Mathematics : asked on jeffrijv
 27.08.2020

if a triangle weighs 3 grams and a circle weighs 6 grams how much does a square weigh

. 6

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Mathematics
Step-by-step answer
P Answered by Master

Equation of Hanger A:

x + y = z

z = 9 grams

Equation for hanger B

x + y = p

p = 9 grams

Step-by-step explanation:

Note: This question is not complete, and lacks necessary data to answer this question. But for the sack of concept, we wil be solving this question using our own data.

Data given:

Triangle weight = 3 grams

Circle weight = 6 grams

There are two hangers A and B.

We have to find weight of the square in Hanger A and weight of the pentagon in Hanger B.

So, for your understanding I have drawn the two hangers A and B. In A we have triangle and circle on the LHS and the square on the right. On the other hand, we have pentagon on the right and triangle and circle.

Sketch is attached in the attachment.

Let's suppose: Hanger A is balanced, So,

Triangle weight = 3 grams = x

Circle weight = 6 grams = y

weight of the pentagon in Hanger B = p

weight of the square in Hanger A = z =?

So,

Equation of Hanger A:

x + y = z

z = 3 + 6

z = 9 grams  = weight of the square in Hanger A

Similarly for Hanger B.

Equation for hanger B

x + y = p

p = 3 + 6

p = 9 grams


A triangle weighs 3 grams and a circle weighs 6 grams. Find the weight of a square in Hanger A and t
A triangle weighs 3 grams and a circle weighs 6 grams. Find the weight of a square in Hanger A and t
Mathematics
Step-by-step answer
P Answered by Master

Equation of Hanger A:

x + y = z

z = 9 grams

Equation for hanger B

x + y = p

p = 9 grams

Step-by-step explanation:

Note: This question is not complete, and lacks necessary data to answer this question. But for the sack of concept, we wil be solving this question using our own data.

Data given:

Triangle weight = 3 grams

Circle weight = 6 grams

There are two hangers A and B.

We have to find weight of the square in Hanger A and weight of the pentagon in Hanger B.

So, for your understanding I have drawn the two hangers A and B. In A we have triangle and circle on the LHS and the square on the right. On the other hand, we have pentagon on the right and triangle and circle.

Sketch is attached in the attachment.

Let's suppose: Hanger A is balanced, So,

Triangle weight = 3 grams = x

Circle weight = 6 grams = y

weight of the pentagon in Hanger B = p

weight of the square in Hanger A = z =?

So,

Equation of Hanger A:

x + y = z

z = 3 + 6

z = 9 grams  = weight of the square in Hanger A

Similarly for Hanger B.

Equation for hanger B

x + y = p

p = 3 + 6

p = 9 grams


A triangle weighs 3 grams and a circle weighs 6 grams. Find the weight of a square in Hanger A and t
A triangle weighs 3 grams and a circle weighs 6 grams. Find the weight of a square in Hanger A and t
Mathematics
Step-by-step answer
P Answered by Specialist

3.75 g

Step-by-step explanation:

Assume the weight of the square is x.

The hanger is in balance so the left side is equal to the right side.

Equation therefore is:

Triangle + Square + 3 * circle = 5* square + circle

3 + x + (3 * 6) = 5x + 6

3 + x + 18 = 5x + 6

5x - x = 3 + 18 - 6

4x = 15

x = 15/4

x =  3.75 g


A triangle weighs 3 grams, and a circle weighs 6 grams. Use this applet to help find the weight of a
Mathematics
Step-by-step answer
P Answered by Specialist

3.75 g

Step-by-step explanation:

Assume the weight of the square is x.

The hanger is in balance so the left side is equal to the right side.

Equation therefore is:

Triangle + Square + 3 * circle = 5* square + circle

3 + x + (3 * 6) = 5x + 6

3 + x + 18 = 5x + 6

5x - x = 3 + 18 - 6

4x = 15

x = 15/4

x =  3.75 g


A triangle weighs 3 grams, and a circle weighs 6 grams. Use this applet to help find the weight of a
Mathematics
Step-by-step answer
P Answered by PhD

1. D

2. D

3. C

4. C

5. C

6. C

7. D

8. A

9. No question given (shown)

10. 8047 meters


Step-by-step explanation:


1.

If 2 cakes feed 11 people, then 1 cake feeds \frac{11}{2}=5.5 people

To find how many cakes it will require to feed 58 people, we divide 58 by 5.5:

\frac{58}{5.5}=10.55

We can't make fractional cakes, so we will need 11 cakes.

Answer choice D is right.


2.

To get ratio of banana to all fruit, we make the fraction with total number of bananas on top and total number of fruits on bottom.

Total bananas = 4

Total fruits = 12 +4 +8 = 24

So the ratio is \frac{4}{24}

Reducing it, we get \frac{4}{24}\\=\frac{1}{6}

We can write this as 1:6

Correct answer D


3. "What is 34% written as a ratio?"

To write in ratio (fraction), we divide the number in front of the percent sign (which is 34) by 100. So we have \frac{34}{100}

We can write this as 34:100

C is right


4.

First, 5 pounds per foot for 12 foot is 12 * 5 = 60 pounds

We need to change foot to meter and pounds to kg. We need two unit ratios for this. It is shown below:

\frac{60Pounds}{12Feet}*\frac{0.454Kg}{1Pound}*\frac{1Feet}{0.305Meters}\\=\frac{(60)(0.454)}{(12)(0.305)}\\=7.44\frac{Kg}{Meters}

Answer choice C is right.

Note: in the calculation above, pounds and pounds cancel as well as feet and feet cancel


5.

To get ratio (fraction) of blue to red marbles, we divide total number of blue by total number of red.

Total blue = 60 (given)

Total red = 90 - 60 = 30

So Ratio is \frac{60}{30}=2:1

Answer choice C is right.


6. Clark gives \frac{3}{10} to charity, this in percentage is 30%

We do long division and get a decimal and then multiply the decimal by 100 and stick a "%" sign after that:

\frac{3}{10}=0.3\\0.3*100=30

Hence 30%

Answer choice C is right.


7.

The first 5 level points are 20, 25, 30, 35, & 40. As we can see from the pattern, for each level inrease, the number of stars increase by 5.

Fifth level is 5 * 8 = 40

-------------------------------- Now,

Sixth level will be 40 + 5(6 -5) = 40+5=45 Seventh level will be 40 + 5(7 -5) = 40 + 5(2)=50Eight level will be 40 + 5(8 -5) = 40 + 5(3) = 55

Seeing the pattern, 30th level would be : 40 + 5(30 -5) = 40 +5(25) = 165

Answer choice D gives us the correct answer.


8.

To get dollar rate per minute, we divide dollars by minutes for each and whichever is lowest, that is the BEST.

A)240 minutes for $50 a month: \frac{50}{240}=.21 dollars per minute

B)140 minutes for $70 a month: \frac{70}{140}=.50 dollars per minute

C)200 minutes for $45 a month: \frac{45}{200}=.23 dollars per minute

D)800 minutes for $250 a month: \frac{250}{800}=.31 dollars per minute

So we can see that the lowest and best rate is that of A).

Answer choice A is correct.


9. Question not given (shown).


10. "1 mile = 5,280 feet 1 foot = 0.3048 meters Convert 5 miles to meters (round to the nearest meter)."

We first change 5 miles to feet, and then to meters by setting up the ratio shown below:

5Miles*\frac{5280Feet}{1Mile}*\frac{0.3048Meters}{1Feet}\\=5(5280)(0.3048)\\=8046.72 meters

*Note: miles and miles cancel and feet and feet cancel when doing the conversion

Rounded to nearest meter, 8047 meters

Mathematics
Step-by-step answer
P Answered by PhD

1. D

2. D

3. C

4. C

5. C

6. C

7. D

8. A

9. No question given (shown)

10. 8047 meters


Step-by-step explanation:


1.

If 2 cakes feed 11 people, then 1 cake feeds \frac{11}{2}=5.5 people

To find how many cakes it will require to feed 58 people, we divide 58 by 5.5:

\frac{58}{5.5}=10.55

We can't make fractional cakes, so we will need 11 cakes.

Answer choice D is right.


2.

To get ratio of banana to all fruit, we make the fraction with total number of bananas on top and total number of fruits on bottom.

Total bananas = 4

Total fruits = 12 +4 +8 = 24

So the ratio is \frac{4}{24}

Reducing it, we get \frac{4}{24}\\=\frac{1}{6}

We can write this as 1:6

Correct answer D


3. "What is 34% written as a ratio?"

To write in ratio (fraction), we divide the number in front of the percent sign (which is 34) by 100. So we have \frac{34}{100}

We can write this as 34:100

C is right


4.

First, 5 pounds per foot for 12 foot is 12 * 5 = 60 pounds

We need to change foot to meter and pounds to kg. We need two unit ratios for this. It is shown below:

\frac{60Pounds}{12Feet}*\frac{0.454Kg}{1Pound}*\frac{1Feet}{0.305Meters}\\=\frac{(60)(0.454)}{(12)(0.305)}\\=7.44\frac{Kg}{Meters}

Answer choice C is right.

Note: in the calculation above, pounds and pounds cancel as well as feet and feet cancel


5.

To get ratio (fraction) of blue to red marbles, we divide total number of blue by total number of red.

Total blue = 60 (given)

Total red = 90 - 60 = 30

So Ratio is \frac{60}{30}=2:1

Answer choice C is right.


6. Clark gives \frac{3}{10} to charity, this in percentage is 30%

We do long division and get a decimal and then multiply the decimal by 100 and stick a "%" sign after that:

\frac{3}{10}=0.3\\0.3*100=30

Hence 30%

Answer choice C is right.


7.

The first 5 level points are 20, 25, 30, 35, & 40. As we can see from the pattern, for each level inrease, the number of stars increase by 5.

Fifth level is 5 * 8 = 40

-------------------------------- Now,

Sixth level will be 40 + 5(6 -5) = 40+5=45 Seventh level will be 40 + 5(7 -5) = 40 + 5(2)=50Eight level will be 40 + 5(8 -5) = 40 + 5(3) = 55

Seeing the pattern, 30th level would be : 40 + 5(30 -5) = 40 +5(25) = 165

Answer choice D gives us the correct answer.


8.

To get dollar rate per minute, we divide dollars by minutes for each and whichever is lowest, that is the BEST.

A)240 minutes for $50 a month: \frac{50}{240}=.21 dollars per minute

B)140 minutes for $70 a month: \frac{70}{140}=.50 dollars per minute

C)200 minutes for $45 a month: \frac{45}{200}=.23 dollars per minute

D)800 minutes for $250 a month: \frac{250}{800}=.31 dollars per minute

So we can see that the lowest and best rate is that of A).

Answer choice A is correct.


9. Question not given (shown).


10. "1 mile = 5,280 feet 1 foot = 0.3048 meters Convert 5 miles to meters (round to the nearest meter)."

We first change 5 miles to feet, and then to meters by setting up the ratio shown below:

5Miles*\frac{5280Feet}{1Mile}*\frac{0.3048Meters}{1Feet}\\=5(5280)(0.3048)\\=8046.72 meters

*Note: miles and miles cancel and feet and feet cancel when doing the conversion

Rounded to nearest meter, 8047 meters

Mathematics
Step-by-step answer
P Answered by PhD

1. 6518.75 m^2

2. 295 m of fencing is needed

3. V=653,120cm^{3}

4. $18,480

5. Part 1: 62\frac{3}{4}Hours=3,765Minutes

AND Part 2:

Mike Chewer 870 mins =  14.5 hours

Jennifer Glass 225 mins = 3.75 hours

Fred Carlton 75 mins = 1.25 hours

Amy Amaretto 720 mins = 12 hours

6. Part 1: $237.6; AND Part 2: 540 cm (or 5.4m)

7. Part 1: 6.3 m;  AND Part 2: 96.8ºF

8. No.

9. Part 1: 15 kg = 33 pounds AND Part 2: 48.4 pounds = 22 kgs

10. 1.475 hours


Step-by-step explanation:

1. Area of car park is area of rectangle (length * width) - area of half circle of arena (half circle area is \frac{\pi r^2}{2}

Length is given as 100 and width is 75, also the radius of the circle is half of 50, which is 25. Putting all of these we get:

Area of car park = (100*75)-(\frac{\pi (25)^2}{2})=6518.75 m^2

2. Looking at the diagram carefully, we can see that the perimeter (sum of all the sides) would be sum of top side (100 m), right side (75 m ), bottom side (100 m) and left side that is left ( area covers 50m and gate of 5 m, so covers 55m, left is 75 - 55 = 20)

Perimeter is 100+75+100+20=295. So 295 m of fencing is needed

3. Volume of cylinder is V=\pi r^2 h

We need in cm, so we need to convert 1.3m to centimeters. Since there are 100 cm in 1 m, 1.3m is equal to 130 cm. Also, radius is half of 80cm, which is 40 cm. Putting these into the formula we get:

V=\pi r^2 h\\V=(3.14)(40)^2(130)\\V=653,120cm^{3}

4. If $1.54 : £1 , then £12,000 would be 12,000 multiplied by 1.54. So:

12,000*1.54=18,480 dollars

5. Part 1: To convert to minutes, we multiply 62\frac{3}{4} by 60. Thus we have  62\frac{3}{4}*60=3,765 minutes

Part 2: Mike Chewer worked 870 minutes, to convert to hours, we divide by 60. So \frac{870}{60}=14.5 hrs

Jennifer Glass worked 225 minutes, to convert to hours, we divide by 60. So \frac{225}{60}=3.75 hrs

Fred Carlton worked 75 minutes, to convert to hours, we divide by 60. So \frac{75}{60}=1.25 hrs

Amy Amaretto worked 720 minutes, to convert to hours, we divide by 60. So \frac{720}{60}=12 hrs

6. Part 1: If £1 = $1.76, to get australian dollars for £135, we multiply 135 by 1.76. So we have 135*1.76=237.6

So that's $237.6

Part 2: Converting 8 m to cm, we multiply 8 by 100, so it is 8*100=800cm. Since both sides will be taken by 130 cm speakers, so a total space of 2*130=260cm will be taken. So amount of space left for the band, in cm, is 800 - 260 = 540 cm (or 5.4m)

7. Part 1: To convert cm to meters, we divide it by 100. So we have:

\frac{631}{100}=6.31

Rounding to 1 decimal place, it is 6.3m

Part 2: The formula to convert Celsius to Fahrenheight is F=1.8C+32

Plugging C=36 into this, we get F:  F=1.8C+32\\F=1.8(36)+32\\F=96.8degrees

8. One item weights 0.76 kg so 40 items (in 1 box) would weigh  40*0.76=30.4kg

According to policy, it is over 30, so you won't be allowed to lift it. So, NO!

9. We can see that 1 kg is 2.2 lbs (conversion factor). So 15 kg is 15 * 2.2 = 33 pounds.

Also, To get pounds into kgs, we divide the pounds by 2.2. So 48.4 lbs is 48.4 divided by 2.2 which is 22 kg.

10. We need to divide 59 km by 40 to get the amount of time it will take (distance divided by rate is time). So  \frac{59}{40}=1.475Hours

Second answer choice is a bit wrong, it should be 1.475 hours. Correct answer is 1.475 hours.

Mathematics
Step-by-step answer
P Answered by PhD

1. 6518.75 m^2

2. 295 m of fencing is needed

3. V=653,120cm^{3}

4. $18,480

5. Part 1: 62\frac{3}{4}Hours=3,765Minutes

AND Part 2:

Mike Chewer 870 mins =  14.5 hours

Jennifer Glass 225 mins = 3.75 hours

Fred Carlton 75 mins = 1.25 hours

Amy Amaretto 720 mins = 12 hours

6. Part 1: $237.6; AND Part 2: 540 cm (or 5.4m)

7. Part 1: 6.3 m;  AND Part 2: 96.8ºF

8. No.

9. Part 1: 15 kg = 33 pounds AND Part 2: 48.4 pounds = 22 kgs

10. 1.475 hours


Step-by-step explanation:

1. Area of car park is area of rectangle (length * width) - area of half circle of arena (half circle area is \frac{\pi r^2}{2}

Length is given as 100 and width is 75, also the radius of the circle is half of 50, which is 25. Putting all of these we get:

Area of car park = (100*75)-(\frac{\pi (25)^2}{2})=6518.75 m^2

2. Looking at the diagram carefully, we can see that the perimeter (sum of all the sides) would be sum of top side (100 m), right side (75 m ), bottom side (100 m) and left side that is left ( area covers 50m and gate of 5 m, so covers 55m, left is 75 - 55 = 20)

Perimeter is 100+75+100+20=295. So 295 m of fencing is needed

3. Volume of cylinder is V=\pi r^2 h

We need in cm, so we need to convert 1.3m to centimeters. Since there are 100 cm in 1 m, 1.3m is equal to 130 cm. Also, radius is half of 80cm, which is 40 cm. Putting these into the formula we get:

V=\pi r^2 h\\V=(3.14)(40)^2(130)\\V=653,120cm^{3}

4. If $1.54 : £1 , then £12,000 would be 12,000 multiplied by 1.54. So:

12,000*1.54=18,480 dollars

5. Part 1: To convert to minutes, we multiply 62\frac{3}{4} by 60. Thus we have  62\frac{3}{4}*60=3,765 minutes

Part 2: Mike Chewer worked 870 minutes, to convert to hours, we divide by 60. So \frac{870}{60}=14.5 hrs

Jennifer Glass worked 225 minutes, to convert to hours, we divide by 60. So \frac{225}{60}=3.75 hrs

Fred Carlton worked 75 minutes, to convert to hours, we divide by 60. So \frac{75}{60}=1.25 hrs

Amy Amaretto worked 720 minutes, to convert to hours, we divide by 60. So \frac{720}{60}=12 hrs

6. Part 1: If £1 = $1.76, to get australian dollars for £135, we multiply 135 by 1.76. So we have 135*1.76=237.6

So that's $237.6

Part 2: Converting 8 m to cm, we multiply 8 by 100, so it is 8*100=800cm. Since both sides will be taken by 130 cm speakers, so a total space of 2*130=260cm will be taken. So amount of space left for the band, in cm, is 800 - 260 = 540 cm (or 5.4m)

7. Part 1: To convert cm to meters, we divide it by 100. So we have:

\frac{631}{100}=6.31

Rounding to 1 decimal place, it is 6.3m

Part 2: The formula to convert Celsius to Fahrenheight is F=1.8C+32

Plugging C=36 into this, we get F:  F=1.8C+32\\F=1.8(36)+32\\F=96.8degrees

8. One item weights 0.76 kg so 40 items (in 1 box) would weigh  40*0.76=30.4kg

According to policy, it is over 30, so you won't be allowed to lift it. So, NO!

9. We can see that 1 kg is 2.2 lbs (conversion factor). So 15 kg is 15 * 2.2 = 33 pounds.

Also, To get pounds into kgs, we divide the pounds by 2.2. So 48.4 lbs is 48.4 divided by 2.2 which is 22 kg.

10. We need to divide 59 km by 40 to get the amount of time it will take (distance divided by rate is time). So  \frac{59}{40}=1.475Hours

Second answer choice is a bit wrong, it should be 1.475 hours. Correct answer is 1.475 hours.

Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

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