After 200 years, 9.84 grams of Cesium would remain.
Let N represent the amount of substance after t years
The half-life of a cesium is 30 years., hence, this can be represented by exponential function:
[tex]N(t)=ab^t[/tex]
where a is the initial value and b is the multiplier.
There were initially 1000g of the substance
a) The exponential model for this situation is:
[tex]N(t) =1000(\frac{1}{2} )^{\frac{1}{30} t}\\\\N(t) =1000(\frac{1}{2} )^{\frac{t}{30}[/tex]
b) After 200 years (t = 200), the amount of Cesium remaining is:
[tex]N(200)=1000(\frac{1}{2} )^\frac{200}{30} \\\\N(200) = 9.84g[/tex]
Hence after 200 years, 9.84 grams of Cesium would remain
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Examine the last statements made by the Dormouse:
(1) I breathe when I sleep.
(2) I sleep when I breathe.
Write each of the statements in "If .... then” form.
Answer:
I believe what your teacher is looking for is
"If I breathe when I sleep, then I sleep when I breathe."
"If I sleep when I breathe, then I breathe when I sleep."
Step-by-step explanation:
I hope I'm correct ^-^
Which function represents the graph
Answer:
A
Step-by-step explanation:
the function is moved up by 8 on the y axis which means you need a +8 that isn't directly attached to the x
A pizza shop charges $5 for a slice of pizza. They cut each whole pizza into 8 slices. They sold 107 pizzas by the slice. How much money did they make?
Answer:
$4280
Step-by-step explanation:
$5x8= $40
107x$40= $4280
que es un prisma rectangular y que es un prisma triangular??Plisa es para ahorita en una hora
Answer:
un prisma rectangular es una forma 3D con 6 caras rectangulares listo
Will give BRAINLIEST!!!! No spam pls :)
(Pic is provided)
1. Why is segment B'C' on the same line as its corresponding side, segment BC?
2. Explain how you know that segment A'C' is parallel to its corresponding side, segment AC.
3. What relationship does angle ACB have with its corresponding angle A'C'B'? Explain or show your reasoning.
Please help me answer this step by step
y + 1/2 = 3/4
Answer:
just translate
Step-by-step explanation:
thats bot much, ñ
Answer:
[tex]y + \frac{1}{2} = \frac{3}{4} \\ y + \frac{2}{2 \times 2} = \frac{3}{4} \\ y + \frac{2}{4} = \frac{3}{4} \\ y = \frac{3}{4} - \frac{2}{4} \\ y = \frac{1}{4} \\ thank \: you[/tex]
joes grandmother is suffering from fever from many days.he wants to go to his hometown Southampton to see his grandmother.His house is 325 km away from oxford.he covered 1/5th of his journey by bus.227.5km by train.16.25km by taxi and rest on foot.now give ans for the following questions; how much distance did he covered by bus.what fraction of total journey covered by train. How much distance he covered on foot? how much is the difference in distance covered by train and covered by bus?
The distance that will be covered by the bus will be 65km.
Since his house is 325 km away from Oxford and he covered 1/5th of his journey by bus. Then, the distance that's covered by bus will be:
= 1/5 × 325km
= 65 km.
Since 227.5km is covered by train, then the distance covered by train will be: = 227.5/325 = 7/10
The distance covered by foot will be:
= 325 - (65 + 227.5 + 16.25)
= 325km - 308.75km
= 16.25km
The difference in distance covered by train and covered by bus will be:
= 227.5km - 65km
= 162.5km
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The largest virus known to man is the Megavirus, which measures 0.00000044 meters across Express this number in scientific notation.
Answer:
4.4x10⁻⁷
Step-by-step explanation:
Decimal moves 7 places to the right so the exponent if negative.
How would the domain and range of the function
Y = (1/4)x - 6
be determined? Explain.
Answer:
Domain and range both [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
The range is determined by finding the domain of the inverse of the function(if it has one, in this case it does). The domain is easily determined, because [tex]x[/tex] can obviously range from [tex](-\infty, \infty)[/tex] without restriction.
The inverse of the function can be found as such:
[tex]x=(1/4)f^{-1}(x)-6\\x+6=(1/4)f^{-1}(x)\\4(x+6)=f^{-1}(x)\\f^{-1}(x)=4x+24[/tex].
Here, [tex]x[/tex] can also range from [tex](-\infty, \infty)[/tex] without restriction.
So, the domain and range are both [tex]\boxed{(-\infty, \infty)}[/tex]
You need 3 sticks of butter for every 24 cookies you bake.how much will you get for 5 stick of butter
Answer:192 cookies
Step-by-step explanation:
8•24=192
What’s the rise over run pleas???
9514 1404 393
Answer:
-1/5
Step-by-step explanation:
To find the ratio of rise to run on a graph, it is convenient to start by looking for points where the graph crosses the intersection of grid lines. This lets you read the exact coordinates of the points, without any guessing.
In the attachment, the grid crossings we chose are circled.
The "rise" is the vertical distance between the points. If the right point is lower, the "rise" is negative.
The "run" is the horizontal distance between the points.
The reason for choosing grid crossings is that it then becomes fairly easy to count the grid lines between the points, vertically and horizontally.
On this graph, the "rise" is -1 for a "run" of 5. Then the slope, or ratio of rise to run, is ...
m = rise/run = -1/5 . . . . . . slope of the line
The Lucas numbers are defined by the recursive formula t1 = 2, t2 = 1, tn = tn - 1 + tn - 2, where n âN and n > 2. What are the first 9 Lucas numbers?
The first two are given to you, [tex]t_1=2[/tex] and [tex]t_2=1[/tex]. Use the recursive formula to get the 3rd term; then use the 2nd and 3rd terms to get the 4th; and so on.
Since the n-th Lucas number is the sum of the previous two Lucas numbers, you have
[tex]t_3 = t_2 + t_1 = 1 + 2 = 3[/tex]
[tex]t_4 = t_3 + t_2 = 1 + 3 = 4[/tex]
[tex]t_5 = t_4 + t_3 = 4 + 3 = 7[/tex]
[tex]t_6 = t_5 + t_4 = 7 + 4 = 11[/tex]
[tex]t_7 = t_6 + t_5 = 11 + 7 = 18[/tex]
[tex]t_8 = t_7 + t_6 = 18 + 11 = 29[/tex]
[tex]t_9 = t_8 + t_7 = 29 + 18 = 47[/tex]
a. Draw a scaled copy of Polygon A with scale factor 1/2. b. Draw a scaled copy of Polygon B with scale factor 2. c. Draw a scaled factor of Polygon C with scale factor 1/4.
What is -6 multiplied by -2x minus -6 multiplied by 1
Answer:
72
Step-by-step explanation:
Answer:
-6 multiplied by -2x minus -6 multiplied by 1
= [tex]-6 * -2x - -6 * 1[/tex]
= [tex](-6 * -2x) - (-6 * 1)[/tex]
= [tex]12x - -6[/tex]
= [tex]12x -(-6)[/tex]
= [tex]12x + 6[/tex]
2. Frank has been driving at a constant speed for 3 hours, during which time he traveled 195 miles. Frank would like to know how long it will take him to complete the remaining 455 miles, assuming he maintains the same constant speed. Help Frank determine how long the remainder of the trip will take.The remainder of Frank's trip is _______ hours.
Answer:
1: 195 divide by 3=65m/h
2: 455divide by 65=7hours
The remainder of Frank's trip is __7_____ hours.
Quadratics by taking square roots (intro)
Answer:
Lesser: -6
Greater: 6
Step-by-step explanation:
h(x) = -5x^2 + 180
-5(x^2 - 36)
-5(x+6)(x-6)
x = -6, 6
Stella and Hazel are the two fastest typists in their computer class. Last week, they had a competition to see whose typing speed was greater.
The table below shows the number of words Stella typed in x minutes during the competition.
Stella's Typing Speed
Time
(minutes) Words
Typed
2 112
4 224
6 336
8 448
The equation below represents the number of words Hazel typed in x minutes during the competition.
Which of the following is true?
A.
Stella typed more words per minute than Hazel during the competition.
B.
There is not enough information to determine the number of words typed per minute during the competition.
C.
Stella and Hazel typed the same number of words per minute during the competition.
D.
Hazel typed more words per minute than Stella during the competition.
Answer:
b
Step-by-step explanation:
20 books are 20$ 30 books are 75$ and 40 books are 100$ WHAT IS THE ANSWER
assuming you're trying to find 50 books = $n
n = 160$
Which of the following represents the function graphed? F(x)=1/2 x f(x)=x f(x)= x+2
Which equation best represents the line graphed above?
Answer: x=2 because for any y value the x value is always 2.
PLEASE HELP ANSWER THIS QUESTION
(ILL GIVE BRAINLIEST TO THE BEST ANSWER TOO)
In Earth's southern hemisphere, the summer season is from December to March and winter is from June to September. The table shows the highest temperatures recorded at the South Pole for three different months.
Graph model:
South Pole Temperatures
Month Highest temperature (°F)
January 6
June –24
November –2
Each month's highest recorded temperature is plotted on the number line.
4. Which month had the coldest of the three temperatures? Explain.
#4
June is the most coldest.
How?
Mention the temperatures
January=+6°CJune=-24°CNovember=-2°CLowest is the coldest .(June is the coldest month)
Answer:
January = 6°F
June = -24°F
November = -2°F
By the above given observation we can say that June is the coldest as it has the lowest temperature in all.
You don’t have to do all of them only some if you want this these are my last question!
Find the value of x that makes the lines u and v parallel.
I will mark you
Answer:
Q11. 20x=120° (vert opp angles)
x=120÷20
=10
Q12. x+68°=60° (vert opp angles)
x=60-68
=-8
Q13. 80°+x+106°=180° (int angles, u//v)
x+186°=180°
x=180-186
=-6
Q14. 6x+8°=50°
6x=50°-8°
=42°
x=42÷6
=7
Nine hundred sixty seven divided by four with remander
Answer:
240
Step-by-step explanation: If this helped pls give this Brainliest answer.
Answer:
967÷4= 241 r 3
Step-by-step explanation:
Find the value of the expression 2x2 - 4x2 + 7x – 7 if x= 3. What is the value if x = 2?
Answer:
if x= 3, so it's 32 if x= 2, so it's 7
Step-by-step explanation:
Axel and Carl both volunteer at a science museum. The manager needs one helper at a time for at most 18 hours this month. Axel wants to work at least 6 hours. The manager wants Carl to work no more than twice as many hours as Axel. Let a represent the number of hours that Axel works. Let c represent the number of hours Carl works. Which system of inequalities represents the constraints of this problem situation?
We want to find a system of inequalities that models the given situation.
We will find the system:
a + c ≤ 18
a ≥ 6
c ≤ 2*a
First we define the variables:
c = number of hours that Carl works.a = number of hours that Axel worksThe given information is:
The manager needs one helper at a time for at most 18 hours.
From this we can write:
a + c ≤ 18
Axel wants to work at least 6 hours.
a ≥ 6
The manager wants carl to work no more than twice as many hours as Axel.
c ≤ 2*a
The system is then:
a + c ≤ 18
a ≥ 6
c ≤ 2*a
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Pleaseeee help asappp!
Answer: A and C
Step-by-step explanation:
plugging the ordered pairs into the suction on a graph is a good way to find them!
Answer:
I answered in comments but it was the first and last one :)
Step-by-step explanation:
175% of what number is 217?
Please help me with this! I really need help!
Answer:
18
Step-by-step explanation:
$18 haircut; 10% discount
work it out
Answer:
$16.20 with the discount
Answer:
$16.20
Step-by-step explanation:
A negative to a even power is always
Answer:
a positive number
Step-by-step explanation:
i hopw this help chu:>
