The equation in integral form by taking the inverse Laplace transform: x(t) = L^-1((s^2 - 9s + 20)X(s)) + L^-1(F(s) + sx(0) + x'(0) - 8x(0)), where L^-1 represents the inverse Laplace transform.
To express the given initial value ordinary differential equation (ODE) using convolution notation with *, we can rewrite it as:
(x'' - 8x' + 12x) = f(t)
Taking the Laplace transform of both sides, we have:
s^2X(s) - sx(0) - x'(0) - 8(sX(s) - x(0)) + 12X(s) = F(s)
where X(s) is the Laplace transform of x(t), x'(0) is the initial condition of the derivative of x(t), x(0) is the initial condition of x(t), and F(s) is the Laplace transform of f(t).
Simplifying the equation, we get:
(s^2 - 8s + 12)X(s) - sx(0) - x'(0) + 8x(0) = F(s)
Now, let's express the left-hand side of the equation using convolution notation. Using the property that the Laplace transform of the derivative of a function f(t) is sF(s) - f(0), we can rewrite the equation as:
((s^2 - 8s + 12) - s + 8)X(s) = F(s) + sx(0) + x'(0) - 8x(0)
Simplifying further, we have:
(s^2 - 9s + 20)X(s) = F(s) + sx(0) + x'(0) - 8x(0)
Finally, we can express the equation in integral form by taking the inverse Laplace transform:
x(t) = L^-1((s^2 - 9s + 20)X(s)) + L^-1(F(s) + sx(0) + x'(0) - 8x(0))
where L^-1 represents the inverse Laplace transform.
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Assume that females have pulse rates that are normally distributed with a mean of u=72.0 beats per minute and a standard deviation of a 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 70 beats per minute The probability is (Round to four decimal places as needed.) b. If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 307 OA. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size OB. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size OC. Since the onginal population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. OD. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute The probability is (Round to four decimal places as needed.) b. I 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 309 O A Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. OB. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size OC. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample site OD. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size
The probability that a randomly selected adult female has a pulse rate less than 70 beats per minute is about 0.4371.
What is the probabilitya. To find the probability that a randomly selected adult female has a pulse rate less than 70 beats per minute, one have to calculate the z-score and use the standard normal distribution.
The z-score can be calculated as:
z = (x - μ) / σ
where:
x = the value (70 beats per minute)
μ = the mean (72.0 beats per minute)
σ = the standard deviation (12.5 beats per minute).
So putting it into the formula, it will be:
z = (70 - 72.0) / 12.5
z = -0.16
One can know probability using the z-score.
Check z-score in the standard normal distribution table, and the value will be 0.4371 (rounded to four decimal places).
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Which investment choice carries the greatest price risk?
Common stocks
Preferred stocks
Corporate bonds
Government bonds
The investment choice that carries the greatest price risk is common stocks. (Option-A)
Common stocks are shares of ownership in a company and their price can be very volatile, changing rapidly depending on market conditions and factors affecting the company. Their prices can be influenced by factors such as overall economic conditions, company financial performance, and investor sentiment.
On the other hand, preferred stocks and corporate bonds are typically less risky than common stocks. Preferred stocks are a type of stock that pays a fixed dividend and has a priority claim on company assets in the event of bankruptcy, while corporate bonds are debt instruments that pay a fixed interest rate.
Lastly, government bonds are considered the least risky of all of these investment choices because they are backed by the government, which has a reputation for always repaying its debts.
In summary, while all types of investments carry some level of risk, common stocks have the greatest price risk due to their volatility and sensitivity to changing market conditions.(Option-A)
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Let A {2, 3, 4}, B = { 3, 4, 5, 6}, and suppose the universal set is U = {1, 2, ..., 9}. List all elements in
a. (A U B)' (' - means complement)
b. (A ∩ B) x A
The solutions are: (A U B)' = {1, 7, 8, 9} and (A ∩ B) x A = {(3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4)}.
a. (A U B)' represents the complement of the union of sets A and B. To find (A U B)', we need to list all the elements in the universal set U that are not in the union of sets A and B. The union of sets A and B, A U B, includes all the elements that are in either set A or set B (or both). So, A U B = {2, 3, 4, 5, 6}. The complement of A U B, (A U B)', will contain all the elements in the universal set U that are not in the set A U B. Therefore, (A U B)' = {1, 7, 8, 9}.
b. (A ∩ B) x A represents the Cartesian product of the intersection of sets A and B with set A. To find (A ∩ B) x A, we need to list all possible ordered pairs that can be formed by selecting one element from the intersection of sets A and B and pairing it with an element from set A. The intersection of sets A and B, A ∩ B, contains the elements that are common to both sets A and B. In this case, A ∩ B = {3, 4}.
Now, we take each element from A ∩ B and pair it with each element from set A. So, (A ∩ B) x A = {(3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4)}. Therefore, (A U B)' = {1, 7, 8, 9} and (A ∩ B) x A = {(3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4)}.
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The graph of f(x) = x3 + x2 - 9x - 9 is shown.
Based on the graph, what are the solutions of x3 + x2 -
9x-9 = 0?
15
12
O x= -1,3
O x = -3, -1
O x= -3,-1,3
O x= -9, -3, -1,3
9
6
3
-5
4
-2
1
2.
4
X
3
-9
- 12
-15
Save and Exit
Next
Submit
Mark this and return
Answer:
-1, 3, -3
Step-by-step explanation:
I don't see the graph, but you can solve by factoring:
[tex]x^3+x^2-9x-9=0\\x^2(x+1)-9(x+1)=0\\(x+1)(x^2-9)=0\\(x+1)(x+3)(x-3)=0[/tex]
By the factor theorem, the solutions of f(x) are -1, 3, and -3.
The requried solutions of x³ + x² - 9x - 9 = 0 is x = -3, -1, 3. Option C is correct.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
To find the solutions of equation x³ + x² - 9x - 9 = 0, we need to find the x-intercepts of the graph of the function f(x) = x³ + x² - 9x - 9.
From the graph, we can see that the function intersects the x-axis at three points, which are approximately -3, -1, and 3. Therefore, the solutions of the equation are x = -3, x = -1, and x = 3.
Thus, the correct answer is x = -3, -1, 3.
Options A, B, and D are incorrect because they either do not include all three solutions or include additional solutions that are not present in the graph of the function.
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help ASAP Ill mark u brainliest
Answer:
30% or none of these
Step-by-step explanation:
since least of the girls voted for biking it would be the least percent amount.
Hope this helped and have a wonderful day! <3 :))
An investor in the stock market is more likely to prefer a normal distribution of stock market returns over a distribution of returns that are right-skewed. True False QUESTION 10 The critical T-value for a 95% confidence interval, given a sample size of 15, is closet to: Hint: Remember the significance level is simply one less the confidence interval. 2.56 1.96 2.14 1.65
The answers are =
1) False.
2) The closest value to 2.14 would be the appropriate critical T-value for a 95% confidence interval.
1) False.
An investor in the stock market is more likely to prefer a distribution of returns that are right-skewed rather than a normal distribution.
A right-skewed distribution means that there is a higher probability of large positive returns, which is desirable for investors seeking higher profits. In the stock market, there is a phenomenon called "positive skewness," where large gains are more likely than large losses.
Investors typically aim to maximize their returns, and a right-skewed distribution offers the potential for higher returns compared to a normal distribution, which has equal probabilities for gains and losses.
2) The critical T-value for a 95% confidence interval, given a sample size of 15, is closest to 2.14. The critical T-value is determined by the desired confidence level and the degrees of freedom, which is the sample size minus 1. In this case, the sample size is 15, so the degrees of freedom would be 15 - 1 = 14. Looking up the critical T-value in a T-distribution table or using statistical software, the closest value to 2.14 would be the appropriate critical T-value for a 95% confidence interval.
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HHHHHHHHHHHHHELLLLLPPPPPPP ME PLS PLS PLS a school wants to add a new sports team. The school sent out surveys asking for the students' favorite sport. seventeen students named swimming. Others named hockey or volleyball . Use pencil and paper. Explain how to use the circle graph and ratios to find the number of students surveyed. Then find this number.
Answer:
Total 100% or 25 students
Swimming 36% or 9 students
Lacrosse 48% or 12 students
Volleyball 16% or 4 students
Step-by-step explanation:
To do a circle graph, you draw a circle and divide it into all sections.
To know the size of each section, you need to know the total number of every category.
You could draw it with percent.
100% is total, and you know the percent of each sport.
They told you 12 students choose lacrosse so, this represents 48%.
Now, you can find the other numbers with cross-multiplication.
48%____12
100%____X=
X=(100x12)/48=25
Total students: 25
Students that named lacrosse: 12 or 48%
100%____25
16%____X=
X=(16x25)/100=4
Students that named Volleyball: 4 or 16%
100%____25
36%____X=
X=(36x25)/100=9
Students that named Swimming: 9 or 36%
To confirm: 12 + 9 + 4 = 25
Brainlist Pls!
Answer:
50
Step-by-step explanation:
∠A and \angle B∠B are vertical angles. If m\angle A=(7x-8)^{\circ}∠A=(7x−8)
∘
and m\angle B=(6x+17)^{\circ}∠B=(6x+17)
∘
, then find the value of x.
identify the pattern 3,7,11,15
Answer:
Step-by-step explanation:
3 7 11 15 19 23 27
In a recent year, a research organization found that 228 of the 350 respondents who reported earning less than $30,000 per year said they were social networking users. At the other end of the income scale, 290 of the 472 respondents reporting earnings of $75,000 or more were social networking users. Let any difference refer to subtracting high-income values from low-income values. Complete parts a through d below. Assume that any necessary assumptions and conditions are satisfied. a) Find the proportions of each income group who are social networking users. The proportion of the low-income group who are social networking users is 0.6514 The proportion of the high-income group who are social networking users is 0.6144 (Round to four decimal places as needed.)
The proportion of the low-income group who are social networking users is 0.6514.
The proportion of the high-income group who are social networking users is 0.6144.
We have the following information from the question:
A research organization found that 228 of the 350 respondents who reported earning less than $30,000 per year said they were social networking users.
Another income scale, 290 of the 472 respondents reporting earnings of $75,000 or more were social networking users.
We have to find proportions of each income group who are social networking users.
Low-income group:
228 users / 350 respondents = 0.6514
The proportion of the low-income group who are social networking users is 0.6514.
High-income group:
290 users / 472 respondents = 0.6144
The proportion of the high-income group who are social networking users is 0.6144.
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Solve the system with the addition method: S-60 8y * + 5y - 24 26 Answer: (x,y) Preview 2 Preview y Enter your answers as integers or as reduced fraction(s) in the form A/B.
The solution to the system of equations is (x, y) = (-4, 6).
To solve the system using the addition method, we want to eliminate one variable by adding or subtracting the equations.
Let's solve it step by step:
First, let's multiply the second equation by 6 to make the coefficients of x in both equations equal:
6(x + 5y) = 6(26)
6x + 30y = 156
Now, we can add the modified second equation to the first equation:
(-6x - 8y) + (6x + 30y) = -24 + 156
The -6x and 6x terms cancel each other out:
-8y + 30y = 132
Simplifying the equation further:
22y = 132
To solve for y, divide both sides of the equation by 22:
y = 132 / 22
y = 6
Now that we have the value of y, we can substitute it back into either of the original equations.
Let's use the second equation:
x + 5(6) = 26
x + 30 = 26
x = 26 - 30
x = -4
Therefore, the solution to the system of equations is (x, y) = (-4, 6).
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Complete question =
Solve the system with the addition method:
-6x - 8y = - 24
x + 5y = 26
Answer: (x,y)
Hey guys I really need help please help me
Answer:
I believe x would be 30
Step-by-step explanation: When you add 20+10 it will give you the other triangle side, which is 30, and then 22+11 will be 33. And for the final side 24+12 will give you 36
estado tratando esto por mucho tiempo
Answer:
1/2
Step-by-step explanation:
Paso Uno: [tex]\frac{5}{1}* \frac{5}{1} *\frac{5}{1}* \frac{5}{1} *\frac{5}{1}[/tex]* 1/10= 5/10
Paso Dos: Simplificar:
5/5=1
10/5=2
Paso Tres: fracción es 1/2
I need help with this please lol
Answer:
360 degrees
Step-by-step explanation:
3-6 x (34 divided by 30)2
Answer:
3-6
Step-by-step explanation:
The expression 3⁻⁶ × (3⁴ ÷ 3⁰)² value is 9 which is 3².
To simplify the given expression: 3⁻⁶ × (3⁴ ÷ 3⁰)², let's break it down step by step:
First, let's simplify the exponent expressions within the parentheses:
3⁴ = 81 (because 3⁴ = 3 × 3 × 3 × 3 = 81)
3⁰ = 1 (because any number raised to the power of 0 is 1)
Now, we can rewrite the expression with the simplified exponents:
3⁻⁶ × (81 ÷ 1)²
Next, simplify the division within the parentheses:
81 ÷ 1 = 81
Now, the expression becomes:
3⁻⁶ × 81²
Simplify the exponent:
81² = 6561 (because 81 × 81 = 6561)
Now, the expression becomes:
3⁻⁶ × 6561
1/729 × 6561
6561/729
dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 9:
729/81
We get 9 which is equal to 3².
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4x + 14 = 4x + 24 its to hard for me
Answer:
x=10
Step-by-step explanation:
Bella is going to redecorate her room using wallpaper. Her wall has a large window in the middle. The diagram below shows the wall she is decorating with the window. How many square feet of the wallpaper will she need?
A-42 sq ft
B-82 sq ft
C-104 sq ft
D-130 sq ft
82sq ftAnswer:
Step-by-step explanation:
Solve: 6x - 13 = 4(x + 10) + 2x
Answer:
null
Step-by-step explanation:
Answer: 0=53
Step-by-step explanation:
A store owner offers a discount of 20% off the regular price of all jackets. Jessica has a coupon that gives her an additional 5% off the discounted price. The original price of the jacket Jessica buys is $84. What is the price of the jacket after the discount and Jessica's coupon?
Answer:
21
Step-by-step explanation:
I haven't done this in a long time but this is what I know: the discount would overall be 25%. So, you set it up by .25(84) = 21. Therefore the jacket would cost $21.
I hope this is right and helps!
Maths equation need help please
Answer:
I FIGURED IT OUT!
Step-by-step explanation:
a = 3
b = 3
c = 5
d = 2
give me brainliest
Michael Scott, regional manager at Dunder mifflin Scranton, bought a coin from a magic shop that is designed to flip heads much often than tails. Dwight Schrute, his employee, wants to estimate the proportion of all glips of this coin that will be heads. In 400 flips of the coin Dwight flipped 312 times. Construct and interpret the 90% confidence interval for the population proportion of flips that will be heads. show at least 2 decimal digits in your endpoints.
The 90% confidence interval for the population proportion of flips that will be heads is given as follows:
(0.746, 0.814).
The interpretation is that we are 90% sure that the true proportion of all tosses with this coin is between these two bounds.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The parameters for this problem are given as follows:
[tex]n = 400, \pi = \frac{312}{400} = 0.78[/tex]
The lower bound of the interval is given as follows:
[tex]0.78 - 1.645\sqrt{\frac{0.78(0.22)}{400}} = 0.746[/tex]
The upper bound is given as follows:
[tex]0.78 + 1.645\sqrt{\frac{0.78(0.22)}{400}} = 0.814[/tex]
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Find the equation of the exponential function represented by the table below:
Answer:
[tex]y=0.01(4)^x[/tex]
Step-by-step explanation:
A poker hand consists of 5 cards. A flush is a hand for which all cards are the same suit,but not of consecutive denominations (where Ace can be high or low.For example,2,3,4,5,7 of Hearts is a flush,but 2,3,4,5,6 of Hearts is not a flush. Find the probability that a poker hand from a well-shuffled deck is a flush. b Anne and Barney are playing poker. On each hand, Anne has a 20% chance of bluffing and Barney has a 30% chance of bluffing; the two players bluff in- dependently. What is the probability that Anne is bluffing,given that at least one player is bluffing?
The probability that a poker hand from a well-shuffled deck is a flush is 0.00198.
The probability that Anne is bluffing, given that at least one player is bluffing is 1.95.
a) Probability that a poker hand from a well-shuffled deck is a flush:
Consider the following points for a poker hand from a well-shuffled deck is a flush:
There are 4 suits in a deck of cards.
There are 13 denominations in each suit.
When choosing a flush hand, any of the suits can be selected.
Therefore, the probability of choosing a suit is: P(Suit) = 4/4 = 1.
Therefore, the probability of selecting a suit is 1.The first card may be of any denomination. Therefore, the probability of selecting any denomination is 1.
Since all 5 cards must have the same suit, the second card must be of the same suit as the first card. Therefore, the probability of selecting the second card of the same suit is:
P(Same Suit) = 12/51
The third card must also be of the same suit as the first card and second card. Therefore, the probability of selecting the third card of the same suit is:
P(Same Suit) = 11/50
The fourth card must also be of the same suit as the first card, second card, and third card. Therefore, the probability of selecting the fourth card of the same suit is:
P(Same Suit) = 10/49
The fifth card must also be of the same suit as the first card, second card, third card, and fourth card. Therefore, the probability of selecting the fifth card of the same suit is:
P(Same Suit) = 9/48
Multiplying all probabilities together, we have:
P(Suit) × P(Same Suit) × P(Same Suit) × P(Same Suit) × P(Same Suit)= 1 × 12/51 × 11/50 × 10/49 × 9/48= 0.00198
Therefore, the probability that a poker hand from a well-shuffled deck is a flush is 0.00198.
Ans: 0.00198.
b) Probability that Anne is bluffing, given that at least one player is bluffing:
Consider the following points for the probability that Anne is bluffing, given that at least one player is bluffing:
Anne has a 20% chance of bluffing.
Barney has a 30% chance of bluffing.
The two players bluff independently.
P(Anne is bluffing) = 20/100 = 1/5P(Barney is bluffing) = 30/100 = 3/10
Let A be the event that Anne is bluffing and B be the event that Barney is bluffing.
Let C be the event that at least one player is bluffing.
P(C) = 1 - P(none is bluffing) = 1 - (1 - P(Anne is bluffing)) × (1 - P(Barney is bluffing))= 1 - (1 - 1/5) × (1 - 3/10)= 1 - (4/5) × (7/10)= 1 - 28/50= 22/50= 11/25
Now, P(A ∩ C) = P(A) × P(C|A)
Where P(C|A) is the probability that at least one player is bluffing given that Anne is bluffing.= (3/10 + 7/10 × 4/5) / (1 - 4/5)= (3/10 + 28/50) / (1/5)= (15/50 + 28/50) / (1/5)= 43/50 × 5= 215/50
Therefore, P(A|C) = P(A ∩ C) / P(C)= 215/50 × 25/11= 1.95
Therefore, the probability that Anne is bluffing, given that at least one player is bluffing is 1.95. Ans: 1.95.
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Select the simplification that accurately explains the following statement.
Answer:
look below I got it right
Step-by-step explanation:
look carefully, for some people it’s a, for some it’s different so just look and compare to the answers
A parliament has seats for 2 parties, party A has 60 members and party B has 80. While voting on resolution R, 60% of party A votes against the resolution while only 25% of party B votes against the resolution. If we were to randomly select 40 members from the parliament, what is the probability of:
1. At least 25/40 members vote against the resolution
2. At least 25/40 members vote for the resolution
1. The probability of at least 25/40 members voting against the resolution is 0.92114
2. the probability of at least 25/40 members voting for the resolution is 0.92114.
We are to find the probability of the following events:
First, we find the number of members who are likely to vote against the resolution from each party.
Number of members from Party A who would vote against the resolution = 60% of 60 = 0.60 × 60 = 36.
Number of members from Party B who would vote against the resolution = 25% of 80 = 0.25 × 80 = 20.
Thus, the total number of members who would vote against the resolution = 36 + 20 = 56.
Number of members who would vote in favor of the resolution = Total members − Number of members who would vote against the resolution= 60 + 80 − 56 = 84.
Let X be the number of members voting against the resolution. If X follows a binomial distribution with n = 40 and p = 56/140 = 0.4, we can find the probability of the events as follows:
1. The probability of at least 25/40 members voting against the resolution:
P(X ≥ 25) = 1 − P(X < 25)
We can use the binomial distribution table to find the probabilities associated with different values of X.
P(X < 25) = P(X = 0) + P(X = 1) + ... + P(X = 24)
Using the binomial distribution formula, we get:
P(X = k) = (nCk) × pk × (1 − p)n−k, where nCk is the number of ways of choosing k members out of n.
Using the formula, we can calculate the probabilities of P(X < 25) and P(X ≥ 25) as follows:
P(X < 25) = 0.000236 + 0.003226 + 0.020408 + 0.076306 + 0.182424 + 0.291878 + 0.338993 + 0.245031= 0.078858P(X ≥ 25) = 1 − P(X < 25)= 1 − 0.078858= 0.92114
Thus, the probability of at least 25/40 members voting against the resolution is 0.92114
2.The probability of at least 25/40 members voting for the resolution:
P(X ≥ 25) = 1 − P(X < 25)
We can use the binomial distribution table to find the probabilities associated with different values of X.P(X < 25) = P(X = 0) + P(X = 1) + ... + P(X = 24)
Using the binomial distribution formula, we get:
P(X = k) = (nCk) × pk × (1 − p)n−k, where nCk is the number of ways of choosing k members out of n.
Using the formula, we can calculate the probabilities of P(X < 25) and P(X ≥ 25) as follows:
P(X < 25) = 0.000236 + 0.003226 + 0.020408 + 0.076306 + 0.182424 + 0.291878 + 0.338993 + 0.245031= 0.078858
P(X ≥ 25) = 1 − P(X < 25)= 1 − 0.078858= 0.92114
Thus, the probability of at least 25/40 members voting for the resolution is 0.92114.
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plz tell about congruent and similar triangles
Similar: If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
____________________________________________________________
Congruent: SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal. If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
BRAINLIST. BRAINLIST. BRAINLIST. PLS HELP.
Answer:
Mild- 5x=50 4x=40
Medium- 90- 48=42, 42/2=21 so, 2x=21
Spicy- 90-25=65, 65+18=83
Step-by-step explanation:
I'm gonna guess that this is the angle measurement so.....
Which expression represents the area of the shaded region?
Given:
A circle of radius r inscribed in a square.
To find:
The expression for the area of the shaded region.
Solution:
Area of a circle is:
[tex]A_1=\pi r^2[/tex]
Where, r is the radius of the circle.
Area of a square is:
[tex]Area=a^2[/tex]
Where, a is the side of the square.
A circle of radius r inscribed in a square. So, diameter of the circle is equal to the side of the square.
[tex]a=2a[/tex]
So, the area of the square is:
[tex]A_2=(2r)^2[/tex]
[tex]A_2=4r^2[/tex]
Now, the area of the shaded region is the difference between the area of the square and the area of the circle.
[tex]A=A_2-A_1[/tex]
[tex]A=4r^2-\pi r^2[/tex]
[tex]A=4r^2-\pi r^2[/tex]
[tex]A=r^2(4-\pi )[/tex]
Therefore, the correct option is (a).
What is the volume of the solid figure?
Enter your answer in the box.
Please help..
Answer:
188
Step-by-step explanation:
10*5*4 - 6*2
Consider the points A (-1, 1), B (1,5) and C (5, 1). M is the midpoint of AB, and N is the
midpoint of BC.
Show that MN is parallel to AC
Step-by-step explanation:
IN ΔAMN ΔABC
Since MN∣∣BC
∠AMN=∠ABC (Corresponding angles)
∠ANM=∠ACB (Corresponding angles)
∴ΔAMN∼ΔABC(By $$AA similarity criterion)
⇒
AB
AM
=
AC
AN
=
BC
MN
(CPST)
Since, M is mid-point of AB,
AM=
2
1
AB,or,
AB
AM
=
2
1
or,
AB
AM
=
AC
AN
=
2
1
AC
AN
=
2
1
5
AN
=
2
1
[∵AC=5cm]
AN=
2
5
cm=2.5cm
Also,
AB
AM
=
BC
MN
=
2
1
7
MN
=
2
1
[∵BC=7cm]
MN=
2
7
=3.5
Ans=AN=2.5cm and MN=3.5cm
solution