Answer && Step-by-step explanation:
I will justify steps. (1/2)s == s/2
s/2=112
mult 2 to each side
=> s=112*2
s=224
Answer:
C. 1/3
Step-by-step explanation:
1. convert 3x + y = 1 to slope form: y = -3x +1
2. Perpendicular slope: negative reciprocal of the given slope
3. Given slope = -3x
4. Perpendicular slope = -(1/-3) = 1/3
Answer:
a) Frequency table:
Category Frequency
Dog 4
Cat 3
Fish 2
Hamster 1
b) Relative frequencies of each animal type
- Dog: 4/10 = 0.4
- Cat: 3/10 = 0.3
- Fish: 2/10 = 0.2
- Hamster: 1/10 = 0.1
c) Popularity
- Dog is the most popular because it has the highest relative frequency.
- Hamster is the least popular because it has the lowest relative frequency.
Explanation:
<u>a. Make a frequency table for the results.</u>
There are four kind of pets: dog, cat, hamster, and fish.
A <em>frequency table </em>shows the number of items for each category (kind of pets).
Count the number of each kind of pet:
- Dog: 4
- Cat: 3
- Hamster: 1
- Fish: 2
- Total: 10
With that you build your frequency table.
Frequency table:
Category Frequency
Dog 4
Cat 3
Fish 2
Hamster 1
<u>b. Relative frequencies of each animal type.</u>
The relative frequency is how often an outcome appears divided by the total number of outmcomes.
Here the total number of outcomes is 10 (the ten pets).
So, calculate each relative frequency:
- Dog: 4/10 = 0.4
- Cat: 3/10 = 0.3
- Fish: 2/10 = 0.2
- Hamster: 1/10 = 0.1
An important feature of the relative frequency is that they must add up 1. Check:
- 0.4 + 0.3 + 0.2 + 0.1 = 1.
<u>c. Using the relative frequencies explain which animals are most and least popular.</u>
Popularity is determined by the frequency with each outcome is repeated. The most popular is the most repeated. The least popular is the least repeated.
- Dog is the most popular because it has the highest relative frequency.
- Hamster is the least popular because it has the lowest relative frequency.
Answer:
x = 2,94 ft
h = 0,88 ft
C(min) = 12,23 $
Step-by-step explanation:
Let x be radius of the base and h th hight of th cylinder then
Area of the bottom A₁ = π*x²
And cost of the bottom C₁ = 0,15*π*x²
Lateral area A₂
A₂ = 2*π*x*h but V = 24 ft³ V = π*x²*h h = V/ π*x²
A₂ = 2*π*x* (24/ π*x²)
A₂ = 48 /x
Cost of area A₂
C₂ = 0,05 * 48/x
C₂ = 2,4/x
Total cost C C = C₁ + C₂
C(x) = 0,15*π*x² + 24/x
Taking derivatives on both sides of the equation
C´(x) = 0,3**π*x - 24/x²
C´(x) = 0 0,3**π*x - 24/x² = 0
0,942 x³ = 24
x³ = 25,5
x = 2,94 ft and h = V/π*x² h = 24 /3,14* (2,94)²
h = 0,88 ft
C(min) = 0,15 * 3,14 * (2,94)² + 24/2,94
C(min) = 4,07 + 8,16
C(min) = 12,23 $
Answer:
And we can find the probability with this difference and using the normal standard table:
Step-by-step explanation:
Let X the random variable that represent the wages, and for this case we know the distribution for X is given by:
Where 
and 
We want to find this probability:
And we can use the z score formula given by:
Using this formula we have:
And we can find the probability with this difference and using the normal standard table:
