All categories

2 years ago

A cookie recipe calls for 3 cups of sugar and yields 24 cookies how much sugar will be needed to make 3 dozen cookies

Mathematics

1 answer:

Sindrei [870]2 years ago

5 0

Answer:4.5 cups of sugar

Step-by-step explanation:

Okay so 24 cookies is 2 dozen

1 cup of sugar would be used for every 8 cookies

3 dozen is equal to 36 cookies

36/8=4.5 so you would need 4.5 cups of sugar

You might be interested in

Ples help me find slant assemtotes

FrozenT [24]

A polynomial asymptote is a function $p(x)$ such that

$\displaystyle\lim_{x\to\pm\infty}(f(x)-p(x))=0$

$(y+1)^2=4xy\implies y(x)=2x-1\pm2\sqrt{x^2-x}$

Since this equation defines a hyperbola, we expect the asymptotes to be lines of the form $p(x)=ax+b$ .

Ignore the negative root (we don't need it). If $y=2x-1+2\sqrt{x^2-x}$ , then we want to find constants $a,b$ such that

$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

We have

$\sqrt{x^2-x}=\sqrt{x^2}\sqrt{1-\dfrac1x}$
$\sqrt{x^2-x}=|x|\sqrt{1-\dfrac1x}$
$\sqrt{x^2-x}=x\sqrt{1-\dfrac1x}$

since $x\to\infty$ forces us to have $x>0$ . And as $x\to\infty$ , the $\dfrac1x$ term is "negligible", so really $\sqrt{x^2-x}\approx x$ . We can then treat the limand like

$2x-1+2x-ax-b=(4-a)x-(b+1)$

which tells us that we would choose $a=4$ . You might be tempted to think $b=-1$ , but that won't be right, and that has to do with how we wrote off the "negligible" term. To find the actual value of $b$ , we have to solve for it in the following limit.

$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-4x-b)=0$

$\displaystyle\lim_{x\to\infty}(\sqrt{x^2-x}-x)=\frac{b+1}2$

We write

$(\sqrt{x^2-x}-x)\cdot\dfrac{\sqrt{x^2-x}+x}{\sqrt{x^2-x}+x}=\dfrac{(x^2-x)-x^2}{\sqrt{x^2-x}+x}=-\dfrac x{x\sqrt{1-\frac1x}+x}=-\dfrac1{\sqrt{1-\frac1x}+1}$

Now as $x\to\infty$ , we see this expression approaching $-\dfrac12$ , so that

$-\dfrac12=\dfrac{b+1}2\implies b=-2$

So one asymptote of the hyperbola is the line $y=4x-2$ .

The other asymptote is obtained similarly by examining the limit as $x\to-\infty$ .

$\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

$\displaystyle\lim_{x\to-\infty}(2x-2x\sqrt{1-\frac1x}-ax-(b+1))=0$

Reduce the "negligible" term to get

$\displaystyle\lim_{x\to-\infty}(-ax-(b+1))=0$

Now we take $a=0$ , and again we're careful to not pick $b=-1$ .

$\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-b)=0$

$\displaystyle\lim_{x\to-\infty}(x+\sqrt{x^2-x})=\frac{b+1}2$

$(x+\sqrt{x^2-x})\cdot\dfrac{x-\sqrt{x^2-x}}{x-\sqrt{x^2-x}}=\dfrac{x^2-(x^2-x)}{x-\sqrt{x^2-x}}=\dfrac
 x{x-(-x)\sqrt{1-\frac1x}}=\dfrac1{1+\sqrt{1-\frac1x}}$

This time the limit is $\dfrac12$ , so

$\dfrac12=\dfrac{b+1}2\implies b=0$

which means the other asymptote is the line $y=0$ .

4 0

3 years ago

Your friend is willing to pay no more than $17.000 on aneu cor.

belka [17]

Answer:

With rare exceptions, cars decrease in value with age. Depending on other factors, like accidents, repairs, or other damage, the value of a car may decrease even faster. If you borrowed money to buy a car, you might owe more on your car loan than its current value. When that happens, you have negative equity in the car. Some car dealers say you won’t be responsible for the remaining balance on your old car loan when you trade in your old car. But that might not be true. Dealers sometimes just roll over the negative equity into your new car loan, so you still end up paying it.

Step-by-step explanation:

Say you want to trade in your car for a newer model.

Your loan payoff is $18,000

Your car is worth $15,000

You have negative equity of $3,000. That must be paid if you want to trade in your vehicle. If the dealer promises to pay off the $3,000, it shouldn’t be included in your new loan.

But some dealers

add that $3,000 to the loan for your new car

subtract the amount from your down payment

or do both

5 0

3 years ago

I Need help!!! please??

gladu [14]

Answer:

-25/12

Step-by-step explanation:

Hope this helps

3 0

2 years ago

Ryan has 25 tiles and 12% of them are green. how many tiles are green

Lady_Fox [76]

Answer:

208.33. this is it your welcome

6 0

3 years ago

In one month, Claudia rides her favorite bike trail 12 times. She travels a total distance of 1182 km. What is the length of Cla

kati45 [8]

The length of the trail is 98.5 KM, all you need to do is divide the total distance by the number of times she went on it.

4 0

3 years ago

Read 2 more answers