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Goshia [24]
3 years ago
13

Ruby conducted a survey and found that 5/6 of her classmates have a pet and 2/3 of those pets are dogs. what fraction of her cla

ssmate has dogs?
Mathematics
1 answer:
bekas [8.4K]3 years ago
3 0
It would be 1/6th of them has dogs. 
You might be interested in
In base $10$, the number $2013$ ends in the digit $3$. in base $9$, on the other hand, the same number is written as $(2676)_{9}
skelet666 [1.2K]
Note that

2013_{10}=2(10)^3+1(10)^1+3(10)^0

so that

\dfrac{2013}{10}=200+1+\dfrac3{10}

i.e. the remainder upon dividing 2013 (in base 10) by 3 is 3. The point is that any base-b representation of 2013_{10} will end in the digit 3 whenever division of 2013 by b leaves a remainder of 3.

First, we require that b\ge4, because any smaller base simply won't have 3 as a possible digit.

Second, we clearly can't have b\ge2014, because any value of b beyond that point will have 2013 as its first digit. That is, in base 2014, for instance, if we separate the digits of numbers by colons, we would simply have 2013_{10}=0:0:0:2013_{2014} (the 0s aren't necessary here, but only used for emphasizing that 2013 would be its own digit, regardless of how we represent digits outside of 0-9).

Third, we can't have b=2013 because 2013 divides itself and has no remainder. That is, 2013_{10}=10_{2013}.

So we've reduced the possible domain of solutions from all positive integers to just those lying within 4\le b\le2012.

Now, in terms of modular arithmetic, we're essentially solving the following equivalence for b:

2013\equiv3\pmod b

which, if you're not familiar with the notation or notion of modular arithmetic, means exactly "2013 gives a remainder of 3 when divided by b". It's equivalent to saying "there exists an integer n such that 2013=bn+3.

From this equation, we have 2010=bn. Now, we know both b,n must be integers, so we need only find the factors of 2010. These are

1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010

So we have 16 total possible choices for b,n. But we're omitting 1, 2, and 3 from the solution set, which means there are 13 base-b representations of the base-10 number 2013_{10} such that the last digit 2013_b is 3. They are

2013_{10}=31,023_5
2013_{10}=13,153_6
2013_{10}=2013_{10}
2013_{10}=8:14:3_{15}
2013_{10}=2:7:3_{30}
2013_{10}=30:3_{67}
2013_{10}=15:3_{134}
2013_{10}=10:3_{201}
2013_{10}=6:3_{335}
2013_{10}=5:3_{402}
2013_{10}=3:3_{670}
2013_{10}=2:3_{1005}
2013_{10}=1:3_{2010}

- - -

Added a link to some code that verifies this solution. In case you're not familiar with Mathematica or the Wolfram Language, in pseudocode we are doing:

1. Start with a placeholder list called "numbers", consisting of all 0s, of length 2010. We know 4\le b\le2013, which contains 2010 possible integers.
2. Iterate over b:
2a. Start with b=4.
2b. Ensure b doesn't exceed 2013.
2c. After each iteration, increment b by 1; in other words, after each step, increase b by 1 and use this as a new value of b.
2d. Check if the last digit of the base-b representation of 2013 ends is a 3. In the WL, IntegerDigits[x, n] gives a list of the digits of x in base-n. We only want the last digit, so we take Last of that. Then we check the criterion that this value is exactly 3 (===).
2d1. If the last digit is 3, set the (b-3)-th element of "numbers" to be a list consisting of the base b and the list of digits of 2013 in that base.
2d2. Otherwise, do nothing, so that the (b-3)-th element of "numbers" remains a 0.
3. When we're done with that, remove all cases of 0 from "numbers" (DeleteCases). Call this cleaned list, "results".
4. Display "results" in Grid form.
5. Check the length of "results".
7 0
3 years ago
Charlie used a regression calculator to generate the
Firdavs [7]

Answer:

Answer below, let me know if it didn't make sense.  

Step-by-step explanation:

I attached a picture of the scatterplot with a line connecting the points.  There is a definite upside down u type shape, and it doesn't look close to a line at all, so linear is not a good choice.  

an upside down u shape (or right side up u shape for that matter) is exactly what a quadratic is, or any polynomial if you do it right, but quadratic is the simplest, so let's go with that.

8 0
3 years ago
Read 2 more answers
Last month you spent $30 on clothing. This month you spent 150% of what you spent last month. How much did you spend this month?
mafiozo [28]

Answer:

you spent 45 dollars this month

6 0
3 years ago
Read 2 more answers
The table below shows the fifth powers of different numbers:
Lera25 [3.4K]
Part A. Yes, because y=f(x)=x⁵.
Part B. f(4)=2(4)+12=8+12=20.
5 0
3 years ago
A student's grade for the four quarters are 95, 83, 91, and 85. What does the student need to earn on the final exam to have an
gulaghasi [49]

Answer:

The least score the student can get is 71 to get an overall B average at the end of the year.

Step-by-step explanation:

Let the score she needs to get be = x

We now have to take the mean of all the five subjects <em>(including x)</em> and equate it to the least score she can have to get a B grade.

Let us take the least score the student needs to get a B grade to be 85

Mean of all 5 scores =

\frac{95+83+91+85+x}{5}=85

\frac{354+x}{5} =85

354+x = 425

x = 71

The least score the student can get is 71 to get an overall B average at the end of the year.

3 0
3 years ago
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