Classify each of the following as a rate, ratio, or proportion.
Example Classification
The price of bananas at the grocery store is $ 0.70 divided by 100 g blank
Considering the cost of bananas above, you can
also, express the price as $ 0.07 separated by g blank
A bag of gumballs consists of 7 blue gumballs
and 3 pink ones.
This can be expressed as 7 colons 3. blank
Carly walked 2 km in 25 minutes. If she continues
to walk at the same rate, how long will it take her to
walk 5 km?
fraction numerator 2 space k m over denominator 25 space m I n end fraction equals fraction numerator 5 space k m over denominator x end fraction
blank
Ratio Rate Proportion Unit Rate
The price of bananas at the grocery store is $0.70 divided by 100 g - Proportion
Considering the cost of bananas above, you can also express the price as $0.07 separated by g - Proportion
A bag of gumballs consists of 7 blue gumballs and 3 pink ones. This can be expressed as 7 colons 3 - Ratio
Carly walked 2 km in 25 minutes. If she continues to walk at the same rate, how long will it take her to walk 5 km? - Proportion
Jennifer surveyed her class to find out the most popular type of pizza. Her data is shown below.
Total students in the class 32
Favorite pizza = Hawaiian 10
Favorite pizza = Pepperoni 5
Favorite pizza = Veggie Deluxe 6
Favorite pizza = Meat Lovers 4
Favorite pizza = BBQ Chicken 7
Match each simplified fraction or ratio to its corresponding ratio.
5 over 27
Answer 1
Choose...
3 over 5
Answer 2
Choose...
3 over 2
Answer 3
Choose...
2 colon 1
Answer 4
Choose...
7 colon 4
Answer 5
Choose...
1 over 6
It is cheaper to buy three 400 g jars of peanut butter for $3.97 each than it is to buy a 1 Kg jar of peanut butter $8.99.
Select one:
True
False
True
The scale of a monster truck model is 1 cm represents 10 inches. The length of the model of the monster truck is 5.15 cm. What is the actual length of the monster truck?
Select one:
a.
1.94 inches
b.
0.515 inches
c.
51.5 inches
d.
128.75 inches
a. 1.94 inches
Use $1 USD = $0.71 CAD to complete the proportion below to convert $225 CAD to USD.
Let space x space equals space the space amount space of space USD space equivalent space to space $ 225 space CAD
fraction numerator 1 over denominator 0.71 end fraction space equals an over b
After space sovling space this space proportion comma space the space value space of space x space is space c.
a = Answer
b = Answer
c = Answer
*Enter your answers without $ and rounded appropriately for money.
a = $158.45
b = $225
c = $158.45
Suppose the the pressure on the surface of a windsurfer’s sail varies directly with the speed of the wind. If there are 2200 units of pressure when the wind is blowing at 17 km/h, how many units of pressure will there be when the wind is blowing 21 km/h?
L e t space x space equals space t h e space u n i t s space o f space p r e s u r e space t h a t space w i l l space b e space w h e n space t h e space w i n d space i s space b l o w i n g space a t space 21 space k m divided by h
2200 over a space equals b over c
A f t e r space s o v l i n g space t h i s space p r o p o r t i o n comma space space t h e space v a l u e space o f space x space i s space d.
a = Answer
b = Answer
c = Answer
d = Answer
*Round your answer to the nearest whole number
a = 2200
b = x (unknown value)
c = 17
d = Answer (unknown value)
To solve for d, we can set up the proportion:
2200/17 = b/x
Multiplying both sides by x and dividing by 17:
2200x = 17b
To find d, we need to solve for x when the wind speed is 21 km/h. Plugging in the known values:
2200 * 21 = 17b
46200 = 17b
b ≈ 2717.65
Therefore, the units of pressure when the wind is blowing at 21 km/h is approximately 2718 units.
A hard drive has a transfer rate of 256 MB every 3 seconds. If there is 8.5 GB of information to transfer, how long will the transfer take in minutes and b seconds? [1GB = 1024MB]
Step 1: Convert 8.5 GB to MB
blank
Step 2: Calculate transfer time in seconds.
blank
Step 3: Convert the answer from part 2 to minutes and seconds.
blank
102 s 120 MB 1 min 7 s 360 s 6 min 1 min 42 s 8704 MB
Step 1: Convert 8.5 GB to MB
8.5 GB * 1024 MB/GB = 8704 MB
Step 2: Calculate transfer time in seconds.
256 MB/3 seconds = 8704 MB/x seconds
Cross-multiplying:
256x = 3 * 8704
256x = 26112
x = 26112/256
x ≈ 102 seconds
Step 3: Convert the answer from part 2 to minutes and seconds.
102 seconds = 1 minute and 42 seconds
Therefore, the transfer will take approximately 1 minute and 42 seconds.
Melia works in a dress boutique. She earns a base pay plus commision. In April she earned a total of $1,825 and sold $5,500 worth of merchandise. In May she sold $6,700 in merchandise and earned $2,005 in total. What is Melia's earnings/sales or her commission?
Select one:
a.
$6.67
b.
$15
c.
$3 495.27
d.
15%
To find Melia's commission, we need to subtract her base pay from her total earnings in each month.
In April, Melia earned a total of $1,825 and sold $5,500 worth of merchandise. Therefore, her commission can be calculated as:
Commission = Total earnings - Base pay
Commission = $1,825 - $5,500
Commission = -$3,675.
In May, Melia earned a total of $2,005 and sold $6,700 worth of merchandise. Therefore, her commission can be calculated as:
Commission = Total earnings - Base pay
Commission = $2,005 - $6,700
Commission = -$4,695.
Based on the given information, Melia's commission is negative in both months, which indicates that she did not earn any commission. Therefore, the correct answer is none of the options provided.
the temperature on a spring day was observed over a 12-hour period from 6:00 am to 6:00 pm.
- the temperature starts at 1 Degrees C at 6 a.m. and increases to 8 Degrees C by 9 a.m.
- the temperature then remains constant for 2 hours.
- Next, the temperature increases by 4 Degrees C over 3.5 hours.
- Finally, the temperature remains constant until 6 p.m.
Determine the rate of change in temperature for each of the 4-time intervals. [Hint: When working with time, it can be useful to represent the afternoon times in 24 hour format]
To determine the rate of change in temperature for each time interval, we need to calculate the change in temperature divided by the change in time for each interval.
1. From 6:00 am to 9:00 am (3 hours):
Change in temperature = 8°C - 1°C = 7°C
Change in time = 3 hours
Rate of change = Change in temperature / Change in time = 7°C / 3 hours = 2.33°C/hour
2. From 9:00 am to 11:00 am (2 hours):
Change in temperature = 0°C (constant temperature)
Change in time = 2 hours
Rate of change = Change in temperature / Change in time = 0°C / 2 hours = 0°C/hour
3. From 11:00 am to 2:30 pm (3.5 hours):
Change in temperature = 4°C
Change in time = 3.5 hours
Rate of change = Change in temperature / Change in time = 4°C / 3.5 hours = 1.14°C/hour
4. From 2:30 pm (14:30) to 6:00 pm (18:00) (3.5 hours):
Change in temperature = 0°C (constant temperature)
Change in time = 3.5 hours
Rate of change = Change in temperature / Change in time = 0°C / 3.5 hours = 0°C/hour
Therefore, the rate of change in temperature for each time interval is:
1. 2.33°C/hour
2. 0°C/hour
3. 1.14°C/hour
4. 0°C/hour
Determine the scale factor used to transform diagram X into diagram Y. Express the scale factor as a fraction and a percent.
I'm sorry, but I cannot determine the scale factor or compare diagrams as I am a text-based AI model and do not have visual capabilities. Please provide me with more information or describe the diagrams in words, and I will do my best to assist you.
A rectangular drawing is enlarged by 40%. The original dimensions of this drawing are 16cm x 24cm. Determine the scale factor of this enlargement, as a fraction, then determine the dimensions of the enlarged drawing.
The scale factor of the enlargement can be calculated by adding the percentage increase in dimensions to 100% and converting it to a decimal. In this case, the percentage increase is 40%, so the scale factor would be 1 + 0.40 = 1.40.
To determine the dimensions of the enlarged drawing, we can multiply the original dimensions by the scale factor:
Length of enlarged drawing: 16 cm * 1.40 = 22.4 cm
Width of enlarged drawing: 24 cm * 1.40 = 33.6 cm
Therefore, the scale factor of the enlargement is 1.40 (or 7/5 as a fraction), and the dimensions of the enlarged drawing are 22.4 cm x 33.6 cm.
A patch of grass in front of an office building is in the shape of an isosceles trapezoid. Recall that in a trapezoid
2 parallel sides are not the same length. In an isosceles trapezoid, the 2 sides that are not
parallel are equal in length.
The length of the patch of grass against the building is 20 m. The length of the side parallel to the building is 12
m. The distance between the two parallel sides is 8m.
a) Create a scaled drawing of the patch of grass on the grid below. State a reasonable scale for your
drawing in the form ___m = __ box (or boxes). [Note: A reasonable scale will make your scale drawing
take up more than half of the grid below.]
Scale: _____________________
I apologize, but as a text-based AI model, I am unable to create or display images or grids. However, I can help you with the calculations and provide guidance on how to create a scaled drawing.
To create a scaled drawing of the patch of grass, you need to determine a consistent scale that allows you to accurately represent the dimensions of the patch on a smaller scale. Here's an example of how you can determine a reasonable scale for your drawing:
Let's say we want to use a scale of 1 cm = 2 meters. This means that every centimeter on the drawing represents 2 meters in reality.
Based on this scale, the length of the patch of grass against the building (20 meters) would be represented by 10 centimeters on the drawing, since 10 cm * 2 m/cm = 20 meters. Similarly, the side parallel to the building (12 meters) would be represented by 6 centimeters on the drawing, and the distance between the parallel sides (8 meters) would be represented by 4 centimeters on the drawing.
Once you have determined the scale, you can use a ruler and graph paper to draw the shape of the patch of grass, ensuring that the proportions and dimensions accurately match the scaled measurements.
I hope this explanation helps, and I apologize for any inconvenience caused by not being able to provide a visual representation.
A patch of grass in front of an office building is in the shape of an isosceles trapezoid. Recall that in a trapezoid
2 parallel sides are not the same length. In an isosceles trapezoid, the 2 sides that are not
parallel are equal in length.
The length of the patch of grass against the building is 20 m. The length of the side parallel to the building is 12
m. The distance between the two parallel sides is 8m.
a) Create a scaled drawing of the patch of grass on the grid below. State a reasonable scale for your
drawing in the form ___m = __ box (or boxes). [Note: A reasonable scale will make your scale drawing
take up more than half of the grid below.]
Scale: _____________________
b) the owner of this building plans to remove the grass and replace it with a cement pad of the same shape but larger. They would like the area of the cement to be double the area of the grass. Determine the scale factor that would apply to the grass to create this cement pad. Round your answer to the nearest hundredth.
I apologize for the confusion, but I am still unable to create or display images or grids. However, I can assist you with the calculations and provide guidance.
a) To create a scaled drawing of the patch of grass, you will need to determine a reasonable scale that allows you to accurately represent the dimensions of the patch on a smaller scale. Since the patch of grass has dimensions of 20m, 12m, and 8m, you can choose a scale that fits the available space in the grid while still being clear and accurate. For example, you can use a scale of 1cm = 2m. This would mean that every centimeter on the drawing represents 2 meters in reality.
b) To determine the scale factor to create a cement pad with double the area of the grass, we need to calculate the area of the grass and then determine the scale factor to achieve the desired area.
The area of the grass is given by the formula for the area of a trapezoid: A = (b1 + b2) * h / 2, where b1 and b2 are the lengths of the parallel sides, and h is the distance between them.
For the grass:
b1 = b2 = 12m (the length of the side parallel to the building)
h = 8m (the distance between the parallel sides)
A = (12 + 12) * 8 / 2 = 96 square meters
To create a cement pad with double the area, the new area would be 2 * 96 = 192 square meters.
Now, we can calculate the scale factor using the formula: Scale factor = square root of (new area / original area).
Scale factor = sqrt(192 / 96) = sqrt(2) ≈ 1.41
Therefore, the scale factor to create the cement pad would be approximately 1.41.
A patch of grass in front of an office building is in the shape of an isosceles trapezoid. Recall that in a trapezoid 2 parallel sides are not the same length. In an isosceles trapezoid, the 2 sides that are not parallel are equal in length. The length of the patch of grass against the building is 20 m. The length of the side parallel to the building is 12m. The distance between the two parallel sides is 8m.
b) the owner of this building plans to remove the grass and replace it with a cement pad of the same shape but larger. They would like the area of the cement to be double the area of the grass. Determine the scale factor that would apply to the grass to create this cement pad. Round your answer to the nearest hundredth.
To determine the scale factor to create a cement pad with double the area of the grass, we first need to calculate the area of the grass.
The area of a trapezoid is given by the formula A = (base1 + base2) * height / 2.
For the grass:
Base1 = Base2 = 20m (the length of the patch of grass against the building)
Height = 8m (the distance between the two parallel sides)
Area of the grass = (20 + 20) * 8 / 2 = 160 square meters.
To find the scale factor, we need to determine the square root of the ratio of the desired area of the cement to the area of the grass.
Double the area of the grass = 2 * 160 = 320 square meters.
Scale factor = √(Desired area / Area of the grass)
Scale factor = √(320 / 160)
Scale factor = √2 ≈ 1.41 (rounded to the nearest hundredth)
Therefore, the scale factor to create the cement pad would be approximately 1.41.
The side length of a cube is reduced from 25 inches to 15 inches.
a). State the linear scale factor for this reduction as a simplified ratio and as a decimal.
To find the linear scale factor for the reduction, we divide the new side length by the original side length.
The linear scale factor as a simplified ratio is 15:25, which can be further simplified to 3:5.
The linear scale factor as a decimal is found by dividing the new side length by the original side length:
Scale factor = 15 inches
The side length of a cube is reduced from 25 inches to 15 inches.
b) Nadya says the new surface area of the smaller cube will decrease by a factor of 0.6 but Sharma says it will decrease by a factor of 0.36. Who is correct? Describe the mistake that the incorrect person is making.