Which of the following BEST describes how to use the addition property of equality to isolate the variable y below? 2=Y-2/3

Mathematics

1 answer:

damaskus [11]3 years ago

4 0

To solve this equation isolate the variable and add 2/3 to both sides

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Let f(x) = cxe−x2 if x ≥ 0 and f(x) = 0 if x < 0.

sergij07 [2.7K]

(a) If f(x) is to be a proper density function, then its integral over the given support must evaulate to 1:

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx = \int_0^\infty cxe^{-x^2}\,\mathrm dx=1$

For the integral, substitute u = x ² and du = 2x dx. Then as x → 0, u → 0; as x → ∞, u → ∞:

$\displaystyle\frac12\int_0^\infty ce^{-u}\,\mathrm du=\frac c2\left(\lim_{u\to\infty}(-e^{-u})-(-1)\right)=1$

which reduces to

c / 2 (0 + 1) = 1 → c = 2

(b) Find the probability P(1 < X < 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):

$\displaystyle\int_1^3 2xe^{-x^2}\,\mathrm dx = \boxed{\frac{e^8-1}{e^9}} \approx 0.3678$

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3 years ago

The Richter scale is used to measure the magnitude of an earthquake. The magnitude, R, is given by the earthquake. Determine the

8090 [49]

A) $R=0.65log(0.39E)+1.45

7.5=0.65log(0.39E)+1.45$

B) $6.05=0.65log(0.39E) Subtracted 1.45 from~ both~ sides~ of~ equation.

9.31=log(0.39E) Divided each side by 0.65. 

$

C) $9.31=log(0.39E)

10^(9.31)=0.39E

E=5.24*10^9 kilowatt hours$

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3 years ago

In the above figure (not drawn to scale), Find ∠AEC.

n200080 [17]

Answer:

C. 75°

Step-by-step explanation:

We have been given a circle and we are asked to find the measure of angle AEC.

We will use Intersecting chords theorem to find the measure of angle AEC, which states that measure of angle formed inside a circle by two intersecting chords is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

We can see that measure of arc AC is 110 degrees and measure of its vertical arc BD is 40 degrees.

$m\angle AEC=\frac{110^o+40^o}{2}$