Answers
The amount of the radioactive substance is 374.6 g
How to determine the amount of radioactive substance?The given parameters are:
Initial, a = 424 mgRate, r = 6%Time, t = 2 hoursThe amount of the radioactive substance is calculated as:
A(t) = a(1 - r)^t
This gives
A(t) = 424 * (1 - 6%)^t
At 2 hours, we have:
A(2) = 424 * (1 - 6%)^2
Evaluate
A(2) = 374.6
Hence, the amount of the radioactive substance is 374.6 g
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Related Questions
You are finding a measure of center in the data sets below using either the mean or the median. In which of the data sets should you find the median? Select all that apply.
A) 68, 73, 77, 75, 23, 62 B) 84, 73, 28, 91, 93, 77 C) 24, 22, 21, 19, 23, 25 D) 18, 13, 56, 21, 12, 19 E) 77, 15, 81, 83, 84, 72
Answers
The whole given data sets can have their median calculated after being arranged either in an ascending or descending order. That is option A,B,C,D and E.
What is median of a data set?The median of a data set is defined as the data that is found at the center, otherwise known as the measure of center of a data set, after being arranged in ascending or descending order.
For example the median of option A) is calculated as follows:
Data set= 23,62,68,73,75,77
Median = 68+73/2 = 70.5
Therefore the median is between 68 and 73 which is = 70.5
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Flying against the wind a jet travels 5040 miles in 8 hours flying with the wind the same jet travels 6780 miles in 6 hours. What is the rate of the jet in still air and what is the rate of the wind?
Answers
Answer:
(Wind speed: 81,000) and (Rate of the jet in still air: 11,820)
Step-by-step explanation:
We know that 5040 times 8 is 40320.
And 6780 times 6 is 40680.
Then, add them together and the rate of the wind is 81,000.
The rate of the jet, add them (6780 plus 5040) and you'' get 11,580.
Factor k3 + 1 completely.
Answers
Answer:
(k+1)(k²-k+1)
Step-by-step explanation:
Philip is twice as old as Annie. Paul is 4 years older than Phillip and Chris is 2 years younger than Annie. Which represents the order of the children by age, from oldest to youngest? A. Paul, Phillip, Annie, Chris B. Chris, Paul, Annie, Phillip C. Annie, Phillip, Paul, Chris D. Paul, Phillip, Chris, Annie
Answers
Option -A is correct that is the order of the children by age, from oldest to youngest is Paul, Phillip, Annie, Chris.
Given that,
There are 4 children's. The names of the children's are Philip, Annie, Paul and Chris.
Philip is twice as old as Annie. Paul is 4 years older than Phillip and Chris is 2 years younger than Annie.
We have to find which represents the order of the children by age, from oldest to youngest.
We know that,
Lets us take the ages if the children's as a,b,c,d of Philip, Annie, Paul and Chris.
Philip is twice as old as Annie.
That means a = 2b
Paul is 4 years older than Phillip and
That mean c =4+a
Chris is 2 years younger than Annie.
That means d=b-2
So,
If we take the age of Philips as 20
Then Annie is 10, Paul is 24 and Chris is 8.
Therefore, Option -A is correct that is the order of the children by age, from oldest to youngest is Paul, Phillip, Annie, Chris .
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Pedro thinks that he has a special relationship with the number 5. In particular, Pedro thinks that he would roll a 5 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Pedro will roll a 5. (Note you will need to find the probability of getting a four when rolling a fair 6-sided die like we did in chapter 3 so that you can compare p to this value.)
(a) State the null and alternative hypotheses for testing Pedro's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =", ">=", or "<=" and express any values as a fraction e.g. p = 1/3) H0 = Ha =
(b) Now suppose Pedro makes n = 38 rolls, and a 5 comes up 8 times out of the 38 rolls. Determine the P-value of the test: P-value =
(c) Answer the question: Does this sample provide evidence at the 5 percent level that Pedro rolls a 5 more often than you'd expect? (Type: Yes or No)
Answers
Answer:
1.)
H0 : p = 1/6
H1 : p > 1/6
2.)
Pvalue = 0.3029
3.)
No
Step-by-step explanation:
Probability of rolling 5 in a 6-sided die by chance :
Number of 5's = 1
Number of 6 = 6
p = 1/6
The Null hypothesis :
H0 : p = 1/6
Since Pedro thinks he'd roll more than just by chance ;
Alternative hypothesis :
H1 : p > 1/6
Given that :
n = 38 ` x = 5
Phat = x / n = 5 / 38
Teat statistic : (phat - p) / √p(1-p)/n
1-p = 1 - 1/6 = 5/6
phat - p = 5/38 - 1/6 = −0.035087
√p(1-p) /n = (1/6 * 5/6) / 30 = √0.0046296 = 0.0680
Test statistic = −0.035087 / √0.0046296 =
Test statistic = −0.515673
Using the Pvalue calculator :
Pvalue at 0.05 , 1 - tail = 0.3029
Pvalue = 0.3029
Hence, at α = 0.05
Pvalue > α ;
There is no evidence to support Pedro's claim
A study was conducted to determine if the salaries of the professors from two neighbouring universities were
equal. A sample of 20 professors from each university was randomly selected. The mean from the first university
was $109,100 with a population standard deviation of $2300. The mean from the second university was $110,500
with a population standard deviation of $2100. Assume that the distribution of professor salaries, at both
universities, are approximately normally distributed. Level of significance = 0.05.
Use the four-step P-value approach and test the claim that the salaries from both universities are equal.
Answers
Answer:
After calculating values from test statics we come to know that value of if null hypothesis is true then it will rejected
As critical values of z is ±1.96 after apply the test statics formula , we get the value of z that is - 4.50 As we consider the equation that
H₀ > z
Apply test statistic we fine the true value . So there is sufficient evidence to reject the claim.
Step-by-step explanation:
critical values z₀ = ±1.96; standardized test statistic z ≅ -4.50;
reject H₀
There is sufficient evidence to reject the claim.
All eighth-grade students can choose to take one of the following elective courses: art, chorus, band, or woodworking. There are 20 more students enrolled in chorus than art. Band has 3/4 the enrollment as chorus. Woodworking has 5 fewer students enrolled than band. Which expressions represent this situation?
Answers
(7/2)x + 45 is the expression for the total number of students.
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Art students = x
Chorus students = x + 20
Band students = 3/4 (x + 20)
Woodworking students = 3/4(x + 20) - 5
Now,
Total students.
= x + x + 20 + 3/4(x + 20) + 3/4(x + 20) - 5
= 2x + 20 + 3x/4 + 15 + 3x/4 + 15 - 5
= 2x + 3x/4 + 3x/4 + 45
= 2x + 6x/4 + 45
= 2x + 3x/2 + 45
= (4x + 3x)2 + 45
= 7x/2 + 45
Thus,
(7/2)x + 45 is the expression.
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Kaylee owns a food truck that sells tacos and burritos. She only has enough supplies to make 120 tacos or burritos. She sells each taco for $3 and each burrito for $6. Kaylee must sell at least $480 worth of tacos and burritos each day. If xx represents the number of tacos sold and yy represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
Answers
The system of inequalities is:
x + y ≤ 120
x*3 + y*6 ≥ 480
And one possible solution to it is x = 20 and y = 80.
How to find the system of inequalities?
First, we need to define two variables, we will be using:
x = number of tacos.y = number of burritos.We know that she can make at most 120 units, then:
x + y ≤ 120
And she wants to win at leastt $480, then:
x*3 + y*6 ≥ 480
So our system of inequalities is:
x + y ≤ 120
x*3 + y*6 ≥ 480
And the graph can be seen in the image below, the solution set of the system is given by the region where both shaded areas intersect.
There we can see that one possible solution is x = 20 and y = 80, in that case the total number of items made is:
20 + 80 = 100, which is less than 120
And the income is:
20*3 + 80*6 = 540.
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The spinner at the right is divided into eight equal parts. Find the theoretical probability of landing on the given section(s) of the spinner.
P(not less than 5)
Answers
Answer:
P(not less than 5) = 0.5
Step-by-step explanation:
Given
Parts of spinner = 8 equal parts
Required
P(not less than 5)
First, it'll be assumed that the parts of the spinner is numbered 1 - 8.
This gives the following sample space (S)
S = {1,2,3,4,5,6,7,8}
Total = 8
To calculate PP(not less than 5), the number of parts not less than 5 is needed.
Parts not less than 5 = {5,6,7,8}
Number of parts = 4
So, P(not less than 5) = Number of parts not less than 5 divided by total number of parts
Mathematically, P(not less than 5) = 4/8
P(not less than 5) = 4/8
P(not less than 5) = ½
P(not less than 5) = 0.5
Hence, the theoretical probability of PP(not less than 5) is 0.5.
What is the formula forfinding the area of a circle using its radius or diameter.
Answers
Answer:
The formula for finding the area of a circle using its radius is:
The formula for finding the area of a circle using its radius is:A = πr²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14
Step-by-step explanation:
Hope it Helps
The formula for finding the area of a circle using its radius is π * r².
The formula for finding the area of a circle using its diameter is (π/4) * d².
The formula for finding the area of a circle using its radius is:
A = π * r²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
r represents the radius of the circle.
If you have the diameter of the circle instead of the radius, you can use the following formula:
A = (π/4) * d²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
d is the diameter of the circle.
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pls help!! show work with it too!
Answers
1) the surface area of the composite object is approximately 45.07 cm².
2) the volume of the composite object is approximately 1.66 cm³.
What is the rationale for the above response?1) Let's start by finding the dimensions of the cones. We know that the slant heights of the cones are 2.7 cm and the diameter of the cylinder is 1.4 cm, which means the radius of the cylinder is 0.7 cm.
Using the Pythagorean theorem, we can find the height of the cones:
h = √(2.7² - 0.7²) ≈ 2.61 cm
The total height of the composite object is the sum of the height of the cylinder and the height of one cone:
H = 7.5 + 2.61 ≈ 10.11 cm
The lateral surface area of the cylinder is:
A_cylinder = 2πrh = 2π(0.7)(7.5) ≈ 33.18 cm²
The lateral surface area of one cone is:
A_cone = πrl = π(0.7)(2.7) ≈ 5.56 cm²
So the total lateral surface area of the composite object is:
A_total = 2A_cone + A_cylinder = 2(5.56) + 33.18 = 44.3 cm²
We also need to add the areas of the circular bases of the cylinder and the two cones:
A_circular_base = πr²
A_cylinder_base = π(0.7/2)² ≈ 0.385 cm²
A_cone_base = π(0.7/2)² ≈ 0.385 cm²
So the total surface area of the composite object is:
A_total = 2A_cone + A_cylinder + 2A_circular_base
= 44.3 + 2(0.385)
≈ 45.07 cm²
Therefore, the surface area of the composite object is approximately 45.07 cm².
2) The volume of the composite object is the sum of the volumes of the cylinder and the two cones.
The volume of the cylinder is:
V_cylinder = πr^2h = π(0.7/2)^2(7.5) ≈ 1.32 cm³
The volume of one cone is:
V_cone = (1/3)πr^2h = (1/3)π(0.7/2)^2(2.61) ≈ 0.17 cm³
So the total volume of the composite object is:
V_total = 2V_cone + V_cylinder = 2(0.17) + 1.32 ≈ 1.66 cm³
Therefore, the volume of the composite object is approximately 1.66 cm³
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Lena is 10 years old. She asks her dad how old he is. He tells her that the lcm of their ages is 14 times the hcf of their ages. She knows that her dad is at least 30 years old but younger than 45. Work out how old her dad is.
Answers
Answer:
35
Step-by-step explanation:
Let x represent the HCF of the ages. Then we can have ax = 10 represent Lena's age, and bx can represent her dad's age.
The LCM will be abx = 14x, so we have ab = 14.
Factors of 14 are 1·14 and 2·7. Since the ratio of ages is between 30/10 = 3 and 45/10 = 4.5, we must have b/a in that range. This will be the case for ...
a=2, b=7
For a=2 and ax=10, we have x=5.
The dad's age is bx = 7·5 = 35.
Use technology to solve the following problem: A ferry will safely accommodate 79 tons of passenger cars. Assume that the mean weight of a passenger car is 1.9 tons with standard deviation 0.5 tons. If a random sample of 39 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded
Answers
Answer:
0.05155 or 5.155%
Step-by-step explanation:
We are given;
Weight of passenger cars the ferry can accommodate = 79 tons of passenger cars
Number of cars loaded = 39
Thus;
population mean weight; μ = 1.9
Since it can accommodate 79 tons of passenger cars, then their average weight should not exceed;
79/39 = 2.03 thus;
Sample mean; x¯ = 2.03
Standard deviation; σ = 0.5
Sample size; n = 39
Let's find the z-score value;
z = (x¯ - μ)/(σ/√n)
Thus;
z = (2.03 - 1.9)/(0.5/√39)
z = 0.13/0.08
z ≈ 1.63
Thus; P(z > 1.63) = 1 - P(z < 1.63)
From the z-score table attached, the p-value which is the probability is P(z < 1.63)
Thus;
P = 1 - 0.94845
P = 0.05155 or 5.155%
15 Points please help me fast i need help please help me
"For the first question u can choose " Less than , Greater than , The same as"
"For the second question you can choose " Less than , Greater than , The same as"
"For the third question you can choose " The measure of center " or A measure of variability"
Please help me fast PLEASE NO LINKS
Answers
Answer:
Look at the image.
Step-by-step explanation:
HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: 142825
Step-by-step explanation:
If \(t\) is the number of years, then the population is \(P(t)=100000(1.02)^t\).
Setting \(t=18\). \(P(18)=100000(1.02)^{18} \approx 142825\).
McDonalds sold 7 boxes of chicken nuggets for $25.90 Burger King sold 3 boxes of chicken fingers for $11.07. Which food item has a higher unit price? (1 Point McDonalds O Burger King.
Answers
Answer:
burger king
Step-by-step explanation:
math
To isolate the variable on one side of the equal sign, divide both sides of the equation by .
Answers
To isolate the variable on one side of the equal sign, divide both sides of the equation by the coefficient of the variable.
Which transformation results in the function?
Answers
The transformations of f(x) are (a) a horizontal shrink by a factor of 1/4,
How to describe the transformation from the parent function?From the question, we have the following functions that can be used in our computation:
f(x) = x²
g(x) = (4x)²
Mathematically, these equations can be represented as
g(x) = f(4x)
The above equations implies that, we have the transformation to be:
The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4
Hence, the transformed function is (a)
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-
A rectangle has dimensions 2x – 12 by 3x + 9 and area 60 cm². What are the actual
dimensions of the rectangle?
Answers
Answer:
2 x 30 cm
Step-by-step explanation:
L x W = 60
(2x-12)(3x+9) = 60
6x^2 -18x-168=0
use quadratic fromula to find x = 7 or -4 (throw out)
the sides then become ( using 7)
2 and 30 cm
Mr Rosario is ordering the yearbook for branch middle school
Answers
Hope he's got a satisfying teaching career.
The sum of the measures of the angles of a triangle sum to 180 degrees. The sum of the measures of the second and third angles is 3 times the measure of the first angle. The third angle is 13.2 more than the second angle. Find the measure of the third angle.
Answers
When solving systems of equations, we must first assign variables to given subjects, and reword the problem into equations.
Solving the QuestionLet the angles be x, y and z.
We're given:
Sum of angles = 180⇒ Rearrange into equation:
⇒ \(x+y+z=180\)Second angle + third angle = 3 times first angle
⇒ Rearrange into equation:
⇒ \(y+z=3x\)Third angle = 13.2 more than second angle
⇒ Rearrange into equation:
⇒ \(z = 13.2+y\)
Combine the first and second equations using substitution:
\(x+y+z=180\\x+3x=180\\4x=180\\x=45\)
Therefore, the first angle measures 45 degrees.
Plug this answer into \(x+2y=166.8\) and solve for y:
\(x+2y=166.8\\45+2y=166.8\\2y=121.8\\y=60.9\)
Therefore, the second angle measures 60.9 degrees.
Finally, subtract these answers from 180 to find the third angle:
\(180-60.9-45\\=74.1\)
Therefore, the third angle measures 74.1 degrees.
Answer
First angle: 45 degrees
Second angle: 60.9 degrees
Third angle: 74.1 degrees
please answer these questions
Answers
Step-by-step explanation:
you need to multiple first by second
what is the surface area of a sphere with a radius of 12 centimeters
A) 302cm^2
B) 452cm^2
C) 576cm^2
D) 1810cm^2
Answers
The surface area of the sphere is 1810 cm²
What is a sphere?A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.
The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of sphere is expressed as;
A = 4πr². where r is the radius.
A = 4 × 3.14 × 12²
A = 1809.7 cm²
approximately to the nearest whole number
A = 1810 cm²
Therefore the surface area of the sphere to the nearest whole number is 1810 cm².
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The Language Arts department conducts a study to see if the number of books a student reads per month affects the score on the SAT Verbal Test. Here is the data that the Language Arts department collected for 8 students. Create the scatter plot for this data set. What is the equation of the line of best fit?
Answers
A scatter plot visually represents the relationship between two variables. It shows a positive correlation between the number of books read per month and SAT Verbal Test scores, with the equation y = 6.4828x + 520.6962.
A scatter plot is a graphical representation of a set of data that allows the observer to observe the relationship between two variables. It is used to graphically display how one variable is affected by the other. It is a chart of data points plotted on a two-dimensional graph with one variable represented on the X-axis and the other variable on the Y-axis.
Scatter Plot of the Data: From the data provided by the Language Arts department, we can create the scatter plot as shown below:
Equation of the line of best fit: The line of best fit is a straight line that is used to model the relationship between the two variables. It is determined by minimizing the sum of the squares of the differences between the observed values and the predicted values.
From the scatter plot, we can see that there is a positive correlation between the number of books read per month and the score on the SAT Verbal Test. This suggests that the more books a student reads per month, the higher their score on the SAT Verbal Test.
The equation of the line of best fit for the given data set is y = 6.4828x + 520.6962. Here, y represents the score on the SAT Verbal Test and x represents the number of books read per month.
To find the equation of the line of best fit, we can use a regression analysis tool such as Excel. The regression analysis will give us the values of the slope and intercept of the line of best fit, which we can use to write the equation of the line.
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The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. (1 point)
Function 1
(look at the graph below)
Function 2
f(x) = −x2 + 2x − 15
Function 1 has the larger maximum at (4, 1).
Function 1 has the larger maximum at (1, 4).
Function 2 has the larger maximum at (−14, 1).
Function 2 has the larger maximum at (1, −14).
Answers
A function that has a greater maximum include the following: A. Function 1 has a larger maximum at (4, 1).
How to determine the function that has a larger maximum?In order to determine the maximum value of function 2, we would have to take the first derivative with respect to x and then, substitute this x-value into the original function while equating it to zero (0), and then evaluate as follows;
f(x) = −x² + 2x - 15
f(x) = −2x + 2
0 = −2x + 2
2x = 2
x = 2/2
x = 1
For the maximum value of function 2, we have:
f(1) = −(1)² + 2(1) - 15
f(1) = -14
For the maximum value of function 1, we can logically deduce that it is equal to 1 based on the graph in image attached above.
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My sallary was first increased by 10% and then decreased by 10%.find the net change in my salary.
Answers
Hello,
x = departure's sallary
increasing a value by 10% means multiplying it by 1,1decreasing a value by 10% means multiplying it by 0,9x*1,1*0,9 = 0,99x
multiplying by 0,99 is equivalent to decreasing by 1%the net change in my salary is 1%
2x² + 5x, what will it a Perfect Square? make
Answers
Answer:
2x² + 5x + c = 0
For this quadratic equation to have one double root, the discriminant must equal 0.
5² - 4(2)(c) = 0
25 - 8c = 0
c = 25/8
2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.
Explanation:2x² + 5x is not a perfect square.
A perfect square is an expression that can be factored into the square of a binomial. To determine if an expression is a perfect square, we can look at the coefficient of x². In this case, the coefficient is 2, which is not a perfect square.Learn more about Perfect Square here:https://brainly.com/question/34063927
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Please help will mark Brainly
Answers
The number of tickets day and evening combined should be more then 8 since it says at least 8 tickets. However the cost of the tickets which is 15x+30y (multiply the amount of tickets bought by the cost) should be less then 300 bucks since they have a budget. Hope this helps!
Rebecca picked a bunch of flowers from her garden. She gave 19 flowers to her mother. If she now has 34 flowers, how many flowers did she pick?
Answers
19 + 34 = 53
Consider the line y = 5x - 3 Find the equation of the line that is parallel to this line and passes through the point (- 8, 2) Find the equation of the line that is perpendicular to this line and passes through the point (- 8, 2) Note that the ALEKS graphing calculator may be helpful in checking your answer
Answers
Answer:
First, we know the slopes of perpendicular lines are negative reciprocals of each other. So, the negative reciprocal of -1 is 1. This is the slope of our new line. From here, we can use this new slope along with our given point to find the y-intercept (b) of our new equation:
y = mx + b
-4 = 1(-2) + b
-4 = -2 + b
-2 = b
The y-intercept of our new line is (0,-2). Now, we can write our equation of the new line:
y = x - 2