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The equation for the line of best fit for a data set is y = 2x + 1.5. If the point (1, 4) is in the data set, what is the residu

Andreas93 [3]

A. 0.5 well at least that's the answer in ingenuity.<span />

5 0

2 years ago

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You randomly draw A marble from a bag, record it’s color, and then replace it. You draw a blue marble 11 out of 50 times. What i

BlackZzzverrR [31]

Answer:

since you recorded the first marble then replaced it, you drew 10 blue marbles, so therefore we can predict the next marble you drew, was blue.

Step-by-step explanation:

4 0

3 years ago

Let f(x) = x2 − 16. Find f−1(x)

Yanka [14]

Answer:

$f^{-1}(x)=\pm\sqrt{x+16}$

Step-by-step explanation:

$f(x)=x^2-16$

To find the inverse of this function, temporarily the f(x) with a y (or whatever else you want) and then solve for the x.

$y=x^2-16\\y+16=x^2\\x=\pm\sqrt{y+16}$

Now, you can swap the variables again and write the function.

$f^{-1}(x)=\pm\sqrt{x+16}$

3 0

2 years ago

3. What are the intersection points of the line whose equation is y=3x +3 and the

densk [106]

Answer:

Points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

Step-by-step explanation:

Equation of the circle → (x - 2)² + y² = 25 ---------(1)

→ (x - 2)² + (y - 0)² = 5²

By comparing this equation with the standard equation of the circle,

(x - a)² + (y - b)²= r²

Here (a, b) is the center and r is the radius of the circle.

Therefore, center of the circle is (2, 0) and radius = 5 units

Second equation is a linear equation → y = 3x + 3 -------(2)

x-intercept of the equation → x = -1

y-intercept of the equation → y = 3

By graphing these equations we can get the point of intersections.

Solving these equations algebraically,

Substitute the value of y from equation (2) in the equation (1),

(x - 2)² + (3x + 3)² = 25

x² - 4x + 4 + 9x² + 18x + 9 = 25

10x² + 14x - 12 = 0

5x² + 7x - 6 = 0

x = $\frac{-7\pm \sqrt{7^2-4(5)(-6)}}{2(5)}$

x = $\frac{-7\pm \sqrt{169}}{10}$

x = $\frac{-7\pm13}{10}$

x = -2, 0.6

From equation (2),

y = -3, 4.8

Therefore, points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

6 0

3 years ago

Question1) Describe three scenarios that involve a real-world linear or exponential function. At least one must be exponential.

elixir [45]

Answer:

1) Let's suppose that you go in a straight line, in a car that moves at a constant speed of 80km/h.

Then the distance from your house (assuming that you start the drive in your house) can be modeled with a linear equation:

D(t) = 80km/h*t

where t is time in hours.

This will be a linear function.

2) Suppose that you have a population of some animal, that grows by 2% each month, and initially, there are 100 individuals of that animal.

Then the first month, the population is 100.

The second month the population increased by a 2%, then it will be:

100 + 100*0.02 = 100*(1.02)

The third month, the population will be 100*(1.02) + 0.2*100*(1.02) = 100*(1.02)^2.

and so on, this is an exponential relation, where the population as a function of the number of months, can be written as:

P(m) = 100*(1.02)^(m - 1)

3) Suppose that you have $100 saved, and each month you can save another $80, let's find a function that says the amount of money that you have saved as a function of the number of months. S(m)

The month number zero (before you started saving) you had $100 saved.

S(0) = $100.

One month after, you have saved $80 more, then you have:

S(1) = $100 + $80

Another month after, you have:

S(2) = $100 + $80 + $80 = $100 + 2*$80

And so on, you already can see the pattern, after m months, you will have:

S(m) = $100 + m*$80 saved.

5 0

2 years ago