An article in Technometrics (Vol. 19, 1977, p. 425) presents the following data on the motor fuel octane ratings of several blends of gasoline:
88.5 98.8 89.6 92.2 92.7 91.8 91.0 91.0 94.7 88.3 90.4 83.4 87.9 88.4 87.5 90.9 84.3
90.4 91.6 91.0 93.0 92.6 87.8 89.9 90.1 91.2 90.7 88.2 94.4 93.7 88.3 91.8 89.0 90.6
88.6 88.5 90.4 96.5 89.2 89.7 89.8 92.2 88.3 93.3 91.2 84.3 92.3 92.2 91.6 87.7 94.2
87.4 91.2 93.2 88.9 90.3 91.1 85.3 91.1 86.7 88.6 89.8 90.0 86.7 90.1 90.5 94.2 88.7
92.7 91.5 93.4 89.3 100.3 90.8 92.7 93.3 89.9 96.1 91.1 87.6 90.1 89.3 86.7
Required:
Construct a stem-and-leaf display for these data. Calculate the median and quartiles of these data.
Answer:
[tex]Median = 90.4[/tex]
[tex]Q_1 = 88.6[/tex]
[tex]Q_3 = 92.2[/tex]
Step-by-step explanation:
Given
The above data
Required
- A stem and leaf display
- The median
- The quartiles
First, determine the range of the data
[tex]Smallest = 83.4[/tex]
[tex]Highest = 100.3[/tex]
Next, group each dataset base on common whole numbers.
So, we have:
[tex]83.4[/tex]
[tex]84.3\ 84.3[/tex]
[tex]85.3[/tex]
[tex]86.7\ 86.7\ 86.7[/tex]
[tex]87.4\ 87.5\ 87.6\ 87.7\ 87.8\ 87.9[/tex]
[tex]88.2\ 88.3\ 88.3\ 88.3\ 88.4\ 88.5\ 88.5\ 88.6\ 88.6\ 88.7\ 88.9[/tex]
[tex]89.0\ 89.2\ 89.3\ 89.3\ 89.6\ 89.7\ 89.8\ 89.8\ 89.9\ 89.9[/tex]
[tex]90.0\ 90.1\ 90.1\ 90.1\ 90.3\ 90.4\ 90.4\ 90.4\ 90.5\ 90.6\ 90.7\ 90.8\ 90.9[/tex]
[tex]91.0\ 91.0\ 91.0\ 91.1\ 91.1\ 91.1\ 91.2\ 91.2\ 91.2\ \ 91.5\ 91.6\ 91.6\ 91.8\ 91.8[/tex]
[tex]92.2\ 92.2\ 92.2\ 92.3\ 92.6\ 92.7\ 92.7\ 92.7[/tex]
[tex]93.0\ 93.2\ 93.3\ 93.3\ 93.4\ 93.7[/tex]
[tex]94.2\ 94.2\ 94.4\ 94.7[/tex]
[tex]96.1\ 96.5[/tex]
[tex]98.8[/tex]
[tex]100.3[/tex]
Next, we construct the stem and leaf plot.
The whole numbers will be the stem while the decimal parts will be the leaf.
So, we have:
[tex]\begin{array}{ccc}{Stem} & {} & {Leaf} & {83} & {|} & {.4} & {84} & {|} & {.3\ .3} & {85} & {|} & {.3} & {86} & {|} & {.7\ .7\ .7} & {87} &{|} & {.4\ .5\ .6\ .7\ .8\ .9} & {88} & {|} & {.2\ .3\ .3\ .3\ .4\ .5\ .5\ .6\ .6\ .7\ .9} &{89} & {|} & {.0\ .2\ .3\ .3\ .6\ .7\ .8\ .8\ .9\ .9} & {90} & {|} &{.0\ .1\ .1\ .1\ .3\ .4\ .4\ .4\ .5\ .6\ .7\ .8\ .9} & {91} &{|}&{.0\ .0\ .0\ .1\ .1\ .1\ .2\ .2\ .2\ .5\ .6\ .6\ .8\ .8} &{92} &{|} &{.2\ .2\ .2\ .3\ .6\ .7\ .7\ .7} \ \end{array}[/tex]
[tex]\begin{array}{ccc} {93} & {|} & {.0\ .2\ .3\ .3\ .4\ .7} & {94} &{|} & {.2\ .2\ .4\ .7} &{96} & {|} & {.1\ .5} & {98} & {|} & {.8} & {100} &{|} &{.3} \ \end{array}[/tex]
From the above plot,
[tex]n = 83[/tex]
The median is calculated as:
[tex]Median = \frac{n+1}{2}th[/tex]
[tex]Median = \frac{83+1}{2}th[/tex]
[tex]Median = \frac{84}{2}th[/tex]
[tex]Median = 42nd[/tex]
i.e. the median is at the 42nd position.
From the above stem and leaf plot.
The 42nd position is at stem 90 and the leaf .4
So the median is:
[tex]Median = 90.4[/tex]
The lower quartile (Q) is calculated as:
[tex]Q_1 = \frac{n+1}{4}th[/tex]
[tex]Q_1 = \frac{83+1}{4}th[/tex]
[tex]Q_1 = \frac{84}{4}th[/tex]
[tex]Q_1 = 21st[/tex]
i.e. the lower quartile is at the 21st position.
From the above stem and leaf plot.
The 42nd position is at stem 88 and the leaf .6
So the lower quartile is:
[tex]Q_1 = 88.6[/tex]
The upper quartile (Q3) is calculated as:
[tex]Q_3 = 3 * \frac{n+1}{4}th[/tex]
[tex]Q_3 = 3 * \frac{83+1}{4}th[/tex]
[tex]Q_3 = 3 * \frac{84}{4}th[/tex]
[tex]Q_3 = 3 * 21th[/tex]
[tex]Q_3 = 63rd[/tex]
i.e. the upper quartile is at the 63rd position.
From the above stem and leaf plot.
The 63rd position is at stem 92 and the leaf .2
So the upper quartile is:
[tex]Q_3 = 92.2[/tex]
Determine the amplitude or period as requested. Amplitude of y = 1/2 * cos 5x
Answer:
The amplitude is [tex]\frac{1}{2} = 0.5[/tex]
Step-by-step explanation:
Trigonometric function:
A trigonometric function has the following format:
[tex]A\sin{bx}[/tex] or [tex]A\cos[bx}[/tex]
In which the amplitude is A and the period is [tex]\frac{2\pi}{b}[/tex]
Amplitude of y = 1/2 * cos 5x
The multiplier is 1/2, so this is the amplitude.
help plss will give brainly promise
Answer:
101
Step-by-step explanation:
Pls answer fast pls pls pls pls
Answer:
13.93
Step-by-step explanation:
use the Pythagorean theorem
Frank is going to plant x vegetable seeds in one garden and 3x+7 vegetable seeds in another. How many seeds is Frank going to plant?
Answer:
no. of plants frank plants in one garden = x vegetables
no. of plants frank plants in another garden = 3x + 7
total no. of plants frank plants = x + 3x + 7 = 4x + 7
hope this answer helps you.....
please mark as brainliest.. thank you!
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
sides of this triangle?
5 cm and 8 cm
6 cm and 7 cm
• 7 cm and 2 cm
•
8 cm and 9 cm
Answer:
8cm and 9cm
Step-by-step explanation:
8cm and 9cm would be the two possible lengths for the triangle because for the triangle to work you need the other two other sides when added together needs to be greater then 13. Furthermore 5 + 8 = 13 and as 13 is the same length as the one side that is given, a triangle couldn't possibly be formed as it would just be a straight line. Moreover, this is the same with 6 + 7 which is also 13. 7 + 2 is 9 and because 9<13 a triangle couldn't possibly be formed. Finally, 8 + 9 which equals to 17 are the only two possible lengths for the triangle as 17 > 12.
Anna is 9 years old, and this year she received $10 from her aunt on her birthday. Her aunt has told
her that she will send $10 every birthday from now on. Which function best describes how much
money, M, Anna will have received from her aunt, in total, given how many years, y, have passed
since her 9th birthday?
O M(y) = 10y
OM(y) = 10y + 10
O M(y) = 10y - 10
M(y) = y + 10
Answer:
[tex]M(y)=10y+10[/tex]
Step-by-step explanation:
What is the value of f(3) in the function below?
F(x) = 1/4 • 2^x
Answer:
Value is 2
Step-by-step explanation:
f(3)= 1/4 x 2^(3) ------- 2 x 2 x 2= 8
1/4 x 8 = 8/4 = 2
Find the length of the rectangular prism if the volume is 66 and width is 3 and height is 2
Answer:
l=11
Step-by-step explanation:
w Width
3
h Height
2
V Volume
66
please I need to answer three brainliest questions
what question? where is the question???????????????????????????????????????????????????
Simplify:
5.5 + 7 [(6.3 + 2.1) X 4+ (10 – 4) = 21
Answer:
x=4√−0.45068027,−4√0.45068027
Step-by-step explanation:
Question
A shirt is on sale for 15 percent off the original price of x dollars. If a customer has a coupon for 5 dollars off the sale price, which of the following represents the price, in dollars, the customer will pay. excluding tax, for the shirt?
0.15x -5
O 0.85x -5
0.85(x - 5)
5-0.85x
Answer:
.85x-5
Step-by-step explanation:
If you say .15x suppose x is 1
.15*1= .15
Is 15% off 1 = .15 no its .85 thats why in these types of problems we do 100%-15%=85% and then .85*x
After deducting the discounts given to the customer, the current price the customer will pay is $(0.85x - 5).
Given parameters:
discount rate of the shirt, = 15%
original price of the shirt, = $x
additional discount on the sales price = $5
To find:
the current price the customer will payNote: the original price of the shirt = 100% of x
The current price of the shirt = original price - given discounts
The current price of the shirt = 100%x - 15%x - 5The current price of the shirt = 85%x - 5Convert the percentage to decimal by dividing it by 100
The current price of the shirt becomes 0.85x - 5Thus, after the discount the customer will pay $(0.85x - 5)
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what is the effect on the graph of f(x)= 1/x when it is transformed to g(x)= 1/x-7?
A. The graph of f(x) is shifted 7 units up
B. The graph of f(x) is shifted 7 units to the left
C. The graph of f(x) is shifted 7 units down
D. The graph of f(x) is shifted 7 units to the right
Answer:
Answer:
C. the graph of f(x) is shifted 7 units down
The volume of a cuboid is 450cm3.
The length is 10cm and the width is 15cm.
Work out the height of the cuboid.
Answer:
3cm
Step-by-step explanation:
The formula for the volume of the cuboid is [tex]w*l*h=volume[/tex]
We already have the length, width, and volume, so we have to plug it in to the equation.
[tex]15*10*h=450[/tex] (Just a heads up in case you didn't know: the centimeters cubed is just part of the units, so you don't need to worry about it when plugging it in to the equation.)
To solve for h:
1. Multiply 15 and 10
[tex]150*h=450[/tex]
2. Divide both sides by 150
[tex]h = 450/150[/tex]
h = 3
This is in centimeters, so the final answer is 3cm.
The height of a cuboid with a volume of 450cm³ with a length of 10cm and width of 15cm is 3cm.
How to calculate volume?The volume of a cuboid can be calculated using the following formula:
Volume = length × width × height
According to this question, the volume of a cuboid is 450cm³ and has a length of 10cm and the width is 15cm. The height is as follows:
450cm³ = 15cm × 10cm × h
450cm³ = 150²h
h = 450/150
h = 3
Therefore, the height of a cuboid with a volume of 450cm³ with a length of 10cm and width of 15cm is 3cm.
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Which equation will create a system of equations with infinitely many solutions?
A) 3x - y=5
B) -3x +y=5
C) 12x + 4y = 20
D) 12x - 4y= 20
Answer:
A and D
Step-by-step explanation:
for infinitely many solutions, ratio of coefficients should be equal.
since ratio = 1/4 so they will have infinitely many solutions.
what two steps are necessary to put this equation into standard form? x^2-3x+27=8x-3
Answer:Add 3 to both sides and subtract 8x from both sides.Step-by-step explanation:The standard form of a quadratic equation isHere a should not be zero.Now, we have to write the given equation in this formwe have to take 8x and -3 to the left side of the equation in order to write the equation in standard form.Therefore, we have to subtract 8x and add 3 to both sides of the equation.When we do this operation, we'll get the equation in standard form which is given byHence, option is correct.Add 3 to both sides and subtract 8x from both sides.
(MATH) (6) ((PHOTO))
label is in cubed
Jamie buys a new fish tank, which is 55 cm long, 25 cm wide and 40 cm high. He needs
to fill the tank with water that has to be 35 cm deep. How much water does he need to fill
the tank, if 1000 cm = 1 litre? Give your answer rounded to the nearest litre.
Answer:
0.155litre
Step-by-step explanation:
55+25+40+35=155cm
100Cm=1litre
155cm_ ?
155cm×1litre/1000cm
0.155Litre
URGENT giving 100 pts no links no fakes give evidence srong answers or gueses will be reported
Answer:
C. The IQR is the best measure of variability because the distribution has an outlier.Step-by-step explanation:
We see 75% of data lies in the interval 0 - 48, and the 120 is the outlier.
We wouldn't use the range as it won't be a representation of variability.
The best measure would be IQR:
The interquartile range is the best measure of variability for such a distribution. Because it's based on values that come from the middle half of the distribution, and not influenced by outliersCorrect choice is C.
PLEASE HELP EXTRA POINTS AND BRAINLIEST, NO LINKS
The dot plot below shows the number of excused absences students in Mr. Beckett's class have.
What is the median number of excused absences?
A. 2
B. 3
C. 2.5
D. 1.5
Answer:
D. 1.5
Step-by-step explanation:
The median number of excused absences from given data is 1.5.
We have given that,
The dot plot below shows the number of excused absences students in Mr. Beckett's class have.
We have to determine the median
What is the median?
The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the middle value.
Therefore the median number of excused absences from given data is 1.5.
Therefore option D is correct.
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A piecewise function is given.
Find f(-4)
Answer:
3
Step-by-step explanation:
For x<=0, f is constant: f(x) =3
-4<0, so f(-4)=3
Dominic invested $93,000 in an account paying an interest rate of 6.8% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $202,800?
Answer:
11
Step-by-step explanation:
A pair of laces has a price tag of $7.00. The sales tax is 0.08 on every $1 . Which is the total price of the laces?
Plz show work. Need help fast please please.
Step-by-step explanation:
10:
[tex] \sqrt{50} = \sqrt{2 \times 25} = \sqrt{2} \times \sqrt{25} = \: 2 \times \sqrt{5} [/tex]
11:
[tex] \sqrt{88} = \sqrt{4 \times 22} = \sqrt{4} \times \sqrt{22} = \: \: \: \: \: 2 \times \sqrt{22} [/tex]
12:
[tex] \sqrt[3]{54} = \sqrt[3]{ {3}^{3} \times 2} = \sqrt[3]{ {3}^{3} } \times \sqrt[3]{2} = \: \: \: \: \: 3 \times \sqrt[3]{2} [/tex]
Find the distance between the points (-4, 3) and (3, 3).
Answer:
great job
Step-by-step explanation:
Help me with this question please
The volume of the rectangular prism is 312 cm2 h 4 cm 6 cm What is the height of the prism? Height = cm
Answer:
h=13
Step-by-step explanation:
volume=w*h*l
312=(4)(6)(X)
Select the compound inequality shown on the graph. -5 -4 -3 -3 -2 -1 0 1 2 3 4 5 5 o A. x>-1 and x 4, or -1 -1 and x < 2, or -1 -1 and x = 5, or -1
Answer:
c
Step-by-step explanation:
c is the only one containing the number three, which is shown on the graph.
A law firm ordered 90 boxes of paper clips. There were 80 paper clips in each box. How many
paper clips did the law firm order in all?
Answer:
7200
Step-by-step explanation:
80*90=7200
Answer:
7,200 paper clips
Step-by-step explanation:
80*90=7,200
Question 5 of 10
The function f(x) = 2X is shifted 4 units left. The result is g(x). What is g(x)?
O A. g(x) = 2x + 4
O B. g(x) = 2X – 4
C. g(x) = 2x - 4
D. g(x) = 2x + 4
Answer:
None
See below under Remark.
Step-by-step explanation:
When you shift left, you think of moving in the negative direction. But it is not shown that way. You need to show what happens when you substitute a value in for x. Usually a graphing program helps to show which choice is right.
g(x) = f(x+4) = 2(x + 4)
None of the choices are this result, so we have to assume that the brackets were just omitted. The graph below shows what the answer given is the correct one.
Remark
Look at the graph carefully. The red line is f(x) = 2x
The blue line is g(x) = f(x-4) = 2(x - 4)
Notice that g(x) has shifted 4 units to the left. The x intercept has gone from 0,0 to (-4,0) and is so labeled.
If you have an answer with brackets around (x + 4) that's the one you choose. It needs the 2 outside the brackets.