A piece of charcoal used for cooking is found at the remains of an ancient campsite. A 0.8 kg sample of carbon from the wood has an activity of 1770 decays per minute. Find the age of the charcoal. Living material has an activity of 15 decays/minute per gram of carbon present and the half-life of 14C is 5730 y. Answer in units of y
Answer:
t = 15825.11 years
Step-by-step explanation:
From the given information:
We can make use of the activity of the sample present after time "t" to determine the age of the sample.
This can be expressed by the formula:
[tex]A = A_o e^{-\lambda t}[/tex] --- (1)
where;
[tex]A_o[/tex]= activity of the sample at time t = 0
[tex]\lambda[/tex] = disintegration constant
[tex]\lambda = \dfrac{0.693}{T_{1/2}}[/tex]
If we replace the value of [tex]\lambda[/tex] into equation (1), we have:
[tex]A = A_o e^{ \Bigg [ -{ \dfrac{0.693}{T_{1/2}} \Bigg ] } t}[/tex]
[tex]\dfrac{A}{A_o} = e^{ \Bigg [ -{ \dfrac{0.693}{T_{1/2}} \Bigg ] } t}[/tex]
By rearrangement:
[tex]t = \dfrac{-T_{1/2} In (\dfrac{A}{A_o})}{0.693}[/tex]
[tex]t = - \dfrac{\left(5730\ \cdot\ \ln\left(\frac{\left(1770\right)}{0.8\cdot10^{3}\cdot15}\right)\right)}{0.693}[/tex]
t = 15825.11 years
A package of 8 notebooks cost $5. How much will 24 notebooks cost?
О.
Oь
Ос
12
15
10
Answer: B: 15
Step-by-step explanation:
Given f(x) = -8 + 1, find f(5)
Answer:
im guessing its actually -8x +1, so
-8 (5) +1
-40 +1
-39
It takes Evan 3/4 hour to mow his backyard how much will the yard be mowed after 2/3 hour
Answer:
88.88% or 8/9 of the yard is mowed
Step-by-step explanation:
First step is to get the denominator to the same number. Both denominators have a least common multiple of 12.
3/4 * 3/3 = 9/12
2/3 * 4/4 = 8/12
9/12 hours is how long it takes Evan to mow his backyard. He has 8/12 hours of work already done. If we divide the time already passed by the time still needed to mow the backyard, we can get how much of the yard is already mowed.
(8/12) / (9/12)
8/12 * 12/9
96/108 = 88.88
HELP ME ILL GIVE BRAINLEST !!!!!!!!! PLEASEEEEEEE
Answer:
The m<PML + m<PMQ + m<QMN = 180° since they are supplementary
therefore,
45°+(6x-5)+x=180°
45+7x-5=180
40+7x=180
7x=140
x=20
To test it we should plug in x for each equation and the sum of those answers should equal 180
45+(6x20-5)+20=180?
45+115+20=180?
160+20=180?
180=180
x=20 is valid
Step-by-step explanation:
Which is the completely factored form of 12x3 – 60x2 + 4x – 20? 4(3x2 – 1)(x – 5) 4x(3x2 + 1)(x – 5) 4x(3x2 – 1)(x + 5) 4(3x2 + 1)(x – 5)
Answer:
The answer is 4(3x² + 1)(x - 5).
Step-by-step explanation:
First, you have to take out all the common ratios :
12x³ - 60x² + 4x - 20
= 4(3x³ - 15x² + x - 5)
Next, you have to factorize the inner brackets :
3x³ - 15x² + x - 5
= 3x²(x - 5) + (x - 5)
= (3x² + 1)(x - 5)
Answer:
4(3x² + 1)(x - 5)
Step-by-step explanation:
Given
12x³ - 60x² + 4x - 20 ← factor out 4 from each term
= 4(3x³ - 15x² + x - 5)
Factor the first/second and third/fourth terms inside the parenthesis
= 4[ 3x²(x - 5) + 1(x - 5) ] ← factor out (x - 5) from each term
= 4(3x² + 1)(x - 5)
PLS HELP FAST I NEED HELP
Answer:
50 snail shells
Step-by-step explanation:
5. Sasha is signing her daughter up for dance classes. There is a one-time
costume fee of $35 and each dass costs $15. Sasha paid a total of $155.
how many classes did she sign up for?
Answer:
She paid for 8 classes
Step-by-step explanation:
Take away $35 from $155 because it was a one time custom fitting. And they’re asking for how many classes. So 35-155=120. Now you didvide 15 (charge per class) by 120 (total for all classes). And your answer is 8 classes. Hope this helped :)
A new process for producing a type of novolac resin is supposed to have a mean cycle time of 3.5 hours per batch. Six batches are produced, and their cycle times, in hours, were 3.45 3.47 3.57 3.52 3.40 3.62. Can you conclude that the mean cycle time is greater than 3.5 hours
Answer:
Yes, the mean cycle time is greater than 3.5 hours
Step-by-step explanation:
Let us try to calculate the mean cycle time here. Consider the given cycle times. To obtain the mean cycle time, we have.
3.45 + 3.47 + 3.57 + 3.52 + 3.40 + 3.62/6 = 3.505 hours
Hence the difference 3.505 -3.5 = 0.005
Hence mean cycle time is greater than 3.5 by 0.005
a plant measured x inches tall this week
if the cost of 2 dozen pens is Rs 600 how much more is the cost of 30 pens
Answer:
Step-by-step explanation:
2dozens= 24
24 pens cost Rs. 600
30 pens cost = (600x30)/24 = 18000/24 = Rs. 750
6) What is the equation of the green line? HELP PLEASE
Answer:
y=2/3x+18
Step-by-step explanation:
y-intercept=18 as seen
slope seems to be 2/3
3 bananas cost $0.99. At this rate, how much do 5 bananas cost?
Answer:
$1.65
Step-by-step explanation:
first i divided 0.99 by 3, equalling 0.33. i then multiplied 5 times 0.99 to equal 1.65.
In analyzing this diagram, which statement represents a crucial step to proving the pythagorean theorem using this diagram?
A) The large square on the left contains two smaller squares
B) The large square on the right contains a smaller square with side length c
C) The perimeter of the blue square is equal to the perimeter of the yellow square.
D) Recognize that BOTH of the large squares contain 4 right triangles with base a and height b
Answer:
D: recognize that BOTH of the large squares contain 4 right triangles with base a and height b
Step-by-step explanation:
A scuba diver used the expression below to describe his position in relation to sea level. 2 + (-20) + 8
Which statement could describe the diver’s movements?
A. Starting on a platform 2 feet above sea level, dive down to a location that is 18 feet below sea level, and then rise 8 feet.
B. Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
C. Starting 2 feet below sea level, dive down 20 more feet, and then rise to a location that is 8 feet below sea level.
D. Starting 2 feet below sea level, dive down 18 more feet, and then rise to a location that is 8 feet below sea level.
Answer:
-20
Step-by-step explanation:
i think
Answer:
Your answer should be B
Step-by-step explanation:
126 diminished by
the product of two consecutive
integers
Given x=1/2 and y=-x, what is the value of x-y
Answer:1
Step-by-step explanation:x=1/2 , y =-1/2
X-y = 1/2-(-1/2)=1
Answer:
x-y = 1
Step-by-step explanation:
Question: Given x = 1/2 and y = -x, what is the value of x - y?
Step-by-step:
We know that x = 1/2 and y = -x but we need to find out what -x is equal to.
To find the value of -x, we need to multiple -1 on both sides of the equation: x = 1/2
(You can think of it like -1 acts like an invisible number)
x*-1 = 1/2*-1 which is -x = -1/2
Since y is equal to -x, y = -1/2
We need to find x - y which is 1/2 - (-1/2)
Because the negative and subtraction signs cancel out, we add instead. The equation becomes 1/2 + 1/2
One half + half = 1
Therefore, x-y = 1
please help me out here kings and queens
Answer:
∠D=42°
Step-by-step explanation:
Since both triangles are congruent and are right triangles that t ∠D has to be 42°.
2222222222222222222222222222222222222222222222222222...
Answer:
222,222,222,222,222,222,222,222,222,222
Step-by-step explanation:
Intellegenc.
Determine weather the following graph represents a function
Answer:
it doesn't because there are places where there are two y values which just doesn't work out.
Congressional Terms Below is given the summary from
112th Congress of Senators whose
terms end in 2013, 20.
2017.
2015
20
15
CAPPARE
PRESENTADAL
SCHED
2013
Democrat
21
Republican 8
Choose one of these Senators at random and find
a. P(Democrat and term expires in 2015)
b. P(Republican or term expires in 2013)
c. P(Republican given term expires in 2017)
2017
The answers to all the subparts are:
(A) P(Democrat and term expires in 2015) = 20/78(B) P(Republican or term expires in 2013) = 57/78(C) P(Republican given term expires in 2017) = 13/14(D) The two events are not independent.A table is drawn according to the given information.
(Refer to the table below)
So,
let d be the event that the person is a Democrat.let r be the event that the person is republican.let 2013 be the event that the person retires 2013.let 2015 be the event that the person retires 2015.let 2017 be the event that the person retires in 2017.From the table:
p(d) = 42 / 78 because there are 42 democrats out of a total of 78 senators who retired in either 2013 or 2015 or 2017.p(r) = 36 / 78 because there are 36 republicans out of a total of 78 senators who retired in either 2013 or 2015 or 2017.p(2013) = 29 because there are 29 senators who retired in 2013 out of a total of 78 senators who retired in all 3 yearsp(2015) = 35 because there are 35 senators who retired in 2015 out of a total of 78 senators who retired in all 3 years.p(2017) = 14 because there are 14 senators who retired in 2017 out of a total of 78 senators who retired in all 3 years.Then,
Our universe is 78 senators who retired in all 3 years (2013, 2015, 2017).
42 are democrats and 36 are republicans.29 retired in 2013 and 35 retired in 2015 and 14 retired in 2017.(A) From the table, we can see that there are 20 democrats who retired in 2015.
p(d and 2015) = 20/78.(B) This one is asking for p(r or 2013)
The formula to use here is p(r or 2013) = p(r) + p(2013) - p(r and 2013).
From the table, we can see that:
p(r) = 36/78p(2013) = 29/78p(r and 2013) = 8So, p(r or 2013) is equal to p(r) + p(2013) - p(r and 2013) which is equal to 36/78 + 29/78 - 8/78 = 57/78.
(C) This is one is asking for p(r given 2017).
The formula to use here is p(r given 2017) = p(r and 2017) / p(2017).
From the table, you can see that:
p(2017) = 14/78p(r and 2017) = 13/78So, p(r given 2017) = p(r and 2017) / p(2017) = (13/78) / (14/78) = 13/14.
(D) if they were independent, then p(r and 2017) would be equal to p(r) * p(2017).
Therefore p(r given 2017) would be equal to p(r and 2017) / p(2017) which would be equal to p(r) * p(2017) / p(2017) which would be equal to p(r).From the table, you can see that p(r) = 36/78.From the table, you can see that p(r and 2017) = 13/78) and p(2017) = 14/78.Therefore p(r given 2017) = p(r and 2017) / p(2017) = (13/78) / (14/78) which is equal to 13/14 which is not equal to p(r) = 36/78Therefore the two events are not independent.Therefore, the answers to all the subparts are:
(A) P(Democrat and term expires in 2015) = 20/78(B) P(Republican or term expires in 2013) = 57/78(C) P(Republican given term expires in 2017) = 13/14(D) The two events are not independent.Know more about the random selection here:
https://brainly.com/question/24466382
#SPJ4
The complete question is given below:
Congressional Terms Below is given the summary from
112th Congress of Senators whose
terms end in 2013, 20.
2017.
2015
20
15
CAPPARE
PRESENTADAL
SCHED
2013
Democrat
21
Republican 8
Choose one of these Senators at random and find
a. P(Democrat and term expires in 2015)
b. P(Republican or term expires in 2013)
c. P(Republican given term expires in 2017)
d. Are the events “Republican” and “term expires in 2015” independent? Explain.
(-1,1)becames? (0,0)becomes?(1,1)becomes?
Answer:
(-1,1) becames 0, (0,0) becomes 0, (1,1) becomes 2
Trust Onepunchman (and maybe brainlist if I get it right)
A credit card company charges 22% interest fee on any charges not paid at the end of the month.. If the bill totals $450 for this month, how much interest would you have to be paid on the balance?
Answer:
B
Step-by-step explanation:
Because
True or False: 24x+16 can be combined to 40x.
Answer: Answer:
True
Step-by-step explanation:
No need for explanation
Other question.........
Answer:
m<1=85; m<2 =5
Step-by-step explanation:
[tex]5x + x - 12 = 90(right \: angle \: ) \\ 6x - 12 = 90 \\ 6x = 90 + 12 \\ 6x = 102 \\ x = 102 \div 6 \\ x = 17 \\ hence \: x = 17 \\ 5x = 5 \times 17 \\ = 85 [/tex]
[tex]x - 12 = 17 - 12 \\ = 5[/tex]
[tex]to \: check \\ \\ 5x + x - 12 = 90 \\ 85 + 5 = 90 \\ hope \: it \: helps \\ pls \: mark \: it \: as \: brainliest...[/tex]
Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.
Answer: m=3 radical 2 and n=3
Line g is dilated by a scale factor of 3 from the origin to create line g'. Where are points E' and F' located after dilation, and how are lines g and g' related? coordinate plane with point E at negative 4 comma 0 and point F at 0 comma 2, line g intersects points E and F The locations of E' and F' are E' (−4, 0) and F' (0, 2), and lines g and g' are the same line. The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' intersect at point F. The locations of E' and F' are E' (−1, 0) and F' (0, 0), and lines g and g' are not related. The locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
Dilation involves changing the size of a shape.
The true statement is that the locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
The given parameters are:
[tex]k =3[/tex] --- the scale factor
[tex]E = (-4,0)[/tex]
[tex]F =(0,2)[/tex]
Multiply the coordinates of point E and F by the scale factor (k), to determine the new coordinates of E and F.
[tex]E' = E \times k[/tex]
[tex]E' = (-4,0) \times 3[/tex]
[tex]E' = (-12,0)[/tex]
[tex]F' = F \times k[/tex]
[tex]F' = (0,2) \times 3[/tex]
[tex]F' = (0,6)[/tex]
Given that line g is represented by points E and F; line g' would be represented by points E' and F'
So, both lines would be parallel.
Hence, the true option is (d)
Read more about dilation at:
https://brainly.com/question/3457976
Answer:
The locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
Step-by-step explanation:
A truck driver is carrying eleven bills. Some of the bills are
$10 bills (x), and some are $5 bills (y). Together, the bills
total $85. How many $10 bills does she have?
Answer:
6 ten-dollars bills
Step-by-step explanation:
x + y = 11
10x + 5y = 85
5( x + y ) = 5(11)
5x + 5y = 55
10x + 5y = 85
-5x + 0 = -30
x = 6
Best and Correct answer gets BRAINLIEST!!!!!
Answer:
3
Step-by-step explanation:
3/1 = 3
3 is the correct answer
What is the common ratio for the geometric sequence below, written as a fraction?
768, 480, 300, 187.5,
Answer:
5/8
Step-by-step explanation:
Hope this helps :)