layered one way, then layered another way to fill as much of the remaining space as possible.) In the real world, 3 trucks are needed to move 200 of these boxes.
___
10) The area of the end triangle of the chalet is ...
A = (1/2)bh = (1/2)(5 m)(7.1 m) = 17.75 m^2
Then the volume of the chalet is ...
V = Bh = (17.75 m^2)(4 m) = 71 m^3 . . . volume of the chalet
At 15 m^3 per person, there is enough volume for ...
(71 m^3)/(15 m^3/person) = 4.73 persons
4 persons can stay in the chalet.
No, the entire family cannot stay in the chalet.
The field was 5⁄6 of an acre and 1⁄3 of the field was planted in strawberries. How many acres are planted in strawberries?
acres
Answer:
333 miliacres
Step-by-step explanation:
First of all, you should know that 1 acre is the same as 4046.9 m²
So, 1/3 of those 4046.9 m² is fully covered by strawberries.
By the way, 4046.9m² . 1/3 = 1348.96 m². This is our planted field.
Let's convert the measure to acres, though:
1348.96 m² . 1 acre / 4046.9 m² = 0.333 acres
0.333 acres . 1000 / 1 acre = 333 miliacres
If you want to know in another unit, let's do another conversion
0.333 acre . 43560 square feet / 1 acre = 14520 square feet
If SinP + SinQ = 7/5 and angle P + angle Q = 90 degrees, without the use of a calculator, determine the value of Sin2P
Answer:
sin2P ≈ 1Step-by-step explanation:
Given SinP + SinQ = 7/5...1 and
∠P + ∠Q = 90°... 2
From compound angle; SinP +SinQ = [tex]2sin(\frac{P+Q}{2} )cos(\frac{P-Q}{2} )[/tex]... 3
Substituting equation 2 into 3 we will have;
SinP +SinQ = [tex]2sin(\frac{90}{2} )cos(\frac{P-Q}{2} )[/tex] = 7/5
[tex]2sin45^{0} cos\frac{P-Q}{2}=7/5[/tex]
since P = 90-Q from equation 1, then;
[tex]2sin45^{0} cos\frac{90-Q-Q}{2}=7/5\\2sin45^{0} cos\frac{90-2Q}{2}=7/5\\2(\frac{1}{\sqrt{2} } ) cos\frac{90-2Q}{2}=7/5\\cos\frac{90-2Q}{2} = 7/5* \frac{\sqrt{2} }{2} \\cos\frac{90-2Q}{2} = \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = cos^{-1} \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = 8.15\\90-2Q = 16.30\\2Q = 90-16.3\\2Q = 73.7\\Q = 36.85^{0} \\\\P = 90-36.85\\P = 53.15^{0}[/tex]
To get sin2P; Accoding to the trig identity;
Sin2P = 2SinPCosP
Sin2P = 2Sin53.15cos53.15
sin2P = 0.9598
sin2P ≈ 1
You need to arrange six of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you?
ways
(Type a whole number.)
Answer:
The first book can be chosen from ANY of the 6 books,
the second book can be chosen from the OTHER 5 books and continuing in this way, we get:
6 * 5 * 4 * 3 * 2 * 1 = 720 ways
Step-by-step explanation:
A coffeepot contains 1 1⁄2 quarts of coffee. After Tonya pours an equal amount of coffee into two cups, 3 1⁄2 cups of coffee remain in the pot. How much coffee did Tonya pour into each cup? (cups and oz)
Answer:
2 cups
Step-by-step explanation:
to find the extra cup of coffee
[tex]3\frac{1}{2}-1\frac{1}{2}=\frac{7}{2}-\frac{3}{2}=\frac{4}{2}=2 cups[/tex]
what expression is equal to -4x²-36?
Answer:
−4(x^2+9)
Step-by-step explanation:
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Which graph represents the solution for x2 + x - 12 > 0?
Answer:it’s c on edge, sorry i’m late but for anyone else who needs help it’s c !!
Step-by-step explanation:
Answer:
C. on edg2020
Step-by-step explanation:
Hope this helps!!! Have a great day!!! : )
Please answer this correctly
Answer:
= 16 12/13 mm
Step-by-step explanation:
To find the perimeter, we add all the sides
P = 4 3 /13 +4 3/13+ 4 3 /13 +4 3/13
Adding the whole numbers
4+4+4+4 = 16
Adding the fractions
3/13+3/13+3/13+3/13 = 12/13
Putting this back together
= 16 12/13 mm
A coal mine worker is 650 feet below the ground in a mine. Another coal mine worker is 7 feet above ground operating machinery.
Write an integer for the position of each worker relative to the ground.
Find the absolute value of each integer.
Which worker is farther from the ground surface?
Answer:
The first coal mine worker is 650 feet below, so they're -650 ft.
The second coal mine worker is 7 feet above, so they're +7 ft.
| -650 | = 650 ft
| 7 | = 7 ft
650 > 7, so the first worker is farther from the surface.
A fair die has just been rolled five times – giving scores of 1, 2, 3, 4, 5 in that order. How likely is it that the score on the next roll will be a 6?
A. no chance B. less than evens C. evens D. better than evens E. certain
Answer:
b. less than evens
Step-by-step explanation:
the probability that the next roll is 6 is
[tex] \frac{1}{6} [/tex]
B. less than evens should be the answer
A broth used to manufacture a pharmaceutical product has its sugar content, in mg/mL, measured several times on each of three successive days.
Day 1: 5.0, 4.8, 5.1, 5.1, 4.8, 5.1, 4.8, 4.8, 5.0, 5.2, 4.9, 4.9, 5.0
Day 2: 5.8, 4.7, 4.7, 4.9, 5.1, 4.9, 5.4, 5.3, 5.3, 4.8, 5.7, 5.1, 5.7
Day 3: 6.3, 4.7, 5.1, 5.9, 5.1, 5.9, 4.7, 6.0, 5.3, 4.9, 5.7, 5.3, 5.6
Can you conclude that the variability of the process is greater on the third day than on the second day?
Answer:
Yes
Step-by-step explanation:
To compare the variability of the measured sugar content for each day, we can estimate the standard deviation using the Range rule.
Standard Deviation =[tex]\dfrac{\text{Maximum Value-Minimum Value}}{4}[/tex]
Day 1
5.0, 4.8, 5.1, 5.1, 4.8, 5.1, 4.8, 4.8, 5.0, 5.2, 4.9, 4.9, 5.0
Maximum Value=5.2Minimum Value=4.8Standard Deviation =[tex]\dfrac{5.2-4.8}{4}[/tex]
=0.1
Day 2
5.8, 4.7, 4.7, 4.9, 5.1, 4.9, 5.4, 5.3, 5.3, 4.8, 5.7, 5.1, 5.7
Maximum Value=5.8Minimum Value=4.7Standard Deviation =[tex]\dfrac{5.8-4.7}{4}[/tex]
=0.275
Day 3
6.3, 4.7, 5.1, 5.9, 5.1, 5.9, 4.7, 6.0, 5.3, 4.9, 5.7, 5.3, 5.6
Maximum Value=6.3Minimum Value=4.7Standard Deviation =[tex]\dfrac{6.3-4.7}{4}[/tex]
=0.4
Since the estimated standard deviation of the third day is higher than that of the second day, the variability of the process is greater on the third day than on the second day.
A company offers earthquake insurance. Annual premiums are modeled by an exponential random variable with mean 2. Annual claims are modeled by an exponential random variable with mean 1. Premiums and claims are independent. Let X denote the ratio of claims to premiums. What is the density function of A?
Answer:
The density function of X is : [tex]h_{X} (x) = \left \{ {{\frac{2}{(1+2x)^{2} } \quad x\geq0} \atop {x=0 \qquad x<0 }} \right.[/tex]
Step-by-step explanation:
[tex]h_{X} (x) = \left \{ {{\frac{2}{(1+2x)^{2} } \quad x\geq0} \atop {x=0 \qquad x<0 }} \right.[/tex]
For easiness and clarity of expression, the calculations are handwritten and attached as files. The files are broken into bits for easy understanding. Check the six files below for the calculations.
