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zhannawk [14.2K]
2 years ago
12

Solve for a. a^2=-3a+88

Mathematics
1 answer:
Sergio [31]2 years ago
5 0

Answer:

a=8,-11

Step-by-step explanation:

a^2=-3a+88

a^2+3a=88

a^2+3a-88=0

x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}

x=\frac{-3\pm\sqrt{3^2-4(1)(-88)} }{2(1)}

x=\frac{-3\pm\sqrt{9+352} }{2}

x=\frac{-3\pm\sqrt{361} }{2}

x=\frac{-3\pm19 }{2}

x=-11 and x=8

Therefore, the values of a are 8 and -11.

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One bus averages 58 mi/h, and the other bus averages 54 mi/h. When will they be 365 miles apart?
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16. From past experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain o
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Answer:

E(x)=0.15

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S(x)=0.5545

Step-by-step explanation:

The mean of a discrete variable is calculated as:

E(x)=x_1*p(x_1)+x_2*p(x_2)+...+x_n*p(n)

where x_1,x_2,...,x_n are the values that the variable can take and p(x_1),p(x_2),...,p(x_n) are their respective probabilities.

So, if we call x the number of defective transistors in cartons, we can calculate the mean E(x) as:

E(x)=(0*0.92)+(1*0.03)+(2*0.03)+(3*0.02)=0.15

Because there are 0 defective transistor with a probability of 0.92, 1 defective transistor with a probability of 0.03, 2 defective transistors with a probability of 0.03 and 3 defective transistors with a probability of 0.01.

At the same way, the variance V(x) is calculated as:

V(x)=E(x^2)-(E(x))^2

Where E(x^2)=x_1^2*p(x_1)+x_2^2*p(x_2)+...+x_n^2*p(n)

So, the variance V(x) is equal to:

E(x^2)=(0^2*0.92)+(1^2*0.03)+(2^2*0.03)+(3^2*0.02)=0.33\\V(x)=0.33-(0.15)^2\\V(x)=0.3075

Finally, the standard deviation is calculated as:

S(x)=\sqrt{V(x)} \\S(x)=\sqrt{0.3075} \\S(x)=0.5545

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