Mathematics, 15.10.2020 08:01 Weser17

For Anthony's birthday, his mother is making cupcakes for his 8 friends at his daycare. The recipe calls for 3 1/3 cups of flour. This recipe makes 2 1/2 dozen cupcakes. Anthony's mother has only 1 cup of flour. Is there enough flour for each of his friends to get a cupcake?

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Answer from: Rayinz9174

Anthony mother's has enough flour for each of Anthony's friends to get a cupcake.

Step-by-step explanation:

Let suppose that Anthony and his friend will receive at least one cupcake, which means that Anthony's mother should make at least 9 cupcakes ( $\frac{3}{4}$ dozens).

From statement we notice that quantity of cupcakes is directly proportional to the quantity of flour.

According to the recipe, the required amount of flour and cupcakes are, respectively:

Flour

$3\,\frac{1}{3}\,cups = 3 \,cups +\frac{1}{3}\,cups = \frac{10}{3}\,cups$

Cupcakes

$2\,\frac{1}{2}\,dozens = 2\,dozens +\frac{1}{2}\,dozens = \frac{5}{2}\,dozens$

If Anthony's mother has 1 cup of flour at her disposal, the amount of cupcakes is obtained by simple rule of three:

$x = \frac{5}{2}\,dozen\times\frac{1\,cup}{\frac{10}{3}\,cups }$

$x = \frac{3}{4}\,dozen$

In a nutshell, Anthony mother's has enough flour for each of Anthony's friends to get a cupcake.

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answer from: Quest

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

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For Anthony's birthday, his mother is making cupcakes for his 8 friends at his daycare. The recipe c...