Answer:
b = -2
Step-by-step explanation:
We need to use <u>the binomial theorem</u>, to expand
the expression (3 + bx )⁵ :
(3 + bx )⁵ = 3⁵ + 5(3)⁴(bx)¹ + 10(3)³(bx)² + 10(3)²(bx)³ + 5(3)¹(bx)⁴ + (bx)⁵
= 243 + 5×81×(bx)¹ + 10×27×(bx)² + 10×9×(bx)³ + 5×3×(bx)⁴ + (bx)⁵
= 243 + 405(bx)¹ + 270(bx)² + 90(bx)³ + 15(bx)⁴ + (bx)⁵
= 243 + (405b)x + (270b²)x² + (90b³)x³ + (15b⁴)x⁴ + (bx)⁵
Then
(3 + bx )⁵ = 243 + (405b)x + (270b²)x² + (90b³)x³ + (15b⁴)x⁴ + (bx)⁵
Then
The coefficient of x³ in the expansion of (3 + bx )⁵ is 90b³
<u>Comparing the coefficients</u> :
90b³ = -720
Then
b³ = (-720) ÷ 90 = -8
Then
b³ = -8
Then
b = -2
Answer:
she had 12 baseball cards
Step-by-step explanation:
They will be forming a right triangle.
long leg is the height of Lyra. 22 meters high from the entrance.
short leg is the distance of Donna. 50 meters from the entrance.
We need to solve for the hypotenuse or the range of communication.
a² + b² = c²
22² + 50² = c²
484 + 2500 = c²
2,984 = c²
√2,984 = √c²
54.63 = c
The range of communication for the two radios is 55 meters.
Answer:
828
Step-by-step explanation:
To cut the margin of Error in half, the clinic needs quadruple of the sample size.
If the sample size is 207 women,
Then quadruple of 207 = 4 * 207 = 828
