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Arturiano [62]
3 years ago
8

Use algebraic rules of equations to predict the solution to the system of equations. Include all of your work for full credit.

Mathematics
2 answers:
dolphi86 [110]3 years ago
4 0
X+2y=10
x=10-2y

6y=-3(10-2y)+30
6y=-30+6y+30
0=0
kompoz [17]3 years ago
3 0

Answer:

infinite solutions

Step-by-step explanation:

x+2y=10

6y=-3x+30

To solve for x  and y we use substitution method

LEts solve the first equation for x

x+2y=10

Subtract 2y on both sides

x=10-2y

Now plug in x in second equation

6y=-3x+30

6y=-3(10-2y)+30

6y=-30+6y+30

6y=6y

Both sides are same , so both x  and y have infinite solutions.

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The lengths of lumber a machine cuts are normally distributed with a mean of 106 inches and a standard deviation of 0.3 inch. ​(
Vinvika [58]

Answer:

a) P(X>106.11)=P(\frac{X-\mu}{\sigma}\frac{106.11-106}{0.3})=P(z>0.37)

And we can find this probability with the complement rule:

P(z>0.37)=1-P(z

b) z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}=  2.431

And if we use the z score we got:

P(z>2.431) =1-P(z

Step-by-step explanation:

Let X the random variable that represent the lengths of a population, and for this case we know the distribution for X is given by:

X \sim N(106,0.3)  

Where \mu=106 and \sigma=0.3

Part a

We are interested on this probability

P(X>106.11)

And we can use the z score formula given by:

z=\frac{x-\mu}{\sigma}

And using this formula we got:

P(X>106.11)=P(\frac{X-\mu}{\sigma}\frac{106.11-106}{0.3})=P(z>0.37)

And we can find this probability with the complement rule:

P(z>0.37)=1-P(z

Part b

For this case we select a sample of n =44 and the new z score formula is given by:

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}

And if we find the z score we got:

z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}=  2.431

And if we use the z score we got:

P(z>2.431) =1-P(z

6 0
3 years ago
What is the equation of the graphed line written in standard form?
Dmitry_Shevchenko [17]

Answer:

A

Step-by-step explanation:

4 0
3 years ago
12. The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each.
Debora [2.8K]

Answer:

The number of tickets they have sold in advance are summed up with the following equation and solution:

Equation: \frac{6842.50}{17.50} [the final answer should be in dollars]

Solution: The Opera sold 391 tickets in advance.

Step-by-step explanation:

First: Review some background information:

Let's see what the problem gives us to answer it. I'll bold out the important parts:

The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each. If they have collected $6842.50 already, then how many tickets have they sold in advance?

We know how much the tickets cost and how much money they have earned from selling tickets, we can find out how much tickets they have sold.

Second: Solve the problem:

We can solve this problem using many ways, but I'm just going to pick one. We will use proportions to answer this. Now thoughts might be going through your head like this: What is this guy saying? What in the world is proportions? Well hopefully you learn from this example (Please don't take offense if you <em>do</em> know how to do proportions).

First we set up two fractions. One ticket costs $17.50, so we will use it to set up our first fraction: \frac{1}{17.50}. We don't know how many tickets all together cost $6842.50 so we will use the variable: x. Now, we can set up our second fraction. x tickets costs $6842.50 so our second fraction will be: \frac{x}{6842.50}. Now we must use cross multiplication. We multiply the numerator of the first fraction times the denominator of the second fraction, and then we multiply the denominator o the first fraction times the numerator of the second fraction. That's what we would do usually. But now, since we have a variable, we must use cross multiplication to solve for this variable. So we multiply the the numerator of the first fraction times the denominator of the other fraction and then we divide that answer times the denominator of the first fraction (You don't have to set it up like this).So let's solve this question:

\frac{1}{17.50}  \frac{x}{6842.50}

1 x 17.50 = 17.50

6842.50 ÷ 17.50 = 391

So our equation is 6842.50 ÷ 17.50, and our solution is 391 tickets

Topic: Proportions

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