Name three numbers that would be placed between 5.89 and 5.9 on a number line

Answers

Answer 1

Answer: The answer is 5.891 and 5.894 you just had to add a extra number

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4 friends share 3 apples equally. What fraction of the apple does each friend get ?
Can someone please help me solve x + 0.018 = 9
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What is the time that is 9 hours and 40 minutes before 4:25am

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6:45pm. because from 4 to 12 would be 4 hours then subtract 5 more hours leaves you at 7:25 pm. now subtract 45 from that which leaves you at 6:45 pm.

What radian measure is equivalent to 900°?
5n
10n
1/5n
9n

Answers

Answer: 5n

Sources: Just trust me

9n is the answer to this question

What is the fraction ten twelves in its simplest form

Answers

You just divide each by one of there common factors (except from 1 and 0)

Eg.10÷2=5

12÷2=6

This would look like:

10/12

Next look for a common divisor that works for both the top (numerator) and bottom (denominator) numbers. Incidentally, think 'Notre Dame' or ND if you cannot remember which is which.

Dividing by 2 works for both numbers, so dividing the '10' and the '12' by 2 gives you a simplified form of 5/6.

And voila! That's your answer!

Allison has a poster that is 15 in by 18 in. What will the dimensions of the poster be if she scales it down by a factor of 1/3 ?

Answers

Answer:

Answer 4 : 5in by 6in

Step-by-step explanation:

15 times 1/3 is 5.

18 times 1/3 is 6.

Hope I helped!!

Water fills a tank at a rate of 150 litres during the first hour, 350 litres during the second, 550 litres during the third and so on. Find the number of hours necessary to fill a rectangular tank 16m x 7m x 7m.

Answers

Putting this as an arithmetic sequence gives:

$u_n = 150+200(n-1)$

The sum of the series = 16 x 7 x 7 = 784 m^3 = 784 000 L

The sum of an arithmetic series can be written as:

$S_n=n/2 [2a+(n-1)d] = 784 000\nn/2[2(150)+(n-1)200] = 784 000\nn[300+200(n-1)=1 568 000\n300n+200n^2-200n = 1 568 000\n200n^2+100n- 1 568 000 = 0\n2n^2 +n- 15680 = 0\nn= 88.2...,-88.7$

n has to be positive, so we get

n = 88.2 hours (3 s.f.)

Volume of tank = (16m)(7m)(7m) = 784 m³

Conversion of m³ to L:
(784 m³) × (1000L / 1m³) = 784,000 L

Rate in the 1st hour:
150 liters/hr

Rate in the 2nd hour:
350 liters/hr

Rate in the 3rd hour:
550 liters/hr

It is apparent that the Fill Rate is increasing by 200 liters/hr every subsequent hour . . . so that can be represented by the following equation

where:
t = number of hours

Fill rate (i.e. volume of water filled into tank within the specified hour) = 150 + 200(t - 1)

For t = 1 . . . Fill rate = 150 L/hr
For t = 2 . . . Fill rate = 350 L/hr
For t = 3 . . . Fill rate = 550 L/hr

Because after every hour there has been more water added to the tank, this problem can be represented as a geometric sequence in order to account for the compounding of the volume after each time step, but it can also be tabulated (which seems to me to be the more direct/simple approach), so I will build a table that accounts for the increasing Fill Rate and the compounding of water volume after each time step . . .

(see attached)

The answer (after all of this) is . . . t = 88 hrs 17 1/2 mins (approx)

What is the seventh term of (x + 4)8?A. 114,688x2
B. 114,688x3
C. 114,688x4
D. 114,688x5

Answers

The (p+1)-th term of the Newton binomial expansion

$(a+b)^(n)$

is given by

$t_(p+1)=\dbinom{n}{p}\,a^(n-p)\,b^(p)$
__________________________

We want the 7th term. Hence, we set $p+1$ to be $7:$

$p+1=7~~\Rightarrow~~p=6$

Then, the 7th term is

$t_(7)=\dbinom{8}{6}\,x^(8-6)\,4^(6)\n\n\n t_(7)=(8!)/(6!\cdot (8-6)!)\cdot x^(8-6)\cdot 4^(6)\n\n\n t_(7)=(8\cdot 7\cdot \diagup\!\!\!\! 6!)/(\diagup\!\!\!\! 6!\cdot 2!)\cdot x^(2)\cdot 4^(6)\n\n\n t_(7)=(8\cdot 7)/(2\cdot 1)\cdot x^(2)\cdot 4^(6)\n\n\n t_(7)=28\cdot x^(2)\cdot 4,096\n\n \boxed{\begin{array}{c} t_(7)=114,688\,x^(2) \end{array}}$

Correct answer: $\text{A. }114,688\,x^(2).$

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