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kiruha [24]
3 years ago
13

Mark gathered data about the number of pink and red flowers that bloomed on several of his flowering shrubs. The scatter plot sh

ows the data he gathered and the line of best fit.
Mathematics
1 answer:
fgiga [73]3 years ago
8 0

The scatter plot showing data gathered and line of best fit is attached below :

Answer:

69

Step-by-step explanation:

Given the regression model :

y = 1.73x + 0.0924

Where,

y = number of pink flowers

x = Red flowers

Slope = 1.73

Intercept = 0.0924

The number of pink flower that are predicted to bloom on a shrub of 40 red flowers :

Put x = 40 and calculate the value of y

y = 1.73(40) + 0.0924

y = 69.2 + 0.0924

y = 69.2924

Number of pink flowers = 69

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Answer:

(2,6,6) \not \in \text{Span}(u,v)

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Step-by-step explanation:

Let b=(b_1,b_2,b_3) \in \mathbb{R}^3. We have that b\in \text{Span}\{u,v\} if and only if we can find scalars \alpha,\beta \in \mathbb{R} such that \alpha u + \beta v = b. This can be translated to the following equations:

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Case (2,6,6)

Using equations 1 and 2 we get

-\alpha + 3 \beta = 2

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Case (-9,-2,5)

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-\alpha + 3 \beta = -9

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whose unique solutions are \alpha=3, \beta=-2. Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.

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