Mario has a unit rate of 900 miles/hour.
Explanation:
It is given that Mario travels at a rate of 2/3 miles every 10 minutes.
We use the relation between speed, time, and distance, described by
We have,
Distance = 
Time = 10 minutes
By substituting these values into the preceding formula, we get
![\text{Speed} = \frac{2/3}{10}\\\\ \text{Speed} =\frac{2}{10\cdot 3}\\\\ \text{Speed} =[tex]\frac{1}{15}](https://tex.z-dn.net/?f=%5Ctext%7BSpeed%7D%20%3D%20%5Cfrac%7B2%2F3%7D%7B10%7D%5C%5C%5C%5C%20%5Ctext%7BSpeed%7D%20%3D%5Cfrac%7B2%7D%7B10%5Ccdot%203%7D%5C%5C%5C%5C%20%5Ctext%7BSpeed%7D%20%3D%5Btex%5D%5Cfrac%7B1%7D%7B15%7D)
\text{ miles/min}[/tex]
To express the unit rate in miles per hour, we must multiply by 60.
Thus, the resulting unit rate is
Step-by-step explanation: The entertainment company’s net value after t months can be expressed by the equation; v(t) = 4t² - 24t - 28.
To factor this expression, we need to simplify the equation:
v(t) = 4t² - 24t - 28,
dividing everything by 4 yields:
v(t) = t² - 6t - 7,
v(t) = t² - 7t + t - 7,
v(t) = t(t-7) + 1(t-7),
v(t) = (t+1)(t-7).
Thus, the function in factored form is v(t) = (t+1)(t-7).
To find when the company hits its lowest value, substitute v(t) = 0 into the factored expression:
v(t) = (t+1)(t-7).
Setting equal to zero provides:
(t+1)(t-7) = 0, leading to t + 1 = 0 and t - 7 = 0; thus, t = -1 and t = 7.
Since time cannot be negative, therefore, t equals 7 months.
This indicates that after 7 months, the company will reach its minimal net value.
The illustration is omitted. Please see the attachment below.
Answer:
The area of the shaded sector is 144π square units.
Step-by-step breakdown:
Given:
The central angle for the sector is, 
The circle's radius is, 
The area of a sector with radius 'R' and angle 
can be determined with:
Substituting 
gives
Thus, the area of the shaded sector calculates to 144π square units.
12 m^2/h to cm^2/min
12 m^2/h × 1 h/60 min = 0.2 m^2/min
0.2 m^2/min × 10000 cm^2/1 m^2 = 2000 cm^2/min
2000 cm^2/min
The total number of bills and coins is 14.
Step-by-step explanation:
To minimize the count of bills and coins, start with the largest denominations that fit within the amount.
The change due is $39.49.
Start with:
-$20 bill (largest under $39.49)
Remaining: $19.49
-$10 bill (largest under $19.49)
Remaining: $9.49
-$5 bill (largest under $9.49)
Remaining: $4.49
Then:
4 × $1 bills (to cover $4.49)
Remaining: $0.49
-$0.25 coin (quarter)
Remaining: $0.24
2 × $0.10 coins (dimes)
Remaining: $0.04
4 × $0.01 coins (pennies)
The final composition includes:
1 twenty-dollar bill
1 ten-dollar bill
1 five-dollar bill
4 one-dollar bills
1 quarter
2 dimes
4 pennies
Totaling 14 pieces.
