7. You and 3 friends divide the proceeds of a garage sale equally. The garage sale earned $412. How much money did you receive?

Answers

Answer 1

Answer: The answer is 103. 412 divided by 4 is 103.

Answer 2

Answer:

Final answer:

To find out how much money you received from the garage sale proceeds, you need to divide the total amount by the number of people sharing it. In this case, you and 3 friends are dividing $412 equally. So, you would divide $412 by 4 (3 friends + yourself). The money you received from the garage sale is $103.

Explanation:

Step 1:

Divide $412 by 4 to find the equal share for each person.

Step 2:

Perform the division: $412 ÷ 4 = $103.

Step 3:

The money you received from the garage sale is $103.

Learn more about Garage sale proceeds here:

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She traveled 60 miles to the appointment place.

Step-by-step explanation:

Let the distance to appoint be s and time for appointment trip be t.

The return trip took one fifth hr longer because of heavy traffic.

Time for return trip = t + one fifth hour = (t + 0.2) hr

Speed of appointment trip = 60 mph

Speed of return trip = 50 mph

We have

s = 60 t and

s = 50 (t + 0.2)

s = 50 t + 10

60t = 50 t + 10

10 t = 10

t = 1 hour

Distance to appointment = 60 t = 60 x 1 = 60 miles

She traveled 60 miles to the appointment place.

Peggy works as a busperson and earns \$7.50/h. She also receives 9\% of the gratuities earned by all the staff. In one week she worked 35 hours and the gratuities totalled \$1936.80. What was Peggy's gross pay?

Answers

Answer: $ 436.81

Step-by-step explanation:

Given: Hourly rate for Peggy= $7.50

Also, she receives 9% of the gratuities earned by all the staff.

Total hours she worked = 35 hours

Total gratuities = $1936.80

Gross pay = (Hourly rate ) x (Number of hours worked)+ 9% of (Total gratuities )

= $ [(7.50 ×35)+(0.09 ×1936.80)]

= $ (262.5 +174.31)

= $ 436.81

Hence, her gross pay = $436.81

The vertical height v, in feet, of a snowboarder jumping off of an overhang can be modeled by the function h(t)=15-10t-16t^2, where 15 is the initial height (in feet) of the overhang, -10 is the initial vertical velocity (in feet per second), and t is the time (in seconds). How long does it take the snowboarder to land after jumping off the overhang?"

Answers

Step-by-step explanation:

It is given that, the vertical height v, in feet, of a snowboarder jumping off of an overhang can be modeled by the function as :

$h(t)=15-10t-16t^2$

Where

15 is the initial height of the overhang

-10 is the initial vertical velocity

t is in second

We need to find the time taken by the snowboarder to land after jumping off the overhang. At this condition,

h(t) = 0

So, $15-10t-16t^2=0$

On solving above equation using online calculator, we get the value of t = 0.705 seconds. So, the time taken by the snowboarder to land after jumping off the overhang is 0.705 seconds.

I don't know for sure, but I think there might be an error in the way you copied your function. In all of my dealings with these types of problems, I have learned the formula to be h(t) = 15 + 10t - 16t^2. Notice the plus in front of the "10t". This is due to the fact that if he pushes off of the overhang he would have an upward force of 10 feet per second as soon as his feet left the ground. The only thing pulling him back to Earth is gravity, modeled by the "-16t^2". This is derived from a bit of slightly advanced physics involving the gravitational constant, but let's work under my formula for a second...

Either way, we will wind up using the Quadratic Formula (or possibly factoring if the numbers are easy enough to work with). So let's start.

h(t)= 15 +10t - 16t^2

In order to use the QF or factoring I will need to make h(t)=0. Simply done by:

0= 15 +10t -16t^2

Looking at the numbers, I'd prefer to use the QF so here it is:

$x= \frac{-b + or - \sqrt{b^(2)-4ac } }{2a}$

I know that my answer will need to be positive since you can't have a negative value when dealing with time, so I will eliminate the positive sign from the "+or-" part leaving me with:

$x= \frac{-b -\sqrt{b^(2)-4ac } }{2a}$

And I know that a= -16, b= 10, and c=15. So all that's left to do is substitute and solve.

$x= \frac{-10 -\sqrt{-16^(2)-4*-16*15 } }{2*-16}$

There's a decent amount of math that would be difficult and sloppy for me to do over the computer, but all you need to do is solve the rest of the equation and you would get your answer.

Exact answer: $(5-4 √(15) )/(8)$ or rounded answer: ≈1.31 seconds.

Hope this helps!
NoThisIsPatrick

if a right circular cone has a volume of 15 cubic ft and a radius of 3 ft, what is the height of the cone?

Answers

volume of cone=1/3 times height times pir^2
v=15
r=3
15=1/3 hpi3^2
15=1/3hpi9
15=9/3hpi
15=3hpi
divide 3
5=hpi
h=5/pi
pi=aprox 3.14
5/3.14=1.59

1.59 ft

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