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3 years ago

Suppose you deal three cards from a regular deck of 52 cards. What is the probability that they will all be jacks?

Mathematics

2 answers:

shusha [124]3 years ago

5 0

3 chances of jacks out of 52 cards

andrew-mc [135]3 years ago

4 0

Answer:

Probability of getting three jacks = $\frac { 3 } { 5 2 }$

Step-by-step explanation:

It is given that you deal three cards from a regular deck which contains 52 cards.

We are to find the probability of getting all three Jack cards.

We know that there are a total of 4 jacks in a regular deck of 52 cards.

Therefore, the probability of getting three jacks = $\frac { 3 } { 5 2 }$

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Find the surface area of the composite figure.

Serggg [28]

Fhfhfhejdhfhebcbfbdbcbrdhfhfbfhfhfhffhfhchfhdhchfhdhhchfjdhf

5 0

1 year ago

Which set of ordered pairs has point symmetry with respect to the origin (0, 0)?

Leya [2.2K]

Answer:

(-8, 3), (8, -3)

Step-by-step explanation:

Point symmetry about origin means reflection of the given point about the origin.

The reflection of a point about the origin will cause the 'x' and 'y' value of the point to change its sign.

Therefore, the coordinate rule for point symmetry about the origin is given as:

$(x,y)\to (-x,-y)$

Now, let us check each of the given options.

Option 1:

(-8, 3), (8, -3)

Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3)

So, option 1 is correct.

Option 2:

(-8, 3), (-3, 8)

Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (-3, 8)

So, option 2 is not correct.

Option 3:

(-8, 3), (-8, -3)

Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (-8, -3)

So, option 3 is not correct.

Option 4:

(-8, 3), (8, 3)

Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (8, 3)

So, option 4 is not correct.

Hence, only option 1 is correct.

5 0

3 years ago

Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Solution:

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

2 years ago

The sum of two consecutive integers is 345. What are the integers? need help with it

horrorfan [7]

Answer:

hi there ☺️

Here we will use algebra to find three consecutive integers whose sum is 345. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 345. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 345

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 345

3X + 3 = 345

3X + 3 - 3 = 345 - 3

3X = 342

3X/3 = 342/3

X = 114

Which means that the first number is 114, the second number is 114 + 1 and the third number is 114 + 2. Therefore, three consecutive integers that add up to 345 are 114, 115, and 116.

114 + 115 + 116 = 345

We know our answer is correct because 114 + 115 + 116 equals 345 as displayed above.

Step-by-step explanation:

pls rate me the brainiest

3 0

2 years ago

-5x + 4 = 2x + 16 How do I solve this

Cloud [144]

Subtract 2x from both sides then you’d have -7x+4=16 Then you subtract 4 from both sides and you’d get -7x=12. Next you divide both side by -7 so x=1.75 rounded to the nearest hundredth.

8 0

2 years ago