Element X is a radioactive isotope such that every 81 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 1800 grams, how much of the element would remain after 28 years, to the nearest whole number?

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2350\\ r=rate\to 35\%\to \frac{35}{100}\dotfill &0.35\\ t=years\dotfill &4\\ \end{cases} \\\\\\ A=2350(1 - 0.035)^{4}\implies A=2350(0.965)^4\implies A\approx 2037.87[/tex]

Answer:

n³ ≠ 108

Step-by-step explanation:

1/3 ≠ 18n² * 2n

1/3 ≠ 18 * n² * 2 * n

1/3 ≠ 18 * 2 * n² * n

1/3 ≠ 36n³

Cross multiply,

1 * n³ ≠ 3 * 36

n³ ≠ 108

Hence simplified.

Answer:

ok

Step-by-step explanation:

Δ = (-5)² - 4*1*6 = 25 - 24 = 1 = 1²

x' = (5 + 1) / (2*1) = 6/2 = 3

x" = (5-1) / (2*1) = 4/2 = 2

2 solutions : 2 and 3

x² - 5x + 6 = (x - 2) (x - 3)

well, let me not bore you to death on how we test it and test it.

[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=5-sin(11\theta )\implies (-r)=5-sin[11(-\theta )]\implies -r=5-sin(-11\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=5-\stackrel{\downarrow }{[-sin(11\theta )]}}\implies\implies r=-5-sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=5-sin(11\theta )\implies r=5-sin[11(-\theta )]\implies r=5-sin(-11\theta ) \\\\\\ r=5-[-sin(11\theta )]\implies r=5+sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underline{\textit{testing for symmetry to the pole}\qquad \qquad r=-r} \\\\\\ r=5-sin(11\theta )\implies -r=5-sin(11\theta )\implies r=-5+sin(11\theta )\qquad \textit{no dice}[/tex]

so the symmetry tests didn't pass, notice the picture below though, looks a bit deceiving, it looks as if it'd have π/2 symmery, but it doesn't show in the test.

Answer:

first you distribute the five making it 10x-30+20=10

second you combine like terms making it 10x-10=10

third you isolate the variable making it 10x=20

Finally you divide both terms by ten giving you x=2 as your answer.

Answer:

60%

Step-by-step explanation:

36= heads

36/60= 60%

Answer:

60x24x36=51,840%

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

The function of the seat’s height from the ground level is given as,

[tex]h(t)=-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1[/tex]

Here, t denotes the time.

(a) The height will be maximum or minimum when the derivative of the function of height is equal to zero.

[tex]\begin{aligned}h^{\prime}(t) &=0 \\\frac{d}{d t}\left(-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1\right) &=0 \\-1.1 \times \frac{2 \pi}{3}\left(-\sin \left(\frac{2 \pi}{3} t\right)\right) &=0 \\t &=0,1.5\end{aligned}[/tex]

The height of the seat at time t = 0 s can be determined as,

[tex]\begin{aligned}h(0) &=-1.1 \cos \left(\frac{2 \pi}{3}(0)\right)+3.1 \\&=2 \mathrm{ft}\end{aligned}[/tex]

Therefore, the maximum height of the swing is 4.2 ft and the minimum height of the swing is 2 ft.

(b) The height of the swing is given as,

[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\t &=0.7 \mathrm{~s}\end{aligned}[/tex]

Therefore, the first time after t = 0 s that the swing’s height of 3 ft is 0.7 s.

(c) The height of the swing is given as,

[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\\frac{2 \pi}{3} t &=1.47976+2 \pi \\t &=3.7 \mathrm{~s}\end{aligned}[/tex]

Therefore, the second time after t = 0 s that the swing’s height of 3 ft is 3.7 s.

Answer:

Formula for area of circle;

A = π[tex]r^{2}[/tex]

Where 'π' represents pi (22/7 or 3.14), and 'r' is the radius which is being squared.

Plug in your values:-

A = π[tex]r^{2}[/tex]

A = 3.14(2.5^2)

A = 3.14(6.25)

A = 19.625 meters is your answer.

Answer:

5(c+3)=85

divide both sides by 5

c+3=17

taking 3 to the other side gives us -3

c=17-3

c=14

Answer:

What shape is the object in question?

Function: y = 2x²-5

Find y-intercept:

y = 2(0)²-5

y = -5

Find x-intercept:

2x²-5 = 0

2x² = 5

x² = 2.5

x = ±√2.5

x = -1.5811 , 1.5811

Graph plotted:

Answer:

Vertex and y-intercept (0, -5)

x-intercepts (-1.58, 0)  (1.58, 0)

opens upwards

other plot points: (-2, 3) (-1, -3) (1, -3) (2, 3)

Step-by-step explanation:

The graph is not quite correct - it's a little too narrow and doesn't go through the points on the graph.

The y-intercept is when x = 0:

f(0) = 2(0)² - 5

      = - 5

Therefore, the y-intercept is at (0, -5)

We also know that the y-intercept is the vertex since the equation is in the form [tex]f(x)=ax^2+c[/tex]

The x-intercepts are when f(x) = 0:

[tex]\implies 2x^2 - 5 = 0[/tex]

[tex]\implies x^2 =\dfrac52[/tex]

[tex]\implies x=\pm1.58113883...[/tex]

As the leading coefficient is positive, the parabola opens upwards.

Finally, input values -2 ≤ x ≤ 2 to find plot points:

(-2, 3)

(-1, -3)

(0, -5)

(1, -3)

(2, 3)

Answer:

on k12 im pretty sure its 90

Step-by-step explanation:

there is 360 minutes and between the 37 and 41 (this took me a while ) then you should get 90!!!!! hope this helped

Answer:

75.062

Step-by-step explanation:

just add and multiply then remember that 1/100 or 1/1000 is just 0.001 or 0.01

Answer:

5/8

Step-by-step explanation:

because 1 minus 3/8 is 5/8

Answer:

113 ft²

Step-by-step explanation:

π = 3.14
r = 6

Use the formula for the area of a circle:
A = πr²
A = 3.14*6²
A = 3.14*36
A = 113.04
A = 113
Hope this helps :)

Answer:

Area = 113 ft²

Step-by-step explanation:

The formula to find the area of a circle is:

Area = π × r²

r is the radius that can be found by taking half of the diameter.

r = [tex]\frac{12}{2}[/tex] = 6

Area = π × 6²

Area = π × 36

Area = 113.09 = 113 [ to the nearest whole number ]

Answer:

Triangle JLK congruent to Triangle RTS is the only true statement

Step-by-step explanation:

AngleJKL is not corresponding to AngleRTS because AngleRTS is a right angle and AngleJKL is not.

The triangles are congruent by HL because one leg and the hypotenuse are congruent.

Triangle congruence can be determined so the third statement is incorrect.

TR is not congruent to KJ. TR=3.7 and KJ=4.5

Answer:

1000cm

Step-by-step explanation:

there are 100cm in a meter. so we multiply 10 by 100 to get the amount of centimeters in 10 meters which is 1000cm

Answer: There Are 1000 Centimeters(Cm) In 10 Meters(M)

The order of investment options from least to greatest risk is:

A B rated bond is considered safer than the rest because there is a high chance that the owners of the bond will redeem it. Property is not very risky but can be susceptible to market shocks.

Speculative stock is the third riskiest because its prices are prone to fluctuation. Starting a business is by far the riskiest because a lot of new businesses fail.

Find out more on risky investments at https://brainly.com/question/25219850.

Answer:

B-rated bond

property

starting a business

speculative stock

Step-by-step explanation:

The missing length is 18

Using Pythagorean rule

Hyp^2 = Opp^2 + adj^2

Opp^2 = hyp^2 - adj^2

Opp^2 = 30^2 - 24^2

Opp^2 = 900 - 576

Opp^2 = 324

Opp = sqrt ( 324 )

Opp = 18

[tex]\text{Let it be x percent}\\ \\\dfrac 14 \times x\% = \dfrac 15\\\\\\\implies\dfrac 14 \times \dfrac x{100} = \dfrac 15\\ \\\\\implies x = \dfrac{400}{5} = 80\\\\\\\text{Hence the answer is}~ 80\%[/tex]

Answer: 6

Step-by-step explanation:

Because you have to multiply then remove the fraction and set equal to 0 and solve for x which I’m pretty sure gives u 6

Step-by-step explanation:

the ratio of the pool lengths is 3/5.

that means for every 3 meters of length on Shantel's pool, there are 5 meters of length on Juan's pool.

it the other way around : to get to the size of Shantel's pool, every 5 meters of length on Juan's pool are converted to 3 meters.

x = length of Juan's pool

x × 3/5 = 30

3x = 150

x = 50 meters

you see the relationship ?

3/5 = 30/50 = 300/500 = ...

but it is true for any factor

3/5 = 15/25 = 24/40 = 6/10 = ...

once you see the factor for one part of the ratio, you know there is the same factor for the other part (or parts) of the ratio. otherwise the ratio would not stay the same and keep the relationship.

The dimensions of the rectangle that would have a value of 14/32 inches square are a length of 2/16 and a width of 31/2 inches.

A rectangle is a 2-dimensional quadrilateral with four right angles that has a value of 360 degrees. It has two diagonals that bisect each other.

Area of a rectangle = length x width

2/16 x 7/2 = 14/32

To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449

Answer:

the answer in the question mark that was in the green box ???

Answer:

independent - number of hours (h)

dependent - the score (s)

Step-by-step explanation:

[tex]m+m+m+m=(1+1+1+1)m=4m[/tex]