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3 years ago

7.

Mathematics

1 answer:

mylen [45]3 years ago

5 0

The cafeteria sold 41 corn chips and 80 potato chips.

Step-by-step explanation:

Let,

Corn chips = x

Potato chips = y

Price of corn chips = $0.80

Price of potato chips = $0.60

According to given statement;

x+y= 121 Eqn 1

0.80x+0.60y=80.80 Eqn 2

Multiplying Eqn 1 by 0.80

$0.80(x+y= 121)\\0.80x+0.80y=96.80\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$(0.80x+0.80y)-(0.80x+0.60y)=96.80-80.80\\0.80x+0.80y-0.80x-0.60y=16\\0.20y=16$

Dividing both sides by 0.20

$\frac{0.20y}{0.20}=\frac{16}{0.20}\\y=80$

Putting y=80 in Eqn 1

$x+80=121\\x=121-80\\x=41$

The cafeteria sold 41 corn chips and 80 potato chips.

Keywords: linear equation, subtraction

Learn more about linear equations at:

#LearnwithBrainly

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Kim sold christmas pies for 5.00$ each. She earned 156 how many pies she sold also let x repersent the number of pies, x, kim so

MA_775_DIABLO [31]

Answer: 31.2 pies

Step-by-step explanation:

Kim sold pies for $5.00 each and earned $156 from doing so.

The number of pies she sold to get to this was x pies.

The formula for doing so is therefore:

5 * x pies = 156

5x = 156

x = 156 / 5

= 31.2 pies

4 0

3 years ago

Need help simplifying this

diamong [38]

The simplified answer is $\frac{\left(12 x^{2}+7 x y-4 y z-3 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$ .

<u>Step-by-step explanation:</u>

$$\frac{3 y+2 x}{z+2 x}-\frac{2 y-3 x}{3 x+y}-\frac{2 z(y+3 x)}{6 x^{2}+3 x z+2 x y+y z}$

To add or subtract denominators of the fraction must be same.

If it is not the same, we must take LCM of the denominators. and so we can add the fractions.

To make the denominator same multiply the 1st term $(\frac{3x+y}{3x+y})$ and 2nd term by $(\frac{z+2x}{z+2x})$

= $\frac{(3 y+2 x)(3 x+y)}{(z+2 x)(3 x+y)}-\frac{(2 y-3 x)(z+2 x)}{(3 x+y)(z+2 x)}-\frac{2 z(y+3 x)}{6 x^{2}+3 x z+2 x y+y z}$

LCM of the denominators is 6x²+ 3xz + 2xy +yz.

Multiply the factors in the numerator.

= $\frac{\left(6 x^{2}+3 y^{2}+11 x y\right)}{(z+2 x)(3 x+y)}-\frac{\left(2 y z+4 x y-3 x z-6 x^{2}\right)}{(3 x+y)(z+2 x)}-\frac{2 z y+6 x z}{6 x^{2}+3 x z+2 x y+y z}$

Now, the denominators are same, you can subtract it.

= $\frac{\left(6 x^{2}+6 x^{2}+11 x y-4 x y-2 y z-2 y z+3 x z-6 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$

= $\frac{\left(12 x^{2}+7 x y-4 y z-3 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$

Thus the simplified solution is $\frac{\left(12 x^{2}+7 x y-4 y z-3 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$

4 0

3 years ago

Let P = 0.50.30.50.7 be the transition matrix for a Markov chain with two states. Let x0 = 0.50.5 be the initial state vector fo

pav-90 [236]

Answer:

Probability distribution vector = $\left(\begin{array}{c}0.375\\ 0.625 \end{array} \right)$

Step-By-Step Explanation

If $P=\left(\begin{array}{cc}0.5&0.3\\ 0.5&0.7 \end{array} \right)$ is the transition matrix for a Markov chain with two states.

$x_{0}=\left(\begin{array}{c}0.5\\ 0.5 \end{array} \right)$ be the initial state vector for the population.

$X_{1}=P x_{0}=\left(\begin{array}{cc}0.5&0.3\\ 0.5&0.7 \end{array} \right) \left(\begin{array}{c}0.5\\ 0.5 \end{array} \right) =\left(\begin{array}{c}0.4\\ 0.6 \end{array} \right)$

$X_{2}=P^{2} x_{0}=\left(\begin{array}{c}0.38\\ 0.62 \end{array} \right)$

$X_{3}=P^{3} x_{0}=\left(\begin{array}{c}0.38\\ 0.62 \end{array} \right)$

$X_{30}=P^{30} x_{0}=\left(\begin{array}{c}0.37499\\ 0.625 \end{array} \right)$

In the long run, the probability distribution vector Xm approaches the probability distribution vector $\left(\begin{array}{c}0.375\\ 0.625 \end{array} \right)$ .

This is called the steady-state (or limiting,) distribution vector.

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3 years ago

It takes 50 oz of grass seed to seed 3000 ft2 of lawn. At this rate, how much would be needed for 7200 ft2 of lawn?

saw5 [17]

Answer:

120 ounces

Step-by-step explanation:

First find how many ft2 of lawn 1 once can seed.

To do this we simply divide 3000 by 50 ( because 50 ounces of grass seed can seed 3000 ft2 of lawn )

3000 / 50 = 60

So 1 ounce can seed 60ft2 of lawn

To find how many ounces would be needed to seed 7200 ft2 of lawn we would divide 7200 by the amount of lawn 1 once can seed ( which is 60ft2 )

7200/60 = 120

So 120 ounces of grass seed would be needed to seed 7200 ft2 of lawn

6 0

2 years ago

Everything is in the picture can you please show your work

sladkih [1.3K]

To get the Greates Common Factor (GCF) of 15 and 36 we need to factor each value first and then we choose all the copies of factors and multiply them:

15: 3 5

36: 2 2 3 3

GCF: 3

The Greates Common Factor (GCF) is: 3

6 0

4 years ago