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3 years ago

What is the equation? Picture attatched

Mathematics

1 answer:

Cerrena [4.2K]3 years ago

6 0

Answer:

y = x - 5

Step-by-step explanation:

Equation of any two parallel lines differ only by a constant.

Therefore, the equation of the line parallel to $ax + by + c_1 = 0$ would be ax + by + c₂ = 0.

The equation of the line parallel to $y = x - 3$ should be equal to

x - y + c = 0.

Since, a point intersecting the line is given this means that the line passes through this point. This can be used to determine the value of c.

⇒ 3 -(-2) + c = -5 + c = 0

⇒ c = - 5.

Substituting we get: x - y - 5 = 0

⇒ y = x - 5 is the required equation of the line.

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HELP

Nikitich [7]

Equations

Let the number of liters of 80% acid = x

Let the number of liters of 40% acid = y

x + y = 2

80%x + 40%y = 65% * 2

Step One

multiply the 2nd given by 100

(80/100)x + (40/100)y = (65/100)*2

80x + 40y = 2*65 = 130 (3)

Step Two

Multiply the first given equation by 80

80x + 80y = 160 (4)

Step Three

Subtract (4) - (3)

80x + 80y = 160

40y = 30 Divide by 40

y = 30/40

y = 3/4 = 0.75

What you have found is that out of 2 liters, 0.75 L must be the 40% acid.

Step Four

Find the 80% volume

x + y = 2

y = 0.75 L

x + 0.75 = 2

x = 2 - 0.75

x = 1.25 L

Answers

80% Volume = 1.25 L

40% Volume = 0.75 L

4 0

3 years ago

A sociologist wishes to estimate the percentage of the United States population living in poverty. What size sample should be ob

andriy [413]

Answer:

a) We need a sample size of at least 705.

b) We need a sample size of at least 1692.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

a) If she uses 1999 estimate of 11.8% obtained from the Current Population Survey.

We need a sample of size at least n

n is found when $M = 0.02, \pi = 0.118$ .

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.645\sqrt{\frac{0.118*0.882}{n}}$

$0.02\sqrt{n} = 1.645\sqrt{0.118*0.882}$

$\sqrt{n} = \frac{1.645\sqrt{0.118*0.882}}{0.02}$

$(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.118*0.882}}{0.02})^{2}$

$n = 704.08$

Rounding up

We need a sample size of at least 705.

b) She does not use any estimate.

Same thing as above, we just use $\pi = 0.5$ when do not use any estimate.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.645\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.645\sqrt{0.5*0.5}$

$\sqrt{n} = \frac{1.645\sqrt{0.5*0.5}}{0.02}$

$(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.5*0.5}}{0.02})^{2}$

$n = 1691.2$

Rounding up

We need a sample size of at least 1692.

4 0

3 years ago

On the first day of school, Mr. Vilani gave his third- grade students 5 new words to spell. On each day of school after that, he

FinnZ [79.3K]

So, the best way to solve this problem is by creating a equation for which we can substitute any number of days. For this problem that equation would be W=5+3(t-1)
W=number of words
T=time or number of days
-1= This is here because we are already accounting for the first day of school so we need to have 1 less day than the number of days they have been in school.
So in 20 days the students had received
5+3(19) or 62words.
Answer: 62 words

6 0

3 years ago

when carbon dioxide is frozen it is called dry ice in order to keep it frozen the tempter has to be -109.3 fahrenheit or lower f

elixir [45]

Degrees Celsius = (Fahrenheit -32) * 5/9
Degrees Celsius = (-109.3 -32) * 5/9
Degrees Celsius = -141.3 * 5/9
Degrees Celsius = -78.5

Therefore dry ice must be kept at a temperature of < = -78.5 Celsius

8 0

3 years ago

Find 3 different ratios that are equivalent to 7:3.

ratelena [41]

Answer:

14:6

21:9

28:12

Step-by-step explanation:

Given the initial ratio of 7:3, you can find equivalent ratios by multiplying the two numbers by the same factor:

7 x 2 = 14

3 x 2 = 6

14:6

7 x 3 = 21

3 x 3 = 9

21:9

7 x 4 = 28

3 x 4 = 12

28:12

5 0

3 years ago

Read 2 more answers