All categories

3 years ago

There are 10 playing cards in a bag. 3 of those cards are spades.

Mathematics

1 answer:

yawa3891 [41]3 years ago

6 0

Answer:

3/10

Step-by-step explanation:

10 is the denominator 3 is the numerator

You might be interested in

Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list.

SOVA2 [1]

Answer:

23.92°, 78.503°, and 77.577°

Step-by-step explanation:

The coordinates of the vertices of the triangle are;

X(-3, -5), Y(2, 6), Z(6, 3)

The vectors are;

z = $\left \langle 2 - (-3), 6 - (-5) \right \rangle$ = $\left \langle 5, 11 \right \rangle$

y = $\left \langle 6 - (-3), 3 - (-5) \right \rangle$ = $\left \langle 9, 8 \right \rangle$

x = $\left \langle 2 - 6, 6 - 3 \right \rangle$ = $\left \langle -4, 3 \right \rangle$

$cos (\alpha ) = \dfrac{z \cdot y}{\left | z \right | \times \left | y \right |}$

Therefore, we get;

$cos (\alpha ) = \dfrac{5 \times 9 + 11 \times 8 }{\left | \sqrt{5^2 + 11^2} \right | \times \left | \sqrt{9^2 + 8^2} \right |} = \dfrac{133}{\sqrt{146} \times \sqrt{145} } \approx 0.91409$

α = arccos(0.91490) ≈ 23.92°

γ = The angle between -y and x

-y = $\left \langle -9, -8 \right \rangle$

We get;

$cos (\gamma) = \dfrac{-y \cdot x}{\left | -y \right | \times \left | x \right |}$

Therefore;

$cos (\gamma) = \dfrac{-9 \times -4 + -8 \times 3 }{\left | \sqrt{(-9)^2 + (-8)^2} \right | \times \left | \sqrt{(-4)^2 + 3^2} \right |} = \dfrac{12}{\sqrt{145} \times \sqrt{25} } \approx 0.199309$

γ = arccos(0.199309) ≈ 78.503°

γ ≈ 78.503°

By angle sum property, β = 180° - (α + β)

β ≈ 180° - (23.92° + 78.503°) = 77.577°

β ≈ 77.577°

The interior angles are;

23.92°, 78.503°, and 77.577°

4 0

2 years ago

If you draw just one card for me standard deck what are the chances you will draw a non-prime number

bixtya [17]

Answer:

53.85%

Step-by-step explanation:

there are 24 prime cards in a deck

52-24=28

28 is the number of non prime cards in a deck of cards

then you do 28/52=53.85%

3 0

2 years ago

Write an equation of the line that passes through (-6.0) and (0, – 24).

Ipatiy [6.2K]

Answer:

y = -4x - 24

Step-by-step explanation:

Firstly, figure out the slope. To do that, plug the coordinates in the formula.

y2 - y1 / x2 -x1

= -24 - 0 / 0 - (-6)

= -4

The slope is -4/1x.

To figure out the y-intercept, you need to plug one of the coordinates into

y = -4x + b

0 = -4(-6) + b

0 = 24 +b

-24 = b

4 0

3 years ago

Read 2 more answers

Determine the domain of the function (f o g)(x) where f(x)= 3/x+2 and g=5/x.

vitfil [10]

Answer:

The Domain is all real values of x except x = 0 and x = -2.5.

Step-by-step explanation:

I am assuming that f(x) = 3/(x + 2).

(f o g)x is found by substituting 5/x for the x in 3/(x + 2).

(f o g) x = 3/ ( 5/x + 2)

= 3 / ( 5+2x) / x

= 3x / (5 + 2x).

When finding the domain you first check for values of x which make g(x) undefined then values of x which make (f o g)(x) undefined.

x = 0 makes g(x) = 5/0 so it is undefined and x = -2.5 makes g o f undefined also.

7 0

3 years ago

A regular polygon has a exterior of 18 degrees. How many sides does it have?

blondinia [14]

The formula of the measurement of an exterior angle of a regular polygon is
β = 360°/n
where β = exterior angle and n = number of sides

Therefore,
n = 360°/β = 360°/18° = 20 sides

4 0

3 years ago

Read 2 more answers