Answers
(a) After 25 years 47.37g of the initial sample left in the sample. (b) 12.83 years takes the initial sample to decay half of its original amount.
Given:
[tex]A(t) = 200 e^{-0.054t}[/tex]
Substituting 25 for t in the expression, we get:
A(25) = 200e⁰.⁰⁵⁴ × 25
= 47.37 g
Thus, after 25 years, there will be 47.37g of the initial sample left in the sample.
(b.) 12.83 years takes the initial sample to decay half of its original amount.
We want to find t such that
[tex]A(t) = 200e^{0.054} \times t[/tex]
where, t = 100.
Solving for t, we get:
[tex]200e^{0.054} \times t = 100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.054 × t = ln(0.5)
Therefore,
[tex]t = \frac{\ln(0.5)}{0.054}[/tex]
= 12.83 years.
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Related Questions
Assume that the function [tex]f(x) = ax^{2} + bx + c, a \neq 0[/tex] has two real zeros. Prove that the x-coordinate of the vertex of the graph is the average of the zeros of [tex]f[/tex].
(Hint: Use the Quadratic Formula)
Answers
multiply 1/2 x 1/4 equals ?
Answers
1/2 * 1/4 = 1/8
Answer:
1/8 or 0.125
Step-by-step explanation:
1/2×1/8
multiply the numerators 1×1=1 and multiply the denominators 2×4=8
Final answer =1/8 or 0.125
Find the equivalent measure.
19 qt L
Click the icon to view the customary and metric unit equivalents.
-
19 qtL
(Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
The equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.
What is the equivalent measure?
In mathematics, and more specifically in measure theory, equivalence refers to the idea that two measures are qualitatively similar. The two measures specifically agree on which events have measure zero.
The unit "qt" stands for quart, which is a unit of volume.
It is equal to 32 fluid ounces or 0.946 liters.
Therefore, 19 quarts is equal to 19 * 32 = 1932= 608 fluid ounces,
or 19 * 0.946 = 190.946 =18.094 liters.
Hence, the equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.
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Sam and Liam raced up and then back down a hill. Sam's average speed up the hill
was 1 mph, and his average speed down the hill was 9 mph. Liam ran up the hill
and down the hill at 2 mph. If the trail from the bottom to the top of the hill is 1
mile long, how much time did it take each boy to finish? Who was the winner?
Answers
Using the speed formula, we know that Liam finished in 1 hour as opposed to Sam's 1/ 19 hours, earning him the victory.
What is speed?Speed is calculated as follows: speed = distance * time.
Knowing the units for distance and time is necessary to calculate the units for speed.
The units will be in meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).
So, the speed formula is:
Speed = Distance/Time
Taking time for the subject:
Time = distance/Speed
Now, Sam:
Time spent ascending the hill = 1/1 = 1 hour
Time spent descending the hill = 1/9 hours
Sam spent 1 1/the9 total minutes climbing and descending the hill.
Now, Lian:
Time spent ascending the hill = 1/2 hours
Time spent descending the hill = 1/2 hour
Total time spent ascending and descending the hill = 1/2 + 1/2 = 1 hour
Sam, therefore, took 1/9 hour longer than Liam.
Therefore, using the speed formula, we know that Liam finished in 1 hour as opposed to Sam's 1/ 19 hours, earning him victory.
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If there are 20 voters and 5 candidates , how many total points would there be in a Borda count
Answers
Answer:
25
Step-by-step explanation:
A scuba diver is at an elevation of −18 ft. She then descends 30 ft deeper. What is the scuba diver’s new elevation?
Answers
Answer: -48
Step-by-step explanation:
-18-30 = -48
Cedric deposited $796.00 in a savings account that earned 2.5% simple interest annually. Determine the amount of interest Cedric's account earned after 1 year and 9 months. (4 points)
$37.81
$34.83
$348.25
$295.56
Answers
The of interest earned by Cedric's account after 1 year and 9 months is $34.83.
What is the amount of interest in Cedric's account after 1 year and 9 months?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $796Interest rate r = 2.5%Elapsed time t = 12months + 9months = 21 monthsInterest I = ?Plug the given values into the above formula and solve for interest.
I = P × r × t
I = $796 × 2.5% × 21/12
I = $796 × 0.025 × 1.75
I = $796 × 0.025 × 1.75
I = $34.83
Therefore, the interest earned in the account is $34.83.
Option B is the correct answer.
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4 There are between 20 and 50 flags.
They can be shared equally among
2 tents or 4 tents or 5 tents.
How many flags are there?
Answers
When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.
How to illustrate the information?From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.
It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.
Therefore, the number of flags is 40.
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Find the direction of the sum of these two vectors:
Answers
By using the concept of vector, it can be calculated that
Direction of the sum is 10.87° below the horizontal.
What is vector?
Anything that has both magnitude and direction and follow the vector addition law is called vector.
A = 2.71 m
[tex]A_x = 2.71 cos 60 = 1.355 \ m\\A_y = -2.71 sin 60 = -2.35 \ m[/tex]
B = 3.14 m
[tex]B_x = 3.14 cos 30 = 2.71 \ m\\B_y = 3.14 sin 30 = 1.57 \ m[/tex]
Sum of A and B = (1.355 +2.71) i + (-2.35 + 1.57) j
= 4.065i - 0.78j
Let the angle be [tex]\theta[/tex]
[tex]tan\theta = \frac{0.78}{4.065}\\tan\theta = 0.192\\\theta = tan^{-1}(0.192)\\\theta = 10.87^{\circ}[/tex]
Direction of the sum is 10.87° below the horizontal.
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In a recent poll, 280 people were asked if they liked dogs, and 42% said they did. Find the margin of error of this poll, at the 90% confidence level.
Answers
If in a recent poll, 280 people were asked if they liked dogs, and 42% said they did. the margin of error of this poll, at the 90% confidence level is 0.05.
How to find the margin of error?Sample proportion =42%(phat)
Sample size =280
Standard error = √(0.42×( 1- 0.42)/280)
Standard error = √(0.42×(.58)/280)
Standard error =0.029
Hence,
Margin of error = z-critical for 90% confidence level× Standard error
Zα/2 = 1.645 for 90% confidence
Margin of error = 1.645 × 0.029
Margin of error = 0.047
Margin of error =0.05 (Approximately)
Therefore the margin of error is 0.05.
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For 3, use the table at the right.
3. Jose has $100 to spend at the pet store. He needs to buy
1 bag of dog food and 2 chew toys. How many catnip toys
can Jose buy? Write equations to show each step.
DATA
Barky's Pet Store
Product
Bag of Dog Food
Tex
Bag of Cat Food
Tex
Chew Toy
Catnip Toy
Cost
$35
$18
$12
39
Answers
The number of catnip toys that Jose can buy will be 3 catnip toys. All the steps are described below.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The table is given below.
Product Cost
Bag of Dog Food $35
Bag of Cat Food $18
Chew Toy $12
Catnip Toy $9
In the event that, your numbers are unique, you should simply supplant the qualities you have with the methodology here, and you ought to find an exact solution.
Presently, Emma has $100 to spend at the store. Along these lines, we really want to ascertain the amount she spends on shopping:
$35 + 2 x $12 = $59
In this way, she burned through $59 in the store, so she has left:
$100 - $59 = $41
She has $41 left to spend on something different. How about we check whether she has sufficient means to purchase multiple times catnip toys as bite toys:
Chew toys: 3 x 12 = $36
Catnip toy: 3 x 9 = $27
Furthermore, Emma has $41 left, so she can either purchase multiple times bite toys or multiple times catnip toys, however not the two of them at that point, on the grounds that the all-out would be 63% dollars, and she will be missing $22.
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What is the area of the polygon below?
A. 147 square units
B. 111 square units
C. 120 square units
D. 156 square units
Answers
Answer:
A. 147
Step-by-step explanation:
Divide the polygon into rectangles.
You will have 2 rectangles:
1) 3 x 10
2) 9 x 13
Now you just need to find the area of this 2 rectangles and add them up.
Solve each equation.
|x+5|=-3
Answers
Answer:
No solution
Step-by-step explanation:
The absolute value function outputs non-negative values.
Answer: No solutions
This is because absolute value is never negative. It represents distance, and negative distance does not make sense.
The smallest possible output of |x+5| is zero.
You are investing money at 10.5 percent annual interest, compounded continuously. It will take you ______ years to double your investment.
Answers
let's take it from the basic of one dolla!, how long will it take for $1 to become $2, namely double, at 10.5%?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ t=years \end{cases} \\\\\\ 2=1e^{0.105\cdot t} \implies \log_e(2)=\log_e(e^{0.105t})\implies \log_e(2)=0.105t \\\\\\ \ln(2)=0.105t\implies \cfrac{\ln(2)}{0.105}=t\implies 6.6\approx t\qquad \textit{about 6 years and 219 days}[/tex]
What is slope-intercept form?
O not this one
O a² +6² = = C
O Ax+By = C
O y = mx + b
Answers
Answer:
O y = mx + b
Step-by-step explanation:
y = y coordinate
m = slope
x = x coordinate
b = y intercept
Please help, math modeling with distribution and statistics
Answers
The probability of having fewer than three television sets in the apartment is 0.7
How to find the probability of having fewer than three television setsProbability is solved by finding the ratio of required outcome to the total sample
In the given problem the total sample space is the sum of the frequencies which
sum of the frequencies
= 1 + 6 + 14 + 7 + 2
= 30
The required outcome is the number of people that have less than three tv sets in their apartment, In this case 3 is not inclusive from 2 to o is added
= 1 + 6 + 14
= 21
The probability P(X < 3) = 0.7
= 21 / 30
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Graph the polygon with the given vertices and its image after a reflection in the line y = x.
A(6, - 3), B(1, - 2), C(4, 1)
Answers
The image of the polygon after a reflection in the line y=x is having vertices at A'(-3, 6), B'(-2, 1) and C'(1, 4) as shown in the diagram attached.
What is a reflection?A reflection is a sort of transformation that creates a new shape by flipping a shape, called the preimage, across a line, called the line of reflection (called the image). You may imagine what would occur if the form were turned over the line to graph a reflection.
A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image).
You can picture what would happen if you flipped the form over the line in order to graph a reflection.
If a point A(x, y) is reflected about the line y = x,
the new point would be at A'(y, x)
Given the polygon with vertices at A(6, -3), B(1, -2) and C(4, 1).
The image of the polygon after a reflection in the line y=x has vertices at:
A'(-3, 6), B'(-2, 1) and C'(1, 4)
The image of the polygon is attached.
Therefore, according to the attached graphic, the vertices of the polygon's image after a reflection in the line y=x are located at A'(-3, 6), B'(-2, 1), and C'(1, 4).
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By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is (a) greater than zero. (b) less than zero. (c) 0.93 . (d) 6.4 (e) Can't tell without seeing the data.
Answers
As per the given least square regression line, the correlation between the height and the arm span is (a) greater than zero.
Regression line:
In statistics, regression line refers the an estimate of the line that describes the true, but unknown, linear relationship between the two variables.
Given,
Here we need to find the correlation between the height and the arm span by using the given least square regression line.
Let us consider the following situation,
"Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm)."
While we looking into this one we have identified that the predicted function y = 6.4 + 0.93x, is defines the value of height.
So, here y is the dependent variable and the x is the independent value.
This means that the value x is smaller comparatively y value.
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which inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) on the boundary?
y<-3/2 x²+9 x+21/2
y<3/2 x²+9 x-21/2
y<-3/2 x²-9 x+21/2
y<3/2 x²-9 x-21/2
Answers
The inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) quadratic function is
y < 3/2 x² + 9 x - 21/2How to show the inequality requiredThe problem seeks the inequality that will be less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).
Therefore the quadratic function should have zeros at -7 and 1
Substituting the point (2, 27/2) to the quadratic function to check the one that gives the points shows that
3/2 x² + 9 x - 21/2 at x = 2
3/2 * 2² + 9 * 2 - 21/2
= 27/2
Solving for the zeros in the quadratic function 3/2 x² + 9 x - 21/2
shows that the zero are at
x = -7 and
Therefore the inequality that meets the condition is y < 3/2 x² + 9 x - 21/2
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Three varieties of coffee Coffee A, Coffee B, and Coffee C are combined and roasted, yielding a 55-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for $10.39 per lb, are needed as Coffee A, which sells for $14.99 per lb. Coffee B retails for $13.99 per lb. How many pounds of each coffee should be used in a blend that sells for $12.61 per lb?
Answers
Coffee A is 12.241 pounds, Coffee B is 18.269 pounds and Coffee C is 24.482 pounds.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Let a pounds of coffee A needed
Let b pounds of coffee B needed
Let c pounds of coffee C needed
c= 2a.................(1)
a+ b+c= 55..........(2)
and, 14.99 a+ 13.99 b + 10.39 c /55 = 12.61
1499a + 1399 b + 1039 c = 69,355...............(3)
Subtract (2) from (3), we get
1499 a+ 1399 b + 1039 c= 69355
- 1039 a - 1039 b - 1039 c = 57145
_____________________________
460 a + 360 b = 12210
46a+ 36 b = 1221
b= 1221/ 36 - 46 a/ 36
b= 407 / 12 - 23 a / 18
Put b in Equation (2)
a + 407 / 12 - 23 a / 18 + 2a= 55
-5a / 18 + 2a + 407/ 12 = 55
31a/ 18 = 253/ 12
a= 4554 / 372
a = 2277/ 186
a= 759/ 62
a= 12.241
and, c=2a = 24.482
b= 33.91 - 15.641
b= 18.269
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Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $700, 3 prizes of $100, 5 prizes of $10, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
Answers
This raffle's expected value per ticket is $ 0.25.
Given that 5,000 tickets are sold at $1 apiece for a charity raffle, and tickets are to be picked at random, the following monetary prizes will be awarded.
To estimate the expected value of this raffle if you buy 1 ticket, apply the following calculation: 1 prize of $ 500, 3 prizes of $ 200, 5 prizes of $ 10, and 20 prizes of $ 5.
⇒ (500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X
⇒ (500 + 600 + 50 + 100) / 5000 = X
⇒ 1250/5000 = X
Apply the division operation, and we get
⇒ 0.25 = X
Therefore, this raffle's expected value per ticket is $ 0.25.
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Please help
Whats
30-19+29+30-29-10=
Answers
Answer:
31Step-by-step explanation:
[tex]\tt 30-19+29+30-29-10[/tex]
[tex]\tt 11+29+30-29-10[/tex]
[tex]\tt 40+30-29-10[/tex]
[tex]\tt 70-29-10[/tex]
[tex]\tt 41-10[/tex]
[tex]\tt 31[/tex]
__________________
Hope this helps you!
Have a nice day!
Dwayne has collected data on the number of occupants of cars travelling on the road past his house for the past week. Based on his data, he has constructed a probability model for the number occupants of a randomly-selected car on his street. Which of the following could be his model?
Answers
The option that can be the model when Dwayne has collected data on the number of occupants of cars travelling on the road is Table B.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true
Given the information, the probability for a will be illustrated as:
a. = 0.6 + 0.2 + 0.2 + 0.1 + 0.05 = 1.15 > 1
b. = 0.5 + 0.25 + 0.05 + 0.06 + 0.04 = 1
c. 2 + 1 + 0.1 + 0.1 + 0.4 = 3.6 > 1
d. 0.5 + 0.25 + 0.25 + 0.125 + 0.125 = 1.25 > 1
e. 0.5 + 0.2 + 0.1 + 0.05 + 0.05 = 0.9 < 1
The correct option that illustrates this is Table B.
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Expand the log completely
Answers
Answer:
log(2)√xy
________
y
there good luck
Use the L-shaped composite figure formed by two rectangular prisms to answer the question.
What is the surface area of the composite figure in square inches?
(WILL GIVE BRAINLIEST)
Answers
The surface area of the composite figure is calculated as: 640 square inches.
What is the Surface Area of a Rectangular Prism?The surface area of a rectangular prism = 2(w*l + h*l + h*w), where:
l = length w = width h = heightThe composite figure can be decomposed into two rectangular prisms, 1 and 2.
Rectangular prism 1:
l = 10 in.
w = 0.5 ft. = 6 in.
h = 4 + 7 = 11 in.
Surface area = 2*(6*10 + 11*10 + 11*6) = 472 in.²
Rectangular prism 2:
l = 10 in.
w = 0.5 ft. = 6 in.
h = 4 in.
Surface area = 2·(6·10+4·10+4·6) = 248 in.²
The area of the surface where both meet = (l)(w) = (10)(4) = 40 in.²
Therefore:
Surface area of the composite figure = 472 + 248 - 2(40) = 640 in.².
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(Please Help!) For each quantity decide whether circumference or area would be needed to calculate it.
A: The distance around a ferris wheel
B:The amount of paint needed to paint a bullseye
C: The amount of whipped cream needed to go around the edge of a pie
D The amount of material needed to make a drum head (the part of the drum you hit).
Answers
The quantities we need circumference for are: A and C.
The quantities we need area for are: B and D.
What is the Circumference and Area of a Circular Shape?The circumference of a circular shape is described as the distance around the circular shape. It is calculated using the formula, 2πr.
On the other hand, the area of a circular shape is the amount of space a circular shape has. It is calculated as πr².
Therefore:
For quantity A, to know the distance around a Ferris wheel, we would need to calculate is the circumference, so also for quantity C.
For quantity B, to know the amount of paint needed, we would calculate the area, so also is it for quantity D.
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ZA and ZB are vertical angles. If m/A = (6x +29)° and m
LB = (7x+25)°, then find the value of x.
Answers
The value of x is 4.
What are vertical angles?
The opposing angles formed when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.
Here, we have
Given the following parameters
m∠A= (6x +29)° and
m∠B = (7x+25)°
Now, we equate both angles to find the value of x and we get
6x+29 = 7x + 25
6x-7x = 25 - 29
-x = -4
x = 4
Hence, the value of x is 4.
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easy proportional relationship help wanted
Answers
Answer:
y = [tex]\frac{1}{8}[/tex]x
Step-by-step explanation:
You need to find the unit rate. In a proportional relationship, you can find this by taking any point on the line and putting it the form y/x
Look at point (16,2) y/x = 2/16 = 1/8
Lucas is 5 inches taller than Tamika, and the sum of their heights is 137 inches?
Answers
Answer:
Lucas 71 inches
Tamika 66 inches
Find two positive numbers whose difference is 11 and whose product is 1692.
Answers
The positive numbers are 36 and 47.
What is a positive number?
Any positive number is one that is higher than zero.
A number can be zero, negative, or positive. Zero has no positive or bad aspects. The most frequent positive numbers in daily life include 34, 9.22, and other examples such as these. They are typically depicted on a number line to the right of zero, increasing bigger as you move to the right.
Assume that the positive numbers be x and y.
Given that the difference x and y is 11.
Therefore x - y = 11
x = y + 11 ....(i)
The product of the numbers is 1692.
xy = 1692 .....(ii)
Putting x = y - 11 in equation (ii):
(y + 11)y = 1692
y² +11y = 1692
y² +11y - 1692 = 0
y² +47y - 36y - 1692 = 0
y(y + 47) - 36(y+47) = 0
(y + 47) (y-36)=0
y = -47 and 36
Since the numbers are positive, thus y = 36.
The value of x is 36 + 11 = 47
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