A survey of 100 families showed that 35 had a dog: 28 had a cat: 10 had a dog and a cat: 42 had neither a cat nor a dog nor a pa
rakeet: 0 had a cat, a dog, and a parakeet. How many had a parakeet only? A. 20 B. 15 C. 5 D. 10
1 answer:
<h2>Answer:</h2>
Option: C is the correct answer.
C. 5
<h2>Step-by-step explanation:</h2>We will solve the following problem with the help of the Venn diagram.
Based on the Venn diagram we are asked to find the value of v i.e. those who have parakeet only.
From the information that:
- 35 had a dog we have:
x+y+10=35
i.e.
x+y=25
Also, based on the information :
- 28 had a cat we have:
u+z+10=28
i.e.
u+z=18
Also, 42 had neither a cat nor a dog nor a parakeet.
This means it cover the outer region of the three circles.
Total 100 families were surveyed it means that:
42+x+y+10+u+z+v=100
i.e. 42+25+10+18+v=100
i.e. 95+v=100
i.e. v=100-95
i.e. v=5
Hence, the number of families who have only parakeet are: 5
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Answer:
Step-by-step explanation:
step 1
Find the area of the garden space
First convert mixed number to an improper fraction
step 2
Find how much more land Farmer Jack needs to plant the rest of his corn
Answer:
a) f(0)=4
b) f(-2)=2
c) x∈{-8,-4,4,8}
d) x∈{-9,-3,3,9}
e) x∈(-∞,-9)∪(-3,3)∪(9,∞).
f) x∈[-9,-3]∪[3,9]
g) Domain is x∈[-10,10]. Range is y∈[-4,4]. Zeros are at elements of x in {-9,-3,3,9}
h) Increasing on x∈ (-6,0) ∪ (6,10) and
decreasing on x∈ (-10,-6) ∪ (0,6).
Step-by-step explanation:
a) f(0) means what is the y-coordinate of the point at x=0.
So find 0 on the x-axis. I'm going to go up because the curve is at y=4 there.
Conclusion: f(0)=4.
b) f(-2) means what is the y-coordinate of the point at x=-2.
So find -2 on the x-axis. I'm going to go up because the curve is at y=2 there.
Conclusion: f(-2)=2.
c) f(x)=-2 means what is x when y=-2. So go on the y-axis and find -2. Now anything on that line y=-2 (horizontal line going through y=-2 on the y-axis) we need to look at.
There are 4 value we need to look at then.
x=-8
x=-4
x=4
x=8
At all of these the y-coordinate is -2.
d) f(x)=0 means what is x when y=0. So go on the y-axis and find 0. Now anything on that line y=0 (horizontal line going through y=0 on the y-axis; also knowing as the x-axis for y=0) we need to look at.
There are 4 values we need to look at then.
x=-9
x=-3
x=3
x=9
e) f(x)>0 means where is the curve above the x-axis.
The curve is above the x-axis:
- Before x=-9
- Between x=-3 and x=3
- After x=9
The interval notation is:
(-∞,-9)∪(-3,3)∪(9,∞).
d) f(x)≥0 means where is the curve below or on the x-axis (also known as y=0).
The curve is below or on the x-axis:
- Between -9 and -3 (inclusive of both endpoints because they include y=0).
- Between 3 and 9 (inclusive of both endpoints because they include y=0).
The interval notation is:
[-9,-3]∪[3,9]
g) The domain is where the curve exists for the x-values.
The domain is all real numbers between -10 and 10 (inclusive of both).
The curve starts at x=-10 and stops at x=10. The function exists a y value for any number between -10 and 10 (including both).
Interval notation is:
[-10,10]
The range is where the curve exists for the y-values.
Looking from bottom to top I see that it starts at y=-4 and stops at y=4. I notice the curve exists at some point between those two horizontal lines. It also exists at both of those endpoints" -4 and 4.
The range is between -4 and 4 (including both).
Interval notation is:
[-4,4]
The zeros are where the graph crosses the x-axis.
The graph crosses the x-axis at:
x=-9
x=-3
x=3
x=9
h) Reading left to right the graph increases when you see the curve going up.
I see this from x=-6 to x=0 (exclusive of both).
I see this from x=6 to x=10 (exclusive of both).
So interval notation is (-6,0) ∪ (6,10).
Reading left to right the graph decreases when you see the curve going down.
I see this from x=-10 to x=-6 ( exclusive of both).
I see this from x=0 to x=6 (exclusive of both).
