Jen ran 1 2/3 miles in 1/4 of an hour, and Max ran 1 1/2 miles in 1 /5 of an hour. What is the average speed of each of Jen and Max? Who runs faster?
Jen: 1 2/3 = 5/3 *4 = 20/3 = 6 2/3 miles per hour
Max: 1 1/2 = 3/2 * 5 = 15/2 = 7 1/2 miles per hour
Max runs faster
Answer:
Max runs faster than Jen.
Average speed = 7.085 Miles per Hour
Step-by-step explanation:
Distance covered by Jen = [tex]1\frac{2}{3} = \frac{5}{3} \text{ miles}[/tex]
Time taken by Jen = [tex]\frac{1}{4}\text{ hours}[/tex]
Distance covered by Max = [tex]1\frac{1}{2} = \frac{3}{2} \text{ miles}[/tex]
Time taken by Jen = [tex]\frac{1}{5}\text{ hours}[/tex]
Formula:
[tex]Speed = \displaystyle\frac{Distance}{Time}[/tex]
Speed of Jen = [tex]\displaystyle\frac{\frac{5}{3} }{\frac{1}{4} } = \frac{20}{3} = 6.67 \text{ miles per hour}[/tex]
Speed of Max = [tex]\displaystyle\frac{\frac{3}{2} }{\frac{1}{5} } = \frac{15}{2} = 7.5 \text{ miles per hour}[/tex]
Hence, Max runs faster than Jen.
Average speed:
[tex]\displaystyle\frac{\text{Speed of Max + Speed of Jen}}{2} \\\\= \dsplaystyle\frac{6.67 + 7.5}{2} = 7.085\text{ Miles per Hour}[/tex]
Solve the equation. Explain each step and identify the property used to reach each step.
0.6x + 0.8 = 1.4
The value of x is 1 after applying the property of the subtraction and division if the equation is 0.6x + 0.8 = 1.4.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The linear equation is:
0.6x + 0.8 = 1.4
Subtract 0.8 on both sides
0.6x = 1.4 - 0.8 (Subtraction property of the equality)
0.6x = 0.6
Divide by 0.6 into both sides
x = 1 (Division property of equality)
Thus, the value of x is 1 after applying the property of the subtraction and division if the equation is 0.6x + 0.8 = 1.4.
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What does 39.75 divided by 8 equal
On the first day of school, the school bookstore sold 348 notebooks, some at 25¢ each and the rest at 38¢ each. The total amount of money paid for the notebooks was $100.91. How many of each kind were sold?
Final answer:
The bookstore sold 107 notebooks at 38¢ each and 241 notebooks at 25¢ each. A system of equations was used to determine the number of each notebook sold.
Explanation:
Let's denote the number of notebooks sold at 25¢ each as [tex]x[/tex] and the number of notebooks sold at 38¢ each as [tex]y[/tex] .
We are given two pieces of information:
The total number of notebooks sold is [tex]348: x + y = 348[/tex]The total amount of money collected is [tex]$100.91: 0.25x + 0.38y = 100.91[/tex]We can set up a system of two equations to represent this information:
[tex]x+ y = 348[/tex] (Equation 1)
[tex]0.25x + 0.38y = 100.91[/tex] (Equation 2)
Now, we can solve this system of equations to find the values of x and y.
Multiply Equation 1 by 0.25 to make the coefficients of x in both equations the same:
[tex]0.25x + 0.25y = 87[/tex] (Equation 3)
Now, subtract Equation 3 from Equation 2 to eliminate [tex]x[/tex] :
[tex]( 0.25x + 0.38y ) - ( 0.25x +0.25 y) = 100.91 - 87[/tex]
[tex]0.13 y = 13.91[/tex]
[tex]y = 107[/tex]
Now that we have the value for y, substitute it back into Equation 1 to find x:
[tex]x + 107 = 348[/tex]
[tex]x = 241[/tex]
Hence , the solution is x = 241 and y = 107, meaning 241 notebooks were sold at 25¢ each and 107 notebooks were sold at 38¢ each.
a certain number of quartersz five times as many pennies as quarters, and 12 more dimes than quarters are worth 8.00. dollars how many of each coins are there
Answer:
Step-by-step explanation:
HELP ASAP!!!!!!
A figure skater needs a total score of at least 90 to move on to the next round. Her total score is the average of four judges’ scores. The first three judges’ scores were 83, 88, and 92. The figure skater found out she made it to the next round.
What is the minimum score the fourth judge could have given her?
Which shows the correct way to find
1
,
745
×
47
?
1,745×47?
1,745 multiplied by 47 equals 82,015.
To correctly find the product of 1,745 and 47, you should use long multiplication.
Here's the step-by-step process:
1,745
x 47
-------------
12,215 (1,745 times 7)
8,725 (1,745 times 4, shifted one position to the left)
-------------
82,015
Begin by multiplying 1,745 by 7, which gives 12,215.
Then, multiply 1,745 by 4 and shift the result one position to the left, yielding 8,725.
Finally, add these two results together to get the product, which is 82,015.
So, 1,745 multiplied by 47 equals 82,015.
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−8x+5−2x−4+5x− when x=2
Joseph has $32.40. he wants to buy several comic books that each cost 2.70. how many comic books can he buy?
a veterinary student estimated the weight of a snapping turtle to be 147 pounds. the actual weight was 175 pounds. what is the percent error between the actual weight of the turtle and the estimated weight
Please Hurry Again!!
Which Exponent Property would you apply FIRST to simplify this problem
(4^5 × 4^−7)^2
A Power to Power Property
B Quotient Property
C Product Property
D Zero Exponent Property
Azul needs to buy 3,500 ml of juice. How many liters of juice should Azul buy?
Find the value of x so that the function has the given value.
m(x)=4x+15 m(x)=7
The value of x so that the function is equal to -2
Given the following function
m(x) = 4x + 15
m(x) = 7
Since both of them are m(x), hence;
4x + 15 = 7
Subtract 15 from both sides
4x + 15 - 15 = 7 - 15
4x = -8
Divide both sides by 4
4x/4 = -8/4
x = -2
Hence the value of x so that the function is equal to -2
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solve the equation for y:
x=2y-3
Find the area of the model!!! ASAP PLEASE
area of a square is S^2
2.6^2 = 6.76 square cm
Each day, Viktor practices piano for x minutes and practices violin for 30 minutes.
To find how many minutes he will spend practicing instruments over 5 days, Viktor calculates:
x + 30 + x + 30 + x + 30 + x + 30 + x + 30
What is another way Viktor can calculate how many minutes he will practice in total over the 5 days?
Drag and drop the equivalent expression in the box.
5x + 30
x + 150
5 (x +30)
x + 30
13. Which equation has no solution? (1 point) 5v + 3 = 5v – 5 2x – 4 = 2x + 7 – x 2y + 5 – y = 2y – 3(y – 6) 7z + 9 = –7z – 6
there are 72 members of the show choir .There are 6 more boys than girls in the choir .
Write a model of a system for the above situation
what is 7y+4x=3 that is in slope-intercept form of the equation and is the perpendicular to the line that passes through the point of (-4, -7)
Which expression is equivalent to 2(m − 4) + 1?
A. 2m − 7
B. 2m − 3
C. 2m + 9
D. 2m + 10
Answer:
I believe the answer is 2m - 7 but I could be wrong, I'm only guessing to what seems to be the most accurate
Step-by-step explanation:
A basketball player scored 29 times during one game. she scored a total of 45 points, two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws?
x = 2 point shot
y = free throw
x +y = 29
x = 29-y
2x +y = 45
2(29-y) + y = 45
58 -2y +y = 45
58-y = 45
-y = -13
y = 13
29-13 = 16
16*2 = 32
16 two pint shots and 13 free throws
Answer:
16 two pint shots and 13 free throws
Step-by-step explanation:
What is the solution to the proportion? m/18 15/12 A. m=10 B. m=14.4 C. m=22.5 D. m=27
m/18 = 15/12
m12 = 270
m = 270 /12 = 22.5
C. m = 22.5
It took a truck, which is moving at 60 mph, 8 hours to get from Boston to Washington DC. How long will it take a car to get from Boston to Washington DC, if it travels at 75 mph?
For this case we have that by definition the time is given by:
[tex]t=\frac{d}{v}[/tex]
Where the variable "d" represents the distance and "v" represents the speed.
So, first we need to know the total distance:
[tex]d=(v)(t)[/tex]
[tex]d=(60)(8)[/tex]
[tex]d=480 mi[/tex]
Then, the time for 75mph is given by:
[tex]t=\frac{480}{75}[/tex]
[tex]t=6,4[/tex]
Answer:
6,4 hours
Answer:
6.4 hours
Step-by-step explanation:
60*8/75=
480/75=
6.4
Write the doubles fact you used to solve the problem. 7+8
A rectangular park is 150 yards on one side and 125 on the other
Without actually calculating, how much greater is the product of 98x50 than the product of 97x50
The graph shows the total fare, y, for a taxi ride with respect to the miles traveled, x.
What is the y-intercept and what does it represent?
Question options:
The y-intercept is 3 and it represents the initial fee before any miles are traveled.
The y-intercept is 3 and it represents the cost of traveling 1 mile.
The y-intercept is 0 and it represents the initial fee before any miles are traveled.
The y-intercept is 20 and it represents the cost of the cab ride.
Mrs. Gordon measured three rectangular rooms she wants to tile. What is the total rooms? the family room is 25 ft by 16 ft the kitchen is 15 ft by 12,75 ft the laundry room is 10.5 ft by 10.5 ft. I have to describe the steps i would have to take to solve this problem
Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.
Answer:
Yes, she is correct.
Step-by-step explanation:
A real number that can be expressed as [tex]\frac{p}{q}[/tex],
Where,
p and q are integers,
Such that, q ≠ 0,
is called a rational number.
A terminating decimal is always a rational number,
Thus, 2.11 is a rational number,
Verification :
2.11 = [tex]\frac{211}{100}[/tex]
Where,
Both 211 and 100 are integers,
Such that 100 ≠ 0.
The value 2.11 is a rational number and not a repeating decimal.
Given the number 2.11 ;
Rational numbers Can be expressed in the form p/q ; where q ≠ 0. However, irrational numbers cannot be be expressed in the form p/q. 2.11 is written into two decimal places ; therefore it can be expressed thus ;(2.11 × 100) ÷ 100 [tex] \frac{211}{100} [/tex][tex]since \: 2.11 = \frac{211}{100} [/tex]
Then, we can conclude that 2.11 is a rational number
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What is the average speed of a runner if he ran 2 1/3 of a mile in 20 minutes?
Answer:
The average speed of the runner is 7 miles per hour.
Step-by-step explanation:
Given:
Distance ran by [tex]2\frac{ 1}{3} miles[/tex]
Time taken by the runner = 20 minutes.
To find:
The average speed of a runner=?
Solution:
Now, we know that ,
distance = speed x time
Then, [tex]2\frac{ 1}{3} miles[/tex] = average speed x 20 minutes
=> average speed = [tex]\frac{(2 \frac{1}{3} miles)}{(20 minutes)}[/tex]
=> average speed = [tex](\frac{(2 x 3 + 1)}{3} miles)}{(20\times\frac{1}{60} hours)[/tex]
=> average speed=[tex]\frac{(\frac{(6+1)}{3})}{(\frac{20}{60})}[/tex]
=> average speed = [tex]\frac{ (\frac{7}{3})}{(\frac{1}{3})}[/tex]
=>average speed = [tex]\frac{7}{3}\times\frac{3}{1}[/tex]
=>average speed = 7