Emily spent 1/2 of her money at the grocery store.Then, she spent 1/2 of what was left at the bakery. Next, at the music store, she spent 1/2 of what is left on a CD that was on sale. She spent the remainder $6.00 on lunch at the diner. find how much money Emily start with?

Answers

Answer 1

Answer: I believe the answer is $48 because 6 * 2 is 12 and 12 * 2 is 24 and 24 * 2 is 48, thus 48$. Please feel free to check my work, though.

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Is 1/x + 3y = -5 a function ?

Answers

We can say that a relationship between two variables is a function if, for every input, we get one and only one unique output. If we want to talk about y as a function of x in this problem, we want to make sure that every x has only one y associated with it. We can do this by solving our equation for x and seeing whether we can have more than one y that satisfies that equation. Here, I'll do the algebra and briefly explain my steps:

Multiply either side by x to cancel the denominator in 1/x:

$x((1)/(x)+3y)=x(-5)\n1+3xy=-5x$

Add 5x to either side to collect all of the x terms on one side, and subtract 1 to get all of the constants on one side:

$(1+3xy)+5x-1=-5x+5x-1\n3xy+5x=-1$

Factor an x out of the left side of the equation:

$x(3y+5)=-1$

Divide either side by 3y + 5 to get the x by itself:

$(x(3y+5))/(3y+5)=(-1)/(3y+5) \n\nx=(-1)/(3y+5)$

For every x we pick, only one y can satisfy the above equation, so we can say that yes, $(1)/(x)+3y=-5$ is a function.

Tim had 4 paper fraction pieces, each of thirds, fourths, sixths, and twelfths. He did not have enough pieces to show both 2/4 and 1/3 as equivalent fractions with the same denominator. How could he form enough pieces by making 1 cut with a scissors

Answers

I think that poor boy Tim has enough pieces(1/3, 1/4, 1/6, 1/12) and does not need to cut anything.

1/3 + 1/6=4/12 + 2/12=6/12=2/4

1/4 + 1/12=3/12 + 1/12= 4/12= 1/3or 1/4

Wich box is greater, a 1.5- pound box of raisins or a 650-gram box of rocks?

Answers

❅☃ 1.5 pounds.
❅☃ 1.5 pounds weighs 680.389 grams.
❅☃ Leaving it higher then the 650 gram box of rocks.

The first step of this is to convert them both to the same unit. since 1 pound is equal to .45 kg, .45*1.5=.68 kg. now we need to convert kg to grams, when we do this we get 680 grams of raisins and 650 grams of rocks. we can obviously see that the box of raisins is heavier.

2. On the spinner below, what is P(multiple of 2)