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4 years ago

Determine which system below will produce infinitely many solutions.

2 answers:

8 0

First task:
To determine this we need to make difference between system that doesn't have solution and system that has infinite number of solution. If when solving equations we get 0 = 0 that means system has infinite number of equations.
If we get 0 = some number that means that system doesn't have solution.

Multiplying first equation of second system by 2 and adding it to second equation we get 0=0 which means that this system has infinite number of solutions.

Answer is second system

Second task:
For this we need to set a system of equations and solve it. System looks like this:
x + y = 224
x*12 + y*8=2520
-------------------------
x represents older than 18 and "y" 18 and younger than that.
first equation we multiply with -12 and sum it with second.
-4y = -168
y=168/4 = 42

Answer is 42.

frosja888 [35]4 years ago

6 0

-2x + 4y = 18
<span>4x - 8y = -36

This system has infinite solutions as one equation is a factor of the other

for the second we can check that
a number of visitors older than 18
b number of visitors younger than 18

a(12) +b(8) = 2520
a + b = 224

solving the equation system we have
that 182 visitors were 18 or younger

</span>

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John runs a computer software store. Yesterday he counted 123 people who walked by the store, 56 of whom came into the store. Of

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Answer:

a) There is a 45.53% probability that a person who walks by the store will enter the store.

b) There is a 41.07% probability that a person who walks into the store will buy something.

c) There is a 18.70% probability that a person who walks by the store will come in and buy something.

d) There is a 58.93% probability that a person who comes into the store will buy nothing.

Step-by-step explanation:

This a probability problem.

The probability formula is given by:

$P = \frac{D}{T}$

In which P is the probability, D is the number of desired outcomes and T is the number of total outcomes.

The problem states that:

123 people walked by the store.

56 people came into the store.

23 bought something in the store.

(a) Estimate the probability that a person who walks by the store will enter the store.

123 people walked by the store and 56 entered the store, so $T = 123, D = 56$ .

$P = \frac{D}{T} = \frac{56}{123} = 0.4553$

There is a 45.53% probability that a person who walks by the store will enter the store.

(b) Estimate the probability that a person who walks into the store will buy something.

56 people came into the store and 23 bought something, so $T = 56, D = 23$ .

$P = \frac{D}{T} = \frac{23}{56} = 0.4107$

There is a 41.07% probability that a person who walks into the store will buy something.

(c) Estimate the probability that a person who walks by the store will come in and buy something.

123 people walked by the store and 23 came in and bought something, so $T = 123, D = 23$ .

$P = \frac{D}{T} = \frac{23}{123} = 0.1870$

There is a 18.70% probability that a person who walks by the store will come in and buy something.

(d) Estimate the probability that a person who comes into the store will buy nothing.

Of the 56 people whom came into the store, 23 bought something. This means that 56-23 = 33 of them did not buy anything. So:

$D = 33, T = 56$

$P = \frac{D}{T} = \frac{33}{56} = 0.5893$

There is a 58.93% probability that a person who comes into the store will buy nothing.

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At the north campus of a performing arts school, 20% of the students are music majors. At the south campus, 70% of the stude

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Answer:

The north campus had $800$ while the south campus had $200$ .

Step-by-step explanation:

The question stated that there are $1000$ students in the merged campus. That's the sum of the number of students in the north and the south campus before the merger.

Let $x$ denote the number of students in the north campus before the merger. The other $(1000 -x)$ students would all belong to the south campus before the merger.

Before the merger, $20\%$ of the students of the north campus are of music majors. In terms of $x$ , that's $(20\%)\cdot x = 0.20\,x$ students.

On the other hand, $70\%$ of the students of the south campus are of music majors. That corresponds to $(70\%)\cdot (1000 - x) = 0.70\cdot (1000 - x) = 700 - 0.70\, x$ students.

With a similar logic, the number of music students in the merged east campus will be $30\% \times 1000 = 300$ .

The question implies that the sum of students in the two campuses should be equal to the number of music students in the east campus. That is:

$0.20\, x+ (700 - 0.70\, x) = 300$ .

Solve for $x$ :

$x = 800$ .

In other words, there are $800$ students in the north campus and $(1000 - 800) = 200$ students in the south campus before the merger.

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