a radioactive substance that has half-life lof 32 years. Find the constant k in the decay formula for the substance

I put up 50 PTS if you just say a random word I will report you

Answers

Answer 1

Answer:

[tex]\displaystyle k = \frac{1}{32}\ln\frac{1}{2} \approx -0.02166[/tex]

Step-by-step explanation:

The decay formula is given by:
[tex]\displaystyle P(t) = P_0e^{kt}[/tex]

Where k is some constant, P₀ is the initial population, and t is the number of years.

Because the substance has a half-life of 32 years, P(t) = 1/2P₀ when t = 32. Substitute:
[tex]\displaystyle \frac{1}{2}P_0 = P_0 e^{k(32)}[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} \frac{1}{2} & = e^{32k} \\ \\ \ln\left(e^{32k}\right) & = \ln\left(\frac{1}{2}\right) \\ \\ 32k & = \ln\frac{1}{2} \\ \\ k & = \frac{1}{32}\ln\frac{1}{2} \\ \\ &\approx -0.02166\end{aligned}[/tex]

In conclusion, the value of k is about -0.02166.

Answer 2

The value of k in the exponential decay formula is k = 0.022

How to find the value of k?

To find the constant k in the decay formula for the radioactive substance, we can use the formula for exponential decay, which is given by:

N(t) = N₀*exp(-kt)

where:

N(t) is the amount of the radioactive substance at time t.N₀ is the initial amount of the substance at t = 0 (time of measurement).e is the base of the natural logarithm (approximately 2.71828).k is the decay constant we need to find.t is the time elapsed (in this case, t is measured in years since the half-life is given in years).

The half-life of the substance is the time it takes for half of the substance to decay, which is 32 years in this case. So, after one half-life, N(t) = N₀ / 2.

Now, let's set up the equation for one half-life:

N(t) = N₀ * exp(-k * 32)

Since N(t) = N₀ / 2 after one half-life, we can write:

N₀ / 2 = N₀ * e^(-k * 32)

Now, divide both sides by N₀:

1/2 = exp(-k * 32)

To solve for k, take the natural logarithm (ln) of both sides:

ln(1/2) = -k * 32

k = ln(1/2) / -32

k = 0.022

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Related Questions

All change 5. Three friends collected aluminum cans from the neighborhood to recycle. In total they collected 300 cans. Manny collected 90, Jim collected 100, and Bib collected 110. What percentage did each collect?

A. Manny 30% Jim 25% Bob 45%

B. Manny 30% Jim 33.3% Bob 36.7%

C. Manny 20% Jim 33.3% Bob 46.7%

D. Manny 18% Jim 42% Bob 50%

Please help I'll mark brainliest​

Answers

Answer:

i think it b i dont know for sure

Step-by-step explanation:

Find the amount of work W done by a force F = 115i +350j
in moving an object in a straight line given by the displacement vector D = -13i+15j.

Answers

The work is equal to the dot product of the force and displacement vectors:
W = (115 i + 350 j) • (-13 i + 15 j)

W = 115 × (-13) + 350 × 15

W = 3755

3. The number 84 can be expressed as the
sum of 54 + 30. Which shows how to use
the distributive property to rewrite that
sum as a multiple of a sum whose addends
have no common factors greater than 1?
A. 2(27 + 15)
B. 3(18 + 10)
C. 5(11 + 0)
D. 6(9 + 5)

Answers

Answer:

D. 6(9 + 5)

Step-by-step explanation:

the three sides of a triangle are 11/3 cm , 15/4 cm and 26/9 cm . find it's perimeter .​

Answers

☘︎Answer :-

[tex] \sf\longmapsto \: \frac{371}{36} [/tex]

☘︎ Solution :-

Given : Three sides are 11/3 cm , 15/4 cm and 26/9 cm To find : perimeter of the triangle

Perimeter of a triangle = Sum of the length of the three sides

perimeter of the given triangle = 11/3 + 15/4 + 26/9

Make the denominator same by taking the LCM of the denominators .

( LCM of 3 , 4 and 9 is 36 )

[tex]\sf\longmapsto \: \frac{132 \: + \: 135 \: + \: 104}{36} \: \: \: [/tex]

[tex]\sf\longmapsto \: \frac{371}{36} \: cm \: [/tex]

Therefore, the perimeter of a triangle is 371/36 cm

round to nearest tenth. Please solve
0.48 divide 9.23
8 divide 6.43
0.4 divide 28.08
3.5 divide 2.29
.072 divide 345
2.1 divide 1.488

thank you

Answers

Answer:

.1, 1.2, 0, 1.5, 0, 1.4 // 19.2, .8, 70.2, .7, 4791.7, .7

Step-by-step explanation:

The first set is if you meant the first number divided BY the second and the second set of numbers is if you meant it vice versa. If it was worded better I could understand better.

Find the length of the second base of a trapezoid with one base measuring 15 feet, a height of 7.6 feet, and an area of 98.8 square feet

answer choices
9 ft

10 ft

11 ft

12 ft

Answers

Answer:

11 feet

Explanation:

area of trapezoid: 1/2 * (a + b) * h

Here given:

a = 15 feetheight = 7.6 feetarea = 98.8 feet²

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

Solving steps:

⇒ 1/2 * (15 + b) * 7.6 = 98.8

⇒ (15 + b) * 7.6 = 197.6

⇒ (15 + b) = 26

⇒ b = 11 ft

Area =1/2(Sum of parallel sides)(Height)

Let unknown be x

1/2(x+15.5)(7.6)=98.83.8(x+15.5}=98.8x+15.5=26x=26 .03-15.5x=10.53x≈11ft

Problem Situation: Gabi buys tickets to the movies.
She buys 1 adult ticket for $14 and 3 youth tickets.
She pays a total of $35.
What is the cost of each youth ticket?
Complete the equation to represent this situation.
The letter t represents the cost of a youth ticket.

Answers

Let that be y

14+3y=35

Now solve

3y=35-143y=21y=21/3y=7

Each youth ticket costs 7$

Answer So you can add a number with the letter t and then add and then you can 35 dollers

HELP PLS 50 PTS! To the nearest 50 square feet, what is the area of the actual store?

Question 1 options:

2,350 square feet


2,450 square feet


2,500 square feet


2,400 square feet

Answers

○ 2,350 square feet

○ 2,450 square feet

○ 2,500 square feet

● 2,400 square feet answer

Step-by-step explanation:

wellcome

rip

What is 180-90-37 as a degree?

Answers

Answer:

53 degrees

Step-by-step explanation:

since 180 is a straight line and 90 is half of that, all you need to do is take 37 away from 90 and you get 53

The equivalent degree of the of the expression is 53 degrees .

Given,

180° - 90° - 37°

Now,

The equivalent value of the expression :

180° - 90° - 37°

Firstly compute the like terms,

-90° - 37°

= -127°

Now,

180° - 127°

= 53°

Know more about degrees,

https://brainly.com/question/364572

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please help!! very important!!

Answers

Answer:

d

Step-by-step explanation:

Hardware store:

4 bulbs = $20

1 bulb = $20 / 4 = $5

Grocery store:

6 bulbs = $24

1 bulb = $24 / 6 = $4

The difference in price = $5 - $4 = $1

The grocery store sells at the lesser price.

So, the grocery store charges $1 less per light bulb than the hardware store.

Use the quadratic formula to find the solutions to the quadratic equation below. x^2 - 6x - 5 = 0

Answers

Step-by-step explanation:

We know the quadratic formula, which is :

[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}} \\ \\ [/tex]

Here,

a = 1b = -6c = -5

So,

[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ - ( - 6) \pm \sqrt{ {( - 6)}^{2} - 4(1)( - 5) } }{2(1)} }}} \\ \\ [/tex]

[tex] {\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 36 - 4( - 5) } }{2} }}} \\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 36 + 20 } }{2} }}} \\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 56 } }{2} }}} \\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(28) } }{2} }}} \\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(2)(14) } }{2} }}} \\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(2)(2)(7) } }{2} }}} \\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2} . \sqrt{2} . \sqrt{2 . 7} }{2} }}} \\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm 2 \sqrt{14} }{2} }}} \\ \\ [/tex]

Now, Separating the solutions :

[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ 6 + 2 \sqrt{14} }{2} }}} \\ \\ [/tex]

[tex] {\longrightarrow \qquad{ \sf{x = 3 + \sqrt{14}}}}\\ \\ [/tex]

[tex]\\ {\longrightarrow \qquad{ \sf{x = \frac{ 6 - 2 \sqrt{14} }{2} }}} \\ \\ [/tex]

[tex] {\longrightarrow \qquad{ \sf{x = 3 - \sqrt{14}}}}\\ \\ [/tex]

please i reallly need help right now 25 points

Answers

Answer:

D) all real numbers except x = 6

Step-by-step explanation:

If there is a solid line or dot at an x value, then it is included in the domain. Since there are open dots at x = 6, that means it is not included in the domain. With that being said, the domain can be written as:

(-∞, 6)∪(6, ∞)

Hope this helps!

PLEASE HELP
What can you say about the y-values of the two functions f(x) = 3x2 -3 and
g(x) = 2* -3?
A. f(x) and g(x) have equivalent minimum y-values.
B. f(x) has the smallest possible y-value.
C. The minimum y-value of g(x) approaches -3.
D. g(x) has the smallest possible y-value.

Answers

Answer:  


g(x) has the smallest possible y-value of -3

Step-by-step explanation:


f(x) = 3ˣ - 3   This is an exponential graph shifted down three units. So, it has an asymptote at y = -3, which means it approaches -3 but does not touch it.Range: y > 3   (-3, ∞)   g(x) = 7x² - 3  ⇒ g(x) = 7(x - 0)² - 3   This is a parabola with vertex at (0, -3) Range: y ≥ 3   [-3, ∞)

Hector was thinking of a two-digit counting number, and he asked Simon to guess the number. Describe how you can find the probability that Simon will guess correctly on the first try.​

Answers

Answer:

1/89

Step-by-step explanation:

Two digit numbers include all numbers from 10 to 99. 99-10 = 89. Therefore the probability that Simon guesses the number correctly on the first try is 1 out of 89 which can be written as 1/89.

Please help me! Thank you

Answers

Answer: 4

Step-by-step explanation: how i know by guessing

What is the measure, in degrees, of

Answers

Answer:

Hi good job

Step-by-step explanation:

write an expression for the cost of t books at 13 cents each​

Answers

Answer:

13n+20 is the correct answer to ypur question

Step-by-step explanation:

NEED HELP STAT if you dont know the answer for sure then dont say it, 100 POINTS
Which statements include two quantities in the real world that are additive inverses?

Select each correct answer.


A rock climber ascends 19 feet and then descends 9 feet.

A child runs 10 feet to the right and then runs 10 feet to the left.

A person removes 14 cans from a shelf and puts 15 cans back on the shelf.

A person deposits $430 in to a bank account and then withdraws $430 from the account.

Answers

B

&

D

Step-by-step explanation:

Answer:

The Answers are A and D

Step-by-step explanation:

I took the test and got em right!

arrange in ascending order. : 5/8, 3/4, 7/12, 1/2

Answers

Answer:

1/2, 7/12, 5/8, 3/4.

Step-by-step explanation:

I did that in ascending order.

If you spin the spinner 9 times, what is the best prediction possible for the number of times it will land on yellow?

Answers

Answer:

0? There's no yellow.

Step-by-step explanation:

During its grand opening sale, a local electronics store gave customers a chance to win a new flat screen TV. Customers only had to fill out a card with their name, address, and telephone number and drop it into a box. One winner would be chosen at random. This is an example of a

Answers

Using sampling concepts, it is found that this is an example of a random sample.

How are samples classified?

Samples may be classified as:

Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.

In this problem, one winner is chosen at random from all the participants, hence random sampling is used.

More can be learned about sampling concepts at https://brainly.com/question/25122507

Pls help me
Pls show your answer pls and thank you

Answers

Answer:

Step 1

According to given details

Number of delivered pizzas at the weekly meeting=5

Number of slices in one pizza =8

(a)

Now evaluate total number of slices

Number of slices in one pizza =8

Total slices =8x5

=40 slice

(b)

Yes, we can find more than one way

= 5 ÷ 1/8

= 5x8/1

=40/1

The temperature in Denver, Colorado this
morning was -7°. In the afternoon, the
temperature rose to 16º.
What does this mean?
A. The temperature is 16° below zero
B. The temperature is 16° above zero
PLEASE HELP!!

Answers

The answer is b
Hope this helps

This equation shows the relationship between the amount of water (w), in liters, filled in Tank A and the number of minutes (m) it took to fill it.


w = 100 + 80.5m


This table shows the relationship between the amount of water, in liters, filled in Tank B and the number of minutes it took to fill the tank


Amount of water filled in Tank B:

Minutes: Amount of water: (liters)

0 154

2 384

6 844


What is the difference, in liters, between the total amount of water filled in Tank A and Tank B after 4 minutes?

Answers

Answer:

192 liters

Step-by-step explanation:

Tank A

w = 100 + 80.5m

where:

w = water in litersm = time in minutes

Therefore, when m = 4:

⇒ w = 100 + 80.5(4) = 422 liters

Tank B

Given ordered pairs:  (0, 154)  (2, 384)  (6, 844)

[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{384-154}{2-0}=115[/tex]

Point-slope form of linear equation: [tex]\sf y-y_1=m(x-x_1)[/tex]

(where m is the slope and (x₁, y₁) is a point on the line)

[tex]\sf \implies y-154=115(x-0)[/tex]

[tex]\sf \implies y=115x+154[/tex]

Therefore, the equation for Tank B is:

w = 115m + 154

Therefore, when m = 4:

⇒ w = 115(4) + 154 = 614 liters

Difference

614 - 422 = 192 liters

Find equation for tank B

(0,154)(2,384)

Slope:-

m=384-154/2=230/2=115

Equation in point slope form

w-154=115(m)w=115m+154

For tank B

w=100+80.5m

Put 4on both

Tank A:-

w=100+80.5(4)w=100+322w=422L

TankB

w=115(4)+154w=460+154w=614L

Difference:-

614-422192L

Please HELP NEED ASAP>
Tyrone conducted an experiment with a spinner. He spun the arrow on the spinner 20 times and recorded the results in the table shown. Which statement below is a true statement based on the statement above. Please no links.

Answers

Answer:

A)

Step-by-step explanation:

The experimental probability on 'A' is higher than the theoretical probability  of landing on 'A'.

Help help help help math math

Answers

Answer:

[tex]x = \geqslant 34[/tex]

Step-by-step explanation:

x is greater than or equal to 34, because the illustration shows, that it can go beyond 34. The filled in dot also means that x can also be equal to 34. (i hope i explained it in a good way)

Answer correctly for brainliest I dont want to rush you but i need this in like 1-2 minutes

Answers

Answer:

the correct answers are A, C, and D

Step-by-step explanation:

Those are the only ones that make sense enough!

What is the average height of 6th grade students?

And

What was the low temperature...?

Those responses will be given as numerical values

E.G. 162cm or 2 degrees Celsius (2*C)

(Edit: the first & third options are the correct ones)

Hope this helps!

Please help me as soon as posable!! In hurry!!(24 points)

In a geometric sequence, a_ 2 = 2, a_ 3 = 20, and a_4 = 200.
Which equation can be used to find the nth term of the sequence, a_n?

A) a_n =2^n-1
B) a_n =2 · 18^n-1
C) a_n =10 · 2^n-1
D) a_n =1/5 · 10^n-1

Answers

The sequence is geometric, so

[tex]a_n = r a_{n-1}[/tex]

for some constant r. From this rule, it follows that

[tex]a_3 = r a_2 \implies 20 = 2r \implies r = 10[/tex]

and we can determine the first term to be

[tex]a_2 = r a_1 \implies 2 = 10 a_1 \implies a_1 = \dfrac15[/tex]

Now, by substitution we have

[tex]a_n = r a_{n-1} = r^2 a_{n-2} = r^3 a_{n-3} = \cdots[/tex]

and so on down to (D)

[tex]a_n = r^{n-1} a_1 = 10^{n-1} \cdot \dfrac15[/tex]

(notice how the exponent on r and the subscript on a add up to n)

Need this asap first gets brainliest

Answers

Answer:

Step-by-step explanation:

5a)→Solution,

[tex]\hookrightarrow 46+90=x[Sum\: of\: interior \:angle\: is\: equal\: to \:exterior\:angles]\\\\\hookrightarrow x=136[/tex]

5b)→Solution,

77+x=180

x=180-77

x=103

Calculus Problem

1. Find the volume of the solid whose base is bounded by the graphs of y = 8 - x^2and y = x^2,
with the indicated cross sections perpendicular to the x-axis:
a. Squares
b. Semi-Circles
C. Equilateral Triangles

Answers

The two parabolas intersect for

[tex]8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2[/tex]

and so the base of each solid is the set

[tex]B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}[/tex]

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, [tex]|x^2-(8-x^2)| = 2|x^2-4|[/tex]. But since -2 ≤ x ≤ 2, this reduces to [tex]2(x^2-4)[/tex].

a. Square cross sections will contribute a volume of

[tex]\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x[/tex]

where ∆x is the thickness of the section. Then the volume would be

[tex]\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}[/tex]

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

[tex]\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x[/tex]

We end up with the same integral as before except for the leading constant:

[tex]\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx[/tex]

Using the result of part (a), the volume is

[tex]\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}[/tex]

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

[tex]\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x[/tex]

and using the result of part (a) again, the volume is

[tex]\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}[/tex]

Other Questions
Select the correct text in the passage.Which sentence in this excerpt from 'The American Crisis* by Thomas Paine illustrates that it is a persuasive essay?I shall conclude this paper with some miscellaneous remarks on the slate of our affairs;and shall begin with asking thefollowing question, Whyis it that the enemy hath left the NewEngland provinces, and made those middle once the fear of war? The answer is easy, New England is notinfested with Tories, and weare. I have been under in raising the cry against these men, and used numberless arguments to shew them theirdanger. .. The period is now arrived, in which either they ormust change our sentiments,or one orboth must fall. And what is a Tory? GoodGODI what is he? I should not be afraid to gothey to attempt to get into arms. Every Torywith a hundred Whigs against a thousand Tories, wereIs a coward, orservile, slavish, self-interested fear iys the foundation of Toryism; and a man under such influence, though he may be cruel,never can be brave.But before the lineof irrecoverable separation be drawn between us, let us reason the matter together: Your conduct is an invitation to theenemy, yet not one nthousand of you has heart enough to join him. Howeas much deceived by you as the American cause is injured byyou. He expects you will all takeup arms, and flock to his standard with muskets on your shoulders, Your opinions are of no useto him, unlessyou support him personally; for 'tis soldiers, and not Tories, thatwants....Quitting this class of men, I turn with the warm ardor of a friend to those who have nobly stood, and areret determined to stand the matter out:I call not upon a few, but upon all: not on thisstatethat state, but on every state: up and help us; lay your shoulders to the wheel; better havetoo much force than too little, when so great an so object is at stake. Let it be told to the future world, that in the depth of winter, when nothing buthope and virtue could survive, that the city andthe country, alarmed at one common danger, came forth to meet and to repulse it. Say not that Othousands aregone, turn out your tens of thousands; throw not the burden of the day upon Providence, but "show your faith by your works,"that God may bless you.It matters not where you live,what rank of life you hold,the evil or the blessing will reach you all. The far and thenear, the home countles and the back, therich and the poor, will suffer or rejoice alike. The heart that feels not now is dead;the blood of hischildren will curse his cowardice, who shrinks back at a time when a little might have saved the whole, and madethem happy, I love the manthat can smile in trouble, that can gather strengthfrom distress, and grow brave by reflection. Tis the business of little minds to shrink; but hewhose heart is firm,and whose conscience approves his conduct, will pursue his principles unto death.Next A strange woman's house is the way to what?? (King James Version) This is a Christian question!!! How long is most information retained on a credit report?. The volume of a cylinder is 54 1 cm3. If the radius is 3 cm, what is the height of the cylinder? 3 cm O A. 6 cm O B. 3 cm O C. 18 cm OD. 9 cm Which causes a drop in female hormone levels? the onset of the menstrual flow the release of an egg from the ovary the thickening of the uterine wall the failure of an egg to be fertilized The formation of the Transportation Security Administration (TSA) was inresponse to - terrorist attacks in Afghanistan. terrorist attacks on American soil.civil liberties violations by the federal government act. nuclear weapons discovered in Iraq. what is the volume occupied by 6.8gm of H2S at STP (at mass H=1,S=32) Write a function that can find the largest item in the array and returns it. The function takes the array as an input. From the main function, send initial address, type and length of the array to the function. You can use registers to send the data to the function. Also return the largest item in the array using EAX register. 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How does the author develop her main idea over the course of the text?Propaganda: Battling for the Mind Why did the officers ask Kai what the chairs in his home looked like?A They had seen the Chinese poems engraved on the walls.B They thought it was a good question for a 12-year-old.C They wanted to see if Kai was really a skilled furniture maker.D They wanted to make sure Kai's answers matched his father's. Identify the adjective in the sentence below. Type them in the order in which they appear in the sentence. Do not include articles a, an, or the. The young child is affectionate. first adjective: second adjective: Robert is going to invest $640 and leave it in an account for 20 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest hundredth of a percent, would be required in order for Robert to end up with $1,280? The side lengths of JKL are 60 cm, 80 cm, and 100 cm. Which formula can be used to show that JKL is a right triangle? 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