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otez555 [7]
3 years ago
11

Please help. 40 points

Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
5 0

Answer:

number 2

Step-by-step explanation:

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"three times a number is greater than or equal to 12 and less than 21"
Diano4ka-milaya [45]

Answer:

The required inequality is: 12 ≤ 3x < 21

Step-by-step explanation:

We are given: three times a number is greater than or equal to 12 and less than 21

We need to answer following questions:

1) The inequality translated in numerical form

Let number = x

12 ≤ 3x < 21

2) Your work solving the inequality

We need to find value of x. Divide the inequality by x

4 ≤ x < 7

3) The solution graphed on a number line

It is shown in figure attached.

4) The solution in set notation

The set notation is: Considering x belongs to natural numbers N

{∀ x|x∈N, 4 ≤ x < 7}

5) The solution in interval notation

The interval notation is: [4,7)

because we have 4 less than equal to x and x is less than 7

8 0
3 years ago
the difference between a number and two times a number is seven the number is greater than zero what is the number
bagirrra123 [75]
7 is the answer

2x - x = 7
x = 7

3 0
3 years ago
To make a certain shade of orange calvin uses a rate of 2 ounces of yellow paint to 5 ounces of red paint if he uses 200 ounces
ycow [4]
Answer: 80 ounces of yellow paint

Working:
As we know 2 ounces of yellow paint to 5 ounces of red paint, we can make a ratio:

2:5

Then we look at the question which says 200 ounces of red paint, so we replace the 5 ounces of red paint in the ratio with 200.

2:200

Then we figure out how much the 5 has been multiplied by to get to 200. We do this by doing

200 divide 5 = 40

Therefore we times the 2 ounces of yellow paint by 40 which gets us:

80:200

We can think of it as a fraction too to confirm our answer:

Simplify 80 / 200

We get 2 / 5.

If you need me to further explain something please just ask :)
4 0
3 years ago
A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and
nasty-shy [4]

Answer:

correct option is C)  2.8

Step-by-step explanation:

given data

string vibrates form =  8 loops

in water loop formed =  10 loops

solution

we consider  mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = \rho

case (1)  

when 8 loop form with 2 adjacent node is \frac{\lambda }{2}

so here

l = \frac{8 \lambda _1}{2}      ..............1

l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}

and we know velocity is express as

velocity = frequency × wavelength   .....................2

\sqrt{\frac{Tension}{mass\ per\ unit \length }}   =   f × \lambda_1

here tension = mg

so

\sqrt{\frac{mg}{\mu}}   =   f × \lambda_1     ..........................3

and

case (2)  

when 8 loop form with 2 adjacent node is \frac{\lambda }{2}

l = \frac{10 \lambda _1}{2}      ..............4

l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}

when block is immersed

equilibrium  eq will be

Tenion + force of buoyancy = mg

T + v × \rho × g = mg

and

T = v × \rho - v × \rho × g    

from equation 2

f × \lambda_2 = f  × \frac{1}{5}  

\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}     .......................5

now we divide eq 5 by the eq 3

\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}

solve irt we get

1 - \frac{\rho _{stone}}{\rho _{water}}  = \frac{16}{25}

so

relative density \frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}

relative density = 2.78 ≈ 2.8

so correct option is C)  2.8

3 0
3 years ago
-6x-16 &lt; 2x please help asap! and help me solve it
ICE Princess25 [194]

1. Divide both sides by 2

2. Add 16 to each side

Answer  x > -2

         

3 0
3 years ago
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