Answer:
there are 3 solutions which can be done by substitution method, elimination method,graphical method, 9f you need solution than contact me 8n comments I can show solutions
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]
Which of the following is true?
a. The p-value for a one-tailed test would be the same as the current p-value.
b. The p-value for a one-tailed test would be half the current p-value.
c. If this test was one-tailed instead of two-tailed g, you would reject the null.
d. If this test was one-tailed instead of two-tailed, you would still fail to reject the null.
d. The p-value for a one-tailed test would be double the current p-value.
Answer:
The correct option is c which is if this test was one-tailed instead of two-tailed, you would reject the null.
Step-by-step explanation:
a: This statement cannot be true as the p-value for a 1 tailed test is dependent on the level of significance and other features.
b: This statement cannot be true as there is no valid mathematical correlation between the p-value of the one-tailed test and the current p-value.
c: This statement is true because due to the enhanced level of significance, the null hypothesis will not be rejected.
d: This statement is inverse of statement c which cannot be true.
e: The statement cannot be true as there is no correlation between the current p-value and the p-value of 1 tailed test. The correlation exists between the values of one-tailed and two-tailed p-values.
Which describes the effect of the transformations on the graph of f(x) = x^2 when changed to f(x) = 3(x+2)^2 - 4
Three methods for teaching mathematics to first graders are to be compared. Ten students are
randomly assigned to each of the methods, and the score on a quiz is recorded. What are the
response and treatment for this experiment?
Answer: The three methods are the treatments and the response is the score achieved on the quiz.
Step-by-step explanation:
The three techniques are the treatments, and the results are the final score.
what is response variable in the experiment?
The researcher predicts that a variable will change if the controlled variable changes; this variable is known as a responsive variable. A dependent variable is another name for a responsive variable.
Solution:
Three methods are assigned for teaching mathematics.
Randomly ten students are assigned to each of the method.
There scores are then recorded on a quiz.
It is clear that the response will be the score card of the students either scoring high marks or not being able to clear it.
And the treatments are three for if the student is not able to understand any of the method.
Hence the three methods serve as treatments, and the outcomes determine the final grade.
Learn more about "Logical reasoning questions" here-
brainly.com/question/25175983
#SPJ2
What is the median of the data set?
History Test Scores
50 8
65 6 8 9
70 3 5 8
80 6 7 7 7
9 0 1 3 5 6 8 99
50 = 50 points
50
0 87
49
86.5
86
Helppp!!
Answer:
86
Step-by-step explanation:
Median : the middle value of a set of data arranged in numerical order.
To solve: Place number in order from least to greatest then began crossing one off at the beginning of the data set and one at the end. (like your playing the game one for you , and one for me) The median will be the last number left without a match in the middle.
Answer:
The answer is 86 beacause
Step-by-step explanation:
I did the lesson so its correct if you think its wrong then i dont care at all or if u think i stole answer i really dont care
Which function represents a quantity growing exponentially?
A y = 2(0.5)
В y = 0.5(2)
C y = 2(0.5)2X
D y = 6)
Answer: c
Step-by-step explanation:
Name an interior angle that is supplementary to <7.
Will give BRAINLIEST!!!!
Answer:
2, 4, and 6
Step-by-step explanation:
Supplementary angles are angles that add to 180°.
We can see that the angles that make a straight line/straight angle with ∠7 are supplementary to it, because a straight line is 180°.
Those numbers would be be 2, which equals to 4, which equals to 6 and also 8, but that number isn't one of the answers
2,4, and 6
Find the missing dimension of the triangle. A triangle with base labeled b, height labeled 6 feet, and height labeled 14 square feet.
Answer:
4.67 feet
Step-by-step explanation:
The computation of missing dimension of the triangle is given below:
As we know that
Area of the triangle = 1 ÷ 2 × base × height
14 = 1 ÷ 2 × base × 6
14 = 3 × base
So, the base is
= 14 ÷ 3
= 4.67 feet
Here we assume the area to be 14 square feet
Answer:
4⅔ or 4.67 feet
Step-by-step explanation:
Area of a triangle is ½bh
½×b×6=14
3b=14
14÷3=4⅔
Pls answer this for me. How many paving stones, each 1m long and 80cm wide, are needed to cover a compound 13.6m long and 11m wide?
Answer: 187
Step-by-step explanation:
Given
Dimension of stone is [tex]1\ m\times 80\ cm[/tex]
Dimension of compound [tex]13.6\ m\times 11\ m[/tex]
Area of the stone
[tex]\Rightarrow a=1\times 0.8=0.8\ m^2[/tex]
Area of compound
[tex]\Rightarrow A=13.6\times 11=149.6\ m^2[/tex]
No of the stones needed is
[tex]\Rightarrow n=\dfrac{A}{a}\\\\\Rightarrow n=\dfrac{149.6}{0.8}\\\\\Rightarrow n=187[/tex]
Thus, 187 stones are needed
can someone explain how to solve and graph this step-by-step?
What is the median of 1, 3, 6, 8, 9, 9
Answer choices: A. 6
B. 7
C. 8
D. 9
Answer:
B
Step-by-step explanation:
The median is the middle value of the data arranged in ascending order. If there is no exact middle value then it is the average of the values either side of the middle.
1, 3, 6, 8, 9, 9
↑ middle
median = [tex]\frac{6+8}{2}[/tex] = [tex]\frac{14}{2}[/tex] = 7 → B
Answer:
B. 7
Step-by-step explanation:
(6 + 8) ÷ 2 = 7
I hope this is right if its not im sorry
find the angle measure x in the following figures
Find the measure of major arc QPN.
M
0
coll
IN
Answer:
218°
Step-by-step explanation:
m(arc)QPN = m(arc)QPO + m(arc)NO
m(arc)QPN = 180° + 38°
m(arc)QPN = 218°
Find mean & margin of error if 28.4 < µ < 38.8
Answer:
The mean is of 33.6
The margin of error is of 5.2.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this question:
Lower bound: 28.4
Upper bound: 38.8
Mean
(28.4+38.8)/2 = 33.6.
The mean is of 33.6
Margin of error:
(38.8 - 28.4)/2 = 5.2
The margin of error is of 5.2.
What is 32 divided by 4 to the second power plus 35-20 divided by 5
HELP! Does the pythagorean theorem work for every triangle or just for right triangles?
a. everytriangle
b. only right triangles
Answer:
This is so easy!
ONLY RIGHT TRIANGLES
Did you really ask this question?
Tip: You should learn the basics first.
If Mike loses $5 per week, how much does he lose in 4 weeks?
Answer:
$ 20Step-by-step explanation:
[tex]1week \: = 5 \\ 4 \: weeks = x \\ \\ x = 20[/tex]
hope this helps you.
Can I have the brainliest please?
Have a nice day!
Find the area
10 yd
12 yd
13 yd
Answer:
138
Step-by-step explanation:
a+b/2xh
What is the answer? Thank you!
Complete the missing parts of the table for the following function y=7^x
Answer:
x= -2 y = ([tex]\frac{1}{49}[/tex])
x= 0 y = 1
x= 2 y = 49
Step-by-step explanation:
x= -2 -> (7)² = 49, negative power makes it inverse to a fraction
y = ([tex]\frac{1}{49}[/tex])
x= 0 -> anything to the power of 0 is always 1
y = 1
x= 2 -> 7² = 7 × 7 = 49
y = 49
Please help I'll give brainliest
Hope it helps you
Have a good day
PLZ RESPOND AS SOON AS POSSIBLE
What point is located at (-2, -6)
a. F
b. G
c. H
d. K
Answer:
Can we get an image of the graph
Step-by-step explanation:
0.22 divided by 11 If you answer this you will be the BRAINLIEST
Answer:
0.02
Step-by-step explanation:
i dont know if u want explanation
Jackie bought a CD for $11.50. The sales tax is 6%. How
much did Jackie pay for the CD, including the sales tax?
$12.19
before the tax price is $11.50
and %6 is equal to $0.69
therefore if you add those together you'll get an answer of $12.19
Determine the equation of this circle. *
Answer:
b is correct center of circle is x=4 y=-2
radius = 3
(10x - 4) ÷ 5 = 20 what is x
Answer: 10.4
Step-by-step explanation:
(10x - 4) ÷ 5 = 20
* 5 * 5
10x - 4 = 100
+ 4 + 4
10x = 104
/ 10 / 10
x = 10.4
In an isosceles triangle, angle B is 40 degrees, and angle E is 2x+4. What is x?
Answer:
x = 40°
Step-by-step explanation:
In order to answer this problem, you will need to know the definition of an isosceles triangle.
An Isosceles triangle is specified as a triangle with 2 of its 3 sides having equal lengths.
Step 1: Draw your triangle.
Since 2 of your 3 sides are equal length and the primary angle measures 100°, you are dealing with an obtuse triangle or, properly named, a obtuse isosceles triangle.
Step 2: Label your angles inside of your triangle.
Remember that the sum of the angles inside of a triangle must add up to equal 180°.
Since we know the triangle we are dealing with in this problem, we can label our unknown angles 'x'.
Caution: The above statement ONLY applies to this type of triangle.
Step 3: Write an equation.
100° + x° + x° = 180°
Step 4: Solve for x.
100° + x° + x° = 180°
100° + 2x° = 180°
2x = 80°
x = 40°
please help me.......
Answer:
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
Let's use CAH 1st , on the Lenovo building, b/c we have they Hypotenuse (Hyp) and an angle and we want to know the other side of the Lenovo building
Cos(30) = x/294
294*Cos(30) = x
254.611 = x
Sin(30) = y / 294
294*Sin(30) = y
147 = y
perimeter = 147+254.611+294
perimeter Lenovo = 695.611 feet
For Asus building
hyp = sqrt [ ( 144.5*[tex]\sqrt{2}[/tex])^2 + 144.5*[tex]\sqrt{2}[/tex])^2 )]
hyp = 289
perimeter = 289+144.5*[tex]\sqrt{2}[/tex]+144.5*[tex]\sqrt{2}[/tex]
perimeter Asus = 697.7077
The difference of the two buildings is
697.7077 - 695.611 =2.09671 feet
the difference is 2.10 feet ( rounded to nearest 100th)
A number n is at most −110.
Answer:
n ≤ -110
Step-by-step explanation:
1) A bag contains six red marbles and eight blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. Both marbles are red.
Answer:
You would have 4 red marbles and 8 blue marbles since you didn't return the ones you took out to the bag.
Step-by-step explanation:
6 - 2 = 4
The 8 would stay the same
There for you would have 4 red marbles and 8 blue marbles left in the bag. Totalled you have 12 marbles in the bag and 2 out of the bag. (8 + 4 = 12)
Including the marbles in and out of the bag you have 14 marbles. The 12 inside the bag + the 2 outside of the bag = 14 marbles totalled.