Middle SchoolMathematics 5+3 ptsStudents are entering an auditorium at a constant rate .When the Auditorium opens there are already 23 students sitting in it after it has been feeling for 10 minutes There are now 473 students in the auditorium.

Find average rate of change for the first 10 minutes

how many students will be in the auditorium after 15 minutes of filling

Answers

Answer 1

Answer:

To find the rate of change, we must find the amount of people that have changed over a given time period, and then find the unit rate. As 473-23=450 (we can subtract because we have the end number minus the starting number to find the amount changed) students enter over 10 minutes, and we want to find the rate of change for 1 minute, we can divide 450 10 times. As we move the decimal point of a number 1 to the left when dividing by 10, we have 450.00 -> 45.000 after dividing by 10. Therefore, the average rate of change is 45 students per minute. To find how many students will be in the auditorium after 15 minutes of filling, we can use this average rate of change to figure out approximately how many students will enter in 5 minutes. Therefore, as 45 students come in every minute, after 1 minute, 45 more students will come in. After 2, 45+45=45*2=90 students will come in, and so on. Thus, 45*5=225 students will come in after 5 minutes. Since we know that 473 students are in the auditorium after 10 minutes, we can add 225 to 473 to get 698 students after 15 minutes.

Feel free to ask further questions, and Happy Holidays!

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The scale on the map is 1 cm to 10 km. The distance from Clevend to Cincinnati is 40cm. The scale on the second map is 1 cm to 50 km. What is the distance from Clevend to Cincinnati on the second map? Explain your reasoning

Answers

1cm *10 = 10km
40cm * 10 = 400 km

50km/50 = 1cm
400km/50 = 8cm

A: 8cm

At a track meet, Jacob and Daniel complete in the 220 m hurdles. Daniel finishes in 3/4 of a minute. Jacob finishes with 5/12 of a minute remaining. Who ran the race in the faster time. Bonus: Express the difference in their times as a fraction of a minute.

Answers

Jacob ran the race in the faster time

Further Explanation:

Daniel complete the hurdle at = 3/4 of a minute

Recall, 1 minute = 60 seconds

Therefore, Daniel complete the hurdle at 3/4 of 60 [secs]

= 3/4 x 60

= 3 x 60 ÷ 4

= 180 ÷ 4

= 45 seconds

Jacob complete the hurdle with a remainder = 5/12 of a minute

Recall, 1 minute = 60 seconds

Therefore, Jacob complete the hurdle with the remainder of 5/12 of 60 [secs]

= 5/12 x 60

= 5 x 60 ÷ 12

= 300 ÷ 12

= 25 seconds

To find out how many minute Jacob used to complete the race:

60 seconds – 25 seconds=

= 35 seconds

Since Daniel complete the race in 45 seconds, and Jacob complete the race in 35 seconds, in Athletics, the fastest of the two in completing the race is Jacob because, the time at which he complete the race is not greater than the time at which Daniel complete the race. And as such, the fastest of the two (Jacob) whose time is lesser is adjudged the winner of the race.

Deriving the difference in their times as a fraction of a minute:

The difference in their times is expressed as:

Daniel’s time [45 seconds] – Jacob’s time [35 seconds]

Therefore,

= 45 – 35

= 10 seconds

Expressing the difference as a fraction of a minute:

Since 1 minute = 60 seconds

Hence, the fraction would be:

10/60

= 1/6

The given answers were derived as a result of the usage of Multiplication, Division and Subtraction, being functions of a number problem in mathematics.

LEARN MORE:

Track brainly.com/question/362542

KEYWORDS:

Seconds
Minute
Fraction
Difference
Time

Well, 60(sec.) divided by 4 = 15. 15x3= 45 seconds is Daniel's time.
60 divided by 12 = 5. 5x5 = 25 seconds is Jacob's time. Jacob finished faster. Hope this helps!

A sphere and the base of a cone have a radius of 3 inches. The volume of the sphere equals the volume of the cone. what is the height of the cone, in inches?

Answers

So the volume of a sphere is $V= (4)/(3) \pi r^3$ , and the volume of a cone is $V= \pi r^2 (h)/(3)$ (h=height, r=radius). Knowing only the radius, we can solve for the volume of the sphere. (Also I'm going to be leaving answers in pi form.)

$V= (4)/(3) \pi 3^3$
Solve the exponents to get $V= (4)/(3) \pi 9$
Multiply 4/3 and 9 to get $V=13.5 \pi$

Now that we know the volume of the sphere, we can solve for the height of the cone since the volumes for both are the same.

$13.5 \pi = \pi 3^2 (h)/(3)$

Solve the exponents to get $13.5 \pi =9 \pi (h)/(3)$

Divide $9 \pi$ on each side to get $1.5= (h)/(3)$

Multiply 3 on each side, and your answer should be $4.5=h$

If a test has 95 questions how many points would each question be worth? Using your answer how many could you miss without going below an 80?

Answers

One can miss up to 24 questions and still achieve an 80% score.

In order to calculate the points each question is worth and determine how many questions you can miss while maintaining an 80% score.

To find the points each question is worth, we divide the total points by the number of questions. Let's assume the test is out of 100 points, which is a common scale. Therefore, each question would be worth $(100)/(95)$ or approximately 1.05 points.

Now, let's determine how many questions you can miss while still achieving an 80% score (which is 80 out of 100 points). We'll set up an equation to solve for the maximum number of questions you can miss, denoted by "x":

$80 = (100 - x)/(95) * 100$

To solve for "x," first, we'll simplify the equation:

$80 = (10000 - 100x)/(95)$

Next, we'll isolate "x" by multiplying both sides by 95:

$7600 = 10000 - 100x$

Now, isolate "-100x" by subtracting 7600 from both sides:

$-2400 = -100x$

Finally, divide both sides by -100 to solve for "x":

$x = (-2400)/(-100) = 24$

So, you can miss up to 24 questions and still achieve an 80% score.

To know more about Score here

brainly.com/question/29138242

#SPJ2

100/95= 1.05. Each question worth 1.1 rounded. You could miss 19 but if you miss 20 you go under 80.

Martin earns $15 a week doing chores for his neighbors.Martin saves 1/4 of his money each week to spend on new cars

How much is this?

Answers

Answer:

$(1)/(4) * 15 = (15)/(4) = 3.75$

Martin saves $3.75 each week.

Martin saves $3.75 to spend on new cars. You can find this buy dividing 15 by 4. Or you can find this by multiplying 15 by 1/4. Either way will result you in $3.75

What is 27/32 divided by 7/8