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SOVA2 [1]
2 years ago
10

Alice and Betsy agreed to meet at 3:00PM and o shopping in one of the 6 clothing stores in their hometown.. However, they forgot

to specify which store. If Alice and Betsy were both on time and each went to one of the 6 stores, find the number of ways in which they could miss each other.

Mathematics
1 answer:
Norma-Jean [14]2 years ago
5 0
They could miss each other 30 different ways. I solved this by drawing it out six different stores and making Alice and Betsy go to each one may different times. Example photo included for how I got the first five. Then I did the same thing, but switch A and B, counted that towards the total and continued the is drawing until all the possibilities were found.

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A salesman’s commission on a $150,000 sale is $3,000. What percent is his commission?
Elenna [48]

Answer:

The commission percentage is 2%

Step-by-step explanation:

To find the percentage of a commission, start by dividing the commission amount by the total amount sold.

3,000/150,000 = .02 = 2%

5 0
2 years ago
Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and rene
mrs_skeptik [129]

Question Completion:

How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.)

Answer:

1. The percentages are concentrated from 20% to 60%.

2. These data are strongly skewed left.

3. There are no gaps in the data.

Step-by-step explanation:

1. Data

Percentage loss of wetlands per state

46 37 36 42 81 20 73 59 35 50

87 52 24 27 38 56 39 74 56 31

27 91 46 9 54 52 30 33 28 35

35 23 90 72 85 42 59 50 49

48 38 60 46 87 50 89 49 67

2. Re-arrangement of

Percentage loss of wetlands per state (in ascending order)

9    20  23  24  27  27   28  30

31   33  35  35  35  36   37  38  

38  39  42  42  46  46   46 48

49  49   50  50  50  52   52 54

56 56   59  59  60  67   72  73  

74  81  85  87   87   89  90  91  

5 0
2 years ago
EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi
Valentin [98]

If there is such a scalar function <em>f</em>, then

\dfrac{\partial f}{\partial x}=4y^2

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}

\dfrac{\partial f}{\partial z}=16ye^{4z}

Integrate both sides of the first equation with respect to <em>x</em> :

f(x,y,z)=4xy^2+g(y,z)

Differentiate both sides with respect to <em>y</em> :

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}

\implies\dfrac{\partial g}{\partial y}=4e^{4z}

Integrate both sides with respect to <em>y</em> :

g(y,z)=4ye^{4z}+h(z)

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

f(x,y,z)=4xy^2+4ye^{4z}+h(z)

\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}

\implies\dfrac{\mathrm dh}{\mathrm dz}=0

Integrate both sides with respect to <em>z</em> :

h(z)=C

So we end up with

\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}

7 0
1 year ago
Danny Henry made a waffle on his six-inch-diameter circular griddle using batter containing a half a cup of flour. Using the sam
Mekhanik [1.2K]

Answer:

He'll need 288 cups to make a waffle on his 24 foot diameter circular griddle.

Step-by-step explanation:

In order to find out how much batter Danny needs we first need to compute the area of the first pans, since it is a circular pan their area is given by A = 2*pi*r. So we have:

Area of the first pan = 2*pi*(6/2) = 18.84 square inches

Area of the second pan = 2*pi*(24/2) = 75.36 square foots

We now need to convert these values to be in the same unit, we'll convert from square foots to square inches:

Area of the second pan = 75.36 * (12)^2 = 10851.84 square inches

We can now use a proportion knowing that the batter and the thickness of the waffles are the same. If 0.5 cup of flour can make a waffle on 18.84 square inches then x cup of flour can make a waffle on 10851.85 square inches. Writing this in a mathematical form, we have:

0.5/x = 18.84/10851.84

18.84x = 0.5*10851.85

x = 10851.85*0.5/18.84 =288 cups

7 0
2 years ago
The circumference of a tire is 96 inches. Determine the radius of the tire use 3 for pie
masya89 [10]

Circumference = 2*pi*radius.

Pi = 3.

2 * pi * r = 96

2 * 3 = 6.

2 * 3 * r = 96

Find r: 96/6 = 16.

2 * 3 *16 = 96.

r = 16.

7 0
1 year ago
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