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Daniel [21]
1 year ago
14

Johann fits a linear model to a set of data. The line of best fit has the equation y=0.331986x+5.33286. The scatter plot with th

e line of best fit is given below.
What is the residual value for x = 3? Give your answer as a decimal to the nearest hundredth.

Mathematics
1 answer:
Rasek [7]1 year ago
5 0

Answer:

6.33

Step-by-step explanation:

Here, we are asked to give a residual value at x = 3

This mean we are to predict the value of y at the point x= 3

To do this, what we need to do is to input the value x = 3 into the line of best fit equation.

The line of best fit equation according to the question is;

y=0.331986x+5.33286

Substituting x here, we have

y = 0.331986(3) + 5.33286

y = 0.995958 + 5.33286 = 6.328818

Question asks to give answer to the nearest hundredth and that is 6.33

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An isosceles triangle has base 6 and height 11. find the maximum possible area of a rectangle that can be placed inside the tria
svetoff [14.1K]
The area of the triangle is 33
5 0
2 years ago
A line passes through the points (15,−13) and (16,−11). Hollis writes the equation y+13=(x−15) to represent the line. Which answ
Andru [333]

The equation formula is y - y1 = m(x-x1)

Using the first point for x1, y1:

Y +13 = m(x-15)

M is the slope which is the change in y over the change in x:

M = -11–13 / 16-15 = 2/1 = 2

The equation becomes y +13 =2(x+15)

The answer is:

He incorrectly wrote the slope in his equation. He should have written y+13=2(x−15).

8 0
2 years ago
Lesson 1-1: The periodic comet named Johnson has been seen at every return since its discovery in 1949, as shown in the table be
stiks02 [169]

Answer:

Step-by-step explanation:

Occurrence                 Year seen          Difference

1                                      1949                       -  

2                                     1956               1956 - 1949 = 7

3                                     1963               1963 - 1956 = 7

4                                     1970                1970 - 1963 = 7

Difference between each successive term of year seen = 7 years

Therefore, there is a common difference of 7 years between each successive term.

Function defining the year seen will be a linear function and will increase in the same pattern. (multiple of 7 years)

2017 - 1970 = 47 (It's not the multiple of 7)

2018 - 1970 = 48 (It's not the multiple of 7)

2019 - 1970 = 49 (multiple of 7)

2020 - 1970 = 50 (It's not the multiple of 7)

Therefore, comet will be seen next in 2019.

Option (C) will be the answer.

If a person is born in 2005

Then difference between 2005 and 1949 = 56 years

Number of times comet seen after 1949 = \frac{56}{7}=8 times

Total number of comet seen in the lifetime = 8 times

5 0
2 years ago
Jack was so frustrated with his slow laptop that he threw it out of his second story window. The height, h, of the laptop at tim
jeyben [28]

Answer:

The domain of the function is the interval [0,2.23]

see the explanation

Step-by-step explanation:

Let

t ----> the time in seconds

h(t) ----> the height of the laptop in units

we have

h(t)=-16t^{2}+28t+17

we know that

When the laptop hits the ground, the value of h(t) is equal to zero

so

For h(t)=0

-16t^{2}+28t+17=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-16t^{2}+28t+17=0

so

a=-16\\b=28\\c=17

substitute in the formula

x=\frac{-28(+/-)\sqrt{28^{2}-4(-16)(17)}} {2(-16)}

x=\frac{-28(+/-)\sqrt{1,872}} {-32}

x=\frac{-28(+/-)12\sqrt{13}} {-32}

x_1=\frac{-28(+)12\sqrt{13}} {-32}=-0.477

x_1=\frac{28(-)12\sqrt{13}} {32}=-0.477  ---> is not a solution

x_2=\frac{-28(-)12\sqrt{13}} {-32}

x_2=\frac{28(+)12\sqrt{13}} {32}=2.23\ sec

therefore

The domain of the function is the interval [0,2.23]

All real numbers greater than or equal to 0 seconds and less than or equal to 2.23 seconds

0\ sec \leq x \leq 2.23\ sec

5 0
2 years ago
Kent has a collection of pennies and nickels with a value of 1.98$. the number of pennies he has is five less than twice the num
Alex73 [517]

<span>Kent has a collection of pennies and nickles with a value of $1.98. The number of pennies he has is five less than twice the number of nickles. How many of each coin does Kent have?
----
p + 5n = 198
p = 2n - 5
</span>---
Sub for p
2n-5 + 5n = 198
8 0
2 years ago
Read 2 more answers
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