Suppose you have 60 kg of a radioactive material that decays 50% of its mass every year how much material would you have left after 4 years?

Answer:

One pound of jelly beans costs $3.75.

One pound of trail mix costs $1.75.

Step-by-step explanation:

Let [tex]x[/tex] be equal to one pound of jelly beans.

Let [tex]y[/tex] be equal to one pound of trail mix.

1) Form equations

We're given:

7 pounds of jelly beans + 9 pounds of trail mix = $42

⇒ [tex]7x+9y=42[/tex]

5 pounds of jelly beans + 3 pounds of trail mix = $24

⇒ [tex]5x+3y=24[/tex]

Now, we have our two equations:

[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]

2) Solve for x using elimination

[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]

Multiply the second equation by 3 to change 3y to 9y:

[tex]5x+3y=24\\3(5x+3y)=3(24)\\15x+9y=72[/tex]

Subtract the first equation from the second to eliminate y:

[tex]15x+9y=72\\- 7x+9y=42\\\rule{2.5cm}{0.4pt}\\8x=30[/tex]

Divide both sides by 8 to isolate x:

[tex]\displaystyle x=\frac{30}{8} \\\\x=3.75[/tex]

Therefore, one pound of jelly beans costs $3.75.

2) Solve for y using substitution

[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]

Now, we know that x=3.75. Plug this value into one of the equations and solve for y:

[tex]5x+3y=24\\5(3.75)+3y=24\\18.75+3y=24\\3y=24-18.75\\3y=5.25\\\\\displaystyley=\frac{5.25}{3} \\\\y=1.75[/tex]

Therefore, one pound of trail mix costs $1.75.

I hope this helps!

Answer:

See below.

Step-by-step explanation:

The rule moves points 3 units to the left and 4 units up.

(-6, 0) moves to (-6 - 3, 0 + 4) = (-9, 4)

(3, -4) moves to (3 - 3, -4 + 4) = (0, 0)

The rule is a function because each point is moved to exactly one new location.  There is no case in which two different points are moved to the same location.

Answer:

3.42

Step-by-step explanation:

24/7=3.42

Hi ;-)

[tex]x=7 \ and \ y=10\\\\4x+5y=4\cdot7+5\cdot10=28+50=\boxed{78}[/tex]

Step-by-step explanation:

4x + 5y

4 × 7 + 5 × 10

28 + 50

78

Therefore its 78.

Answer:

Platonic solids

Step-by-step explanation:

To solve this we must be knowing each and every concept related to geometry. Therefore, icosahedron and the dodecahedron represents geometry of molecule.

Molecular geometry in chemistry depicts a molecule's three-dimensional form as well as the relative location of its atomic nuclei.

Understanding a molecule's molecular geometry is critical since the spatial connection between atoms dictates its reactivity, color, bioactivity, state of matter, polarization, as well as other features. A molecule's form influences its physical and chemical properties, including its colour, sensitivity, and bioactivities. Icosahedron and the dodecahedron represents geometry of molecule.

Therefore, icosahedron and the dodecahedron represents geometry of molecule.

To learn more about geometry, here:

https://brainly.com/question/30124665

#SPJ6

9514 1404 393

Answer:

   √53 units

Step-by-step explanation:

The distance between G(-5, 4) and H(2, 6) can be found using the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((2-(-5))² +(6-4)²) = √(7² +2²) = √53

The distance between the two points is √53 units.

Step-by-step explanation:

hopefully it is visible and makes sense

:)

Answer:

x=67 degrees

y=63 degrees (vertically opposite angles)

z=32 degrees

Step-by-step explanation:

x=130-63(sum of 2 interior angles of a triangle is equal to the opposite     exterior angle)

x=67 degrees

y=63 degrees (vertically opposite angles)

z+y+85=180

z+63+85=180

z+   148  =180

       z     =32 degrees

Answer:

9/10

Step-by-step explanation:

0.90 = 0.9 = 90/100 = 9/10

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer: B

Step-by-step explanation:

[tex]5(x-2)+x=6(x-3)+8\\remove the parentheses\\5x-10+x=6x-18+8\\combine like terms \\6x-10=6x-10\\xER[/tex]

Answer:

D. 40

Step-by-step explanation:

A central angle is equal to the measure of its corresponding arc.

angle AOB is a central angle and it's corresponding arc is arc AB

this means that arc AB = measure of angle AOB

If angle AOB = 80 degrees then arc AB equals 80 degrees too.

An inscribed angle is equal to half the measure of its intercepted arc.

Angle ACB is an inscribed angle and the arc it intercepts is arc AB

This means that angle ACB = 1/2 of arc AB

We have found that the measure of arc AB is 80 degrees.

This means that angle ACB = 1/2 of 80 which is 40

Answer and Step-by-step explanation:

An easy way of doing this is to first square root the numerator and the denominator.

[tex]\sqrt{\frac{36}{81} } =\frac{\sqrt{36}}{\sqrt{81} } =[/tex] ±[tex]\frac{6}{9} =[/tex] ±[tex]\frac{2}{3}[/tex] <- This is the answer.

#teamtrees #PAW (Plant And Water)

I hope this helps!

Answer:

78,000

Step-by-step explanation:

Step-by-step explanation

work out the question in bracket first then separate numericals and variables to make it easier.

Answer:

distribute

5 + 8 = 3 ( + 2 )

expand to

 5 + 8 = 3 + 6

subtract 8 from both sides

5 + 8 = 3 + 6

5 + 8 − 8 = 3 + 6 − 8

simplify

5 = 3 − 2

subtract 3 from both sides

5 − 3 = 3 − 2 − 3

simplify

2 = − 2

then divide both sides by 2

2 / 2  = − 2/ 2

= − 2/ 2

answer is

= −1

Step-by-step explanation:

Hope that helps>3

Answer:

250 ÷ 100 (so we'd reciprocate the right side and also change the sign to multiplication one) =250/1 x 1/100 (now we will cut 250 and 100 as much as they can be cut or reduced) =5/1 x 1/2 (now as they can no more be reduced we directly multiply them) =5/2 (now we will divide them both to get our anwer)

Step-by-step explanation:

if you served me crown please

Answer:

By using the GCF/HCF method 5/2 is the simplified fraction for 250/100.

Step-by-step explanation:

The step by step calculation of how to simplify the fraction 250/100 to its lowest term or simplest form. One of two methods used to convert the fraction to its lowest terms is the GCF or HCF method       

Given Fraction: 250/100

The GCF for 250 and 100 is 50

= (250/50) / (100/50)

= 5/2

Answer:

% of apple juice = 100-20 = 80%

mango : apple

= 20 : 80

= 1 : 4

Answer:

1:4

Step-by-step explanation:

20:80 is basically mango to apple juice, so all you have to do is simplify this ratio to the lowest form, which is in fact 1:4

Answer:

<ACB = 19°

Step-by-step explanation:

<BAD is a peripheral angle, meaning the angle it intersects is twice it. This means that arc AB is 2*19 or 38. Now, <ACB is an inscribed angle because it has a vertex on the circle. An inscribed angle is half the angle it intercepts. This means <ACB is 1/2 arc AB or 19.

Answer:

32

Step-by-step explanation:

let number=b

twice a number=2b

Condition:

2b+13=75

2b=75-13

2b=62

b=62/2

b=31

Note:if you need to ask any question please let me know.

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

10 students

Step-by-step explanation:

10 students=2 fail

50 students=10 fail

Hope this helps! Thanks.

Answer:

it will be ten left

Step-by-step explanation:

the cake max is 20

Answer: 1.10 pounds

Step-by-step explanation:

Answer:

-4.375

.......................

Math in many areas is used to create models, mathematical systems the describe real-world situations.

During the pandemic, a model called exponential model was used to predict the how many people will get infected given certain parameters, such as infection rate, average age of population, ...

We picked this particular model because viruses spread at an exponential rate, just like for example bacteria division would be modeled with something like [tex]2^t[/tex] where t is day number. After 1 day there are 2, after 2 days there are [tex]4, 8, 16, 32, \dots[/tex] which is known as exponential behaviour -- viruses spread that way, first person gets infected, aka patient 0, then that person likely infects others and others likely infect more people.

In particularly [tex]R_0[/tex] also known as basic reproduction number was used as a base, that is, [tex]R_0^t[/tex].

You can see if, [tex]R_0\lt 1[/tex] then we have a reciprocating behaviour, less and less infected with time passing, this is ideal and it means the pandemic is waning.

However if, like in case with current pandemic, [tex]R_0\gt 1[/tex] then the behaviour is exactly the opposite, more and more get infected with time. The current pandemic had a highest [tex]R_0[/tex] of 6.49 with a mean of 3.28 and a median of 2.76.

That means at its heighest, 1 new infected person meant potentially 6 new infected people which meant 36 because each of them would probably infect which means [tex]216,1296,7776,46656,\dots[/tex].

So the main goal is to prevent [tex]R_0[/tex] from getting larger ie. minimization, that is why vaccination, masks, good hygiene.

Of course the model is much much more complex and parameterized.

The exponential model took a lot into account and came up with various prediction graphs of for example the next week.

The graphs served to the states to decide what to do next.

So in all, everything that you are witnessing was at some point just, math.

Hope this helps :)

Answer:

it was online math cause of the pandemic

Step-by-step explanation:

The course of Action that should be undertaken is ; ( II ) The government should generate more power

The power supply in an area can be affected by several factors and some of these factors can be natural disasters or man made factors . the effects of these factors can lead to a reasonable decrease in power supply and some of these factors includes;

WAPDA is not charged with going after power thieves, they are saddled with the responsibility of harnessing hydropower resources to produce/generate enough clean electricity Therefore this course of action is not valid

The correct course of action that will improve the power supply on state X is for the government to generate more power through its agencies like WAPDA.

Hence the right course of action is The government should generate more power

learn more : https://brainly.com/question/22239770

Answer:

Yes, the table represents a function.

Step-by-step explanation:

A function doesn't have multiple x values (inputs).

If the table were to have more than one 5 (or more than one 4 etc.) in the input column then it would not be a function.

Answer:

According to the graph the point (0, 4) is the maximum of the function.

So the domain:

The range:

Answer:

Question unclear

Step-by-step explanation:Your probally asking what times 8 gives us 80. If you are than 10!

Answer:

Here is your answer. HOPE THIS HELPS YOU! STAY BLESSED.

Answer:

28,21

Step-by-step explanation:

let the numbers be x and y

x+y=49

y=49-x

xy=588

x(49-x)=588

49x-x²=588

x²-49x+588=0

[tex]x=\frac{49 \pm \sqrt{49^2-4*1*588} }{2*1} \\=\frac{49 \pm \sqrt{2401-2352} }{2} \\=\frac{49 \pm\sqrt{49} }{2} \\=\frac{49 \pm 7}{2} \\=\frac{49+7}{2} ,\frac{49-7}{2} \\=28,21[/tex]

C: 10 L of the 20% solution

Let

x = amount of 8% solution

y = amount of 20% solution

The chemist wants to end up with a 12-L mixture, so

x + y = 12

x L of 8% solution contains 0.08x L of salt, and y L of 20% solution contains 0.2y L of salt. When combined, the resulting mixture should have a concentration of 18% salt, or 18% of 12 L = 2.16 L of salt, so

0.08x + 0.2y = 2.16

Solve for y :

x = 12 - y

0.08 (12 - y) + 0.2y = 2.16

0.96 - 0.08y + 0.2y = 2.16

0.12y = 1.2

y = 10