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WITCHER [35]
3 years ago
12

You receive a $35 gift certificate from an online retailer that sells digital music and games. Each song costs $1.29 and each ga

me costs $2.10. You want to purchase at least 12 items with this card. Provide at least 2 combinations of music and games that can be purchased.
Mathematics
1 answer:
Mars2501 [29]3 years ago
3 0

Answer:

So, we purchased 9 songs and 4 games for 20.1$.

So, we purchased 10 songs and 6 games for 25.5$.

So, we purchased 10 songs and 10 games for 33.9$.

Step-by-step explanation:

We have receive a $35 gift certificate from an online retailer that sells digital music and games. Each song costs $1.29 and each game costs $2.10.

First case:

9\cdot 1.29=11.61\\\\4\cdot 2.10=8.4\\\\8.4+11.61=20.01

So, we purchased 9 songs and 4 games for 20.1$. We have 13 items  for 20.1$.

Second case:

10\cdot 1.29=12.9\\\\6\cdot 2.10=12.6\\\\12.9+12.6=25.5

So, we purchased 10 songs and 6 games for 25.5$. We have 16 items  for 25.5$.

Third case:

10\cdot 1.29=12.9\\\\10\cdot 2.10=21\\\\12.9+21=33.9

So, we purchased 10 songs and 10 games for 33.9$. We have 20 items  for 33.9$.

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Write the equation of the line that goes through each set of points------ (-1.6),(3-,2)
Maksim231197 [3]

Answer:

The equation that goes through this set of points is y = -x + 5

Step-by-step explanation:

In order to find this, we need to start by finding the slope. For that we use the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (6 - -2)/(-1 - 3)

m = 4/-4

m = -1

Now that we have this, we can use the slope and a point in point-slope form to get the equation.

y - y1 = m(x - x1)

y - 6 = -1(x - -1)

y - 6 = -1(x + 1)

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y = -x + 5

3 0
3 years ago
What is the area of the squares with sides (2x-3)feet?​
LUCKY_DIMON [66]

Answer:

4x^2 -12x +9   ft^2

Step-by-step explanation:

The area of a square is

A = s^2 where s is the side length

A = (2x-3) ^2

A = (2x-3) (2x-3)

FOIL

first 2x*2x =4x^2

outer 2x (-3) = -6x

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Add them together

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4x^2 -12x +9

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5 0
3 years ago
Read 2 more answers
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than on
Kazeer [188]

Answer:

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

Step-by-step explanation:

We have to write the transition matrix M for the population.

We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.

We can write the transition matrix, in which the rows are the actual state and the columns are the future state.

- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. <em>Then, the probability of staying in the same state is 90%.</em>

-  For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. <em>Then, the probability of staying in the same state is 80%.</em>

- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. <em>Then, the probability of staying in the same state is 82%.</em>

<em />

The transition matrix becomes:

\begin{vmatrix} &NS&P1&PM\\NS&  0.90&0.08&0.02 \\  P1&0.10&0.80 &0.10 \\  PM& 0.08 &0.10&0.82 \end{vmatrix}

The actual state matrix is

\left[\begin{array}{ccc}5,000&2,500&2,500\end{array}\right]

We can calculate the next month state by multupling the actual state matrix and the transition matrix:

\left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4950&2650&2400\end{array}\right]

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:

\left[\begin{array}{ccc}4950&2650&2400\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4912&2756&2332\end{array}\right]

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:

\left( \left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] \right)^{12} =\left[\begin{array}{ccc}4792.63&3005.44&2201.93\end{array}\right]

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

3 0
4 years ago
2 (2f+2)= help me fast
8_murik_8 [283]

Distribute

2 × 2f + 2 × 2

Simplify 2 × 2f to 4f

4f + 2 × 2

Simplify 2 × 2 to 4

<u>4f + 4</u>

4 0
3 years ago
Read 2 more answers
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