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irinina [24]
3 years ago
11

Probability question.

Mathematics
1 answer:
dimaraw [331]3 years ago
5 0
To find the probability that they are both aces, you will find the probability of them being aces in both cases and then multiply these together.

There are 4 aces in a deck of cards.

<u>4</u>         <u>4</u>
52  x   52

You can factor out 4's all the way around to get
<u>1 </u>        <u>1 </u>      <u>   1</u>
13  x    13   = 169

The probability is 1/169 change of both being aces.
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Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +
slava [35]
\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx

Taking x=7\tan\theta gives \mathrm dx=7\sec^2\theta\,\mathrm d\theta, so that the integral becomes

\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta
=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta
=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta
=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta
=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta

When \sec\theta>0, we have

=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta
=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta

and from here we can substitute u=\tan\theta to proceed from here.

Quick note: When we set x=7\tan\theta, we are implicitly enforcing -\dfrac\pi2 just so that the substitution can be undone later via \theta=\tan^{-1}\dfrac x7. But note that over this domain, we automatically guarantee that \sec\theta>0, so the absolute value bars can be dropped immediately.
6 0
3 years ago
PLEASE HELP! 50 POINTS ON THE LINE!
MAVERICK [17]

Answer: hello! I'm here to help.

Let's work the problem using just the thousands and leave the zeros off.  We'll add them back at the end.

Let M be the salary of the Master's degree, and B be the salary of the Bachelor's degree.

 

M + B = 120

M + 39 = 2B

 

M = 2B - 39

2B - 39 + B = 120

3B - 39 = 120

3B = 159

B = 53

M = 120 - B = 120 - 53 = 67

<h2>PLEASE BRAINLIEST! :)</h2>
8 0
3 years ago
Identify the number sets to which number 4/5 belongs to.
Brrunno [24]

Answer:

rational

Step-by-step explanation:

7 0
3 years ago
f(x)=x^2; vertical shrink by a factor of 1/2 and a reflection in the y-axis, followed by a translation 1 unit down​
NeX [460]

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down​

is g(x) = \frac{1}{2} x² - 1

Step-by-step explanation:

Lets revise:

1. The vertical shrink

A vertical shrinking is the squeezing of the graph toward the x-axis.

if 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically

shrunk by multiplying each of its y-coordinates by k

2. The reflection

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

3. Vertical translation

If the function f(x) translated vertically up  by m units, then its image

is g(x) = f(x) + m

If the function f(x) translated vertically down  by m units, then its image

is g(x) = f(x) - m

Now let us solve the problem

∵ f(x) = x²

∵ f(x) shrunk by a factor of \frac{1}{2}

∴ The image of f(x) = \frac{1}{2} x²

∵ The image of f(x) reflected across y-axis

∴ The sign of x will change

∴ The new image of f(x) = \frac{1}{2} (-x)²

∵ The new image of f(x) translated 1 unit down

∴ We will subtract the new image of f(x) by 1

∴ The last image of f(x) is g(x) = \frac{1}{2} (-x)² - 1

<em>V.I.Note:</em>

(-x)² = x² because even exponents reject the negative sign

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down​

is g(x) = \frac{1}{2} x² - 1

The attached graph for more understand

Learn more:

you can learn more about transformation in brainly.com/question/2415963

#LearnwithBrainly

4 0
3 years ago
Find the volume of the cone
Alik [6]

Volume =  

1  πr2h

3

=  

1 ×π×42×7

3

=  117.28612573402 centimeters^3

3 0
2 years ago
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