Answer:
0.024
Step-by-step explanation:
Given,
Red marbles = 4,
Green marbles = 7,
Total marbles = 4 +7 = 11,
Ways of choosing 3 marbles =[tex]^{11}C_3[/tex]
Ways of choosing 3 red marble = [tex]^4C_3[/tex]
Hence, the probability of 3 red marble = [tex]\frac{^4C_3}{^{11}C_3}[/tex]
[tex]=\frac{\frac{4!}{3!1!}}{\frac{11!}{3!8!}}[/tex]
[tex]=\frac{4}{165}[/tex]
≈ 0.024
at the beginning of the day the stock market goes up 301/2 points. at the end of the day the stock market goes down 120 1/4 points. what is the total change in the stock market from the beginning of the day to the end of the day?
Answer:
just saying
Step-by-step explanation:
subtract them lol use a mixed number calculator online
let's change the mixed fractions first to improper fractions and then get their sum.
we don't know the beginning point of the market, however from that point on, it spikes up by 30½and then goes down by 120¼, we're being asked on the total change or namely the displacement, and that'd be the sum of the spike line going up and the dive line going down.
[tex]\bf \stackrel{mixed}{30\frac{1}{2}}\implies \cfrac{30\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{61}{2}}~\hfill \stackrel{mixed}{120\frac{1}{4}}\implies \cfrac{120\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{481}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{481}{4}+\cfrac{61}{2}\implies \stackrel{\textit{using an LCD of 4}}{\cfrac{(1)481+(2)61}{4}}\implies \cfrac{481+122}{4}\implies \cfrac{603}{4}\implies 150\frac{3}{4}[/tex]
What is the area of a regular polygon with 16 sides and side length 4 inches? PLease explain in detail with a diagram. Thank You.
Answer:
Area is 321.6 square inches.
Step-by-step explanation:
A regular polygon with 16 sides is a Regular Hexadecagon. Regular means all sides are equal dimension. See image attached.
Side length is 4 inches.
side length=s=4 inches
You need to calculate the apothem.Apothem=s*2.51367
Apothem=10.054
2. You can use the formula to calculate de area of an hexadecagon:
[tex]A=\frac{Perimeter*Apothem}{2}[/tex]
Perimeter=16 sides*4inches
Perimeter= 64 inches
[tex]A=\frac{64*10.054}{2}[/tex]
[tex]A=321.6 inches^{2}[/tex]
Team A and team B play against each other repeatedly until one team wins two games in a row or a total of three games. 1) how many ways can the tourney be played? 2) what is the probability of 5 games being played? 3) what is the probability of a team winning two games in a row. Show work.
Answer:
1) The tournament can be played in 10 different ways
2) The probability of 5 games being played is 0.40
3) The probability of a team winning two games in a row is 0.80
Step-by-step explanation:
a) From the tree diagram below we can observe that the tournament can be played in 10 different ways.
b)The probability of 5 games being played is
P= (number of possibilities where 5 games are being played) / (Total games)
P = 4 / 10
P= 0.40
c) The probability of a team winning two games in a row is
P = (number of possibilities where a team wins two games in a row) / Total games
P = 8 / 10
P = 0.80
A liquid oral concentrate of morphine sulfate contains 2.4 g of morphine sulfate in a 120-mL bottle. Calculate the concentration of morphine sulfate on a mg/mL basis.
Answer:
20 mg/ml.
Step-by-step explanation:
We have been given that a liquid oral concentrate of morphine sulfate contains 2.4 g of morphine sulfate in a 120-mL bottle.
[tex]\text{Concentration of morphine sulfate on g/mL basis}=\frac{\text{2.4 g}}{\text{120 ml}}[/tex]
To convert the concentration of morphine sulfate on a mg/mL basis, we need to convert 2.4 grams to milligrams.
1 gram equals 1000 milligrams.
[tex]\text{Concentration of morphine sulfate on mg/mL basis}=\frac{\text{2.4 g}}{\text{120 ml}}\times\frac{\text{1,000 mg}}{\text{1 g}}[/tex]
[tex]\text{Concentration of morphine sulfate on mg/mL basis}=\frac{2.4\times\text{1,000 mg}}{\text{120 ml}}[/tex]
[tex]\text{Concentration of morphine sulfate on mg/mL basis}=\frac{2400\text{ mg}}{\text{120 ml}}[/tex]
[tex]\text{Concentration of morphine sulfate on mg/mL basis}=\frac{20\text{ mg}}{\text{ml}}[/tex]
Therefore, the concentration of morphine sulfate would be 20 mg per ml.
Answer:
Step-by-step explanation:
x=25.36+0.45(25.36)
LaTeX: x=
Answer:
[tex]x=36.772[/tex]
Step-by-step explanation:
Given : Expression [tex]x=25.36+0.45(25.36)[/tex]
To find : Solve the expression ?
Solution :
Step 1 - Write the expression,
[tex]x=1(25.36)+0.45(25.36)[/tex]
Step 2 - Apply distributive, [tex]ab+ac=a(b+c)[/tex]
Here, a=25.36, b=1, c=0.45
[tex]x=25.36(1+0.45)[/tex]
Step 3 - Solve the expression,
[tex]x=25.36\times 1.45[/tex]
[tex]x=36.772[/tex]
Therefore, [tex]x=36.772[/tex]
Use induction to prove that for all integers n 2 1 we have 1.1! +2.2! +3.3! + ... +nin! = (n + 1)! - 1.
Step-by-step explanation:
Let's assume that
P(n)=1.1! +2.2! +3.3! + ... +n.n! = (n + 1)! - 1.
For n = 1
L.H.S = 1.1!
= 1
R.H.S = (n + 1)! - 1.
=(1 + 1)! - 1.
= 1
L.H.S = R.H.S
Hence the P(n) is true for n=1
Fort n = 2
L.H.S=1.1! +2.2!
=1+4
=5
R.H.S = (2 + 1)! - 1.
=(2 + 1)! - 1.
= 5
L.H.S = R.H.S
Hence the P(n) is true for n=2
Let's assume that P(n) is true for all n.
Then we have to prove that P(n) is true for (n+1) too.
So,
L.H.S = 1.1! +2.2! +3.3! + ... +n.n!+(n+1).(n+1)!
= (n + 1)! - 1 +(n+1).(n+1)!
= (n+1)![1+(n+1)]-1
=(n+1)!(n+2)-1
=(n+2)!-1
=[(n+1)+1]!-1
So, P(n) is also true for (n+1).
So, P(n) is true for all integers n.
Statements :
For the statement #1, "e x is rational for some nonzero integer x.", write the negation of this statement.
Answer:
"[tex]e^x[/tex] is irrational for every nonzero integer x"
Step-by-step explanation:
The original statement is
"[tex]e^x[/tex] is rational for some nonzero integer x."
The negation is technically:
"It is NOT true that [tex]e^x[/tex] is rational for some nonzero integer x."
So it's expressing that it's false that [tex]e^x[/tex] can be rational for some nonzero integer x.
This just means that [tex]e^x[/tex] is always irrational when x is a nonzero integer.
Which can be worded as
"[tex]e^x[/tex] is irrational for every nonzero integer x"
The negation of the statement "e^x is rational for some nonzero integer x" is "For all nonzero integers x, e^x is not rational."
To write the negation of the statement "ex is rational for some nonzero integer x", we can express it as "For all nonzero integers x, ex is not rational." This implies that there does not exist any nonzero integer x such that ex is rational. The original statement is an existential statement, asserting the existence of an x that makes the statement true. Its negation is a universal statement, asserting that for every x the statement is false.
The approach to negating the statement involves changing the existential quantifier ("There is some" or "For some") to a universal quantifier ("For all") and negating the predicate of the original statement. This is similar to how we represent negations in symbolic logic, aligning with the principle of contradiction. To negate existential statements, the corresponding universal statement is negated and vice versa.
Many states are carefully considering steps that would help them collect sales taxes on items purchased through the Internet. How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the Internet? Assume that we want to be 95% confident that the sample percentage is within two percentage points of the true population percentage for all sales transactions.
Answer:
96
Step-by-step explanation:
Step 1
Divide your confidence interval by 2. In this case the confidence is 95% = 0.095, so 0.095/2 = 0.0475
Step 2
Use either a z-score table or a computer to find the closest z-score for 0.0475 and you will find this value is 1.96
Step 3
Divide the margin error by 2. In this case, the margin error is 2%. When dividing this figure by 2, we get 1% = 0.01
Step 4
Divide the number obtained in Step 2 by the number obtained in Step 3 and square it
1.96/0.01 = 196 and 196 squared is 38,416
Step 5
As we do not now a proportion of people that purchase on line, we must assume this value is 50% = 0.5. Square this number and you get 0.25
Step 6
Multiply the number obtained in Step 5 by the number obtained in Step 4, round it to the nearest integer and this is an appropriate size of the sample.
38,416*0.25 = 9,604
Given the statement "If I have the disease, then I will test positive." Show all work. (Discrete Mathematics)
a) Write the converse.
b) Write the inverse.
c) Write the contrapositive.
d) Write the statement as a disjunction.
e) Write the negation.
Answer with Step-by-step explanation:
We are given that a statement ''If I have the disease , then I will test positive.''
Let p:I have the disease.
q:I will test positive.
a.Converse :[tex]q\implies p[/tex]
''If I will test positive, then I have the disease''.
b.Inverse :[tex]\neg p\implies \neg q[/tex]
''If I have not the disease, then I will not test positive.''
c. Contrapositive:[tex]\neg q\implies \neg p[/tex]
''If I will not test positive, then I have not the disease''.
d.Disjunction:p or q=[tex]p\vee q[/tex]
''I have the disease or I will test positive''.
e.Negation :If p is true then its negation is p is false.
Negation of conditional statement is equivalent to [tex]p\wedge \neg q[/tex]
I have disease and I will not test positive.
The returns from an investment are 4% in Year 1, 7% in Year 2, and 10.8% in the first half of Year 3. Calculate the annualized return for the entire period.
To calculate the annualized return of an investment with varying yearly returns, convert the percentage returns to decimal format, add 1, multiply them together, take the cube root (for a 3-year period), subtract 1 and convert back to a percentage. This provides a simplified approach to understanding how each year contributes to the overall growth, demonstrating the power of compound interest over time.
Explanation:To calculate the annualized return for an investment over a multi-year period with varying yearly returns, you can use the formula for geometric mean. The returns provided are 4% in Year 1, 7% in Year 2, and 10.8% for the first half of Year 3. Since the return in Year 3 is only for half the year, we annualize this by considering the effective annual rate that would lead to this return over half a year, which could be simplified for calculation purposes here without altering the principle of geometric mean calculation for annualization. Assuming each return compounds, the computation involves converting the percentage returns to their decimal form, adding 1 to each (to account for the total value, not just the gain), multiplying these values together, then taking the cube root (since we're considering a period slightly over 2.5 years), and finally subtracting 1 and converting back to a percentage.
This simplifies to:
Annualized Return = ((1 + 0.04) * (1 + 0.07) * (1 + 0.108)) 1/3 - 1, which when solved gives the annualized return. However, correctly accounting for the exact duration (slightly over 2.5 years) could involve more precise financial formulas or software for exactitude.
It is crucial to recognize each year's return contributes to the calculation differently because of compound interest, which is why each year must be calculated based on its specific return, then all are combined to find the overall annualized performance of the investment.
During the 2010 baseball season, the number of wins for three teams was three consecutive integers. Of these three teams, the first team had the most wins. The last team had the least wins. The total number of wins by these three teams was 228228. How many wins did each team have in the 2010 season?
Answer:
76075, 76076, 76077
Step-by-step explanation:
There are 3 teams; Team A, Team B and Team C
Team A has most wins
Team C has least wins
Team B is in between
All these will be consecutive numbers.
Team B: x
Team A: x + 1 (most wins)
Team C: x - 1 (least wins)
Team A + Team B + Team C = Total number of wins
x + x + 1 + x - 1 = 228228
3x = 228228
x = 76076
Wins of Team B : x = 76076
Wins of Team A : x + 1 = 76076 + 1 = 76077
Wins of Team C : x - 1 = 76076 - 1 = 76075
Therefore, in the 2010 season, Team A had 76077 wins, Team B had 76076 wins and Team C had 76075 wins.
!!
What does flipped E means and upside down A means in discrete math?
A backward e means "there exists".
An upside down A means "for all".
The flipped E symbol (∃) is used to assert that there exists at least one element in a set that satisfies a given property in discrete math. The upside-down A symbol (∀) is used to assert that all elements in a set satisfy a given property.
Explanation:The flipped E and upside-down A are symbols used in discrete math to represent logical operations. The flipped E symbol (∃) is called the Existential Quantifier and is used to assert that there exists at least one element in a set that satisfies a given property. The upside-down A symbol (∀) is called the Universal Quantifier and is used to assert that all elements in a set satisfy a given property.
For example, if we have a set of integers S = {1, 2, 3, 4, 5}, the statement ∃x(x > 3) would be true because there exists at least one element in set S (in this case, 4 or 5) that is greater than 3. On the other hand, the statement ∀x(x > 3) would be false because not all elements in set S are greater than 3, as 1, 2, and 3 are also included in the set.
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what is the answer to - (4y - 8) + 11
Answer:
you would multiply the 11 so 88-44y tjen divide which is 22
Step-by-step explanation:
Answer:
19-4y
Step-by-step explanation:
-(4y-8)+11
-4y+8+11
it becomes - 4y and +8 because you multiply the - into the equation-4y+19
19-4y
Help quickly D is Triangle EFH is congruent to triangle HFE by the Angle-Angle Theorem.
The correct answer is A, because the angles are proven same by the line of symmetry marked.
Answer:
A
explanation:
because the angles are proven same
Need some assistance with the following problem.
Any equation or inequality with variables in it is a predicate in the domain of real numbers. For the following statement, tell whether the statement is true or false.
(3x)(x^2 − 4 = 1)
Answer:
The provided statement [tex]\exists x(x^2-4=1)[/tex] is true in the domain of real number.
Step-by-step explanation:
Consider the provided information.
Any equation or inequality with variables in it is a predicate in the domain of real numbers.
The provided statement is:
[tex]\exists x(x^2-4=1)[/tex]
Here, we need to find the value of x for which the above statement is true.
Since the value of x can be any real number so we can select the value of x as √5
(√5)²-4=1
5-4=1
Which is true.
Thus, the provided statement [tex]\exists x(x^2-4=1)[/tex] is true.
A poll found that a particular group of people read an average of 12.8 books per year. The pollsters are 99% confident that the result from this poll is off by fewer than 3.93 books from the actual average x. Express this situation as an inequality involving absolute value, and solve the inequality for x to determine the interval in which the average is likely to fall.
Answer: [tex]|x-12.8|\leq3.93[/tex]
The interval in which the average is likely to fall : [tex]8.87\leq x\leq16.73[/tex]
Step-by-step explanation:
Given : A poll found that a particular group of people read an average of 12.8 books per year.
The pollsters are 99% confident that the result from this poll is off by fewer than 3.93 books from the actual average x.
The inequality to express this situation involving absolute value will be :-
[tex]|x-12.8|\leq3.93\\\\\Rightarrow\ -3.93\leq x-12.8\leq3.93 \\\\\text{Add 12.8 on both sides , we get}\\\\\Rightarrow\ -3.93+12.8\leq x\leq3.93+12.8\\\\\text{Simplify}\\\\\Rightarrow\ 8.87\leq x\leq16.73[/tex]
Hence, the interval in which the average is likely to fall : [tex]8.87\leq x\leq16.73[/tex]
The problem involves using confidence intervals and absolute value inequalities. The poll results suggest that the actual average number of books read by the group per year is between 8.87 books and 16.73 books, with a 99% confidence level.
Explanation:In this problem, the pollsters are 99% confident which means that the actual average (x) of books read by the group is within 3.93 books of the given average (12.8 books). This situation can be expressed as an inequality involving absolute value as follows: |x - 12.8| < 3.93
To find the interval of values that x (the actual average) can take, we will solve the inequality for x. This inequality is saying that the distance between x (actual average) and 12.8 is less than 3.93.
This gives us two inequalities when broken down: x - 12.8 < 3.93 and -(x - 12.8) < 3.93. Solving these two inequalities gives us an interval for x as 8.87 < x < 16.73.
So, the pollsters are 99% confident that the actual average number of books read by the group per year is between 8.87 books and 16.73 books.
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Find the area of AABC. Where: A = (-3,3), B=(-4,1), C = (-6,0). W Area:
Answer: [tex]1.5\text{ square units}[/tex]
Step-by-step explanation:
We know that the area of triangle with coordinates [tex](x_1,y_1),(x_2,y_2)[/tex] and [tex](x_3,y_3)[/tex] is given by :-
[tex]\text{Area}=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Given : The coordinates of ΔABC are A = (-3,3), B=(-4,1), C = (-6,0).
Then, the area of ΔABC will be :-
[tex]\text{Area}=\dfrac{1}{2}|-3(1-0)+(-4)(0-3)+(-6)(3-1)|\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|-3-4(-3)-6(2)|\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|-3+12-12|\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|-3|=\dfrac{1}{2}(3)=1.5 [/tex]
Hence, the area of ΔABC= [tex]1.5\text{ square units}[/tex]
(CO 4) In a sample of 8 high school students, they spent an average of 24.8 hours each week doing sports with a sample standard deviation of 3.2 hours. Find the 95% confidence interval, assuming the times are normally distributed.
(21.60, 28.00)
(22.12, 27.48)
(22.66, 26.94)
(24.10, 25.50)
Answer:
(22.12, 27.48)
Step-by-step explanation:
Given : Significance level : [tex]\alpha: 1-0.95=0.05[/tex]
Sample size : n= 8 , which is a small sample (n<30), so we use t-test.
Critical values using t-distribution: [tex]t_{n-1,\alpha/2}=t_{7,0.025}=2.365[/tex]
Sample mean : [tex]\overline{x}=24.8\text{ hours}[/tex]
Standard deviation : [tex]\sigma=3.2\text{ hours}[/tex]
The confidence interval for population means is given by :-
[tex]\overline{x}\pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
i.e. [tex]24.8\pm(2.365)\dfrac{3.2}{\sqrt{8}}[/tex]
[tex]24.8\pm2.67569206001\\\\\approx24.8\pm2.68\\\\=(24.8-2.68, 24.8+2.68)=(22.12, 27.48)[/tex]
Hence, the 95% confidence interval, assuming the times are normally distributed.= (22.12, 27.48)
You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 700 eggs and 1350 cups of cream. How many quarts of each flavor should you make in order to use up all the eggs and cream? HINT [See Example 6.]
Answer:
You should make 250 quarts of Creamy Vanilla and 200 of Continental Mocha to use up all the eggs and cream.
Step-by-step explanation:
This problem can be solved by a first order equation
I am going to call x the number of quarts of Creamy Vanilla and y the number of quarts of Continental Mocha.
The problem states that each quart of Creamy Vanilla uses 2 eggs and each quart of Continental Mocha uses 1 egg. There are 700 eggs in stock, so:
2x + y = 700.
The problem also states that each quart of Creamy Vanilla uses 3 cups of cream and that each quart of Continental Mocha uses 3 cups of cream. There are 1350 cups of cream in stock, so:
3x + 3y = 1350
Now we have to solve the following system of equations
1) 2x + y = 700
2) 3x + 3y = 1350
I am going to write y as function of x in 1) and replace it in 2)
y = 700 - 2x
3x + 3(700 - 2x) = 1350
3x + 2100 - 6x = 1350
-3x = -750 *(-1)
3x = 750
x = 250
You should make 250 quarts of Creamy Vanilla
Now, replace it in 1)
y = 700 - 2x
y = 700 - 2(250)
y = 700 - 500
y = 200.
You should make 200 quarts of Continental Mocha
Final answer:
To use up all eggs and cream at the ice cream factory, the manager should produce 250 quarts of Creamy Vanilla and 200 quarts of Continental Mocha, by solving the system of linear equations derived from the given recipe requirements.
Explanation:
To solve the problem of how many quarts of Creamy Vanilla and Continental Mocha ice cream can be produced with 700 eggs and 1350 cups of cream, we need to set up a system of equations.
Let x be the number of quarts of Creamy Vanilla and y be the number of quarts of Continental Mocha.
From the information given:
2 eggs and 3 cups of cream are used for each quart of Creamy Vanilla.1 egg and 3 cups of cream are used for each quart of Continental Mocha.We have the following equations:
2x + y = 700 (eggs)3x + 3y = 1350 (cups of cream)To simplify the second equation we can divide by 3, resulting in:
x + y = 450Now we solve this system of linear equations. By subtracting the second equation from the first, we get:
x = 700 - 450x = 250 quarts of Creamy VanillaNow, substitute x into the second equation:
250 + y = 450y = 450 - 250y = 200 quarts of Continental MochaTo use up all the eggs and cream, the factory should make 250 quarts of Creamy Vanilla and 200 quarts of Continental Mocha.
4. Rephrase the following statements in standard "if.. then" form:
(a) "We are buying a new TV only if the old TV breaks down."
(b) "In the United States, a good credit score is necessary for obtaining a loan."
(c) Unless you make me a better offer, I will keep my current job.
(d) The observation of faster than light travel would be sufficient reason to question relativity theory.
Answer:
See step-by-step explanation.
Step-by-step explanation:
a) If the old TV breaks down then we are buying a new TV.
b) If you have a good credit score in the United States, then you obtain a loan.
c) If you don't make me a better offer then I will keep my current job.
d) If we observe faster than light travel then we would question relativity theory.
Final answer:
Conditional statements, often structured in "if... then" form, express logical relationships between propositions. The provided statements have been reformulated as clear conditionals, preserving their logical meaning.
Explanation:
The statements provided by the student can be rephrased in standard "if... then" form as follows:
If the old TV breaks down, then we are buying a new TV.If you want to obtain a loan in the United States, then a good credit score is necessary.If you do not make me a better offer, then I will keep my current job.If we observe faster than light travel, then that would be a sufficient reason to question relativity theory.These rephrased statements maintain the same logical meaning but are now in the clear structure of conditionals that indicate a cause-and-effect relationship.
Cookies are sold singly or in packages of 7 or 21. With this packaging, how manyThere are ways can you buy 42 cookies? different ways to buy 42 cookie
Final answer:
There are 5 different ways to buy 42 cookies: three 21-cookie packages, two 21-cookie packages and one 7-cookie package, one 21-cookie package and three 7-cookie packages, one 21-cookie package, two 7-cookie packages, and one single, and three 7-cookie packages and seven singles.
Explanation:
To determine how many different ways you can buy 42 cookies, we can break it down into different combinations of packages. The packages are sold in singles, 7-cookie packages, and 21-cookie packages.
Let's start with the largest packages, the 21-cookie packages. We can buy zero, one, two, or three packages. For each number of packages, we can then calculate the number of remaining cookies we need to buy with singles and 7-cookie packages. We repeat this process for the 7-cookie packages, and then for the singles.
Using this method, we find that there are 5 different ways to buy 42 cookies:
Three 21-cookie packagesTwo 21-cookie packages and one 7-cookie packageOne 21-cookie package and three 7-cookie packagesOne 21-cookie package, two 7-cookie packages, and one singleThree 7-cookie packages and seven singles
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:
shock resistance
scratch resistance high low
high 70 9
low 16 5
Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch resistance. If a disk is selected at random, determine the following probabilities. Input your answers in the fractional form (do not simplify).
P(A)=86/100
P(B)=79/100
P(A')=7/50
P(A U B)=95/100
P(A' U B)= ???
Answer:
[tex]P(A'\cup B)=\frac{84}{100}[/tex]
Step-by-step explanation:
Let A and B represents the following events.
A denote the event that a disk has high shock resistance.
B denote the event that a disk has high scratch resistance.
Given probabilities:
[tex]P(A)=\frac{70+16}{100}=\frac{86}{100}[/tex]
[tex]P(B)=\frac{70+9}{100}=\frac{79}{100}[/tex]
[tex]P(A')=\frac{9+5}{100}=\frac{7}{50}[/tex]
[tex]P(A\cup B)=\frac{70+16+9}{100}=\frac{95}{100}[/tex]
The probability of intersection of A and B is,
[tex]P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]
Substitute the above values.
[tex]P(A\cap B)=\frac{86}{100}+\frac{79}{100}-\frac{95}{100}=\frac{70}{100}[/tex]
The probability of union of A' and B is,
[tex]P(A'\cup B)=P(A')+P(A\cap B)[/tex]
Substitute the above values.
[tex]P(A'\cup B)=\frac{7}{50}+\frac{70}{100}[/tex]
[tex]P(A'\cup B)=\frac{14}{100}+\frac{70}{100}[/tex]
[tex]P(A'\cup B)=\frac{84}{100}[/tex]
Therefore, [tex]P(A'\cup B)=\frac{84}{100}[/tex].
Using Venn probabilities, it is found that the desired probability is given by:
[tex]P(A' \cup B) = \frac{21}{25}[/tex]
The or probability of Venn sets is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In this problem, we want:
[tex]P(A' \cup B) = P(A') + P(B) - P(A' \cap B)[/tex]
We have that:
[tex]P(A') = \frac{7}{50}[/tex]
[tex]P(B) = \frac{79}{100}[/tex]
[tex]P(A' \cap B)[/tex] is probability of A not happening and B happening, thus low shock resistance and high scratch resistance, thus [tex]P(A' \cap B) = \frac{9}{100}[/tex]
Then
[tex]P(A' \cup B) = P(A') + P(B) - P(A' \cap B)[/tex]
[tex]P(A' \cup B) = \frac{7}{50} + \frac{79}{100} - \frac{9}{100}[/tex]
[tex]P(A' \cup B) = \frac{14}{100} + \frac{70}{100}[/tex]
[tex]P(A' \cup B) = \frac{84}{100}[/tex]
[tex]P(A' \cup B) = \frac{21}{25}[/tex]
A similar problem is given at https://brainly.com/question/23508811
Find the surface area of the part of the paraboloid z=5-3x^2-2y^2 located above the xy plane. (10 points) z
Answer:
Use the formula [tex]Area(S)=\iint_{S} 1 dS= \iint_{D} \lVert r_{u}\times r_{v} \rVert dudv[/tex]
Step-by-step explanation:
Let [tex]r(x,y)=(x,y,5-3x^2-2y^2)[/tex] be the explicit parametrization of the paraboid. The intersection of this paraboid with the xy plane is the ellipse given by
[tex]\dfrac{x^2}{\frac{5}{3}}+\dfrac{y^{2}}{\frac{5}{2}}=1[/tex]
The partial derivatives of the parametrization are:
[tex]\begin{array}{c}r_{x}=(1,0,-6x)\\r_{y}=(0,1,-4y)\end{array}[/tex]
and computing the cross product we have
[tex]r_{x}\times r_{y}=(6x,4y,1)[/tex]. Then
[tex]\lVert r_{x}\times r_{y}\rVert =\sqrt{1+36x^{2}+16y^{2}}[/tex]
Then, if [tex]R[/tex] is the interior region of the ellipse the superficial area located above of the xy is given by the double integral
[tex]\iint_{R}\sqrt{1+36x^2+16y^2}dxdy=\int_{-\sqrt{5/3}}^{\sqrt{5/3}}\int_{-\sqrt{5/2}\sqrt{1-\frac{x^2}{5/3}}}^{\sqrt{5/2}\sqrt{1-\frac{x^2}{5/3}}}\sqrt{1+36x^2+16y^2}dy dx=30.985[/tex]
The last integral is not easy to calculate because it is an elliptic integral, but with any software of mathematics you can obtain this value.
The Centers for Disease Control and Prevention Office on Smoking and health is the lead federal agency responsible for comrehensive tobacco prevention and control. OSH was established in 1965 to reduce the death and disease caused by tobacco use and exposure to secondhand smoke. One of the many responsibilites of the OSH is to collect data on tobacco use. The following data show the percentage of U.S. adults who were users of tobacco for a recent 11-year period.
Year Percentages of Adults who smoke
1 22.8
2 22.5
3 21.6
4 20.9
5 20.9
6 20.8
7 19.8
8 20.6
9 20.6
10 19.3
11 18.9
a. Construct a time series plot. What type of pattern exists in the data?
b. use simple linear regression to fidn the parameters for the line that minimizes MSE for this time series.
c. One of OSH's goals is to cut the percntage of use adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does yoru regression model from part b suggest that OSH is on target to meet this goal? if not use your model from part b to estimate the number of years that must pass after these data have been collected before OSH will achieve this goal.
Answer:
a) The percentage of adults who smoke are decreasing with time. b) the equation that best described this data is y=-0.3364x+22.809 (R^2=0.859) in which y is the percentage of adults who smoke and x the number of years. c) the percentage of adults who smoke will be 19.8% and it will not meet the expected 12%, it would take 32 years to reach that value.
Step-by-step explanation:
The data can be plotted to which years is the independent variable and percentage of adults who smoke is the dependent variable. The linear trendline that described this data has a negative slope which indicates that the percentage of adults is decreasing with time. In order to determine if the OSH target is being met, the x is replaced by 9 which is the goal period of nine years. The y is 19% which is higher than the 12% goal. In order to know the period it will take to the reach the goal of 12%, the y is replaced by 12 in the curve and the x is the answer in years = 32 years.
TRUE OR FALSE. World population growth is steady since prehistoric times and so the exponential growth model is applicable and accurate
Final answer:
The statement is FALSE. Human population growth has experienced different rates and is not described accurately by an exponential growth model for all periods, with various factors affecting growth rates. Population is projected to stabilize in the future, not grow indefinitely.
Explanation:
The statement is FALSE. Human population growth has not been steady since prehistoric times. While it is true that the human population growth since 1000 AD has often exhibited exponential patterns, it has also undergone various phases and rates of growth due to many factors such as economics, wars, disease, technological advancement, and social changes. For instance, the population in Asia, which has many economically underdeveloped countries, is increasing exponentially. However, in Europe, where most countries are economically developed, population is growing much more slowly. Additionally, historic events like the Black Death and the World Wars caused noticeable dips in population growth. Hence, the exponential growth model does not accurately describe all periods in human history. Modern projections suggest that the world's population will stabilize between 10 and 12 billion, indicating that population growth will not continue exponentially indefinitely.
Some earlier descriptions of population growth suggested a more stable growth during early human history, with high birth and death rates. Over time and especially in the recent centuries, more data has allowed us to understand that the population growth has experienced different growth rates. The issue of ongoing exponential growth and its sustainability is a topic of significant debate, considering the finite resources of the planet and the impacts of overpopulation.
Your 401(k) retirement account is currently worth $55,000. Assuming no more contributions, what will your account be worth in 20 years at an annual rate of 10.5%?
N= I/Y= PV= PMT= FV= P/Y=
Answer:
Your account is going to be worst $405,142.92
Step-by-step explanation:
This is a compound interest problem.
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
So, for this problem:
We want to find A
[tex]P = 55,000[/tex]
[tex]n = 1[/tex]
[tex]r = 0.105[/tex]
[tex]t = 20[/tex]
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A = 55000(1 + \frac{0.105}{1})^{20}[/tex]
[tex]A = 405,142.92[/tex]
Your account is going to be worst $405,142.92
I need this input into MATLAB. I'm so lost on how to code it.
Evaluate the integral sintcos tdt .
I have already solved and found the answer to be -cost 2cost cos t + C 5 9 7
I just need to prove my work with MATLAB
Answer:
>>syms t
>>f=sin(t)*cos(t);
>>int(f)
Step-by-step explanation:
It's actually pretty easy, just use symbolic variables.
First, create the symbolic variable t using this command:
syms t
Now define the function
f=sin(t)*cos(t)
Finally use the next command in order to calculate the indefinite integral:
int(f)
I attached a picture in which you can see the procedure and the result.
To evaluate the integral of sintcost tdt in MATLAB, use the symbolic math toolbox and the 'int' function.
Explanation:To evaluate the integral sintcost tdt in MATLAB, you can use the symbolic math toolbox. First, define the extended variable t using 'syms t'. Then, determine the integrand using the symbolic expression 'f = sin(t) * cos(t)'. Finally, use the 'int' function to find the integral, 'int(f, t)'.
Here's the MATLAB code:
syms tThe resulting 'integral_value' will be the evaluated integral.
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What is the answer to 9 - (-8) =
Consider the Quadratic function f(x) = 4x^2 - 1. Its vertex is Preview The x value of its largest x-intercept is x = The y value of the y-intercept is y = Preview Preview Preview
Answer:
Vertex = (0,-1)
The x value of its largest x-intercept is [tex]x=\frac{1}{2}[/tex].
The y value of the y-intercept is y = -1.
Step-by-step explanation:
The given function is
[tex]f(x)=4x^2-1[/tex] .... (1)
The vertex form of a parabola is
[tex]g(x)=a(x-h)^2+k[/tex] ..... (2)
where, a is a constant, (h,k) is vertex of the parabola.
From (1) and (2) we get
[tex]a=4,h=0,k=-1[/tex]
So, the vertex of the parabola is (0,-1).
Substitute f(x)=0 in equation (1) to find x-intercepts.
[tex]0=4x^2-1[/tex]
Add 1 on both sides.
[tex]1=4x^2[/tex]
Divide both sides by 4.
[tex]\frac{1}{4}=x^2[/tex]
Taking square root both sides.
[tex]\pm \sqrt{\frac{1}{4}}=x[/tex]
[tex]\pm \frac{1}{2}=x[/tex]
The x-intercepts are [tex]-\frac{1}{2}[/tex] and [tex]\frac{1}{2}[/tex].
Therefore the x value of its largest x-intercept is [tex]x=\frac{1}{2}[/tex].
Substitute x=0 in equation (1) to find the y-intercept.
[tex]f(0)=4(0)^2-1=-1[/tex]
Therefore the y value of the y-intercept is y = -1.
The vertex of the quadratic function f(x) = 4x^2 - 1 is at (0, -1). The x-intercepts are x = 0.5 and x = -0.5. The y-intercept is at y = -1.
Explanation:The quadratic function you provided is f(x) = 4x^2 - 1. This is indeed a second-order polynomial or more commonly referred to as a quadratic function.
The vertex of this quadratic function, which represents its maximum or minimum point, can be found using the formula -b/2a. Since this quadratic has no 'x' term, the vertex's x-value is 0. Plugging this into the function gives a y-value of -1. So, the vertex is at (0, -1).
The x-intercepts of the quadratic, i.e., the points where the function intersects the x-axis, can be found by setting f(x) = 0 and solving for x. Doing so gives two solutions: x = 0.5 and x = -0.5, with 0.5 being the larger of the two.
Finally, the y-intercept (the point where the function intersects the y-axis) is found by setting x = 0. Doing so gives a y-value of -1. So, the y-intercept is at y = -1.
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Determine whether the relation describe c as a function of w.
The cost to mail a letter, c, is related to how much it weighs, w, in the following way: Letters that cost $0.49 to mail weigh up to 1 ounce, letters that cost $0.70 to mail weigh between 1 and 2 ounces, and letters that cost $0.91 to mail weigh between 2 and 3 ounces.
Question 3 options:
a)
Not a function
b)
Function
Answer:
Function:
c = f(w) = 0.49, 0 < w ≤ 1
= 0.70, 1 < w ≤ 2
= 0.91, 2 < w ≤ 3
Step-by-step explanation:
Yes, the relation described can be interpreted as a function.
Here, c is the cost of a mail letter. c depends upon w, which is the weights of the mail letter.
As described in the question, the relation can be expressed as a function.
c can be expressed as a function of w in the following manner:
c(cost of mail) = f(w), where w is the independent variable and c is the dependent variable
c = f(w) = 0.49, 0 < w ≤ 1
= 0.70, 1 < w ≤ 2
= 0.91, 2 < w ≤ 3
where, c is in dollars and w is in ounces.