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3 years ago

9

Sally cycle 14 miles north and 13 miles east. To return to her starting points she took the shortest distance shown in the diagr

am by the dotted line

1 answer:

tankabanditka [31]3 years ago

7 0

Answer:

Step-by-step explanation:

There's no diagram and no question, but I assume it shows a right triangle.

distance = √(14²+13²) = √365 ≅ 19.1 miles

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A single card is drawn from a deck of 52 cards, find the following

aleksandr82 [10.1K]

Answer:

a. 1/13

b. 1/78

c. 1/4

d. 1/12

e. 1/6

f. 1/4

Step-by-step explanation:

First, lets write some basic data

There are total 52 cards.
26 cards are red and 26 cards are black
Out of 26 red cards; 13 cards are of diamond and 13 cards are of heart
Out of 26 black cards; 13 cards are of spade and 13 cards are of clubs
In spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jack

<u>a. result is a queen</u>

<em>Each set has one queen; 1 of spade, 1 of clubs, 1 of heart, 1 of heart</em>

There are total 4 queens

Total number of cards is 52

<em>Probability = Number of favourable outcomes/total number of outcomes</em>

Probability = 4/52

Probability = 1/13

<u>b. result is a queen result is a face card </u>

<em>From my understanding, this question is result is a queen given that result is a face card.</em>

<em>Queen: 4 cards</em>

<em>Face card means King, Queen and Jack</em>

<em>Each set has one King, one Queen and one Jack</em>

<em>There are total 4 sets</em>

<em>Therefore, there are 4 Kings, 4 Queens and 4 Jacks</em>

<em>Face cards: 12-4 (because 4 queens have already been taken out) = 8</em>

<em>Total number of cards: 52-4 (because 4 queens have already been taken out) = 48</em>

Probability (A|B) = P(A) * P(A|B)

P(A) = result is a queen = 4/52 = 1/13

P(A|B) = result is a face card = 8/48 = 1/6

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/13 * 1/6

Probability (A|B) = 1/78 or 0.01282

<u>c. result is a heart</u>

<em>Out of the 52 cards, there are 26 red cards and out of the 26 red cards, there are 13 cards of heart</em>

Heart = 13 cards

Total number of cards = 52 cards

<em>Probability = Number of favourable outcomes/total number of outcomes</em>

Probability = 13/52

Probability = 1/4

<u>d. result is a heart | result is a red card </u>

Result is a heart = P(A) = 13/52 = 1/4

<em>Result is a red card=26/52 Total number of red cards is 26 but 13 cards (heart) are already taken out so 13 will be subtracted from the numerator and denominator</em>

= 13/39 = 1/3

Result is a heart given that result is a red card P(A|B) = 1/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1/3

Probability (A|B) = 1/12

<u>e. result is a heart result is a black card </u>

Result is a heart = P(A) = 13/52 = 1/4

<em>Result is a black card=26/52 Total number of cards is 52 but 13 cards (heart) are already taken out so 13 will be subtracted from the denominator</em>

<em>= 26/39 = 2/3</em>

Result is a heart given that result is a black card P(A|B) = 2/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 2/3 = 1/6

<u>f. result is a heart result is not a diamond</u>

Result is a heart = P(A) = 13/52 = 1/4

<em>Result is not a diamond = there are 13 diamonds in a deck so cards that are not diamond are 52-13 = 39</em>

Total cards = 52 - 13 (because hearts are already taken out) = 39

= 39/39 = 1

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1 = 1/4

!!

4 0

4 years ago

Whats the red angle?<br>i cant seem to understand anything

Harrizon [31]

Answer:

65°

Step-by-step explanation:

Sum of interior angles of a triangle = 180°

⇒ m∠EAB = 180 - 90 - 70 = 20°

⇒ m∠DAG = 90 - 45 - 20 = 25°

⇒ m∠AGD = 180 - 90 - 25 = 65°

ΔADG ≅ ΔAFG

⇒ m∠AGD = m∠AGF = 65°

ΔABE ≅ ΔAFE

⇒ m∠AEB = m∠AEF = 70°

4 0

3 years ago

HELP PLEASE PLEASE PLEASE!!!! WILL GIVE BRAINLIEST

Readme [11.4K]

9514 1404 393

Answer:

y ≈ 12.3

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to help you remember the relationship between trig functions and side of a right triangle. In particular, when the adjacent side and hypotenuse are involved, the desired relation is ...

Cos = Adjacent/Hypotenuse

cos(35°) = y/15

y = 15·cos(35°)

y ≈ 12.3

5 0

3 years ago

Algebraic expression for x more than 5.

Lina20 [59]

Answer:

5 + x

Step-by-step explanation:

x more than 5 is 5 + x

7 0

4 years ago

Read 2 more answers

How do I solve this?<br><br> -6x-1+5x^2 = 8x^2<br><br> Thanks

max2010maxim [7]

Answer:

$\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}$

Or, by approximating:

$x\approx-0.1835\text{ or } x\approx -1.8165$

Step-by-step explanation:

Let’s convert this to standard form. We have:

$-6x-1+5x^2=8x^2$

Subtract 5x² from both sides:

$-6x-1=3x^2$

And add 6x and 1 to both sides:

$0=3x^2+6x+1$

This is not factorable. So, we will need to use the quadratic formula.

The quadratic formula for a quadratic in standard form is given by:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}$

In this case, a=3; b=6, and c=1.

Substitute appropriately:

$\displaystyle x=\frac{-6\pm\sqrt{6^2-4(3)(1)}}{2(3)}$

Simplify:

$\displaystyle x=\frac{-6\pm\sqrt{24}}{6}$

We can simplify the square root:

$\sqrt{24}=\sqrt{4}\cdot\sqrt{6}=2\sqrt{6}$

Hence:

$\displaystyle x=\frac{-6\pm2\sqrt{4}}{6}$

Simplify:

$\displaystyle x=\frac{-3\pm\sqrt{6}}{3}$

Hence, we will have two solutions:

$\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}$

Approximating them, we can see that our solutions are approximately:

$x\approx-0.1835\text{ or } x\approx -1.8165$

7 0

3 years ago