Of the 400 eighth-graders at pascal middle school, 117 take algebra, 109 take advanced computer, and 114 take industrial technol
ogy. furthermore, 70 take both algebra and advanced computer, 34 take both algebra and industrial technology, and 29 take both advanced computer and industrial technology. finally, 164 students take none of these courses. how many students take all three courses
2 answers:
Number of students that take all three courses is 29 students
<h3>Further explanation</h3>A set is a clearly defined collection of objects.
To declare a set can be done in various ways such as:
- With words or the nature of membership
- With set notation
- By registering its members
- With Venn diagrams
Multiplying set A x B is by pairing each member of set A with each member of set B.
<u>Example: </u>
<em>A = {1, 2, 3} </em>
<em>B = {a, b} </em>
Then
A x B = {(1, a), (1, b), (2, a), (2, b), (3, a), (3, b)}
Union of set A and B ( A ∪ B ) is rewriting each member A and combined with each member B.
Intersection of set A and B ( A ∩ B ) is to find the members that are both in Set A and Set B.
<u>Example: </u>
<em>A = {1, 2, 3, 4} </em>
<em>B = {3, 4, 5} </em>
A ∪ B = {1, 2, 3, 4, 5}
A ∩ B = {3, 4}
Let us now tackle the problem!
To solve this problem, it is better to draw the Venn diagram as shown in the picture in the attachment.
Let :
x → students take all three courses
y = 34 - x → students only take both algebra and industrial technology
z = 29 - x → students only take both computer and industrial technology
w = 70 - x → students only take both algebra and computer
p = 117 - w - x - y = 13 + x → students only take algebra
q = 114 - x - y - z = 51 + x → students only take industrial technology
r = 109 - x - z - w = 10 + x → students only take computer
t = 164 → students take none of these courses
Because the total number of students is 400 people, then :
- Mean , Median and Mode : brainly.com/question/2689808
- Centers and Variability : brainly.com/question/3792854
- Subsets of Set : brainly.com/question/2000547
Grade: High School
Subject: Mathematics
Chapter: Sets
Keywords: Sets , Venn , Diagram , Intersection , Union , Mean , Median , Mode
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a) The dimensions of original rectangle are length= 5 and width= 4.
b) The dimensions of new rectangle are length= 15 and width=8.
<u>Step-by-step explanation</u>:
- length of a rectangle = l
- width of a rectangle = w
- Perimeter of a rectangle = 2(l+w)
<u>Original rectangle</u> :
18 = 2(l+w)
18 = 2l + 2w ---------(1)
<u>New rectangle</u> :
46 = 2(3l+2w)
46 = 6l + 4w ---------(2)
<u>Solving the equations</u> :
Multiply (1) by 2 and subtract (2) from (1)
4l + 4w = 36
-(<u>6l + 4w = 46</u>)
<u>-2l = -10</u>
l = 10/2
length = 5 inches.
Substitute l=5 in (1)
18 = 2(5)+2w
18 = 10+2w
2w = 8
w = 8/2
width = 4 inches.
length of new rectangle = 3(l) = 35 = 15 inches.
width of new rectangle = 2(w) = 24 = 8 inches.
Answer:
Y will arrive earlier than X one fourth of times.
Step-by-step explanation:
To solve this, we might notice that given that both events are independent of each other, the joint probability density function is the product of X and Y's probability density functions. For an uniformly distributed density function, we have that:
Where L stands for the length of the interval over which the variable is distributed.
Now, as X is distributed over a 1 hour interval, and Y is distributed over a 0.5 hour interval, we have:
.
Now, the probability of an event is equal to the integral of the density probability function:
Where A is the in which the event happens, in this case, the region in which Y<X (Y arrives before X)
It's useful to draw a diagram here, I have attached one in which you can see the integration region.
You can see there a box, that represents all possible outcomes for Y and X. There's a diagonal coming from the box's upper right corner, that diagonal represents the cases in which both X and Y arrive at the same time, under that line we have that Y arrives before X, that is our integration region.
Let's set up the integration:
We have used here both the independence of the events and the uniformity of distributions, we take the 2 out because it's just a constant and now we just need to integrate. But the function we are integrating is just a 1! So we can take the integral as just the area of the integration region. From the diagram we can see that the region is a triangle of height 0.5 and base 0.5. thus the integral becomes:
That means that one in four times Y will arrive earlier than X. This result can also be seen clearly on the diagram, where we can see that the triangle is a fourth of the rectangle.
<h2>Explanation:</h2>
A cube is a prism whose sides all have the same length. You can think of a cube like the three dimensional version of a square. In this problem, we know that Mary is using a microscope in order to look at a salt crystal and discovers it is shaped like a cube. Each square face has side length:
This diagram is shown in the first figure below. A crystal's square face is one of the six faces of the cube. So in order to draw it we need to know how many units we'll have in each side. Since we know that 1 unit on the grid represents 0.01mm, then:
So we will have 10 units that measure 0.01mm in each side. This is shown in the second figure below.