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Rom4ik [11]
3 years ago
14

USE FOR MASTERY Number of attempts allowed: 1 Write two rational numbers a/b and c/d, where a, b, c, and d are the digits 2, 3,

4, or 5, such that no digit can be used more than once and that the two rational numbers are the greatest distance apart on the number line. Explain how you got this answer.
Mathematics
1 answer:
iogann1982 [59]3 years ago
5 0

Answer:

We want to craft:

a/b and c/d

where a, b, c and d can be 2, 3, 4 and 5.

Such that the distance in the number line between these two numbers is maximized.

Then we want one number to be really small, and the other to be really large.

Remember two things:

for numbers like a/b.

if a is smaller than b, then a/b is smaller than 1.

Now, if a is larger than b, then a/b is larger than 1.

And two things,

1/10 = 0.1

10/1 = 10

So when the numerator is larger, the distance displaced in the number line is larger.

Then we want to have:

a number where the numerator is the largest option and the denominator is the smallest option:

a/b = 5/2

And the two remaining options in such way that the numerator is smaller than the denominator:

c/d = 3/4.

The distance between these two numbers is:

D = 5/2 - 3/4 = 10/4 - 3/4 = 7/4.

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Katrina owns a 9-acre farm. Last month, she bought her neighbor’s adjoining 8-acre farm. How large is Katrina’s farm now?
blondinia [14]

Answer:

17 acres

Step-by-step explanation:

9 acres + 8 acres = 17 acres, if that wasn't what the question meant please let me know and I'll change the answer or try to help clear confusion.

3 0
3 years ago
Paul spent 3/8 of her allowance on clothes in 16 on Entertainement what fraction of her allowance did she spend on other items
nasty-shy [4]

Answer:

11 / 24

Step-by-step explanation:

i'm assuming you mean 1/6


We have to calculate the fraction of Paula`s allowance that she spent on other items if she already had spent 3/8 on clothes and 1/6 on entertainment. First we have to add: 3 / 8 + 1 / 6 = ( LCD is 24 ) = 9 / 24 + 4 / 24 = 13 / 24. Then : 1 - 13 / 24 = 24 / 24 - 13 / 24 = 11 / 24. Answer: She has spent 11 / 24 of her allowance on other items.



6 0
3 years ago
Assume the time required to complete a product is normally distributed with a mean 3.2 hours and standard deviation .4 hours. Ho
Alex787 [66]

Answer: 3.712 hours or more

Step-by-step explanation:

Let X be the random variable that denotes the time required to complete a product.

X is normally distributed.

X\sim N(\mu=3.2\text{ hours},\ \sigma=0.4\text{ hours} )

Let x be the times it takes to complete a random unit in order to be in the top 10% (right tail) of the time distribution.

Then, P(\dfrac{X-\mu}{\sigma}>\dfrac{x-\mu}{\sigma})=0.10

P(z>\dfrac{x-3.2}{\sigma})=0.10\ \ \ [z=\dfrac{x-\mu}{\sigma}]

As, P(z>1.28)=0.10  [By z-table]

Then,

\dfrac{x-3.2}{0.4}=1.28\\\\\Rightarrow\ x=0.4\times1.28+3.2\\\\\Rightarrow\ x=3.712

So, it will take 3.712 hours or more to complete a random unit in order to be in the top 10% (right tail) of the time distribution.

3 0
3 years ago
Helppppppppppppppppp
Softa [21]

Answer:

CA = 32

Step-by-step explanation:

By intersecting chords theorem:

12(4x + 1) = 14(3 + 3x) \\  \\ 48x + 12 = 42 + 42x \\  \\ 48x - 42x = 42 - 12 \\  \\ 6x = 30 \\  \\ x =  \frac{30}{6}  \\  \\ x = 5

CA = 14 + ( 3 + 3x)

CA = 14 + ( 3 + 3*5)

CA = 14 + ( 3 + 15)

CA = 14 + 18

CA = 32

8 0
2 years ago
No matter what the base,
Liula [17]

Answer:

(0, 1)

Step-by-step explanation:

6^0 = 1

For exponential function, always > 0, never = 0

3 0
2 years ago
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