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2 years ago

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

Mathematics

1 answer:

shepuryov [24]2 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 <u>add </u>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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2 years ago

Which diagram shows parallel lines cut by a transversal?

Arada [10]

Only the third model shows parallel lines cut by a transversal.

We can solve this problem by using some properties that parallel lines cut by a transversal have. First of all, corresponding angles are congruent, and since the angles in figure 1 are corresponding but not congruent, that means that figure one is out.

In addition, in figure two, alternate exterior and interior angles of parallel lines intersected by a transversal are congruent, so since they are not in the picture, that means that this figure is also out.

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2 years ago

Read 2 more answers

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

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2 years ago

The hardware store sells green buckets, which hold 7 liters of water, and white buckets, which hold 1 liter. Austin bought 8 buc

qaws [65]

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2 years ago

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Zina [86]

Your answer correct good night

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2 years ago