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allsm [11]
3 months ago
11

You are volunteering to help with the soccer team's Valentine's Day fundraiser. Each 16-ounce bag of nuts the team sold must inc

lude at least 60% chocolate-covered nuts inside.
However, instead of receiving a shipment of separated plain nuts and chocolate nuts, they delivered two large containers of mixed nuts. The first says it is 50/50 plain and chocolate covered. The second contains 80% chocolate-covered nuts.

The team is dismayed, but you come up with a solution. You suggest combining

ounces* of the 50/50 nuts with

ounces* of the 80% chocolate-covered nuts, to create the 60% mixture required for each bag.

*estimate

Then Bob, another student on the team says, "Wait, we promised at least 60%. So if we just do half and half, won't we be giving them at least 60%?"

Bob

correct.
Mathematics
1 answer:
vazorg [7]3 months ago
4 0

Proportionately, if they do half and half of 50% and 80% of the two bags, <u>Bob is correct</u>.

<h3>What is a proportion?</h3>

A proportion is a mathematical measure that compares two variables or numbers.

Proportions can be stated in percentages or ratios, as decimals or fractions.

<h3>Data and Calculations:</h3>

Content of 16-ounce bag of nuts = 60% chocolate-covered nuts

Content of first bag = 50/50 plain and chocolate-covered nuts

Content of second bag = 80% chocolate-covered nuts

A mixture of half of 50% bag with half of 80% bag will result in 65% (50% + 80%)/2.

Thus, since the promise for each 16-ounce bag is for at least 60% chocolate-covered nuts, <u>Bob is correct</u>.

Learn more about proportion at brainly.com/question/870035

#SPJ1

<h3>Question Completion:</h3>

Is Bob correct?

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Answer:

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The two lines, P and Q, are graphed below: Line P is drawn by joining ordered pairs negative 8,15 and 6, negative 12. Line Q is
andreyandreev [35.5K]

Solution:

Keep in mind ,

Equation of line joining two points (a,b) and (p,q) is given by :

     \frac{q-b}{p-a}=\frac{y-b}{x-a}

Equation of line P which is obtained by  joining  (- 8,15) and (6, - 12) is given by:  

\frac{y-15}{x+8}=\frac{-12-15}{6+8}\\\\ 14(y-15)=-27(x+8)\\\\ 14 y -210= -27 x - 216\\\\ 27 x+14 y+6=0

Equation of line Q which is obtained by  joining  (4,16) and (-9, 10) is given by:  

\frac{y-16}{x-4}=\frac{16-10}{4+9}\\\\ 13(y-16)=6(x-4)\\\\ 13 y -208= 6 x - 24\\\\ 6 x-13 y+184=0

Equation of line P and Q are

27 x+14 y+6=0-------(1)× 2

6 x-13 y+184=0-------(2)× 9

54 x + 2 8 y+12=0---(1)

54 x -117 y +1656=0----(2)

(1) - (2)

145 y= 1644

y=11.33,

27 x+14 y+6=0-------(1)×13

6 x-13 y+184=0-------(1)×14

351 x + 182 y + 78=0-----(1)

84 x - 182 y +2576=0----(2)

(1) + (2)

435 x + 2654=0

x = - 6.11

So, solution set is (-6.11, 11.33)

Option (C) is true. (−2, 4), because this point makes both the equations incorrect.


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Answer:

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