Alice purchased 4 1⁄2 kilograms of olive oil for $27. What is the price per kilogram?

Answer:

A. Combining one pound of pistachios with one pound of almonds costs $20.

C. Decreasing the almond quantity by one pound leads to a total price of $40.

E. The price p (in dollars) per pound of pistachios is represented by the equation 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let:

x = cost per pound of pistachios

y = cost per pound of almonds

We know that

x = y + 4 (Equation A)

2x + 3y = 48 (Equation B)

Substitute x from Equation A into Equation B:

2(y + 4) + 3y = 48

2y + 8 + 3y = 48

5y = 48 – 8

y = 8

Find x:

x = 8 + 4 = 12

Therefore, pistachios cost $12 per pound and almonds cost $8 per pound.

Verify the statements:

Case A) One pound of each equals $20.

True, since 12 + 8 = 20.

Case B) Pistachios cost twice as much as almonds.

False, because 2 × 8 = $16 ≠ $12.

Case C) Reducing almond pounds by 1 yields $40 total.

True, as 2(12) + 2(8) = 24 +16 = 40.

Case D) The almond cost modeled by 2(a – 4) + 3a = 48.

False; it should be 2(a + 4) + 3a = 48.

Case E) The pistachio cost modeled by 2p + 3(p – 4) = 48.

True, since p = a + 4 implies a = p – 4.

Answer:

     The angles m∠Q and m∠S together equal 90°

Step-by-step explanation:

A right angle measures 90°.

The total measure of angles in a triangle sums to 180°.

This gives us:

m∠Q + m∠S + ∠R = 180°

m∠Q + m∠S + 90° = 180°

Rearranging yields:

m∠Q + m∠S = 180° - 90°

m∠Q + m∠S = 90°

x:200

x/200 =.2121212121...

200(x/200) = 200(.2121212121...)

x = 42.4242...

The expectation is that a player would achieve 42 hits over 200 at-bats.

Response:

n = 0 or 3

Detailed explanation:

2n² - 5n + 2

2n² - 4n - n + 2

2n(n - 2) -1(n - 2)

(n - 2)(2n - 1)

A prime number is defined as one that can only be divided by itself and 1

Setting n-2 = 1 gives n = 3

Setting 2n-1 = 1 gives n = 0