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3 years ago

a tram moved downward 15 meters in 5 seconds at a constant rate. what was the change in the team's elevation each second?

Mathematics

1 answer:

Sergio [31]3 years ago

4 0

Answer: 3 meters downward per second

Step-by-step explanation:

If it moved downward 15 meters for every 5 seconds and to find the change in the elevation each second then divide the meters by 5.

15/5 = 3

3 meters per second

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3 years ago

1. Consider the following hypotheses:

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Answer:

See deductions below

Step-by-step explanation:

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)

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.

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b) P (x, y) ↔ ¬P (y, y) for some x, and for all y (Universal instantiation of a)

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3 years ago

Mary is rolling a standard six-sided die and spinning on a spinner with the number 1-8.

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Answer:

a) Dice and spinner are different objects, with no relation between themselves, and thus her dice rolls and spinning outcomes are independent.

b) $\frac{1}{48}$ probability of her rolling a 4 and spinning an 8.

c) $\frac{1}{8}$ probability of her rolling an even number and spinning a number less than 3.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

A) Are her dice rolls and spinning outcomes independent or dependent?

Dice and spinner are different objects, with no relation between themselves, and thus her dice rolls and spinning outcomes are independent.

B) What is the probability of her rolling a 4 and spinning an 8?

Since the events are independent, we find each separate probability and multiply them.

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One side out of 6 on the dice. So

$P(A) = \frac{1}{6}$

Probability of spinning an 8:

One side out of 8 on the spinner. So

$P(B) = \frac{1}{8}$

Probability of rolling a 4 and spinning an 8:

$P(A \cap B) = P(A)P(B) = \frac{1}{6} \times \frac{1}{8} = \frac{1}{48}$

$\frac{1}{48}$ probability of her rolling a 4 and spinning an 8.

C) What is the probability of her rolling an even number and spinning a number less than 3?

Since the events are independent, we find each separate probability and multiply them.

Probability of rolling an even number:

2, 4 or 6(3 sides out of 6). So

$P(A) = \frac{3}{6} = \frac{1}{2}$

Probability of spinning a number less than 3:

Two numbers(1 or 2) out of 8 on the spinner. So

$P(B) = \frac{2}{8} = \frac{1}{4}$

Probability of rolling an even number and spinning a number less than 3:

$P(A \cap B) = P(A)P(B) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$

$\frac{1}{8}$ probability of her rolling an even number and spinning a number less than 3.

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Answer:

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a tram moved downward 15 meters in 5 seconds at a constant rate. what was the change in the team's elevation each second?​

a tram moved downward 15 meters in 5 seconds at a constant rate. what was the change in the team's elevation each second?