Answer:
it's true
Step-by-step explanation:
A sample of 500 g of radioactive lead-210 decays to polonium-210 according to the function A(t)=500e^-0.032t , where t is time in years. Find the amount of radioactive lead remaining after (a) 3yr, (b) 8yr, (c) 10 yr. (d) Find the half-life.
Answer:
Step-by-step explanation:
Using the equation A(t) = 400e-.032t
a) replace t with 4 so A(4) = 400e((-.032)(4))
The hardest part about this is making sure to use order of operations. Be certain it works like this:
A(4) = 400e-.128
A(4) = 400(.8799)
A(4) = 351.9 grams
b) A(8) = 400e((-.032)(8)) = 309.7 grams
c) A(20) = 400e((-.032)(20)) = 210.9 grams
Note here that even after 20 years, not quite half of the original amount is gone. So, we can anticipate that in finding the half life, that our answer should be slightly greater than 20 years.
d) 200 = 400e(-.032t)
Divide both sides of the equation by 400.
.5 = e(-.032t)
Change this to logarithmic form.
Ln .5 = -.032t
-.6931≈ -.032t
t ≈ 21.7 years
Hope this helps!
The amount of radioactive lead,
(a).After 3 years is 454.23 grams
(b).After 8 years is 387.07 grams
(c).After 10 years is 363.07 grams.
(d). half life is 21.66 years.
The decay of radioactive lead is given by function,
[tex]A(t)=500e^{-0.032t}[/tex]
The amount of radioactive lead After 3 years is,
[tex]A(3)=500e^{-0.032*3}=0.908*500=454.23g[/tex]
The amount of radioactive lead After 8 years is,
[tex]A(8)=500e^{-0.032*8}=500*0.774=387.07g[/tex]
The amount of radioactive lead After 10 years is,
[tex]A(10)=500e^{-0.032*10}=500*0.726=363.07g[/tex]
Half life is defined as the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.
So, [tex]250=500e^{-0.032t}[/tex]
[tex]e^{-0.032t}=0.5\\\\-0.032t=ln(0.5)\\\\-0.032t=-0.693\\\\t=0.693/0.032=21.66 years[/tex]
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Convert into slope-intercept form: [tex]y-1=m(x-3)[/tex]
Answer:
y=2x-5
Step-by-step explanation:
First simplify: y-1=2x-6
y-1=2(x-3)
First simplify and distribute everything.
y-1=2x-6
So, x equals 2 because it got distributed into the numbers inside the parenthesis. Same with the 2 and -3. They multiplied to become -6.
Since it's y-1=2x-6, you can simplify it even more so the -1 goes to the other side and turns into positive 1.
y - 1 (+ 1) = 2x -6 (+ 1)
-1(+1)=0 which leaves just the variable y on the left side.
-6(+1)=-5 which leaves 2x-5 on the right side.
This results in y=2x-5. Hope this helped ;)
Answer:
y = 2x - 5
Step-by-step explanation:
y - 1 = 2(x - 3)
y - 1 = 2x - 6
y - 1 + 1 = 2x -6 + 1
y = 2x - 5
Please answer question
Answer:
87.6yd²
Step-by-step explanation:
Base: =1/2bh
=1/2(6)(5.2)=15.6
Sides: =1/2bh
=1/2(6)(8)=24 (3 of them)
15.6+24+24+24=87.6yd²
1. Find the greatest common divisor of the term 144x3y2and 81xy4
Answer:
[tex]1296x^3y^4[/tex]
Step-by-step explanation:
Given the terms:
[tex]144x^3y^2[/tex]
and [tex]81xy^4[/tex]
To find:
Greatest Common Divisor of the two terms or Least Common Multiple (LCM) of two numbers = ?
Solution:
First of all, let us find the HCF (Highest Common Factor) for both the terms.
i.e. the terms which are common to both.
Let us factorize them.
[tex]144x^3y^2 = \underline{3 \times 3} \times 16\times \underline x \times x^{2}\times \underline{y^{2} }[/tex]
[tex]81xy^4= \underline {3\times 3}\times 9 \times \underline{x} \times \underline{y^2}\times y^2[/tex]
Common terms are underlined.
So, HCF of the terms = [tex]9xy^2[/tex]
Now, we know the property that product of two numbers is equal to the product of the numbers themselves.
HCF [tex]\times[/tex] LCM = [tex]144x^3y^2[/tex] [tex]\times[/tex] [tex]81xy^4[/tex]
[tex]LCM = \dfrac{144x^3y^2 \times 81xy^4}{9xy^2}\\\Rightarrow LCM = 144x^3y^2 \times 9x^{1-1}y^{4-2}\\\Rightarrow LCM = 144x^3y^2 \times 9x^{0}y^{2}\\\Rightarrow LCM = \bold{1296x^3y^4 }[/tex]
Determine the equation of the inverse of y = 1/4 x^3 - 2
All of 4x+8 is under a cube root sign.
=====================================================
Work Shown:
To find the inverse, we swap x and y, then solve for y.
[tex]y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\[/tex]
------------
Side note:
If [tex]f(x) = \frac{1}{4}x^3 - 2[/tex] and [tex]g(x) = \sqrt[3]{4x+8}[/tex], then [tex]f(g(x)) = x[/tex] and [tex]g(f(x)) = x[/tex]for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.
Which data set matches the box-and-whisker plot?
A) 12 13 15 19 23 23 25 26.5 28 30
B) 15 13 19 21 23 24 27 29 32
C) 11 31 13 15 19 21 21 25 27 29 31
D) 11 13 15 19 23 23 24 26.5 28 33
Answer:
D) 11 13 15 19 23 23 24 26.5 28 33
Step-by-step explanation:
The box-and-whisker plot displayed above has the following key values that we can use to identify which of the given data set it matches. It has:
Minimum value = 11
Q1 = 15
Median = 23
Q3 = 26
Maximum value = 33
From the options given, using just the max and min value, we can conclude that the data set in option D matches the box plot.
The data set in option D has a minimum value of 11, and a maximum value of 33.
HELP ASAP ITS SO HARD! Kelsey did the following division problem. Her teacher says that the quotient she found is wrong. −2 5/6 ÷ 1 1/3 −17/6 ÷ 4/3 −6/17• 3/4 −6×3 divided by 17×4 −18/68 −9/34 A. Identify what Kelsey did wrong in her calculations. B. Find the correct quotient, showing all of your calculations.
Part A
Her steps were
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{6}{17} \times \frac{3}{4}\\\\-\frac{6\times 3}{17\times4}\\\\-\frac{18}{68}\\\\-\frac{9}{34}\\\\[/tex]
Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.
The third step should look like [tex]-\frac{17}{6}\times \frac{3}{4}[/tex]
=======================================================
Part B
Here's what she should have written
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{17}{6} \times \frac{3}{4}\\\\-\frac{17\times 3}{6\times 4}\\\\-\frac{51}{24}\\\\-\frac{17}{8}\\\\[/tex]
If you want to convert that improper fraction to a mixed number, then you could do something like this
[tex]-\frac{17}{8} = -\frac{16+1}{8}\\\\-\frac{17}{8} = -\frac{16}{8}-\frac{1}{8}\\\\-\frac{17}{8} = -2 \frac{1}{8}\\\\[/tex]
Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.
Find the value of x.
76
what is the answer for 6x-4=-26+5x
Answer: x=-22
Step-by-step explanation:
6x-4=-26+5x
6x-4-5x=-26+5x-5x ⇔ subtraction property of equality
x-4=-26
x-4+4=-26+4 ⇔ addition property of equality
x=-22
Answer:
x = - 22Step-by-step explanation:
6x - 4 = - 26 + 5x
First of all group like terms
Send the constants to the right side of the equation and those with variables to the left
That's
6x - 5x = 4 - 26
Simplify
We have the final answer as
x = - 22Hope this helps you
What is the slope of the line?
A) -1/3
B) 1/3
C) -3
D) 3
Answer:
Hey there!
A simple way to think about slope is rise over run. Between any two points on this line, the rise is 3, and the run is -1.
3/-1=-3, so the slope is -3.
Let me know if this helps :)
I need help please will give you 5 stars and good rating
Answer:
Step-by-step explanation:
Answer:
x=12
Step-by-step explanation:
To solve for the variable, we must isolate the variable, which is x.
[tex]\sqrt{x+4} -3=1[/tex]
3 is being subtracted from the square root of x+4. The inverse of subtraction is addition. Add 3 to both sides of the equation.
[tex]\sqrt{x+4} -3+3=1+3[/tex]
[tex]\sqrt{x+4} =1+3[/tex]
[tex]\sqrt{x+4} =4[/tex]
The square root of x+4 is being taken. The inverse of a square root is a square. Square both sides of the equation.
[tex](\sqrt{x+4})^2 =4^2[/tex]
[tex]x+4=4^2[/tex]
Evaluate the exponent.
4^2= 4*4=16
[tex]x+4=16[/tex]
4 is being added to x. The inverse of addition is subtraction. Subtract 4 from both sides of the equation.
[tex]x+4-4=16-4[/tex]
[tex]x=16-4[/tex]
[tex]x=12[/tex]
The solution to this equation is x=12.
Convert 25 feet per second to miles per hour.
1 mile = 5,280 feet
1 hour = 3600 seconds
3600/5280 = 0.681818 feet per second
25 ft per second x 0.681818 = 17.045 miles per hour
Round the answer as needed.
Answer:
The correct answer is 17.045 miles per hour.
PLEASE help me with this question. This is really URGENT
Changing the exponent by 1/2 ( going from x to 1/2x)
This does not change the y-intercept.
It does sharpen the curve, which means the y value does not increase as quickly when x is increased.
THe 3rd choice is correct.
Proof: make x=2
Y = 3^2 = 9
Y = 3^1/2(2) = 3^1 = 3
You can see y is smaller with the 1/2 included.
Covert the verbal expression into an algebraic expression.
Two more than five times a number x.
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------------
"Two more than five times a number x." means:
2 + 5 × x
Which graph best represents the function f(x) = 2(1.5)x? graph of increasing exponential function going through point 0, 2 graph of increasing exponential function going through point 0, 3 graph of increasing exponential function going through point 0, 1 graph of increasing exponential function going through point 0, 4
Graph of increasing exponential function going through point (0, 2)
=======================================================
Explanation:
Assuming you meant to say f(x) = 2(1.5)^x, then we can see the equation is an exponential and it is increasing. It is increasing because the base b = 1.5 is larger than 1.
Plug in x = 0 to find y
y = 2(1.5)^x
y = 2(1.5)^0
y = 2(1)
y = 2
We have x = 0 and y = 2 pair up together meaning (0,2) is on the function curve. This is the y intercept.
Answer:
A. graph of increasing exponential function going through point 0, 2
Step-by-step explanation:
write a equation of a line that has a slope of 5 and passes through the point (2,13)
Answer:
y = 5x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5, thus
y = 5x + c ← is the partial equation
To find c substitute (2, 13) into the partial equation
13 = 10 + c ⇒ c = 13 - 10 = 3
y = 5x + 3 ← equation of line
It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches. Which function models the horizontal displacement as a function of time in seconds? y = 5 cosine (StartFraction 2 pi Over 3 EndFraction x) y = 5 cosine (StartFraction 4 pi Over 3 EndFraction x) y = 10 cosine (StartFraction 2 pi Over 3 EndFraction x) y = 10 cosine (StartFraction 4 pi Over 3 EndFraction x)
Answer:
Step-by-step explanation:
Given functions are
y = 5 cos ( 2π / 3 ) t
y = 5 cos ( 4π / 3 ) t
y= 10 cos ( 2π / 3 ) t
y = 10 cos ( 4π / 3 ) t
The pendulum half oscillation from left extreme to right extreme takes 1.5 s
So its time period of oscillation T = 1.5 x 2 = 3 s .
standard equation of oscillation is
y = A cos ω t where A is amplitude and ω is angular frequency .
Amplitude of oscillation A = 10 / 2 = 5 inch .
Among the given equation of motion only first two has amplitude equal to 5 . So both the last two are ruled out .
The angular frequency of first motion as per given equation
ω = 2π / 3
If time period is T
2π / T = 2π / 3
T = 3 s
So it matches with the time period of oscillation of pendulum .
Hence the first equation truly represents the oscillation of pendulum.
The function models the horizontal displacement as a function of time in seconds is [tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex] and this can be determined by using the given data.
Given :
It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches.
For the oscillation the standard equation is given below:
[tex]\rm y = A\;cos \;\omega t[/tex]
where A is the amplitude, [tex]\omega[/tex] is the angular velocity, and t is the time.
Now, determine the time period that is:
T = 1.5 [tex]\times[/tex] 2
T = 3sec
Now, the angular frequency is given by:
[tex]\omega = \dfrac{2\pi}{3}[/tex]
So, the function models the horizontal displacement as a function of time in seconds is given below:
[tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex]
Therefore, the correct option is C).
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M1: L12a: Solving Equations Exit Ticket Determine which of the following equations have the same solution set. Must show work. 1. 3y + 8 = -10 - 3y 2. 6r+ 7 = 13 + 7r 3. 13 - 4m = 1 - m 4.-8-h=-3h 5. 38+7f=8f + 32 6. -6n + 20 = -14n - 4
determine which of the following has the same solution set must show work
Answer:
uhfcytuyyytt ryffffffffgtgghhh
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). (1 point) [tex]y=\frac{7}{x^{2} } +10[/tex]
Answer:
The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.
Step-by-step explanation:
Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:
[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]
[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]
Thus,
[tex]f(x) = 7\cdot x + 10[/tex]
The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.
Ten people were chosen at random and surveyed. The survey asked participants for the number of hours they sleep per night and the amount of their annual income. Letting X represent the number of hours the participant sleeps per night and Y represent the participant's annual income, the surveyor calculated the correlation coefficient between X and Y to be 0.29. Interpret the correlation coefficient calculated by choosing the statement below which correctly describes the correlation between X and Y. A. weak negative correlation B. strong negative correlation C. strong positive correlation D. weak positive correlation
Answer:
A. R=0.86; strong correlation
Step-by-step explanation:
The correlation coefficient of 0.29 indicates that the correlation is a weak positive correlation. Thus option (D) is the correct answer.
What is correlation?"Correlation is a statistical tool that studies the relationship between two variables. Data sets have a positive correlation when they increase together, and a negative correlation when one set increases as the other decreases".
For the given situation,
Correlation coefficient = 0.29
Positive correlation: the two variables change in the same direction.
Negative correlation: the two variables change in opposite directions.
No correlation: there is no association or relevant relationship between the two variables.
The correlation coefficient lies between 0 to 0.3 indicating that the correlation is a weak positive correlation.
Hence we can conclude that option (D) weak positive correlation is the correct answer.
Learn more about correlation here
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ASAP PLZ ANSWER!!! Can you tell me step by step to this question 8,595 ÷ 24?
Answer:
358 and remainder of 3
Step-by-step explanation:
1. Divide it like any other problem
24 goes into 85, 3 times with 13 left overBring down the 9 and 24 goes into 139, 5 times with 19 left overThen bring down the 5 and 24 goes inside 195, 8 times with 3 left overSo your remainder would be 3Hope this helps
Anna's back Garden consists of a rectangular lawn measuring 9m by 7m, surrounded by a gravel path of width X metres. Find, and simplify, an expression for the total area of the garden.
A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width.
The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower
:
Let x = the width of flower bed
:
Then the overall dimensions (flower bed & lawn) will be:
(2x + 8) by (2x + 4)
:
Overall area
(2x+8)*(2x+4) = 165
FOIL
4x^2 + 8x + 16x + 32 = 165
A quadratic equation
4x^2 + 24x + 32 - 165 = 0
4x^2 + 24x - 132 = 0
Simplify, divide by 4, results:
x^2 + 6x - 33 = 0
Use the quadratic formula to solve this
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
square root of the quantity x minus 3 end quantity plus 5 equals x
Answer:
Step-by-step explanation:
[tex]\sqrt{x-3} +5=x\\\sqrt{x-3} =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4[/tex]
put x=7 in the given equation
[tex]\sqrt{7-3} +5=7\\\sqrt{4} +5=7\\2+5=7\\7=7[/tex]
which is true .
∴ x=7 is a solution of the given eq.
now put x=4 in the given eq.
[tex]\sqrt{4-3} +5=7\\1+5=7\\6=7\\[/tex]
which is not true.
∴x=4 is an extraneous solution.
The Muller family are on holiday in New Zealand. a. They change some euros (€) and receive $1962 (New Zealand dollars). The exchange rate is €1 = $1.635. Calculate the number of euros they change. [3] b. The family spend 15% of their New Zealand dollars on a tour. Calculate the number of dollars they have left. [4]
Answer:
a. €1200;$1667.70
Step-by-step explanation:
a. Number of euros
[tex]\text{euros} = \$1962 \times \dfrac{\text{1 euro}}{\text{\$1.635}} = \textbf{1200 euros}[/tex]
b. Dollars remaining
Dollars on hand = $1962.00
Less 15 % spent = 0.15 × 1962 = -294.30
Balance remaining = $1667.70
Which of the following symbols could correctly finish the statement. Select all that apply. 0___-8 = ≠ > < ≥ ≤
Answer:
>
Step-by-step explanation:
Even though its 0 its still greater than any negative number.
Answer:
Step-by-step explanation:
write down the missing number in the following 1,,4,9,16,25,?
Answer:
36
Step-by-step explanation:
you know the number based on the sequence
the values increase in the form of x+2
e.g. 4-1=3
9-4=5
16-9=7
25-16=9
you can see the number adds 2 for every increased number
and by following this sequence you will get the number 36
Answer:
by the square of 1, 2 ,3 the sequence has been made
Step-by-step explanation:
1 for 1²
4 for 2²
9 for 3²
16 for 4²
25 for 5²
so the later one will be 36 for 6²
so the answer is 36 thats all
PLEASE HELP! 17 points! Use the right-hand rule for magnetic force to determine the charge on the moving particle. This is a _____ charge.
Answer: Positive Charge
Answer:
negative
Step-by-step explanation:
When using the Right-Hand Rules, it is important to remember that the rules assume charges move in a conventional current (the hypthetical flow of positive charges). In order to apply either Right-Hand Rule to a moving negative charge, the velocity (v) of that charge must be reversed--to represent the analogous conventional current.
The opposite charge is a negative charge.
help help help me plZZZZZ ill give you brainly ;DDD
Answer:
the answer is 60.7
Step-by-step explanation:
60 to has a between numbers like given in the picture
so as number line it's
60.1 . 60.2 60.3 60.4 60.5 60.6 60.7 60.8 and continue
if u get any 3 digit number like 600 to 650 in number line
u do it like it the same 600.1 600.2.... and go on
Answer:
63½ or 63.5
Step-by-step explanation:
65-60=5
10points=5
1point=?
1×5/10= ½
that means the sequence continues after adding ½ i.e
60..60½...61...61½...62...62½...63...63½...64..64½...65
you have been asked the 8th number which is 63½
A sequence of transformations is described below. A reflection over a line \overleftrightarrow{PQ} PQ P, Q, with, \overleftrightarrow, on top A rotation about the point PPP Another reflection over \overleftrightarrow{PQ} PQ P, Q, with, \overleftrightarrow, on top A rotation about the point QQQ Which of the following must be preserved under this sequence of transformations? Choose 1 answer: Choose 1 answer: (Choice A) A Angle measures only (Choice B) B Segment lengths only (Choice C) C Both angle measures and segment lengths (Choice D) D Neither angle measures nor segment lengths
Answer:
The correct option is;
(Choice C) Both angle measures and segment lengths
Step-by-step explanation:
The given transformations are;
The reflection over the line, [tex]\overleftrightarrow{PQ}[/tex], with, A rotation about the point P. Another reflection over [tex]\overleftrightarrow{PQ}[/tex]. A rotation about the point Q, we have;
The transformations involve changes only in the orientation and location of the pre-image, which remain rigid, therefore, there are no changes in the segment lengths or angle dimensions
Therefore, the correct option is, both angle measures and segment lengths.
(Choice C) C Both angle measures and segment lengths
Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis
(Choice B)
B
(b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis
(Choice C)
C
2(b)+2(3c)2(b)+2(3c)2,
Answer:
B. (b+3c)+(b+3c) C. 2(b)+2(3c)Step-by-step explanation:
Given this expression 2(b+3c), its equivalent expression is derived by simply opening up the bracket as shown below;
Open the parenthesis by multiplying the constant outside the bracket with all the variables in parenthesis.
= 2(b+3c)
= 2(b)+ 2(3c)
= 2b +2*3*c
= 2b +6c
It can also be written as sum of b+3c in 2 places i.e (b+3c)+(b+3c) because multiplying the function b+3c by 2 means we are to add the function by itself in two places.
Hence the equivalent expression are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c
