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4 years ago

Solve the following system of equations using the substitution method.

Mathematics

2 answers:

egoroff_w [7]4 years ago

6 0

Answer: x=8.5 y=1.5

Step-by-step explanation:

Use the second problem and get X by itself. X= 5y+1. Now plug that equation into the 1st equation.

-(5y+1) +9y =-5.

-5y-1+9y=-5.

-5y+9y= 1+5

4y= 6

Y=1.5

Now that you know what is the value of Y you can plug that into any equation.

5(1.5) +1

7.5+1

X=8.5

OverLord2011 [107]4 years ago

4 0

For this case we have the following system of equations:

$-x + 9y = -5\\x-5y = 1$

We clear "x" from the second equation and replace it in the first:

$x = 1 + 5y$

Substituting in the first equation:

$- (1 + 5y) + 9y = -5\\-1-5y + 9y = -5$

We have similar terms:

$-1 + 4y = -5$

Adding 1 to both sides of the equation:

$4y = -5 + 1\\4y = -4\\y = \frac {-4} {4}\\y = -1$

We look for the value of "x":

$x = 1 + 5 (-1)\\x = 1-5\\x = -4$

Answer:

$(x, y): (- 4, -1)$

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There is a 0.05 chance that we will have an earthquake this year. What is the probability we won't have an earthquake this year

viktelen [127]

Answer:

0.95‬ chance or 95% chance.

Step-by-step explanation:

If there is a 0.05 chance of there being and earthquake subtract 0.05 from 1 to find out what the chance of not having an earthquake it. Since probability is a fraction out of a whole percentages can be used to find the answer.

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3 years ago

Describe the transformation using the values for slope (m) and the y-intercept b. Compare the graph to the parent y = x.

ra1l [238]

Answer:

See attached

Step-by-step explanation:

y = mx + b - slope-intercept form

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4 years ago

The ages of 11 students enrolled in an on-line macroeconomics course are given in the following steam-and-leaf display:

blsea [12.9K]

Answer:

The standard deviation of the age distribution is 6.2899 years.

Step-by-step explanation:

The formula to compute the standard deviation is:

$SD=\sqrt{\frac{1}{n}\sum\limits^{n}_{i=1}{(x_{i}-\bar x)^{2}}}$

The data provided is:

X = {19, 19, 21, 25, 25, 28, 29, 30, 31, 32, 40}

Compute the mean of the data as follows:

$\bar x=\frac{1}{n}\sum\limits^{n}_{i=1}{x_{i}}$

$=\frac{1}{11}\times [19+19+21+...+40]\\\\=\frac{299}{11}\\\\=27.182$

Compute the standard deviation as follows:

$SD=\sqrt{\frac{1}{n}\sum\limits^{n}_{i=1}{(x_{i}-\bar x)^{2}}}$

$=\sqrt{\frac{1}{11-1}\times [(19-27.182)^{2}+(19-27.182)^{2}+...+(40-27.182)^{2}]}}\\\\=\sqrt{\frac{395.6364}{10}}\\\\=6.28996\\\\\approx 6.2899$

Thus, the standard deviation of the age distribution is 6.2899 years.

7 0

3 years ago

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that th

lisov135 [29]

Answer:

$z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074$

Now we can calculate the p value with this probability:

$p_v =P(z>2.074)=0.019$

If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.

Step-by-step explanation:

Information given

n=78 represent the random sample taken

X=36 represent the students with jobs

$\hat p=\frac{36}{78}=0.462$ estimated proportion of students with jobs