Answer:
See Explanation for answers
Step-by-step explanation:
Given
[tex]Grade\ X: 568, 570, 575, 578, 584[/tex]
[tex]Grade\ Y: 573, 574, 575, 577, 578[/tex]
Solving (a): Mean, median, and standard deviation of both grades
Mean is calculated as:
[tex]Mean = \frac{\sum x}{n}[/tex]
For grade X:
[tex]Mean = \frac{568 + 570+ 575+578+584}{5}[/tex]
[tex]Mean = \frac{2875}{5}[/tex]
[tex]Mean = 575[/tex]
For Grade Y
[tex]Mean = \frac{573+ 574+ 575+ 577+ 578}{5}[/tex]
[tex]Mean = \frac{2877}{5}[/tex]
[tex]Mean = 575.4[/tex]
[tex]Median = \frac{N+1}{2}th[/tex]
[tex]Median = \frac{5+1}{2}th[/tex]
[tex]Median = \frac{6}{2}th[/tex]
[tex]Median = 3rd\ item[/tex]
For grade X and Y.
[tex]Median = 575[/tex]
Standard deviation (s) is calculated as:
[tex]s = \sqrt{\frac{\sum(x_i - \bar x)^2}{n}}[/tex]
For Grade x
[tex]s = \sqrt{\frac{(568 - 575)^2+(570 - 575)^2+(575 - 575)^2+(578- 575)^2+(584- 575)^2}{5}}[/tex]
[tex]s = \sqrt{\frac{164}{5}}[/tex]
[tex]s = \sqrt{32.8}[/tex]
[tex]s = 5.73[/tex]
For Grade Y
[tex]s = \sqrt{\frac{(573 - 575.4)^2+(574 - 575.4)^2+(575 - 575.4)^2+(577 - 575.4)^2+(578 - 575.4)^2}{5}}[/tex]
[tex]s = \sqrt{3.44}[/tex]
[tex]s = 1.85[/tex]
Solving (b): If the last value is b, the following will occur.
The mean will increase.
The median will remain unaltered
The standard deviation will increase.
See proof below
For Grade Y: Mean is:
[tex]Mean = \frac{573+ 574+ 575+ 577+ 588}{5}[/tex]
[tex]Mean = \frac{2887}{5}[/tex]
[tex]Mean = 577.4[/tex]
Median still remains the 3rd item.
[tex]Median = 575[/tex]
The standard deviation is:
[tex]s = \sqrt{\frac{(573 - 575.4)^2+(574 - 575.4)^2+(575 - 575.4)^2+(577 - 575.4)^2+(588 - 575.4)^2}{5}}[/tex]
[tex]s = \sqrt{\frac{169.2}{5}}[/tex]
[tex]s = \sqrt{33.84}[/tex]
[tex]s = 5.82[/tex]
Solving (c): Which grade provides better quality.
Grade X provides better quality.
This is so because the mean value, the standard deviation of grade X is greater than grade Y
Mean medium and standard deviation are the statistics tools used to measure the center tendency of the given data set.
The mean, medium standard deviation are computed and value obtained. If value last value of data set Y is 588 instead of 578 the mean and standard deviation will increase but medium will remain same for data set Y.The value of mean and standard deviation of the Tyre X is greater thus the Tyre X provide the better quality.Given information-Grade X: 568, 570, 575, 578, 584
Grade Y: 573, 574, 575, 577, 578
a) Compute the mean, median, and standard deviation for each grade of tire.MeanMean is the average of the given data or the ratio of the sum of the given data set to the number of data in the set.
Mean for grade X,
[tex]\overline x=\dfrac{568+570+575+578+584}{5} \\ \overline x=575[/tex]
Mean for grade Y,
[tex]\overline x=\dfrac{573+574+575+577+578}{5} \\ \overline x=575.4[/tex]
MedianMedian is the middle number when the data set is arranged in the assenting or descending order.
The middle number for both the data set is 575 milimeter. Thus the median is 575 for both the data set.
Standard deviationStandard deviation refers that how much the group member of a data set is differ from the mean value. Standard deviation can be given as,
[tex]\sigma=\sqrt{\dfrac{\sum(x_i-\mu)^2}{N} } [/tex]
Standard deviation for X
[tex]\sigma=\sqrt{\dfrac{(568-575)^2+(570-575)^2+(575-575)^2+(578-575)^2+(584-575)^2}{5} } \\ \sigma=5.73[/tex]
Standard deviation for Y
[tex]\sigma=\sqrt{\dfrac{(573-575.4)^2+(574-575.4)^2+(575-575.4)^2+(577-575.4)^2+(578-575.4)^2}{5} } \\\sigma=1.85[/tex]
b) Effect on the answers in (a) and (b) if the last value for grade Y was 588 instead of 578.
Mean for grade Y,
[tex]\overline x=\dfrac{573+574+575+577+588}{5} \\ \overline x=577.4[/tex]
Thus the mean increased with value 2 mm.
Medium remain the same as the middle value is still 575.
Standard deviation for Y
[tex]\sigma=\sqrt{\dfrac{(573-575.4)^2+(574-575.4)^2+(575-575.4)^2+(577-575.4)^2+(588-575.4)^2}{5} } \\\sigma=5.82[/tex]
c) Tire which provide better quality-
The value of mean and standard deviation of the Tyre X is greater thus the Tyre X provide the better quality.
Hence
The Mean medium and standard deviation are computed and value obtained. If value last value of data set Y is 588 instead of 578 the mean and standard deviation will increase but medium will remain same for data set Y.The value of mean and standard deviation of the Tyre X is greater thus the Tyre X provide the better quality.Lean more about the Mean medium and standard deviation here;
https://brainly.com/question/24391622
What is an equivalent expression for 8(3x+2)
Answer:
8(3x+2)=24x+16.
Step-by-step explanation:
there
Answer:
24x+16
Step-by-step explanation:
ANSWER ASAP WILL GIVE BRAINLIEST FOR THE RIGHT ANSWER
Answer:
10 quarts
Step-by-step explanation:
hope i helped you!!
Find the measure of
Answer:3Y+6=12
3(2)+6=12
Step-by-step explanation:Because 3 + 3 is 6 So That means that you repeat the pattern 4 times 3 Times 4 equals 12
cual es el resuido de 729÷38
Answer:
19
Step-by-step explanation:
☺
prorate the following expenses and find the corresponding monthly expense. Lan pays a semiannual premium of $450 for automobile insurance, a monthly premium of $135 for health insurance, and an annual premium of $300 for life insurance.
the monthly expense is ____$
Step-by-step explanation:
$135 health insurance
After you do $300÷12=25 so
$25 monthly for life insurance
after you can do $450÷6=$75
and then we add all that up
$135
$75
$25
=That will equal $235 for the monthly cost
(20 POINTS!!) Find the probability that a multiple of 3 or an odd number is rolled on a number cube.
Answer:
1/8
Step-by-step explanation:
A “standard number cube” has six sides, marked 1 2 3 4 5 and 6. Of those, exactly half are even and exactly half are odd, so we can dispense with the 6 part and just go 1/2 (the same as 3/6, after all)
So the first roll is even half the time. If it is, the second roll is odd half the time, so the chances of an even then odd pair are 1/2*1/2=1/4.
If those two happen in the correct order, the chances of the third roll being even are again 1/2… so we have 1/2*1/2*1/2=1/8
Hope it helps
On Monday, the temperature was 64°. By Friday, it rose to 96°. What was the percent of increase in temperature?
Answer:32
Step-by-step explanation:96-64=32 half of 64 is 32 also equal to 50%
Answer:
the increase is 50%
Step-by-step explanation:
96-64= 32
percentage= 32/64*100
=50%
-3z-z I need help pleeeaaassseee
your friend writes 4.8% as 4.888 is your friend correct?
Answer: No
Step-by-step explanation:
4.8%
=> 4.8 / 100
=> 4.8 = 0.048
What is this I’m confused and my teacher won’t help me
Answer:
I think it is a number line to help you answer the question.
Step-by-step explanation:
In order to answer it, you must find the equivalent number to the answer and that should complete it. (This is the best I can do.)
7. The first term of a geometric sequence is 27, the last term is 8 and the sum of the
associated series is 65.
What is the common ratio and how many terms are there in the series?
Step-by-step explanation:
nddjdjdkdkfbfbnfkfkgkngnngn
Write an equation of the line that passes through point P and is parallel to the line with the given equation. P(3,5); y=2x-6
Answer:
y = -(5/2)x + 3 is a line perpendicular to y = (2/5)x + 2. This line is also perpendicular to y = (2/5)x + 9 because it has the same slope.
Step-by-step explanation:
A) So the line you are given is written in slope intercept form y = mx + b meaning that the slope of the line is m = 2/5 and the intercept b = 9 (so the line hits the y axis at 0,9). A line that is parallel has to have the same slope so we know our m is the same. So we have y = (2/5)x + b. We need b. It passes (0, 2) since the x coordinate is 0 you know the y intercept is 2 but you can verify this using the point slope formula:
y - y1 = m(x - x1) plug in values
y - 2 = (2/5)(x - 0) now simplify
y - 2 = (2.5)x last solve
y = (2/5)x + 2 see how when the x coordinate is 0 you can automatically use the point slope intercept formula? Neato!
B) Now we want a line perpendicular to y = (2/5)x + 2 and that passes through 0,3. What are the properties of a line perpendicular to a line of the form y = mx + b and passes through (0, 3)? We know that the slope of this new line will be the reciprocal and have the opposite sign of m. So the new slope we will call it mnew = -(1/m) so plug in for m and you get mnew = -(1/[2/5]) if you simplify you get that the mnew = -(5/2). So we have half of our equation for the perpendicular: y = -(5/2)x + b. If you look at (0, 3) you see that the y intercept is 3 so b = 3. So:
The equation of the line that passes through given point and is parallel to the line with the given is y = 2x-1
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, we need to find the equation of a line passing through the point (3, 5) and is parallel to y = 2x-6,
Comparing the given equation with the general equation of line y = mx+c
m = 2 (the slope)
We know that the two parallel lines have equal slope.
Therefore, the required equation is =
y = 2x+c
To find the value of c, put x = 3 and y = 5,
5 = 2(3) + c
c = -1
Therefore,
The required equation is =
y = 2x-1
Hence, the equation of the line that passes through given point and is parallel to the line with the given is y = 2x-1
Learn more about equation, click;
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what is -3m2 x -5 x m2
Felicity baby sat 4 hours each night for 5 nights. She earned a total of $240 babysitting. Felicity wants to calculate her hourly rate. How much did Felicity earn per hour babysitting?
Answer: $60 per hour
Step-by-step explanation:
So 5 nights , every 4 hours , Felicity earned a total of $240
240 / 4 = 60
Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function?
A.) It is linear because the graph decreases over time.
B.) It is linear because there is both an independent and a dependent variable.
C.) It is nonlinear because linear functions are increasing functions.
D.) It is nonlinear because linear functions increase or decrease at the same rate.
please help meeeeee :)
Answer: d
Step-by-step explanation:
Help and explain
Don’t take points or I’ll take it back
Answer:
Since there are two angles which are equal in the triangle we can make our equation as-
2x+60=180
(180 cuz the sum of all angles in a triangle will ALWAYS be 180)
so if we solve,
2x=120
x=120/2
x=60
thus x=60
Answer
60
Explanation:
So a given shape will always have a degree of 180.
We know one of the degrees is 60, so we can subtract that to find the missing degree angles: 180 - 60 = 120
We can divide 120 by 2 to spilt that into two degrees: 120 ➗ 2 = 60
(If you have math sense, you can tell that they all have the same angle, so same angle means same degree)
Well hope ya have a great day!
please help me with this math problem
Answer:
The perimeter is:
(3rd option) 2(x + y)
(5th option) 2x + 2y
The area is:
(7th option) xy
Step-by-step explanation:
Perimeter = the length (represented by y) + the width (represented by x) + length + width
Another way to state this is multiplyimg length by 2 and width by 2 and then adding them together as this equals the same outcome
Area = length (y) × width (x)
Find the slope of a line that passes through the points (-5,2)and(1,-1).
Answer:
y = mx + b, so:
y = -.5x + -1
Step-by-step explanation:
1. Find the slope of the line. In this case, it's [tex]\frac{6}{-3}[/tex], which converts to -0.5
2. Start the first part of your equation. In this case, y = -.5x
3. Find the y-intercept. In this case, it's -1
4. Finish your equation. In this case, it's y = -.5x + 1
Here is a list of ingredients for making 24 Rocky Road Crunchy Bars.
Silvester wants to make 30 Rocky Road Crunchy Bars.
Work out the amount of marshmallows he needs.
Answer:
Step-by-step explanation:
which expressipm is equilivant to 6x + 7 - 12 * 2 -(9 + 2) - x
Answer:
7x * 14
Step-by-step explanation:
hope this helps :)
Solve for W. What does W equal?
Answer:
w=-11/6
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]-8\frac{5}{9}=4\frac{2}{3}w\\ \\ -\frac{77}{9}=w\frac{14}{3}\\ \\ w=-\frac{77}{9}\left(\frac{3}{14}\right)\\ \\ w=-\frac{11}{6}\\ \\ w=-1\frac{5}{6}[/tex]
PLZ HELP ITS DUE SOON
What is the value of x
Answer:
15
Step-by-step explanation:
The first thing we have to do is find angle A
I will assume that you know SOH CAH TOA (if not ,ask)
We will use TOA
Tan(angle)=5/10
angle= 26.565
Now that we know angle A we will look at these two triangles as one big one
We know that side CA=30 and that anglea=26.56 so we can use TOA again
Tan(26.565)=x/30
30tan(26.565)=x
x=15
Answer:
the answer is 15
Step-by-step explanation:
Hii please help I need help also I am almost done with this 2 more question left
Answer:
2p-10 trust me sksksksk
2/3 X 12 for simplest form
Answer:
yufcyiciygciykgc, nbhgcv
Step-by-step explanation:
98yfgouyfuchkgcbvkhgcihdiytdiytditdytdiytdityghvhgcxdfsrtyuhkjbhcgfdxzsaewrsdxfhgyujkhjmnb cvngfjkhji
Answer:
2/3 x 12 = 8/x
8x
please answer 24<11+x
Answer:
x can be 14 or more
Step-by-step explanation:
Answer:
x>13! I hope I helped? :')
Steps for answer!
1. Subtract 11 from both sides.
24−11<x
2. Simplify 24-11 to 13.
13<x
3. Switch sides.
x>13
David is going to invest $330 and leave it in an account for 20 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for David to end up with $680?
Answer:
$1255.
Step-by-step explanation:
Mark me brainlest!
six less than twice a number is four in algebraic expression?
Answer:
6 < 2n = 4
Step-by-step explanation:
ig
a rabbit weighs 3 150 grams. what does the rabbit weight measured in kilograms?
Answer:
3.15 kg
Step-by-step explanation:
3150 = 3.15 kg
Answer:
3.15 kg
Step-by-step explanation:
I just took the test, hope this helped!
The figures are similar. Find x
Answer:
[tex]x=\frac{20}{3} =6.67[/tex]
Step-by-step explanation:
[tex]x=15*\frac{4}{9}=\frac{20}{3} =6.67[/tex]
Answer:
6 2/3 or 20/3 or 6.6667
Step-by-step explanation:
Since the figures are similar, you can find x through comparing ratios. To get from 9 to 4, multiply 9 by 4/9. To find x, you must then multiply 15 by 4/9.
15 x 4/9 = 6 2/3 or 20/3 or 6.6667
Which describes the shaded portion of the figure? PLEASE HELP MEEE
Answer:
1/5=20%
Step-by-step explanation: