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ki77a [65]
3 years ago
7

A bug completes one lap along the edge of a circular planter of radius 11.7 cm in 13.91 s. How fast was it traveling? 1. 10.8518

2. 7.53496 3. 12.0428 4. 6.06143 5. 13.9643 6. 8.63381 7. 7.9597 8. 5.28492 9. 13.1952 10. 7.74398 Answer in units of cm/s.
Mathematics
1 answer:
IrinaK [193]3 years ago
8 0

Answer:

8.5.28492 cm/s

Step-by-step explanation:

We are given that

Radius of circular planter=11.7 cm

Time taken by bug =13.91 s

We have to find the speed of bug.

We know that

Speed =\frac{distance}{time}

Distance traveled by bug =2\pi r

Distance traveled by bug =2\times 3.14\times 11.7

Because \pi=3.14

Speed of bug=\frac{2\times 3.14\times 11.7}{13.91}=5.28224 cm/s

Hence, speed of bug=5.2822 4 cm/s

Answer:8.5.28492 cm/s

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anastassius [24]

Answer:

a) About 48 of the shoppers, that is 230\frac{21}{100} of the shoppers, received a free set of​ earbuds.

b) About 58 shoppers, that is \frac{230}{4} received ​$5 off their first​ purchase.

Step-by-step explanation:

a. About how many shoppers received a free set of​ earbuds?

21% out of 230. So

230\frac{21}{100} = 2.3(21) = 48.3

About 48 of the shoppers, that is 230\frac{21}{100} of the shoppers, received a free set of​ earbuds.

b. About how many shoppers received ​$5 off their first​ purchase?

25% out of 230, so:

230\frac{25}{100} = 230\frac{1}{4} = \frac{230}{4} = 57.5

About 58 shoppers, that is \frac{230}{4} received ​$5 off their first​ purchase.

5 0
3 years ago
The sum of two expressions
vagabundo [1.1K]

Answer:

4x + 2y

Step-by-step explanation:

If you subtract 5x + 3y from 9x + 5y, you get:

  9x + 5y

<u> - 5x + 3y</u>

  4x + 2y

7 0
3 years ago
Let P(n) be the statement that n! &lt; nn where n is an integer greater than 1.
Ira Lisetskai [31]

Answer: See the step by step explanation.

Step-by-step explanation:

a) First, Let P(n) be the statement that n! < n^n

where n ≥ 2 is an integer (This is because we want the statement of P(2).

In this case the statement would be (n = 2): P(2) = 2! < 2^2

b) Now to prove this, let's complet the basis step:

We know that 2! = 2 * 1 = 2

and 2^2 = 2 * 2 = 4

Therefore: 2 < 4

c)  For this part, we'll say that the inductive hypothesis would be assuming that k! < k^k for some k ≥ 1

d) In this part, the only thing we need to know or prove is to show that P(k+1) is also true, given the inductive hypothesis in part c.

e) To prove that P(k+1) is true, let's solve the inductive hypothesis of k! < k^k:

(k + 1)! = (k + 1)k!  

(k + 1)k!  < (k + 1)^k  < (k + 1)(k + 1)^k

Since k < k+1 we have:

= (k + 1)^k+1

f) Finally, as the base and inductive steps are completed, the inequality is true for any integer for any n ≥ 1. If we had shown P(4)

as our basis step, then the inequality would only be proven for n ≥ 4.

6 0
3 years ago
How do you interpret the statement that F(60)=86?
igor_vitrenko [27]

Answer:

Step-by-step explanation:

"F" is the name of a function.  If we choose "60" as the input to this function, the resulting output vaue is 86.  The function F maps 60 (input) onto 86 (output).

5 0
3 years ago
Read 2 more answers
Evaluate f(x) = x2 – 12 when x = 5
Ede4ka [16]

Answer:

f(5) = 13

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS

<u>Algebra I</u>

  • Function notation and substitution

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = x² - 12

x = 5

<u>Step 2: Evaluate</u>

  1. Substitute:                   f(5) = 5² - 12
  2. Exponents:                  f(5) = 25 - 12
  3. Subtract:                      f(5) = 13
4 0
3 years ago
Read 2 more answers
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