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Jlenok [28]
2 years ago
10

Find the equation of a line that passes through the point (3,1) and has a gradient of -3. Leave your answer in the form y = m x

+ c
Mathematics
1 answer:
Bingel [31]2 years ago
3 0

Answer:

y = (-3)\, x + 10.

Step-by-step explanation:

The question requires that the equation should be in the slope-intercept form y = m \, x + c. The m and c in this equation are constants. In particular:

  • m\! would represent the slope of this line (also known as the gradient of this line,) whereas
  • c would be the y-intercept of this line.

The question states that the slope of this line is (-3). Therefore, m = -3. Thus, the equation for this line should be in the form y = (-3)\, x + c.

The value of constant c could be found using the other piece of information: the point (3,\, 1) is in this line. In other words, the solution \text{$x = 3$ and $y = 1$} should satisfy the equation y = (-3)\, x + c.

Substitute \text{$x = 3$ and $y = 1$} into the equation y = (-3)\, x + c and solve for c:

1 = (-3) \times 3 + c.

1 = -9 + c.

c = 10.

Hence, y = (-3) \, x + 10 would be the slope-intercept form of the equation of this line.

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g (15 points) Suppose 42 out of 600 rats exposed to a potential carcinogen develop tumors. A control group of 350 rats not expos
vazorg [7]

Answer:

a) The relative risk is 1.8\overline{846153}

b) The attributable risk is 0.69 \overline{047619}

c) There is a relationship between exposure and tumor risk

Step-by-step explanation:

The number of exposed rats that develop tumors, a = 42

The number of rats exposed to the carcinogen = 600 rats

The number of exposed rats that did not develop tumors, b = 600 - 42 = 558

The number of not exposed rats in the control group = 350 rats

The number of rats that develop tumors in the control group, c = 13 tumors

The number of not exposed rats that did not develop tumors, d = 350 - 13 = 337  rats

a) The relative risk, RR = a/(a + b)/(c/(c + d))

∴ RR = (42/(42 + 558))/(13/(13 + 337)) = 49/26 = 1.8\overline{846153}

b) The attributable risk = (a - c)/a

∴ The attributable risk = (42 - 13)/42 = 0.69 \overline{047619}

c) The odds ratio = (a·b)/(c·d)

∴ The odds ratio = 42 × 558/(13 × 337) = 23439/4381 ≈ 5.35

Given that the result of attributable risk is positive, there is an indication that there is a higher probability to develop tumor when exposed to the potential carcinogen, therefore, there is a relationship between exposure and tumor risk

7 0
3 years ago
the water temperature of a swimming pool is 76f. the temperature is currently 74f. which graph shows how much the temperature ne
Nikolay [14]

Answer:

Bacteria, algae and other organisms thrive under warm water conditions this is obviously harmful not just for athletes but the general public in a commercial swimming pool, for competitive pools the water should be no higher than 82°F (28°C), for recreational pools the recommended maximum is 84°F (29°C).

Step-by-step explanation:

3 0
3 years ago
Sam ran 63,756 feet in 70 minutes. What is Sam’s rate in miles per hour?
MArishka [77]

Answer:

63756/70=910.8 ft per minute

The choice is in order so just make the lines straight

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6 0
3 years ago
A typical middle-income household in 1980 earned $34,757. A similar household in 2009 earned $38,550. What was the relative incr
S_A_V [24]

Given conditions are :

In 1980's, a typical middle-income household earned=  $34,757

In 2009, a similar middle-income household earned= $38,550

And we have to find relative increase in income for these households from 1980 to 2009.

So first we will find the total increase in amounts.

38550-34757=3793

Relative increase = \frac{3793}{34757}*100

= 10.91% or rounding it off we get approx 11%.

Hence, the answer is 11%.

5 0
3 years ago
Read 2 more answers
Andrea calls two truck rental companies to compare costs. Action trucks charges $80 for the day plus $0.22 per kilometer and tru
Amanda [17]

Answer:it will take 200 kilometers for the costs to be the same.

Step-by-step explanation:

Let x represent the number of kilometers that Andrea would have to drive for the total cost of renting from both companies to be the same.

Action trucks charges $80 for the day plus $0.22 per kilometer. It means that the total cost of x miles would be

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Therefore, for the cost of renting from both companies to be the same,

80 + 0.22x = 100 + 0.12x

0.22x - 0.12x = 100 - 80

0.1x = 20

x = 20/0.1 = 200

4 0
3 years ago
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