Jordan and Manuel are on the track and field team at school.running around the track one day, Jordan ran 444m and Manuel ran 777 m. They both ran an even number of times around the track. How far is the track
Answer:
The track is 111 m
Step-by-step explanation:
The easiest way to calculate the meters in the track is to find the Greatest Common Divisor (GCD). This method is used to find the largest number to exactly divide both numbers 444 and 777, which are the meters both guys ran. The resulting number will give us the longest distance the track could have.
There are various techniques used to find the GCD. One of the is to find all divisors of both numbers and then look for the biggest one they have in common.
D 444 = { 1, 2, 3, 4, 6, 12, 37, 74, 111, 148, 222, 444 }
D 777 = { 1, 3, 7, 21, 37, 111, 259, 777 }
As we can see, the only divisors they have in common are 1, 3 ,37 and 111. The greatest of them is 111 ----> GCD(444,777) = 111.
This means the track has 111 m.
(Actually, the track could have been as long as any of the other common divisors, but it wouldn't have been realistic for the track to be 1, 3 or 37 meters).
Write 125.06 million 4 different ways.
Answer:
125.0600 million
[tex]\frac{6253}{50} million[/tex]
125,060,000
125 million 60 thousand
Step-by-step explanation:
It does not matter how many zeroes we add to the right end after the decimal, it does not change the value of the number.
Thus, 125.06, 125.060, 125.0600,.... all have the same values.
Similarly 125.06 can be change into the rational form
Thus, [tex]125.06=\frac{6253}{50} =\frac{12506}{100} \text{all have same values}[/tex]
We can also write the word "million" into the digits.
Thus, 125.06 million = 125,060,000 = 125 million 60 thousand
What's the answer to 2z-31=-9z+24
You are baking cookies for your class. There are 23 total students in your class and you have baked 12 cookies. Write and solve an equation to find the additional number x of cookies you need to bake in order to have 2 cookies for each student. Write your equation so that the units on each side of the equation are cookies per student.
Select the answer for this number showing three significant figures. Remember to round. 566 (1)600 (2)570 (3)566(4) 500
We have to round 566, such that , it has three significant figures.
→ Option 1
600=It has only one Significant figure.Zeroes which lie on right side of digit ,if there is no decimal after zeroes are not significant.
→ Option 2
570=Two Significant figure.
→ Option 3
566=Three Significant figure.
→ Option 4
500=One Significant figure.
⇒Option 3 ,which is equal to 566, is most appropriate ,among given Options, that is when this number is rounded , it has three significant figures.
Express 192 as a prime factors in order
You have been able to do the dishes in 30 minutes and vacuum in 15 minutes. youer roomate takes 40 minutes to do the dishes and 60 minutes to vacuum. based on this scenario
a triangle has two sides that are 2 inches and 12 inches what could be the length of the third side of the triangle
Answer:18
Step-by-step explanation:6+12>x
18>x
Nick can read 3 pages in 1 minute. Write the ordered pairs (number of minutes, number of pages read) for Nick reading 0,1,2,and 3 minutes.
Which graph represents a reflection across the x-axis of g(x) = (3)x?
Answer:
the answer is B
Step-by-step explanation:
the curve starting at -4 all the way down.
Just did this on edge hope this helps :)
Out of 106 total sophomores, there were forty-eight boys who received either an a, b, or c on their first math test. out of the twenty-eight total a’s, sixteen girls received a’s. out of the total fifty-four b’s, thirty girls received b’s. twelve boys received a c out of the twenty-four total c’s on the test. which two-way table represents this information
The two-way table that represents this information correctly is: Table B.
What is a Two-Way Table?A two-way table is used to demonstrate the frequencies for two variables collated from a single group. Rows and columns are used to represent information. The pieces of information stated above are well represented by chart B.
For instance, in the horizontal row, the total number of boys that had a, b, and c was shown to be 48. This means that there were forty-eight boys who received either an a, b, or c on their first test.
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Which of the following is the inverse of y=3^x
Please hurry
A. y= 1/3^x
B. y=log3x
C. y=(1/3)^x
D. y=log1/3x
Answer:
[tex]y=log_3x[/tex]
Step-by-step explanation:
We want to find the inverse of [tex]y=3^x[/tex].
We interchange [tex]x[/tex] and [tex]y[/tex] to obtain,
[tex]x=3^y[/tex].
We now make y the subject by taking logarithm of both sides to base 3 to get,
[tex]log_3x=log_33^y[/tex].
[tex]log_3x=y\:log_33[/tex].
[tex]\Rightarrow log_3x=y\:(1)[/tex].
[tex]\Rightarrow y=log_3x[/tex]
The correct answer is B.
Rodrigo is starting his own part time business. He plans to earn $25 per hour. He has the following expenses each month, $750 for overhead, $110 for phone and fax and $75 for materials. a. Write an equality that describes the number of hours h he must work to earn a profit of $625. b. How many hours should he have worked to earn a profit of at least $625?
The equality that describes the number of hours h he must work to earn a profit of $625 is h = 62.4 hours and The inequality that describes the number of hours h he must work to earn a profit of atleast $625 is [tex]\rm h \geq 62.4\;hours[/tex] and this can be determine by using arithmetic operations.
Given :
Rodrigo plans to earn $25 per hour.Total expenses each month - $750 for overhead, $110 for phne and fax and $75 for materials.a). Let the total number of hours be 'h'. The equality that describes the number of hours Rodrigo needs to work to earn a profit of $625 is given by:
25h - (750 + 110 + 75) = 625
25h = 1560
h = 62.4 hours
b). Then the inequality that describes the number of hours Rodrigo needs to work to earn a profit of atleast $625. is given by:
[tex]\rm 25h -(750+110+75)\geq 625[/tex]
[tex]\rm 25h - 935 \geq 625[/tex]
[tex]\rm 25h \geq 625+935[/tex]
[tex]\rm 25h \geq 1560[/tex]
[tex]\rm h \geq 62.4\; hours[/tex]
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A container holds 7 quarts of water. How much is this in gallons?
To convert 7 quarts to gallons, divide 7 by 4, as there are 4 quarts in a gallon. The result is that 7 quarts equal 1.75 gallons.
To convert quarts to gallons, one must understand the unit equivalence between the two. One gallon is equivalent to 4 quarts. To find out how many gallons are in 7 quarts, divide the number of quarts by the number of quarts in a gallon.
Using the equivalence provided:
1 gallon = 4 quartsYou would perform the following calculation:
7 quarts
4 quarts per gallon = 1.75 gallons
Therefore, 7 quarts is equal to 1.75 gallons.
Answer:
7 quarts of water is equivalent to 1.75 gallons.
Explanation:
To convert quarts to gallons, you can use the conversion factor that 1 gallon is equal to 4 quarts.
Given that the container holds 7 quarts of water, you can use the conversion factor to find out how many gallons that is:
[tex]\[ \text{Number of gallons} = \frac{\text{Number of quarts}}{4} \][/tex]
[tex]\[ \text{Number of gallons} = \frac{7 \text{ quarts}}{4} \][/tex]
[tex]\[ \text{Number of gallons} = 1.75 \text{ gallons} \][/tex]
1 point) the solution of a certain differential equation is of the form y(t)=aexp(3t)+bexp(4t), y ( t ) = a exp ( 3 t ) + b exp ( 4 t ) , where a a and b b are constants. the solution has initial conditions y(0)=3 y ( 0 ) = 3 and y′(0)=3. y ′ ( 0 ) = 3 . find the solution by using the initial conditions to get linear equations for a a and
A copy machine makes
105
copies in
3
minutes and
45
seconds. How many copies does it make per minute?
What number is needed to complete the pattern below?
66 73 13 21 52 __ 10 20
Jessica earned $13.50 babysitting one night. After babysitting the next day, she had a total of $31.75. How much did she earn babysitting the next day? Equation: 13.50 + x = 31.75
−20≤10n i need a solution.
What is the relationship between the measure of angle and the reflex measure of the angle
Angles are measured in degrees and their reflex measures can be obtained by adding 180 degrees to their measures.
In mathematics, an angle is a measure of the amount of turn between two lines or rays that share a common endpoint. The measure of an angle is given in degrees, and it represents the amount of rotation needed to move from one ray to the other.
The reflex measure of an angle is the sum of the angle's measure and 180 degrees. It represents the amount of rotation needed to move from one ray to the other while going in the opposite direction. For example, if an angle has a measure of 30 degrees, its reflex measure would be 30 degrees + 180 degrees = 210 degrees.
So, the relationship between the measure of an angle and its reflex measure is that the reflex measure is obtained by adding 180 degrees to the measure of the angle.
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Factor 3x^3-24x^2+36x
To receive a C grade, a student must average more than 77 but less than or equal to 85 . If Ethan received a C in the course and had five grades of 78 , 79 76 , 64 , and 85 before taking the final exam, what were the possible grades for his final if there were 100 points possible?
Round 8473227 to the nearest 100000
Put these decimals in order from least to greatest.
7.0,0.07,0.7,0.077
The initial population of a town is 2600, and he grows with the doubling time of 10 years. What will the population be in 12 years?
What is 9 X 10 to the fifth?
A man has 24 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 345 cents, how many dimes and how many quarters does he have?
The man has 17 dimes and 7 quarters.
A system of equations was set up, using the total number of coins and their total value, to determine the quantity of each coin type.
Let's denote the number of dimes as d and the number of quarters as q. We are given two facts: (1) the man has a total of 24 coins, and (2) the total value of the coins is 345 cents. Thus we have two equations:
d + q = 24 (since the total number of coins is 24)10d + 25q = 345 (since the value of each dime is 10 cents and each quarter is 25 cents, and their total value is 345 cents)We can solve this system of equations to find the values of d and q.
Subtracting the first equation from the second (multiplied by 10) to eliminate the variable d:
10d + 25q = 345
-(10d + 10q = 240)
-------------------------
15q = 105
Dividing by 15 to solve for q, we get q = 7. This means the man has 7 quarters. Substituting q = 7 into the first equation:
d + 7 = 24
d = 24 - 7
d = 17
So, the man has 17 dimes.
Therefore, the man has 17 dimes and 7 quarters.
find the equation of the circle where (-9,4),(-2,5),(-8,-3),(-1,-2) are the vertices of an inscribed square.
The equation of the circle where the vertices of an inscribed square are (-9,4),(-2,5),(-8,-3),(-1,-2) is (x+5)² + (y-1)² = 25. This is found by getting the average x and y coordinates to find the center of the circle, calculating the radius, and applying it to the standard equation of a circle.
Explanation:To find the equation of the circle where the vertices of an inscribed square are located at (-9,4),(-2,5),(-8,-3),(-1,-2), first, you need to find the center of the circle. In the case of a square inscribed in a circle, the center of the square is the same as the center of the circle. This can be found by averaging the x and y coordinates of the vertices of the square.
The average x-coordinate = [(-9) + (-2) + (-8) + (-1)] / 4 = -5
The average y-coordinate = [4 + 5 - 3 - 2] / 4 = 1
So, the center of the circle is at (-5, 1).
Next, you need to calculate the radius of the circle. The radius in an inscribed square is the half of the square's diagonal. Calculate the distance between two opposite vertices of the square - for example (-9,4) and (-1,-2). Apply the distance formula: √[(-1 - (-9))^2 + (-2 - 4)^2 ]. That's √[64 + 36], giving a distance of √100 = 10. As this is the diagonal of the square, the radius would be half of this, giving us a radius of 5.
Finally, the equation of the circle in its standard form (x-h)² + (y-k)² = r² can be written as (x+5)² + (y-1)² = 5².
Thus, the equation of the circle is (x+5)² + (y-1)² = 25.
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3x^2-5x-1 from 8x^2+2x-9
Your car is skidding to a stop from a high speed. you may want to review ( pages 112 - 114) . part a identify all forces acting on the object.
The forces acting on a car which is skidding to a stop are its weight due to gravity, a normal force coming from the ground, and the friction force due to the relative movement between the tires and the ground. Theoretically, we should also consider the friction force due to air viscosity, however practically we can neglect this force since it's contribution is very small in comparsion to the others (specially at low speeds).
Further explanationBy making the free body diagram of the car, we can observe 3 things:
The car has a certain mass, therefor due to the effect of gravity, it will have certain weight pointing towards the ground. It is important to remember that the weight always points downwards, even if the car would be on an inclined plane.Even though weight pulls the car down, the floor excerts a force over the car upward which keeps it in place. This is called the normal force and it is always perpendicular to the ground.Due to the roughness of the tires and the concrete, there will be a friction force do the relative movement between them. This friction force always goes in the opposite direction in which the car is moving (so if the car is heading to the right, the friction force aims towards the left, thus slowing it down).As a reference you can check the attached image, which shows how the forces would be in case the car would brake on a horizontal street. In case the car would be slowing on a floor which is not horizontal, like on a hill, the forces would have different directions.
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