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Gala2k [10]
3 years ago
6

There is a bag with 50 popsicles inside. 5

Mathematics
1 answer:
Allisa [31]3 years ago
8 0

Answer:

25%

Step-by-step explanation:

We know that there are ten purple popsicles. Together without the purple popsicles, there are 40 popsicles in total. Therefore there is a 10/40 chance to get purple. We need to turn this into a percentage so we do (10 / 40) x 100. This would equal to 25%, therefore, there is a 25% probability to get a purple popsicle.

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What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (5 points)
zzz [600]

Answer:

B) 4√2

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Parametric Differentiation

Integration

  • Integrals
  • Definite Integrals
  • Integration Constant C

Arc Length Formula [Parametric]:                                                                         \displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.

Interval [0, π]

<u>Step 2: Find Arc Length</u>

  1. [Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]:         \displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.
  2. Substitute in variables [Arc Length Formula - Parametric]:                       \displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx
  3. [Integrand] Simplify:                                                                                       \displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx
  4. [Integral] Evaluate:                                                                                         \displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametric Integration

Book: College Calculus 10e

4 0
3 years ago
A tennis racket normally costs $80. The tennis racket is on sale for 30% off. What is the sale price of the tennis racket
velikii [3]
The answer would be $56
The reason is you would do 80*.3(30% in decimal form) which would equal 24
24 is what is being taken off of the normal cost.
So you would then do 80-24 which would equal $56.
6 0
3 years ago
Jennifer earns $39 for 6 hours of babysitting.how much will she earn for 10 hours
nadya68 [22]
Find the unit rate.

39/6 = 6.5

$6.50 an hour

multiply this by ten to find the cost for 10 hours

$6.5 x 10 = $65

she will earn $65 in ten hours.
 hope this helps! :D

4 0
3 years ago
Read 2 more answers
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. two to
Lubov Fominskaja [6]

Answer:

The answer is " \sqrt[8]{2^5} ".

Step-by-step explanation:

Given value:

\to \frac{2 \frac{7}{8}}{2 \frac{1}{4}}

They understand that, by using algebraic expressions laws, they subtract that inverse whenever we subtract powers with the same base. Every exponent's core is 2, therefore we subtract:

\to \frac{7}{8} - \frac{1}{4}

They have a shared denominator. It's least that is equally divided

among 8 or 2 is 8:

\to \frac{7}{8} - \frac{2}{8}\\

\to \frac{7-2}{8}\\\\\to \frac{5}{8}\\\\

This gives us:

\to 2 \frac{5}{8}

As rational notation is written as extremists, that root was its denominator as well as the power seems to be the numerator.

Which means 8 is the root and 5 the force that gives us:

\sqrt[8]{2^5}

7 0
3 years ago
-5x-y=12<br> 3x-5y=4<br> Linear systems by substitution
alukav5142 [94]
You would do 3 times 5 mines 5 which equals 10 and the you would do 5x12 

4 0
3 years ago
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