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Law Incorporation [45]
2 years ago
7

Which expressions are equivalent to 1 divided m/6? Check all that apply

Mathematics
1 answer:
jenyasd209 [6]2 years ago
6 0

Answer:

option A, option C, option D

Step-by-step explanation:

a) 1 ÷ m/6

can be written as

\frac{1}{1}÷ \frac{m}{6}

b) sides in (m/6) will change if both has to multiply

c) 1 ÷ m/6

can be written as

1 * 6/m

1(\frac{6}{m}) and wont make change to answer. so matches with the question.

d)

1 ÷ m/6

1 * 6/m

1 * 6 * \frac{1}{m}

6 * \frac{1}{m}

6 ÷ m ..therefore true

e)

1 ÷ m/6

1 * 6/m

6/m    ....does not match or can be converted to the following so wrong

  • Therefore A, C, D are correct and B and E is wrong.
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<em><u>Option A </u></em>will be your answer

Step-by-step explanation:

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5 0
3 years ago
Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec
vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}

Hence, we have:

\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\  \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}

Divide the expression for the fifth term by the expression for the second term:

\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}

Substituting the value of r into any of the expression:

\begin{gathered} ar\text{ =  18} \\ a\text{ }\times\text{ 2 =  18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}

Hence, the explicit rule for the sequence is:

a_n\text{ = 9\lparen2\rparen}^{n-1}

5 0
1 year ago
The curved part of this figure is a semicircle. What is the best approximation for the area of this figure? 18+12.125π units² 36
andreyandreev [35.5K]

Answer:

18+12.125π units²

Step-by-step explanation:

The diameter of the semicircle can be found by the use Pythagoras theorem.

Δx²+Δy²=d²

Δx=3--1=4

Δy=3--6=9

d²=4²+9²

d=√(16+81)

Area=πr²/2

=π×(√(16+81)/2)²÷2

=[π×(97)/4]/2

=97π/8

=18+12.125π units²

97π/8 is equivalent to 18+12.125π units²

3 0
3 years ago
The time needed to complete a final examination in a particular college course is normallydistributed with a mean of 80 minutes
Artist 52 [7]

Answer:

a) 0.023

b) 0.286

c) 10 students will be unable to complete the exam inthe allotted time.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 80 minutes

Standard Deviation, σ = 10 minutes

We are given that the distribution of time to complete an exam is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(completing the exam in one hour or less)

P(x < 60)

P( x < 60) = P( z < \displaystyle\frac{60 - 80}{10}) = P(z < -2)

Calculation the value from standard normal z table, we have,  

P(x < 60) =0.023= 2.3\%

b) P(complete the exam in more than 60 minutes but less than 75 minutes)

P(60 \leq x \leq 75) = P(\displaystyle\frac{60 - 80}{10} \leq z \leq \displaystyle\frac{75-80}{10}) = P(-2 \leq z \leq -0.5)\\\\= P(z \leq -0.5) - P(z < -2)\\= 0.309- 0.023 = 0.286= 28.6\%

c) P(completing the exam in more than 90 minutes)

P(x > 90)

P( x > 90) = P( z > \displaystyle\frac{90 -80}{10}) = P(z > 1)

= 1 - P(z \leq 1)

Calculation the value from standard normal z table, we have,  

P(x > 90) = 1 - 0.8413 = 0.1587 = 15.87\%

15.87% of children of class will require more than 90 minutes to complete the test.

Number of children =

\dfrac{15.87}{100}\times 60 = 9.52\approx 10

Approximately, 10 students of class will require more than 90 minutes to complete the test.

4 0
4 years ago
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