Option B:
The 12th term is 354294.
Solution:
Given data:
and ![a_7=1458](https://tex.z-dn.net/?f=a_7%3D1458)
To find ![a_{12}:](https://tex.z-dn.net/?f=a_%7B12%7D%3A)
The given sequence is a geometric sequence.
The general term of the geometric sequence is
.
If we have 2 terms of a geometric sequence
and
(n > K),
then we can write the general term as
.
Here we have
and
.
So, n = 7 and k = 4 ( 7 > 4)
![a_7=a_4\ .\ r^{7-4}](https://tex.z-dn.net/?f=a_7%3Da_4%5C%20.%5C%20r%5E%7B7-4%7D)
![1458=54\ . \ r^3](https://tex.z-dn.net/?f=1458%3D54%5C%20.%20%5C%20%20r%5E3)
This can be written as
![$r^3=\frac{1458}{54}](https://tex.z-dn.net/?f=%24r%5E3%3D%5Cfrac%7B1458%7D%7B54%7D)
![$r^3=27](https://tex.z-dn.net/?f=%24r%5E3%3D27)
![$r^3=3^3](https://tex.z-dn.net/?f=%24r%5E3%3D3%5E3)
Taking cube root on both sides of the equation, we get
r = 3
![a_{12}=a_7\ .\ r^{12-7}](https://tex.z-dn.net/?f=a_%7B12%7D%3Da_7%5C%20.%5C%20r%5E%7B12-7%7D)
![=1458\ .\ r^5](https://tex.z-dn.net/?f=%3D1458%5C%20.%5C%20r%5E5)
![=1458\ .\ 3^5](https://tex.z-dn.net/?f=%3D1458%5C%20.%5C%203%5E5)
![a_{12}=354294](https://tex.z-dn.net/?f=a_%7B12%7D%3D354294)
Hence the 12th term of the geometric sequence is 354294.
Answer:
Difference = 250 students
Step-by-step explanation:
Let the total number of students be x.
Given the following data;
% driving = 30%
% riding = 60%
% walking = 10%
Number of students driving = 375
First of all, we would determine the total number of students.
Total = 30/100 * x = 375
0.3x = 375
Total, x = 375/0.3
Total, x = 1250 students.
Next, we determine the number of students walking;
Walking = 10/100 * 1250
Walking = 12500/100
Walking = 125 students
Finally, we would determine many more students drive to school than walk to school;
Difference = 375 - 125
Difference = 250 students
Answer:
T=30
Step-by-step explanation:
1) inverse mean opposite, so they want us to solve this equation using the opposite operation
So we can see here that 5 is being multiplied with t, so we should perform the opposite operation, division.
So
5t=150
(divide both sides by 5)
T=30
Hope this helps
V=hπr^2
(15π(3.5^2)ft^3)(55/100)(7.5gal/ft^3)≈2381.23 gal (to nearest hundredth of a gallon)
Answer:
5/6
Step-by-step explanation:
Step 1: Find Alicia's share of the gift. To do this, all you have to do is multiply 120 by 2/5, which is 40%. 120 * 40% (0.4) is 48. Alicia's share is $48.
Step 2: Find Jason's share of the gift. In this case, divide 120 by 3. 120/3 is 40. Jason's share is $40.
Step 3: Express the numbers as a fraction and simplify it. 40/48 is the common fraction. Find the GCF of 40 and 48. When you solve for it, the GCF is 8. Divide both the numerator and the denominator by 8. 40/8 is 5/ 48/8 is 6. There. 5/6 is our simplified fraction, which is the ratio.