Solve for x: −7 < x − 1 < 8

Answer: Yes it is true. We can write an equation by setting an expression equal to itself.

Step-by-step explanation:

Let we take an expression say 2x.

Since we know that any expression is equal to itself, so we can write it as 2x=2x, which does not give any solution or we can say this equation has no solution but we can not say it is false because they are actually equal.

Therefore, we can write an equation by setting an expression equal to itself. It would be a true equattion.

When you need to round a number. First you need to look at the placement number that the question is asking to round to the nearest.

In this case it's the nearest tenths.

.8  is in the tenths place.

Now look to the number to the right of that number 3  that's the number that tells you if you will round up or down.

If the number is 5 or more you round up, if it's less than 5 you round down.

In this case the 3 is less than 5 so you round down.

So your answer would be 8.8

Hope this helps.

Answer: 251.87

Hope it helps

Answer:   14112

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Explanation:

We'll be using the n C r combination function. To make the notation a bit easier to deal with, I will write "C(n,r)" instead of "n C r".

The formula is

C(n,r) = (n!)/(r!*(n-r)!)

where the exclamation marks represent factorials.

A factorial is where you start with a positive integer, and count down to 1 multiplying all along the way.

Examples:

5! =           5*4*3*2*1

8! = 8*7*6*5*4*3*2*1 = 120

Note how the string "5*4*3*2*1" is in both 5! and 8!

We can say 8! = 8*7*6*5!

Because we can replace the "5!" at the end with "5*4*3*2*1" later if we wanted. This strategy is used to help find a shortcut to simplification.

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We have n = 9 appetizers and r = 6 items we can select from this pool.

C(n,r) = (n!)/(r!*(n-r)!)

C(9,6) = (9!)/(6!*(9-6)!)

C(9,6) = (9!)/(6!*3!)

C(9,6) = (9*8*7*6!)/(6!*3*2*1)

C(9,6) = (9*8*7)/(3*2*1) .... the "6!" terms canceled out

C(9,6) = 504/6

C(9,6) = 84

There are 84 ways to choose six appetizers from the pool of nine available

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Repeat those steps for the main courses. Use n = 8 and r = 5 this time.

C(n,r) = (n!)/(r!(n-r)!)

C(8,5) = (8!)/(5!*(8-5)!)

C(8,5) = (8!)/(5!*3!)

C(8,5) = (8*7*6*5!)/(5!*3*2*1)

C(8,5) = (8*7*6)/(3*2*1)

C(8,5) = (336)/(6)

C(8,5) = 56

There are 56 ways to choose five main course meals from the pool of eight available

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Then do the same for the desserts. Use n = 3 and r = 2.

C(n,r) = (n!)/(r!(n-r)!)

C(3,2) = (3!)/(2!*(3-2)!)

C(3,2) = (3!)/(2!*1!)

C(3,2) = (3*2*1)/(2*1*1)

C(3,2) = 6/3

C(3,2) = 3

There are 3 ways to choose two desserts from the pool of three available

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The last step is to multiply all these results:

84*56*3 = 14112

This is the number of ways to select all of the items given the restrictions listed. The order does not matter.

Answer: The patient will receive 13 more grams of dose.

Step-by-step explanation:

Hi, to answer the question we have to analyze the information given.

grams of medicine received: 65 grams

dose increase: 20%

So, we have to calculate the 20 percent of the 65 grams.

• 65 x 0.2 =13 grams

In conclusion, the patient will receive 13 more grams of dose.

Feel free to ask for more if it´s necessary or if you did not understand something.

The patient will receive 13 grams more as 65+20%=13