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3 years ago

3x+y=3 7x−y=2 The system of equations above has solution (x,y). What is the value of x?

Mathematics

2 answers:

Snowcat [4.5K]3 years ago

5 0

Answer:

$x=\frac{1}{2}$

Step-by-step explanation:

We can solve this system of equations using elimination.

In this case, we can eliminate y by adding the two equations:

$3x+7x+y+(-y)=3+2\\10x+y-y=5\\10x=5$

Divide both sides by 10

$x=\frac{1}{2}$

Gennadij [26K]3 years ago

4 0

Answer:

x=1/2

Step-by-step explanation:

3x+y=3..............(1)

7x-y=2...........(2)

for equation (1)

y=3-3x...........(3)

substitute y=3-3x into equation(2)

7x-(3-3x)=2

7x-3+3x=2

C L T

7x+3x=2+3

10x=5

x=5/10

x=1/2

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Answer:

The 99% confidence interval for the population proportion of oil tankers that have spills each month.

(0.6489 , 0.7311)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 836

Suppose a sample of 836 tankers is drawn. Of these ships, 577 did not have spills.

sample proportion

$p^{-} = \frac{x}{n} = \frac{577}{836} = 0.690$

The 99% confidence interval for the population proportion is determined by

$(p^{-} - Z_{0.01} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.01} \sqrt{\frac{p(1-p)}{n} })$

Step(ii):-

The Z- value = 2.576

$(0.690 - 2.576 \sqrt{\frac{0.690(1-0.690)}{836} } , 0.690 + 2.576 \sqrt{\frac{0.690(1-0.690)}{836} })$

On calculation , we get

(0.690 - 0.0411 , 0.690 + 0.0411)

(0.6489 , 0.7311)

Final answer:-

The 99% confidence interval for the population proportion of oil tankers that have spills each month.

(0.6489 , 0.7311)

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4 years ago

Sam watched television for the past five nights for 42 mins, 23 mins, 56mins,19 mins , and 67 mins what was the median amount sa

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Answer:

42 minutes is the median amount of time

Step-by-step explanation:

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If there is "odd" number of numbers, and there are n numbers, the median is:

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If there is "even" number of numbers, and there are n numbers, the median is:

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3rd number

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Step-by-step explanation:

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3 years ago

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3 years ago

May I please receive help

aliya0001 [1]

Answer:

y = 120°

z = 32°

Step-by-step explanation:

For the sake of simplicity, I labeled one of the interior angles as m < 1 (Please see the attached screenshot). I did this because m < 1 and the exterior angle on the same side of the transversal have the same measure of m < 60°.

Therefore, m < 1 = m < 60°

Next, since m < 1 = 60°, then we can add its measure to < y°, which will sum up to 180° (given that they are supplementary angles).

We can establish the following formula to solve for < y°:

m < 1 + < y ° = 180°

Let's rearrange the formula to isolate < y°:

< y ° = 180° - m < 1

Substitute the value of m < 1 into the revised formula:

< y = 180°- 60°

< y = 120°

Now that we have the value for y°, we can find out what the value of z is by creating another formula:

< (5z - 100)° = 180° - y°

Substitute the value of y° into the formula:

5z - 100° = 180° - 120°

Combine like terms:

5z - 100° = 60°

Add 100° on both sides:

5z - 100° + 100° = 60° + 100°

5z = 160°

Divide both sides by 5:

$\frac{5z}{5} = \frac{160}{5}$

< z = 32°

Double-check whether we derived the correct answers by plugging in the values of y° and z° into the following formula:

y° + (5z - 100)° = 180° (because they are supplementary angles)

120° + [5(32) - 100]° = 180°

120° + [160 - 100]° = 180°

120° + 60° = 180°

180° = 180° (True statement).

Therefore, the value of y = 120° and z = 32°.

Please mark my answers as the Brainliest if you find my explanations helpful :)

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