if you know the order from least to greatest of 5 negative rational numbers how can you use the information to order the absolute value of those numbers from least greatest
Answers
Consider the ordering
... -2 < -1
Now consider the ordering of their absolute values:
... 1 < 2
_____
Hopefully, you see that changing the sign reflects the sequence across the origin, so that the ordering is reversed when the signs are changed.
Related Questions
Write in standard form 80010000
Quarterly withdrawls of $650 for 6 years; interest rate is 4.5% compounded quarterly.Find the amount necessary to fund the given withdrawls.
2. In an industrial training program, students have been averaging about 64 points on a standardized test. The lecture system was replaced by teaching machines with a lab instructor. There was some doubt as to whether the scores would decrease, increase, or stay the same. A sample of n = 60 students using the teaching machines was tested, resulting in a mean of 68 and a standard deviation of 12. Perform a hypothesis test to see if scores would decrease, increase, or stay the same. Use α = 0.05. Be sure to:1. State your hypotheses. 2. Find the value of the Test Statistic. 3. Find the p-value 4. State your decision (Reject or not) 5. State your conclusion.
Solve this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7
Answers
Answer:
The value of l = 3.64
Step-by-step explanation:
Consider the provided information.
μ=3.8 and σ=0.2mmol/l and n=4
As we know
We have given α = 0.05
So by the standard normal table:
Compute
Hence, the value of l = 3.64
Solve the inequality.
Answers
Answer:
y > 9
Step-by-step explanation:
Given inequality:
To solve the given inequality, we need to isolate y on one side of the equation.
Begin by multiplying both sides of the inequality by 3 to eliminate the fraction on the right side:
Now, divide both sides of the inequality by -8 to isolate y. Remember to reverse the inequality sign, as we are dividing by a negative number.
Therefore, the solution is:
The solution of the equation is .
(Type the value of x.)
Answers
Answer:
x=14/4
Step-by-step explanation:
2x-4x+12 = -5+2x+3
-2x+12 = -2+2x
-2x-2x = -12-2
-4x=-14
x=-14/-4
x=14/4
Use rules of inference to prove that the following conclusion follows from these hypotheses:
C : ∃x (p(x) ∧ r(x))
Clearly label the inference rules used at every step of your proof.
2. Consider the following hypotheses:
H1 : ∀x (¬C(x) → ¬A(x)) H2 : ∀x (A(x) → ∀y B(y)) H3 : ∃x A(x)
Use rules of inference to prove that the following conclusion follows from these hypotheses:
C : ∃x (B(x) ∧ C(x))
Clearly label the inference rules used at every step of your proof.
3. Consider the following predicate quantified formula:
∃x ∀y (P (x, y) ↔ ¬P (y, y))
Prove the unsatisfiability of this formula using rules of inference.
Answers
Answer:
See deductions below
Step-by-step explanation:
1)
a) p(y)∧q(y) for some y (Existencial instantiation to H1)
b) q(y) for some y (Simplification of a))
c) q(y) → r(y) for all y (Universal instatiation to H2)
d) r(y) for some y (Modus Ponens using b and c)
e) p(y) for some y (Simplification of a)
f) p(y)∧r(y) for some y (Conjunction of d) and e))
g) ∃x (p(x) ∧ r(x)) (Existencial generalization of f)
2)
a) ¬C(x) → ¬A(x) for all x (Universal instatiation of H1)
b) A(x) for some x (Existencial instatiation of H3)
c) ¬(¬C(x)) for some x (Modus Tollens using a and b)
d) C(x) for some x (Double negation of c)
e) A(x) → ∀y B(y) for all x (Universal instantiation of H2)
f) ∀y B(y) (Modus ponens using b and e)
g) B(y) for all y (Universal instantiation of f)
h) B(x)∧C(x) for some x (Conjunction of g and d, selecting y=x on g)
i) ∃x (B(x) ∧ C(x)) (Existencial generalization of h)
3) We will prove that this formula leads to a contradiction.
a) ∀y (P (x, y) ↔ ¬P (y, y)) for some x (Existencial instatiation of hypothesis)
b) P (x, y) ↔ ¬P (y, y) for some x, and for all y (Universal instantiation of a)
c) P (x, x) ↔ ¬P (x, x) (Take y=x in b)
But c) is a contradiction (for example, using truth tables). Hence the formula is not satisfiable.
Answers
Answer:
35 degrees
Step-by-step explanation:
Final answer:
Points A', B', and C' are the images of 180-degree rotations of points A, B, and C, respectively, around point O. These rotations involve equal angles but different arc lengths due to the varying distances from the center of rotation.
Explanation:
When objects rotate about some axis, each point in the object follows a circular path. In the given question, points A', B', and C' are the images of 180-degree rotations of points A, B, and C, respectively, around point O. These rotations are represented by the angles AO, BO, and CO.
Since all three rotations are 180 degrees, the angles AO, BO, and CO are equal. However, the arc lengths As2, Bs2, and Cs2 are not equal because the points A', B', and C' move through greater arc lengths due to their greater distance from the center of rotation.
Therefore, the rotation of points A, B, and C results in the images A', B', and C' moving through the same angle AO, but covering different arc lengths As2, Bs2, and Cs2 due to their varying distances from the center of rotation.
Learn more about Rotations here:
#SPJ2
Answers
9514 1404 393
Answer:
560 m
Step-by-step explanation:
Jill's distance is given as 250 m.
John's distance can be computed as ...
distance = speed × time = (70 m/min)(3 min) = 210 m
Suzy's distance is given as 100 m.
Then the total distance is ...
250 m + 210 m + 100 m = 560 m
The distance traveled is 560 m in this relay.