The equation that can be used to represent the proportional relationship between time and the distance a greyhound dog can travel is:
y = 44x.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is found with the multiplication of the input variable and the constant of proportionality, as follows:
y = kx.
In which k is the constant of proportionality, also representing the rate between the output and the input for any pair of (input, output) except (0,0).
From the table of distances and time given in this problem, the constant is found as follows:
k = 220/5 = 440/10 = 660/15 = 44.
Hence the constant is of 44 and the relation is given by:
y = 44x.
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I need to make sure these are correct thank you in advance!
Using the unit rate, the graphs that best represent the amount they earn for different amount of time is: C.
How to Interpret the Slope?The slope of a graph can be interpreted as the unit rate of the scenario that is being represented by the graph. For example, money earned in dollars per hour worked is the unit rate or slope of the graph given in this scenario.
The larger the unit rate value, the steeper the slope of the line of the graph.
Let Lin's unit rate be represented as x, therefore,
Lin's unit rate = x
Diego's unit rate = 2x
Jada's unit rate = 2(2x) = 4x
This shows that unit rate of Jada is the highest, and therefore, the graph that would represent how much Jada earns would be the steepest, followed by Diego's, and the least is Lin's.
Therefore, the all the graphs would be: C.
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Determine the rate of change of the graph (HELP PLEASE)
Activity 4: Fair Share!
Directions: apply the rules in multiplication of integers in answering the following activity.
Answer:
1. P
2. U
3. K
4. A
5. M
6. C
7. E
8. J
9. L
10. I
A factory adds three red drops and two blue drops of coloring to white paint to make each pint of purple paint. The factory will make 50 gallons of the purple paint.
How many drops of red and blue coloring will the factory need in the 50-gallon batch of purple paint?
Answer: 1200 red and 800 blue
Two-fifths of a number decreased by 3 is 1. Find the number.
By using the basics of the number system the calculated number from the given statement is 10.
What is number system?
In mathematics, the number system can be used to express the numbers in a way of writing to make the mathematical expression. Basically, it provide the unique representation of the number with the help of the algebraic structures and operations.
According to the question, the expression can be formed by the given statement is as follows:
Let us assume the number be 'a'
Using basics of the number system for the formation of an expression:
Therefore,
(2/5)a - 3 = 1
⇒ (2/5)a = 4
⇒ a = 10
Hence, by using the basics of the number system the calculated number from the given statement is 10.
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100 points give me an explanation.
Dont lie or I will report you.
Answer:
Both ans are attached
A company takes 16 minutes to wash 24 cars. How many cars can be
washed in 1 minute?
Answer:1.5 cars can be washed in 1 minute but realistically only 1 car can be washed
Step-by-step explanation: 24/16 =1.5 and that get you your answer of 1.5 but the correct answer is 1.5 or 1 depending on if they are asking you to round down or not.
The graph of y = f(x) is shown below. Find all values of x where f(x) = 0
The values of x when f(x) = 0 are 2 and 8
Graphs are used mostly to show the relationship between two variables (usually x and y).
The graph of y = f(x) is attached
To get the values of x when f(x) = 0 , we consider where the line of the graph crosses the x-axis.
The graph crosses the x-axis at:
x = 2
x = 8
This means that the values of x when f(x) = 0 are 2 and 8
Therefore, in the graph of y = f(x), the values of x where f(x) = 0 are 2 and 8
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Disclaimer : The question mentined is not provided with a graph, the above solution is done as per the graph attached.
which answer?
pls help
Answer:
1. C: y = 3x - 5
2. B: y = -3x - 9
Step-by-step explanation:
1.
y = 3x + 9; (2, 1) (parallel)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - 1 = 3(x - 2)
y - 1 = 3x - 6
+1 +1
-------------------
y = 3x - 5
----------------------------------------------------------------------------------------------------------
2.
y = (1/3)x - 6 ; (-3, 0) (perpendicular)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - 0 = -3(x - (-3))
y - 0 = -3(x + 3)
y - 0 = -3x - 9
+0 +0
----------------------
y = -3x - 9
I hope this helps!
Help and please explain how answer is right
The new conditional statement that follows from the pair of true statement is If 4x + 5 = 13; then -5x = -10
What is law of syllogism?The law of Syllogism states that if the following two statements are true:
Statement 1: If x , then y
Statement 2: If y , then z
Then we can derive a third true statement:
Statement 3: If x , then z
From the given;
Statement 1: If x , then y
If 4x + 5 = 13; then x = 2
Statement 2: If y , then z
If x = 2; then -5x = -10
Statement 3: If x , then z
If 4x + 5 = 13; then -5x = -10
In conclusion, according to the law of Syllogism, the statement that follows from the pair of true statement is If 4x + 5 = 13; then -5x = -10
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HELP
What is the slope of the line?
Answer:
y= 1/2x+3.5
Step-by-step explanation:
Answer:
y= 1/2x+3.5
I took the test this is right
Step-by-step explanation:
lin and her brother earn 15 dollars for shoveling snow for their grandma and 35 dollars for cleaning the garage how much money does lin get if she split the money equally with her brother
Answer:
35+15 =50
50/2= 25 dollars
what is 10.88+10.88+10.88
Answer:
32.64
Step-by-step explanation:
Customer number two gives you a
15% off coupon. What is the new cost
of the order? 11.50
Answer:
$8.50 ? let me know if im wrong
Step-by-step explanation:
Lisa spent $27 on fruit at the grocery store. She spent a total of $30 at the store. What percentage of the total did she spend on fruit?
Lisa spent 90% of the total money on the fruits.
What is Percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Given is Lisa spent $27 on fruits at the grocery store. She spent a total of $30 at the same store.
Money spent by Lisa on fruits = $27
Total money spent by Lisa = $30
Therefore, percentage of the total money she spend on fruits will be -
(27/30) x 100 = 90%
Hence, Lisa spent 90% of the total money on the fruits.
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an ecologist wishes to mark off a circular sampling region having radius 13 m. however, the radius of the resulting region is actually a random variable r with the following pdf.
The expected area of a circular sampling region is 531.56 m²
Given,
The radius of the circular sampling region = 13m
f(r) = [tex]\left \{ {\frac{3}{4} } \atop {0}} \right.[/tex] [1 - (13 - r)²] 12 ≤ r ≤ 14
We have to find the area of the circular sampling region = E (π r²)
E (π r²) = π E (r²)
Lets find E (r²)
E (r²) =₁₂ [tex]\int\limits^[/tex]¹⁴ r² f(r) dr
= ₁₂∫¹⁴ (3r²/4) (1 - (13 -r)²) dr
= 3/4 ₁₂∫¹⁴ r² (1 - 169 - r² + 26r) dr
= 3/4 ₁₂∫¹⁴ r² (26r³ - r⁴ - 168r²) dr
= 3/4 [ 26r⁴/4 - r⁵/5 - 168r³/3]₁₂¹⁴
= 3/4 [ (26 × 14⁴)/4 - 14⁵/5 - (168 × 14³)/3] - [ (26 × 12⁴)/4 - 12⁵/5 (168 × 12³)/3]
= 3/4 [ (26 × 38416)/4 - 537824/5 - (168 × 2744)/3] - [ (26 × 20736)/4 - 248832/5 - (168 × 1728)/3]
= 3/4 [ 249704 - 107564.8 - 153664] - [ 134784 - 49766.4 - 96768]
= 3/4 [-11524.8] - [-11750.4]
= 3/4 [225.6]
= 169.2
∴ E(r²) = 169.2
Now lets find the expected area of the circular sampling region:
Area = E(π r²) = π E (r²)
Here, E(r²) = 169.2
So, area = π × 169.2 = 531.56 m²
That is, the expected area of a circular sampling region is 531.56 m²
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select the correct answer. a 500-gallon water tank drains at a rate of 50 gallons per minute. the amount of water left in the tank depends on the number of minutes it has been draining. what is the range of this relation? 0 ≤ y ≤ 500 0 ≤ y ≤ 10 y ≤ 500 y ≥ 0
Our range is 0 x 10, We could also graph this with x along with the x-axis and w along the y-axis then every minute 50x gallons are gone
We have 500 gallons of the water tank and it drains at the rate of 50 gallons per minute,
.Let's suppose after 5 minutes,
W = 500 - 50 * 5W = 500 - 250W = 250
After 5 minutes, 250 gallons are left in the water tank.
Here the lowest value is 0 so our maximum time is once the tank emptied, or when w is equal to 0.
0 = 500 - 50x
50x = 500X = 500/50X = 10
So, our range is 0 x 10
We could also graph this with x along with x-axis and w along the y-axis, in the graph the x- intercept where the tank is empty
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The 89 members of the Taft School Band spend
a total of $4,628 for tickets to Hammond's
Amusement Park. What is the cost of each
amusement park ticket?
By using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52
The total number of members of the Taft school = 89 members
The total cost for the ticket to Hammond's amusement park = $4628
The cost of each amusement park ticket = The total cost for the ticket to Hammond's amusement park ÷ The total number of members of the Taft school
Substitute the values in the equation
The cost of each amusement park ticket = 4628/89
= $52
Hence, by using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52
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9. The amount of water used by a washing
machine varies directly with the weight of the
load being washed. The washing machine uses
28 gallons to wash 7 pounds of clothing. How
many gallons of water will the machine
use to wash 24.5 pounds of laundry?
The machine will use 90 gallons of water to wash 24.5 pounds of laundry.
What is Direct Variation?If two quantities change by the same amount, they are said to follow a direct variation. As a result, when one quantity changes, the other follows suit, increasing when the first increases and decreasing when the first decreases. To put it another way, two quantities are said to be directly proportional to one another if the ratio of the first to the second is a constant term. The coefficient or constant of proportionality is the name given to this constant quantity. Assuming that x and y are two quantities that are directly varying, they are stated as follows:y ∝ x
Consequently, y = kx, where k is the proportionality constant.
Given:
The amount of water used by a washing machine varies directly with the weight of the load being washed.
Let's assume,
The amount of water used by a washing machine is y.
The weight of the load being washed is x.
According to the question,
y = 28 gallons
x = 7 pounds
Putting the values we get,
y = kx
28 = k × 7
k = 4
Now, we have to find y when x = 24.5
y = 4 × 24.5 = 98
Hence the machine will use 90 gallons of water to wash 24.5 pounds of laundry.
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What is the least common multiple of 34, 17, and 31?
Answer: 31, 34, 17
Step-by-step explanation:
The points (0,k) and (1,4) fall on a line with a slope of 9. What is the value of k?
Answer:
Formula for gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2), where x and y are the coordinates of the points.
(k-4)÷(0-1) = 9
k-4 = 9(0-1)
k-4 = -9
k = -5
Hi ! Please help, this came up as one of my questions and I don’t know how to do it well. Thanks!
Answer:
y = (3/2)x + 3
Step-by-step explanation:
Comment
The general equation is
y = mx + b
Finding m
The equation for the slope is
m = (y2 - y1)/(x2 - x1)
Givens
y2 = 3
y1 = 0
x2 = 0
x1 = - 2
m = (3 - 0)/(0 - -2)
m = 3 / 2
m = 3/2
Finding b
b is the y intercept which is (0,3)
x = 0
y = 3
3 = 0*3 + b
b = 3
So the equation is
y = (3/2) x + 3
The mean of five numbers is 8.2. Four of the numbers are 8, 10, 12 and 10.
Work out the fifth number.
Answer:
1
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
let x be the fifth number , then
[tex]\frac{8+10+12+10+x}{5}[/tex] = 8.2 ( multiply both sides by 5 to clear the fraction )
40 + x = 41 ( subtract 40 from both sides )
x = 1
the fifth number is 1
professor moore forgets to set his alarm with a probability of 0.10. if he sets the alarm, it will wake him on time to make his first class with a probability of 0.95. if he forgets to set the alarm, he wakes up in time for his first class with a probability of 0.25. professor moore was late to his first class. what is the probability that professor moore set his alarm given this information?
Answer: -The probability of setting his alarm is 1-0.1=0.9
-The probability of being in time is therefore calculated as:
0.9 x 0.95 + 0.1 x 0.25
= 0.88
Hence, the probability that the professor shows up in time is 0.88
Step-by-step explanation:
Amanda is driving a racecar. The table below gives the distance D (1) (in meters) she has driven at a few times t (in seconds) after she startsTimer(seconds)Distance D (1)(meters)
From the question;
we are to calculate average rate of change of distance with respect to time
The average rate of change is given as
[tex]\text{Average rate of change = }\frac{D_2-D_1}{T_2-T_1}[/tex]From the question we are given the table below
a. we are to find the average rate of change of the distance driven from 0 secons to 3 seconds
From the information
we have
[tex]undefined[/tex]Given m\_EBC = (3x + 20)° and m \_ABC = (17x-40)° find m\_ EBC and m LABC.
Answer:
18. m<EBC = 43°, m<CBD = 47°
19. m<EBC = 50°, m<ABC = 130°
Step-by-step explanation:
18. Find m<EBC and m<CBD
m<EBC = (5x + 8) and m<CBD = (6x + 5)
these two angles add up to a right angle, therefore their sum is 90°
5x + 8 + 6x + 5 = 90
11x + 13 = 90 , 11x = 77 , x = 7
m<EBC: 5(7) + 8 = 43
m<CBD: 6(7) + 5 = 47
19. Find m<EBC and m<ABC
m<EBC = (3x + 20) and m<ABC = (17x - 40)
these two angles are supplementary, meaning that they add up to 180°
3x + 20 + 17x - 40 = 180
20x - 20 = 180, 20x = 200, x = 10
m<EBC: 3(10) + 20 = 50
m<ABC: 17(10) - 40 = 130
this past semester, a professor had a small business calculus section. the students in the class were . suppose the professor randomly selects two people to go to the board to work problems. what is the probability that is the first person chosen to go to the board and is the second?
Given : Professor randomly selects two people to go to board to work on problems.
To find: Probability of chosen first or second person to go to the board.
Let [tex]x[/tex] be the total no. of students.
After the first student is chosen, no of students left = [tex]x[/tex] - 1
Therefore,
the required probability = 1 / total no. of students x no. of students left
⇒ 1 / [tex]x[/tex] ([tex]x[/tex]- 1 )
= 1 / ([tex]x^{2} - x[/tex])
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I’ll try to give brainliest to the first answer
Answer:
[tex]-2(x+5) = -2x -10[/tex]
Step-by-step explanation:
Hi there,
For us to answer the question we have to check if whether the end product on the both LHS and RHS are equal or not , so lets take each equation is whether both the sides are similar or not :
First eq :-
[tex]-2(x-5) = -2x + 5\\giving\\-2x+10\neq -2x+5[/tex]
Since it is not equal it is incorrect.
Second eq:-
[tex]-2(x+5) = -2x-5\\giving\\-2x-10\neq -2x-5[/tex]
Since it is not equal it is incorrect.
Third eq:-
[tex]-2(x+5) = -2x -10\\giving\\-2x-10=-2x-10\\[/tex]
Now we got the equation that equals both in LHS and RHS.
So our Answer is
[tex]-2(x+5) = -2x -10[/tex]
Hope this helped you out if so do mark me as the brainliest,
a fellow mate,
cheers!
One pound of apples costs $3.25. Five pounds of apples costs $16.25.
Answer:
what do you mean?
Step-by-step explanation:
- 1 2/5 - 3 1/3. Please help.
Answer:
-4 11/15
Step-by-step explanation: