Answer:
$405.60
Step-by-step explanation:
If Isaac works for 40 hours will earn $8.45×40=$388. Since he worked 4 extra hours, he will earn $8.45×2×4 since he worked 4 extra hours. $8.45×2=$16.90, which is the amount he earns for every extra hour he works. $16.90×4=$67.60. Now if we add $67.60+$388=$405.60.
Hope this helps!
A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for of the successful bids and of the unsuccessful bids the agency requested additional information. a. What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to decimal)?
Answer:
A or D i think..
Step-by-step explanation:
who can answer this question the fastest
Step-by-step explanation:
1. 45/5 = 9
2. 53 is not a multiple of 5
3. 164 - 20 = 144
4. 372 rounded is 400.
5. 5 edges
6. 382 + 200 = 582
7. 6500 meters
8. -6
9. 65 cm
10. 90/2 = 45
11. idk since i live in us
12. 8 * 3 = 24
13. July 30th
14. 6
15. 28
16. 2.5 * 3 = 7.50
What is the square root of -1?
–i
i
–1
1
Answer:
[tex]i[/tex]
Step-by-step explanation:
[tex]\sqrt{-1} =i[/tex]
[tex]i[/tex] is an imaginary number that represents the square root of -1.
Write a matrix equation for the given systems of equations.
2x-6y-2z = 1
3y - 2z = -5
2y + 2z = -3
Answer:
[tex]\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right][/tex]
Step-by-step explanation:
Given system of equations are
2x-6y-2z = 1
3y - 2z = -5
2y + 2z = -3
given
2 x - 6 y - 2 z = 1
0 x + 3 y - 2z = -5
0 x +2y + 2 z = - 3
The Matrix form of the given system of equations
A X = B
[tex]\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right][/tex]
at a school concert the total value of tickets sold was $994. Student tickets sold for $5 and adult tickets sold for $8. The number of adults tickets sold was 14 more than 2 times the number of student tickets. How many student tickets and adult tickets were sold?
Answer:
42 student tickets and 98 adult tickets
Step-by-step explanation:
Let's call the number of student tickets 's' and the number of adult tickets 'a'.
Then, we can write the two equations below:
5s + 8a = 994
a = 2s + 14
Using the value of 'a' from the second equation in the first one, we have:
5s + 8*(2s + 14) = 994
5s + 16s + 112 = 994
21s = 882
s = 42
Now, finding the value of 'a', we have:
a = 2*42 + 14 = 98
Answer:
The total sold was 98 tickets for adults and 42 for students.
Step-by-step explanation:
In order to calculate the number of tickets of each kind sold we need to create a system of equations with the given information. The first equation can be created is that the sum of adult tickets multiplied by its cost with the student tickets also multiplied by its cost must be equal to the total value of tickets sold, so:
[tex]5*\text{students} + 8*\text{adults} = 994[/tex]
We also know that the number of adult tickets was 14 more than 2 times the number of student tickets, therefore:
[tex]\text{adults} = 2*\text{students} + 14[/tex]
If we apply the second expression on the first one we can solve for the number of tickets sold to students, we have:
[tex]5*\text{students} + 8*(2*\text{students} + 14)= 994\\5*\text{students} + 16*\text{students} + 112 = 994\\ 21*\text{students} = 994 - 112\\\text{students} = \frac{882}{21} = 42[/tex]
We can use this value to find the number of adults ticket sold:
[tex]\text{adults} = 2*42 + 14\\\text{adults} = 98[/tex]
The total sold was 98 tickets for adults and 42 for students.
Identify the like terms in the algebraic expression 2x/5-5.2y+2.2+x/3
Question:
Identify the like terms in the algebraic expression
[tex]\frac{2x}{5} -5.2y +2.2 + \frac{x}{3}[/tex]
Answer:
The like terms in the given expression are [tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex]
Step-by-step explanation:
Given:
[tex]\frac{2x}{5} -5.2y +2.2 + \frac{x}{3}[/tex]
Required:
Identify the like terms
To solve this, we need to understand what like term is all about.
Like term simply refer to terms or entities that have the same variable and exponents (power)
From the expression above, there are two variables;
x and y.
To get the like terms of x and/or y;
we simply look for another occurrence of x and/or y in the expression; and this occurrence must have the same exponent as x and/or y.
For x
[tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex] have the same variable and exponent; Hence, they are like terms
There's only one occurrence of variable y;
Conclusively, the like terms in the given expression are [tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex]
2x/5 and -5.2y
hope this helps
A chemist has 20% and 50% solutions of acid available. How many liters of each solution should be mixed to obtain 75 liters of 28% acid solution?
Answer:
we will mix 55 liters of 20% solution and 20 Liters of 50% solutions.
Step-by-step explanation:
let the 20% solution = x liters
let the 50% solution = y liters
total solution of the mixture of the two solutions in % = 28%
total solution of the mixture of the two solutions in liters = 75 liters
considering the total solutions given, we will have the following equations if we mix the solutions in equal proportion;
20x + 50y = 28 (75)
0.2x + 0.5y = 0.28(75)
0.2x + 0.5y = 21 -------equation 1
Also,
x + y = 75 ------equation 2
y = 75 - x
(substitute this into equation 1)
0.2x + 0.5(75 - x) = 21
0.2x + 37.5 - 0.5x = 21
0.2x - 0.5x = 21 - 37.5
-0.3x = -16.5
x = -16.5 / -0.3
x = 55 liters
Recall, y = 75 - x
y = 75 -55
y = 20 Liters
Thus, we will mix 55 liters of 20% solution and 20 Liters of 50% solutions.
In the town of Maplewood a certain type of DVD player is sold at just two stores. 36% of the sales are from store A and the rest of the sales are from store B. 7% of the DVD players sold at store A are defective while 3% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A
Answer:
56.76% probability that it came from store A
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Defective.
Event B: Store A.
36% of the sales are from store A
This means that [tex]P(B) = 0.36[/tex]
7% of the DVD players sold at store A are defective.
This means that [tex]P(A|B) = 0.07[/tex]
Probability of a defective DVD:
36% come from store A, and of those, 7% are defective.
100 - 36 = 64% come from store B, and of those, 3% are defective. So
[tex]P(A) = 0.07*0.36 + 0.03*0.64 = 0.0444[/tex]
What is the probability that it came from store A
[tex]P(B|A) = \frac{0.36*0.07}{0.0444} = 0.5676[/tex]
56.76% probability that it came from store A
SOLVE THIS EXTREMELY IMPORTANT EQUATION
Answer:
Option B; EF = ( About ) 4.47 units, Perimeter of Δ EFG = ( About ) 12.94 units
Step-by-step explanation:
If we were to consider the height of this triangle EFG, it would be 4 units of length, supposedly splitting base GF into two ≅ parts, each 2 units of length. First let us name the point drawn to base GF ⇒ point H, so that the height of Δ EFG ⇒ EH. Now as EH splits GF into two ≅ parts, by Converse to Coincidence Theorem, Δ EFG ⇒ Isosceles Δ;
EH and FH are legs of a right triangle EFH, so that Pythagorean Theorem can be applied to solve for the length of EF and EG, knowing that as Δ EFG ⇒ Isosceles Δ, EF ≅ EG;
( EH )^2 + ( FH )^2 = ( EF )^2,
( 4 )^2 + ( 2 )^2 = ( EF )^2 ⇒ take square of 4 & 2,
16 + 4 = ( EF )^2 ⇒ combine like terms,
( EF )^2 = 20 ⇒ take square root on either side to solve for EF,
EF = √ 20 = ( About ) 4.47 units = EG,
Perimeter of Δ EFG = EF + GF + EG = 4.47 + 4 + 4.47 = ( About ) 12.94 units,
Solution; Option B
simplify without using the table log 6 - log 16 + log 4 - log 3 + log 20 equals to
Answer:
[tex]1[/tex]
Step-by-step explanation:
[tex]log(6)-log(16)+log(4)-log(3)+log(20)[/tex]
[tex]0.77815125038-1.20411998266+0.60205999132-0.47712125472+1.30102999566[/tex]
[tex]=0.99999999998[/tex]
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 222 days and standard deviation sigma equals 15 days.
What is the probability that a random sample of 26 pregnancies has a mean gestation period of 216 days or less?
The probability that the mean of a random sample of 26 pregnancies is less than 216 days is approximately
Answer:
[tex] z = \frac{216-222}{\frac{15}{\sqrt{26}}}= -2.040[/tex]
And we can find this probability on this way:
[tex]P(z<-2.040)=0.0207[/tex]
Step-by-step explanation:
Let X the random variable that represent the lenghts of the pregnencies of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(222,15)[/tex]
Where [tex]\mu=222[/tex] and [tex]\sigma=15[/tex]
We are interested on this probability
[tex]P(\bar X<216)[/tex]
The z score formula is given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score we got:
[tex] z = \frac{216-222}{\frac{15}{\sqrt{26}}}= -2.040[/tex]
And we can find this probability on this way:
[tex]P(z<-2.040)=0.0207[/tex]
Bacteria culture doubles every 20 minutes. After two hours there are 28800 bacteria. What was the initial amount?
Answer:
450 bacteria.
Step-by-step explanation:
To find this, we can set up an exponential equation as shown:
[tex]28800 = a (2)^{\frac{120}{20} }[/tex]
**'a' being the initial value
** '2' representing the culture doubling
Simplify the equation down:
[tex]28800 = a (2)^{6}[/tex]
[tex]28800 = 64a\\a = 450.[/tex]
Therefore, the initial amount of bacteria was 450.
Mary is building a sandcastle with rectangular prism molds. One mold is 4 inches long, 6 inches wide, and 2 inches tall. The other mold is 3 inches long, 5 inches wide, and 1 inch tall. If she creates a castle by stacking these molds on top of each other, what volume of sand will be contained in her castle?
Answer:
63 cubic inches
Step-by-step explanation:
You have to first find the volume of each mold:
6 × 4 × 2= 48 cubic inches
3 × 5 × 1= 15 cubic inches
Add these two volumes together to find the overall volume of the whole sand castle.
48+15= 63 cubic inches
Answer:
The whole castle can hold 63 in² of sand.
Step-by-step explanation:
First, find the volume of the first mold.
V = whl Substitute
V = (6)(2)(4) Multiply
V = 48 in²
Now, find the volume of the second mold.
V = whl Substitute
V = (5)(1)(3) Multiply
V = 15 in²
Add together both volumes to find the volume of the whole castle.
48 + 15 = 63 in²
Between what two integers does square root 10 lie on?
Answer:
between 3 and 4
Step-by-step explanation:
type sqrt(10) into your calculator
The requried, square root 10 lies between integers 3 and 4.
What are integers?Integers are a set of whole numbers and their negative counterparts. They include positive numbers, negative numbers, and zero.
Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on.
The integer squares nearest to 10 are 9 and 16, which are the perfect squares of 3 and 4, respectively.
Since [tex]$\sqrt{9}=3$[/tex] and [tex]$\sqrt{16}=4$[/tex], we know that [tex]$\sqrt{10}$[/tex] is between these two integers, we can say that [tex]$3 < \sqrt{10} < 4$[/tex].
Learn more about integers here:
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Micaela tried to rotate the square 180 about the origin. Is her rotation correct? If not, explain why
Answer:no the vertices of the image and pre image don’t correspond
Step-by-step explanation:
Just did it
No, the vertices of the image and pre-image do not correspond
Step-by-step explanation:
It’s correct
Which problem situation matches the equation below 59+74+62+x/4=70
Answer:
x = 85Step-by-step explanation:
The equation is not properly written. Here is the correct expression
[tex]\frac{59+74+62+x}{4} = 70[/tex]
Find the problem situation that matches according to the steps below:
Step 1: We will cross multiply
[tex]59+74+62+x = 4*70\\59+74+62+x = 280\\195+x = 280\\[/tex]
Step 2: Subtract 195 from both sides of the equation
[tex]195+x-195 = 280-195\\x = 280-195\\x = 85[/tex]
What’s the correct answer for this?
Answer:
x=5
Step-by-step explanation:
5x- 7 = 18
5x=18+7
5x=25
Therefore, 5 will cancel 25 five(5) times.
x= 5.
Answer:
x = 5
Step-by-step explanation:
Since AB is the bisector, so MO is equal to NO
MO = NO
5x-7 = 18
5x = 18+7
5x = 25
Dividing both sides by 5
x = 5
A circle has a circumference that is greater than 8 meters. The inequality 3.14d> 8 can be used to determine the possible lengths
of the diameter of the circle. What are the possible values of d, the length of the diameter in meters?
d<25.1
d>25.1
d<25
d>2.5
Answer:
(D)d>2.5
Step-by-step explanation:
Given that the circumference of a circle is greater than 8 meters.
For a circle of diameter d:
Circumference[tex]=\pi d[/tex]
Since [tex]\pi =3.14[/tex]
[tex]3.14d>8[/tex]
To obtain possible values of the diameter d, we divide both sides of the equation by 3.14.
[tex]\dfrac{3/14d}{3.14}>\dfrac{8}{3.14}\\\\ d>2.5$ (correct to 1 decimal places)[/tex]
The correct option is D.
Answer:
To simplify the answer above, D
Step-by-step explanation:
94 cities were surveyed to determine sports teams. 26 had baseball, 23 had football, 22 had basketball, 12 baseball and football, 13 had baseball and basketball, 14 had football and basketball, and 7 had all three.A) How many had only a basketball team?B) How many had baseball or football?C) How may had baseball or football, but not basketball?
Answer:
A) 2
B) 33
C) 13
Step-by-step explanation:
Baseball =26
Football = 23
Basketball = 22
Baseball and Football (BF) = 12
Baseball and basketball (BK) = 13
Football and basketball (FK) = 14
All three (BFK) = 7
A) The total number of cities that have basketball teams is given by the cities with basketball only, added to the cities with basketball and football and cities with basketball and baseball, minus the cities with all three sports:
[tex]22=K+BK+FK-BFK\\22=K+13+14-7\\K=2[/tex]
B) The total number of cities with baseball of football is given by sum of the cities with either sport, minus the number of cities with both sports:
[tex]B\ or\ F = 23+22-12\\B\ or\ F =33[/tex]
C) If 22 cities have basketball and only 2 have basketball only, 20 cities have basketball and either baseball, football or all three sports. The number of cities with baseball or football, but not basketball is:
[tex](B\ or\ F)\cap (not\ K) = 33-20=13[/tex]
What is the midpoint of Line segment A B ?
point F
point G
point H
point I
Answer:
the answer is Point G
In a previous year, 54% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 700 females aged 15 and older and finds that 369369 are living alone. Is there sufficient evidence at the alphaαequals=0.10.1 level of significance to conclude the proportion has changed? Because np 0 left parenthesis 1-p 0 right parenthesis np01−p0 equals= nothing not equals≠ less than< greater than> equals= 10, the sample size is less than greater than 5% of the population size, and the sample cannot be reasonably assumed to be random, is given to be random, can be reasonably assumed to be random, is given to not be random, the requirements for testing the hypothesis are not satisfied. (Round to one decimal place as needed.) 1. Identify the null and alternative hypotheses for this test. Upper H 0: alpha α p μ greater than> not equals≠ equals= less than< nothing versus Upper H 1: α μ p equals= not equals≠ less than< greater than> nothing (Type integers or decimals. Do not round.) 2. Find the test statistic for this hypothesis test. z 0 equals= nothing (Round to two decimal places as needed.) 3. Determine the P-value for this hypothesis test. P-value equals= nothing (Round to three decimal places as needed.) 4. State the conclusion for this hypothesis test. A. Do not reject Upper H0. There is not sufficient evidence at the alpha α equals=0.10.1 level of significance to conclude that the proportion of females who are living alone has changed. B. Reject Upper H 0. There is sufficient evidence at the alpha equals=0.10.1 level of significance to conclude that the proportion of females who are living alone has changed. C. Reject Upper H 0. There is not sufficient evidence at the alpha α equals=0.10.1 level of significance to conclude that the proportion of females who are living alone has changed. D. Do not reject Upper H0. There is sufficient evidence at the alpha α equals=0.10.1 level of significance to conclude that the proportion of females who are living alone has changed.
Answer:
D.
Step-by-step explanation:
On average, 24% of customers who buy shoes in a particular store buy two or more pairs. One weekend, 350 customers purchased shoes. How many can be predicted to buy two or more pairs? If 107 customers buy more than two pairs, did more customers than normal buy two or more pairs?
It is predicted that__________
customers bought two or more pairs out of 350 customers. There were customers than normal who bought two or ___ pairs.
simplify the expression 4^4/4^6
Answer:
[tex]1/16[/tex]
Step-by-step explanation:
[tex]\frac{4^{4} }{4^{6} }[/tex]
[tex]4^{4-6}[/tex]
[tex]4^{-2}[/tex]
[tex]\frac{1}{4^{2} }[/tex]
[tex]\frac{1}{16}[/tex]
What is the area of an rectangle with sides lengths of 5/12 foot and 2/3 foot
Answer:
Area = 5/18 square feet
Step-by-step explanation:
To find the area of a rectangle, you need to multiply 5/12 and 2/3. You multiply the numerators and then multiply the denominators. Then you should get 10/36. This fraction can be simplified into 5/18. To do this find the greatest common factor of 10 and 36 (you'll get 2 as the GCF). Then divide 2 to both the numerator and denominator.
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.917 g and a standard deviation of 0.303 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 37 cigarettes with a mean nicotine amount of 0.872 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 37 cigarettes with a mean of 0.872 g or less.
Answer:
[tex] z = \frac{0.872-0.917}{\frac{0.303}{\sqrt{37}}}= -0.903[/tex]
And we can find this probability to find the answer:
[tex] P(z<-0.903)[/tex]
And using the normal standar table or excel we got:
[tex] P(z<-0.903)=0.1833 [/tex]
Step-by-step explanation:
Let X the random variable that represent the amounts of nocatine of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(0.917,0.303)[/tex]
Where [tex]\mu=0.917[/tex] and [tex]\sigma=0.303[/tex]
We have the following info from a sample of n =37:
[tex] \bar X= 0.872[/tex] the sample mean
And we want to find the following probability:
[tex] P(\bar X \leq 0.872)[/tex]
And we can use the z score formula given by;
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for the value of 0.872 we got:
[tex] z = \frac{0.872-0.917}{\frac{0.303}{\sqrt{37}}}= -0.903[/tex]
And we can find this probability to find the answer:
[tex] P(z<-0.903)[/tex]
And using the normal standar table or excel we got:
[tex] P(z<-0.903)=0.1833 [/tex]
What is the value of x in the equation?4 (2x + 6) –10 = 30?
Answer: 10
Step-by-step explanation: 4(2 x 10 + 6) -10
choose the equation of the line that is parallel to the x axis x=4, x+y=0, x=y, y=4
Answer:
y=4
Step-by-step explanation:
if we draw a function we see that y=4 is paralel to the x axis
A line that is parallel to the x-axis will pass through the y-axis, horizontally.
The equation of line parallel to the x-axis is y = 4
A line that is parallel to the x-axis is represented with the following equation
y = n
Where n can be any real number.
In other words, the following equations are parallel to the x-axis
y = 2
y = 3
y = -2
y = 10
And so on....
Hence, the equation of line parallel to the x-axis is y = 4
Read more about parallel equations at:
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I need help with this please.
Any help would be appreciated
Answer: 18.48
Step-by-step explanation:
To solve this problem, you would use the order of operations. You would solve the parenthesis first and then solve the rest.
(5.6-2.3)(5.4+0.2)
3.3(5.6)
18.48
Answer:
18.48Step-by-step explanation:
(5.6 - 2.3) (5.4 + 0.2) 3.3 × 5.6
18.48
The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of the Thomas Supply Company Inc. invoices.13 13 13 20 26 28 30 34 34 34 35 35 36 37 38
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82(Round your answer to 2 decimal places.)a. Determine the first and third quartiles.
b. Determine the second decile and the eight decile.c. Determine the 67th percentile.
Answer:
Q1 = 33
Q3 = 49.75
D2 = 28.4
D8 = 29.6
67th percentile = 46.10
Step-by-step explanation:
Given the data:
13 13 13 20 26 28 30 34 34 34 35 35 36 37 38
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82
The first quartile (Q1) ;
1/4(n + 1)
Where n = number of observations
n = 30
Q1 = 0.25(30 + 1) = 0.25 × 31 = 7.75
7 : corresponds to 30
0.75 : (34 - 30) × 0.75 = 4 × 0.75 = 3
30 + 3 = 33
Third quartile (Q3) :
3/4(n + 1)
Where n = number of observations
n = 30
Q3 = 0.75(30 + 1) = 0.75 × 31 = 23.25
23 : corresponds to 49
0.25 : (52 - 49) × 0.25 = 3 × 0.25 = 0.75
49 + 0.75 = 49.75
Determine the second decile and the eighth decile.
Second decile (D2)
((n+1) × (2)) / 10
= (30 + 1)(2)/10 = 6.2
6 : corresponds to 28 +
0.2 : (30 - 28 )× 0.20 = 0.4
28 + 0.4 = 28.4
Eight decile (D8)
((n+1) × (8)) / 10
= (30 + 1)(8)/10 = 24.8
24 : corresponds to 52 +
0.8 : (54 - 52 )× 0.80 = 1.6
28 + 1.6 = 29.6
67th percentile :
67% × n = 0.67 × 30 = 20.10
20: corresponds to 46
0.1 : (47 - 46) × (0.1) = 0.1
46 + 0.1 = 46.10
The first quartiles is 33 and third quartiles is 23.25.
The second decile is 24.8 and the eight decile is 29.6
The 67th percentile is 46.10.
Given that,
Sample of the Thomas Supply Company Inc. invoices.13 13 13 20 26 28 30 34 34 34 35 35 36 37 38.
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82
We have to determine,
Determine the first and third quartiles.
Determine the second decile and the eight decile.
Determine the 67th percentile.
According to the question,
The first quartile (Q1) ; [tex]\dfrac{1(n+1)}{4}[/tex]Where n = number of observations
n = 30
Then,
[tex]= \dfrac{1(30+1)}{4}\\\\= 0.2 \times 31\\\\= 6.2[/tex]
Then, 7 : corresponds to 30,
[tex](34 - 30) \times 0.75 = 4 \times 0.75 = 3\\\\30 + 3 = 33[/tex]
And Third quartile (Q3) is; [tex]\dfrac{3(n+1)}{4}[/tex]
Where n = number of observations
n = 30
Then,
[tex]= \dfrac{3(30+1)}{4}\\\\= 0.75 \times 31\\\\= 23.25[/tex]
23 : corresponds to 49
[tex]0.25 : (52 - 49) \times 0.25 = 3 \times 0.25 = 0.75\\\\49 + 0.75 = 49.75[/tex]
To determine the second decile and the eighth decile.
Second decile (D2) ; [tex]\dfrac{2(n+1)}{10}[/tex]
Where n = 30
Then,
[tex]= \dfrac{2(30+1)}{10}\\\\= 0.2 \times 31\\\\= 6.1[/tex]
6 : corresponds to 28,
[tex](30 - 28 ) \times 0.20 = 0.4\\\\28 + 0.4 = 28.4[/tex]
And the Eight decile (D8); [tex]\dfrac{8(n+1)}{10}[/tex]
Where n = 30,
Then,
[tex]\dfrac{(30 + 1)(8)}{10} = 24.8[/tex]
24 : corresponds to 52,
[tex](54 - 52 ) \times 0.80 = 1.6\\\\28 + 1.6 = 29.6[/tex]
To determine the 67th percentile :
67% × n = 0.67 × 30 = 20.10
20: corresponds to 46
0.1 : (47 - 46) × (0.1) = 0.1
46 + 0.1 = 46.10
The 67th percentile is 46.10
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