Answer:
0.001709
Step-by-step explanation:
The probability of getting 9 tails then 1 head is:
(½)⁹ (½)¹ = (½)¹⁰
The probability of getting 10 tails then 1 head is:
(½)¹⁰ (½)¹ = (½)¹¹
The probability of getting 11 tails then 1 head is:
(½)¹¹ (½)¹ = (½)¹²
The total probability is:
(½)¹⁰ + (½)¹¹ + (½)¹²
0.001709
distance = 500 feet
Since Δ VWX and Δ YZX are similar then the ratios of corresponding sides are equal, that is
= 
= 
completing the required values gives
= 
( cross- multiply )
60l = 30 × 100 = 3000 ( divide both sides by 60 )
l = 500
distance across the swamp is 500 feet
Answer:
.6
Step-by-step explanation:
Answer:
h(1.5) = 7.3 ft
h(10.3) = 24.9 ft
Step-by-step explanation:
Given the function h(d) = 2d + 4.3,
where:
h = height of the water in a fountain (in feet)
d = diameter of the pipe carrying the water (in inches)
<h3>h(1.5)</h3>
Substitute the input value of d = 1.5, into the function:
h(1.5) = 2(1.5) + 4.3
h(1.5) = 3 + 4.3
h(1.5) = 7 feet
The height of the water in a fountain is 7 feet when the diameter of the pipe is 1.5 inches.
<h3>h(10.3)</h3>
Substitute the input value of d = 10.3, into the function:
h(10.3) = 2(10.3) + 4.3
h(10.3) = 20.6 + 4.3
h(10.3) = 24.9 feet
The height of the water in a fountain is 24.9 feet when the diameter of the pipe is 10.3 inches.
<h3>Context of the solutions to h(1.5) and h(10.3):</h3>
The solutions to both functions show the relationship between the diameter of the pipe to the height of the water in a fountain. The height of the water in fountain increases relative to the diameter of the pipe. In other words, as the diameter or the size of the pipe increases or widens, the height of the water in a fountain also increases.
Answer:
Infinitely many solutions.
Step-by-step explanation:
5x-8y=-11
-10x+16y=22
---------------------
2(5x-8y)=2(-11)
-10x+16y=22
---------------------
10x-16y=-22
-10x+16y=22
---------------------
0+0=0
infinitely many solutions
