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algol13
4 years ago
14

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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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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b- y-intercept, if be is positive it indicates vertical shift up, when negative- vertical shift down

8 0
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

p_o=0.35 is the value that we want to test

z would represent the statistic

p_v represent the p value

Hypothesis to test

We want to test if the proportion of students with jobs is higher than 0.35, the system of hypothesis are:  

Null hypothesis:p \leq 0.35  

Alternative hypothesis:p > 0.35  

The statistic is given by:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing the info we got:

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.

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krek1111 [17]

Answer:

Correct answer is A

Step-by-step explanation:

7 0
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