PLEASE HELP SUPER EASYYYY

What is the solution of the inequality x^3+3x^2>7x+6

sveta [45]

Answer:

x>2

Step-by-step explanation:

x3+3x2=7x+6

x3+3x2−(7x+6)=7x+6−(7x+6)

x3+3x2−7x−6=0

(x−2)(x2+5x+3)=0

x−2=0 or x2+5x+3=0

x=2 or x=−0.6972243622680054 or x=−4.302775637731995

x<−4.302776

−4.302776<x<−0.697224

−0.697224<x<2

x>2(Works in original inequality)

3 0

3 years ago

Question is in the attachment

ruslelena [56]

Sorry I can’t see the pic

6 0

3 years ago

Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X > 10) b. P(X > 20) c

GrogVix [38]

Answer:

(a) The value of P (X > 10) is 0.3679.

(b) The value of P (X > 20) is 0.1353.

(c) The value of P (X < 30) is 0.9502.

(d) The value of x is 30.

Step-by-step explanation:

The probability density function of an exponential distribution is:

$f(x)=\lambda e^{-\lambda x};\ x>0, \lambda>0$

The value of E (X) is 10.

The parameter λ is:

$\lambda=\frac{1}{E(X)}=\frac{1}{10}=0.10$

(a)

Compute the value of P (X > 10) as follows:

$P(X>10)=\int\limits^{\infty}_{10} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{10} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{10}\\=|e^{-0.10 x} |^{\infty}_{10}\\=e^{-0.10\times10}\\=0.3679$

Thus, the value of P (X > 10) is 0.3679.

(b)

Compute the value of P (X > 20) as follows:

$P(X>20)=\int\limits^{\infty}_{20} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{20} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{20}\\=|e^{-0.10 x} |^{\infty}_{20}\\=e^{-0.10\times20}\\=0.1353$

Thus, the value of P (X > 20) is 0.1353.

(c)

Compute the value of P (X < 30) as follows:

$P(X$

Thus, the value of P (X < 30) is 0.9502.

(d)

It is given that, P (X < x) = 0.95.

Compute the value of x as follows:

$P(X$

Take natural log on both sides.

$ln(e^{-0.10x})=ln(0.05)\\-0.10x=-2.996\\x=\frac{2.996}{0.10}\\ =29.96\\\approx30$

Thus, the value of x is 30.

7 0

3 years ago

Find the vertex of the following equation y= (x+9)^2+8

Olegator [25]

(-9,8) is the answer (h,k) is the equation

8 0

3 years ago

I don't really understand how to put anything into standard form. If anyone could help that would be great...thanks.

zalisa [80]

I believe you would first distribute within the parentheses and then make it so A and B are the only things on the left side and I and the other random characters are on the right.

5 0

3 years ago