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3 years ago

A single card is drawn from a deck. Find the probability of selecting

Mathematics

1 answer:

shepuryov [24]3 years ago

5 0

Answer:

A. 1/2.

B. 15/26.

Step-by-step explanation:

Note when you have an 'OR' in the statement we add the probabilities.

A . Club or a diamond . There are 13 clubs and 13 diamonds so

The Required Probability = 13/52 + 13/52

= 1/4 + 1/4 = 1/2.

B. There are 4 jacks and 26 black cards.

The Required Probability = 4/52 + 26/52

= 1/13 + 1/2

= 2/26 + 13/26

= 15/26.

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Which of the following is the weight of the cargo in a truck if 1/3 of the weight is 516 Ibs?

Anni [7]

Answer:

1548 lb

Step-by-step explanation:

Let the truck's weight be w.

Then (1/3)w = 516 lb

Solve for the truck's weight by multiplying both sides of this equation by 3:

w = 1548 lb (Answer B)

8 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

3 years ago

Simplify the expression 6h +(-7.1d) – 17 + 4d – 2.4h

Alexxx [7]

Answer:

11.1d + 3.2h - 15

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Write the set of real numbers from - 10 through 10 in interval notation.

Klio2033 [76]

Answer:

1) $(-10,10)$ - Greater than -10 and less than 10.

2) $[-10, 10]$ - Greater than or equal to -10 and less than or equal to 10.

3) $[-10, 10)$ - Greater than or equal to -10 and less than 10.

4) $(-10, 10]$ Greater than -10 and less than or equal to 10.

Step-by-step explanation:

There are four form of describing that set in interval notation, which presented below:

1) $(-10,10)$ - Greater than -10 and less than 10.

2) $[-10, 10]$ - Greater than or equal to -10 and less than or equal to 10.

3) $[-10, 10)$ - Greater than or equal to -10 and less than 10.

4) $(-10, 10]$ Greater than -10 and less than or equal to 10.

8 0

3 years ago

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zavuch27 [327]

First we must set up the problem

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3 years ago