Answer:
The original length of the rope is 140
Step-by-step explanation:
21x (100/15)
Answer:
140
Step-by-step explanation:
.
Answer:
comparison of two sample proportions independent
Step-by-step explanation:
Given that the percent of managers at High Tech Inc. that pay over $8 per day for lunch is the same as the percent of technicians.
The data can be given as follows:
The samples are as follows
Managers 60 149
Who paid >8 46 98
Hence we compare sample proportions here.
The appropriate test would be
comparison of two sample proportions independent
30 cents for each additional minute. Find the cost
of a 15-minute call.
Answer: $4.40 is the cost for the call
Add the complex numbers: (4 + 8i) + (–2 – i)
Answer:
2 + 7i
Step-by-step explanation:
(4 + 8i) + (-2 - i)
open the brackets
4 + 8i - 2 - i
add or subtract like terms
2 + 7i
Answer:
2+7i
Step-by-step explanation:
Open the brackets.
4+8i-2-i
You will get…
2+7i
x in simplest radical form with a rational denominator.
The length of sides x in the simplest radical form is 2√2
Let's find x using trigonometric ratios
sin ∅ = opposite / hypotenuse
Therefore,
sin 30° = √2 / x
x sin 30° = √2
x = √2 / sin 30°
x =
x = × 2
x = 2√2
learn more on right angle triangle: brainly.com/question/15948053?referrer=searchResults
Answer:
y = (-1/19)(x - 8)² + 1521/76
Step-by-step explanation:
A parabola moves in such a way that it's distance from it's focus and directrix are always equal.
Now, we are given that directrix is y = 9.75 and focus is at (8, 0.25). Focus can be rewritten as (8, ¼) and directrix can be rewritten as y = 39/4
If we consider a point with the coordinates (x, y), it means the distance from this point to the focus is;
√((x - 8)² + (y - ¼)²)
Distance from that point to the directrix is; (y - 39/4)
Thus;
√((x - 8)² + (y - ¼)²) = (y - 39/4)
Taking the square of both sides gives;
((x - 8)² + (y - ¼)²) = (y - 39/4)²
(x - 8)² + y² - ½y + 1/16 = y² - (39/2)y + (39/4)²
Simplifying this gives;
(x - 8)² - (39/4)² = (½ - 39/2)y
(x - 8)² - 1521/4 = -19y
(x - 8)² - 1521/4 = -19y
Divide both sides by -19 to get;
y = (-1/19)(x - 8)² + 1521/76
As given by the question
There are given that the inside edge is 4 in.
Now,
Since sphere fits snugly inside a cube therefore diameter of sphere will be equal to side of the cube
So,
Then,
Volume of the sphere is given by:
And,
The volume of a cube is:
Then,
The volume of the space between the sphere and cube = 64-33.5 = 30.5.
Hence, the answer is 30.5 cube inches.