Answer:
P ( 5 < X < 10 ) = 1
Step-by-step explanation:
Given:-
- Sample size n = 49
- The sample mean u = 8.0 mins
- The sample standard deviation s = 1.3 mins
Find:-
Find the probability that the average time waiting in line for these customers is between 5 and 10 minutes.
Solution:-
- We will assume that the random variable follows a normal distribution with, then its given that the sample also exhibits normality. The population distribution can be expressed as:
X ~ N ( u , s /√n )
Where
s /√n = 1.3 / √49 = 0.2143
- The required probability is P ( 5 < X < 10 ) minutes. The standardized values are:
P ( 5 < X < 10 ) = P ( (5 - 8) / 0.2143 < Z < (10-8) / 0.2143 )
= P ( -14.93 < Z < 8.4 )
- Using standard Z-table we have:
P ( 5 < X < 10 ) = P ( -14.93 < Z < 8.4 ) = 1
For numbers 15-17, we need to remember that two of a triangle's angles are always acute and the third angle will allow us to classify the triangle based on its angles. now that we know this, let's look at #15. the first two angles listed are acute, and the third is an obtuse angle, therefore it is an obtuse triangle. on #16 we have three acute angles, so it is an acute triangle. #17 has two acute angles and a right angle so it is a right triangle.
on numbers 21-23, we need to know that a triangle with all congruent sides is called equilateral, a triangle with two equal sides is isosceles, and a triangle with no equal sides is called scalene. #21 shows two equal sides so it is an isosceles triangle. #22 has three equal sides so it is an equilateral triangle. #23 has no equal sides so it is scalene. hope this helped! :)
Answer:
{ y = 3x + 3
{ 3x - y = 3
B
(Just did the assignment 3/23/21)
This question is incomplete. The attached image was obtained online
Answer:
41 square units
Step-by-step explanation:
Looking at diagram that was attached, we can see that the Polygon s the combination of a square and a triangle.
In square CDEF we have:
The lengths of the side of the square= 4 units
Hence, the area of square is: length ²
Area of square= 4²
=16 square units
Also, in ΔBFA we have:
The base of the triangle is calculated as
=6 + 4= 10 units
height of the triangle is: FA= 5 units
The formula for Area of a triangle = 1/2 × Base × Height
Hence, we have area of ΔBFA as:
= 1/2 × 10 × 5
Area= 25 square units
The Area of the Polygon = Area of the square + Area of the triangle
16 square units + 25 square units
= 41 square units
