Marc mows lawns for $25 each lawn, plus $5 for every hour he spends mowing. The equation for his total earnings per lawn is y =
1 answer:
Answer:
The constant pay of $25 signifies the intercept
Step-by-step explanation:
To address this query, we first need to comprehend and relate it to the formula for a straight line.
i.e this represents the line's equation
where m= slope
y= dependent variable
x= independent variable
c= intercept
Given
by comparing the two expressions, we can observe that
25 is equivalent to c, which denotes the intercept
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Answer:
After five years beyond the initial 20-year stretch, the population of this small community will be 4268.
Step-by-step explanation:
t | 0 | 5 | 10 | 15 | 20
p | 100 | 200 | 450 | 950 | 2000
The representation of the exponential function is:
p = aeᵏᵗ
where a and k represent constants.
Taking the natural logarithm on both sides:
In p = In aeᵏᵗ
In p = In a + In eᵏᵗ
In p = In a + kt
In p = kt + In a.
We can apply linear regression to model the relationship between In p and t, thereby determining the values of k and In a.
t | 0 | 5 | 10 | 15 | 20
p | 100 | 200 | 450 | 950 | 2000
In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601
In p = kt + In a.
y = mx + b
Here m corresponds to k and b is In a
By conducting a linear regression on the transformed linear relationship among In p and t and creating a graph of the variables, we derive the regression equation:
y = 0.151x + 4.584
The first image illustrates the equations needed for estimating the parameters of linear regression.
The second image displays the regression calculations alongside the graph of In p versus t.
By comparing
y = 0.151x + 4.584
to
In p = kt + In a.
y = In p
k = 0.151
x = t
In a = 4.584
a = 97.905
Thus, the exponential relationship between p and t is formulated as:
p = 97.905 e⁰•¹⁵¹ᵗ
In order to forecast the population for 5 years ahead from the 20-year mark, we need to find p at t=25 years.
0.151 × 25 = 3.775
p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41, which rounds down to 4268.
Hope this assists!!!
∠ROT=160°
∠SOT=100°
Now we calculate ∠SOR as follows: ∠SOR = ∠ROT - ∠SOT
∠SOR = 160° - 100°
∠SOR = 60°
It is stated that the angles ROQ, QOS, and POT all have the same measure.
Thus, ∠SOQ + ∠QOR = 60°
Since ∠SOQ equals ∠QOR, we can express this as:
2∠SOQ = 60°
From which we find ∠SOQ = 60° ÷ 2
∠SOQ = 30°
Also, ∠POT = ∠SOQ = ∠ROQ = 30°
