Answer:
(a) [tex]A = A_0 * e^{kt}[/tex]
(b) There will be 1lb left after 14 hours
Step-by-step explanation:
Solving (a): The equation
Since the substance decomposes at a proportional rate, then it follows the following equation
[tex]A(t) = A_0 * e^{kt}[/tex]
Where
[tex]A_0 \to[/tex] Initial Amount
[tex]k \to[/tex] rate
[tex]t \to[/tex] time
[tex]A(t) \to[/tex] Amount at time t
Solving (b):
We have:
[tex]t = 4.6hr[/tex]
[tex]A_0 = 8[/tex]
[tex]A(4.6) = 4[/tex]
First, we calculate k using:
[tex]A(t) = A_0 * e^{kt}[/tex]
This gives:
[tex]A(4.6) = 8 * e^{k*4.6}[/tex]
Substitute: [tex]A(4.6) = 4[/tex]
[tex]4 = 8 * e^{k*4.6}[/tex]
Divide both sides by 4
[tex]0.5 = e^{k*4.6}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.5) = \ln(e^{k*4.6})[/tex]
This gives:
[tex]-0.6931 = k*4.6[/tex]
Solve for k
[tex]k = \frac{-0.6931}{4.6}[/tex]
[tex]k = -0.1507[/tex]
So, we have:
[tex]A(t) = A_0 * e^{kt}[/tex]
[tex]A(t) = 8e^{-0.1507t}[/tex]
To calculate the time when 1 lb will remain, we have:
[tex]A(t) = 1[/tex]
So, the equation becomes
[tex]1= 8e^{-0.1507t}[/tex]
Divide both sides by 8
[tex]0.125= e^{-0.1507t}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.125)= \ln(e^{-0.1507t})[/tex]
[tex]-2.0794= -0.1507t[/tex]
Solve for t
[tex]t = \frac{-2.0794}{-0.1507}[/tex]
[tex]t = 13.7983[/tex]
[tex]t = 14[/tex] --- approximated
Solve the equation by completing the square. Round to the nearest hundredth x^2 + 2x = 15
Answer:
x = 3, x = -5
Step-by-step explanation:
A perfect square trinomial is represented in the form a^2 + 2ab + b^2. We are already given the a^2 term, x^2, and the 2ab term, 2x. From this we can say:
a^2 = x^2
a = x
Now, we can substitute x for a in the other expression to create the equation:
2ab = 2x
2(x)b=2x
b = 1
From this, b^2 is one, so, to get our trinomial all on one side, we add 1 to both sides:
x^2 + 2x = 15
x^2 + 2x + 1 = 16
Now, we can factor. The perfect square trinomial factors into (a + b)^2. In this case, a is x, and b is one. We can factor and get:
(x + 1)^2 = 16
Now, we take the square root of both sides:
x + 1 = ± 4
We can separate this into two equations and solve:
x + 1 = 4
x = 3
x + 1 = -4
x = -5
Answer:
Step-by-step explanation:
x^2 + 2x = 15
x^2 + 2x + [1/2(2)]^2 = 15 + [1/2(2)]^2
(x + 1/2(2) )^2 = 15 + [(1/2)(2)]^2
(x + 1)^2 = 15 + 1^2
(x + 1)^2 = 15 + 1
(x+1)^2 = 16 Take the square root of both sides.
sqrt( (x + 1)^2 ) = sqrt(16)
x + 1 = +/- 4
x + 1 = 4
x = 4 - 1 = 3
x + 1 = -4
x = -4 - 1
x = - 5
So the roots are 3 and - 5
by selling 33m of cloth ,prabha gained the selling price 11 m.what is the gain percent
Answer:
The gain percent is 33.3 %
Step-by-step explanation:
Let the selling price of 1 m cloth is p.
Cost of 33 m = 33 p
gain = cost of 11 m = 11 p
The gain percentage is given by
[tex]\frac{11 p}{33 p}\times 100\\\\= 33.3 %[/tex]
The gain percent is 33.3 %.
The length of a rectangle is four times its width.
If the area of the rectangle is 100 yd”, find its perimeter.
Answer: 50yd
Step-by-step explanation:
We know that the area of any rectangle is length times width. The perimeter is the sum of twice the length and twice the width.
Let width = x
Let length = 4x
Area = 100m2
Next, we can write an equation using these variables and formula for area.
4x2 = 100
x2 = 25
x = -5 and x = 5
Since the dimensions cannot be negative, we accept the positive value:
x = 5
Next, we can substitute this value of x into the variables.
width = 5 m
length = 20 m
Finally, we can find the perimeter by plugging in these dimensions into the perimeter formula,
Perimeter = 2(5 m) + 2(20 m)
= 10 m + 40 m
= 50 m
Suppose that g(x)= f(x)+ 6. Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted 6 units down.
B. The graph of g(x) is the graph of f(x) shifted to the right.
C. The graph of g(x) is the graph of f(x) shifted 6 units to the left.
D. The graph of g(x) is the graph of f(x) shifted 6 units up.
Answer:
D
Step-by-step explanation:
The + 6 moves it up 6 units.
The correct answer is (D) "The graph of g(x) is the graph of f(x) shifted 6 units up."
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
When we add a constant to a function, such as in the case of g(x) = f(x) + 6, it will shift the graph of f(x) upward by 6 units.
This is because, for any value of x, the value of f(x) will be added to 6, resulting in a vertical shift of the entire graph.
Option (A) is incorrect because adding 6 to f(x) would shift the graph up, not down.
Option (B) is incorrect because adding a constant to a function does not cause it to shift horizontally.
Option (C) is incorrect because adding 6 to f(x) would shift the graph right, not left.
D. The graph of g(x) is the graph of f(x) shifted 6 units up. Adding a constant term to a function will shift the graph of the function vertically. In this case, adding 6 to f(x) will shift the graph of f(x) upward by 6 units, resulting in the graph of g(x).
Learn more about function here:
https://brainly.com/question/29633660
#SPJ7
C
What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?
SER
O y=-*x+33
y=-*x+36
O y =
O y = 4x - 16
O y = 4x + 16
Mark this and retum
Save and Exit
Nex
Submit
9514 1404 393
Answer:
y = 4x + 16
Step-by-step explanation:
You can replace the point coordinates in the given point-slope form to get ...
y - 32 = 4(x -4)
Then rearrange to put this into slope-intercept form.
y = 4x -16 +32 . . . . eliminate parentheses, add 32
y = 4x +16 . . . . . . . . simplify
Sketch the region enclosed by the given curves and calculate its area.
y=4-x^2 ,y=0
The answer is 32/3. But how do I get to that answer?
Answer:
Step-by-step explanation:
1.) we need to find the bounds of integration which is just the points of intersection
here is it (-2,0) and (2,0)
which means we will integrate from -2 to 2
next, we take the upper equation and subtract that from the lower one
kind of confusing but it would look like (sketch it out if you're not sure)
(4-x²)-0= 4-x²
then we can integrate
[tex]\int\limits^2_{-2} {4-x^2} \, dx =4x-\frac{x^3}{3}|_{-2}^{2}=(4*(2)-\frac{2^3}{3})-(4(-2)-\frac{-2^3}{3})=5.333333-(-5.3333333)= 10.666666667=\frac{32}{3}[/tex]
I 0 ×I 1× I 2 ×I 3×I 4
Answer:
the answer is twelve by multiplying them all.
Answer:
2 , 40,420
Step-by-step explanation:
10 × 11 × 12 × 13 × 14
1,320 × 182
2,40,240
cort
Here are ten numbers:
3 7 2 4 7 5 7 1 8 8
Write down the mode.
b)
Work out the median.
c)
Calculate the mean.
What is the range?
Answer:
The mode is 7 and 8
The mean is 5.2
The range is 7
Simplify log2 20-log2 30.
Answer:
[tex] log_{2}(20) - log_{2}(30) \\ log_{2}(20 \div 30) \\ log_{2}(0.667) [/tex]
hope this helps you
Brainliest appreciated
log1(20)-log2(30)
log2 (20÷30)
log2=0.667
Find the value of PR if Q is between P and R
when PQ=25, PQ=2x+1, and QR=x.
X
ат
X=8
Answer:
[tex]PR = 37[/tex]
Step-by-step explanation:
Given
[tex]PQ = 25[/tex]
[tex]PQ = 2x +1[/tex]
[tex]QR = x[/tex]
Required
PQ
Since Q is between the given points, then:
[tex]PR = PQ + QR[/tex]
This gives:
[tex]PR = 2x + 1 + x[/tex]
Collect like terms
[tex]PR = 2x + x+ 1[/tex]
[tex]PR = 3x + 1[/tex]
Next, solve for x
We have:
[tex]PQ = 25[/tex]
[tex]PQ = 2x +1[/tex]
This gives:
[tex]2x + 1 = 25[/tex]
Collect like terms
[tex]2x = 25 -1[/tex]
[tex]2x = 24[/tex]
Divide by 2
[tex]x = 12[/tex]
So:
[tex]PR = 3x + 1[/tex]
[tex]PR = 3 * 12 + 1[/tex]
[tex]PR = 37[/tex]
Find the slope of each line (each block is one unit):
Answer:
-2
Step-by-step explanation:
Slope formula for any given two points
(y2 - y1 / x2 - x1)
The points chosen may vary but the points I chose were (0,1) and (2,-3)
Our next step is to identify the variables
y2 = -3
y1 = 1
x2 = 2
x1 = 0
We then plug in the values into the slope formula
slope = ( -3 - 1 ) / ( 2 - 0 )
Simply
Slope = -4 / 2
Simply even further
Slope = -2
the slope of each line is -2.
Answer:
Solution Given:
let's find out the given points.
1st point[tex] (x_1,y_1)=(0,1)[/tex]
another point is:
[tex](x_2,y_2)=(2,-3)[/tex]
now
By using slope formula
[tex] \green{\boxed{m=\frac{y_2-y_1}{x_2-x_1}}}[/tex]
now
substituting value
we get
m=[tex]\frac{-3-1}{2-0}=\frac{-4}{2}=-2[/tex]
A meeting on an unpopular topic has been announced. The number of attendees may be modeled by X where What is the probability that at least 5 people attend the meeting given that at least 2 attend
Answer:
The probability that at least 5 people attend the meeting given that at least 2 attend is 12.50%.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
A meeting on an unpopular topic has been announced. The number of attendees may be modeled by X where:
P(X = x) = 1 / 2^(x+1), for x = 0,1,2,...
What is the probability that at least 5 people attend the meeting given that at least 2 attend?
The explanation of the answer is now provided as follows:
Given:
P(X = x) = 1 / 2^(x+1), for x = 0,1,2,... (1)
Since it is given that at least 2 attend, it implies that we need to calculate P(x) at x = 2.
Substituting x = 2 into equation (1), we have:
P(X = 2) = 1 / 2^(2 + 1)
P(X = 2) = 1 / 2^3
P(X = 2) = 1 / 8
P(X = 2) = 0.1250, or 12.50%
Therefore, is the probability that at least 5 people attend the meeting given that at least 2 attend is 12.50%.
Graph the equation. Let x3, 2, 1, 0, 1, 2, and 3. y=3x-1
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The attachment shows the table of point values and the graph.
The football and soccer teams at Juan's middle school are selling movie tickets. He wants to determine the average
number of tickets sold at the school. First, he surveyed eight random players on the football team. Then, he surveyed
every third athlete on the football and soccer team. Which sampling technique should produce a more representative
sample?
The first sampling method, surveying eight random football players, is the most representative.
O Neither sample will be representative.
Both samples should be exactly the same.
The second sampling method, survey.ing the both teams, is the most representative.
Step-by-step explanation:
both samples should be exactly the same
Can anyone help me with this question
Answer:
50%
Step-by-step explanation:
If angle f is 50 degrees and cuts it to 75 degrees
Find the difference between the two numbers
75-50 = 25
Divide by the correct value
25/50 = 1/2
Change to percent form
50%
Determine which value best approximates the length of the arc represented by the integral ∫_0^1 √1 + [d/dx(4/x+1)]² dx.
(Make your selection on the basis of a sketch of the arc and not
by performing any calculations.)
(a) 10
(b) -5
(c) 2
(d) 4
(e) 1
Answer:
Option C
Step-by-step explanation:
From the question we are told that:
Length of arc integral
[tex]l=\int_0^1 \sqrt{1 + [\frac{d}{dx}(\frac{4}{x+1})]^2 dx}[/tex]
The Sketch is attached below
From the Graph
Approximation gives length of arc as
[tex]l=\sqrt{5}[/tex]
[tex]l=2[/tex]
Option C
Please help me with this question
The upwards acceleration of a small rocket at time t s is given by a = 16 − 1.5t. The rocket is subject to this
acceleration for 3 seconds. Given that it starts from rest at t = 0, calculate the height reached by the rocket in
this time
Answer:
11.5
Step-by-step explanation:
plug 3 in for x
then solve
Look at the illustration.
What is WX?
Answer:
O 0.5 units
Step-by-step explanation:
so the first thing we have to do is to calculate for the dilation factor. Taking point G as the reference point, we can see that the distance of point G from rectangle W'X'Y'Z is 1.5 while the distance from rectangle WXYZ is (1.5 + 7.5) = 1.5 / 9 = 1/6
Since WX has an initial measure of 3 units, therefore the measure of W'X' is:
W'X' = 3 units *(1/6) = 0.5 units
Find the area of the rectangle if the perimeter is 52 cm
Answer:
No solution is possible from the information provided
Step-by-step explanation:
what is 1.0185 rounded to the nearest thousandth???
Answer:
1.019 is the answer
If 21% of kindergarten children are afraid of monsters, how many out of
each 100 are afraid?
Answer:
The appropriate answer is "21".
Step-by-step explanation:
Given:
Afraid percentage,
p = 21%
or,
= 0.21
Sample size,
n = 100
As we know,
⇒ [tex]X=np[/tex]
By putting the values, we get
[tex]=0.21\times 100[/tex]
[tex]=21[/tex]
A cyclist travels at an average speed of 18 mph for 2 hours.
How far did she travel in miles?
Answer:
36
Step-by-step explanation:
18 miles per hour so for 2 hours which is double, she should have traveled 36 miles.
Good Luck!
I'm not good with ordering fractions from smallest to largest. Can help anyone help with this problem?
Write the formulae of area and volume of different solid shapes. Find out the variables and constants in them.
Answer:
Step-by-step explanation:
1 . Sphere :
[tex]Surface \ Area = 4\pi r^2\\\\ Volume = \frac{4}{3} \pi r^3[/tex]
Variable is ' r '
Others Constants.
2. Cone :
[tex]Surface \ Area = \p r^2 + \pi rs[/tex] [tex][ \ s = \sqrt { r^2 + h^2 } \ , r = base \ radius, h = height \ ][/tex]
[tex]Volume = \frac{1}{3} \pi r^2 h[/tex]
Variables are ' r ' and ' h '
Others constants.
3. Cuboid ( Rectangular Prism )
[tex]Surface \ Area = 2 ((l\times b) + ( b \times h) + ( l \times h)) \\\\Volume = l \times \ b \times \ h[/tex]
Variables : l , b , h
Constant is 2
4. Cylinder
[tex]Surface \ Area = 2 \pi r h + 2 \pi r^2 \\\\Volume = \pi r^2 h[/tex]
Variables : ' r ' and ' h '
Others constants..
Answer:
shapes. cuboid. cube. cylinder. prism. sphere. pyramid. rightcircularcone. volumeformula. l×w×h. v=a . 3. v=πr . 2. h. v=b×h. v=( 3. 4)πr . 3. v=( 3. 1)×h×b. v=( 3. 1)πr . 2. h. variables. l=length,w=width,h=height. a=side. r=radius,h=height. b=base,h=height. r=radiusofthesphere. b=areaofthebase,h=heightofthepyramid. r=radiusofthecircularbase,h=height
Step-by-step explanation:
how to solve letters and numbers in a box
it cost $246 to turf a lawn of 43m ² . how much will it cost to turf a lawn of 61m square 2 .
Answer:
$348.96
Step-by-step explanation:
246÷43=5.72
61-43=18
18×5.72=102.96
102.96+246=348.96
Four students want to have their picture taken together. They will stand side-by-side for the picture. In how many different ways can the four students be arranged to take a picture?
Show your work, please :')
Answer:
24 waysStep-by-step explanation:
This is the permutation of 4:
4P4 = 4! = 1*2*3*4 = 24 ways[tex]\huge\qquad \mathbb{\fcolorbox{red}{lavenderblush}{✰Answer}}[/tex]
✶⊶⊷⊶⊷❍❁❥❀❥❁❍⊶⊷⊶⊷✶
Four students want to have their picture taken together. They will stand side-by-side for the picture. In how many different ways can the four students be arranged to take a picture
so we have to find the permutation of 4
4×3×2×124.°. In 24 different ways can the four students be arranged to take a picture
help pleaseeee it’s timed!!!
Answer:
C
Step-by-step explanation:
The solution triangle is attached below :
Tonobtinnthe Angle formed, θ; we apply trigonometry ;
Using ;
Cos θ = Adjacent / hypotenus
Cos θ = 4 / 7
θ = Cos^-1(4/7)
θ = 55.15°
θ = 55°
To estimate the difference we need four averages for the categorized groups i.e., control group before change, control group after change, treatment group before change and treatment group after change.
a. True
b. False
Answer:
b. False
Step-by-step explanation:
In a research study, when a researcher wants to find the impact of a new treatment, then the researcher randomly divides the the study participants into two groups. The groups are :
-- control group
-- treatment group
The control group is a group that is used to establish the cause-and-effect relationship by making the effect of an independent variable isolate. It receives no treatment or some standard treatment for the which the effect is already known.
The treatment group receives the treatment for which the effect the researcher is interested in.
Thus the averages of the four categorized groups are not required for estimating the difference.
Therefore, the answer is FALSE.