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neonofarm [45]
3 years ago
7

a bottling machine can fill 300 bottles in 5 minutes at this rate how many bottles can be filled in 8 minutes

Mathematics
2 answers:
kirill [66]3 years ago
6 0
480 bottles because 300 divided by 5 is 60 so then you multiply 60 by 8 and you get 480!
Gennadij [26K]3 years ago
4 0

Answer:

480 bottles

Step-by-step explanation:

It is given that a bottling machine can fill 300 bottles in 5 minutes. So, rate of filling is

Rate=\dfrac{Bottles}{Time}

Rate=\dfrac{300}{5}

Rate=\dfrac{Bottles}{Time}=60

It means a machine can fill 60 bottles per minute.

We need to find the number of bottles that can be filled in 8 minutes.

\text{Bottles that can be filled in 8 minutes}=8\times 60=480

Therefore, the machine can fill 480 bottles in 8 minute.

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The 13th term of a geometric sequence is 16, 384 and the first term is 4. What is the common ratio?
AleksAgata [21]

Answer:

\large \boxed{2}

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

In your geometric sequence, a₁ = 4 and a₁₃ = 16 384.

\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}

Check:

\begin{array}{rcl}16384 & = & 4(2)^{12}\\16384 & = & 4(4096)\\16384 & = & 16384\\\end{array}

It checks.

7 0
2 years ago
For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive term
elena55 [62]

Answer:

The no. of variations in sign is 3

Step-by-step explanation:

Variation in sign occurs when every single time a negative product is produced by a pair of consecutive terms.

Therefore, the determination of the number of changes in sign in the given sequence is must.

Therefore, we take the product of the pair of consecutive terms as:

1\times (-3) = - 3, variation in sign

(-3)\times 2 = - 6,  variation in sign

2\times 5 = 10,  no sign variation

5\times (- 4) = - 20,  variation in sign

- 4\times (-6) = 24, no sign variation

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Answer:

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STEP BY STEP EXAMPLE:

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