Answer:
Original sum of money = $2246.51
Step-by-step explanation:
Interest = $96.60
Interest is compounded 6 times in a year ; n = 6
time = 1 year ; Rate of interest (r) = 4.2%
Interest = Future Value - Principal Value ...........(1)
![\text{Future Value = }Principal\cdot (1+\frac{r}{100\times n})^{n\cdot t}\\\\\text{Substituting this value in equation (1) , We get }\\\\Interest=Principal\cdot (1+\frac{r}{100\times n})^{n\cdot t}-Principal\\\\\implies 96.60=Principal[\cdot (1+\frac{4.2}{100\times 6})^{6\cdot 1}-1]\\\\\implies Principal=\$2246.51](https://tex.z-dn.net/?f=%5Ctext%7BFuture%20Value%20%3D%20%7DPrincipal%5Ccdot%20%281%2B%5Cfrac%7Br%7D%7B100%5Ctimes%20n%7D%29%5E%7Bn%5Ccdot%20t%7D%5C%5C%5C%5C%5Ctext%7BSubstituting%20this%20value%20in%20equation%20%281%29%20%2C%20We%20get%20%7D%5C%5C%5C%5CInterest%3DPrincipal%5Ccdot%20%281%2B%5Cfrac%7Br%7D%7B100%5Ctimes%20n%7D%29%5E%7Bn%5Ccdot%20t%7D-Principal%5C%5C%5C%5C%5Cimplies%2096.60%3DPrincipal%5B%5Ccdot%20%281%2B%5Cfrac%7B4.2%7D%7B100%5Ctimes%206%7D%29%5E%7B6%5Ccdot%201%7D-1%5D%5C%5C%5C%5C%5Cimplies%20Principal%3D%5C%242246.51)
Hence, the original sum of money borrowed = $2246.51
Answer:
Step-by-step explanation
let's use g for golf and b for batting cages
So let's start with Sylvester
he plays 5 rounds of mini golf so 5g
and he takes 4 turns in the batting cages so 4b
and he pays 60 dollars for this
SO his equation is 5g+4b=60
Now onto Lin
3g for 3 rounds of golf
6b for 6 turns in the batting cages
He pays 45 dollars
SO his equation is 3g+6b=45
Both equations:
5g+4b=60
3g+6b=45
Now you need to cancel out one variable so you can multiply the first equation by 3 and the second one by -5
15g+12b=120
-15g-30b=-225
Now the g will cancel out when you add both equations
-18b=-105
b=105/18 which is about 5.83 dollars
Now plug in 105/18 into any of the original equations and solve for g
Answer: First option is correct.
Step-by-step explanation:
Enrollment month Actual Predicted Residual
January 500 8 4
February 400 15 -1
March 550 15 -1
April 13 12 -1
May 16 17 -1
June 14 15 -1
Since we know that
Residual value = Actual value - Predicted value
Sum of residuals is given by
since we can see that sum of residual is more than 0.
So, it can't be a good fit .
Hence, No, the equation is not a good fit because the sum of the residuals is a large number.
Therefore, First option is correct.
Answer:
speed of Jada = 6km per hour which is not equal to
speed of Andre = 8km per hour
They did not run at same speed
Step-by-step explanation:
formula of speed = distance covered/ time taken
For Andre
Distance = 2 KM
time = 15 mins
60 mins = 1 hour
15 mins = 1/60 * 15 hour = 0.25 hours
thus,
speed = 2km/0.25 hour = 8 km per hour
Similarly for Jada
Distance = 3 KM
time = 20 mins
60 mins = 1 hour
20 mins = 1/60 * 20 hour = 1/3 hours
thus,
speed = 2km/(1/3)hour = 6 km per hour
Now we have
speed of Jada = 6km per hour which is not equal to
speed of Andre = 8km per hour
