As per the concept of exponential decay, the initial mass of the sample is 5,254.87 kg
What is meant by Exponential decay:
In math, the term exponential decay is a very common process especially when we are talking about radioactive materials.
The standard formula for this type of behavior which is written below:
A = Pe^-rt
where
A refers the amount left after time t
P refers the initial amount at t=0
r refers the rate
Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago.
And we need to find if the sample has a mass of today, then the initial mass of the sample.
Now, we have to substituting the values,
Then we get the equation as,
=> A = (9575 kg)(e^-0.12*5)
When we simplify this one, then we get,
=> A = 5,254.87 kg
Therefore, the initial mass of the sample is 5,254.87 kg
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Which of the following sequences are convergent? Select all that apply (there are 2 answers).
a geometric sequence with r=3
an arithmetic sequence with d=2
a geometric sequence with r=3/5
an arithmetic sequence with d=-2/3
a geometric sequence with r=-1/6
The following sequences are convergent an arithmetic sequence with d=-2/3.
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers where each successive number is obtained by adding a constant value to the previous number. This constant value is referred to as the common difference. Arithmetic sequences are especially useful in mathematics, as they can be used to model real-world phenomena such as population growth and the depreciation of assets. By finding the common difference, one can solve a variety of problems involving the sequence. For example, given two terms of an arithmetic sequence, one can find the sum of the sequence, the nth term, and the number of terms in the sequence.
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Answer:
The other answer is actually wrong.
The answers are: r=3/5 and r=-1/6
Step-by-step explanation:
Match each data set with its range.
The range of the data set are
{10.2, 3.8, 21.9, 33.4, 31.8, 17.2} = 29.6
{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71} = 0.6
{6, 2, 14, 11, 28, 10, 19, 15, 11} = 26
The first data set is
{10.2, 3.8, 21.9, 33.4, 31.8, 17.2}
The range is the difference between the highest value and the smallest value
The highest value = 33.4
Lowest value = 3.8
The range = 33.4 - 3.8
= 29.6
The second data set is
{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71}
The highest value = 0.71
Lowest value = 0.11
The range = 0.71 - 0.11
= 0.6
The third data set is
{6, 2, 14, 11, 28, 10, 19, 15, 11}
Highest value = 28
Lowest value = 2
The range = 28 - 2
= 26
Therefore, the range of the each data set has been found
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6. Write a linear equation with a slope of 1 and the y-intercept of -7
7. Identify the slope and y-intercept of the equation y=-3 x
8. Identify the slope and y-intercept of the equation 2 x+5 y=20
8. Identify the slope and y-intercept of the
9. Identify the slope and y-intercept of the equation 2 x+5 y=20 equation x-2 y=2
10. Write a linear equation given the graph.
11. Write a linear equation given the graph.
The line with a slope of 1 and y - intercept -7 will have an equation of y = x - 7
Given,
Slope of the line. m = 1
Y - intercept = -7
We have to determine the linear equation for the line;
Linear equation;-
A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here,
Equation of line in slope intercept form;
y = mx + b
Here,
-7 = 1x + b
Let b = y intercept (begins from 0)
Then,
y = x - 7
That is,
The linear equation is y = x - 7
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Given question is improper. Proper question is;
Write a linear equation with a slope of 1 and the y-intercept of -7
Round 13.689 to the nearest hundredth
It snowed and Bobby had to shovel for his parents. It took 30 minutes to do the steps, 45 minutes to do the path, and one hour to do the driveway. How long did he shovel? Write it in time and as a fraction.
Answer: Time: 2 hours and 15 minutes, Fraction: I don't know
Step-by-step explanation:
1 hour=1 hour
30+45=1 hour and 15 minutes
1 hour+1 hour+15 minutes=2 hours and 15 minutes
Illegal trafficking of some items in a country was banned by its government in 2007. Is this supported by a majority, or a minority, of the population of the country? In a global poll conducted by an international agency for a reputed newspaper in January 2010 involving 900 residents of the country that asked whether the ban should stand or be repealed, 55% supported the banning.
(a) Find the standard error
(b) Find the test statistic
(c) Find the P-value, and interpret in context
a) The standard error is of: 0.0167.
b) The test statistic is of: 2.99.
c) The p-value is of 0.0013, representing the probability of finding a sample proportion of at least 55%.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that a majority of the population supports the measure, hence:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that a majority of the population supports the measure, hence:
[tex]H_1: p > 0.5[/tex]
What is the test statistic?The equation that defines the test statistic is given as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The values of these parameters in this problem are given as follows:
[tex]p = 0.5, n = 900, \overline{p} = 0.55[/tex]
Then the standard error is calculated as follows:
Standard error = square root (0.5 x 0.5/900) = 0.0167.
Then the test statistic is calculated as follows:
z = (0.55 - 0.5)/0.0167 = 2.99.
What is the p-value?We have a right-tailed test, as we are testing if the mean is different of a value, hence the p-value represents the probability of finding a sample proportion of at least 0.55.
Using a z-distribution calculator, with z = 2.99, the p-value is of:
0.0013.
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Here are the first 5 terms of a quadratic sequence.
2
10
24
44
Find an expression, in terms of n, for the nth term of this sequence.
70
The sequence is f(n)=3[tex]n^{2}[/tex]−n.
What is sequence?Sequences are ordered collections of numbers, often known as "terms," such as 2,5,8. There are some sequences that adhere to a particular pattern that allows for endless extension. For instance, 2,5,8 adheres to the "add 3" pattern, thus we may now continue the process. There are formulae for sequences that show us where to locate any given term.
We have 2 10 24 44 70 (which we refer to as the first column)
If we have 10 - 2 = 8, 24- 10 = 14, 44- 24 = 20, and 70- 44 = 26,
(this is second column)
The third column is now 14 - 8 = 6, 20 - 14 = 6, and 26 - 20 = 6.
First, create the second column sum formula.
Sum(x)
S(x)=8+6(x1)=6x+2 is the second digit of the phrase.
Next make the first column formula f(n)
f(n)= 2+[tex]sum_{n-1}[/tex]
=2+(n−1)[3(n−1)+5]
=2+(n−1)(3n−3+5)
=2+(n−1)(3n+2)
=2+3[tex]n^{2}[/tex]+2n−3n−2
=3[tex]n^{2}[/tex]−n
The sequence is f(n)=3[tex]n^{2}[/tex]−n.
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he graphed line shown below is y = negative 2 x minus 8.
On a coordinate plane, a line goes through (negative 4, 0) and (negative 2, negative 4).
Which equation, when graphed with the given equation, will form a system that has infinitely many solutions?
y = negative (2 x + 8)
y = negative 2 (x minus 8)
y = negative 2 (x minus 4)
Answer: A
Step-by-step explanation:
Our given equation is: y = -2x - 8
In order to have an equation with infinitely many solutions, it needs to be the same as the given equation.
Look at the answer choices:
A) y = -(2x + 8) = -2x - 8
This is the exact same equation, which means that any solutions for the given will also be solutions for this one. That means there will be infinitely many solutions.
B) y = -2(x - 8) = -2x + 16
We can tell this is definitely not the same as the given, so eliminate.
C) y = -2(x - 4) = -2x + 8
Again, this has a +8 instead of -8, so it's not the same and wrong.
D) y = -(-2x + 8) = 2x - 8
Here, we have positive 2 as the slope instead of -2, so it's not the same and wrong. Thus, the answer is A.
This graph shows Jesemy's distance from home each hour he is on a car trip. How many miles will he be from home after 10 hours?
500 miles
550 miles
400 miles
350 miles
From the graph that shows Jeremy's distance from home each hour , then he will be 500 miles from home after 10 hours .
In the question ,
a graph is given ,
we have to find the distance that Jeremy's car will travel after 10 hours.
from the graph we can see that the points in the graph form a straight line .
we can see that ,
in 1 hour Jeremy's car travels a distance of 50 miles .
So , in 10 hours Jeremy's car will travel = 10×50 miles .
= 500 miles .
So , Jeremy's car will be 500 miles away from home after 10 hours .
Therefore , the correct option is (a) 500 miles .
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consider a pair of integers (a b) the following operations can be performed on (a,b) in any order, zero or more times
If we consider a pair of integers (a b) and the given operations, then the java program that depicts it is as written below.
How to carry out programming in Java?The program that carries out the required operations on the pair of integers is;
static LinkedList<Pair<Integer,Integer>> pairs = new LinkedList<Pair<Integer, Integer>>();
public static String isItPossible(Integer a, Integer b, Integer c, Integer d){
pairs.addLast(new Pair<Integer, Integer>(a,b));
while (!pairs.isEmpty()){
Pair<Integer,Integer> pair = pairs.poll();
Integer key = pair.getKey();
Integer value = pair.getValue();
if(key.equals(a) &&
value.equals(b)){
return "YES";
}
int sum=key+value;
if (sum<=c){
pairs.addLast(new Pair<Integer, Integer>(sum,value));
}
if (sum<=d){
pairs.addLast(new Pair<Integer, Integer>(key,sum));
}
}
return "NO";
}
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Complete question is;
Consider a pair of integers, (a, b). The following operations can be performed on (a, b) in any order, zero or more times:
• (a, b)(a + b, b)
• (a, b) → (a, a + b)
Return a string that denotes whether or not (a, b) can be converted to to (c,d) by by performing zero or more of the operations specified above. Example
(a, b) = (1, 1)
(c,d) = (5,2)
Perform the operation (1,1 + 1) to get (1, 2), perform the operation (1 + 2, 2) to get (3, 2), and perform the operation (3+2, 2) to get (5,2). Alternatively, the first operation could be (1+1, 1) to get (2, 1) and so on.
Complete the function is possible in the editor below. isPossible has the following parameter(s): int a: first value in (a, b) int b: second value in (a, b) int c: first value in (c,d) int d: second value in (c,d) Returns: str: Return 'Yes' if (a, b) can be converted to (c,d) by performing zero or more of the operations specified above, or 'No' if not Constraints • 1 sa,b,c,ds 1000
46. The table shows the temperature (in degrees) for eight consecutive days as well as the
respective number of ice cream cones an ice cream shop sold on each of these days.
Temperature 68 77 83 85 89 94 96 99
Number of Cones 403 447 457 465 489 503 543 576
About how many ice cream cones would you expect the shop to sell if the temperature one day
is 106 degrees? Find a line of best fit for this data and use it to make your prediction.
0579 cones
0585 cones
O 602 cones
(617 cones
A line of best fit for this problem is y = 5.08x + 46.59. The number of ice cream cones that you would expect the shop to sell if the temperature one day is 106 degrees is; 585 cones
How to find the line of best fit?A graph of the scatter plot and line of best fit is as shown in the attached file.
The temperature in this problem is the independent variable, or x. This is due to the fact that we are assuming that the particular number of ice cream cones sold will depend on the temperature. Therefore, we can say that the number of ice cream cones will be the dependent variable, or y.
Therefore in our graphing calculator, we will enter temperature in the first list and then the number of cones in the second.
Sequel to drawing the scatter plot, we run the linear regression; we get the values for a and b in our equation, y = ax + b:
a = 5.08
b = 46.59
Therefore, the equation is;
y = 5.08x + 46.59.
Entering our temperature of 106 degrees, for x gives;
y = 5.08(106) + 46.59
= 585.07
≈ 585
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10. Suppose a small library has five book shelves labeled A-E. In how many different ways can 30 books be placed on these shelves if the books are. (a) all different? (b) all identical?
All different: Since there are 30 books and 5 shelves, the books can be placed in 30!/(5!*25!) ways, which is 5,852,114,406 ways.
What is library?A library is a collection of books, periodicals, audio and visual materials, and other educational and informational resources that are made available for public use. Libraries typically provide a range of services and resources, such as access to computers, books, reading materials, reference assistance, classes, and programs.
A. (a) All different: Since there are 30 books and 5 shelves, the books can be placed in 30!/(5!*25!) ways, which is 5,852,114,406 ways. This is because the number of ways to arrange 30 different books across 5 shelves is the same as the number of permutations of 30 objects taken 5 at a time.
B. (b) All identical: Since there are 5 shelves and 30 books, the books can be placed in 5^30 ways, which is 922,337,203,685,477,439,232,000 ways. This is because there are 5 choices for each book, so the total number of possible arrangements is 5^30.
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HELP QUICK!! Which set of side measurements could be used to form a right triangle?
Answer:
3, 4, 5
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
Here is the preference schedule for a recent election among four candidates:
Number of voters 7 1 11 5 2 19 9
1st choice A X D A X A G
2nd choice X G G G A D X
3rd choice D D A X G X D
4th choice G A X D D G A
How many voters voted in this election?
How many first place votes are needed for a majority?
Which candidate/choice had the most first-place votes?
Which candidate/choice has the least first-place votes?
Which candidate/choice had the most last-place votes?
Which candidate/choice has the least last-place votes?
Answer:
There were a total of 7 + 1 + 11 + 5 + 2 + 19 + 9 = 44 voters in this election.
To get a majority, a candidate would need at least 44 / 2 + 1 = 23 first place votes.
The candidate with the most first-place votes is A, with a total of 7 + 1 + 5 = 13 first-place votes.
The candidate with the least first-place votes is X, with a total of 1 first-place vote.
The candidate with the most last-place votes is G, with a total of 9 + 2 + 9 = 20 last-place votes.
The candidate with the least last-place votes is X, with a total of 0 last-place votes.
Step-by-step explanation:
Imaginary Numbers: Simplify
[tex] \sqrt{ - 80} [/tex]
Answer:
= –4√5
Step-by-step explanation:
√−80
=√ –( 16 × 5
= √ –(4² × 5)
= –4√5
this is what I think I hope I helped
does the object represented in (figure 1) have a positive or negative value of ayay ? explain. assume that yy -axis points upward.
Because the object is moving slowly toward the bottom and the positive y-direction points upward, the object has a positive value for ay.
Motion is the shift in an object's location with regard to time. Motion can be quick or slow, but motion is still present. Due to the significance of motion in the physical world, it is crucial that we pay proper attention to the study of motion. Generally speaking, the following phrases are used to describe motion
DistanceDisplacementSpeedTimeWith the use of equations and derivations, understanding the numerical of physics can be tedious, but with the aid of graphs, it is both entertaining and simple to understand what the answer is describing.
Since they are used in nearly all of the topics in physics, graphs are essential. Give us more information about various graphs in this article.
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Construct a scatter plot. State if there appears to be a positive correlation, negative correlation, or no correlation. When there is a correlation, identify the relationship as linear, quadratic, or exponential. Also find the slope-intercept form of the equation of the line that best fits the data. 10) X Y 10 20 10630 X Y 30 390 40 160 X Y 90 210 100 370 500 10 20 30 40 50 60 70 80 90 100
The scatter plot for provide data is shown above in figure. The slope-intercept form of the equation of the line that best fits the data is
y = - 0.3319 x + 312.16
What is scatter plot Correlation ?Scatter charts are similar to line charts in that they use horizontal and vertical axes to represent points of data. However, they have a very specific purpose. The scatterplot shows how much one variable is influenced by another. The relationship between two variables is called their correlation. There are three types of correlation: positive, negative, and none (no correlation).
• Positive correlation: when one variable increases, the other also increases. ...
• Negative correlation: an increase in one variable causes a decrease in the other variable. ...
• No Correlation: nothing displayed
We have the following observations,
X Y
10 20
10 630
30 390
40 160
90 210
100 370
Now , we construct a scatter plot for the provide data. The constructed scatter plot is shown above. As we see in plot that there is no increase or decrease with increasing values of one variable .So, there is no correlation between two variables. Now, equation of the line that best fits the data, A best line of fit never connect all the points on the scatter plot. but it connects only a few points. There will have data points above and below the line. The equation of a line of best fit can be represented as y = mx+b y = m x + b , where m is the slope and b is the y-intercept.
here, y = - 0.3319 x + 312.16
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Which equation has no solution?
0 14x-21=-6
012-x1=9
O 13x + 61 = 6
O 1-2x+81 = 0
Step-by-step explanation:
1 , 14x=-6+21
14x=15 , divide both sides by q4 to get the value of x
x=15/14
2 , x1=x
-x=9-12
-x=-3 , divide both side by -1
x=3
3, 13x=6_61
13x= 55 , divide both sides by 13
x=55/13
4, 1-2x+81=1+81_2x
82_2x=0
-2x=-82 , divide both sides by -2
x=41
So, all of them have a solution
The following dot plot shows the number of songs on each album in Saiâs collection.
Each dot represents a different album. What is the total number of albums in Saiâs collection?
A. 10
B. 17
C. 7
Option B) 17
A simple kind of data visualization known as a "dot plot" involves the representation of data points as dots on a graph with x and y axes. Sai has 17 albums in his collection altogether.
Given data;
6 = 0; 7 = 1 ; 8 = 2; 9 = 2; 10 = 4; 11 = 1; 12 = 2; 13 = 2; 14 = 1; 15 = 0; 16 = 2
[tex]= 1+2+2+4+1+2+2+1+2[/tex]
[tex]=17[/tex]
The total number of albums in Sai collection is 17
A basic style of data visualization called a dot plot, often referred to as a strip plot or dot chart, shows data points as dots on a graph with x and y axes. The purpose of these graphs is to visually portray particular data patterns or groups.
Each dot in the provided dot plot represents an album. As a result, the total number of dots in the dot plot equals the total number of albums in Sai's collection.
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which phrase describes the variable expression 7 ÷ s?
a) 7 decreased by s
b) the product of 7 and s
c) 7 increased by s
d) the quotient of 7 and s
The phrase describes the variable expression 7 ÷ s is the quotient of 7 and s.
The correct option is (d).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Expression: 7 ÷ s
We know that the division results to quotient.
So, the expression shows the 7 is divided by s to give the quotient.
Hence, the answer is the quotient of 7 and s.
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Jeff has two pieces of rope.the first piece of rope is 5/10 meter long. The second piece of rope is 52/100 meter long. The length of the third piece of rope is between the lengths of the first and second pieces of rope
Answer: 51/100
Step-by-step explanation:
I'm assuming that the numerator is supposed to be a whole number, because there is an infinite number of answers if it is not a whole number. 5/10 can be rewritten as 50/100 by multiplying the numerator and denominator by 10. The only fraction with a whole number numerator between 50/100 and 52/100 is 51/100. Hope this helped!
exercise 8.25 presents regression output from a model for predicting annual murders per million from percentage living in poverty based on a random sample of 20 metropolitan areas. the model output is also provided below.
regression output from a model for predicting annual murders per million from percentage living in poverty based on a random sample of 20 metropolitan areas with Standard Error: 11.734
Regression Output:
R-squared: 0.674
Standard Error: 11.734
Intercept: -9.572
Poverty (%): 0.108
The interpretation of this output is that an increase of 1% in poverty is associated with an increase of 0.108 annual murders per million people. Additionally, this model explains 67.4% of the variance in annual murders per million people. The standard error of 11.734 indicates that the estimated regression line is likely to be 11.734 murders per million people away from the true population regression line.
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In 8-card poker, each player is dealt 8 cards (go figure) from a standard deck of 52 cards. How many different hands can be dealt?
The answer is 7525381507
what is a combination in math?The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” And the formula is given by [tex]_n C_r=\frac{n !}{r ! (n-r) !}[/tex] [tex]_n C_r[/tex]= number of combinations
n = total number of objects in the set
r = number of choosing objects from the set
Given here, select 8 cards out of a possible 52 thus using the formula we get
[tex]=\frac{52 !}{8 ! (52-8) !}[/tex]
[tex]=\frac{52 !}{8 ! (44) !}[/tex]
= 7525381507
Hence the answer is 7525381507
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how to solve probability of distribution
Answer:
Step-by-step explanation:
How to find the mean of the probability distribution: Steps
Step 1: Convert all the percentages to decimal probabilities. For example: ...
Step 2: Construct a probability distribution table. ...
Step 3: Multiply the values in each column. ...
Step 4: Add the results from step 3 together.
young's modulus is a quantitative measure of stiffness of an elastic material. suppose that for metal sheets of a particular type, its mean value and standard deviation are 85 gpa and 2.3 gpa, respectively. suppose the distribution is normal. (round your answers to four decimal places.)
(a) Calculate P(79 x 81) when n = 25. (b) How likely is it that the sample mean diameter exceeds 81 when n = 36? You may need to use the appropriate table in the Appendix of Tables to answer this question
(a) Probability that sample mean lies between 79 and 81 is 0.9946.
(b) It is 0.04% likely is it that the sample mean diameter exceeds 81 when n = 36.
We are given that the metal sheets of a particular type, its mean value and standard deviation are 85 GPA and 2.3 GPA, respectively.
Suppose the distribution is normal.
Let X = sample mean diameter
The z-score probability distribution for sample mean is given by;
Z = (X - μ) / (σ / √n)
where,
μ = population mean = 85 GPA
σ = standard deviation = 2.3 GPA
n = sample size = 25
(a) Probability that sample mean lies between 79 and 81 is given by
= P(79<X<81) = P(X<81) - P(X≤79)
P(X<81) = P {(X - μ) / (σ / √n) < (81 - 85) / (2.3 / √25) = P(Z < 2.78) = 0.9973
P(X<79) = P {(X - μ) / (σ / √n) < (79 - 85) / (2.3 / √25) = P(Z < 2.78) = 0.0027
The above probability is calculated by looking at the value of x = 2.78 in the z table which has an area of 0.9973.
Here, P(79 < X < 81) = 0.9973 - 0.0027 = 0.9946
(b) Probability that the sample mean diameter exceeds 81 when n = 36 is given by = P(X > 81)
P(X<81) = P {(X - μ) / (σ / √n) < (81 - 85) / (2.3 / √25) = P(Z < 3.33) = 0.0004
The above probability is calculated by looking at the value of x = 3.33 in the z table which has an area of 0.9996.
Therefore, probability that sample mean lies between 79 and 81 is 0.9946 and it is 0.04% likely is it that the sample mean diameter exceeds 81 when n = 36.
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Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS
Answer:
56π/3 m³ or 58.64 m³------------------------------------------------
Find the sum of the volumes of the two given cones.
Cone volume:
V = 1/3 πr²hCone 1, d = 4m, h = 8m:
V = 1/3 π*(4/2)²*8 = 32π/3 m³Cone 2, r = 2m, h = 6 m:
V = 1/3 π*2²*6 = 8π m³Total volume:
V = 32π/3 + 8π = 56π/3 m³ = 58.64 m³ (rounded)Rewrite the set U by listing its elements. Make sure to use the appropriate set
notation.
U= {x|x is an integer and -4
U =
The set U can be rewritten by listing its elements as follows:
U = {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}
In this notation, the "..." symbol indicates that the set continues in both the negative and positive direction, and that all integers from negative infinity to positive infinity are included in the set. This notation is commonly used to represent sets of integers or other infinite sets in mathematics.
An empty aerosol can of hair spray was thrown into a camp fire, causing its temperature to increase from 300 K to 900 K. Which of the following best describes what will happen to the pressure of air inside the can?
A. The pressure will double.
B. The pressure will triple.
C. The pressure will increase 9x.
D. The pressure will decrease to ⅓ of the original value.
The pressure in the can become triple the original value. Option B is correct.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
From the ideal gas equation, we know that,
pressure is directly proportional to the temperature,
So,
P₁ / P₂ = T₁ / T₂
Where,
P₁ and T₁ are the initial pressure and temperature,
P₂ and T₂ are the final pressure and temperature.
Substitute the values,
P₁ / P₂ = 300 / 900
P₂ = 3P₁
Thus, the pressure in the can become triple the original value. Option B is correct.
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an assembly consists of two mechanical components. suppose that the probabilities that the firt and second components meet specfications are 0.81 and 0.84 respectfully. assume that the components are independent. x denotes the number of components in the assembly that meet specifications. obtain the cumulative distribution function (cdf)
The probability of the cumulative distribution function to meet the specification of the components is given by P( X = 0 ) = 0.0304 ,
P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.
As given in the question,
Let probability of the first component to meet the specification be P (M)
= 0.81
And probability of the second component to meet the specification be P (N)
= 0.84
Probability of the first component do not meet the specification be P ( M' )
= 1 - 0.81
= 0.19
Probability of second component do not meet the specification be P(N' )
= 1 - 0.84
= 0.16
X defined the number of components to the meet the specifications
Here X = 0, 1, 2
P( X = 0 ) represents components do not meet any specifications
= P( M' ∩ N' )
= P(M') P(N') ( Independent )
= 0.19 × 0.16
= 0.0304
P( X= 1) represents components meet only one specification
= P( M∩N') ∪ P( M'∩N)
= P( M∩N') + P( M'∩N)
= P(M) P(N') + P(M') P(N)
= 0.81(0.16) + (0.19)(0.84)
= 0.1296 + 0.1596
= 0.2892
P( X=2) represents components meet both the specification
= P( M ∩ N )
= P(M) P(N)
= 0.81(0.84)
= 0.6804
Therefore, the probability of the cumulative distribution function is given by P( X = 0 ) = 0.0304 , P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.
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What is the volume of the cone below?
27
OA. 216 units³
B. 432 units3
units3
OC. 144
OD. 108 units³
The volume of the cone is 144π units³.
How to find volume of a cone?The volume of a cone can be calculated as follows:
volume of a cone = 1 / 3 πr²h
where
r = radius of the coneh = height of the cone.Therefore, the height of the cone is 27 units and the radius of the cone is given as 4 units.
Let's find the volume using the formula,
r = 4 units
h = 27 units
Therefore,
volume of a cone = 1 / 3 πr²h
volume of a cone = 1 / 3 × π × 4² × 27
volume of a cone = 1 / 3 × π × 16 × 27
volume of a cone = 432 / 3 π
Therefore,
volume of a cone = 144π
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