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?

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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.

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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]

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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:

(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

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)

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Answer:

the answer  to your question is 10

Step-by-step explanation:

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

Answer:

decimal form; 0.22222...

exact form; 2/9

Step-by-step explanation:

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.

Answer:

expected value is $4.5

Step-by-step explanation:

expected value is $4.5

Answer:

12.5

Step-by-step explanation:

x = 2.5, 5x = ?

5(2.5) = 5 x 2.5 = 12.5

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°

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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.

[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]

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)

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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:

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:

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:

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:

we need the full question

Answer:

x=2

9+2=11

6+2=8

8x11+88

Step-by-step explanation:

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]

[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

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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

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

[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]

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

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Answer: x = 0.75

Step-by-step explanation:

3x+x - 3 =0

4x - 3=0

4x = 3

x = 0.75

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

Answer:

B. 3.5

Step-by-step explanation:

I believe this is correct :')

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.

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