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Advocard [28]
2 years ago
8

Fiber one bran cereal boasts that it contains 57% of the Daily Value of fiber you need. If 1 serving contains 15 gram of fiber,

how much fiber do you need in one day
Mathematics
1 answer:
Ronch [10]2 years ago
8 0

Answer:

26.3 grams

Step-by-step explanation:

57% of fiber is 15 grams. To find 1% you would divide 15 by 57 which is 0.2631578947. Now multiply 1% by 100 to get 100% fiber. The amount of fiber needed per day is 26.31578947 (the rounded answer is 26.3)

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Answer the following questions for the price-demand equation.
amm1812

Answer:

(A) x = 5,000 - 100·p

(B) R(p) = 5,000·p - 100·p²

(C) The elasticity of demand E(P) = -100·p/x

(D) The demand is elastic when P is larger than 0.01·x

(E) The revenue is decreasing for values of p < 25

(F) The revenue will decrease if P = 20 and the price decreases

(G) The revenue will increase until the price reaches 25

Step-by-step explanation:

The given price demand equation is, p + 0.01·x = 50

(A) The demand, 'x', as a function of price is therefore expressed as follows;

x = (50 - p)/0.01 = 5,000 - 100·p

∴ x = 5,000 - 100·p

(B) The revenue, 'R', as a function of price, R(p) = x·p

p = 50 - 0.01·x

∴ R = R(p) = x·p = x × (50 - 0.01·x) = 50·x - 0.01·x²

The revenue, R = 50·x - 0.01·x²

∴ R(P) = 50 × (5,000 - 100·p) - 0.01 × (5,000 - 100·p)² = 5,000·p - 100·p²

R(P) = 5,000·p - 100·p²

(C) The elasticity of demand E(P) = (dx/dp) × p/x

∴ E(P) = d(5,000 - 100·p)/dp × p/x = -100 × p/x = -100·p/x

E(P) = -100·p/x

(D) The demand is elastic when E(P) > -1

Therefore, we have;

-100·p/x > -1

-p > -0.01·x

p > 0.01·x

The demand is elastic when P is larger than 0.01·x

(E) The revenue is decreasing for the values of 'p', given as follows;

At maximum point, dR/dx = 50 - 0.02·x = 0

∴ x = 50/0.02 = 2,500

p = 50 - 0.01·x = 50 - 0.01 × 2500 = 25

Therefore, the revenue is decreasing for values of p < 25

(F) If the P = 20 and the price decreases, we have;

x = 5,000 - 100·p

∴ x = 5000 - 100 × 20 = 3,000

If the price decreases, the quantity, 'x' increases above 3,000 and the revenue decreases

Therefore the revenue will decrease if P = 20 and the price decreases

(G) If p = 30, we have;

x = 5000 - 100 × 30 = 2,000

Therefore, the revenue is increasing until p = 25

Therefore, if p = 30 and the price decreases, the revenue will increase until the price reaches 25

6 0
2 years ago
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