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RoseWind [281]
3 years ago
14

A recipe calls for 3 1/2 cups of milk and makes 10 servings. How many cups of milk are needed for 8 servings? (Hint: Set up a pr

oportion, don’t forget to label!)
Mathematics
1 answer:
Aleks [24]3 years ago
3 0

Answer:

2.8 or 2 4/5

Step-by-step explanation:

Here's our proportion of cups of milk to servings

3 1/2:10      For my sake I'm using decimals

3.5:10

Now let's try to get our servings to 1 (a unit rate)

0.35:1         I divided by 10 on each side

We need 8 servings not 1 so let's multiply 8 on each side

2.8:8

In case you want it in fraction form we can do 2 8/10 and simplify it to 4/5 by dividing by 2. Our answer is 2.8 or 2 4/5 cups of milk for 8 servings.

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What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?
grin007 [14]

A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.  

1. Z_{11}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10}\}.

Check:

  • 5\cdot 0=\overline{0};
  • 5\cdot 1=\overline{5};
  • 5\cdot 2=\overline{10};
  • 5\cdot 3=15=\overline{4};
  • 5\cdot 4=20=\overline{9};
  • 5\cdot 5=25=\overline{3};
  • 5\cdot 6=30=\overline{8};
  • 5\cdot 7=35=\overline{2};
  • 5\cdot 8=40=\overline{7};
  • 5\cdot 9=45=\overline{1};
  • 5\cdot 10=50=\overline{6}.

The multiplicative inverse of 5 in Z_{11} is 9.

2.   Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.

Check:

  • 5\cdot 0=\overline{0};
  • 5\cdot 1=\overline{5};
  • 5\cdot 2=\overline{10};
  • 5\cdot 3=15=\overline{3};
  • 5\cdot 4=20=\overline{8};
  • 5\cdot 5=25=\overline{1};
  • 5\cdot 6=30=\overline{6};
  • 5\cdot 7=35=\overline{11};
  • 5\cdot 8=40=\overline{4};
  • 5\cdot 9=45=\overline{9};
  • 5\cdot 10=50=\overline{2};
  • 5\cdot 11=55=\overline{7}.

The multiplicative inverse of 5 in Z_{12} is 5.

3.  Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.

Check:

  • 5\cdot 0=\overline{0};
  • 5\cdot 1=\overline{5};
  • 5\cdot 2=\overline{10};
  • 5\cdot 3=15=\overline{2};
  • 5\cdot 4=20=\overline{7};
  • 5\cdot 5=25=\overline{12};
  • 5\cdot 6=30=\overline{4};
  • 5\cdot 7=35=\overline{9};
  • 5\cdot 8=40=\overline{1};
  • 5\cdot 9=45=\overline{6};
  • 5\cdot 10=50=\overline{11};
  • 5\cdot 11=55=\overline{3};
  • 5\cdot 12=60=\overline{8}.

The multiplicative inverse of 5 in Z_{13} is 8.

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Ainat [17]
Hiya.
It would require 4 blocks, so it’s would be C.
5 0
3 years ago
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