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leva [86]
3 years ago
12

Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs.

Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where X X is the age of the crab in months and ˆ Y Y^ is the predicted value of Y Y , the size of the male crab in cm. ˆ Y = 9.1411 + 0.4775 X Y^=9.1411+0.4775X What is the value of ˆ Y Y^ when a male crab is 23.2417 months old? Provide your answer with precision to two decimal places
Mathematics
1 answer:
Eva8 [605]3 years ago
7 0

Answer:

20.24 cm

Step-by-step explanation:

Here, since the age of the crab is given in months and the regression line was computed using the age in months, we just have to replace the value of the age in the formula to estimate the size.

The formula obtained for the estimated size Y was

Y = 9.1411 + 0.4775X  

where X is the age in months

Replacing X with 23.2417, we get

Y = 9.1411 + 0.4775*23.2417 = 20.24 cm

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If a toy rocket is launched vertically upward from ground level with an initial velocity of 120 feet per second, then its height
german

Answer:

Time = 7.5\ seconds

Step-by-step explanation:

Given

Equation:\ h(t) = -16t^2 + 120t

Initial\ Velocity = 160ft/s

Required:

Determine the time taken to return to the ground

From the equation given; height (h) is a function of time (t)

When the rocket returns to the ground level, h(t) = 0

Substitute 0 for h(t) in the given equation

h(t) = -16t^2 + 120t

becomes

0 = -16t^2 + 120t

Solve for t in the above equation

-16t^2 + 120t = 0

Factorize the above expression

-4t(4t - 30) = 0

Split the expression to 2

-4t = 0\ or\ 4t - 30 = 0

Solving the first expression

-4t = 0

Divide both sides by -4

\frac{-4t}{-4} = \frac{0}{-4}

t = \frac{0}{-4}

t =0

Solving the second expression

4t - 30 = 0

Add 30 to both sides

4t - 30+30 = 0+30

4t  = 30

Divide both sides by 4

\frac{4t}{4}  = \frac{30}{4}

t  = \frac{30}{4}

t = 7.5

Hence, the values of t are:

t =0 and t = 7.5

t =0 shows the time before the launching the rocket

while

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Answer:

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Step-by-step explanation:

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