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3 years ago

A card is drawn from a standard deck of 52 cards. What is the theoretical probability, as a decimal, of drawing an ace? Round th

e decimal to the nearest hundredth. (Hint: A standard deck of 52 cards contains 4 aces.)

Mathematics

1 answer:

Alexus [3.1K]3 years ago

6 0

$|\Omega|=52\\ |A|=4\\\\ P(A)=\dfrac{4}{52}=\dfrac{1}{13}\approx0.08$

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If f(x)= x2/x+3, find f(x+h)?

kompoz [17]

f(x+h) = $\frac{x^{2}+2xh+h^{2} }{x+h+3}$

Step-by-step explanation:

Given,

f(x) = $\frac{x^{2} }{x+3}$

To find the value of f(x+h) we need to replace x by x+h

Hence,

f(x+h) = $\frac{(x+h)^{2} }{x+h+3}$

= $\frac{x^{2}+2xh+h^{2} }{x+h+3}$

[Here, we apply the formula of $(a+b)^{2}= a^{2} +2ab+ b^{2}$ ]

6 0

3 years ago

5. Each polygon circumscribes a circle. Find the perimeter.

Oksana_A [137]

See the diagram of the circumscribed polygon attached below:

Answer:

A. 14.2 in.

Step-by-step explanation:

Perimeter = 3.7 + 3.6 + 3.4 + 1.9 + g

Let's find g.

a = 1.9 in. (Tangents drawn from an external point of a circle are congruent)

b = 3.4 - 1.9 = 1.5 in.

b = c = 1.5 in. (Tangents drawn from an external point)

d = 3.6 - 1.5 = 2.1 in.

d = e = 2.1 in. (Tangents drawn from an external point)

f = 3.7 - 2.1 = 1.6 in.

f = g = 1.6 in. (Tangents drawn from an external point)

✔️Therefore,

Perimeter = 3.7 + 3.6 + 3.4 + 1.9 + 1.6 = 14.2 in.

6 0

3 years ago

When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constan

vitfil [10]

Answer:

$a = 6m/s^2$

Step-by-step explanation:

Given

When mass = 4kg; Acceleration = 15m/s²

Required

Determine the acceleration when mass = 10kg, provided force is constant;

Represent mass with m and acceleration with a

The question says there's an inverse variation between acceleration and mass; This is represented as thus;

$a\ \alpha\ \frac{1}{m}$

Convert variation to equality

$a = \frac{F}{m}$ ; Where F is the constant of variation (Force)

Make F the subject of formula;

$F = ma$

When mass = 4kg; Acceleration = 15m/s²

$F = 4 * 15$

$F = 60N$

When mass = 10kg; Substitute 60 for Force

$F = ma$

$60 = 10 * a$

$60 = 10a$

Divide both sides by 10

$\frac{60}{10} = \frac{10a}{10}$

$a = 6m/s^2$

<em>Hence, the acceleration is </em> $a = 6m/s^2$ <em />

4 0

3 years ago

Help with this please

Svet_ta [14]

The answer to the question is D

4 0

3 years ago

Read 2 more answers

Answer correctly please

Paul [167]

Answer:

$\$272,49$

Step-by-step explanation:

7. $\displaystyle /text{The answer makes sense because since the depreciation rate is 15%, we know that we need to use the "exponential decay" formula.}$

6. $\displaystyle /text{After a depreciation rate of 15% for the past 8 years, the stock is now worth approximately $272,49.}$

5. $\displaystyle 1000[0,85]^8 = 272,490525 ≈ \$272,49$

4. $\displaystyle 1000 = a \\ -15\% + 100\% = 1 - r; 85\% = 1 - r \\ 8\:years = time\:[t]$

3. $\displaystyle /text{We need to use the "Exponential Decay" formula} - f(t) = a[1 - r]^t, where a > 0$

2. $\displaystyle /text{How much is the stock worth after a depreciation rate of 15% per year?}$

1. $\displaystyle /text{initial amount: $1000, a depreciation rate of 15%, and a time period of 8 years}$

I am joyous to assist you anytime.

5 0

2 years ago