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Helga [31]
3 years ago
5

t's dark. You have ten grey socks and ten black socks you want to put into pairs. All socks are exactly the same except for thei

r colour. How many socks would you need to take with you to ensure you had at least a pair? a) 3, b) 16, c) 8, or d) 7
Mathematics
2 answers:
Brrunno [24]3 years ago
5 0

the answer is 3. after taking 2 socks, you will either have 2 that match or 2 that differ. to ensure a matching pair, you need to add 1 more sock.

- cherry :)

Nadya [2.5K]3 years ago
5 0

Answer:

a

Step-by-step explanation:

You might be interested in
Which equation below and value for x fits this model?
Alexus [3.1K]

Answer: I wanna say it's B

Step-by-step explanation: but I'm not completely sure.

5 0
2 years ago
If anyone knows about definite integrals for calculus then please I request help! I
kicyunya [14]

Answer:

\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:                                                           \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals

Integration Rule [Fundamental Theorem of Calculus 1]:                                     \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

Integration Property [Multiplied Constant]:                                                         \displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

U-Substitution

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution.</em>

  1. Set <em>u</em>:                                                                                                             \displaystyle u = 4x^{-2}
  2. [<em>u</em>] Differentiate [Basic Power Rule, Derivative Properties]:                       \displaystyle du = \frac{-8}{x^3} \ dx
  3. [Bounds] Switch:                                                                                           \displaystyle \left \{ {{x = 9 ,\ u = 4(9)^{-2} = \frac{4}{81}} \atop {x = 5 ,\ u = 4(5)^{-2} = \frac{4}{25}}} \right.

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Rewrite [Integration Property - Multiplied Constant]:                 \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^9_5 {\frac{-8}{x^3}e^\big{4x^{-2}}} \, dx
  2. [Integral] U-Substitution:                                                                              \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{4}{81}}_{\frac{4}{25}} {e^\big{u}} \, du
  3. [Integral] Exponential Integration:                                                               \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}(e^\big{u}) \bigg| \limits^{\frac{4}{81}}_{\frac{4}{25}}
  4. Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8} \bigg( e^\Big{\frac{4}{81}} - e^\Big{\frac{4}{25}} \bigg)
  5. Simplify:                                                                                                         \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

4 0
2 years ago
2x-3y=42 solve for y
PtichkaEL [24]

Answer:

y=14+(2/3x)

Step-by-step explanation:

Your main goal is to get Y by itself on one side.

To start subtract 2x from both sides. This will give you -3y=42-2x.

Then you divide both sides by -3 to get Y by itself.

That will leave you with ...

y=14+(2/3x)

(remember the negatives cancel each other out)

5 0
2 years ago
Read 2 more answers
The owner of the Rancho Grande has 3,060 yd of fencing with which to enclose a rectangular piece of grazing land situated along
Pavel [41]

Answer:

1170450 yd^2

Step-by-step explanation:

The first thing is to calculate the necessary perimeter, which would be like this:

2 * a + b = 3060

if we solve for b, we are left with:

b = 3060-2 * a

Now for the area it would be:

A = a * b = a * (3060-2 * a )

A = 3060 * a -2 * a ^ 2

To maximize the area, we calculate the derivative with respect to "a":

dA / da = d [3060 * a -2 * a ^ 2

]/gives

dA / day = 3060 - 4 * a

If we equal 0:

0 = 3060 - 4 * a

4 * a = 3060

a = 3060/4

a = 765 and d

Therefore b:

b = 3060 - 2 * a = 3060 - 1530 = 1530

A = a * b

A = 765 * 1530

A = 1170450 and d ^ 2

3 0
2 years ago
Find the value of the lesser root of x 2-8x+7=0
mariarad [96]
Hi there! The answer is x = 1

{x}^{2}  - 8x + 7 = 0

(x - 7)(x - 1)
Rule AB = 0, gives A = 0 or B = 0

x - 7 = 0 \:  \: or \:  \: x - 1 = 0 \\ x = 7 \:  \:  \:  \:   \:  \:  \:  \:  \: or \:  \: x   = 1
Therefore, the smallest of both roots is x = 1.
7 0
2 years ago
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