Answer:
59°
58.3 inches
Step-by-step explanation:
Here is the full question :
A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Please check the attached image for a diagram explaining this question
The angle the ladder makes with the ground is labelled x in the diagram
To find the value of x given the opposite and adjacent lengths, use tan
tan⁻¹ (opposite / adjacent)
tan⁻¹ (50 / 30)
tan⁻¹ 1.667
= 59°
the length of the ladder can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
√(50² + 30²)
√(2500 + 900)
√3400
= 58.3 inches
Answer:
59.04°
58.31 inches
Step-by-step explanation:
The solution triangle is attached below :
Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;
Let the angle = θ
Tanθ = opposite / Adjacent
Tanθ = 50/30
θ = tan^-1(50/30)
θ = 59.036°
θ = 59.04°
The length of ladder can be obtained using Pythagoras :
Length of ladder is the hypotenus :
Hence,
Hypotenus = √(adjacent² + opposite²)
Hypotenus = √(50² + 30²)
Hypotenus = √(2500 + 900)
Hypotenus = 58.309
Length of ladder = 58.31 inches
Answer: 0.6827
Step-by-step explanation:
Given : Mean IQ score :
Standard deviation :
We assume that adults have IQ scores that are normally distributed .
Let x be the random variable that represents the IQ score of adults .
z-score :
For x= 90
For x= 120
By using the standard normal distribution table , we have
The p-value :
Hence, the probability that a randomly selected adult has an IQ between 90 and 120 =0.6827
Answer:
Step-by-step explanation:
F(x) is a transformation from h(x).
So our starting equation is
F(x) is also facing the same direction h(x) is so we dont have to reflect nothing across the x or y axis.
There isn't a vertical or horizontal stretch, compressions.
There isn't a horizontal shift as the x values stay in the same place.
There is a vertical shift. We can simply move h(x) up 6 units to get to f(x).
So our equation looks like.