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3 years ago

14

A card is chosen at random from a deck of 52 cards. What is the probability that a heart or spade is chosen?

2 answers:

klemol [59]3 years ago

7 0

Answer: 0.5

Step-by-step explanation:

Given : The total number of cards in a deck = 52

Number of cards with hearts = 13

Number of cards with spade = 13

Probability of getting a card with heart :-

$P(H)=\dfrac{13}{52}=\dfrac{1}{4}$

Probability of getting a card with spade :-

$P(S)=\dfrac{13}{52}=\dfrac{1}{4}$

Since both the events are independent, then the probability that a heart or spade is chosen :-

$P(H\ or\ S)=P(H)+P(S)\\\\=\dfrac{1}{4}+\dfrac{1}{4}\\\\=\dfrac{2}{4}=\dfrac{1}{2}=0.5$

Hence, the probability that a heart or spade is chosen = 0.5

Vlada [557]3 years ago

6 0

It would be 26 because half of 52 is 26 and because you are looking for the spades plus the hearts is u what that in half too and just want on or the other just divide 26 by 2

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There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

$AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta$ (1)

Where:

$AC$ - The distance from A to C, measured in miles.

$AB$ - The distance from A to B, measured in miles.

$BC$ - The distance from B to C, measured in miles.

$\theta$ - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

$AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta$

$\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}$

$\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right)$ (2)

If we know that $BC = 7\,mi$ , $AB = 8\,mi$ , $AC = 5\,mi$ , then the bearing from island B to island C:

$\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]$

$\theta \approx 38.213^{\circ}$

The bearing needed to navigate from island B to island C is approximately 38.213º.

8 0

3 years ago

The cylinder shown has a radius of 3 inches. The height is three times the radius. Find the volume of the cylinder. Round your s

MrRa [10]

Answer:

254.5 Inches Cubed

Step-by-step explanation:

Formula for Finding the Volume of a Cylinder: $V=\pi r^2h$

The radius is 3 inches.

$r=3$

The height is three times the radius.

Multiply the radius by three to get the height.

$h=3*3\\h=9$

The height is 9 inches.

Use the formula to find the volume.

$\pi (3)^29= \pi (9)9=81\pi$

The exact volume is 81 $\pi$ inches cubed.

$81 * \pi$ ≈ 254.47

254.47 ≈ 254.5

The volume of the cylinder should be about 254.5 inches cubed.

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3 years ago

Evaluate each expression if x = -2 and y = 3<br><br> number 34 <br><br> show step by step please!!

GREYUIT [131]

The answer is I’m the photo

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3 years ago

13x=-21-6y and -8x=36+6y

IgorLugansk [536]

Answer:

$x=3\\y=-10$

Step-by-step explanation:

$13x=-21-6y\\-8x=36+6y$

Let's take one of the equations and solve for x. I'll take the first one.

$13x=-21-6y$

Divide by 13.

$x=\frac{-21-6y}{13}$

Now replace x in the second equation.

$-8x=36+6y\\-8(\frac{-21-6y}{13} )=36+6y$

Distribute -8

$\frac{168+48y}{13}=36+6y$

Break down the fraction.

$\frac{168}{13}+\frac{48}{13}y=36+6y$

Subtract $\frac{168}{13}$

$\frac{48}{13}y=36+6y-\frac{168}{13}$

Subtract 6y

$\frac{48}{13}y-6y=36-\frac{168}{13}$

Combine like terms;

$\frac{48-13*6}{13}y=\frac{36*13-168}{13}$

Solve;

$\frac{48-78}{13}y=\frac{468-168}{13}$

Keep solving;

$\frac{-30}{13}y=\frac{300}{13}$

Multiply by the negative reciprocal of the fraction next to y.

$(-\frac{13}{30} )\frac{-30}{13}y=\frac{300}{13}(-\frac{13}{30} )$

On the right side; 13 and 13 become 1. 300/30 = 30/3 = 10

$y=-10$

After having found y, replace it in any of the equations to find x.

$13x=-21-6y\\13x=-21-6(-10)\\13x=-21+60\\13x=39\\x=\frac{39}{13}\\ x=3$

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3 years ago

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timofeeve [1]

the volume of the cone would be 2.36 I hope this helps ❤️

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