Step-by-step explanation:
y = 2/27 x² − 4/3 x
a) The leading coefficient (the coefficient of the x² term) is positive, so that means the parabola points up. So the vertex is at the bottom of the parabola, making it a minimum.
b) For a parabola y = ax² + bx + c, the x coordinate of the vertex can be found at x = -b / (2a). Here, a = 2/27 and b = -4/3.
x = -(-4/3) / (2 × 2/27)
x = (4/3) / (4/27)
x = (4/3) × (27/4)
x = 9
c) To find the y coordinate of the vertex, we simply evaluate the function at x=9:
y = 2/27 x² − 4/3 x
y = 2/27 (9)² − 4/3 (9)
y = 6 − 12
y = -6
d) The ordered pair is (9, -6). This means that at the lowest point of the dish, the dish is 6 inches deep. Also, since the dish is symmetrical, and the lowest point is 9 inches from the end, then the total width is double that, or 18 inches.
Answer:
3+2=5
Step-by-step explanation:
Answer:
<h3>Area of a circle in terms of radius:</h3>
Area = π·r^2 = 3.14·9.5^2 = 283.5 square meters(*)
Area of a circle in terms of diameter:
Area = π·(d/2)^2 = 3.14·(19/2)^2 = 3.14·(9.5)^2 = 283.5 square meters(*)
Area of a circle in terms of circumference:
Area = C^2/4π = 59.69^2/4π = 3562.9/(4·3.14) = 3562.9/12.56 = 283.5 square meters(*)
(*) 283.52873698648 meters, exactly or limited to the precision of this calculator (13 decimal places).
Note: for simplicity, the operations above were rounded to 2 decimal places and π was rounded to 3.14.
Step-by-step explanation:
Hope it is helpful....
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:
f a doctor makes $152,125 and is being taxed 6% on it, to find the exact value of the income tax you will
$152,125 x .06 = $9127.50 The amount of income tax in dollars would be $9127.50 Step-by-step explanation:
