Use the following half-life graph to answer the following question:

A graph titled half-life graph of a radioactive isotope is shown with mass remaining on the y axis from 0 to 60 grams and time on the x axis from o to 6 minutes. A curve connects the points 0, 50 and 1, 25 and 2, 12.5 and 3, 6.25 and 4, 3.125 and 5, 1.5625.

The graph is attached.

What is the mass of the radioactive isotope remaining at 2.0 minutes? (5 points)


A. 25.0 mg

B. 12.5 mg

C. 6.25 mg

D. 3.13 mg

Use The Following Half-life Graph To Answer The Following Question:A Graph Titled Half-life Graph Of

Answers

Answer 1

Answer:

The correct answer is 12.5.

Step-by-step explanation:

When looking at the x axis, you locate the 2. After 2 minutes, the point connects at (2,12.5). Therefore, the correct answer is 12.5.

Answer 2

Answer:

At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.

Step-by-step explanation:

To get the answer of this question we will solve this further with the help of the equation [tex]A_{t}=A_{0}e^{-kt}[/tex]

where k = decay constant

t = time for decay

[tex]A_{0}[/tex] = Initial quantity taken

From the graph attached we can say that 50 mg of a radioactive element remained half in 1 minute.

So the equation becomes

[tex]50=25e^{-k(1)}[/tex]

Now we take natural log on both the sides of the equation

ln50 = ln[25.[tex]e^{-k}[/tex]

3.912 = ln25 + [tex]ln(e^{-k})[/tex]

3.912 = 3.219 + (-k)lne

3.912 - 3.219 = -k [since lne = 1]

0.693 = -k

k = -0.693

Now we will calculate the remaining quantity of the element after 2 minutes

[tex]A_{t}=50.e^{-(0.693)(2)}[/tex]

              = [tex]50.e^{-1.386}[/tex]

              = [tex]\frac{50}{e^{1.386}}[/tex]

              = [tex]\frac{50}{3.9988}[/tex]

              = 12.50 mg

Now we confirm this value from the graph.

At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.


Related Questions

Julian has worked for a beverage company for the last five years. He currently earns $12.00 an hour and $16.00 an hour overtime for any additional hours he works past his eight hour workday. On his busiest day, he earned $128.00. How much overtime did he work? Let h = the number of overtime hours.

Answers

For the first 8 hours he makes $12.00 per hour.

$12.00 * 8 = $96.00

Now you have $128.00 = 16.00h + $96.00

Subtract 96 from each side:

32 = 16h

Divide both sides by 16:

h = 2

He worked 2 hours of overtime.

Kevin ate 2 slices of cake. Ben ate 1 slice. If Kevin ate 2/6 of the cake and all the slices are the same size, what fraction of the cake was eaten in total

Answers

1/2 of the cake was eaten

1+2=3. 3/6=1/2

All the slices are the same size

Can I get an explanation please.

Answers

Answer:

The correct option is letter D.

Step-by-step explanation:

We have the following expression:

sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)

We now that sqrt(a*b) = sqrt(a)sqrt(b)

Applying this rule, we have:

sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)

sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y)

Also we know that a*sqrt(b) = sqrt(b*a^2)

Applying this we have:

sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y) = sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3)

Then the result is:

sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3) = sqrt(y^3) = y*sqrt(y)

The correct option is letter D.

Claire purchases a new dress for the prom. The dress is priced $160, but it is on sale for 30% off. Claire's aunt works at the store and can give her an additional 10% off. If the sales tax is 7.5%, how much does Claire pay for the dress? a. $93.24 b. $103.20 c. $108.36 d. $120.40

Answers

The dress is originally 160$, but we take 30% off which is that same as .3 .

To find 30% or .3 of 160 we multiply 160 by .3 which gets us 48.

48 is 30% of 160 so to find the new price of the dress we need to subtract

160 - 48 = 112. The new price of the dress is 112$.

Since Claire's aunt works at the store Claire will get an additional 10% off from the "new" price which is 112$.  10% is also .1, so we will multiply 112 by .1 which equals 11.20.

As 10% of 112 is 11.20 so we will subtract 11 dollars and 20 cents from the price. 112 - 11.20 = 100.80$.

For sales tax we will do the same thing, multiply 100.80 by .075 which equals 7.56. This time since we are ADDING sales tax, we will add 100.80 and 7.56 rather than subtract. 100.80 + 7.56 = 108.36.

Claire will be paying 108.36$ for the prom dress.

Answer:

c

Step-by-step explanation:

The box plots below show student grades on the most recent exam compared to overall grades in the class:





Which of the following best describes the information about the medians?
a. The exam outlier at 60 makes the IQR narrower and the median higher.
b. The class data is more evenly spread, which pulls its median down.
c. The class median is lower than the exam median.
d. The class Q3 is higher than the exam Q3.

Answers

i dunno man, B looks about right.

Answer: c. The class median is lower than the exam median.

Step-by-step explanation:

the median is at a lower point on the number line, its to the left of the exam, so that means its lower

Need help,

plezz

What is the length of the major axis of the conic section shown below?

(x-3)^2/49 + (y+6)^2/100=1

A. 20

B. 10

C. 14

D. 7

Answers

Answer:

A. 20.

Step-by-step explanation:

The denominators 49 and 100  are the squares of 1/2 of the lengths of the minor and major axis.  The standard form is x^2/a^2 + y^2/b^2 = 1  so

a = 2 * √49 and b = 2 * √100.

The length of the major axis is therefore    2* √100

= 2 * 10

= 20 (answer).

Answer:  A. 20

Step-by-step explanation:

For the general equation of ellipse :-

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

If a > b , then the length of major axis = 2a

If b> a , then the length of major axis = 2b

The given equation : [tex]\dfrac{(x-3)^2}{49}+\dfrac{(y+6)^2}{100}=1[/tex]

Which can be written as :

[tex]\dfrac{(x-3)^2}{7^2}+\dfrac{(y+6)^2}{10^2}=1[/tex]

Here 10 >7 , then the length of major axis =2(10)=20 units

Using the parallelogram pictured, find the length of the shorter diagonal. Round your answer to the nearest inch.

Answers

Answer:

21 in

Step-by-step explanation:

The law of cosines is helpful for this. The angle opposite the shorter diagonal is the supplement of the angle shown, so is 60°.

If we designate the known sides as "a" and "b", the short diagonal as "c" and the smaller angle as C, then the law of cosines tells us ...

c^2 = a^2 + b^2 -2ab·cos(C)

For the given dimensions, we have ...

c = √(15^2 +24^2 -2·15·24·cos(60°)) = √441 = 21 . . . inches

what are the coordinates of the focus of the parabola? (X+1)^2=-8(y-2)


A. (-1,1)

B. (-1,2)

C. (-1,0)

D. (1,-2)

Answers

Answer:

C. (-1, 0)

Step-by-step explanation:

(You don't need a picture to figure this out...it's simple algebraic manipulation.)

We could start off by rewriting the equation for the parabola with the negative on the other side, which tells us then that the parabola opens downward:

[tex]-(x+1)^2=8(y-2)[/tex]

Dividing both sides by -1 doesn't change anything.  Because this parabola opens downward, the focus is p units below the vertex at the same x-coordinate.  The vertex can be found from the equation to be (-1, 2).  The standard form of a parabola of this type is

[tex]-(x-h)^2=4p(y-k)[/tex]

where is the number of units between the vertex and the focus.  Our equation to find p is:

4p = 8 so p = 2.

That means that the focus is 2 units below the vertex at the x coordinate of -1.  Moving 2 units down from the y coordinate of 2 leaves us at a y coordinate of 0.  Therefore, the coordinates of the focus have to be (-1, 0)

Devon's mom ordered 3 pizzas for the girls slumber party to eat. The girls ate 5/2 of the pizza. How is this amount of pizza written as a mixed number?
A. 2 1/2
b. 2 1/5
C. 3

Answers

Answer:

2 1/2

Step-by-step explanation:

you have 2 whole pizzas and 1 half (1/2)

The half-life of a certain substance is 20 years. How much of a 100 gram sample will be left after 20 years?

Answers

[tex]\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &20 \end{cases} \\\\\\ A=100\left( \frac{1}{2} \right)^{\frac{20}{20}}\implies A=100\left( \frac{1}{2} \right)^1\implies A=50[/tex]

50 grams of that sample will be left after 20 years since it’s only gone through one half-life exactly.

In an experiment, the temperature fell 48° in 8 minutes. If the temperature fell at the same rate every minute, how many degrees did it change each minute?​

Answers

Answer:

6 per minute

Because you divide by 8 minutes

What is the domain of a sine function?

Answers

Answer:

The domain is all real values

Step-by-step explanation:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

In this case, we can observe from the graph that the function is defined for all x-values. So the domain is all real values.

What is the value of X on this triangle?

Answers

[tex]\bf (x-4)+(3x)+100=180\implies x-4+3x+100=180 \\\\\\ 4x+96=180\implies 4x=84\implies x=\cfrac{84}{4}\implies x=21[/tex]

Monica brought some postage stamps.She uses 10 stamps on letters and 5 stamps on postcards.Then her grandmother gives her 20 more stamps. She now has 35 stamps left. How many stamps did Monica originally have?

Answers

to find out how many stamps monica originally had, you’d have to do the equation given, “reversed”

equation given: 35 + 20 - 5 - 10

but because we are trying to find how many she originally had left, you’d have to do opposite operations (reverse) in the equation given.

35 - 20 + 5 + 10 = 30

so, this means that monica had 30 stamps originally

A spherical storage tank has a diameter of 14 ft. How many cubic feet of water will it hold? (Use pi=22/7 .)

Answers

V = (π/6)d^3

Using π = 22/7 and d = 14 ft, the volume is

 V = (22/7)/6*(14 ft)^3 = 4,312/3 ft^3

A fair coin is tossed 6 times. Compute the probability of tossing 6 tails in a row.
-----------------------------

Enter your response as a reduced fraction.

Answers

Answer:

1/6

Step-by-step explanation:

Final answer:

The probability of tossing 6 tails in a row with a fair coin is 1/64, as each toss's outcome is independent and the probability of tail on a single toss is 1/2.

Explanation:

To compute the probability of tossing 6 tails in a row with a fair coin, you recognize that for each individual toss, the probability of getting a tail is ½. Since each toss is independent, you simply multiply the probabilities of each event occurring consecutively. Therefore, the probability of tossing 6 tails in a row is:

(½) × (½) × (½) × (½) × (½) × (½) = ½6

½6 = 1/64

So, the probability of tossing 6 tails in a row is 1/64.

Learn more about probability here:

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for the polynomial


f(x)=-2x^3-2x^2+7x-25

as

x -> -∞, f(x) -> ∞

True
False

Answers

Answer: True

Step-by-step explanation:

By definition for a function of the form:

[tex]ax ^ n + ... + bx + c[/tex]

It is true that if [tex]a <0[/tex] and n is odd then:

[tex]\lim_{n \to -\infty}ax^n + ...+bx+c = \infty[/tex]

In this case

[tex]f(x)=-2x^3-2x^2+7x-25[/tex]

Therefore

[tex]a=-2<0[/tex] and [tex]n =3[/tex] → odd number

Then

[tex]\lim_{n \to -\infty}-2x^3-2x^2+7x-25= \infty[/tex]

This means that when [tex]x \to -\infty,\ f(x) \to \infty[/tex]

The statement  x -> -∞, f(x) -> ∞  is True

Answer: Its is True

Salim bought 31/4kg oranges,151/2kg pineapples and 103/4kg bananas. Find the total weight of fruits. If he used 23/4oranges ,121/4kg pineapples and 61/2kg bananas to make juice in a day then find the weight of fruits left?

Answers

Answer:

109 kg total

57 3/4 after

Step-by-step explanation:

31/4 orange

302/4 pineapples

103/4 bananas

436/4 total=109

436/4-205/4=231/4=57 3/4

What is the answer to the following problem:
1+1

Answers

Answer: 2

Step-by-step explanation:

add the 1 to the other 1 and it equals 2

Answer:

2

Step-by-step explanation:

1 and 1 is 2

Justin packed two suitcases for his trip and compared the weights of the items he packed in each of the suitcases. Which statement is true about the box plots? The data for suitcase 1 have an outlier. The data for suitcase 2 have an outlier. Suitcase 1 contains the lightest and heaviest item. Suitcase 2 contains the lightest and heaviest item.

Answers

Answer:

A

Step-by-step explanation:

(08.06 MC) The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below: Car A y = 55x + 32 Car B y = 42x + 58 After how many hours will the two cars be at the same distance from their starting point and what will that distance be? (5 points) 2 hours, 142 miles 2 hours, 145 miles 3 hours, 142 miles 3 hours, 145 miles

Answers

Answer:

2 hours,  142 miles

Step-by-step explanation:

Write a distance formula for both cars and then equate these formulas:

Car A:  y = 55x + 32  =  y = 42x + 58:  Car B

Then 55x + 32  =  y = 42x + 58  →  13x = 26, and so x = 2

That distance will be 55(2) + 32, or 142 miles.

The cars will reach the same point after 2 hours (first possible answer)

An equation is formed when two equal expressions. The correct option is A, 2hours, and 142 miles.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the equation for the distance covered by car A in x hours is y = 55x + 32, similarly, the equation for the distance covered by Car B in x hours is y=42x+58.

Now, to know at what time and at what distance the two cars will meet we need to solve the two equations. Since the car will cover the same distance we can write,

y = y

55x + 32 = 42x + 58

55x - 42x = 58 - 32

13x = 26

x = 2

Substitute the value of x in any one of the equations,

y = 55x + 32

y = 55(2) + 32

y = 110 + 32

y = 142

Thus, the car will meet after 2 hours, and the distance will be 142 miles.

Hence, the correct option is A, 2hours, and 142 miles.

Learn more about Equation:

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Which statement is true?​

Answers

Hello!

The answer is:

The second option,

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

Why?

Discarding each given option in order to find the correct one, we have:

First option,

[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}[/tex]

Second option,

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

The statement is true, we can prove it by using the following properties of exponents:

[tex](a^{b})^{c}=a^{bc}[/tex]

[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]

We are given the expression:

[tex](\sqrt[m]{x^{a} } )^{b}[/tex]

So, applying the properties, we have:

[tex](\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }[/tex]

Hence,

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

Third option,

[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}[/tex]

Fourth option,

[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }[/tex]

Hence, the answer is, the statement that is true is the second statement:

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

Have a nice day!

The length and width of the base of a rectangular prism are 5.5 cm and 3 cm. The height of the prism is 6.75 cm. Find the exact value of the surface area of the prism, in square centimeters.

Answers

Answer:

147.75

Step-by-step explanation:

2lw+2lh+2wh

2 (5.5)(3)+2 (5.5)(6.75)+2(3)(6.75)

=147.75

Final answer:

To find the surface area of a rectangular prism with dimensions 5.5 cm by 3 cm by 6.75 cm, we calculate the area of each pair of faces and sum them up to get a total surface area of 147.75 square centimeters.

Explanation:

To find the exact value of the surface area of a rectangular prism, we use the formula for surface area, which is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism. Given the dimensions, l = 5.5 cm, w = 3 cm, and h = 6.75 cm, we can calculate the surface area as follows:

Calculate the area of the two length by width sides: 2(5.5 cm  imes 3 cm) = 33 cm²

Calculate the area of the two length by height sides: 2(5.5 cm  imes 6.75 cm) = 74.25 cm²

Calculate the area of the two width by height sides: 2(3 cm  imes 6.75 cm) = 40.5 cm²

Add these areas together to get the total surface area: 33 cm² + 74.25 cm² + 40.5 cm² = 147.75 cm²

Hence, the exact value of the surface area of the rectangular prism is 147.75 square centimeters.

y varies inversely as x. y = 12 when x = 7. Find y when x = 6.

Answers

hope it helps you!!!!!!!!!!!!!

Answer: Y=2 !! ;) XD ;P

How many liters of pure water should be mixed with 18 liters of a 12% saline solution to make a saline solution that is 3% salt?

Answers

Four litres of pure water should be mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.

To find the litres of pure water mixed:

Given:

Pure water is mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.

Amount of pure water mixed =?

Now,

As given in the question, we have

18 litres of 12% saline solution

= 18 × (12/100)

= 2.16 litres

To make a saline solution containing 3% salt

Hence, four litres should be mixed to obtain a saline solution having 3% salt.

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How much carpet do I need for the Master Bedroom?

Answers

Answer:

The carpet needed is [tex]288\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of the master bedroom is the area of a rectangle

so

The area is equal to

[tex]A=bh[/tex]

we have

[tex]b=16\ units[/tex]

[tex]h=18\ units[/tex]

substitute

[tex]A=(16)(18)=288\ units^{2}[/tex]

therefore

The carpet needed is [tex]288\ units^{2}[/tex]

Express the length of the kite string in terms of trigonometric ratios. A) 70cos40° B) 70sin40° C) 40 sin70° D) 70 sin40°

Answers

Answer:

D

Step-by-step explanation:

just took it

70 over sin40 degrees

Answer:

The length of the kite string in terms of trigonometric ratios, if we call it L, is [tex]L=\frac{70}{sin(40\°)}ft[/tex]

Step-by-step explanation:

As we have to use the trigonometric ratios, and knowing that in a right triangle the relation

[tex]hypotenuse*sin(angle)=opposite leg[/tex]

is valid. We call the hypotenuse as L, and we know the other two data (angle and opposite leg), so we have that

[tex]L*sin(40\°)=70ft\Leftrightarrow L=\frac{70}{sin(40\°)}ft[/tex]

Then,

[tex]L=\frac{70}{sin(40\°)}ft[/tex]

is the answer that we are looking for to solve the problem.

?ABC has the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices. The measure of the longest side of ?ABC is units. ?ABC is triangle. If ?ABD is formed with the point D(1, 2) as its third vertex, then ?ABD is triangle. The length of side AD is units.

Answers

The solution involves using the distance formula to calculate the lengths of the sides of triangles ABC and ABD, and the Pythagorean theorem to identify the type of triangles they are by their side lengths.

To determine the characteristics of triangle ABC with vertices A(1, 7), B(-2, 2), and C(4, 2), we use the distance formula which is relevant because the length of the side of the triangle labeled a is the difference in the x-coordinates of points A and B. The same applies for side b, being the difference in the y-coordinates of points B and C. The length of side c is derived from the Pythagorean theorem, understanding that c represents the longest side of a right triangle, which is the hypotenuse.

Considering triangle ABD with an additional point D(1, 2), we first need to determine the lengths of the sides by using the formula for distance between two points in a coordinate plane for sides AB, BD, and AD. This will help to ascertain the type of triangle ABD is, based on the lengths of its sides. The length of side AD can be directly obtained since points A and D have the same x-coordinate.

The longest side of triangle ABC, which we determine by comparing the calculated lengths of AB, BC, and AC, will help us state whether the triangle is isosceles, scalene, or equilateral. For triangle ABD, once we have the lengths of AB, BD, and AD, we can determine its type similarly. This understanding stems from the standard geometric principles and the properties of triangles in a Euclidean space.

If set A = {3, 4, 7, 9} and if set D = {9, 4, 3, 7}, A = D.

True
False

Answers

True, we have the exactly same values in both domains.

Answer:

this is true!

Step-by-step explanation:

it is true because both have the exactly same values in both domains.

hope this helps :)

Find the length of the hypotenuse.

18

9√2

√18

18√2

Answers

Answer:

18

Step-by-step explanation:

The hypotenuse is BC.

According to the Pythagorean Theorem;

[tex]BC^2=AC^2+AB^2[/tex]

Since the base angles are equal:

[tex]AC=BC=9\sqrt{2}[/tex]

We substitute the given values into the formula to obtain:

[tex]BC^2=AC^2+AB^2[/tex]

[tex]BC^2=(9\sqrt{2})^2+(9\sqrt{2})^2[/tex]

[tex]BC^2=81(2)+81(2)[/tex]

[tex]BC^2=162+162[/tex]

[tex]BC^2=324[/tex]

Take positive square root.

[tex]BC=\sqrt{324}[/tex]

[tex]BC=18[/tex]

Hence the hypotenuse is 18 units

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