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Setler79 [48]
2 years ago
14

Last night, Julie’s pet hamster Zoe kept Julie awake for at least an hour running on her exercise wheel and scratching at the co

rner of her cage. Zoe ran on the wheel at least twice as long as she scratched at the quarters of her cage, and she spent more than 1/4 hour rubbing on her wheel.
Which System of inequalities represents the time Zoe kept Julie awake last night if X is the number of hours that she spent running on her wheel and y is the number of hours spent scratching at her cage?
Mathematics
1 answer:
Irina18 [472]2 years ago
6 0

Answer:

x+y\geq 1

x\geq 2y

x\geq \frac{1}{4}

Step-by-step explanation:

In order to solve this problem, we just need to translate mathematically what the problem is talking about. First, we know that:

x=# of hours she spent running on her wheel.

y = # of hourse she spent scratching at her cage.

So, let's split the problem into little chunks of information that will be easier to translate. This is split it into sentences.

So first:

Julie's pet hamster Zoe kept Julie awake for at least an hour running on her exercise wheel and scratching at the corner of her cage. This means that the least amount of time Julie was awake as an hour in total, so this can be written as an inequality like this:

time spent running + time spent scratching is less than or equal to 1 hour

x+y\geq 1

next,

Zoe ran on the wheel at least twice as long as she scratched at the quarters of her cage.

This is:

x\geq 2y

and finally, she spent more than 1/4 of an hour running on her wheel.

x\geq \frac{1}{4}

so the system of inequalities is the following:

x+y\geq 1

x\geq 2y

x\geq \frac{1}{4}

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Step-by-step explanation:

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2 years ago
The janitor at a school discovered a slow leak in a pipe. The janitor found that it was leaking at a rate of 4fl oz per minute.
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3 years ago
What is the square root of 496
blagie [28]

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Step-by-step explanation:

6 0
3 years ago
Danielle and Emilia brought apples, bananas, and oranges to a fruit sale.
lilavasa [31]

Answer:

26 apples

Step-by-step explanation:

bananas, b= $0.50

oranges, o= $0.75

apples, a = $0.75  

Total fruit sold = 50

Total Earned  = $33.50

b + o + a = 50       Because the total number of all 3 fruits sold is 50

.5b + .75o + .75a =  $33.50           The number of each fruit, multiplied by the price of each fruit, and added together is $33.50

They sold twice as many bananas than oranges.

If o is oranges, then 2o = b because there are twice as many bananas so:

b + o + a = 50

2o + o + a = 50  

3o + a = 50

Now we can solve.

3o + a = 50

a = 50 - 3o

.5b + .75o + .75a =  $33.50

.5(2o) + .75o + .75a = $33.50

o + .75o + .75a = $33.50

1.75o + .75a = $33.50

Two equations and 2 unknowns.

a = 50 - 3o

1.75o + .75a = $33.50       Plug in a to solve for o.

1.75o + .75(50 - 3o) = $33.50

1.75o + .75*50 - .75*3o = $33.50

1.75o + 37.5 - 2.25o = $33.50   Combine like terms

1.75o - 2.25o +37.5 = $33.50

-.5o + 37.5 = 33.5     Add .5o to each side so it cancels on the left.

37.5 = 33.5 + .5o   Subtract 33.5 from each side

37.5 -33.5 = .5o

4 = .5o   Divide each side by .5

4/.5 = o

8 = o

Now plug into a = 50 - 3o

a = 50 - 3(8)

a = 50 - 24

a = 26

So even though we know they sold 26 apples, let's finish solving to check our work.

b + o + a = 50

b + 8 + 26 = 50

b + 34 = 50

b = 50 - 34

b = 16      

b = 2o  

b = 2 (8)

b = 16   Which works! Now the last step of checking our work:

.5b + .75o + .75a =  $33.50

.5(16) + .75(8) + .75(26) =  $33.50

8 + 6 + 19.5 = $33.50

14 + 19.5 = $33.50

33.5 = $33.50  Yes! It works too!

bananas = 16

oranges = 8

apples = 26

3 0
3 years ago
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krek1111 [17]

Answer:

Following are the solution to the given points:

Step-by-step explanation:

When the two-tailed were testing then:

Null and alternative hypothesis:

H_0 : p = 0.611\\\\H_a : p \neq 0.611

Testing the statistics:

\to z = 2.08\\\\P-value = 0.0375\\\\\alpha = 0.01\\\\0.0375> 0.01\\\\P-value < \alpha\\\\

therefore, it fails to reject the null hypothesis.

8 0
3 years ago
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