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MaRussiya
8 days ago
12

Write the number 0.21212121.. as a fraction let x=

Mathematics
1 answer:
AnnZ [3.9K]8 days ago
7 0
To work with the repeating decimals, note that since there are two digits repeating, you will be using a 1 followed by two zeros, which is 100. This factor will be important for subsequent calculations.

Let’s denote the repeating decimal as x.

Thus, you can write

x = 0.212121...

Now, if you multiply this equation by 100, you can write it on top of the previous equation.
This results in:

100x = 21.212121...
x = 0.212121...

Next, set up a subtraction by taking the second equation from the first:

100x = 21.212121...
x = 0.212121...
- ----------------------------
99x = 21

Solving for x involves dividing both sides by 3:

33x = 7

Then, divide both sides by 33:

x = 7/33

Thus, we conclude that the repeating decimal 0.212121... equates to the fraction 7/33.

Answer: the fraction is 7/33
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Which function has an inverse that is also a function?
PIT_PIT [3949]

Response:

A. {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}

Detailed explanation:

Having just taken the quiz, it's worth noting that you can interchange the coordinates to observe those of the inverse function. Instances of identical x values indicate that it fails the line test, thus disqualifying it as a function with an inverse.

3 0
8 days ago
Read 2 more answers
Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he play
lawyer [4039]

Answer:

Part A:

x+y= 95

x = y+25

Part B: 35 minutes

Part C: No

Step-by-step explanation:

  • Part A:

Eric spends a total of 95 minutes daily playing basketball and volleyball combined.

x+y= 95

Where:

x =minutes Eric plays basketball

y = minutes he allocates to volleyball

He dedicates 25 minutes more to basketball compared to volleyball.

x = y+25

Equations are:

x+y= 95

x = y+25

  • Part B:

Substituting x=y+25 into the first equation yields:

(y+25) + y =95

Solving for y

y+25+y =95

25+2y=95

2y=95-25

2y=70

y = 70/2

y = 35 minutes

Part C: No

If x = 35

x+y= 95

35+y =95

y= 95-35

y = 60 minutes

Inserting y=60 into the other equation:

x = y+25

35 = 60+25

35 ≠85

5 0
9 days ago
Three people toss a fair coin and the odd one pays for coffee. if the coins all turn up the same, they are tossed again. find th
lawyer [4039]

In the absence of a specific question posed, below are the potential inquiries along with their respective answers:

P(fewer than 4 tosses)
= P(one toss) + P(two tosses) + P(three tosses)
= (3/4) + (3/4)(1/4) + (3/4)(1/4)^2
= 0.984375


Expected value
= 1 / p
= 1 / (3/4)
= 4 / 3

Variance
= (1 - p) / p^2
= (1 - (3/4)) / (3/4)^2
= (1/4) / (9/16)
= 4 / 9

Standard deviation
= sqrt(Variance)
= sqrt(4 / 9)
= 2 / 3

8 0
7 days ago
A department store sells logo shirts at an original price of $20. Every month that a shirt doesn’t sell, the store reduces the s
Inessa [3926]

Answer: Macy's pre-tax shirt price is $5.63

Step-by-step explanation:

Details:

Original cost = 20

sale price drops by 25% every month it remains unsold.


First markdown month:

20 * (100%-25%) = 20 * 75% = 15


Second markdown month:

15 * 75% = 11.25


Macy, being an employee, enjoys a 50% discount on the current price.

11.25 * 50% = 5.625

11.25 - 5.625 = 5.625 or rounded to 5.63

Hope this helps!:)

3 0
2 days ago
Read 2 more answers
In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.
zzz [4035]

Answer:

∠ R > 90°

\angle s + \angle T < \angle 90

\angle R > \angle T

\angle R > \angle S    

Explicación paso a paso:

Dado que en el triángulo RST

\angle R> (\angle s +\angle T)

Ahora, según la condición, un ángulo es mayor que la suma de los otros dos ángulos.

En un triángulo, la suma de los tres ángulos es 180°

Por lo tanto, si un ángulo mide  90°, la suma de los otros dos debe ser igual a 90°

Y si uno de los ángulos es de 90°, solo los otros dos pueden ser de 45° cada uno.

Aquí suponiendo que el ángulo s = ángulo T = 30°, entonces con esta condición el ángulo r sería de 120°, que es mayor que 90°.

De lo anterior, se concluye que

Para, \angle R> (\angle s +\angle T)

∵ ∠ R = 120°, por lo tanto es mayor que 90°.

Es decir, ∠ R > 90°

\angle s + \angle T < \angle 90

\angle R > \angle T

\angle R > \angle S   Respuesta

9 0
11 days ago
Read 2 more answers
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