Answer:
a) A. The population must be normally distributed
b) P(X < 68.2) = 0.7967
c) P(X ≥ 65.6) = 0.3745
Step-by-step explanation:
a) The population is normally distributed having a mean (
) = 64 and a standard deviation (
) = 
b) P(X < 68.2)
First me need to calculate the z score (z). This is given by the equation:
but μ=64 and σ=19 and n=14, 
and 
Therefore: 
From z table, P(X < 68.2) = P(z < 0.83) = 0.7967
P(X < 68.2) = 0.7967
c) P(X ≥ 65.6)
First me need to calculate the z score (z). This is given by the equation:
Therefore: 
From z table, P(X ≥ 65.6) = P(z ≥ 0.32) = 1 - P(z < 0.32) = 1 - 0.6255 = 0.3745
P(X ≥ 65.6) = 0.3745
P(X < 68.2) = 0.7967
To find the length of the ladder, you need to do Pythagorean theorem.
50^2 + 30^2 = x^2
2500 + 900 = x^2
x^2 =3400
x= square root of 3400
58.31 OR 10 root34
To find the angle:
tan theta = opposite/adjacent
50/30 = 5/3
theta = tan inverse of 5/3
= 59.04
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The volume prism refers to the number of cubic units that will exactly fill the figure. The volume of a rectangular prism can be found or calculate by using the formula
V=Bh, where
B represents to the area of the base or in other words the length and width of the rectangle.
In this exercise is given that the measurements of a prism are 5/2ft, 3/2ft, and 7/2ft; and it is asked to find its volume. In order to find the volume of the prism, you should substitute the given values into the previous mention formula.
V=Bh
V=(5/2 ft)(7/2 ft)(3/2 ft)
V=(35/4 ft²)(3/2 ft)
V=105/8ft³ or 
ft³The volume of the rectangular prism is ft³.
Answer:
y = 4/5x + 3/5
Step-by-step explanation:
In the slope-intercept form, y = mx + b, we need to find the values of the slope (m) and the y-intercept.
Using points (-7, -5) and (3, 3), we can calculate for the slope of the equation given the formula:
Let (x1, y1) = (-7, -5)
and (x2, y2) = (3, 3).
Plug the given values into the slope formula:
Therefore, the slope of the line is 4/5.
Next, we need to find out the value of the y-intercept (b).
We can use one of the given points, (3, 3), along with the slope (4/5) to solve for the y-intercept:
y = mx + b
3 = 4/5(3) + b
3 = 12/5 + b
Subtract 12/5 from both sides:
3 - 12/5 = 12/5 - 12/5 + b
3/5 (or 0.6) = b
Therefore, the y-intercept is 3/5.
We can now establish our linear equation as:
y = 4/5x + 3/5
Please mark my answers as the Brainliest if you find this solution helpful :)
