All categories

3 years ago

Which of the following correctly describes the sum of two rational numbers?

Mathematics

1 answer:

Elena-2011 [213]3 years ago

8 0

Answer:

"The sum of two rational numbers is rational."

By definition, a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number.

You might be interested in

The volume of a sphere is 2,143.572,ft cubed. To the nearest foot, what is the radius of the sphere? Use 3.14 for pi.

babymother [125]

Volume of a sphere is defined:

$V=\frac{4\pi r}{3}$

Solve for radius.

$3V=4\pi r\Longrightarrow r=\frac{3V}{4\pi}$

Now put in the data.

$r=\frac{3\cdot2143.572}{4\cdot3.14} \\ \\r=\frac{6430.716}{12.56}\approx\boxed{30010}$

The radius of the sphere is 30010ft.

Hope this helps.

r3t40

6 0

4 years ago

g The total national health expenditures per capita (in dollars) for 2006 and projected to 2021 can be modeled with the equation

Alex73 [517]

Answer:

a) The predicted per capita health expenditures for 2018 is $11943.5.

b) After 2018, it will take 16 years for the 2018 expenditures to double

Step-by-step explanation:

The total national health expenditures per capita, in dollars, is given by the following equation:

$H(t) = 6791e^{0.04343t}$

In which t is the number of years after 2005.

a. Find the predicted per capita health expenditures for 2018.

2018 is 13 years after 2005, so this is H(13).

$H(t) = 6791e^{0.04343t}$

$H(13) = 6791e^{0.04343*13}$

$H(13) = 11943.5$

The predicted per capita health expenditures for 2018 is $11943.5.

b. According to the model, how long will it take the 2018 expenditures to double?

First we find how many years after 2005, in which t is found when H(t) = 2*11943.5.

$H(t) = 6791e^{0.04343t}$

$2*11943.5 = 6791e^{0.04343t}$

$e^{0.04343t} = \frac{2*11943.5}{6791}$

$e^{0.04343t} = 3.5174$

Applying ln to both sides

$\ln{e^{0.04343t}} = \ln{3.5174}$

$0.04343t = \ln{3.5174}$

$t = \frac{\ln{3.5174}}{0.04343}$

$t = 29$

It will take 29 years after 2005 = 29-13 = 16 years after 2018.

After 2018, it will take 16 years for the 2018 expenditures to double

5 0

3 years ago

The vector v has initial point P(1, 0) and terminal point Q that is on the y-axis and above the initial point. Find the coordina

zloy xaker [14]

Answer:

The terminal point is Q(0,4)

Step-by-step explanation:

We are given the following in the question:

Initial point of vector, P(1,0)

The terminal point Q lies on the y-axis, thus Q have coordinates of the form:

$Q(0,y)$

The magnitude of the vector is $\sqrt{65}$

Magnitude is given by:

$v = \sqrt{(x_2-x_2)^2+(y_2-y_1)^2}\\\sqrt{65}=\sqrt{(0-1)^2+(y-0)^2}\\\sqrt{65}=\sqrt{1+y^2}\\65 = 1+y^2\\y^2 = 64\\y = \pm 8$

But since the terminal point is above the initial point, thus,

$y > 0\\\Rightarrow y = 4$

Thus, the terminal point is Q(0,4)

4 0

3 years ago

11.84396 in decimal form nearest thousandth

neonofarm [45]

Answer:

11.844

Step-by-step explanation:

9 is bigger than 5 so it makes the 3 a 4

6 0

3 years ago

One gallon is approximately 3. 875 liters. Mario buys 1. 5 gallons of gasoline for his lawn trimmer. How many liters of gasoline

agasfer [191]

Based on the amount of gasoline Mario bought in gallons, the amount in liters would be 5.8 liters. 

A single gallon is equivalent to 3.875 liters.

If Mario bought 1.5 gallons of gasoline, the amount he bought in liters would be:

= Gasoline in gallons x Number of liters per gallon

= 1.5 x 3.875

= 5.8125

= 5.8 liters

In conclusion, Mario bought 5.8 liters of gasoline.

Find out more at brainly.com/question/237650.

5 0

3 years ago