An orange juice company sells a can of frozen orange juice that measures 9.4 centimeters in height and 5.2 centimeters in diamet
er. The company wants to sell a larger can of juice. The height of the can is kept at 9.4 cm, but the diameter is increased to 8.5 cm. About how many times more juice will the new can hold?
Image is the same question w/ a model.
Image is the same question w/ a model.
1 answer:
<h2>Hello!</h2>
The answer is:
The third option:
2.7 times as much.
<h2>Why?</h2>To calculate how many more juice will the new can hold, we need to calculate the old can volume to the new can volume.
So, calculating we have:
Old can:
Since the cans have a right cylinder shape, we can calculate their volume using the following formula:
Where,
We are given the old can dimensions:
So, calculating the volume, we have:
We have that the volume of the old can is:
New can:
We are given the new can dimensions, the diameter is increased but the height is the same, so:
Calculating we have:
Now, dividing the volume of the new can by the old can volume to know how many times more juice will the new can hold, we have:
Hence, we have that the new can hold 2.7 more juice than the old can, so, the answer is the third option:
2.7 times as much.
Have a nice day!
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Answer:
The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.
Step-by-step explanation:
Mean SAT scores = 1026
Standard Deviation = 209
Mean ACT score = 20.8
Standard Deviation = 4.8
We are given SAT and ACT scores of a student and we have to compare them. We cannot compare them directly so we have to Normalize them i.e. convert them into such a form that we can compare the numbers in a meaningful manner. The best way out is to convert both the values into their equivalent z-scores and then do the comparison. Comparison of equivalent z-scores will tell us which score is higher and which is lower.
The formula to calculate the z-score is:
Here, μ is the mean and σ is the standard deviation. x is the value we want to convert to z score.
z-score for junior scoring 860 in SAT exam will be:
z-score for junior scoring 16 in ACT exam will be:
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Answer:
1. 〈x,y,z〉=〈−1,−7,3〉+t〈−4,−5,−6〉 F
2. 〈x,y,z〉=〈−1,−7,3〉+t〈3,−2,9〉 F
3. 〈x,y,z〉=〈−1,−7,3〉+t〈4,5,6〉 T
4. 〈x,y,z〉=〈3,−2,9〉+t〈−1,−7,3〉 F
5. 〈x,y,z〉=〈3,−2,9〉+t〈4,5,6〉 F
Step-by-step explanation:
The vector AB is the vectorial difference between point A and B, that is:
Given that and
, the vector AB is:
The vectorial equation of the line is represented by:
Where is the parametric variable, dimensionless. Given that
and
Finally, the list of questions are now checked:
1. 〈x,y,z〉=〈−1,−7,3〉+t〈−4,−5,−6〉 F
2. 〈x,y,z〉=〈−1,−7,3〉+t〈3,−2,9〉 F
3. 〈x,y,z〉=〈−1,−7,3〉+t〈4,5,6〉 T
4. 〈x,y,z〉=〈3,−2,9〉+t〈−1,−7,3〉 F
5. 〈x,y,z〉=〈3,−2,9〉+t〈4,5,6〉 F