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3 years ago

"The sum of 4 and a number, divided by 2 is less than -6."

Mathematics

1 answer:

Ksenya-84 [330]3 years ago

3 0

Answer:

$\frac{4+n}{2} < -6$ , n < -16

Step-by-step explanation:

To write this into an inequality you need to recognize keywords. The first keyword is "sum" this means the two numbers must be added; so the first part of the inequality is 4+n. Then, it says the sum is "divided by" 2; this means both numbers must be put over two like $\frac{4+n}{2}$ . Finally, this is "less than" negative. Therefore, this must be an inequality with a sign opening towards -6. So the final answer is $\frac{4+n}{2} < -6$ .

To solve the inequality isolate the variable. Multiply both sides by 2, so the new inequality is $4+n$ . Next, subtract 4 from both sides. The answer is n < -16.

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<h2>Answer:</h2>

Option: C is the correct answer.

C. $a_n=a_{n-1}-3\ ;\ a_1=2$

<h2>Step-by-step explanation:</h2>

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Also, the first term of the sequence is: $a_1$

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$a_1=5-3\times 1\\\\i.e.\\\\a_1=5-3\\\\i.e.\\\\a_1=2$

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$a_n=5-3n\\\\i.e.\\\\a_n=5-3n+3-3\\\\i.e.\\\\a_n=5-3(n-1)-3\\\\i.e.\\\\a_n=a_{n-1}-3$

Hence, the recursive formula which represents the same sequence is:

Option: C

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3 years ago

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Adding or subtracting a constant from each value of a distribution changes the mean, but not the standard deviation.

The standard deviation will equal 3.

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3 years ago

The are of a rectangle is 24 square inches. The length is 6 inches and the width is w inches. How much longer is the length than

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Step-by-step explanation:

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3 years ago

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3 years ago

In one year the perseid metor shower had a metor appear every 1/5 5 minutes on average That same year the Leonid metor shower ha

olga55 [171]

In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor shower had a meteor appear every 4 2/3 minutes on average. How many more meteors fell during the Perseid meteor shower?

Answer:

325,452 meteors

Step-by-step explanation:

We all know that :

We have 365 days in a year and in each day there are 24 hours, Likewise an hour has 60 minutes

SO, the total number of minutes in a year is :

365 × 24 × 60 = 525600 minutes

For Perseid meteor:

$1 + \frac{1}{5} \\ \\ = 1 + 0.2 \\ \\ = 1.2$

So one meteor fall at 1.2 minutes interval Thus, in a year, we will have :

1 meteor - 1.2 minutes.

x meteor - 525600 minutes.

1.2x = 525600

$x = \frac{525600}{1.2}$

x = 438000

∴ 438,000 meteors fell during the Perseid shower.

For Leonid meteor shower:

$4 + \frac{2}{3} = 4.67$

So one meteor fall at 4.67 minutes interval Thus, in a year, we will have :

1 meteor - 4.67 minutes.

x meteors - 525600 minutes.

$4.67x = 525600$

$x = \frac{525600}{4.67}$

x = 112548

112,548 meteors fell during the Leonid Shower.

Finally , the numbers of more meteors that fell during the Perseid meteor shower is calculated by the difference in the number of Perseid meteor shower and Lenoid meteor shower. i.e

438,000 - 112,548 = 325,452

325,452 more meteors fell during the Perseid meteor shower

5 0

3 years ago

"The sum of 4 and a number, divided by 2 is less than -6."​

"The sum of 4 and a number, divided by 2 is less than -6."