Answer:
perimeter=25.12 ft
Area=50.24 ft^2
Step-by-step explanation:
Radius=4 feet
π=3.14
Perimeter=2 x π x Radius
Perimeter=2 x 3.14 x 4
Perimeter=25.12 feet
Area=π x radius x radius
Area=3.14 x 4 x 4
Area=50.24 ft^2
Answer:
y = 1/2x - 2
Step-by-step explanation:
use formula y = mx + c
m = gradient
c = y intercept
Answer:
Part 9) The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13
Part 10) The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot
Step-by-step explanation:
Part 9)
Let
x ----> number of items on Emily's grocery list
x ----> number of items on Bobby's grocery list
we know that
----> equation A
----> equation B
Solve by substitution
Substitute equation A in equation B
![x=(2x+3)-8](https://tex.z-dn.net/?f=x%3D%282x%2B3%29-8)
solve for x
![x=2x-5](https://tex.z-dn.net/?f=x%3D2x-5)
![2x-x=5](https://tex.z-dn.net/?f=2x-x%3D5)
![x=5](https://tex.z-dn.net/?f=x%3D5)
Find the value of y
![y=2(5)+3=13](https://tex.z-dn.net/?f=y%3D2%285%29%2B3%3D13)
therefore
The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13
Part 10)
Let
x ----> the height of the taller bookshelf in feet
y ----> the height of the shorter bookshelf in feet
we have
----> equation A
Remember that
![1\ ft=12\ in](https://tex.z-dn.net/?f=1%5C%20ft%3D12%5C%20in)
To convert inches to feet divide by 12
so
![60\ in=60/12=5\ ft](https://tex.z-dn.net/?f=60%5C%20in%3D60%2F12%3D5%5C%20ft)
----> equation B
Solve the system by substitution
substitute equation A in equation B
solve for y
Find the value of x
![x=5(1)-1=4\ ft](https://tex.z-dn.net/?f=x%3D5%281%29-1%3D4%5C%20ft)
therefore
The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot
Answer:
(a) ![P(x\le 3) = 0.75](https://tex.z-dn.net/?f=P%28x%5Cle%203%29%20%3D%200.75)
(b) ![P(x\le 3) = 0.75](https://tex.z-dn.net/?f=P%28x%5Cle%203%29%20%3D%200.75)
<em>(b) is the same as (a)</em>
(c) ![P(x \ge 5) = 0.10](https://tex.z-dn.net/?f=P%28x%20%5Cge%205%29%20%3D%200.10)
(d) ![P(x = 1\ or\ 2) = 0.55](https://tex.z-dn.net/?f=P%28x%20%3D%201%5C%20or%5C%202%29%20%3D%200.55)
(e) ![P(x > 2) = 0.45](https://tex.z-dn.net/?f=P%28x%20%3E%202%29%20%3D%200.45)
Step-by-step explanation:
Given
![\begin{array}{ccccccc}{CDs} & {1} & {2} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.30} & {0.25} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccccccc%7D%7BCDs%7D%20%26%20%7B1%7D%20%26%20%7B2%7D%20%26%20%7B3%7D%20%26%20%7B4%7D%20%26%20%7B5%7D%20%26%20%7B6%5C%20or%5C%20more%7D%5C%20%5C%5C%20%7BProb%7D%20%26%20%7B0.30%7D%20%26%20%7B0.25%7D%20%26%20%7B0.20%7D%20%26%20%7B0.15%7D%20%26%20%7B0.05%7D%20%26%20%7B0.05%7D%5C%20%5C%20%5Cend%7Barray%7D)
Solving (a): Probability of 3 or fewer CDs
Here, we consider:
![\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccc%7D%7BCDs%7D%20%26%20%7B1%7D%20%26%20%7B2%7D%20%26%20%7B3%7D%20%5C%20%5C%5C%20%7BProb%7D%20%26%20%7B0.30%7D%20%26%20%7B0.25%7D%20%26%20%7B0.20%7D%20%5C%20%5C%20%5Cend%7Barray%7D)
This probability is calculated as:
![P(x\le 3) = P(1) + P(2) + P(3)](https://tex.z-dn.net/?f=P%28x%5Cle%203%29%20%3D%20P%281%29%20%2B%20P%282%29%20%2B%20P%283%29)
This gives:
![P(x\le 3) = 0.30 + 0.25 + 0.20](https://tex.z-dn.net/?f=P%28x%5Cle%203%29%20%3D%200.30%20%2B%200.25%20%2B%200.20)
![P(x\le 3) = 0.75](https://tex.z-dn.net/?f=P%28x%5Cle%203%29%20%3D%200.75)
Solving (b): Probability of at most 3 CDs
Here, we consider:
![\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccc%7D%7BCDs%7D%20%26%20%7B1%7D%20%26%20%7B2%7D%20%26%20%7B3%7D%20%5C%20%5C%5C%20%7BProb%7D%20%26%20%7B0.30%7D%20%26%20%7B0.25%7D%20%26%20%7B0.20%7D%20%5C%20%5C%20%5Cend%7Barray%7D)
This probability is calculated as:
![P(x\le 3) = P(1) + P(2) + P(3)](https://tex.z-dn.net/?f=P%28x%5Cle%203%29%20%3D%20P%281%29%20%2B%20P%282%29%20%2B%20P%283%29)
This gives:
![P(x\le 3) = 0.30 + 0.25 + 0.20](https://tex.z-dn.net/?f=P%28x%5Cle%203%29%20%3D%200.30%20%2B%200.25%20%2B%200.20)
![P(x\le 3) = 0.75](https://tex.z-dn.net/?f=P%28x%5Cle%203%29%20%3D%200.75)
<em>(b) is the same as (a)</em>
<em />
Solving (c): Probability of 5 or more CDs
Here, we consider:
![\begin{array}{ccc}{CDs} & {5} & {6\ or\ more}\ \\ {Prob} & {0.05} & {0.05}\ \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccc%7D%7BCDs%7D%20%26%20%7B5%7D%20%26%20%7B6%5C%20or%5C%20more%7D%5C%20%5C%5C%20%7BProb%7D%20%26%20%7B0.05%7D%20%26%20%7B0.05%7D%5C%20%5C%20%5Cend%7Barray%7D)
This probability is calculated as:
![P(x \ge 5) = P(5) + P(6\ or\ more)](https://tex.z-dn.net/?f=P%28x%20%5Cge%205%29%20%3D%20P%285%29%20%2B%20P%286%5C%20or%5C%20more%29)
This gives:
![P(x\ge 5) = 0.05 + 0.05](https://tex.z-dn.net/?f=P%28x%5Cge%205%29%20%3D%200.05%20%2B%200.05)
![P(x \ge 5) = 0.10](https://tex.z-dn.net/?f=P%28x%20%5Cge%205%29%20%3D%200.10)
Solving (d): Probability of 1 or 2 CDs
Here, we consider:
![\begin{array}{ccc}{CDs} & {1} & {2} \ \\ {Prob} & {0.30} & {0.25} \ \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccc%7D%7BCDs%7D%20%26%20%7B1%7D%20%26%20%7B2%7D%20%5C%20%5C%5C%20%7BProb%7D%20%26%20%7B0.30%7D%20%26%20%7B0.25%7D%20%5C%20%5C%20%5Cend%7Barray%7D)
This probability is calculated as:
![P(x = 1\ or\ 2) = P(1) + P(2)](https://tex.z-dn.net/?f=P%28x%20%3D%201%5C%20or%5C%202%29%20%3D%20P%281%29%20%2B%20P%282%29)
This gives:
![P(x = 1\ or\ 2) = 0.30 + 0.25](https://tex.z-dn.net/?f=P%28x%20%3D%201%5C%20or%5C%202%29%20%3D%200.30%20%2B%200.25)
![P(x = 1\ or\ 2) = 0.55](https://tex.z-dn.net/?f=P%28x%20%3D%201%5C%20or%5C%202%29%20%3D%200.55)
Solving (e): Probability of more than 2 CDs
Here, we consider:
![\begin{array}{ccccc}{CDs} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccccc%7D%7BCDs%7D%20%26%20%7B3%7D%20%26%20%7B4%7D%20%26%20%7B5%7D%20%26%20%7B6%5C%20or%5C%20more%7D%5C%20%5C%5C%20%7BProb%7D%20%26%20%7B0.20%7D%20%26%20%7B0.15%7D%20%26%20%7B0.05%7D%20%26%20%7B0.05%7D%5C%20%5C%20%5Cend%7Barray%7D)
This probability is calculated as:
![P(x > 2) = P(3) + P(4) + P(5) + P(6\ or\ more)](https://tex.z-dn.net/?f=P%28x%20%3E%202%29%20%3D%20P%283%29%20%2B%20P%284%29%20%2B%20P%285%29%20%2B%20P%286%5C%20or%5C%20more%29)
This gives:
![P(x > 2) = 0.20+ 0.15 + 0.05 + 0.05](https://tex.z-dn.net/?f=P%28x%20%3E%202%29%20%3D%200.20%2B%200.15%20%2B%200.05%20%2B%200.05)
![P(x > 2) = 0.45](https://tex.z-dn.net/?f=P%28x%20%3E%202%29%20%3D%200.45)