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Ainat [17]
3 years ago
8

Harry is bundling magazines to recycle. He notices that 4 magazines weigh 5/8 pounds in​ all and that the magazines all weigh th

e same amount. What is the unit rate for pounds per​ magazine?
Mathematics
1 answer:
noname [10]3 years ago
7 0

Answer:one magazine will weigh 0.256 pounds.

Step-by-step explanation:4 magazine =5/8pounds(0.625)

Therefore 1 magazine will weigh 0.625÷4 = 0.156 pound per magazine.

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What value of b will cause the system to have an infinite number of solutions?
irga5000 [103]

b must be equal to -6  for infinitely many solutions for system of equations y = 6x + b and -3 x+\frac{1}{2} y=-3

<u>Solution: </u>

Need to calculate value of b so that given system of equations have an infinite number of solutions

\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}

Let us bring the equations in same form for sake of simplicity in comparison

\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}

Now we have two equations  

\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}

Let us first see what is requirement for system of equations have an infinite number of solutions

If  a_{1} x+b_{1} y+c_{1}=0 and a_{2} x+b_{2} y+c_{2}=0 are two equation  

\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}} then the given system of equation has no infinitely many solutions.

In our case,

\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}

 As for infinitely many solutions \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}

\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}

Hence b must be equal to -6 for infinitely many solutions for system of equations y = 6x + b and  -3 x+\frac{1}{2} y=-3

8 0
3 years ago
In the 2011 New York City Marathon, 29,867 men finished the race, and 16,928 women finished the race. Each finisher was given a
Andreas93 [3]
30,000 shirts for the men and 17,000 shirts for the women

6 0
3 years ago
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stellarik [79]

Answer:

$28.68

Step-by-step explanation:

57.24+64.08

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barxatty [35]

Answer:

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1 year ago
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What percentage of the audience from the 16-25 age group gave the movie a poor rating? 6.19% 10.00% 25.34% 15.70% 16.22%
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We have to find what percent of the audience from the 16-25 age group gave the movie poor rating. There were 113 viewers from this group. There were 7 of them that gave the movie poor rating. We will use the proportion: 113 / 7 = 100% / x% . Then we will cross multiply: 113 x = 700; x = 700 : 113; x = 6.19%. Answer: A ) 6.19%. 

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2 years ago
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