Solve 1500*1.960^2*0.57*(1-0.57)/(1500-1)*2.85+1.960^2*0.57*(1+0.57)

$$\frac { 1500 \times 1.960 ^ { 2 } \times 0.57 \times ( 1 - 0.57 ) } { ( 1500 - 1 ) \times 2.85 + 1.960 ^ { 2 } \times 0.57 \times ( 1 + 0.57 ) }$$

Evaluate

$$\frac{154864500}{468814457}\approx 0.330332177$$

Solution Steps

Calculate 1.96 to the power of 2 and get 3.8416.

$$\frac{1500\times 3.8416\times 0.57\left(1-0.57\right)}{\left(1500-1\right)\times 2.85+1.96^{2}\times 0.57\left(1+0.57\right)}$$

Multiply 1500 and 3.8416 to get 5762.4.

$$\frac{5762.4\times 0.57\left(1-0.57\right)}{\left(1500-1\right)\times 2.85+1.96^{2}\times 0.57\left(1+0.57\right)}$$

Multiply 5762.4 and 0.57 to get 3284.568.

$$\frac{3284.568\left(1-0.57\right)}{\left(1500-1\right)\times 2.85+1.96^{2}\times 0.57\left(1+0.57\right)}$$

Subtract 0.57 from 1 to get 0.43.

$$\frac{3284.568\times 0.43}{\left(1500-1\right)\times 2.85+1.96^{2}\times 0.57\left(1+0.57\right)}$$

Multiply 3284.568 and 0.43 to get 1412.36424.

$$\frac{1412.36424}{\left(1500-1\right)\times 2.85+1.96^{2}\times 0.57\left(1+0.57\right)}$$

Subtract 1 from 1500 to get 1499.

$$\frac{1412.36424}{1499\times 2.85+1.96^{2}\times 0.57\left(1+0.57\right)}$$

Multiply 1499 and 2.85 to get 4272.15.

$$\frac{1412.36424}{4272.15+1.96^{2}\times 0.57\left(1+0.57\right)}$$

Calculate 1.96 to the power of 2 and get 3.8416.

$$\frac{1412.36424}{4272.15+3.8416\times 0.57\left(1+0.57\right)}$$

Multiply 3.8416 and 0.57 to get 2.189712.

$$\frac{1412.36424}{4272.15+2.189712\left(1+0.57\right)}$$

Add 1 and 0.57 to get 1.57.

$$\frac{1412.36424}{4272.15+2.189712\times 1.57}$$

Multiply 2.189712 and 1.57 to get 3.43784784.

$$\frac{1412.36424}{4272.15+3.43784784}$$

Add 4272.15 and 3.43784784 to get 4275.58784784.

$$\frac{1412.36424}{4275.58784784}$$

Expand \frac{1412.36424}{4275.58784784} by multiplying both numerator and the denominator by 100000000.

$$\frac{141236424000}{427558784784}$$

Reduce the fraction \frac{141236424000}{427558784784} to lowest terms by extracting and canceling out 912.

$$\frac{154864500}{468814457}$$

Factor

$$\frac{3 \cdot 43 \cdot 2 ^ {2} \cdot 5 ^ {3} \cdot 7 ^ {4}}{17 \cdot 31 \cdot 37 \cdot 24043} = 0.3303321765949722$$