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3 years ago

Is a terminating decimal always rational

Mathematics

2 answers:

AlladinOne [14]3 years ago

5 0

Yes....because a terminating decimal can be turned into a fraction, making it rational

Ilia_Sergeevich [38]3 years ago

5 0

Yes because a terminating decimal can be made into a fraction for example:
1/2=0.5

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Someone please help, can’t seem to get the problems

VikaD [51]

Answer:

A) 525,500

B) decreasing by 0.995% per year

C) 430,243

D) After 20 years, the population can be expected to be about 20% smaller.

E) 2009

Step-by-step explanation:

A) t=0 represents the year 2000, so put 0 where t is in the expression and evaluate it. Of course, e^0 = 1, so the y-value is 525.5 thousand, or 525,500.

B) Each year, the population is multiplied by e^-0.01 ≈ 0.99004983, or about 1 - 0.995%. That is, the population is decreasing by 0.995% per year.

C) t represents the number of years since 2000, so the year 2020 is represented by t=20. Put that value in the equation and do the arithmetic.

y = 525.5·e^(-0.01·20) = 525.5·e^-0.2 ≈ 430.243 . . . . thousands

The population in 2020 is predicted to be 430,243.

D) The decrease is about 1% per year, so a rough estimate of the decrease over 20 years is 20%. The population of about 500,000 will decrease by about 100,000 in that time period, so will be about 400,000. The value we calculated is in that ballpark. (The actual decrease is about 18.13%; or about 95.2 thousand.)

E) Your working shows the general idea, but you need to remember the numbers in the equation are thousands:

480 = 525.5·e^(-0.01t)

0.913416 = e^(-0.01t) . . . . divide by 525.5

ln(0.913416) = -0.01·t . . . . take the natural log

-100ln(0.913416) = t ≈ 9.06

The population will be 480 thousand after 9 .06 years, in the year 2009.

5 0

3 years ago

Claire earned $60 babysitting on Friday night. She spent 1/4 of it at the movie, 1/3 going out to dinner, and she saved the rest

In-s [12.5K]

Answer:

25 dollars

Step-by-step explanation:

1/4*60=15

1/3*60=20

20+15=35

60-35=25

6 0

3 years ago

Solve the problem.A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course. At that t

Mice21 [21]

Given:

A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course.

The distance between plan and mountain is 10 km.

A short time later, the bearing to the mountain becomes 45°.

Here NM is the distance between the plane from the mountain when the second bearing is taken.

We need to find the measure of NM.

$We\text{ know that }\angle INM\text{ and }\angle\text{XNM are supplementary angles.}$

The sum of the supplementary angles is 180 degrees.

$\angle INM+\angle XNM=180^o$ $\text{Substitute }\angle XNM=45^o\text{ in the equation.}$

$\angle INM+45^o=180^o$

$\angle INM=180^o-45^o$

$\angle INM=135^o$

We know that the sum of all three angles of the triangle is 180 degrees.

$\angle INM+\angle NIM+\angle INM=180^o$ $\text{Substitute }\angle INM=135^o\text{ and }\angle NIM=35^o\text{ in the equation.}$

$135^o+35^o+\angle INM=180^o$

$170^o+\angle INM=180^o$

$\angle INM=180^o-170^o$

$\angle INM=10^o$

Consider the sine law.

$\frac{\sin N}{IM}=\frac{\sin M}{IN}=\frac{\sin I}{NM}$

Take the equation to find the measure of NM.

$\frac{\sin N}{IM}=\frac{\sin I}{NM}$ $\text{Substitute }\angle N=135^o,\angle I=35^o,\text{ and IM=10 in the equation.}$

$\frac{\sin 135^o}{10}=\frac{\sin35^o}{NM}$

$NM=\frac{\sin 35^o}{\sin 135^o}\times10$ $NM=8.11$

Hence the measure of NM is 8.1 km.

The plane is 8.1 km far from the mountain when the second bearing is taken.

5 0

1 year ago

Write a real-world problem that could be represented by the inequality.<br> 3x + 6 > 27

liubo4ka [24]

Hello! We see that 6 is the fixed amount. x represents the amount of something, and the solution makes a number $27. Let's make a real-world problem and then execute it.

Fawn has $6 in her piggy bank. She makes bracelets to sell to family & friends for $3 each. She wants to buy a video game that with tax, costs a little over $27. How many bracelets would Fawn have to sell in order to have enough money to buy the video game?

How to solve it:

So we have the expression of 3x + 6 > 27. First off, subtract 6 from both sides. 6 - 6 cancels out. 27 - 6 is 21. That's 3x > 21. Now, divide each side by 3 to isolate the x. 3x/3 cancels out. 21/3 is 7. There. x > 7. Fawn will have to sell more than 7 bracelets in order to have enough money for the game.

8 0

3 years ago

Which answer choice correctly completes the sentence? The bridge was closed, but that hasn't __________ us any time. A. costed B

Rainbow [258]

The bridge was closed, but that hasn't <span>cost </span>us any time

7 0

4 years ago