Answer:
A. 3.2307692308 batches of Muffins
B. 16 1/4 cups of flour
Step-by-step explanation:
Lauren is making muffins. Her muffin recipe calls for 3 1 −4 cups of flour. She has 10 1 −2 cups of flour.
A. Explain a method for determining the number of batches of the muffin recipe Lauren can make. Then use your method to find the number of batches she can make.
Her muffin recipe calls for 3 1 −4 cups of flour. She has 10 1 −2 cups of flour.
3 1/4 cups of flour = 1 batch of Muffin recipe
10 1/2 cups of flour = x
3 1/4 × x = 10 1/2 × 1
x = 10 1/2 ÷ 3 1/4
x = 21/2 ÷ 13/4
x = 21/2 × 4/13
x = 42/13
x = 3.2307692308 batches of Muffins
B. If Lauren plans to make 5 batches of the muffin recipe, use what you know about operating with rational numbers to predict the amount of flour she needs. Justify your prediction.
3 1/4 cups of flour = 1 batch of Muffin recipe
Hence,
1 batch = 3 1/4 cups of flour
5 batches = x
Cross Multiply
x = 5 × 3 1/4 cups of flour
x = 5 × 13/4
x = 65/4
x = 16 1/4 cups of flour
"<span>5 to the negative 4th power over 5 to the 3rd</span>" translates to
5⁻⁴ / 5³
So you can just combine exponents.
5⁻⁴ / 5³ = 5⁻⁴ ⁻ ³ = 5⁻⁷ = 1/5⁷
Final answer: 1/5⁷
Answer:
All three.
Step-by-step explanation:
All three of these ratios are equivalent to 15:5. Here's how:
Let's look at the first ratio, 9:3. Did you notice something common? 3 x 3 = 9. 9/3 = 3. 5 x 3 = 15. 15/3 = 5. Both of these numbers are divisible by 3, so these ratios are equivalent.
Second. 6:2. 2 x 3 = 6. 6/3 = 2. 5 x 3 = 15. 15/3 = 5. See the similarity? The same applies to the next problem, number three, although it does slightly differentiate.
Third, 3:1. See, here, since the ratio is smaller than the problem, we can't multiply, since this ratio is smaller than the original number. But, it's still the same thing. A ratio is a number that compares a value to another value. This means that 3:1 is 3 compared to one. Now, let me clarify. 15:5. 3:1. These are the exact same values, except they are just written in a different form, and simplified. Since 5 x 3 = 15, we know that we can divide 15 evenly by 5, which makes it 3, and divide 5 evenly by 5, which equals one. So here we have our answer for the third problem. 5:1.
Ratios are basically division, except simplified. Every single ratio problem works this way. Once you get the hang of it, it's immensely easy. Hope this helped!
Answer: -5
Step-by-step explanation: 2 + -11 = -9 and subtract -4 from it since it’s the sum of 2 + -6. -9 - -4 is -9 + 4 so -5
