A 5kg sample of plutonium-239 has a half-life of 21,400 years by emitting a 5.157 mev (million or mega electron volts) alpha particles. assume that the rate of decay is constant, how long will it take for the sample to degrade to 4.5kg?

Answer:

[tex]V=12\pi\:\text{units}^3[/tex]

Step-by-step explanation:

[tex]\displaystyle V=\frac{\pi r^2h}{3}\\ \\V=\frac{\pi (3)^2(4)}{3}\\\\V=\pi(3)(4)\\\\V=12\pi[/tex]

The side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.

The length of the side of the square and the height will be

6.98 cm and 13.96 cm.

Pyramid is a three dimensional Structure ,having square , rectangle , hexagonal base , the faces for a square pyramid and hexagonal pyramid are triangle meeting at one point .

It is given in the question that

A toy is being constructed in the shape of a pyramid.

the maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters.

the height of the toy is double the side length

Let us assume the side length to be x

and therefore the height of the toy is 2x

The surface area of the toy is given = 250 sq.cm

First let us consider for a square base

The surface area of a square pyramid is given by

[tex]\rm A = a^2 + 2 a\sqrt {\dfrac{a^2}{4}+h^2}[/tex]

Here a is the side length which x for us and h = 2x

[tex]\rm 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+(2x)^2}\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+4x^2}\\\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{17 x^2}{4}}\\\\\\250 = x^2 + x^2 \sqrt{17}\\\\\\250 = 5.132 x^2\\\\\\48.71 = x^2\\\\\\x = 6.98 cm .[/tex]

Therefore the length of the side of the square and the height will be

6.98 cm and 13.96 cm.

For a hexagonal base

The total surface area is given by

[tex]A =6ah + 3 \sqrt{3}a^2\\\\\\A = 6 \times x \times 2x + 3\sqrt{3} (x)^2\\\\250= 12x^2 + 3\sqrt{3} x^2\\\\\\250 = 17.196 x^2\\\\\\14.54 = x^2\\\\x = 3.81 cm\\\\[/tex]

Therefore the side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.

To know more about Pyramid

https://brainly.com/question/13057463

#SPJ1

Check the picture below.

now, we're making an assumption that, the two blue shaded region are equal in shape, and thus if that's so, that area above the 14 is 6 and below it is also 6, 14 + 6 + 6 = 26.

so hmm if we simply get the area of the trapezoid and subtract the area of the yellow triangle and the area of the cyan triangle, what's leftover is what we didn't subtract, namely the shaded region.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ h=15\\ a=14\\ b=26 \end{cases}\implies A=\cfrac{15(14+26)}{2}\implies A=300 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\stackrel{trapezoid}{300}~~ - ~~\stackrel{yellow~triangle}{\cfrac{1}{2}(26)(9)}~~ - ~~\stackrel{cyan~triangle}{\cfrac{1}{2}(15)(6)}} \\\\\\ 300~~ - ~~117~~ - ~~45\implies 138\qquad \textit{blue shaded area}[/tex]

The values of x in f(x) = 3|x - 2| + 6 when f(x) = 18 are 6 and -2

The function is given as:

f(x) = 3|x - 2| + 6

The value of f(x) is

f(x) = 18

So, we have:

3|x - 2| + 6 = 18

Subtract 6 from both sides

3|x - 2| = 12

Divide both sides by 3

|x - 2| = 4

Remove the absolute bracket

x - 2 = 4 or x - 2 = -4

Add 2 to both sides

x = 6 or x = -2

Hence, the values of x are 6 and -2

Read more about absolute values at:

https://brainly.com/question/729268

#SPJ4

Answer:

▪︎ Domain: all real numbers (x can be any number)

▪︎ Range: y <= 0 (y can never become greater than 0 bc the vertex of this function (highest point) is (0,0))

Answer:

$1320

Step-by-step explanation:

4%=0.04

Intrest = 0.04x8

Intrest = 0.32

Intrest = 1000x0.32

Intrest = 320

Then add 1000+320=1320

Answer:

RT = 26

Step-by-step explanation:

Based on the figure we can say :

Scale factor :

Hence, as the proportions are the same :

The triangle ABC and RST will be similar triangles. Then the length of RT will be 26 units.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If the two triangles are similar, the ratio of the corresponding sides will be constant.

The triangle ABC and RST will be similar triangles.

RT / 13 = 24 / 12

      RT = 26

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ5

Applying the Pythagorean theorem, the distance between the Earth's horizon and the satellite would be 5756.70 miles.

To calculate the distance from the satellite to the Earth's horizon, it is necessary to use the Pythagorean Theorem as follows:

We must identify the data we have:

To calculate the distance from the satellite to the Earth's horizon, we must first establish the distance from the center of the Earth to the satellite, for this we calculate the radius of the Earth and add the distance to the satellite:

With these data we can draw an imaginary triangle from the center of the Earth, one of its legs would be the distance between the center of the Earth and the satellite, the other leg would be the distance between the center of the Earth and the Earth's horizon (at 90° to the other leg).

Now, to identify the distance between the horizon and the satellite, we apply the Pythagorean Theorem:

According to the above, the distance between the satellite and the horizon would be 5756.70 miles.

Learn more about Pythagorean Theorem in: https://brainly.com/question/15190643

#SPJ1

Answer:

18

Step-by-step explanation:

science 19 does not fit into 12, you would do 123/19 and the closes would be 19*6 which would get you 114 then you do 123-114 which is 9 then you bring down the 4 then it would be come 94 then you do 19*4 which would be 76 then you subtract 94 by 76 which would get you 18 and with nothing left you bring down, the remainder would be 18

Answer:

See below ~

Step-by-step explanation:

Finding the x-intercepts :

Finding the vertex :

Answer:

2nd option, (6x + 8)(x - 1) = 0

Step-by-step explanation:

Answer:

[tex](6x+8)(x-1)[/tex]

Step-by-step explanation:

We can separate the 2x into -6x + 8x. Then this will give us [tex]6x^2 - 6x + 8x - 8 = 0[/tex]. Now we can factor out a 6x and an 8 to give us [tex]6x(x-1) + 8(x-1) = (6x+8)(x-1)[/tex] by the distributive property.

Hope this helps! :)

Step-by-step explanation:

[tex] = 6 \times \frac{4}{15} \\ [/tex]

[tex] = \frac{6}{1} \times \frac{4}{15} \\ [/tex]

[tex] = \frac{24}{15} \\ [/tex]

Change into lowest term ....

[tex] = \frac{8}{5} \\ [/tex]

Change into mixed....

[tex] = 1 \ \frac{3}{5} \\ [/tex]

Using the z-distribution, the confidence coefficient for the 90% confidence interval is of 1.645.

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.95[/tex], and the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

the mean numbers of point scored is greater than 12 points(C.)

Answer:

Find the area of the triangle side, then multiply by the length of the prism.Area of triangle = 1/2 x height x baseArea  = 1/2 x 2 x 3 = 3 square cmVolume = 3 x 4 = 12 cubic cm.Answer is A)

Step-by-step explanation:

Answers:

=======================================================

Part (a)

Let's find the distance from point D to point E.

In other words, this will compute the length of segment DE.

[tex]D = (x_1,y_1) = (0,-6) \text{ and } E = (x_2, y_2) = (3,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-3)^2 + (-6-1)^2}\\\\d = \sqrt{(-3)^2 + (-7)^2}\\\\d = \sqrt{9 + 49}\\\\d = \sqrt{58}\\\\d \approx 7.6158\\\\[/tex]

Segment DE is roughly 7.6158 units long.

Let's repeat these steps to find the length of segment EF.

[tex]E = (x_1,y_1) = (3,1) \text{ and } F = (x_2, y_2) = (-2,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-2))^2 + (1-1)^2}\\\\d = \sqrt{(3+2)^2 + (1-1)^2}\\\\d = \sqrt{(5)^2 + (0)^2}\\\\d = \sqrt{25 + 0}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

Segment EF is exactly 5 units long.

Lastly, we'll compute the length of segment FD.

[tex](x_1,y_1) = (-2,1) \text{ and } (x_2, y_2) = (0,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-0)^2 + (1-(-6))^2}\\\\d = \sqrt{(-2-0)^2 + (1+6)^2}\\\\d = \sqrt{(-2)^2 + (7)^2}\\\\d = \sqrt{4 + 49}\\\\d = \sqrt{53}\\\\d \approx 7.2801\\\\[/tex]

Segment FD is about 7.2801 units long.

This is close to the length of DE, but not quite.

To recap, we found these segment lengths:

As you can see, all three sides are different lengths. Therefore, triangle DEF is scalene.

----------------------------------

For part (b), follow the same template as part (a).

I'll be skipping the steps.

This is what you should get for the lengths of triangle TRI

Segments TR and IT are the same length (both exactly [tex]\sqrt{37}[/tex] units long), which means triangle TRI is isosceles.

-----------------------------------

For part (c), I'll also be skipping steps.

Here are the lengths you should find

All three lengths are different, making this triangle scalene.

The radius of the cone is 7 feet

The given parameters are:

Surface Area, A = 216π

h = 8/3r

The surface area of a cone is:

[tex]A = \pi r(r + \sqrt{h^2 + r^2})[/tex]

So, we have:

[tex]216\pi = \pi r(r + \sqrt{(8/3r)^2 + r^2})[/tex]

Factor out r

[tex]216\pi = \pi r(r + r\sqrt{(8/3)^2 + 1})[/tex]

Evaluate the exponent

[tex]216\pi = \pi r(r + r * 2.85)[/tex]

Evaluate the sum

[tex]216\pi = \pi r(3.85r)[/tex]

Divide both sides by pi

[tex]216 = 3.85r^2[/tex]

Divide both sides by 3.85

[tex]56.10 = r^2[/tex]

Take the square roots of both sides

r = 7 (approximately)

Hence, the radius of the cone is 7 feet

Read more about cone at:

https://brainly.com/question/6613758

#SPJ4

Answer:

The radius is about 9 feet.

Hope this helps!

Step-by-step explanation:

Answer:

I think 24.

Step-by-step explanation:

Answer:

$5,600

Step-by-step explanation:

1. divide 200 by 2 (this gives you the rate for 1 hour of book sales)

2. multiply the answer by 8 hours

3. multiply your answer (800) by $7

4. You solved it! $5,600 is how much money a company would earn if they sold books for 8 hours.

Answer:

Step-by-step explanation:

Step 1

Find how much books the company sells in 8 hours of selling books

To find this, we see that 2 hours = 200 books. Also, 8/2=4. That means that if we multiply 200 by 4, then we will get our total amount of books sold in 8 hours.

200x4=800

800 books sold in 8 hours

Step 2

Find how much money does 800 books equal to get FINAL ANSWER

To find this, we need to know the price of 1 book, the price of one book is 7$, that means that if we do 7$x800books, then we get our FINAL ANSWER

7x800=$5,600

Answer:

Answer:

People can not be in fractions

Answer:

[tex]r = 2km[/tex]

Step-by-step explanation:

Area =

[tex]area = \pi {r}^{2} [/tex]

[tex]12.56 = 3.14 \times {r}^{2} [/tex]

[tex] {r}^{2} = \frac{12.56}{3.14} [/tex]

[tex] {r}^{2} = 4[/tex]

[tex]r = \sqrt{4} [/tex]

[tex]r = 2km[/tex]

One benefit of attending trade school after high school is to learn practical skills.

A trade school is one which focuses on practical knowledge along with theoretical concepts. In a trade school, they will teach you about the end use of what you are studying.

They provide you with proper practical knowledge in a particular field like welding, machining, forging etc. It is very important to have practical skills along with theoretical subject knowledge.

It increases your chances of being selected by any company and also gives you more opportunities to learn.

Therefore benefit of attending trade school after high school is to learn practical skills.

To know more about trade schools follow

https://brainly.com/question/17727564

#SPJ1

Answer: c. to learn a practical skill

Step-by-step explanation:

Answer:

So, 5, 20, 45, 80,...5N2

Step-by-step explanation:

Divide the sequence by 5 and the answer becomes very obvious:

EX: 1, 4, 9, 16,...N2

              - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\diamond\large\textsf{\textbf{\underline{Given question:-}}}[/tex]

        -0.5=-m/6. what is m?

[tex]\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

    ❖  First, multiply both sides by 6 to get rid of the fraction:-

 ▪︎ -0.5*6=-m/6*6

On the RHS, the 6's cancel:-

◆-0.5•6=-m

➪  [tex]\it{-3=-m}[/tex]

 ➪ [tex]\it{3=m}[/tex]

❒So we conclude that the value of m is 3.

          - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Answer:

m = 3

Step-by-step explanation:

⇒ -0.5 = - m/6

Divide both sides by -1.

⇒ -0.5/-1 = -m/(6 × -1)

⇒ 0.5 = m/6

Multiply both sides by 6.

⇒ 0.5 × 6 = m/6 × 6

⇒ m = 3

Answer:

-18a⁸

Step-by-step explanation:

-2a²(-3a³)²
-2a²*9a⁶ (Opening the square)
-18a⁸

Answer/Step-by-step explanation:

Given:

A gas station offers a lucky draw to customers. Each time you spend more than $20 on gas, you can make a draw to win a prize. The probability of winning a prize is 1/12 suppose you buy gas 4 times.

To Find:

what is the probability of you winning a prize each time?

Solve:

Since, it given that you buy gas 4 times. Thus that means:

1/12 × 1/12 × 1/12 × 1/12 or  1/12⁴

Now solving it:

1/12 × 1/12 × 1/12 × 1/12 = 1/20736

Which also means (0.0048%) in decimal form since, 1 divide by 2076 equal to 0.0048%

Kavinsky

Answer:

54.59

Step-by-step explanation:

carry the 10 over and 1-.41 is .59

Answer:

m = -1/3
b = 0
y = -1/3x

Step-by-step explanation:

The y-intercept is 0, so b is just 0. The slope of the line is 1/3 but it is decreasing not increasing, so it is negative. Then using the slope formula:
y = mx + b

y = -1/3x

Slope:-

Equation in point slope form

b=0