Element X is a radioactive isotope such that every 26 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 680 grams, how much of the element would remain after 19 years, to the nearest whole number?

[tex]\text{Let the number be x.}\\\\\text{According to the condition,}\\\\~~~~~4+2x=3x-8\\\\\implies 3x-2x = 4+8\\\\\implies x = 12\\\\\text{Hence, the number is 12.}[/tex]

Triangle EFG has vertices E(-2, 1), F(-1, 4), and G(3, 4). Graph the figure and its image after a clockwise rotation of 90° about vertex F. Then write the coordinates of triangle E'F'G'.

Answer:

B. 3.5

Step-by-step explanation:

I believe this is correct :')

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's evaluate ~

[tex]\qquad \sf  \dashrightarrow \:2x(2x - 3) - 3x(x - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \:(2x \sdot2x) - (2x \sdot3) - (3x \sdot x) - (3x \sdot - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {x}^{2} - 6x- 3 {x}^{2} - ( - 6x)[/tex]

[tex]\qquad \sf  \dashrightarrow \:4 {x}^{2} - 3 {x}^{2} - 6x + 6x[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} [/tex]

I hope the Step were clear to you ~

Answer:

x²

Step-by-step explanation:

Given: 2x(2x - 3) - 3x(x - 2)

Distributive Property: a(b + c) = ab + ac

1. Distribute

⇒ 2x(2x) + 2x(-3) + -3x(x) + -3x(-2)

⇒ 4x² - 6x - 3x² + 6x

2. Combine like terms

⇒ 4x² - 3x² - 6x  + 6x

⇒ x²

Learn more about the distributive property here:

brainly.com/question/27543580

brainly.com/question/27445861

Answer:

expected value is $4.5

Step-by-step explanation:

expected value is $4.5

Answer: 20x  + 20

Step-by-step explanation:

    We will distribute the four into the expressions to expand, then we will simplify.

   Given:

4(2x + 3) + 4(3x + 2)

   Distribute:

8x + 12 + 12x + 8

   Combine like terms with addition:

20x + 20

                   20x  + 20

Based on the preferred dividends, the dividends for preferred and common stock in each year are:

Preferred stock dividends:

Common stock dividends:

Preferred shares have a specific dividend, and as these are cumulative shares, the dividends that are not paid in one year, will be paid in the next.

Dividends per year:

= 20,000 x 2% x 150

= $60,000

20y1 dividend per share:

= 60,000 / 20,000

= $3.00 per share

20y2 dividend per share:

= 24,000 / 20,000

= $1.20 per share

20y3 dividend per share:

The remaining dividend from 20y2 will have to be paid here:

= (60,000 + (60,000 - 24,000)) / 20,000

= 96,000 / 20,000

= $4.80 per share

Preferred dividends are paid first:

Common dividends are:

= (Amount distributed as dividends - Preferred dividends) / Number of common shares

In 20y1:

= (120,000 - 60,000) / 50,000

= $1.20

In 20y2:

= (45,000 - 45,000) / 50,000

= $0 per share

In 20y3:

= (180,000 - 96,000) / 50,000

= $1.68 per share.

Find out more on preferred dividends at https://brainly.com/question/1416151.

#SPJ1

Answer:

decimal form; 0.22222...

exact form; 2/9

Step-by-step explanation:

The lines that represent the following system of linear equations.

2s +1.5y = -60

2s + y = -50

will intersect at (-15, -20)

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Slope is a ratio of change in y-coordinate w.r.t. change in x-coordinate. The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.

Given,

System of linear equations

2s +1.5y = -60

2s + y = -50

After plotting both the graphs we can see that, point of intersection is  (-15, -20)

Hence, The point of intersection is (-15, -20)

To know more about Lines check:

https://brainly.com/question/17188072

#SPJ1

Answer:

x=2

9+2=11

6+2=8

8x11+88

Step-by-step explanation:

Answer:

the answer  to your question is 10

Step-by-step explanation:

if you divide 40 by 25% then you will get 10

The median is 6.5.

The first quartile is 5.

The third quartile is 8.

The interquartile range is 3.

The numbers in the dot plot are: 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 22

Median is the number in the middle of the dataset.

Median = 1/2 ( n + 1)

1/2 x 21 = 11.5th number = (6+ 7) / 2 = 6.5

First quartile = 1/4 x (n + 1)

1/4 x 21 = 5.25th number = 5

Third quartile = 3/4 x (n + 1)

3/4 x 21 = 15.75th number = 8

Interquartile range = 8 - 5 = 3

Please find attached the dot plot. To learn more about interquartile range, please check:  https://brainly.com/question/3966385

#SPJ1

Answer:

12.5

Step-by-step explanation:

x = 2.5, 5x = ?

5(2.5) = 5 x 2.5 = 12.5

The attached diagram represents the tree diagram for three consecutive mornings.

The probability of arriving on time is given as:

P(On Time) = 65%

Assume that the bus would definitely show up.

Then it means that the event is a binomial event and the possible outcomes are:

On Time and Late

The above means that the number of possible outcomes is 2.

For three consecutive mornings, the total outcome is:

Total = 2³

Evaluate

Total = 8

This means that the tree diagram would have 8 outcomes

Next, we draw the tree diagram (see attachment)

Read more about tree diagrams at:

https://brainly.com/question/9178814

#SPJ1

Answer:

angle A is 63 degrees,

angle B is 57 degrees

Step-by-step explanation:

first, let's create the equation. Pretty simple, because angles a and b become 120 degrees when added up, this this will become:

2x+3+2x-3=120

now, we make it simpler. In this case, just add up the numbers that we can add up. this eventually becomes:

4x=120

now, all we need to do is divide 120 by 4, which becomes 30. So, x=30.

substitute the 30 into the x in the original equation, and this becomes:

60+3+60-3=120

63+57=120

thus, angle A is 63 degrees, and angle b is 57 degrees.

Answer:

8

Step-by-step explanation:

[tex]P = \{3,6,9\}\\\\\text{Number of elements,}~ n = 3\\\\\text{Number of subset} = 2^n = 2^3 = 8[/tex]

Answer: x = 0.75

Step-by-step explanation:

3x+x - 3 =0

4x - 3=0

4x = 3

x = 0.75

Answer:

we need the full question

Answer:

x = 97

y = 83

Step-by-step explanation:

y = 83 (being the vertically opposite angle )

y + x = 180 (being co-interior angle)

or,

83 + x = 180

or,

x = 180 - 83

.•. x = 97

Hi student, let me help you out! :)

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

We are asked to find the solution to the inequality:

[tex]\star~\large\pmb{\cfrac{x}{9}+3 < 4}[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Step 1.

[tex]\star~\large\pmb{\cfrac{x}{9} < 4-3}[/tex]

[tex]\star~\large\pmb{\cfrac{x}{9} < 1}[/tex]

Step 2.

[tex]\star~\large\pmb{\cfrac{x}{9}\times9 < 1\times9}[/tex]

Notice that on the left, the 9s cancel, and we're left with x.

Step 3.

[tex]\star~\large\pmb{x < 9}[/tex]

This is the solution.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

x < 9

Step-by-step explanation:

Given:  

[tex]\dfrac{x}{9} + 3 < 4[/tex]

1. Subtract 3 from both sides of the inequality

[tex]\dfrac{x}{9} + 3 - 3 < 4 - 3\\\\\implies\dfrac{x}{9} < 1[/tex]

2. Multiply both sides of the inequality by 9

[tex]9\left(\dfrac{x}{9}\right) < 1(9)\\\\\implies x < 9[/tex]

Learn more about finding the solution of an inequality:

brainly.com/question/27834517

Answer:

(5√x) / [(3√x)-4]

Step-by-step explanation:

You cannot solve this because 5, 3, and 4 are not factors/multiples of one another

I simplified it though

when the exponent is 1/2, it is the same as taking the square root of something

5x^1/2 is the same as 5√x

3x^1/2 is the same as 3√x

Answer:

A process where you must look for terms that have identical variable parts and then combine their coefficients

Step-by-step explanation:

Combining like terms is adding or subtracting terms that have the same variable parts.

Answer: A process where you must look for terms that have identical variable parts and then combine their coefficients

Answer:

A because the volume of the adult softball is 28.7309120146 inches and the youth softball is 22.4492975038 inches and when u subtract them u get about 6.3 cubic inches :)

Step-by-step explanation:

:)

Answer: IT A!

Step-by-step explanation:

Answer:  The probability of picking a black bead is 4/7, because there are 4 black beads out of seven.  But if you took the first black bead out of the equation then the probability is now 3/7.

Answer:

360 degrees

Step-by-step explanation:

The sum of the INTERior angles of a pentagon equal

      (n-2)(180) = 540

          each angle is then   540/5 = 108

               each is a supplementary angle to the exterior angle

                       so EACH exterior angle is    180 - 108 = 72

         there are 5 of these    5 * 72 = 360 degrees

Problem 9

r+h = 9

SA = 2*pi*r^2 + 2*pi*r*h = 54pi

2*pi*r^2 + 2*pi*r*h = 54pi

2pi*r(r + h) = 54pi

r(r+h) = 27

r(9) = 27

9r = 27

r = 27/9

r = 3

r+h = 9

h = 9-r

h = 9-3

h = 6

Answers:  r = 3 and h = 6 are the radius and height respectively.

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

Problem 10

d = diameter = 68 mm

r = radius = d/2 = 68/2 = 34 mm

SA = surface area of a sphere

SA = 4*pi*r^2

SA = 4*pi*34^2

SA = 4264pi

Answer:  4264pi square mm

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

Problem 11

Plug V = 3000 into the sphere volume formula and isolate r.

V = (4/3)pi*r^3

3000 = (4/3)pi*r^3

(4/3)pi*r^3 = 3000

4pi*r^3 = 3*3000

4pi*r^3 = 9000

r^3 = 9000/(4pi)

r = cube root(  9000/(4pi)  )

r = ( 9000/(4pi) )^(1/3)

r = 8.947002 approximately

Now we can determine the surface area of this sphere.

SA = 4pi*r^2

SA = 4*pi*( 8.947002 )^2

SA = 1005.923451

Answer:  1005.923451 square feet approximately

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

Problem 12

We'll follow the same idea as problem 11, but in reverse.

SA = 4*pi*r^2

400pi = 4pi*r^2

r^2 = (400pi)/(4pi)

r^2 = 100

r = sqrt(100)

r = 10

Luckily we get a nice whole number for the radius r. Use it to find the volume.

V = (4/3)*pi*r^3

V = (4/3)*pi*10^3

V = (4000/3)pi

Answer:   (4000/3)pi   cubic inches exactly

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

Problem 13

The diagram is missing. I don't have enough info to be able to answer.

Answer:

x = √41  which is 6.40 to the nearest hundredth.

Step-by-step explanation:

x^2 = 4^2 + 5^2      (By the Pythagoras theorem)

x^2 = 16 + 25 = 41

x = √41.

The measure of the angle shown is 280°

From the question, we are to determine the measure of the angle shown

For the given protractor,

The measure between any two lines is 10°.

Also, there are 10 tick marks between any two lines.

∴ 15 tick marks will have a measure of 15°

Then,

The measure of a protractor showing an angle going through the fifteenth tick mark after two hundred sixty five degrees will be

265° + 15° = 280°

Hence, the measure of the angle shown is 280°

Learn more on Calculating angles here: https://brainly.com/question/15132158

#SPJ1

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases} \\\\\\ A=500\left(1+\frac{0.06}{1}\right)^{1\cdot 15}\implies A=500(1.06)^{15}\implies A\approx 1198.28[/tex]