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3 years ago

Write the rational number as a decimal. Show your work. 5/9 -3/8 -3/11.

Mathematics

1 answer:

Bad White [126]3 years ago

4 0

I have memorized facts about fractions like these, so can tell you ...

$\dfrac{5}{9}=0.5\overline{5}\\\\-\dfrac{3}{8}=-3\times 0.125=-0.375\\\\-\dfrac{3}{11}=-0.27\overline{27}$

_____

A fraction with 9 as a denominator is a repeating 1-digit decimal with the decimal digit being the numerator of the fraction.

A fraction with 11 as a denominator is a repeating 2-digit decimal with the two digits being 9 times the numerator of the fraction.

1/8 = 0.125, so any multiple of 1/8 is that multiple of 0.125.

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What is the sum of series is numbers 64&66 ? Using the summation notation

iragen [17]

Answer:

64. 6138

66. 8.078125

Step-by-step explanation:

Let's take it one number at a time.

For number 64:

$6(2)^{1-1}=6$

$6(2)^{2-1}=12$

$6(2)^{3-1}=24$

$6(2)^{4-1}=48$

$6(2)^{5-1}=96$

$6(2)^{6-1}=192$

$6(2)^{7-1}=384$

$6(2)^{8-1}=768$

$6(2)^{9-1}=1536$

$6(2)^{10-1}=3072$

Sum = 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072

Sum = 6138

For number 66:

$12(-\frac{1}{2})^{0}=12$

$12(-\frac{1}{2})^{1}=-6$

$12(-\frac{1}{2})^{2}=3$

$12(-\frac{1}{2})^{3}=-1.5$

$12(-\frac{1}{2})^{4}=0.75$

$12(-\frac{1}{2})^{5}=-0.375$

$12(-\frac{1}{2})^{6}=0.1875$

$12(-\frac{1}{2})^{7}=-0.0078125$

$12(-\frac{1}{2})^{8}=0.046875$

$12(-\frac{1}{2})^{9}=-0.0234375$

Sum = 12 + -6 + 3 + -1.5 + 0.75 + -0.375 + 0.1875 + -0.0078125 + 0.046875 + -0.0234375

or to make things simpler:

Sum = 12 - 6 + 3 - 1.5 + 0.75 - 0.375 + 0.1875 - 0.0078125 + 0.046875 - 0.0234375

Sum = 8.078125

4 0

3 years ago

A parks and recreational board in Birch County is interested in estimating the proportion of its residents in favor of having mo

ankoles [38]

Answer:

Step-by-step explanation:

Trust me.

I just did it.

5 0

3 years ago

Area and Circumference of Circles

Thepotemich [5.8K]

Pi( $\pi$ ) is the ratio of circumference to diameter for any circle.

Perimeter is the distance around a circle.

Circumference of circle $C = \pi d$ .

Perimeter of circle $= 2 \pi r$

What is circle ?

A circle is a spherical shape without boundaries or edges.

A circle is a closed, curved object with two dimensions in geometry.

Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.

For smaller values of θ, the arc length AB is almost equal to the length of the line segment $\bar{AB}$ . Similarly, arc CD ≅ $\bar{CD}$ .

Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.

Circumference = $\pi \times$ diameter or circumference = 2 $\pi \times$ radius if this constant equals some value.

So it was proved.

Learn more about Circle click on this:

brainly.com/question/24375372

#SPJ13

7 0

1 year ago

A local university has 2.815 Hispanic students out of a total student population of 20.250. Do the Hispanic students have propor

Over [174]

Given:
The race percent of population is
White: 45%
Hispanic: 27%
Black: 18%
Asian: 7%
Other: 3%

Part a.
The university has 2,815 Hispanic out of the 20,250 total population.
This is equivalent to (2815/20250)*100 = 13.9%
This percentage is less than 27%, so Hispanics do not have proportional representation.

Answer: The Hispanic students do not have proportional representation.

Part b.
Let x = the extra number of Hispanic students needed for proportional representation of 27% or 0.27.
Then
(2815 + x)/20250 = 0.27
2815 + x = 20250*0.27 = 5467.5
x = 5467.5 - 2815 = 2652.5

This means that 2,653 extra Hispanic students are required for a population of 20,250 students.

Answer: 2,653 extra Hispanic students.

5 0

3 years ago

Show how to use substitution or elimination to solve the following system of equations. Write the solution as an ordered pair.

max2010maxim [7]

Answer:

(4, 6)

Step-by-step explanation:

Substitution

Using the second equation, we can substitute for y in the first equation.

4x -(2x-2) = 10

2x +2 = 10 . . . . simplify

x +1 = 5 . . . . . . .divide by 2

x = 4 . . . . . . . . . subtract 1

y = 2(4) -2) = 6 . . . . substitute for x in the equation for y

The solution is (x, y) = (4, 6).

Elimination

Often, we like to start with both equations in standard form when we solve by elimination. That is nice, but not completely necessary.

We can eliminate the y-variable by simply adding the two given equations.

(4x -y) +(y) = (10) +(2x -2)

4x = 8 + 2x . . . . . collect terms. The y-variable has been eliminated.

2x = 8 . . . . . . . . . subtract 2x

x = 4 . . . . . . . . . . divide by 2

Y can be found using the second equation.

(x, y) = (4, 6)

We could have eliminated the x-variable by multiplying the second equation by 2, then adding the two equations.

(4x -y) +2(y) = (10) +2(2x -2)

y = 6 . . . . . . . . . subtract 4x from both sides. The x-variable has been eliminated.

Now, x can be found using either equation.

6 = 2x -2 . . . substitute for y in the second equation

3 = x - 1 . . . divide by 2

x = 4 . . . . . add 1

(x, y) = (4, 6)

3 0

3 years ago