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Mekhanik [1.2K]
3 years ago
15

Julie makes and sells shirts for children and adults. She sells the shirts for $20 per unit. Material for

Mathematics
1 answer:
Alisiya [41]3 years ago
6 0

Answer:

Julie need to sell at least 45 shirts to break even.

Step-by-step explanation:

The  selling cost of each shirt = $ 20

Cost of each shirt = $6

The fixed cost per month = $420

Number of shirts she can make = 80

Hence, the <u>cost of making 80 shirts</u> =  80 x $6  = $480

So, her total capital investment of the month

= Cost of shirts made + Fixed cost = $420 + $480 = $900

Now, let us assume she sell k number of shirts.

⇒ $20 x k  = $900

or, k = 900 / 20 = 45

or, k = 45

Hence, Julie need to sell at least 45 shirts to break even.

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Given that A and B are true and X and Y are false, determine the truth value of the following proposition: ~[(A ⊃ Y) v ~(X ⊃ B)]
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Answer:

The value of the proposition is FALSE

Step-by-step explanation:

~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ ~X) v (B ⊃ X)]

Let's start with the smallest part: ~X. The symbol ~ is negation when X is true with the negation is false and vice-versa. In this case, ~X is true (T)

~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ T) v (B ⊃ X)]

Now the parts inside parenthesis:  (A ⊃ Y),(X ⊃ B),(A ≡ T) and (B ⊃ X). The symbol ⊃ is the conditional and A ⊃ Y is false when Y is false and A is true, in any other case is true. The symbol ≡ is the biconditional and A ≡ Y is true when both A and Y are true or when both are false.

(A ⊃ Y) is False (F)

(X ⊃ B) is True (T)

(A ≡ T) is True (T)

(B ⊃ X) is False (F)

~[(F) v ~(T)] ⋅ [~(T) v (F)]

The two negations inside the brackets must be taken into account:

~[(F) v F] ⋅ [F v (F)]

The symbol left inside the brackets v is the disjunction, and A v Y is false only  with both are false. F v (F) is False.

~[F] ⋅ [F]

Again considerating the negation:

T⋅ [F]

Finally, the symbol ⋅ is the conjunction, and A v Y is true only with both are true.

T⋅ [F] is False.

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Hailey, Megan, and Bailey have saved $458 for a summer trip to the beach. Hailey has saved $167. Megan has saved at least $152,
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Let H = Hailey, M = Megan, B = Bailey

H + M + B = 458
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