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Rudik [331]
3 years ago
9

In a deck of cards with 52 cards and 4 suits, what is the probability of getting an ace?

Mathematics
2 answers:
DedPeter [7]3 years ago
7 0

The probability of picking up an ace in a 52 card deck, where there are 4 aces is 4/54 (simplify to 2/27).

Katarina [22]3 years ago
6 0

The probability of getting a ace is 8/52

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wo race car drivers Ryan and Philip were taking laps around the race track. It was noted that Ryan drove 52.5 miles in the same
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Step-by-step explanation:

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3 years ago
A water cup is shaped like a cone. It has a diameter of 3 inches and a slant height of 5 inches. About how many square inches of
daser333 [38]

Options were missing in the question;

A water cup is shaped like a cone. It has a diameter of 3 inches and a slant height of 5 inches. About how many square inches of paper do you need to make a cup? Use 3.14 to approximate pi.

24 square inches

31 square inches

47 square inches

52 square inches

Answer:

24 square inches

Step-by-step explanation:

Given:

Diameter = 3 in

So we can say that;

Radius is half of diameter.

radius (r) = \frac{3}{2}=1.5\ in

Slant height (l) = 5 in

We need to find how many square inches of paper do you need to make a cup.

Solution:

Now according to question we required to find the amount of paper used to make cup.

Also Water cup is shaped liked cone.

Hence we can say that the base of cone is not covered since it will remain open.

So we will use Lateral surface area of the cone to find the paper requirement.

Now we know that;

Lateral surface area of cone is equal to π times radius times slant height.

framing in equation form we get;

A_L = \pi rl=3.14\times1.5\times5 = 23.55 in^2 \approx 24\ in^2

Hence We can say that 24 square inches of paper will be needed to make the cup.

5 0
3 years ago
Express 2x+1/(x-2)(x²+1) as a partial fraction.
Oduvanchick [21]

Answer:

Partial fraction = 1/(x-2) - x/(x^2+1)

Step-by-step explanation:

Question:

Express 2x+1/(x-2)(x²+1) as a partial fraction.

Note: it will be assumed that there was a typo in the interpretation of parentheses to mean

(2x+1) / ( (x-2)(x^2+1) )

Let

(2x+1) / ( (x-2)(x^2+1) ) = A/(x-2) + (Bx+C)/(x^2+1) .........................(0)

(2x+1) / ( (x-2)(x^2+1) ) = (A(x^2+1)+(Bx+C)(x-2)) / ( (x-2)(B/(x^2+1) )

(2x+1) / ( (x-2)(x^2+1) ) = (Ax^2+A+Bx^2+(C-2B)x-2C) / ( (x-2)(B/(x^2+1) )

(2x+1) / ( (x-2)(x^2+1) ) = ( (A+B)x^2+(C-2B)x+A-2C ) / ( (x-2)(B/(x^2+1) )

Match numerators

2x+1 = (A+B)x^2+(C-2B)x+A-2C

Match coefficients,

A+B = 0 ..................(1)

-2B+C = 2 .................(2)

A-2C = 1 ...................(3)

Solve for A, B and C

Substitute A from (1) in (3)

-B - 2C =1  

transpose and solve for B

B = -2C-1  ....................(4)

Substitue B from (4) in (2)

-2(-2C-1) + C = 2  

simplify

5C = 2-2 = 0

C=0  ..........................(5)

substitute (5)  in (4)

B = -2C-1 = -1  ...............(6)

Substitue (6) in (1)

A+(-1) = 0

A=1 .............................(7)

Using values from (7), (6) and (5) to substitute in (0)

we get

(2x+1) / ( (x-2)(x^2+1) ) = 1/(x-2) - x/(x^2+1)

as the required partial fraction

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Y = x - 7

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f(x) = x - 7
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3 years ago
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What is the volume of a cone (in cubic inches) with a radius of 6 inches and a height of 3 inches? Use 3.14 for π. Round your an
sesenic [268]
\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
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3 years ago
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