The correct answer is option D
D. 597
The solution is as following
Determinant of K = 14 *(8*5+ --1*-2) - (-13)*(3*5- (-1)*(-10)) + 0 *( 3*-2 - 8*-10)
= 14 * 38 + 13 * 5 + 0 * 74
= 532 + 65
= 597
Answer:
2, 5 and 6
Step-by-step explanation:
this is because mode is the most appeared number in a data and 2,5 and 6 all appeared twice
So slope is known as rise over run, or x/y. in your case of 3/4, the slope is y=3 and x=4. The slope is equal to the growth rate. It measures steepness, so in real life you could apply it to finding the steepness of a hill for construction, or perhaps how steeply your speed grows from 0 to 100 when driving a car.
Answer:
$2
Step-by-step explanation:
Let, price of individual child ticket is $x, and price of individual adult ticket is $y.
Now, on Friday we can write an equation is 55x+20y=200....(1).
and on Saturday we can write an equation is 72x+36y=306.....(2).
so, Equation 1: 55x+20y=200
Equation 2: 72x+36y=306
now, we are going to solve both equations.
after solving you will find x=2 and y=4.5
Hence, we can say that the cost of child ticket is $2, and the cost of adult ticket is $4.50.
To solve this we are going to use the future value of annuity due formula:
![FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%2AP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bkt%7D-1%20%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where

is the future value

is the periodic deposit

is the interest rate in decimal form

is the number of times the interest is compounded per year

is the number of deposits per year
We know for our problem that

and

. To convert the interest rate to decimal form, we are going to divide the rate by 100%:

. Since Ruben makes the deposits every 6 months,

. The interest is compounded semiannually, so 2 times per year; therefore,

.
Lets replace the values in our formula:
![FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%2AP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bkt%7D-1%20%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
![FV=(1+ \frac{0.1}{2} )*420[ \frac{(1+ \frac{0.1}{2})^{(2)(15)}-1 }{ \frac{01}{2} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7B0.1%7D%7B2%7D%20%29%2A420%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.1%7D%7B2%7D%29%5E%7B%282%29%2815%29%7D-1%20%7D%7B%20%5Cfrac%7B01%7D%7B2%7D%20%7D%20%5D)
We can conclude that the correct answer is <span>
$29,299.53</span>