1/3 of all students bring lunch
2:3 is the ratio of students who bring their lunch to the number of students who do not
<h2>Question 9:</h2>
1. Use Pythagorean Theorem (a²+b²=c²) to solve for missing side of triangle and rectangle. x²+16²=20², or x²+256=400. So, x²=144, and x=12
2. Use formula: 1/2(h)(b1+b2). 1/2 (12) (30+14).
3. Simplify: 1/2 (12) (44)=1/2(528)=264
Area of whole figure is 264 square mm.
<h2>Question 10:</h2>
Literally same thing but with trigonometry.
1. Use sine to find out length of dotted line: sin(60°)=x/12
2: Simplify: 12*sin(60°)=x. x≈10.4 (rounded to the nearest tenth)
3. Use Pythagorean Theorem to find out last leg of triangle: 10.4²+x²=12²
4: Simplify: 108.16 +x²=144. x²=35.84 ≈ 6
5: Use formula: 1/2(h)(b1+b2). 1/2 (10.4) (30+36)
6: Simplify: 1/2 (10.4) (66) =343.2
7: Area of figure is about 343.2
Remember, this is an approximate answer with rounding, so it might not be what your teacher wants. The best thing to do is do it yourself again.
False they don't have to be whole numbers. As long as they're greater than 0
Answer:
See below
Step-by-step explanation:
Essentially, we have to replace "quantifier words" like "All", "Every" by the universal quantifier ∀.
a) ∀ dinosaur x, x is extinct.
b) ∀ real number x, x is positive, negative, or zero.
c) ∀ irrational number x, x is not an integer.
d) ∀ logician x, x is not lazy.
e) ∀ integer x, x²≠ 2,147,581,953.
f) ∀ real number x, x²≠ -1.
In a) and b) we replace the words without major changes. In the other statements, we modify the statement using negation. For example, "No irrational numbers are integers." is equivalent to "Every irrational number is not integer".