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KengaRu [80]
3 years ago
12

$12.95 for 3 pounds of nuts or $21.45 for 5 pounds of nuts

Mathematics
1 answer:
Zarrin [17]3 years ago
8 0

First, find the base rate of both of the numerals, to do this simply divide the price by the number of units.

12.95 divided by 3 is 4.32 ( rounded to nearest cent )

21.45 divided by 5 is 4.29 ( rounded to nearest cent )

So, if you want the better deal ( which is what I've interpreted ), then 5 pounds of nuts is the better deal <u>BY</u> 3 cents.

Hope this helps, if not, comment below please!!!!

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charle [14.2K]

Answer:

<em>Correct choice: B</em>

Step-by-step explanation:

<u>Equation Solving</u>

The area of a trapezoid with height h and bases b1 and b2 is given by:

\displaystyle A=\frac{1}{2}h(b_1+b_2)

We must solve this formula for h.

First, multiply by 2 to eliminate denominators:

\displaystyle 2A=h(b_1+b_2)

Now, divide by b1+b2:

\displaystyle \frac{2A}{b_1+b_2}=h

Swapping sides:

\displaystyle h=\frac{2A}{b_1+b_2}

Correct choice: B

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3 years ago
At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those c
grandymaker [24]

Answer:

a.)

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b.)

P(B) = P( A₁ ∩ B )  + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

P(B) = 0.345

c.)

For regular gas:

P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

Step-by-step explanation:

We are given the following information

40% of the customers use regular gas (A2)

P(A₁) = 0.40

35% use plus gas (A2)

P(A₂) = 0.35

25% use premium (A3)

P(A₃) = 0.25

Of those customers using regular gas, only 20% fill their tanks (event B).

P(B | A₁) = 0.20

Of those customers using plus, 40% fill their tanks

P(B | A₂) = 0.40

Whereas of those using premium, 50% fill their tanks.

P(B | A₃) = 0.5

a) What is the probability that the next customer will request plus gas and fill their tank?

We are asked to find P(A₂ ∩ B) = ?

Recall that Multiplicative law of probability is given by

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b) What is the probability that the next customer fills the tank?

We are asked to find P(B) = ?

P(B) = P( A₁ ∩ B )  + P( A₂ ∩ B ) + P( A₃ ∩ B )

P( A₂ ∩ B ) is already calculated, we need to calculate

P( A₁ ∩ B ) and P( A₃ ∩ B )

So,

P( A₁ ∩ B ) = P(B | A₁) × P(A₁)

P( A₁ ∩ B ) = 0.20 × 0.40

P( A₁ ∩ B ) = 0.08

P( A₃ ∩ B ) = P(B | A₃) × P(A₃)

P( A₃ ∩ B ) = 0.50 × 0.25

P( A₃ ∩ B ) = 0.125

Finally,

P(B) = P( A₁ ∩ B )  + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

P(B) = 0.345

c) If the next customer fills the tank, what is the probability that the regular gas is requested? Plus? Premium

For regular gas:

P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

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