What number has 300 tenths and 7 thousandths?
1 answer:
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It will take exactly 4 years for these trees to be the same height
Step-by-step explanation:
A gardener is planting two types of trees:
- Type A is 3 feet tall and grows at a rate of 7 inches per year
- Type B is 5 feet tall and grows at a rate of 1 inches per year
We need to find in how many years it will take for these trees to be the
same height
Assume that it will take x years for these trees to be the same height
The height of a tree = initial height + rate of grow × number of years
Type A:
∵ The initial height = 3 feet
∵ 1 foot = 12 inches
∴ The initial height = 3 × 12 = 36 inches
∵ The rate of grows = 7 inches per year
∵ The number of year = x
∴ = 36 + (7) x
∴ = 36 + 7 x
Type B:
∵ The initial height = 5 feet
∴ The initial height = 5 × 12 = 60 inches
∵ The rate of grows = 1 inches per year
∵ The number of year = x
∴ = 60 + (1) x
∴ = 60 + x
Equate and
∴ 36 + 7 x = 60 + x
- Subtract x from both sides
∴ 36 + 6 x = 60
- Subtract 36 from both sides
∴ 6 x = 24
- Divide both sides by 6
∴ x = 4
∴ The two trees will be in the same height in 4 years
It will take exactly 4 years for these trees to be the same height
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The tree diagram of the problem above is attached
There are four outcomes of the two events,
First test - Cancer, Second Test - Cancer, the probability is 0.0396
First test - Cancer, Second Test - No Cancer, the probability is 0.0004
First test - No Cancer, Second Test - There is cancer, the probability is 0.0096
First test - No cancer, Second Test - No cancer, the probability is 0.9054
The probability of someone picked at random has cancer given that test result indicates cancer is
The probability of someone picked at random has cancer given that test result indicates no cancer is
There are four outcomes of the two events,
First test - Cancer, Second Test - Cancer, the probability is 0.0396
First test - Cancer, Second Test - No Cancer, the probability is 0.0004
First test - No Cancer, Second Test - There is cancer, the probability is 0.0096
First test - No cancer, Second Test - No cancer, the probability is 0.9054
The probability of someone picked at random has cancer given that test result indicates cancer is
The probability of someone picked at random has cancer given that test result indicates no cancer is
1)
An irrational number is a number that a) can't be written as a fraction of two whole numbers AND b) is an infinite decimal without any sort of pattern.
For the first answer choice, clearly
does not pass the first criterion so we look at the second choice.
Let's come back to
and 
.
doesn't meet our first criterion, and let's skip 
for now.
It is often easier to disprove an irrational number than to prove one. There are a few famous irrationals to know (although there is an infinite number of irrationals). The most common are
. For now, it's just helpful to know these and recognize them.
So we can check off
and .
2)
For this next question, we know that
. Clearly this isn't irrational. Likewise, 
isn't irrational. 
, which is rational, leaving only 
. By process of elimination, this is the correct answer. Indeed, 
is an irrational number.
3) This notation means that we have 0.3636363636... and so on, to an infinite number of digits. It is called a repeating decimal.
But it can be written as a fraction because its pattern repeats, unlike for an irrational number.
Let's say
. Would you agree that 
? (We choose to multiply by 100 because there are two decimals that repeat. For 1, choose 10, for 3 choose 1,000, and so on.)
Now, let's subtract x from 100x and solve.
Voila!
An irrational number is a number that a) can't be written as a fraction of two whole numbers AND b) is an infinite decimal without any sort of pattern.
For the first answer choice, clearly
Let's come back to
It is often easier to disprove an irrational number than to prove one. There are a few famous irrationals to know (although there is an infinite number of irrationals). The most common are
So we can check off
2)
For this next question, we know that
3) This notation means that we have 0.3636363636... and so on, to an infinite number of digits. It is called a repeating decimal.
But it can be written as a fraction because its pattern repeats, unlike for an irrational number.
Let's say
Now, let's subtract x from 100x and solve.
Voila!