Answer:
7 tenths
Step-by-step explanation:
3 tenths + 4 tenths = 3/10 + 4/10 = 0.3 + 0.4 = 0.7
= 7 tenths
The number 12 is missing in the data set.
<u>Step-by-step explanation</u>:
- The numbers are 9,12,16,18,23.
- The missing number is assumed to be 'x'
Mean = Sum of the integers / Total number of integers.
15 = (9+12+16+18+23+x) / 6
15 = (78+x) / 6
90 = 78+x
x = 90-78
x = 12
Answer:
a. 12 feet b. 12 feet 0.5 inches c. 8.33 %
Step-by-step explanation:
a. How far out horizontally on the ground will it protrude from the building?
Since the rise to run ratio is 1:12 and the building is 12 inches off the ground, let x be the horizontal distance the ramp protrudes.
So, by ratios rise/run = 1/12 = 12/x
1/12 = 12/x
x = 12 × 12
x = 144 inches
Since 12 inches = 1 foot, 144 inches = 144 × 1 inch = 144 × 1 foot/12 inches = 12 feet
b. How long should the ramp be?
The length of the ramp, L is gotten from Pythagoras' theorem since the ramp is a right-angled triangle with sides 12 inches and 144 inches respectively.
So, L = √(12² + 144²)
= √[12² + (12² × 12²)]
= 12√(1 + 144)
= 12√145
= 12 × 12.042
= 144.5 inches
Since 12 inches = 1 foot, 144.5 inches = 144 × 1 inch + 0.5 inches = 144 × 1 foot/12 inches + 0.5 inches = 12 feet 0.5 inches
c. What percent grade is the ramp?
The percentage grade of the ramp = rise/run × 100 %
= 12 inches/144 inches × 100 %
= 1/12 × 100 %
= 0.0833 × 100 %
= 8.33 %
Answer: C 45
Step-by-step explanation:
The dimensions would be 7√2, 7√6 and 14√2.
A 45-45-90 triangle has two equal legs and a hypotenuse that is equal to the leg multiplied by the square root of two (t, t, t√2).
A 30-60-90 triangle has legs that are equal to t, t√3, and 2t.
The longest side on the 45-45-90 triangle will be 14√2. This will also be the longest side of the 30-60-90 triangle; this gives us
2t = 14√2
Dividing both sides by 2, we have
2t/2 = 14√2/2
t = 7√2
We now have t and 2t; we lack t√3:
t = 7√2
t√3 = 7√2(√3) = 7√6.
