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3 years ago

7x−4≥−15+2x solve in interval notation

Mathematics

1 answer:

Leviafan [203]3 years ago

7 0

Answer:

[-11/5,∞)

Step-by-step explanation:

1. Add 4 to both sides: 7x-4+4≥-15+2x+4

2. Simplify: 7x≥2x-11

3. Subtract 2x from both sides: 7x-2x≥2x-11-2x

4. Simplify: 5x≥-11

5. Divide both sides by 5: 5x/5≥-11/5

6. Simplify: -11/5

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What are the factors of 3x^2 + 23x − 8?

Margaret [11]

3x² + 23x − 8 = 3x² + 24x - x - 8 = 3x(x+8) - (x+8) = (x+8)(3x-1)

8 0

3 years ago

Solve -24 + (1-4)^2

ElenaW [278]

Answer:

-15

Step-by-step explanation:

-24 + (1-4)^2 (solve parentheses first)

= -24 + (-3)^2 (solve exponent)

= -24 + 9

= -15

6 0

3 years ago

Read 2 more answers

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.

(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

On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in mile

lions [1.4K]

Complete question :

On a flight New York to London an airplane travels at a constant speed. An equation relating the distance traveled in miles d to the number of hours flying t is t= 1/500d. How long will it take the airplane to travel 800 miles?

Answer:

1.6 hours

Step-by-step explanation:

Given the function :

Time t taken for flying distance d is given by:

t = 1/500 * d

Tine taken to fly 800 miles;

d = 800 miles

t = 1/500 * (800)

t = 800 / 500

t = 1.6

Hence, time t = 1.6 hours

3 0

3 years ago

a scale drawing of a building needs to be made using the scale 1 in = 190 ft. how tall will the builging in the scale drawing be

Artist 52 [7]

Answer:

$\boxed{\text{3 in}}$

Step-by-step explanation:

1 in = 190 ft

x in = 570 ft

We can use ratio and proportion to solve this problem.

$\begin{array}{cccl}\dfrac{1}{x} & = & \dfrac{190}{570} & \\\\570 & = & 190x & \text{Mutiplied by lowest common denominator (570x)}\\3 & = & x & \text{Divided each side by 3}\\\end{array}$

The building will be $\boxed{\textbf{3 in}}$ tall in the scale drawing.

3 0

3 years ago