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3 years ago

Order the numbers from least to greatest.

Mathematics

2 answers:

Vitek1552 [10]3 years ago

5 0

-1.6,0.9,-4/3,2/3,4/5,23

8090 [49]3 years ago

3 0

Begin by converting all of the fractions into decimal fractions. This will make comparisons much easier. Which is the smallest negative number? List that one first.

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Pattern: 10, 17, 26, 37....

Lelu [443]

Answer:

362 is the 17th term of this pattern

Step-by-step explanation:

First differences of the sequence are ...

17-10 = 7, 26-17 = 9, 37 -26 = 11

And second differences are ...

9-7 = 2, 11-9 = 2

The constant second differences tell you the pattern is described by a second degree polynomial. That polynomial can be written as ...

an^2 +bn +c . . . for term number n

Filling in the first 3 sequence values, we get ...

a + b + c = 10

4a +2b +c = 17

9a +3b +c = 26

___

Any of several means can be used to solve these.

We can subtract the first equation from the other two to get ...

3a +b = 7 . . . . . . . . [eq4]

8a +2b = 16 . . . . . . [eq5]

Subtracting [eq4] from half of [eq5], we get ...

(4a +b) -(3a +b) = 8 -7

a = 1

Putting this value into [eq4] gives ...

3 +b = 7

b = 4

and using these values for a and b in the first equation gives ...

1 + 4 + c = 10

c = 5

So the pattern is described by ...

an = n^2 +4n +5

We want to find the term that is more than 350, so ...

350 < n^2 +4n +5

349 < n^2 +4n +4 . . . . subtract 1 to make a square on the right

349 < (n +2)^2

√349 ≈ 18.68 < n +2 . . . . take the positive square root

16.68 < n . . . . . . . . . . . subtract 2

The first term greater than 350 is the 17th term. It is 362.

_____

In the process of "completing the square", we observe that the pattern rule can be written ...

an = (n+2)^2 +1

3 0

4 years ago

You accept a job as a marine biologist that pays a salary of $45,000 the first year. During the next 39 years, you receive a 5.5

melamori03 [73]

45000(1.055)^40=383980.89

7 0

3 years ago

Seema measures the big prize wheel on a game show and calculated that it has a circumference of 12.56 meters. What is the prizes

miss Akunina [59]

Answer:

radius 2 meters

Step-by-step explanation:

Take the circumference formula $12.56=\pi*d$

Divide both sides by pi ÷ 3.14 ÷3.14

4=d

Divide by 2 to find radius 4 divided by 2 is 2

8 0

3 years ago

Estimate in division

aliya0001 [1]

I guess you need help with #3

So you have to 642 by 5

By the way, this is a great question for a calculator to check your answer

The answer 128.4

5 0

4 years ago

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2

ivolga24 [154]

Question:

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to $\frac{1}{2}$ .

If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

5n = 3d and n - 2 = 2d - 4

5n = 3d and 2n - 4 = d - 2

3n = 5d and 2n - 4 = d - 2

Answer:

5n = 3d and 2n – 4 = d – 2

Solution:

Let n be the numerator of the fraction and d be the denominator of the fraction.

Given the numerator and denominator of a fraction are in the ratio of 3 to 5.

This can be written as n : d = 3 : 5.

⇒ $\frac{n}{d}= \frac{3}{5}$ – – – – (1)

Do cross multiplication, we get

⇒ 5n = 3d

When the numerator and denominator are decreased by 2, the fraction is equal to $\frac{1}{2}$ .

⇒ $\frac{n-2}{d-2}= \frac{1}{2}$

Do cross multiplication, we get

⇒ 2(n –2)=1(d – 2)

⇒ 2n – 4 = d – 2

Hence, 5n = 3d and 2n – 4 = d – 2 can be used to solve the problem.

6 0

4 years ago

Read 2 more answers