Answer:
Where 
and 
And the z score is given by:
And since z = 0.75 we can replace like this:
And if we solve for x we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the ACT scores of a population, and for this case we know the distribution for X is given by:
Where and
And the z score is given by:
And since z = 0.75 we can replace like this:
And if we solve for x we got:
Add like terms on the same side:
-10 + 8x = -56
Add ten to both sides
-10 + 8x + 10 = -56 +10
Simplify:
8x = -46
Divide both side by 8
8x/8 = -46/8
Simplify
x = - 5.75
The answer is x = -5.75
(The answer can also be written as -23/4 or -5 3/4)
it’s system of substitutions ?
so try
a = 2
b = 5
Split up each force into horizontal and vertical components.
• 300 N at N30°E :
(300 N) (cos(30°) i + sin(30°) j)
• 400 N at N60°E :
(400 N) (cos(60°) i + sin(60°) j)
• 500 N at N80°E :
(500 N) (cos(80°) i + sin(80°) j)
The resultant force is the sum of these forces,
∑ F = (300 cos(30°) + 400 cos(60°) + 500 cos(80°)) i
… … … + (300 sin(30°) + 400 sin(60°) + 500 sin(80°)) j N
∑ F ≈ (546.632 i + 988.814 j) N
so ∑ F has a magnitude of approximately 1129.85 N and points in the direction of approximately N61.0655°E.
Answer:
<u>The area of the circular garden is 28.3 square feet</u>
Step-by-step explanation:
Let's recall that the area of a circle is π * r², therefore if the diameter of the circular garden is 6 feet, the area is:
Diameter = 6 feet ⇒ radius = (6/2) = 3 feet
Area of the circular garden = π * 3²
Area of the circular garden = 3.1416 * 9
Area of the circular garden = 28.2744
<u>Area of the circular garden = 28.3 square feet</u>
