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Marina86 [1]
3 years ago
14

Justin is starting his own laundry business. Justin thinks he will do a better job than his competitors, so he thinks he can cha

rge $15.16 per hour. If he knows he will only be able to work 50 hours per week, how much money will he earn each week?
Mathematics
1 answer:
joja [24]3 years ago
7 0

Answer:

$758 per week

Step-by-step explanation:

15.16 x 50 = 758

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Prove the formula that:
azamat

Step-by-step explanation:

Given: [∀x(L(x) → A(x))] →

[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

To prove, we shall follow a proof by contradiction. We shall include the negation of the conclusion for

arguments. Since with just premise, deriving the conclusion is not possible, we have chosen this proof

technique.

Consider ∀x(L(x) → A(x)) ∧ ¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

We need to show that the above expression is unsatisfiable (False).

¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

∃x¬((L(x) ∧ ∃y(L(y) ∧ H(x, y))) → ∃y(A(y) ∧ H(x, y)))

∃x((L(x) ∧ ∃y(L(y) ∧ H(x, y))) ∧ ¬(∃y(A(y) ∧ H(x, y))))

E.I with respect to x,

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ ¬(∃y(A(y) ∧ H(a, y))), for some a

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ (∀y(¬A(y) ∧ ¬H(a, y)))

E.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b))) ∧ (∀y(¬A(y) ∧ ¬H(a, y))), for some b

U.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Since P ∧ Q is P, drop L(a) from the above expression.

(L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Apply distribution

(L(b) ∧ H(a, b) ∧ ¬A(b)) ∨ (L(b) ∧ H(a, b) ∧ ¬H(a, b))

Note: P ∧ ¬P is false. P ∧ f alse is P. Therefore, the above expression is simplified to

(L(b) ∧ H(a, b) ∧ ¬A(b))

U.I of ∀x(L(x) → A(x)) gives L(b) → A(b). The contrapositive of this is ¬A(b) → ¬L(b). Replace

¬A(b) in the above expression with ¬L(b). Thus, we get,

(L(b) ∧ H(a, b) ∧ ¬L(b)), this is again false.

This shows that our assumption that the conclusion is false is wrong. Therefore, the conclusion follows

from the premise.

15

5 0
3 years ago
A. what do you know mass =579 g, volume = 30 cm3 B. what do you want to find Density
Kipish [7]
Density= 19.3 because the formula of density is mass divided by volume <span />
3 0
3 years ago
Read 2 more answers
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
pantera1 [17]

Answer:

b

Step-by-step explanation:

8 0
2 years ago
Answer need help plz
satela [25.4K]
MAE - 48 = 36 x 2
mAE - 48 = 72
mAE = 120

Answer
120
4 0
3 years ago
Read 2 more answers
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP
Alenkasestr [34]

Answer:

(0, 6)

explanation:

  • original coordinates of C: (5, -6)

if reflected over x-axis, then use the formula: (x,y) → (x, -y)

  • new coordinates: (5, 6)

then if translated -5 horizontally, there will be change in x axis

  • new coordinates: (5-5, 6) → (0, 6)
3 0
2 years ago
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