First, you need to get their square roots.
4:7
Next, you need to get the cube of their square roots so,
4^3:7^3
The answer is
64:343
Answer: The length of point A(-3,1) and B(2,6) is
.
Step-by-step explanation:
We know that the distance between the two points (a,b) and (c,d) is given by :-
![d=\sqrt{(a-c)^2+(b-d)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28a-c%29%5E2%2B%28b-d%29%5E2%7D)
Given points = A(-3,1) and B(2,6)
Therefore the distance between the points A(-3,1) and B(2,6) is given by :-
![d=\sqrt{(-3-2)^2+(1-6)^2}\\\\\Rightarrow\ d=\sqrt{(-5)^2+(-5)^2}\\\\\Rightarrow\ d=\sqrt{25+25}\\\\\Rightarrow\ d=\sqrt{50}\\\\\Rightarrow\ d=\sqrt{25\times2}\\\\\Rightarrow\ d=\sqrt{5^2\times2}\\\\\Rightarrow\ d=5\sqrt{2}\text{ units}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-3-2%29%5E2%2B%281-6%29%5E2%7D%5C%5C%5C%5C%5CRightarrow%5C%20d%3D%5Csqrt%7B%28-5%29%5E2%2B%28-5%29%5E2%7D%5C%5C%5C%5C%5CRightarrow%5C%20d%3D%5Csqrt%7B25%2B25%7D%5C%5C%5C%5C%5CRightarrow%5C%20d%3D%5Csqrt%7B50%7D%5C%5C%5C%5C%5CRightarrow%5C%20d%3D%5Csqrt%7B25%5Ctimes2%7D%5C%5C%5C%5C%5CRightarrow%5C%20d%3D%5Csqrt%7B5%5E2%5Ctimes2%7D%5C%5C%5C%5C%5CRightarrow%5C%20d%3D5%5Csqrt%7B2%7D%5Ctext%7B%20units%7D)
Hence, the length of point A(-3,1) and B(2,6) is
.
Answer:
The answer to your question is the letter A) 53.1 feet
Step-by-step explanation:
Data
Adjacent side = 20 ft
angle = Ф = 67°
distance from the eyes to the ground = 6 ft
Opposite side = ?
To solve this problem use trigonometric functions. The trigonometric function that relates the Opposite side and the Adjacent side is tangent.
tan Ф = Opposite side / Adjacent side
-Solve for Opposite side
Opposite side = Adjacent side x tan Ф
- Substitution
Opposite side = 20 x tan 67
-Simplification
Opposite side = 20 x 2.36
- Result
Opposite side = 47.1 ft
Height = 47.1 + 6
= 53.1 ft
B, x>5 Because the graph is shaded right from 5 meaning x is greater than 5. It is an open dot meaning 5 is not included so we have to use > not ≥
Answer:
a) P(Y > 76) = 0.0122
b) i) P(both of them will be more than 76 inches tall) = 0.00015
ii) P(Y > 76) = 0.0007
Step-by-step explanation:
Given - The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches.
To find - (a) If a man is chosen at random from the population, find
the probability that he will be more than 76 inches tall.
(b) If two men are chosen at random from the population, find
the probability that
(i) both of them will be more than 76 inches tall;
(ii) their mean height will be more than 76 inches.
Proof -
a)
P(Y > 76) = P(Y - mean > 76 - mean)
= P(
) >
)
= P(Z >
)
= P(Z >
)
= P(Z > 2.25)
= 1 - P(Z ≤ 2.25)
= 0.0122
⇒P(Y > 76) = 0.0122
b)
(i)
P(both of them will be more than 76 inches tall) = (0.0122)²
= 0.00015
⇒P(both of them will be more than 76 inches tall) = 0.00015
(ii)
Given that,
Mean = 69.7,
= 1.979899,
Now,
P(Y > 76) = P(Y - mean > 76 - mean)
= P(
)) >
)
= P(Z >
)
= P(Z >
))
= P(Z > 3.182)
= 1 - P(Z ≤ 3.182)
= 0.0007
⇒P(Y > 76) = 0.0007