1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elina [12.6K]
3 years ago
13

I tell you these facts about a mystery number, $c$: $\bullet$ $1.5 < c < 2$ $\bullet$ $c$ can be written as a fraction wit

h one digit for the numerator and one digit for the denominator. $\bullet$ Both $c$ and $1/c$ can be written as finite (non-repeating) decimals. What is this mystery number?
Mathematics
2 answers:
makkiz [27]3 years ago
8 0

Answer:

Possible answer: \displaystyle c = \frac{16}{10} = \frac{8}{5} = 1.6.

Step-by-step explanation:

Rewrite the bounds of c as fractions:

The simplest fraction for 1.5 is \displaystyle \frac{3}{2}. Write the upper bound 2 as a fraction with the same denominator:

\displaystyle 2 = 2 \times 1 = 2 \times \frac{2}{2} = \frac{4}{2}.

Hence the range for c would be:

\displaystyle \frac{3}{2} < c < \frac{4}{2}.

If the denominator of c is also 2, then the range for its numerator (call it p) would be 3 < p < 4. Apparently, no whole number could fit into this interval. The reason is that the interval is open, and the difference between the bounds is less than 2.

To solve this problem, consider scaling up the denominator. To make sure that the numerator of the bounds are still whole numbers, multiply both the numerator and the denominator by a whole number (for example, 2.)

\displaystyle \frac{3}{2} = \frac{2 \times 3}{2 \times 2} = \frac{6}{4}.

\displaystyle \frac{4}{2} = \frac{2\times 4}{2 \times 2} = \frac{8}{4}.

At this point, the difference between the numerators is now 2. That allows a number (7 in this case) to fit between the bounds. However, \displaystyle \frac{1}{c} = \frac{4}{7} can't be written as finite decimals.

Try multiplying the numerator and the denominator by a different number.

\displaystyle \frac{3}{2} = \frac{3 \times 3}{3 \times 2} = \frac{9}{6}.

\displaystyle \frac{4}{2} = \frac{3\times 4}{3 \times 2} = \frac{12}{6}.

\displaystyle \frac{3}{2} = \frac{4 \times 3}{4 \times 2} = \frac{12}{8}.

\displaystyle \frac{4}{2} = \frac{4\times 4}{4 \times 2} = \frac{16}{8}.

\displaystyle \frac{3}{2} = \frac{5 \times 3}{5 \times 2} = \frac{15}{10}.

\displaystyle \frac{4}{2} = \frac{5\times 4}{5 \times 2} = \frac{20}{10}.

It is important to note that some expressions for c can be simplified. For example, \displaystyle \frac{16}{10} = \frac{2 \times 8}{2 \times 5} = \frac{8}{5} because of the common factor 2.

Apparently \displaystyle c = \frac{16}{10} = \frac{8}{5} works. c = 1.6 while \displaystyle \frac{1}{c} = \frac{5}{8} = 0.625.

stealth61 [152]3 years ago
7 0

Answer: 1.6

This answer is copied and pasted from an online site (aops) and this is what their explanation was, so please do not report for plagiarism!

Step-by-step explanation:

Because $c$ can be written as a finite decimal, we know it can be written as a fraction whose numerator is an integer and whose denominator is a power of $10$. Thus, after simplification, the denominator must still be a divisor of some power of $10$. That is, it must be factorable into $2$s and $5$s.

Since this denominator is a single digit, our choices are $1,$ $2,$ $4,$ $5,$ or $8$. We have the same options for the numerator, since we know $1/c$ also has a finite decimal. From here we could just test all the possibilities to see if they're between $1.5$ and $2,$ but with a little cleverness we can eliminate some of the remaining possibilities. If we don't use $5$ as the numerator or denominator, then $c$ is forced to be a power of $2$, so it can't be between $1.5$ and $2$. So, we must use $5$, and our only plausible choices are $5/2$ (which is $2.5$), $5/4$ (which is $1.25$), and $8/5$ (which is $1.6$). Of these, only $c=\boxed{8/5}$ works.

You might be interested in
Find the slope of the line that passes through the points  (0, 4) and (2, -3).
kifflom [539]
(0,4)(2,-3)
slope = (-3 - 4) / (2 - 0) = -7/2
8 0
3 years ago
Read 2 more answers
Help!!!1!!!!!!!!!!!!!!!!!!!!!!
ad-work [718]
Equation B is written in vertex form, which means you can read the vertex (extreme value) from the numbers in the equation.

Vertex form is
   y = a(x -h)² + k
where the vertex (extreme point) is (h, k). Whether that is a maximum or a minimum depends on the sign of "a". When "a" is negative, the graph is a parabola that opens downward, so the vertex is a maximum.


Equation B reveals its extreme value without needing to be altered.
The extreme value of this equation is a maximum at the point (2, 5).

3 0
3 years ago
What is the number 1,340,000 from standard form to scientific notation
Kisachek [45]
6 1.34*10 Just move it to the left 6 times
7 0
3 years ago
Read 2 more answers
Retail price: $745; discount rate: 12.5% what is the discount?
Mariulka [41]

Answer:

mmmmmmmm

Step-by-step explanation:

the answer ................

7 0
3 years ago
Forty percent of the 30 members of the drama club were members of the senior class
andriy [413]

10%of30=3

3x4=12

A. 40%of 30=12 senior class members.

B. 60% of the class were not senior class members

4 0
2 years ago
Read 2 more answers
Other questions:
  • Can someone help me with number 8 please
    15·1 answer
  • Please explain how you got your answer .
    6·1 answer
  • 1.) Is (0, 3) a solution to the equation y= x+3
    10·2 answers
  • A restaurant sells 12 breakfast meals used what’s 25% of a breakfast meals are pancakes how many orders of pancakes does the res
    7·1 answer
  • Every spring, Marvin plants colorful flowers in his garden. This year, he decides to plant petunias. He buys them at the garden
    6·1 answer
  • What is the what is the simplest form for 13/ 51
    12·2 answers
  • Find the gradient of each of these line y = 2x + 4
    11·2 answers
  • Use the formula d = rt. Find t for r = 46.1 m/h and d = 253.55 m.
    13·2 answers
  • Find the x and y intercept of y = 5x - 2. Random answers will be reported. Who ever answers right first will be marked brainlest
    11·2 answers
  • VHelena has five different flowers. She plans to give one flower to each of her five teachers in any order. She gives the first
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!