What is the domain of the function on the graph?

For f(x) = 4x+1, what is the output for the input 5?

blsea [12.9K]

Answer: f(x) = 21 .The output is 21 when the input is 5.

Step-by-step explanation:

f(x) = 4x+1 Substitute the input, 5, for x on the right side f(x) is the equivalent of y, the output you are looking for

f(x) = 4(5) + 1

f(x) = 20 +1

f(x) = 21

7 0

3 years ago

At a preschool 16 of the students are four years old of a four year olds 3/8 attended the full day program how many other studen

Nikitich [7]

Answer:

6 students at the preschool of four years old attended the full day program.

Step-by-step explanation:

Given:

Number of four years old students = 16

fraction of four years old students attended full day program = $\frac{3}{8}$

We need to find the number of four years old students attended the full day program.

Solution:

Now we can say that;

number of four years old students attended the full day program is equal to fraction of four years old students attended full day program multiplied by Number of four years old students.

framing in equation form we get;

number of four years old students attended the full day program = $\frac38\times 16 =6$

Hence 6 students at the preschool of four years old attended the full day program.

8 0

3 years ago

A. When comparing the "# of Bacteria" each hour, what is the number being multiplied by each time? *

LenaWriter [7]

Answer:

Part a) The number is 8

Part b) The initial number of bacteria is 4

Part c) $y=4(8)^x$

Part d) $y=100(8)^x$

Step-by-step explanation:

we know that

The equation of a exponential function is equal to

$y=a(b)^x$

where

y is the number of bacteria

x is the time in hours

b is the base of the exponential function

a is the initial number of bacteria

Part a) When comparing the "# of Bacteria" each hour, what is the number being multiplied by each time?

we know that

For x=1 h ----> y=32 bacteria

For x=2 h ----> y=256 bacteria

For x=3 h ----> y=2,048 bacteria

For x=4 h ----> y=16,384 bacteria

For x=5 h ----> y=131,072 bacteria

For x=6 h ----> y=1,048,576 bacteria

so

256/32=8

2,048/256=8

16,384\2,048=8

131,072/16,384=8

1,048,576\131,072=8

so

the base of the exponential function b is 8

Part b) What is the initial number of bacteria? (at time zero)

we know that

The number of bacteria at time x=1 hour , divided by the number of bacteria at time x=0 must be equal to 8 (see part a)

so

$\frac{32}{a}=8$

solve for a

$a=32/8=4\ bacteria$

Part c) Write a rule for this table

we have

$y=a(b)^x$

we have

$a=4\\b=8$

substitute

$y=4(8)^x$

Part d) Suppose you started with 100 bacteria, but they still grew by the same growth factor. Write the function rule for this situation

In this case

$a=100$

$b=8$ ---> the growth factor is the same

so

$y=100(8)^x$

6 0

3 years ago

Read 2 more answers

. A binary string containing M 0’s and N 1’s (in arbitrary order, where all orderings are equally likely) is sent over a network

Sophie [7]

Answer:

$P(k) = \frac{\binom{N}{k} \binom{(M+N) - N}{r-k}}{\binom{M+N}{r}}$

Step-by-step explanation:

We can model the string as a hypergeometric distribution, as each bit has two possible values, 1 or 0, and the chance of a 1 or 0 changes with every bit, as there are a finite number M of 0's and N of 1's and every bit takes one of those values.

If M+N (total size of the string) >> r (number of trials), we could model it as a binomial distribution as the probability of a 1 or 0 wouldn't change in a significant amount with every bit, but as we don't know the magnitude of M+N and r, we follow up with hypergeometric distribution.

The distribution has the following formula for probability:

$P(k) = \frac{\binom{K}{k} \binom{N - K}{n-k}}{\binom{N}{n}}$

Where k is the number of sucesses, K is how many total sucess states are in the population, N is the population size and n is the number of draws.

For our case, a 1 would be a sucess, i.e. k the number of 1's we want to know the probability, N our total number of 1's, M+N the length of the string (population size) and we want to analyse what happens in the first r bits (number of draws):

$P(k) = \frac{\binom{N}{k} \binom{(M+N) - N}{r-k}}{\binom{M+N}{r}}$

8 0

3 years ago

Which expressions are equivalent to z + (z + 6) z+(z+6)z, plus, left parenthesis, z, plus, 6, right parenthesis ?

Scorpion4ik [409]

In the question, the given expression is

$z+(z+6)$