Answer:
k = -4
Step-by-step explanation:
The remainder theorem tells you that the remainder from division f(x)/(x -k) is f(k). You want the value of k such that ...
f(k) = -15
Looking on the given graph, you find that k must be -4. That is, ...
f(-4) = -15
k = -4
_____
The divisor with k=-4 is (x -(-4)) = (x +4). The second attachment shows the division of f(x) by (x+4). The remainder is shown on the bottom line.
Answer:
19 million
Step-by-step explanation:
So generally whenever we express a exponential function, it's in the form:
where a=initial value aka when x=0
in this case, b can be expressed as: , where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213
This gives us the following equation:
To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.
So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.
When x=1, we get: , which can be expressed as a 2.13% increase from year 0
When x=2, we get: , which can be expressed as a 2.13% increase from year 1
when x=3, we get: , which can be expressed as a 2.13% increase from year 2.
In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).
So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990
We get the following equation:
Using a calculator this simplifies to approximately:
Rounding this to the nearest integer would yield 19, and since the values are expressed in millions, the answer would be 19 million
<u>Number of terms = 48</u>
<u>common difference = 1.5</u>
This question involves the concept of Arithmetic Progression.
=
(a + l)
where;
a = first term
l = last term
n = number of terms
first term; a = 4
last term; l = 76
Sum of A.P; = 1920
1920 = (4 + 76)
simplifying this gives;
1920 = 40n
n = 1920/40
n = 48
=
+ (n - 1)d
where;
is first term
d is common difference
n is number of term
is the nth term in question
the 48th term is 76
Thus;
76 = 4 + (48 - 1)d
76 - 4 = 47d
72 = 47d
d = 72/47
d ≈ 1.5
Thus;
Number of terms = 48
common difference = 1.5
Read more at; brainly.com/question/16935540
Answer:
Step-by-step explanation:
From the given information; Let's assume that R should represent the set of all possible outcomes generated from a bit string of length 10 .
So; as each place is fitted with either 0 or 1
Similarly; the event E signifies the randomly generated bit string of length 10 does not contain a 0
Now;
if a 0 bit and a 1 bit are equally likely
The probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if a 0 bit and a 1 bit are equally likely is;
so ; if bits string should not contain a 0 and all other places should be occupied by 1; Then:
;