Answer:
1. C, E, G
2. A, D, H
Step-by-step explanation:
Compare each equation to the form ...
f(x) = 1/(4p)(x -h)^2 +k
In this form, p is the distance from the vertex to the focus (positive is up), and (h, k) is the location of the vertex. The focus is (h, k+p); the directrix is y=k-p.
1. The equation tells us ...
(h, k) = (1, 4)
1/(4p) = (-1) . . . ⇒ . . . p = -1/4
So, we have ...
- vertex: (1, 4) . . . . . . . . (G)
- focus: (1, 3 3/4) . . . . . (C)
- directrix: y=4 1/4 . . . . (E)
--
2. The equation tells us ...
(h, k) = (-1, 4)
1/(4p) = 2 . . . ⇒ . . . p = 1/8
So, we have ...
- vertex: (-1, 4) . . . . . . . . (A)
- focus: (-1, 4 1/8) . . . . . . (H)
- directrix: y = 3 7/8 . . . (D)
Answer:
6.4 x 10¹¹ litres
Step-by-step explanation:
Given:
Surface area = 16.0 mi²
Average depth = 51.0 ft
To calculate the volume of the lake in liters,
(i) <em>Convert the average depth to miles.</em>
1 ft = 0.000189 mi
51.0 ft = 51.0 x 0.000189 mi = 0.009639 mi
(ii) <em>Now find the volume in mi³</em>
volume = surface area x average depth.
volume = 16.0 mi² x 0.009639 mi
volume = 0.154224 mi³
(iii) <em>Finally, convert the volume from mi³ to litres</em>
1 mi³ = 4.168 x 10¹² litres
0.154224 mi³ = 0.154224 mi³ x 4.168 x 10¹² litres / 1 mi³
0.154224 mi³ = 6.4 x 10¹¹ litres
Therefore, the volume in litres is 6.4 x 10¹¹
Answer:
The probability that the box will contain less than the advertised weight of 453 g is 0.00034.
Step-by-step explanation:
Let <em>X</em> represent the weight (in grams) of cereal in a box of Lucky Charms.
It is provided that <em>X</em> follows a Normal distribution with parameters, <em>μ</em> = 470 and <em>σ</em> = 5.
Compute the probability that the box will contain less than the advertised weight of 453 g as follows:
*Use the <em>z</em>-table.
Thus, the probability that the box will contain less than the advertised weight of 453 g is 0.00034.
Complementary means they add up to 90.
Split 90 in half. 45,45
Decrease one half by 5, and increase the other by 5
40,50
The angles are 40 and 50 degrees