Answer: 15
Step-by-step explanation:
(r+1)th term of
is given by:-

For
, n= 6

![=\ \dfrac{6!}{4!2!}a^4b^2\ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{6\times5\times4!}{4!\times2}a^4b^2\\\\=3\times5a^4b^2\\\\ =15a^4b^2](https://tex.z-dn.net/?f=%3D%5C%20%5Cdfrac%7B6%21%7D%7B4%212%21%7Da%5E4b%5E2%5C%20%5C%20%5C%20%5B%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D%5D%5C%5C%5C%5C%3D%5Cdfrac%7B6%5Ctimes5%5Ctimes4%21%7D%7B4%21%5Ctimes2%7Da%5E4b%5E2%5C%5C%5C%5C%3D3%5Ctimes5a%5E4b%5E2%5C%5C%5C%5C%20%3D15a%5E4b%5E2)
Hence, the coefficient of the third term in the binomial expansion of
is 15.
Answer:
x = 2
Step-by-step explanation:
180= 90 + 57 + Z
Z = 180 - 90 - 57
Z = 33
33 = 7X + 19
7X = 33 - 19
7X = 14
X = 2
The composite shape is made up of a cube with a side length of 5 inches and a cylinder with a radius of 2 inches and a height of 4 inches.
The composite solid's surface area is 225.4 square inches.
Step-by-step explanation:
Step 1:
The given composite shape is made up of a cube with a side length of 5 inches and a cylinder with a radius of 2 inches and a height of 4 inches.
The surface area of the composite shape is given by summing the individual surface areas.
The composite shape's surface area = The cube's surface area + the cylinder's surface area.
Step 2:
Any cube's surface area is calculated by multiplying 6 with the square of the side length (
).
The cube's surface area =
=
=
square inches.
Step 3:
Any cylinder's surface area is calculated with the following formula;
The cylinder's surface area =
=
=
square inches
Step 4:
The composite shape's surface area = The cube's surface area + the cylinder's surface area.
The composite shape's surface area = 150 + 75.398 = 225.398 square inches. Rounding this off, we get the area as 225.4 square inches.
Answer:
D. $10,540
Step-by-step explanation:
1. 20% of $24,900 is $4,980
2. 20% of $27,800 is $5,560
3. Add $4,980 to $5,560
4. Answer is $10,540 in commission
5+5=10
y=5
b=5
the answer is 5 plus 5