MATHEMATICS COLLEGE

5/3 x − 10 = 1/3 x
What is the value of x?

Answers

Answer 1

Answer:

Answer:

X=1.66666667 hope this hepled

Step-by-step explanation:

Answer 2

Answer: by simplifying both sides of the equation, then isolating the variable.
X =7.5

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Answers

Answers:

9/2

5/1

16/5

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1 Which expression is equivalent to 1/3y?• 1/3(y+12)-12
1/6y+1/3(y+3
1/6y+1/6(y+12)-2
1/3y+1/3(6-y)

Answers

Answer:

1/6y+1/6(y+12)- 2

Step-by-step explanation:

Distribute $(1)/(6)$ through the parentheses : $(1)/(6)$ y + $(1)/(6)$ y + 2 - 2

Remove the opposites and calculate ( since two opposites add up to zero remove them from the expression) : $(1)/(6)$ y + $(1)/(6)$ y

Calculate the sum : $(1)/(3)$ y

Solution : $(1)/(3)$ y

Answer:

The answer is 1/6y+1/6(y+12)-2

Let S(x, y) denote the statement "x has seen y" and D denote the set of all students in our class and M be the set of all movies.a. Express the following English sentence as a quantified proposition using the definitions above:
"For every movie there is a pair of students in our class who have both seen it." Hint: Use three quantifiers - one for the movie and two for a pair of students.

b. Negate the quantified proposition you wrote for part (a) (i.e., place a "Â¬" in front of it). Use de Morganâs law for quantifiers to move the negation inside the quantifiers.
c. Translate you answer for part (b) back to plain English.

Answers

Answer:

Step-by-step explanation:

a) Recall the quantifiers $\forall, \exists$ .

Then, we can translate the proposition as follows

$\forall m \in M \exists x \in D \exists y \in D S(x,m)\land S(y,m)$

b) Recall that an expression of the form $\exists x P(x)$ its negation is of the form $\forall x \neg P(x)$ which means that it is not true that for all elements the proposition P holds. Equivalently, we have that the negation of an expression of the form $\forall x P(x)$ is $\exists x \neg P(x)$ which means that there is at least one x such that P doesn't hold. Using this, we get the following

$\neg(\forall m \in M \exists x \in D \exists y \in D S(x,m)\land S(y,m))= \exists m \in M \neg (\exists x \in D \exists y \in D S(x,m)\land S(y,m))= \exists m \in M \forall x \in D \neg (\exists y \in D S(x,m)\land S(y,m))= \exists m \in M \forall x \in D \forall y \in D \neg(S(x,m)\land S(y,m))$

By De Morgan's law, we have that $\neg (A \land B) = \neg A \lor \neg B$

So, the final statement is

$\exists m \in M \forall x \in D \forall y \in D \neg S(x,m) \lor \neg S(y,m)$

This statement means: There is a movie that for every pair of students, at least one of the students hasn't seen the movie yet.

Final answer:

The quantified proposition expresses that for every movie, there is a pair of students who have both seen it. The negated proposition states that there exists a movie that no pair of students have both seen.

Explanation:

a. The English sentence can be expressed as the quantified proposition: ∀m ∈ M, ∃ (s1, s2) ∈ D^2, S(s1,m) ∧ S(s2,m)
b. The negation of the quantified proposition is: ∃m ∈ M, ∀(s1, s2) ∈ D^2, ¬(S(s1,m) ∧ S(s2,m))
c. The translation of the negated proposition is: There exists a movie that no pair of students in our class have both seen.

Learn more about Quantified proposition here:

brainly.com/question/35127626

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HURRY PLEASE!A new health drink has 170% of the recommended daily allowance (RDA) for a certain vitamin. The
RDA for this vitamin is 40 mg. How many milligrams of the vitamin are in the drink?
There are mg of the vitamin in the drink.

Answers

Answer:

it is 68

Step-by-step explanation:

Consider a home mortgage of $250,000 at a fixed APR of 4.5% for 25 years.a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount paid, what percentage is paid toward the principal and what
percentage is paid for interest.
a. The monthly payment is $ 1389.58.
(Do not round until the final answer. Then round to the nearest cent as needed.)
b. The total amount paid over the term of the loan is $
(Round to the nearest cent as needed.)
ANSWER ALL PARTS PLEASE (A,B,C)