I can't view images or graphs directly. However, I can help you determine whether the scale was appropriate if you can describe the graph and its axes to me. Please provide more details about the scale used on the axes and the data it represents.
Use the image to answer the question. Steve made this graph to show how much gas was left in the gas tank of his truck as he drove. Did he use the appropriate scale for his axes? (1 point) Responses Yes Yes No
11 answers
GRAPH:He starts at 15 gallons of gas and after 40 miles its at 10 gallons
To determine if Steve used an appropriate scale for his graph, consider the following:
-
Range of Data: Since the gas starts at 15 gallons and goes down to 10 gallons, the vertical axis (representing gallons) should accommodate this range. Ideally, it should start at 0 or slightly below to give context and show change clearly.
-
Horizontal Axis: If the horizontal axis represents distance (in miles), ensure it covers the range of values shown. Since he drove 40 miles, the mileage should reflect that distance.
-
Incremental Changes: The scale on both axes should allow for easy interpretation of the data. For example, if the gas level drops by 5 gallons over 40 miles, the intervals should clearly show this drop.
If the graph clearly reflects these points and provides a clear visual representation of the changes in gas level over distance traveled, then the scale could be considered appropriate.
If any of these factors are not addressed appropriately (e.g., if the y-axis doesn’t show the range of 0 to 15 gallons or the increments are too large), then the scale may not have been appropriate.
Given this information, consider labeling the axes and intervals. Based on how you've described it, if the scale indeed reflects the changes appropriately, you might respond with "Yes". If it doesn't, you might choose "No".
The city’s water company charges a fee of $20 a month in addition to $0.25 per every gallon used. Using the function c=0.25x+20 , where c is the total cost per month for water services and x is gallons used, which of the following points on the graph accurately represents a monthly usage of 1,200 gallons?(1 point) Responses (1200, 320) (1200, 320) (1200, 300) (1200, 300) (320, 1200) (320, 1200) (1200, −180)
To find the total cost for using 1,200 gallons of water, we can plug \( x = 1200 \) into the function \( c = 0.25x + 20 \):
\[ c = 0.25(1200) + 20 \]
First, calculate \( 0.25 \times 1200 \):
\[ 0.25 \times 1200 = 300 \]
Now, add the base fee of $20:
\[ c = 300 + 20 = 320 \]
The total cost for using 1,200 gallons is $320. Therefore, the point that accurately represents a monthly usage of 1,200 gallons is:
\[ (1200, 320) \]
So the correct response is (1200, 320).
Question A dog groomer charges her clients by the weight of the dog. The following piecewise function represents the total charge, f(x) , for a dog weighing x pounds f(x)=⎧⎩⎨⎪⎪2.5x if 0≤x≤203.5x if 20 <x≤50 5x if x>50 If she grooms a dog that weighs 20 lbs, she will determine the amount to charge using the equation f(x)=2.5x . What would be the point on the graph to show what she would charge for a 20 lb dog? (1 point) Responses (20, 50) (20, 50) (20, 70) (20, 70) (20, 100) (20, 100) Skip to navigation
To find the charge for a dog that weighs 20 lbs, we use the piecewise function given:
For \( 0 \leq x \leq 20 \): \[ f(x) = 2.5x \]
Since the weight of the dog is 20 lbs, we can substitute \( x = 20 \) into the equation:
\[ f(20) = 2.5(20) \]
Calculating that:
\[ f(20) = 50 \]
The point on the graph that represents the charge for a 20 lb dog would be the coordinates \( (20, 50) \).
Therefore, the correct response is (20, 50).
On Friday, Kaitlyn went to the park to work out. She started with a slow jog at a constant rate for five minutes. She then increased her speed to a faster, constant pace for seven minutes. She took a three-minute break, then ran for another 7.5 minutes at a constant pace to finish her two-mile run. She rested for the remainder of the time. During what domain interval will she be at 1.25 miles? (1 point) Responses 15≤s≤22.5 15≤s≤22.5 5≤s<12 5≤s<12 12≤s≤15 12≤s≤15 22.5≤s≤25 22.5≤s≤25
To find the domain interval during which Kaitlyn is at 1.25 miles, we need to break down her workout:
-
Slow jog for 5 minutes:
- Let's assume a slow jog pace (speed) of \( v_1 \) miles per minute.
- In 5 minutes, she covers \( 5v_1 \) miles.
-
Increased speed for 7 minutes:
- Let's say her faster pace is \( v_2 \) miles per minute.
- In 7 minutes, she covers \( 7v_2 \) miles.
-
Resting for 3 minutes:
- No distance covered during this time.
-
Final run for 7.5 minutes:
- Continuing at the same pace of \( v_3 \) miles per minute.
- In 7.5 minutes, she covers \( 7.5v_3 \) miles.
Let's assume she completes 2 miles total after all activities.
Now, let's analyze her progress over time:
-
At the end of 5 minutes (slow jog):
- Distance: \( 5v_1 \) miles
-
At the end of 12 minutes (5 + 7 minutes):
- Distance: \( 5v_1 + 7v_2 \) miles
-
At the end of 15 minutes (after a 3-minute break):
- Distance: still \( 5v_1 + 7v_2 \) miles
-
At the end of 22.5 minutes (15 + 7.5 minutes):
- Distance: \( 5v_1 + 7v_2 + 7.5v_3 \) miles
Because we’re seeking the interval during which she reaches 1.25 miles:
-
At 5 minutes (jogging): If \( 5v_1 \) (her distance at this point) is below 1.25 miles, she has not reached that distance yet.
-
By 12 minutes: If \( 5v_1 + 7v_2 \) is greater than or equal to 1.25 miles, she has likely crossed that threshold in this segment.
-
Age 15 minutes (after resting): If she confirms at least 1.25 miles during this segment.
Assuming \( v_1 \) and \( v_2 \) are set such that she progresses to that distance during the time frames above, we can conclude:
To reach 1.25 miles, the likely intervals must be within:
- Next, let's analyze the given options. The correct interval when she is running and covering the distance after resting would be 12 ≤ s ≤ 15. This suggests that at some time within this range, she reaches 1.25 miles.
Thus, the answer is 12 ≤ s ≤ 15.
A scientist is observing a particular species of bacteria growing in a petri dish. The number of bacteria can be represented by the equation n(t)=50(1.2)t (where n is the number of bacteria after t hours.) If the scientist checks the population in 4 hours, what would be an appropriate domain for the problem? (1 point) Responses 0≤t≤4 0≤t≤4 0≤t≤104 0≤t≤104 0≤n≤4 0≤n≤4 0≤n≤104
To determine an appropriate domain for the problem that describes the number of bacteria in the petri dish, we need to consider the variables involved in the equation \( n(t) = 50(1.2)^t \).
-
Understanding the Variables:
- \( t \) represents the time in hours.
- \( n(t) \) represents the number of bacteria after \( t \) hours.
-
Checking the Population After 4 Hours:
- Since the scientist is checking the population in 4 hours, the time \( t \) will range from 0 (the beginning of the observation) to 4 hours.
-
Setting the Domain:
- The time \( t \) can take any value from the start (0 hours) to 4 hours. Therefore, the appropriate domain for \( t \) should be \( 0 \leq t \leq 4 \).
The other options provided do not accurately describe the domain for the variable \( t \).
Given this analysis, the appropriate response is: 0 ≤ t ≤ 4.
1 answer