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Rom4ik [11]
3 years ago
6

Dorothy has a mysterious $?$ button on her calculator. When she types in an integer and hits the $?$ button, if the input is odd

, the calculator outputs $1$ less than triple the input. if the input is even but not divisible by $4$, the calculator outputs $1$ more than half the number. if the input is divisible by $4$, the calculator outputs one-fourth of the input. Dorothy typed in an integer, hit the $?$ button, and saw an output of $13$. What are all possible integers Dorothy may have input?
Mathematics
1 answer:
inessss [21]3 years ago
8 0

Answer:

  {52}

Step-by-step explanation:

The calculator function appears to be ...

  f(x) = {3x -1, x odd; x/2 +1, x not divisible by 4; x/4, x divisible by 4}

The inverse of the first function is ...

  x = 3y -1

  (x+1)/3 = y . . . . (y must be odd)

For x = 13, this is 14/3, which is not an integer.

__

The inverse of the second function is ...

  x = y/2+1

  2(x-1) = y . . . . (y must <em>not</em> be divisible by 4)

For x = 13, this is 2·12 = 24, which is divisible by 4, so 24 is not the input value.

__

The inverse of the third function is ...

  x = y/4

  4x = y . . . . (y must be, and is, divisible by 4)

For x = 13, this is 4·13 = 52.

The only possible input value for an output of 13 is 52.

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Which stem-and-leaf plot has a median of 3.2<br><br><br><br> page.2
DiKsa [7]
Find the median of each set:-

Median is middle number of a data set. If a data set has an odd number of numbers then the median is the middle number when ordered form least to greatest but if its an even number you have to find the mean for the middle 2 numbers when ordered for least to greatest. 

A.

1.2, 2.4, 3.2, 3.2, 3.6, 4.0, 4.1, 4.7

Even numbers = 8
3.2 + 3.6 = 6.8
6.8 ÷ 2 = 
Median = 3.4
So this shows that A isn't the answer because the median of A is 3.4, not 3.2. 

B.

1.6, 2.8, 2.9, 3.1, 3.3, 3.6, 4.2, 4.5

Even numbers = 8
3.1 + 3.3 = 6.4
6.4 ÷ 2 = 3.2
Median = 3.2
<span>So this shows that B is the answer because the median of B is 3.2.

C. 

1.8, 2.0, 2.0, 2.2, 3.2, 4.7, 4.8, 4.9
</span>
Even numbers = 8
2.2 + 3.2 = 5.4
5.4 ÷ 2 = 2.7
Median = 2.7
<span>So this shows that C isn't the answer because the median of C is 2.7, not 3.2.
</span>
D. 

1.4, 1.7, 2.9, 3.0, 3.1, 3.2, 3.2, 3.2, 4
Odd numbers = 9
Median = 3.1

<span>So this shows that D isn't the answer because the median of D is 3.1, not 3.2.
</span>
The stem and leaf plot which median is 3.2 is B.
5 0
3 years ago
Find out if the lengths form a right triangle ​
Mila [183]

Answer:

The triangle is a right triangle.

Step-by-step explanation:

Since The Pythagorean Theorem only works on right triangles, we can use this knowledge to prove whether this triangle is right:

a^2 + b^2 = c^2\\10^2 + (2\sqrt{39})^2 = 16^2\\100 + (4 \times 39) = 256\\100 + 156 = 256\\256 = 256

Therefore, the triangle is right.

3 0
2 years ago
HELP ON THESE 2 QUESTIONSS PLSSSS
GaryK [48]

Answer:

1) the third equation  or X/2=2.0

2)  20 bucks

Step-by-step explanation:

for number 1 just plug in the x hi 4 and try to solve it

2) just calculate unit rate by 120/6=20

6 0
3 years ago
Solve for x. Leave your answer in simplest radical form.
pochemuha

Answer:

x = 4√7

Step-by-step explanation:

You can use the pythagorean theorem which is a² + b² = c²

if you plug it in, it would be...

x² + 12² = 16²

x² + 144 = 256, subtract 144 to both sides

x² = 112, square root both sides to make x by itself.

x = 4√7  

6 0
3 years ago
This year the Hawks won 20 games. Last year the Hawks won 16 games. What is the percent increase in the number of games the Hawk
andrey2020 [161]
The answer is 25% 1/4 of 16 is 4 4 +16=20
8 0
3 years ago
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