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4 years ago

Need urgent help Which sets of numbers are closed under addition?

1 answer:

6 0

Hello!

Whole numbers are closed under addition and multiplication

Integers are closed under addition, subtraction, and multiplication

natural numbers are positive whole integers so they are also closed under addition

The answers are A, B and D

Hope this helps!

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Find the obtuse angle between the following pair of straight lines.

ioda

Given:

$y=-2$

$y=\sqrt{3}x-1$

To find:

The obtuse angle between the given pair of straight lines.

Solution:

The slope intercept form of a line is

$y=mx+b$ ...(i)

where, m is slope and b is y-intercept.

The given equations are

$y=0x-2$

$y=\sqrt{3}x-1$

On comparing these equations with (i), we get

$m_1=0$

$m_2=\sqrt{3}$

Angle between two lines whose slopes are $m_1\text{ and }m_2$ is

$\tan \theta=\left|\dfrac{m_2-m_1}{1+m_1m_2}\right|$

Putting $m_1=0$ and $m_2=\sqrt{3}$ , we get

$\tan \theta=\left|\dfrac{\sqrt{3}-0}{1+(0)(\sqrt{3})}\right|$

$\tan \theta=\left|\dfrac{\sqrt{3}}{1+0}\right|$

$\tan \theta=\pm \sqrt{3}$

Now,

$\tan \theta= \sqrt{3}$ and $\tan \theta=-\sqrt{3}$

$\tan \theta= \tan 60^\circ$ and $\tan \theta=\tan (180^\circ-60^\circ)$

$\theta= 60^\circ$ and $\theta=120^\circ$

$120>90$ , so it is an obtuse angle and $60$ , so it is an acute angle.

Therefore, the obtuse angle between the given pair of straight lines is 120°.

6 0

3 years ago

A lottery consists of one $2000 winner, three $500 winners, and ten $100 winners. a total of 1000 tickets are sold for $10 each.

Semenov [28]

Answer: -5.5

WOKINGS

Given that the lottery has the following number of winners:

One $2000 winner

Three $500 winners

Ten $100 winners

Also Given,

A total of 1000 tickets are sold

Each ticket costs $10

The expected winning for a person purchasing one ticket is the sum of the products of the gain/loss and their corresponding probability.

There is one $2000 winner

There are 1000 tickets

The probability of winning $2000

= 1/1000

= .001

There are three $500 winners

There are 1000 tickets

The probability of winning $500

= 3/1000

= .003

There are ten $100 winners

There are 1000 tickets

The probability of winning $100

= 10/1000

= .01

Since each ticket costs $10

Everyone who buys a ticket automatically loses $10.

Therefore, the probability of losing $10 is 1

Now to calculate the expected winning for a person purchasing one ticket

= 2000(.001) + 500(.003) + 100(.01) – 10(1)

= 2 + 1.5 + 1 – 10

= -5.5

The expected winning is -5.5. This implies that a person playing this lottery can expect to lose $5.50 for every one ticket that they purchase.

7 0

3 years ago

What is the length of side AC

natulia [17]

Answer:

7 Units.

Step-by-step explanation:

First of all, you could just count the units, but that's not really too effective. Otherwise, you could start from the coordinates of the "C" point, and see how it's at -Y = -5. Therefore, to get to the line separating the two points, you would have to subtract 5 from 5 to get to the line. Now, you look at point "A". It's Y coordinate is 2. Therefore, adding 5 and 2 together gives you 7 units.

6 0

3 years ago

Determine whether the sides given would form an acute,obtuse, or right triangle<br> 7,7,12

Yuliya22 [10]

Its a obtuse angle since 7^2 is 49 7^2 is 49 and 12^2 is 144
144 is bigger than 90 so its obtuse triangle

5 0

3 years ago

Skylar needs to buy a pair of dress pants for $40, a shirt for $30, and a tie for $20. Skylar has three coupons. The first coupo

IgorC [24]

Dress pants for $ 40, a shirt for $ 30, a tie for $ 20
he uses the dress pants coupon....which is the second coupon which gives him y percent off the dress pants

so ur answer is : (1 - y) * 40

8 0

4 years ago

Read 2 more answers