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3 years ago

Probability question.

1 answer:

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.

4 4
52 x 52

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

The probability is 1/169 change of both being aces.

You might be interested in

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

V.I.Note:

(-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

1 ×π×42×7

= 117.28612573402 centimeters^3

3 0

2 years ago