All categories

2 years ago

Write $\frac{99}{100}\cdot(0.\overline{4})$ as a fully simplified fraction.

Mathematics

1 answer:

Oksi-84 [34.3K]2 years ago

6 0

Answer:

$\frac{11}{25}$

Explanation:

The expression that must be rewritten as a fully simplified fraction is:

$\frac{99}{100}\cdot(0.\overline{4})$

You must, first, convert $0.\overline{4}$ as a fraction.

The line over the decimal 4 means that the digit 4 repeats indefinetly.

To find the fraction that represents this number you follow this procedure:

$F=0.\overline 4\\ \\ 10F=4.\overline 4\\ \\ 10F-F=4\\ \\ 9F=4\\ \\ F=4/9$

Now, you can mutiply both fractions:

$\frac{99}{100}.\frac{4}{9}=\frac{99\times 4}{100\times9}=\frac{11}{25}$

You might be interested in

A machine in a chocolate factory is set to squirt out a predetermined amount of molten chocolate. When the machine is set to x,

finlep [7]

Answer:

Sorry I need Points but I also need help

Step-by-step explanation:

4 0

2 years ago

Which expression is equivalent to 10x2y + 25x2? 5x2(2y + 5) 5x2y(5 + 20y) 10xy(x + 15y) 10x2(y + 25)

olya-2409 [2.1K]

The answer would be A. 5x2(2y+5)

5 0

2 years ago

Read 2 more answers

Find three mutually orthogonal unit vectors in R^3 besides plusminus i, plusminus j, and plusminus k. There are multiple ways to

viktelen [127]

Answer:

u=(1,1,2), v=(-3,1,2), w=(1,-2,1/2)

Step-by-step explanation:

Since the vectors must be orthogonal, then they must satisfy that the dot product between them is 0.

Then

$1(x)+1(-1)+2(2)=0\\x=-3$

and $-3(1)-1y+2z=0 \text{ and }\\1+1y+2z=0\\$ .

Solving for y, y=-2z-1 and substituting in the first equation, -3+2z+1+2z=0, then

z=1/2, and y=-2(1/2)-1=-2

6 0

2 years ago

Suppose a set of data about the spread (in hundreds of acres) of a food-borne bacteria (after t weeks) in lettuce has the follow

Alexxandr [17]

Answer:

A sinusoidal model would be used

The kind of function that have consistency in the periodic rate of change is the Average rate of changes

Step-by-step explanation:

The type of model that would be used is sinusoidal model and this is because there is periodic change in the values given ( i.e the rate of changes given )

For percentage rate of changes :

starting from 0.9% there is an increase to 1.3% then a decrease to 1.1% and a further decrease to 1% before an increase to 1.3% and another decrease to 1%

For Average rate of changes:

starting from 2.9 there is a decrease to 2.4, then an increase to 3.7 and another decrease to 3.1 followed by an increase to 3.6 and a decrease back to 3.2

This relation ( sinusoidal model ) is best suited for a linear model because there is a periodic rate of change in the functions

The kind of function that have consistency in the period rate of change is the Average rate of changes

6 0

2 years ago

Barrett works at an ice cream shop. The function f(x) represents the amount of money PLEASE HELP!!!!!!!!!!!!!

oee [108]

Answer:

$f(g(x))=6x^3+4$ , it is the amount of money earned per number of hours of work, x

Step-by-step explanation:

Here we have two functions:

$f(x)=2x^2 +4$

This function represents the amount of money (the earning) per unit x

Then we have the function

$g(x)=\sqrt{3x^3}$

which represents the number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works.

Here we want to find the composite function

$f(g(x))$

which means that we use the output of $g(x)$ as input for $f(x)$ . In this context, this means that the function $f(g(x))$ represents the amount of money earned per number of hours of work, x.

Substituting g(x) into the x of f(x), we find:

$f(g(x))=2(g(x))^2+4=2(\sqrt{3x^3})^2+4=2(3x^3)+4=6x^3+4$

7 0

2 years ago