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3 years ago

Solve the following linear system of equations using substitution.

Mathematics

2 answers:

DerKrebs [107]3 years ago

4 0

( - 1, - 8 )

since both equations give y in terms of x we can equate them

3x - 5 = 2x - 6

subtract 2x from both sides of the equation

3x - 2x - 5 = - 6

x - 5 = - 6

add 5 to both sides

x = - 6 + 5 = - 1

substitute x = - 1 into either of the 2 equations for y

y = (3 × - 1) - 5 = - 3 - 5 = - 8

solution to the system is (- 1, - 8 )

NeX [460]3 years ago

4 0

Answer:

( - 1, - 8 )

Step-by-step explanation:

just took it on edge

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Natasha_Volkova [10]

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3 years ago

It is 2 miles from Ellie’s house to school, 1 mile = 5280 feet. How many feet is it from Ellie’s house to school ?

Lana71 [14]

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4 years ago

Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 0.80. What is the value of x?

Ivan

Answer:

Step-by-step explanation:

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5 0

3 years ago

Read 2 more answers

Suppose twenty-two communities have an average of = 123.6 reported cases of larceny per year. assume that σ is known to be 36.8

Delvig [45]

We are given the following data:

Average = m = 123.6
Population standard deviation = σ= psd = 36.8
Sample Size = n = 22

We are to find the confidence intervals for 90%, 95% and 98% confidence level.

Since the population standard deviation is known, and sample size is not too small, we can use standard normal distribution to find the confidence intervals.

Part 1) 90% Confidence Interval
z value for 90% confidence interval = 1.645

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.645* \frac{36.8}{ \sqrt{22}}=110.69$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.645* \frac{36.8}{ \sqrt{22}}=136.51$

Thus the 90% confidence interval will be (110.69, 136.51)

Part 2) 95% Confidence Interval
z value for 95% confidence interval = 1.96

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.96* \frac{36.8}{ \sqrt{22}}=108.22$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.96* \frac{36.8}{ \sqrt{22}}=138.98$

Thus the 95% confidence interval will be (108.22, 138.98)

Part 3) 98% Confidence Interval
z value for 98% confidence interval = 2.327

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-2.327* \frac{36.8}{ \sqrt{22}}=105.34$
Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+2.327* \frac{36.8}{ \sqrt{22}}=141.86$

Thus the 98% confidence interval will be (105.34, 141.86)

Part 4) Comparison of Confidence Intervals
The 90% confidence interval is: (110.69, 136.51)
The 95% confidence interval is: (108.22, 138.98)
The 98% confidence interval is: (105.34, 141.86)

As the level of confidence is increasing, the width of confidence interval is also increasing. So we can conclude that increasing the confidence level increases the width of confidence intervals.

3 0

4 years ago

Y 20 18 16 14 12 Total Cost ($) 10 000 2 3 1 2 Time (hours) 2. 3 4 6 8 y = IX +

Monica [59]

To find the m(slope) of our graph we can take two points from the graph, im going to use (0,2) and (1,8) the formula for slope is y2-y1/x2-x1
Plug the points in to get 8-2/1-0
The slope of this equation is 6.

For the y-intercept we just find where the line meets the y-axis and that is at 2.

The equation for this graph is y=6x+2

8 0

3 years ago