Answer:
By 2020, there will be 1,147 species of birds left
Step-by-step explanation:
The general model for an exponential decrease is;
y = I(1 - r)^t
where in this case;
y is the number of bird species at a particular decade from the initial
I is the number of birds initially at 1990
r is the decrease percentage which is 1.5% per decade ; 1.5% = 1.5/100 = 0.015
t in this case will be the number of decades after the initial
Mathematically, a decade is 10 years
The difference between 2020 and 1990 is 30
The number of decades in 30 years is 30/10 = 3
so t will be 3 here
Substituting these values into the equation, we have
y = 1200(1-0.015)^3
y = 1200(0.985)^3 = 1,146.8
To the nearest whole number, this is 1,147
Answer:
Step-by-step explanation:
The equations of the system are
From the graph it can be seen that points 
and 
falls in the bounded region.
The income will be
So, the person can do 3 small jobs and build 1 and a half cabinets per day.
The maximum income will be .
Take an arbitrary vector (<em>x</em>, <em>y</em>, <em>z</em>), which goes from the origin to some point (<em>x</em>, <em>y</em>, <em>z</em>) on the plane we want to find.
Subtract from this vector, the vector that points to 
, which is (-3, 3, 1). This translates the first vector so that it starts at the point and is directed at some point (<em>x</em>, <em>y</em>, <em>z</em>). We get a new translated vector, (<em>x</em> + 3, <em>y</em> - 3, <em>z</em> - 1), which lies in the plane.
The normal vector to the plane is orthogonal to every vector in the plane. So taking the dot product of any vector in the plane with the normal to the plane will always result in 0. We use this to find the plane's equation:
and so the answer is D.
The two algebraic fractions can be added or subtracted only if they have the common denominators. So when adding or subtracting algebraic fractions the first thing that must be done is to take the LCM of the denominators and convert the denominators to same expressions. Only after this step the fractions can be added or subtracted. If this step is not performed, the operations cannot be performed correctly. This concept is similar to the addition and subtraction of simple fractions.
Answer:
29
Step-by-step explanation:
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