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Lynna [10]
2 years ago
7

raquel throws darts at a coordinate grid centered at the origin. her goal is to create a line of darts. her darts actually hit t

he coordinate grid at (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6).
Mathematics
2 answers:
NeX [460]2 years ago
4 0
The equation for the line of best fit can be obtained as follows, using the least square method (for more info visit http://hotmath.com/hotmath_help/topics/line-of-best-fit.html ):

mean of X = 1/6
mean of Y = 2/3

slope, m = 704/1121 = 0.6

Computing the y-intercept using the formula:

b = mean of Y - m (mean of X) = 2/3 - (704/1121)(1/6)
b = 0.562 = 0.6

Therefore, the equation of the line of best fit, given the standard relation:

y = mx + b

y = 0.6x + 0.6

Vaselesa [24]2 years ago
4 0

Answer: the answer is (A)

Step-by-step explanation:

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A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t
11Alexandr11 [23.1K]

Answer:

  • <u>Question 1:</u>      dm/dt=0.2m<u />

<u />

  • <u>Question 2:</u>     m=Ae^{(0.2t)}<u />

<u />

  • <u>Question 3:</u>      m=10e^{(0.2t)}<u />

<u />

  • <u>Question 4:</u>      m=10g<u />

Explanation:

<u>Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m</u>

<u></u>

a) By definition:  m'=dm/dt

b)  Given:  rate=0.2m

c) By substitution:  dm/dt=0.2m

<u>Question 2: Find the general solution of this equation. Use A as a constant of integration.</u>

a) <u>Separate variables</u>

     dm/m=0.2dt

b)<u> Integrate</u>

           \int dm/m=\int 0.2dt

            ln(m)=0.2t+C

c) <u>Antilogarithm</u>

       m=e^{0.2t+C}

       m=e^{0.2t}\cdot e^C

         e^C=A\\\\m=Ae^{(0.2t)}

<u>Question 3. Which particular solution matches the additional information?</u>

<u></u>

Use the measured rate of 4 grams per hour after 3 hours

            t=3hours,dm/dt=4g/h

First, find the mass at t = 3 hours

            dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g

Now substitute in the general solution of the differential equation, to find A:

          m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976

Round A to 1 significant figure:

  • A = 10.

<u>Particular solution:</u>

           

             m=10e^{(0.2t)}

<u>Question 4. What was the mass of the bacteria at time =0?</u>

Substitute t = 0 in the equation of the particular solution:

         m=10e^{0}\\\\m=10g

3 0
3 years ago
F(x) = 7x + 9, g(x) = 4x - 1;<br> Find (fºg)(x).
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Answer: (fºg)(x) = 28x + 2

(Step-by-step explanation:

8 0
3 years ago
Write a variable expression to represent the phrase a number times 8
Nat2105 [25]
A number (we will call X) times 8 Is 8x
4 0
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. The following is a recipe for Gazpacho, a cold vegetable soup. Write how much of each item in the
Andreyy89

Answer: 9 lb of fresh tomatoes

6 c peeled chopped cucumbers

3 c chopped red bell peppers

3 c chopped red onions

6 small jalapenos

6 garlic cloves

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Step-by-step explanation:

3 0
3 years ago
The actual length (L) of a rectangle is 27 centimeters. Use the scale drawing of the rectangle to find the actual width (W).
nata0808 [166]

Answer:

18 cm

Step-by-step explanation:

The ratio of Actual length (L) to scale length is 27 : 3.6

27 ÷ 3.6 = 7.5

Therefore, actual width (W) = scale width x 7.5

                                              = 2.4 x 7.5

                                              = 18 cm

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