A local salesman has forty-five stacks of magazines. If the salesman plans to sell three-fifths of the stacks, how many stacks will he have left?

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:

brainly.com/question/8587717

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Answer:

it equals 1

Step-by-step explanation:

(5)(2)+2x−7=5

Step 1: Simplify both sides of the equation.

(5)(2)+2x−7=5

10+2x+−7=5

(2x)+(10+−7)=5(Combine Like Terms)

2x+3=5

2x+3=5

Step 2: Subtract 3 from both sides.

2x+3−3=5−3

2x=2

Step 3: Divide both sides by 2.

2x

2

=

2

2

x=1

Answer:

The contribution to profit from the special order us $38,000.

Step-by-step explanation:

Consider the provided information.

We need to calculate the contribution on to profit from the special order.

Wolff Construction Company, which operates outside Packer’s normal sales territory, asks Packer to pour 40 slabs for Wolff’s new development of homes. Packer has the capacity to build 300 slabs and is presently working on 250 of them. Wolff is willing to pay only $2,750 per slab.

Sale = 40 × $2,750 = $110,000

To find the profit subtract the materials and labor cost from sale amount.

     Particulars                                              Amount

Sale (40 × $2,750)                                     $110,000

Less: Variable expense

Unit level materials (40× $1,200)              $48,000

Unit level labor(40× $600)                        $24,000

Contribution margin                                   $38,000

The overhead cost will not be considered while determine the contribution to profit from accepting the order of 40 slab.

Hence, the contribution to profit from the special order us $38,000.

Answer: 6.8

Step-by-step explanation:

absolute value turns the number into the positive value.

Answer:

B because when you compare y= mx+ c where M is the slope or gradient

Answer:

y = x⁴ +4x³ +4x² +4x +3

Step-by-step explanation:

The coefficients of the offered quartics (in order) have 1, 1, 1, and 0 sign changes, respectively. Descartes' rule of signs tells you this means the first three choices all have one (1) positive real root, so the negative real roots -1 and -3 are not the only ones.

The only possible polynomial is the last one. Synthetic division of that polynomial by roots -1 and -3 leave the remaining factor as x²+1, which has only complex zeros.

The appropriate choice is ...

... y = x⁴ +4x³ +4x² +4x +3