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3 years ago

Explain why it makes sense for this situation to have a linear equation

Mathematics

1 answer:

IgorC [24]3 years ago

3 0

Answer:

The line of best fit for your specific question is a linear equation.

Step-by-step explanation:

A linear equation has a constant rate of growth/decline and the growth/decline rate will never change in an linear equation.

If you draw a line that approximately splits between all the data plots, you will notice the line you drew is very close to the data points.

If the data plots was a quadratic, it would be very hard to draw a line of best fit.

Linear equations can easily be identified in a graph because it is a straight line.

Perhaps insert this equation into your graphing calculator or other graphing software online (like Desmos): y = 3x+2

A quadratic equation can also easily be identified in a graph because, in most cases, it looks like a U.

Take these examples: y = $3x^2+5x+2$ or y= $-2x^2+10x+30$

You might be interested in

Which describes the first step in solving the equation 4x - 7 = -15?

GalinKa [24]

Answer:

Add 7 to both sides

Step-by-step explanation:

You would need to add 7 to both sides to cancel out the 7 on the right side of the equation to get x one step closer to being by itself.

Then you would get 4x = -8.

Next divide by 4 on both sides to get x by itself so do the inverse operation of what 4 was doing to x.

x = -2

7 0

3 years ago

What is the equation of m=-2/5 b=7/10

IrinaK [193]

Answer:

Use the given slope and point to substitute into the point-slope formula

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−

)

Slope-intercept form:

−

Point-slope form:

−

⋅

(

−

)

4 0

4 years ago

Creating an Exponential Model

MArishka [77]

Answer:

P = $300

r = 0.15

n = 12

$544.61 (to the nearest cent)

$P(1+r)^t$

$524.70 (to the nearest cent)

Step-by-step explanation:

P = principal amount = $300

r = annual interest rate in decimal form = 15% = 15/100 = 0.15

n = number of times interest is compounded per unit t = 12

How much she'll owe in 4 years

P = 300

r = 0.15

n = 12

t = 4

$P(1+\frac{r}{n})^{nt}=300(1+\frac{0.15}{12})^{12 \times 4}$

= $544.61 (to the nearest cent)

Yearly compounding interest rate

$P(1+r)^t$

How much she'll owe in 4 years at yearly compounding interest

$P(1+r)^t=300(1+0.15)^4$

= $524.70 (to the nearest cent)

4 0

2 years ago

Two fair dice are rolled. Find the joint probability mass function of X and Y when (a) X is the largest value obtained on any di

kvasek [131]

Answer:

P(X = x₀, Y = 2x₀) = 1/36

P(X = x₀, Y = k) = 1/18 for k between x₀+1 and 2x₀-1 inclusive

Every other event has probability 0. x₀ is any number between 1 and 6 inclusive.

P(X = x₀, Y = x₀) = x₀/36

P(X = x₀, Y = k) = 1/36 for k between x₀+1 and 6 inclusive.

x₀ is between 1 and 6 inclusive. Every other event has probability 0.

P(X = x₀, Y = x₀) = 1/36

P(X = x₀, Y = k) = 1/18 with k between x₀+1 and 6 inclusive

x₀ between 1 and 6 inclusive. Any other event has probability 0.

Step-by-step explanation:

Note that there are 36 possible results for the dice

P(X = 1, Y = 2)

This is obtained only when both dices are 1, hence its probability is 1/36

P(X = 1, Y = k) = 0 (k > 1)

because if the largest value of the dice is 1, then both dices are 1

P(X = 2, Y = 3)

one dice is 2, the other one is 3, hence there are 2 possibilities and the probability is 2/36 = 1/18

P(X = 2, Y = 4)

This happens only if both dices are 2, hence the probability is 1/36.

P(X = 2, Y = k) = 0 (k > 2)

same argument of above. If the largest dice is 2, then the sum is either 3 or 4.

P(X = 3, Y = 4), P(X = 3, Y = 5)

in both given events we need one dice to be 3 and the other dice to be 1 for the first event and 2 for the second event. In both cases, there are only 2 favourable cases, hence the probability of the event is 2/36 = 1/18

P(X = 3, Y = 6)

This event happens only when both dices are 3, hence the probability is 1/36

This should show a pattern. As long as x₀ is between 1 and 6, if y₀ is between x+1 and 2x-1, then the probability P(X = x₀, Y = y₀) is 1/18 (either first dice is x₀, second dice is y₀-x₀ or first dice is x₀ and second dice is y₀ - x₀), also P(X = x₀, Y = 2x₀) = 1/36 (both dices are x₀). Every other event has probability 0.

b) We can separate them using conditional probability and the fact that both dices results are independent with each other.

P(X = x₀, Y = y₀) = P(X = x₀) * P(Y = y₀ | X = x₀)

P(X = x₀) = 1/6 for any value x₀ between 1 and 6.

If y₀ is x₀, this means that the first dice has the largest value, so the second dice is between 1 and x₀, and the probability of this event is x₀/6 (x₀ favourable cases over 6 possible ones).

If y₀ is not x₀, then it should be higher (otherwise the event would be impossible and it would have probability 0). As long as y₀ is between 2 and 6, the probability of this event is 1/6.

Thus

P(X = x₀, Y = x₀) = 1/6 * x₀/6 = x₀/36

P(X = x₀, Y = x₀ + k) = (1/6)² = 1/36 (k > 0)

Every other probability is 0

P(X = x₀, Y = x₀) = 1/36 (because both dices are equal to x₀ in this event)

P(X = x₀, Y = x₀+k) = 2/36 = 1/18 (here k > 0. One possibility is the first dice is x₀ and the second one is x₀+k, and the remaining possibility is the first dice is x₀+k and the second dice is x₀)

Evert other event has probability 0.

4 0

3 years ago

Solve for z : 4z-6/4=3z+1

ruslelena [56]

Note the equal sign, what you do to one side, you do to the other side. Isolate the variable z.

First, subtract 3z and add 6/4 to both sides

4z (-3z) - 6/4 (+6/4) = 3z (-3z) + 1 (+6/4)

4z - 3z = 1 + 6/4

Simplify. Note that 1 = 4/4.

z = 4/4 + 6/4

Simplify. Combine like terms

z = 10/4

Simplify. Change the improper fraction into mixed fraction and simplify.

z = 10/4 = 2 2/4 = 2 1/2

7 0

4 years ago