Solve and graph 8(p+3)>2(4p-1)

Answer:

the partial derivatives are

fx =5/9

fy =(-13/18)

Step-by-step explanation:

defining the vector v (from (2,1) to (1,3))

v=(1,3)-(2,1) = (-1,2)

the unit vector will be

v'=(-1,2)/√5 = (-1/√5,2/√5)

the directional derivative is

fv(x,y) = fx*v'x + fy*v'y = fx*(-1/√5)+fy(2/√5) =-2/√5

then defining the vector u ( from (2, 1) toward the point (5, 5) )

u=(5,5)-(2,1) = (3,4)

the unit vector will be

u'=(3,4)/5 = (3/5,4/5)

the directional derivative is

fu(x,y) = fx*ux + fy*uy = fx*(3/5)+fy(4/5)=1

thus we have the set of linear equations

-fx/√5*+2*fy/√5 =(-2/√5) → -fx + 2*fy = -2

(3/5) fx+(4/5)*fy=1 → 3* fx+4*fy = 5

subtracting the first equation twice to the second

 3*fx+4*fy -(- 2fx)*-4*fy = 5 -2*(-2)

5*fx=9

fx=5/9

thus from the first equation

-fx + 2*fy = -2

fy= fx/2 -1 = 5/18 -1 = -13/18

thus we have

fx =5/9

fy =(-13/18)

Answer:

Q1 = 54.25 ; Q3 = 82.75 ; IQR = 28.5 ; Outliers = 4, 6, 8  

Step-by-step explanation:

Quartiles divide data into 4 equal parts. Q1 has 25% data below it & 75% above it, Q3 has 75% data below it & 25% data above it.

Quartile Calculation for 30 number of observations

• Ascending order : 4, 6, 8, 20, 45, 48, 52, 55, 56, 60, 63, 65, 67, 68, 70, 74, 75, 77, 78, 79, 80, 81, 82, 85, 87, 88, 90, 92, 95, 99
• Q1 = (N + 1) / 4th observation = [ (30 + 1)/4 ] th obs. = (31 /4) th = 7.75th = 7th item + 0.75 (7th - 8th item) = 52 + 0.75 (55-52) = 52 + 0.75(3) = 52 + 2.25 = 54.25
• Q3 = 3 [(N+1) / 4] th observation = 7.75 x 3 = 23.25th item = 23rd item + 0.25 (24th - 23rd item) = 82 + 0.25 (85-82) = 82 + 0.25 (3) = 82 + 0.75 = 82.75
• Interquartile range (IQR) = Q3 - Q1 = 82.75 - 54.25 = 28.5

Outliers are the observations less than Q1 - 1.5 (IQR) , more than Q3 + 1.5 (IQR)

• Q1 - 1.5 (IQR) = 54.25 - 1.5 (28.5) =  54.25 - 42.75 = 11.5 .So, numbers less than 11.5, ie 4, 6, 8 are outliers
• Q3 + 1.5 (IQR) = 82.75 + 1.5 (28.5) = 82.75 + 42.75 = 125.5 .There are no numbers > 125.5

Final answer:

To find Qi, Q3, and the interquartile range (IQR), first, the data needs to be sorted in ascending order. Then, find Q1 as the median of the lower half and Q3 as the median of the upper half. The IQR is the difference between Q3 and Q1. To determine if there are any outliers, calculate the fences using the formulas: Lower fence = Q1 - (1.5 * IQR) and Upper fence = Q3 + (1.5 * IQR). If any commute times fall outside the fences, they are considered outliers.

Explanation:

To find the quartiles, the data needs to be sorted in ascending order. The sorted list is:

4, 6, 8, 20, 45, 48, 52, 55, 56, 60, 63, 65, 67, 68, 70, 74, 75, 77, 78, 79, 80, 81, 82, 85, 87, 88, 90, 92, 95, 99

Q1 is the median of the lower half (ignoring the median if the number of data points is odd), so Q1 = 56.

Q3 is the median of the upper half, so Q3 = 81.

The interquartile range (IQR) is the difference between Q3 and Q1, so IQR = Q3 - Q1 = 81 - 56 = 25.

To find the fences, use the formulas:

Lower fence: Q1 - (1.5 * IQR)

Upper fence: Q3 + (1.5 * IQR)

Lower fence = 56 - (1.5 * 25) = 56 - 37.5 = 18.5

Upper fence = 81 + (1.5 * 25) = 81 + 37.5 = 118.5

There are no commute times that fall outside the fences, so there are no outliers in the sample.

Learn more about quartiles here:

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Answer:

2. Number of workshops attended.

Step-by-step explanation:

The variable of interest for predicting the final exam score and doing regression analysis is workshop attendance.  Therefore, the response variable should be the number of workshops attended by each student.

This also agrees with what the college tutoring center staff are considering, which forms the research question: "should the center increase the number of math workshops they offer to help students improve their performance in math classes?"

Final answer:

To form teams, divide the total number of players by the number of players per team. In this case, 36 teams are needed.

Explanation:

To find out how many teams will be formed, we divide the total number of players by the number of players assigned to a team. In this case, there are 432 players and 12 players per team. So, we divide 432 by 12:

Number of teams = 432 ÷ 12 = 36 teams

Therefore, the league will need to form 36 teams to accommodate all the players.

Learn more about Calculating the number of teams here:

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Answer:

x = 10

Step-by-step explanation:

4x = 40

you divide both sides by 4

and it gets you

x = 10

hope this helps

Answer:

x=10

Step-by-step explanation:

lets reverse engineer this. 4x=40. What is known in this? We know 40 is the unit amount of 4x. So we need to find out what x is, than multiply it by 4. We can do this by doing the opposite of multiplying, which is dividing! So we divide 4 by 40, which we get the answer 10! We know this is the correct answer because we can factor it into the equation. So 4*10=40!!! hope this helped!!!

Answer:

42m+10n+27

Step-by-step explanation:

Adding like terms

Answer: look at the picture

Step-by-step explanation: Hope this help :D