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 $3. What are all possible integers Dorothy may have input?I got the answer

Answers

Answer 1

Answer: The correct answer is:

12.

Explanation:

Let x be the integer she inputs.

"One less than triple the input" would be 3x-1.

She gets 3 as the output; this means 3x-1=3.

To solve this, add 1 to each side:
3x-1+1=3+1
3x=4

Divide both sides by 3:
3x/3 = 4/3
x=4/3 = 1 1/3.

This will not work, however, as it is not an integer.

"One more than half the number" is 1/2x+1. Since she gets 3 as the output, this gives us:
1/2x+1=3

Subtract 1 from each side:
1/2x+1-1=3-1
1/2x=2

Divide both sides by 1/2:
$((1)/(2)x)/((1)/(2))=(2)/((1)/(2))\n\nx=2/ (1)/(2)$

When dividing fractions, flip the second fraction and multiply:
x=2÷(1/2) = 2×(2/1) = (2/1)×(2/1) = 4/1 = 4

While this is an integer, this does not work either, because this expression is for inputs that are even but not divisible by 4. This is divisible by 4, so it is not accurate.

"One-fourth of the input" is 1/4x. The output is 3, which gives us:
1/4x =3

Dividing both sides by 1/4, we have:
$((1)/(4)x)/((1)/(4))=(3)/((1)/(4))\n\nx=3/ (1)/(4)$

When dividing fractions, we flip the second fraction and multiply:
x=3÷(1/4) = 3×(4/1) = (3/1)×(4/1) = 12/1 = 12

This expression is for an input that is divisible by 4. 12 is divisible by 4, so this is accurate.

Answer 2

Answer:

Final answer:

Given the scenario, no valid integer input would result in an output of $3 from Dorothy's ? button on her calculator. The three conditions specified do not match any integer when the output is $3.

Explanation:

Given that the output of the ? button on Dorothy's calculator is $3, one thing that could have been input and fit one of the conditions is 4, because when an integer is divisible by 4, the calculator outputs its one-fourth. Since 4 is divisible by 4 and one-fourth of 4 equals 1, that's not correct. Now let's check the condition for even numbers not divisible by 4. The calculator outputs 1 more than half the number. So, if we plug in $3 as the output and solve the equation, we get: 3 = 1 + 1/2 (input). Solving for the input, we get 2*2 = 4, which is still wrong. So, finally, we check the condition for odd numbers. Here, the calculator outputs 1 less than triple the input. Substituting $3 as the output, we solve for the input: 3 = 3*(input) - 1. Solving for input, we get input = 4/3, which is not an integer. Therefore, there could not have been an integer input that resulted in a $3 output in this case.

Learn more about Calculator Function here:

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Calculating the Volume of a Hemisphere

The question asks for the volume of a hemisphere with a radius of 3 cm. The formula for the volume of a sphere is V = (4/3)πr³, and since a hemisphere is half of a sphere, the formula adapts to V = (1/2)(4/3)πr³. Using a radius (r) of 3 cm, we get V = (1/2)(4/3)π(3 cm)³.

Let's calculate the volume step by step:

First, calculate the volume of the full sphere using the radius of 3 cm: V = (4/3)π(3³) cm³
Compute the result: V = (4/3)(π)(27) cm³ = (36π) cm³
Since we want the volume of the hemisphere, we divide this number by 2: V = (36π/2) cm³ = (18π) cm³
Finally, we approximate π to 3.142 and round to the nearest tenth: V ≈ 18(3.142) cm³ ≈ 56.6 cm³

Therefore, the approximate volume of the hemisphere is 56.6 cm³, when rounded to the nearest tenth of a cubic centimeter.

Convert 198 grams to kilograms

Answers

Answer:

it's 0.198

Step-by-step explanation:

Answer:

0.198

Step-by-step explanation:

divide 198 by 1,000

a manufacturer of cat toys produces three different toys filled with catnip the toys are the shape of a cone cylinder sphere each with radius 3 inches the cone and the cylinder each have a height of 2 inches which statement about the toys are true choose all that apply help ?