Answer: Equation to describe this situation.
[tex]3s=6300[/tex]
Number of steps in one mile for Gustave =2100
Step-by-step explanation:
Given : Gustave measured his pace and determined that for him, s steps make up one mile.
1 mile = s steps (1)
One day Gustave walked 6300 steps, which was 3 miles.
i.e. 3 miles = 6300 steps (2)
Using (2), the number f steps in 3 steps will be :_
3 miles = 3s steps (3)
From (2) and (3), we have
[tex]3s=6300[/tex]
Dividing both sides by 3 , we get
[tex]s=\dfrac{6300}{3}=2100[/tex]
Hence, the number of steps in one mile for Gustave =2100
Gustave takes 189 steps to walk one mile. We derived this by dividing the total steps, 63,000, by the distance in miles, 333. The equation used was 63000 = s * 333.
To determine how many steps are in one mile for Gustave, we start with the information provided:
Gustave took 63,000 steps, which equals 333 miles.Step 1: Write the Equation
We can write the equation as:
63000 = s * 333
Step 2: Solve for s
To find out how many steps make up one mile, we solve for s by dividing both sides of the equation by 333:
s = 63000 / 333
Step 3: Calculate the Value
When we divide 63,000 by 333, we get:
s = 189
This means that Gustave takes 189 steps to walk one mile.
Example Calculation
Since 63,000 steps equal 333 miles, and dividing both 63,000 steps by 333 miles gives us the number of steps per mile:
189 steps per mile.
In conclusion, Gustave takes 189 steps to walk one mile. This equation and process help us determine the number of steps per mile based on the given total steps and distance covered.
4) For questions a-c use the equation y − 2 = 13(x + 5) given in point slope form.
a) What is the slope of the line? b) What is a coordinate point on the line?
c) Sketch the graph of y − 2 = 13(x + 5) on the graph below:
Answer:
a) 13, b) (-5, 2)
Step-by-step explanation:
Point slope form of a line is:
y − y₁ = m (x − x₁)
where m is the slope and (x₁, y₁) is a point on the line.
In this case, m = 13 and (x₁, y₁) = (-5, 2).
Here's a graph:
desmos.com/calculator/pknwab84xs
A.)List the 4 steps outlined in the lesson on solving equations. (1 points)
B.)Solve each equation and show all work (3 points each)
1.) 5x + 7 = 3x + 21
2.) 3x - 2(5 - x) = -3(x - 10) + 3x
3.) 5(x + 1) = 3(2x + 3) + 5
For this case we must solve the following equations:
[tex]5x + 7 = 3x + 21[/tex]
We subtract 3x on both sides of the equation:
[tex]5x-3x + 7 = 21[/tex]
We subtract 7 on both sides of the equation:
[tex]5x-3x + 21-72x = 14[/tex]
We divide between 2 on both sides of the equation:
[tex]x = \frac {14} {2}\\x = 7[/tex]
The second equation is:
[tex]3x-2 (5-x) = - 3 (x-10) + 3x[/tex]
We apply distributive property to the terms of parentheses:
[tex]3x-10 + 2x = -3x + 30 + 3x[/tex]
We add common terms:
[tex]5x-10 = 30[/tex]
We add 10 to both sides of the equation:
[tex]5x = 30 + 10\\5x = 40[/tex]
We divide between 5 on both sides of the equation:
[tex]x = \frac {40} {5}\\x = 8[/tex]
Third equation:
[tex]5 (x + 1) = 3 (2x + 3) +5[/tex]
We apply distributive property to the terms within parentheses:
[tex]5x + 5 = 6x + 9 + 5[/tex]
We add similar terms:
[tex]5x + 5 = 6x + 14[/tex]
We subtract 6x on both sides of the equation:
[tex]5x-6x + 5 = 14[/tex]
We subtract 5 on both sides of the equation:
[tex]-x = 14-5\\-x = 9\\x = -9[/tex]
Answer:
[tex]x = 7\\x = 8\\x = -9[/tex]
Two trains leave stations 494 miles apart at the same time and travel toward each other. One train travels at 100 miles per hour while the other travels at 90
miles per hour. How long will it take for the two trains to meet? do not do any rounding.
Answer:
The trains will meet after 2.6 hours.
Step-by-step explanation:
Add up the distances traveled by the two trains:
distance1 = (100 mph)(t hours)
distance2 = (90 mph)(t hours)
Sum of distance1 and distance2 = 494 miles = (190 mph)(t hours)
Solving for t, we get t = 494 miles / 190 mph = 2.6 hours
The trains will meet after 2.6 hours.
It will take 2.60 hours for the two trains to meet.
Explanation:To find out how long it will take for the two trains to meet, we can use the formula: time = distance / speed.
Since the trains are traveling towards each other, we can add their speeds together to get the effective speed: 100 mph + 90 mph = 190 mph.
Now we can plug in the values: time = 494 miles / 190 mph = 2.60 hours.
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Hi, help is very much appreciated!
" Make a box-and-whisker plot of the data 5, 7, 2, 6, 7, 10, 12, 7, 9, 13, 5 "
Maybe a visual explanation please :) ( I already have the numbers in order from Least to Greatest. ) ( 2, 5, 5, 6, 7, 7, 9, 10, 12 )
Here's a visual representation. The numbers are a little blurry though.
Suppose f(x)=x-4.
Find the graph for f(1/4x)
Answer:
#4
Step-by-step explanation:
Graph #4 is the correct one. Multiplying x by 1/4 widens the original graph by a factor of 4. That "-4" shifts the graph 4 units to the right.
Please please help me
Answer:
89.0°
Step-by-step explanation:
The segment from the centre of the circle to the chord is a perpendicular bisector, hence
third side of right triangle = 12.7 ÷ 2 = 6.35
The angle subtended at the centre by arc CD is twice the angle subtended by the right triangle at the centre
The triangle from the centre to C is congruent to the triangle from the centre to D
Calculate the angle (Θ ) in the right triangle using the sine ratio
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6.35}{9.06}[/tex]
Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{6.35}{9.06}[/tex] ) ≈ 44.5°
Hence
measure of CD = 2 × Θ = 2 × 44.5 = 89.0°
E is 3 more than D
F is 5 less than D
A). Write an expression for “e” in terms of “d.
B). Write an expression for “f” in terms of “d.
C). Work out E-F and symplify your answer.
Part A:
We are given that E is 3 more than D. This means that to get the value of E, we will simply add 3 to the value of D
Therefore:
E = D + 3
Part B:
We are given that F is 5 less than D. This means that to get the value of F, we will simply subtract 5 from the value of D
Therefore:
F = D - 5
Part C:
To get the value of E-F, we will simply subtract the equation we obtained from part B from the equation we obtained from part A
Therefore:
E - F = (D+3) - (D-5)
E - F = D + 3 - D + 5
E - F = 8
Hope this helps :)
The expression for 'e' in terms of 'd' is e = d + 3. The expression for 'f' in terms of 'd' is f = d - 5. The difference between 'E' and 'F' is 8.
Explanation:A) e = d + 3
To express 'e' in terms of 'd,' we can simply say that 'e' is equal to 'd' plus 3. This is because the question states that 'E is 3 more than D.'
B) f = d - 5
To express 'f' in terms of 'd,' we can say that 'f' is equal to 'd' minus 5. The question states that 'F is 5 less than D.'
C) E - F = (d + 3) - (d - 5) = d + 3 - d + 5 = 8
To find the difference between 'E' and 'F,' we can substitute the expressions we found for 'e' and 'f' into the equation. Simplifying the expression further, we have 'E - F = (d + 3) - (d - 5) = d + 3 - d + 5 = 8.'
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The area of a triangular flag is 330 square centimeters. If the base of the triangle is 30 centimeters long, what is the height of the triangle?
The height of the triangle is 22 centimeters. When The area of a triangular flag is 330 square centimeters
To find the height of the triangle, we can use the formula for the area of a triangle, which is given by:
Area = (1/2) * base * height
where "base" is the length of the base of the triangle, and "height" is the height of the triangle.
Given that the area of the triangular flag is 330 square centimeters and the base is 30 centimeters, we can plug these values into the formula and solve for the height:
330 = (1/2) * 30 * height
To find the height, first, multiply 30 by (1/2):
330 = 15 * height
Now, divide both sides of the equation by 15 to solve for the height:
height = 330 / 15
height = 22
So, the height of the triangle is 22 centimeters.
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What is the standard deviation for the data set?
359, 320, 365, 310, 349, 351, 310, 314, 364
Express your answer as a decimal to the nearest tenth
Answer:
The standard deviation is 22.6 to the nearest tenth
Step-by-step explanation:
* Lets study how to find the standard deviation (σ) for data set
- First step find the mean of the data
∵ The mean = the sum of the data ÷ the number of the data
# The sum of the data is
359 + 320 + 365 + 310 + 349 + 351 + 310 + 314 + 364 = 3042
# The number of the data is 9
∴ The mean = 3042 ÷ 9 = 338
- Second step find the difference between each data and the mean
and square the difference
# 359 - 338 = 21 ⇒ (21)² = 441
# 320 - 338 = -18 ⇒ (-18)² = 324
# 365 - 338 = 27 ⇒ (27)² = 729
# 310 - 338 = -28 ⇒ (-28)² = 784
# 349 - 338 = 11 ⇒ (11)² = 121
# 351 - 338 = 13 ⇒ (13)² = 169
# 310 - 338 = -28 ⇒ (-28)² = 784
# 314 - 338 = -24 ⇒ (-24)² = 576
# 364 - 338 = 26 ⇒ (26)² = 676
- Third step find the variance (σ²)
# Add all the square difference and divide the sum by the
number of data
∴ σ² = (441 + 324 + 729 + 784 + 121 + 169 + 784 + 576 + 676) ÷ 9
∴ σ² = 4604 ÷ 9 = 511.5555556
- Fourth step find the standard deviation σ it is the square root of
the variance
∴ σ = 22.6 to the nearest tenth
* The standard deviation is 22.6 to the nearest tenth
Answer:
24.0
Step-by-step explanation:
i took the test on k12
Power set: let B=(0), then p(b)=?
If [tex]B=\{0\}[/tex] then [tex]p(B)=\{0\}^{B[0]}=\boxed{1}[/tex].
Hope this helps.
Find the coordinates of the midpoint of a segment with the endpoints
(-4, -14) & (-22, 9).
a. (-13, -2.5)
b. (-15, -2.5)
c. (-18, -4)
d. (-8, -1
Answer:
A es la respuesta a tu pregunta ue acabas de preguntar para que alguien la respondiera.
How many revolutions does a go kart with a wheel circumference of 62.8318 inches make in a 1609 m race? Please answer as quickly as possible!
Answer: 1008 revolutions
Step-by-step explanation:
1 revolution is equal to [tex]2\pi r[/tex]
To find how many revolutions the wheel makes, you must divide the distance traveled in the race between the circumference of the wheel
You must first convert 62.8318 in to meters.
We know that 1 inch is 0.0254 meters
Then
[tex]62.8318\ in*\frac{0.0254\ m}{1\ in}= 1.5959\ m[/tex]
[tex]revolutions = \frac{1609}{1.5959}\\\\revolutions=1008.21\\[/tex]
Finally The wheel made 1008.21 revolutions
If (x2 – 4) ÷ (x + 2) = x – 2, which polynomial should fill in the blank below?
(x + 2) ´ ______ = x2 – 4
x2 – 4
x – 2
x + 2
x2 – 2
Answer:
x - 2
Step-by-step explanation:
Given expression,
[tex](x^2-4)\div (x+2)=x-2[/tex]
[tex]\frac{x^2-4}{x+2}=x-2[/tex]
Multplying both sides by x + 2 ( Division property of equality )
[tex]\frac{x^2-4}{x+2}\times (x+2)=(x-2)\times (x+2)[/tex]
[tex]x^2-4=(x-2)(x+2)[/tex]
[tex]\implies x^2-4=(x+2)(x-2)[/tex] ( By commutative property )
Thus, SECOND OPTION is correct.
Answer:
X-2 is the correct answer! Edge 2020
Step-by-step explanation:
A bag contains 2 red balls and 18 green balls. A ball is chosen at random from the bag. What is the BEST answer for the probability of drawing a green ball? A) impossible B) unlikely C) very likely D) certain
Answer:
C) very likely
Step-by-step explanation:
Out of the 20 balls inside of the bag, 18 of them are green.
That means you have a 18/20 or 90% chance of getting a green ball.
Therefore, the probability of drawing a green ball is [tex]90[/tex] % then the option (C) is correct i.e., very likely.
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Here given that,
A bag contains [tex]2[/tex] red balls and [tex]18[/tex] green balls. A ball is chosen at random from the bag.
So,the total balls are [tex]18+2=20[/tex]
Green balls are [tex]18[/tex].
So the probability is
[tex]\frac{18}{20}[/tex] ×[tex]100=90[/tex] %
Hence, the probability of drawing a green ball is [tex]90[/tex] % then the option (C) is correct i.e., very likely.
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Based on a poll of 200 citizens, a community action group claims that 40% of the population is in favor of a curfew for children under 18 on weekday nights. A local parent group claims that the poll is not valid and that only 22% of the citizens favor a curfew. To determine whether this sample supports the population proportion of 0.40, a simulation of 100 trials is run, each with a sample size of 50 and a point estimate of 0.22. The minimum sample proportion from the simulation is 0.15, and the maximum sample proportion from the simulation is 0.27. The margin of error of the population proportion is found using an estimate of the standard deviation. What is the interval estimate of the true population proportion?
Answer: (0.18,0.26)
Step-by-step explanation: I just finished the test
The midpoint of a line segment is (-1, 4). The endpoints of the line segment are (3, y) and (-5, 10). What is the value of y?
Answer:
-2
Step-by-step explanation:
The midpoint is the average of the end point coordinates, so ...
4 = (y +10)/2 . . . . the y-coordinate is the average of the y-coordinates
8 = y +10 . . . . . . . multiply by 2
-2 = y . . . . . . . . . . subtract 10
Which equation describes this statement? The sum of p and q is equal to 24. Let q = 3. p + 3 = 24 p – 3 = 24 p ÷ 3 = 24 p × 3 = 24
For this case we must write algebraically the following statement:
"The sum of p and q is equal to 24"
The sum of p and q is represented as:
[tex]p + q[/tex]
If the sum is equal to 24 we have:
[tex]p + q = 24[/tex]
If they tell us that [tex]q = 3[/tex], then the expression is:
[tex]p + 3 = 24[/tex]
Answer:
[tex]p + 3 = 24[/tex]
A set of data is described as:
The data is around 7. If another measurement were taken it would probably be around 7.
Which group of measures would lead to this conclusion?
A. Range—10
Mode—7
Median—9
Mean—5
B. Range—4
Mode—6
Median—7
Mean—8
C. Range—12
Mode—9
Median—9
Mean—9
D. Range—5
Mode—9
Median—9
Mean—7
Answer:
B. Range - 5
Mode - 6
Median - 7
Mean - 8
step by step explaination:
if it's actually around 7, that's mean 7 is equal to median. And then, specifically, the mode & the mean number will side-to-side number of 7..which means number 6 and number 8.
The group of measures which would lead to the provided conclusion is range is 6, mean of the data is 8, median is 7 and mode is 6.
What is mean, median and mode of data set?The mean of the data is the average value of the given data. The mean of the data is the ratio of sum of all the values of data to the total number of values of data.
The median of the data is the middle value of the data set when it arrange in ascending or descending order. The data is around 7 which suggest that the median is 7.
Median=7
Mode of a data set is the the value, which occurs most times for that data set. The value which has the highest frequency in the given set of data is known as the mode of that data set.
Mean and mode is around the median. For this case the mean of the data is 8 and mode is 6.
Mode=6
Mean=8
Thus, the group of measures which would lead to the provided conclusion is range is 6, mean of the data is 8, median is 7 and mode is 6.
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What is the total area of the prism?
Answer:
The total area of the prism is [tex]SA=(\frac{9\sqrt{3}}{2}+54)\ in^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the triangular prism of the figure is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the triangular face
P is the perimeter of the triangular face
L is the length of the prism
Find the area of the base B
The base is an equilateral triangle
so
Applying the law of sines the area is equal to
[tex]B=\frac{1}{2}(3)^{2}sin(60\°)[/tex]
[tex]B=\frac{9\sqrt{3}}{4}\ in^{2}[/tex]
Find the perimeter P of the triangular face
[tex]P=(3+3+3)=9\ in[/tex]
we have
[tex]L=6\ in[/tex]
substitute
[tex]SA=2(\frac{9\sqrt{3}}{4})+(9)(6)[/tex]
[tex]SA=(\frac{9\sqrt{3}}{2}+54)\ in^{2}[/tex]
In the triangle below, 8/15 represents which ratio?
tanB
tanC
sinB
cosC
Answer:
tan(B)
Step-by-step explanation:
we know that
The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle
In this problem
tan(B)=AC/AB
substitute
tan(B)=8/15
Answer:
tan(B)
Step-by-step explanation:
Correct
Use the fact that the bacteria is doubling every five minutes. What fraction of the bottle was full at 11:20 a.m.?
Answer: D: 1/16
Step-by-step explanation:
Answer:
the answer is 1/16
Step-by-step explanation:
Select the equation that contains the point (4, -8), and in which the graph of the line has a positive slope.
y – 8 = –4(x + 4)
y – 8 = 4(x + 4)
y + 8 = +4(x – 4)
y + 8 = –4(x – 4)
Answer:
The third equation down is the one you want
Step-by-step explanation:
What you need for this is the point-slope form of a line:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
where y1 is the y coordinate from our point and x1 is the x coordinate from our point. m is the slope. That m has to be positive, according to the instructions. So the first equation and the last one are out, since those are both negative.
If we fit our point into the point-slope form, it looks like this:
[tex]y-(-8)=4(x-(4))[/tex]
which simplifies to
[tex]y+8=4(x-4)[/tex]
and that matches the third equation down.
PLEASE HELP!!
A survey was done that asked visitors at a theme park to indicate whether they drove or flew on a plane to get to the park, and whether they live up to 90 miles or more than 90 miles from the park.
What is the probability that a randomly selected visitor who lives more than 90 miles from the park drove?
Enter your answer, rounded to the nearest whole percent, in the box.
Answer: 28%
Step-by-step explanation:
Add all the numbers in the table = 593
Divide 165/593 = .278
Move decimal 2 places to the right = 27.8
Rounds up to 28%
Which sequence is generated by the function f(n 1) = f(n) – 2 for f(1) = 10? (a) –10, –12, –14, –16, –18, ... (b) –2, 8, 18, 28, 38, ... (c) 8, 18, 28, 38, 48, ... (d) 10, 8, 6, 4, 2, ...
Answer:
d
Step-by-step explanation:
Given
f(n + 1) = f(n) - 2 with f(1) = 10
To generate the sequence substitute values for n into the recursive formula.
f(1) = 10
f(2) = f(1) - 2 = 10 - 2 = 8
f(3) = f(2) - 2 = 8 - 2 = 6
f(4) = f(3) - 2 = 6 - 2 = 4
f(5) = f(4) - 2 = 4 - 2 = 2
The first 5 terms are 10, 8, 6, 4, 2
Answer:
D,10,8,6,4,2
Step-by-step explanation:
At a snack bar, there is a negative correlation between the number of sports drinks sold and the number of hot chocolates sold.
Which variable is most likely the lurking variable that explains the correlation?
ages of customers
number of customers
outside temperature
price of sports drinks
Hi good morning
So answer A. Ages of customers can be the answer
Answer B.Number of customers can be eliminated.
Answer C. Outside temperature can effect the what people want to drink, if its hot sports drink, If its cold Hot chocolate for everyone ! I depends on the temperature.
Answer D. Price of sports drink can be eliminated.
so, MY conclusion is that it could very well be the age group. ( Answer A)
I hope this helps. I am very sorry if it is wrong. At least I tried
Have a good day ^^
Trigonometric Functions help. What is the length of side AB? Type the correct answer rounded to one decimal place.
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
37.0
Step-by-step explanation:
You have a total of 3 triangles in one here. Triangle ABC, triangle ABD, and triangle DBC. If we can find out the length of side BD in triangle DBC that will help us later. We have angle D and side DC and we are looking for the hypotenuse of that right triangle DBC. The trig ratio that relates the side adjacent to the reference angle to the hypotenuse is the cosine:
[tex]cos(40)=\frac{20}{BD}[/tex]
Solving for BD:
[tex]BD=\frac{20}{cos(40)}[/tex]
That gives us that BD = 26.1
Now that we know that, we can move into the obtuse triangle that shares the side BD with the right triangle. We have that angle BDC is 40 degrees, and since angle ADB is supplementary to angle BDC, then angle ADB measures 180 - 40 = 140. So angle A is 30, angle ADB is 140, so that means that angle ABD is 10. Because triangle ABD is obtuse and not right you cannot use Pythagorean's Theorem. But you can use the Law of Sines. Set it up like this:
[tex]\frac{sin(140)}{AB}=\frac{sin(10)}{10}[/tex]
Solve for side AB:
[tex]AB=\frac{10sin(140)}{sin(10)}[/tex]
In degree mode on your calculator you'll find that side AB is 37.0
Water is flowing in a circular pipe varying cross-sectional area, and at all points the water completely fills the pipe.a) At one point in the pipe the radius is 0.210 m. What is the speed of the water at this point if water is flowing into this pipe at a steady rate of 1.10 m3/s?b) At a second point in the pipe the water speed is 2.80 m/s. What is the radius of the pipe at this point?
Final answer:
a) The speed of the water at a point in the pipe with a radius of 0.210 m is 7.97 m/s. b) The radius of the pipe at a second point where the water speed is 2.80 m/s is approximately 0.209 m.
Explanation:
a) To find the speed of the water at a point in the pipe, we can use the equation Q = Av, where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the water. Given that the flow rate is 1.10 m³/s and the radius is 0.210 m, we can find the area using the formula A = πr². Substituting the values, we have A = 3.14(0.210)² = 0.138 m². Solving for v, we get v = Q / A = 1.10 / 0.138 = 7.97 m/s.
b) To find the radius of the pipe at a second point where the water speed is 2.80 m/s, we can use the equation v = Q / A. Rearranging the equation to solve for the radius, we have r = √(Q / (πv)). Substituting the values, we have r = √(1.10 / (π(2.80))) ≈ 0.209 m.
Which box plot represents a set of data that has the least mean absolute deviation?
Answer:
try the second one because it is the smallest and close togehet so maybe that means that the mean is closer to the number and it nots some outlier.
Step-by-step explanation:
If the box plot or the distribution is spread out then the mean absolute deviations i.e. MAD is high.
and if the box plot is clustered that is the distribution is less spread out that is all the data values are close to the center value then the mean absolute deviation i.e. MAD is small.
From the given four box plot we see that the second box plot is less spread and the data values are close to the mean of the data.
Hence, it will lead to the least Mean absolute deviation.
Identify m∠KOL. HELP PLEASE!!
Answer:
30°
Step-by-step explanation:
In m KÔL, the angle is Ô and angle Ô is actually 30 degrees ;)
Answer:
m∠KOL = 30°
Step-by-step explanation:
It is given that mKL = 90and mMN = 30∘.
If two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. So,
m∠KOL= 1/2(mKL− mMN)
Substitute the given values and simplify.
m∠KOL= 1/2 (90∘−30∘)
= 1/2(60∘)
= 30∘
Therefor, m∠KOL=30∘.
Adalyn drove 12 miles from her home to her school and then drove back. Graph A shows her distance from home during the trip. Graph B will show her distance from the school during the trip. Complete each statement about Graph B.
Answer: 60 mph.
(486+316+638)/24
The distances given by the table. The time driven is 24 (given by the problem). So the average speed is simply the total distance divided by the time driven.
Step-by-step explanation:
Answer:
On Graph B, at 0 minutes, the height of the graph will be at 12 miles
Then, the graph will decrease until 15 minutes, when Adalyn reaches the school. At 15 minutes, the height of Graph B will be at 0 miles.
Step-by-step explanation:
Since she is coming back from school the numbers are decreasing.