Express the following repeating decimal as a fraction in simplest form.

Express The Following Repeating Decimal As A Fraction In Simplest Form.

Answers

Answer 1

Answer:

[tex]0.\overline{369} = \frac{41}{111}[/tex]

Step-by-step explanation:

x = 0.369369369...

10x = 3.69369369...

100x = 36.9369369...

1000x = 369.369369...

1000x - x = 369

999x = 369

[tex]x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}[/tex]


Related Questions

Find the equation of the line with Slope = 3 and passing through (4, 10) .write your equation in the form y=mx+b

Answers

The slope is given so you straight away apply it to the equation,

Y=mx+b

Y=3x+b

Now replace the points x and y to find b (y-intercept)

10=3(4)+b

10-12=b

b= -2

Final answer:

Y=3x-2

Hope that answers your question and best of wishes!!

The table shows a linear relationship between x and y.
х
у
-20
96
-12
60
-6
33
-2
15
What is the rate of change of y with respect to x?

Answers

Answer:

[tex] -\frac{9}{2} [/tex]

Step-by-step explanation:

Rate of change of x and y can be calculated using the following formula and using any two given pair of values from the table:

Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using (-12, 60) and (-6, 33).

Where,

[tex] (-12, 60) = (x_1, y_1) [/tex]

[tex] (-6, 33) = (x_2, y_2) [/tex]

Plug is the values

Rate of change = [tex] \frac{33 - 60}{-6 -(-12)} [/tex]

Rate of change = [tex] \frac{-27}{6} [/tex]

Simplify

Rate of change = [tex] \frac{-9}{2} [/tex]

Rate of change = [tex] -\frac{9}{2} [/tex]

In the questions below suppose the variable x represents students and represents courses, and:

•M(y): y is a math course F(x): x is a freshman
•B(x): x is a full-time student T(x,y): x is taking

•Write the statement in good English without using variables in your answers.

Answers

Answer:

Here the answer is given as follows,

Step-by-step explanation:  

The last three parts are coming with a question mark, so can't answer those parts. post the image or write it properly  

a) Every student is taking at least one course.  

[tex]\forall x \exists y T(x,y)[/tex]  

So for all x, there is a y such that T(x,y) is a true will be given by the above statement  

b) There is a part-time student who is not taking any math courses.  

[tex]\exists x \forall y [A(x) \Lambda (M(y) \rightarrow ~T(x,y))][/tex]

write equation of the line below​

Answers

Hi there!

We are given two ordered pairs which are:

(0,0)(5,4)

If you are curious how do I get these ordered pairs, they come from those two big circles or dots. x and y make relation and can be written as (x,y).

1. Find the slope

Yes, our first step is to find the slope of a graph if you want to find an equation. You may be curious how to find that right? No worries! We have got a special formula for you to find the slope!

[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]

Since we have two given points, we can substitute them in the formula.

[tex] \large{m = \frac{4 - 0}{5 - 0} } \\ \large \boxed{m = \frac{4}{5} }[/tex]

2. Form an equation.

Since we have finally found, got or evaluated the slope. Next step is to find the y-intercept. Oh! Before we get to form an equation, do you know the slope-intercept form? We will be using that linear equation form since it is commonly used in the topic.

[tex] \large \boxed{y = mx + b}[/tex]

Where m = slope and b = y-intercept. We substitute m = 4/5.

[tex] \large{y = \frac{4}{5} x + b}[/tex]

Next thing to remember is that when the graph intersects an origin point, b-term or y-intercept would be 0. Therefore b = 0 since the graph intersects (0,0).

[tex] \large \boxed{y = \frac{4}{5} x}[/tex]

3. Answer

Therefore the equation of the line is y = 4x/5.

Examine the geometric relationships in the diagram below which option shows the correct value of x and y?

Answers

Answer:all of them

Step-by-step explanation:

If f(x) is an exponential function where f(-2,5) = 9 and f(7) = 91, then find the value of f(12), to the nearest hundredth.

Answers

Answer:

[tex]f(12) = 323.02[/tex]

Step-by-step explanation:

Given

[tex]f(-2.5) = 9[/tex]

[tex]f(7) = 91[/tex]

[tex]f(12) = 16.7 * 1.28^{12[/tex]

Required

[tex]f(12)[/tex]

An exponential function is:

[tex]f(x) = ab^x[/tex]

[tex]f(-2.5) = 9[/tex] implies that:

[tex]9 = ab^{-2.5}[/tex]

[tex]f(7) = 91[/tex] implies that:

[tex]91 = ab^7[/tex]

Divide both equations

[tex]91/9 = ab^7/ab^{-2.5}[/tex]

[tex]91/9 = b^7/b^{-2.5}[/tex]

Apply law of indices

[tex]91/9 = b^{7+2.5}[/tex]

[tex]10.11 = b^{9.5}[/tex]

Take 9,5th root of both sides

[tex]b = 1.28[/tex]

So, we have:

[tex]9 = ab^{-2.5}[/tex]

[tex]9 = a * 1.28^{-2.5}[/tex]

[tex]9 = a * 0.54[/tex]

[tex]a = 9/0.54[/tex]

[tex]a = 16.7[/tex]

f(12) is calculated as:

[tex]f(x) = ab^x[/tex]

[tex]f(12) = 16.7 * 1.28^{12[/tex]

[tex]f(12) = 323.02[/tex]

one fourth of a number is 5. find the number​

Answers

Hope this helps. Please mark brainliest

Answer: 20

let the number be x

1/4 x = 5

x=5*4

x=20

Answer:

x=20

Step-by-step explanation:

[tex]\frac{1}{4}x=5\\x=20[/tex]

divide [tex]\frac{1}{4}[/tex] on both sides, which gives you 20.

order of operation problem who two operations inside parentheses and two ex outside ( using all add, subtract, multiply and divide)
PLEASE SHOW ALL WORK

Answers

Answer:

17 + 123 (4 - 1) + (36 / 18) 52 =

17 + 123 x 3 + 2 x 52 =

17 + 369 + 104 =

17 + 473 =

490

Step-by-step explanation:

hope this helps! i made up everything so i hope its okay!

3.7 pounds of meat costs $20.35. What is the price per pound?

Answers

Answer:

$5.5 per pound of meat

Step-by-step explanation:

$20.35 ÷ 3.7 = $5.50

Hope this is helpful

peter bought 3 suits and 3 pairs of jeans and paid $2397. James bought 8 suits and 11 pairs of jeans and paid $6989. What is the price of each?

Answers

Answer:

Therefore each suit cost $600 and each jean cost $199

Step-by-step explanation:

Let x represent the price of each suit and let y represent the price of each jeans.

Since 3 suits and 3 pairs of jeans cost $2397, this can be represented by the equation:

3x + 3y = 2397

Dividing through by 3:

3x/3 + 3y.3 = 2397/3

x + y = 799    (1)

Also, 8 suits and 11 pairs of jeans cost $6989, this can be represented by the equation:

8x + 11y = 6989      (2)

To find x and y, solve equation 1 and 2 simultaneously. Multiply equation 1 by 8 and subtract from equation 2 to get y:

3y = 597

y = $199

Put y = $199 in equation 1:

x + 199 = 799

x = $600

Therefore each suit cost $600 and each jean cost $199.

y = 2x - 3
y = -x + 3 solve for x and y

Answers

We are given the system of equations:

[tex] \large{ \begin{cases} y = 2x - 3 \\ y = - x + 3 \end{cases}}[/tex]

Since both are y-isolated equation, we can combine them together.

[tex] \large{2x - 3 = - x + 3}[/tex]

Isolate and solve for x-term.

[tex] \large{2x - 3 + 3 + x = - x + 3 + x + 3} \\ \large{2x + x = 6 \longrightarrow 3x = 6} \\ \large{ \frac{3x}{3} = \frac{6}{3} \longrightarrow \boxed{ \red{x = 2}}}[/tex]

Next, we find the value of y. Simply substitute x = 2 in one of these equations. The less coefficient values, the faster and better. I will substitute x = 2 in y = -x+3. You can substitute x = 2 in y = 2x-3 if you want but the result would be the same.

[tex] \large{y = - x + 3}[/tex]

Substitute x = 2 in the equation.

[tex] \large{y = - 2 + 3} \\ \large \boxed{ \blue{y = 1}}[/tex]

Therefore - when x = 2, y = 1. We can write in coordinate point or ordered pair as (2,1) from (x,y).

Answer

x = 2, y = 1(2,1) --- ordered pair

please help meeeeeeee
pt 4

Answers

Answer:

The answer is

[tex]2 {x}^{2} + 3x - 1 = 0[/tex]

Why? Below I explain

Step-by-step explanation:

That formula has three variables a, b and c.

So, a = 2, b = 3 and c = -1

Because the formula is written like

[tex] \frac{ - b + - \sqrt{ {b}^{2} - 4 \times a \times c} }{2 \times a} [/tex]

The graph of the function f(x)=4/5 sqrt x is shown.
What is the domain of the function?

Answers

Answer:

All real number greater than equal to zero.

Step-by-step explanation:

The function is given by

[tex]f(x) = \frac{4}{5}\sqrt x[/tex]

The domain is defined as the input values so that the function is well defined.

here, the values of x should be all real number and zero also.

So, the correct option is  (d).

Answer:

D

Step-by-step explanation:

need help pls gving brainliest

Answers

-3
-8

X+9=-10
X=-10-9
X=-19

Need help on this question been stuck on it

Answers

Answer:

Exponential Function

Step-by-step explanation:

y values increase by x4

Answer:

exponential function

the ans is b

A jean manufacturer makes three types of jeans, each of which goes through three manufacturing phases: cutting, sewing, and finishing. The number of minutes each type of product requires in each of the three phases is given below:

Jean Cutting Sewing Finishing
I 8 12 4
II 12 18 8
III 18 24 12

There are 5200 minutes of cutting time, 6000 minutes of sewing time, and 2200 minutes of finishing time each day. The company can sell all the jeans it makes and makes a profit of $4 on each Jean I, $4.50 on each Jean II, and 6 on each Jean III.

Required:
a. What number of jeans in each category should be made each day to maximize profits?
b. Formulate a linear programming problem that models the problem given above. Be sure to identify all variables used.
c. Analyze the solution.

Answers

Answer:

z ( max)  =  2000 $

x₁  =  500       x₂ = 0     x₃  = 0

Step-by-step explanation:

                         cutting       sewing    finishing  Profit $

Jean1   (x₁ )           8                 12              4             4

Jean2  (x₂ )          12                18              8              4.5

Jean3  (x₃ )          18                24            12              6

Time available  5200          6000        2200

b) Formulation of a linear programming problem:

Objective Function  z

z  =  4*x₁   +  4.5*x₂  + 6*x₃        to maximize

Constrains:

Constrain 1

Available cutting time  5200 minutes

8*x₁  +  12*x₂  +  18*x₃   ≤  5200

Constrain 2:

Available sewing  time  6000 minutes

12*x₁  +   18*x₂   +  24*x₃    ≤  6000

Constrain 3:

Available finishing time  2200 minutes

4*x₁   +   8*x₂   +  12*x₃    ≤ 2200

General constraints:

x₁    ≥ 0            x₂   ≥ 0             x₃  ≥  0     all integers

After 6 iterations the optimal solution is:

z ( max)  =  2000 $

x₁  =  500       x₂ = 0     x₃  = 0

We can see in the model that times required to make jean 2  and jean 3

are much bigger than jean 1 and but the price of jean 2 is only 0.5 $ above the price of jean 1 and jean 3 is only 2 $.

Find an equation for the line with the given property. (a) It passes through the point (2, −6) and is parallel to the line 4x + y − 10 = 0.
It has x-intercept 6 and y-intercept 4.

Answers

Answer:

[tex]y = -4x + 2[/tex]

Step-by-step explanation:

Required

Determine the equation

From the question, we understand that, it is parallel to:

[tex]4x + y -10 = 0[/tex]

This means that they have the same slope.

Make y the subject to calculate the slope of: [tex]4x + y -10 = 0[/tex]

[tex]y = -4x + 10[/tex]

The slope of a line with equation [tex]y =mx + c[/tex] is m

By comparison:

[tex]m = -4[/tex]

So, the slope of the required equation is -4.

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where:

[tex](x_1.y_1) = (2,-6)[/tex]

So, we have:

[tex]y = -4(x - 2) -6[/tex]

Open bracket

[tex]y = -4x + 8 -6[/tex]

[tex]y = -4x + 2[/tex]

Please help!! First person gets award or whatever it is!! Awarding 10 points

Answers

2c^2
Square root

Brainly wants me to have 20 characters so don’t mind the text down here

x + 3y = 10
-x + y = 6​

Answers

Answer:

X= -2. Y= 4.

Step-by-step explanation:


Write the expression. Then, complete the statements.
twice the difference of a number and seven
The word "twice" means multiplication by 2 v
The words "the difference of indicate

Answers

The answer is b have a good day

HELP!! I don’t know part C or D and I need to know if part A and B are correct

Answers

Answer:

Step-by-step explanation:

A and B are correct!

For part C, just multiply the dimensions given to you by four.

For part D, the answer would be 4 x 4 x 4 which is 264

7 + 8/5-2
Could someone help me with this?​

Answers

Answer:

hope it's helpful for you

Exact form: 33/5 - hope it help

Pls help I’ll brainlest

Answers

2) G
3) E
4) A
5) E
6) C

If P = (7,-4), Find:
(180° (P)
([?], []
Enter

Answers

Step-by-step explanation:

the answer is in the above image

It costs $21.50 to enter an amusement park and $0.50 to ride a ride. You have $24. Write an equation that represents the number r of rides you can ride.

Answers

Answer:

$24.00=$21.50+r*$.50

Step-by-step explanation:

total cost= entrance fee + r (number of rides) * $0.50 (cost of rides)

$24.00=$21.50+r*$.50

2.50=r*.50

2.5/.5=r

r=5

Which function is shown in the graph below?

Answers

Answer:y=log1x

Step-by-step explanation:

If a normal distribution has a mean of 154 and a standard deviation of 15,
what is the value that has a z-score of 1.6?

Answers

Answer:

The correct answer is - 178.

Step-by-step explanation:

The standard deviation is a measure of the amount of dispersion in a set of values.

Given:

Mean of a normal distribution (m) = 154

Standard deviation (s) = 15

z-score = 1.6

Solution:

To find: value (x) that has a z-score of 1.6

z-score is given by = x-u/15

1.6*15 = x-154

=> 154+24 = x

x = 178

Convert the following improper fraction to a whole number or a mixed number: 41/6

Answers

Answer:

6 and 5 over 6

6 5/6

Step-by-step explanation:

it would be a mixed fraction because 6 can't go into 41 evenly

Answer:

6

Hope that this helps!

Rationalize the denominator of the fraction and enter the new denominator below.​

Answers

Answer:

7/19

Step-by-step explanation:

7/19=square root of 11=22-3 19

3+5 plz help will gibe brain

Answers

Answer:

8

Step-by-step explanation:

8 because i said so and i’m smart
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