[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$34000\\ P=\textit{original amount deposited}\\ r=rate\to 4.9\%\to \frac{4.9}{100}\dotfill &0.049\\ t=years\dotfill &9 \end{cases} \\\\\\ 34000=Pe^{0.049\cdot 9}\implies 34000=Pe^{0.441}\implies \cfrac{34000}{e^{0.441}}=P\implies 21875.35\approx P[/tex]
Element X decays radioactively with a half life of 8 minutes. If there are 170
a
grams of Element X, how long, to the nearest tenth of a minute, would it take
the element to decay to 5 grams?
y = a(.5)
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
How to analyze a radioactive decay caseLet suppose that element X experiments a simple radioactive decay, that is, that the element X becomes gradually into another less radioactive stable element in time.
We know that decay behaves exponentially and follows this model:
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (1)
Where:
[tex]m_{o}[/tex] - Initial mass, in gramst - Time, in minutesτ - Time constant, in minutesm(t) - Current mass, in gramsThe time constant can be described in terms of half-life ([tex]t_{1/2}[/tex]), in minutes, through the following expression:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex] (2)
If we know that [tex]t_{1/2} = 8\,min[/tex], [tex]m_{o} = 170\,g[/tex] and [tex]m(t) = 5\,g[/tex], then the time needed for the decay is:
τ ≈ 11.541 min
[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]
t ≈ 40.698 min
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams. [tex]\blacksquare[/tex]
To learn more on radioactive decay, we kindly invite to check this verified question: https://brainly.com/question/27156663
Martin drew a scale drawing of an arcade. The scale he used was 1 inch : 3 feet. If the actual length of an air hockey table is 9 feet, how long is the air hockey table in the drawing?
Answer: 3 inches
Step-by-step explanation: 9 divided by 3 is 3
Figure #3 (Round to the nearest tenth)
Volume =_____cm^3
Which statement is correct?
Answer:
C because the answer is right
Christine went on a passenger train that traveled 80 miles in one hour. How many miles will it travel in six hours?
Answer:
480
Step-by-step explanation:
[tex]80*6[/tex] = 480
Answer:
She will travel 480 miles in 6 hours
Step-by-step explanation:
All you need to do is Multiply 80 by 6 to get an answer of 480.
Hope that helps!
What is the probability of both coins landing on heads?
Write your answer as a fraction or a whole number. With fractions, use a slash ( / ) to separate the numerator and denominator.
Answer:
and with the fractions and then divide the answer by 2.1
Step-by-step explanation:
Can someone explain on how to find this question please?
Answer:
∠ SOU = 138°
Step-by-step explanation:
the opposite angles of a tangent kite are supplementary, sum to 180° , so
∠ SOU + ∠ STU = 180° , that is
∠ SOU + 42° = 180° ( subtract 42° from both sides )
∠ SOU = 138°
just look at the picture.....
Answer:
is equal to 925 i think cuz
Step-by-step explanation:
summation of arithmetic sequence
n=1 , 3n-2=3-2=1 , a=1, d=3.
sn=n+3n(n-1)
-------------
2
a=1 ,d=3 sn= n+3n(n-1)
------------
2
S25=25+3×25(25-1)
--------------
2
25+900=925
so the answer will be 925
What are the new coordinates of the figure above if it is dilated by a scale factor of 4, with the origin as the center of dilation ?
A. A’ (-1,-4), B’(-4,4), C’(2,-4)
B. A’(-4,-1), B’(-4,4),C’(8,-1)
C. A’(-5,-5), B’(-5,5),C’(6,-5)
D. A’(-4,-4), B’(-4,4)C’(8,-4)
Answer:
D. A’(-4,-4), B’(-4,4)C’(8,-4)
Step-by-step explanation:
solve . x -13 < -11
A.
x <-2
B.
x < 2
C.
x > 24
D.
x > -24
x - 13 < - 11
x < - 11 + 13
x < 2
A plane travels a distance of 3,300 miles at a rate of 550 mph. How long will it take
the plane to reach its destination?
Answer:
6 hours
Step-by-step explanation:
Divide 3300 by 550, so it's 6.
look figure and give exact answer.
Answer:
Those two lines are equal
the dimensions of a rectangular dining room are 18 feet by 16 feet long if a scale factor 1/4 is used to make a scale model of the dining room what is the area of the dining room in the scale model.
calculate the sides of the rectangle in scale factor model
Length: 18 * 1/4 = 4.5 feet
Width: 16 * 1/4 = 4 feet
Rectangle area in scale factor model:
Length * Width
4.5 * 4
18 feet²
Answer:
Given dimensions of a rectangular dining table:
width = 18 ftlength = 16 ftIf a scale factor of [tex]\dfrac14[/tex] is used, then we need to multiply each measurement by [tex]\dfrac14[/tex]:
[tex]\implies \textsf{width}=18 \times \dfrac14[/tex]
[tex]=4.5 \textsf{ units}[/tex]
[tex]\implies \textsf{length}=16 \times \dfrac14[/tex]
[tex]=4 \textsf{ units}[/tex]
Therefore, the scale model of the dining room will be 4.5 by 4 units.
what is 62.28 dived by 0.72 step buy step
Answer:
62.28divided by 0.75 = 83.04
Step-by-step explanation:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Find the radius. ddddddddddddddddddddddddddddd
Answer:
Its 3 because the radius if half of the diameter
Step-by-step explanation:
Abigail invested $29,000 in an account paying an interest rate of 2. 1% compounded continuously. Assuming no deposits or withdrawals are made, how much money to the nearest dollar, would be in the account after 8 years?
Answer:
$34,305
Step-by-step explanation:
[tex] a = 29000 {e}^{.021 \times 8} = 34305[/tex]
During which time period was the ANNUAL rate of increase of the speed the GREATEST
Answer:
1-2
Step-by-step explanation: because it went up in speed by 8 and the rest went up not even to 7
Based on the table, we can deduce that the annual rate of increase of the speed was the greatest: A. from year 1 to year 2.
What is speed?Speed can be defined as the distance covered by an object per unit of time. Thus, speed can be measured as meter per seconds.
Mathematically, speed is given by this formula;
[tex]Speed = \frac{distance}{time}[/tex]
Based on the table, we can deduce that the annual rate of increase of the speed was the greatest from year 1 to year 2.
Rate = 46 - 38 = 8.
Read more on speed here: brainly.com/question/10545161
In 2009, the population of the US was approximately 306,370,370. The number of US live births in 2009 was 4,136,000. The birth rate in 2009, which takes into account changes in the population, fell to _____ births for every 1,000 people. (Fill in the blank. Round answer to one decimal place. Enter your answer in the form xx. X)
Using proportions, it is found that the birth rate fell to 13.5 births for every 1000 people.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, for 306,370,370 people, there were 4,136,000 births. How many births were there for 1,000 people? The rule of three is given by:
306,370,370 people - 4,136,000 births
1,000 people - x births
Applying cross multiplication:
306370370x = 1000 x 4136000
x = 1000 x 4136000/306370370
x = 13.5
The birth rate fell to 13.5 births for every 1000 people.
More can be learned about proportions at https://brainly.com/question/24372153
4x^2−24x
that is a 4x to the second power thanks you people are so helpful oh yeah factor it thats it
Answer:
See below.
Step-by-step explanation:
4x^2-24x
Find the GCF.
4 - 1, 2, 4
24 - 1, 2, 3, 4, 6, 8, 12, 24
The GCF of x^2 and x is x.
The complete GCF is 4x.
4x(x-6)
-hope it helps
Cole is buying a new rain barrel to help with watering his garden. The rain barrel is shaped like a right circular cylinder. What is the volume of the rain barrel if it is 26 inches tall and has a diameter of 22 inches? Use straight pi equals 3.14.
A right circular cylinder diameter 22 inches and a height of 26 inches.
V equals_(blank)_ inches cubed
Round to the nearest hundredth if necessary. Type your numerical answer (without units) below.
Answer:
[tex]V = 9878.44 in^3[/tex]
Step-by-step explanation:
The volume of a cylinder, is essentially base multiplied by height. Think of it like this, you are taking a flat 2D circle and extending it in 3rd dimension by a length 'h'.
[tex]V = base * h[/tex]
The base here is the circle area, and the height is the amount you extended that 2d circle in the 3rd dimension.
The area of a circle is [tex]\pi r^2[/tex]. If we put that into our equation we get the volume of a cylinder.
[tex]V = \pi r^2 *h[/tex]
Now applying that to the question; Firstly, we are given the diameter, which is 22 inches. We need radius, to actually put it in the equation. The diameter is essentially 2 multiplied by the radius. That means to get the radius we divide the diameter by 2, giving us 11 inches. Next we are given how tall it is, 26 inches; that is the height.
[tex]r = 11in\\h = 26in[/tex]
Plug these values into the equation.
[tex]V = 3.14(11in)^2 * 26in[/tex]
Calculate this, and you get [tex]V = 9878.44 in^3[/tex]
What is the solution to y=-2x+7 and y=5x-7
Answer:
x-2,y= 3, it can also be written as (2 ,3)
Step-by-step explanation:
2x-7y=5x-7-2x-7=5x-75x+2x=
7+77x=14x=2y=5x-7=5*2-7=10-..
thankyou for the help
Answer:
d because a straight line has the angle of 180
What is a line? What is an angle? How do you describe a line and an angle? How do we know if an angle is right? obtuse? acute? or a full circle?
Answer:
A line is something that goes on endlessly in both directions. An angle is the number of degrees at a point where two rays meet. We know if an angle is right if there is a right angle that measures up to 90°. An obtuse is any angle that measures over 90° and an acute angle is under 90°. Hope this helps! :)
Step-by-step explanation:
PLEASE HELP ME QUICK !!
Answer:
9.138
10.28
11.26
12.55
ANSWER :
9.) 138
10.)28
11.)26
12.)55
HOPE IT HELPS
# CARY ON LEARNINGwhat is the slope between (8, -2) and (-7, 10)?
Answer:
-1/15 is the slope
Use the y2-y1/x2-x1 formula and plug in the variables
[tex]\sqrt[2]{80x^{2}y^{25} }[/tex]
Answer:
4xy^5√5
Step-by-step explanation:
√80 x √x² x √y^25
=4√5 x x x y^5
= 4√5xy^5
Answer:
4xy^12√(5y)
Step-by-step explanation:
Squares under the radical can be factored out.
[tex]\displaystyle \sqrt{80x^2y^{25}}=\sqrt{(4xy^{12})^2\cdot5y}=\boxed{4xy^{12}\sqrt{5y}}[/tex]
_____
Additional comment
Some versions of this question may have different exponents.
Please assist. No links
Answer:
(B) is the answer of your question
Kris’s mom is putting up a border on the walls of Kris’s room. Her room is 12 feet long and 10 feet wide. How many borders will be needed to go all the way around the room?
42 feet
44 feet
22 feet
120 feet
= 12 + 10 + 12 + 10
= 2x12 + 2x10
= 24 + 20
= 44 feet of borders
Answer:
its 44
Step-by-step explanation:
add 10+10 then add 12+12
Guys can you help me with this please
Answer:
AC=18.1cm
Step-by-step explanation:
When we subtract 11-4=7cm we get one cathetus of the right triangle a=7cm also we know hypotenuse which is c=16cm.
We will use Pythagorean theorem to find the second cathetus b
b=√16∧2-7∧2= √256-49= √207 ≈ 14.39cm =DC =>
AC =√(DC)∧2+(AD)∧2= √14.39∧2+11∧2= √207+121= √328= 18.1cm
AC=18.1cm
Please help me complete this chart. No URLS