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vodka [1.7K]
2 years ago
11

Jorge and Mary are both filling cups with fruit punch in preparation for a party. After 3 minutes, Jorge had 53 cups left to be

filled, and after 5 minutes, he had 25 cups left to be filled. Mary’s progress is shown in the table of values below. Assuming that both Jorge and Mary are filling cups at a constant rate, which statement is correct?
Mary’s Cup-Filling Progress
Time (minutes)

0.5

1

1.5

2

2.5
Cups Remaining

99

81

63

45

27

Jorge is filling 14 cups per minute, which is faster than Mary.
Jorge is filling 28 cups per minute, which is faster than Mary.
Mary is filling 18 cups per minute, which is faster than Jorge.
Mary is filling 36 cups per minute, which is faster than Jorge.
Mathematics
2 answers:
makkiz [27]2 years ago
7 0

Answer:

Mary is filling 36 cups per minute, which is faster than Jorge.

Step-by-step explanation:

Lets get Jorge's time :

As the rate is constant, we can find the slope to know the number of cups he is filling per minute.

Slope is found using: \frac{y2-y1}{x2-x1}

= \frac{53-25}{5-3}

= \frac{28}{2}=14

From the table lets get Mary's time:

\frac{99-81}{1-0.5}

= \frac{18}{0.5}=36

Another data: \frac{63-45}{2-1.5}

=  \frac{18}{0.5}=36

Therefore, we can see that Mary is filling 36 cups in a minute and Jorge is filling 14 cups.

Hence, the correct answer is : Mary is filling 36 cups per minute, which is faster than Jorge.

jenyasd209 [6]2 years ago
7 0

Answer:

Mary is filling 36 cups per minute, which is faster than Jorge.

Step-by-step explanation:

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Which expressions simplify to a rational answer? Select each correct answer. 29√⋅4√ 3√⋅16−−√ 73⋅−√3√ 5√⋅5√
PolarNik [594]

Answer:

The correct options are 1, 3 and 4.

Step-by-step explanation:

We need to find the expressions whose simplified form is a rational number.

Rational number: If a number is defined in the form of p/q where p and q are integers and q≠0, then it is called a rational number.

For example: 0,2, 4.3 etc.

Irrational number: If a number can not defined in the form of p/q, where p and q are integers and q≠0, then it is called an irrational number.

First expression is

2\sqrt{9}\cdot \sqrt{4}=2(3)\cdot (2)\Rightarrow 6\cdot 2=12

12 is a rational number.

Second expression is

\sqrt{3}\cdot \sqrt{16}=\sqrt{3}\cdot 4\Rightarrow 4\sqrt{3}

4\sqrt{3} is an irrational number.

Third expression is

7\sqrt{3}\cdot \sqrt{3}\Rightarrow 7\cdot 3=21

21 is a rational number.

Fourth expression is

\sqrt{5}\cdot \sqrt{5}=5

5 is a rational number.

Therefore, the correct options are 1, 3 and 4.

4 0
2 years ago
The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours. Daryl plans to be gone for at l
umka21 [38]

The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours.

Temperature drops by 5°c per hour

So we find the temperature after 6 hours

In 1 hour temperature drops= 5°c

So in 6 hours = 6* 5 = 30°c

In 6 hours , temperature drops by 30°c

the actual temperature is 20°c. after 6 hours the temperature becomes

20°c - 30°c= -10°c

So, after 6 hours the temperature will be -10°c

Daryl plans to be gone for at least 6 hours. so its 6 hours or more than 6 hours

In 6 hours or more than 6 hours , the temperature will drop less than  -10°c.

So, Daryl should move his plant to a warmer location before leaving


7 0
2 years ago
Read 2 more answers
Which expression represents the calculation “subtract 10 from 36, then divide by 6”
SVETLANKA909090 [29]

Answer:

(36 - 10) (divide sign) 6

Step-by-step explanation:

Walk through the problem:

"subtract 10 from 36." = "take ten away from 36." = "36 - 10."

"then divide by 6." = "Divide 36 - 10 by 6." = "(36 - 10) divided by 6."

3 0
2 years ago
Joline is solving the equation 0 = x2 – 5x – 4 using the quadratic formula. Which value is the negative real number solution to
katen-ka-za [31]

Answer:

- 0.7

Step-by-step explanation:

We are given the general quadratic formula, as " x = -b \frac{+}{-}  \sqrt{(b^2-4ac)} / 2a. " This can be represented by two separate formula's, which will come in handy when determining the positive and negative roots of the equation ( and here we need the negative root ):

1 ) x = - b+ ( \sqrt{b^2-4ac} ) / 2a,

2 ) x = - b- ( \sqrt{b^2-4ac} ) / 2a

We know that a = 1, b = - 5, and c = - 4 from the equation " 0 = x^2 - 5x - 4 " ( which can be rewritten in the form 0 = ax^2 + bx + c ). Therefore, simply plug in these values into the quadratic formula to receive two solutions:

x = 5 + ( \sqrt{( - 5 )^2 - 4( 1 )( - 4 )} ) / 2( 1 ),\\x = 5 + ( \sqrt{25 + 16} ) / 2,\\x = 5 + \sqrt{41} / 2,\\x = ( About ) 5.7- This is our positive solution

__________

x = 5 - ( \sqrt{( - 5 )^2 - 4( 1 )( - 4 )} ) / 2( 1 ),\\x = 5 - ( \sqrt{25 + 16} ) / 2,\\x = 5 - \sqrt{41} / 2,\\x = ( About ) - 0.7- And this is our negative solution

You can see that - 0.7 is the negative real number solution to Joline's quadratic equation!

4 0
2 years ago
A company receives shipments of a component used in the manufacture of a component for a high-end acoustic speaker system. When
Tanya [424]

Answer:

ME= 2.33*\sqrt{\frac{0.096*(1-0.096)}{250}}= 0.0434

Step-by-step explanation:

For this case we have a sample size of n = 250 units and in this sample they found that 24 units failed one or more of the tests.

We are interested in the proportion of units that fail to meet the company's specifications, and we can estimate this with:

\hat p = \frac{24}{250}= 0.096

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The confidence interval for a proportion is given by this formula  

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}  

For the 98% confidence interval the value of \alpha=1-0.98=0.02 and \alpha/2=0.01, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=2.33  

And the margin of error would be:

ME= 2.33*\sqrt{\frac{0.096*(1-0.096)}{250}}= 0.0434

4 0
2 years ago
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