the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.
The statements that are true about the reflectional symmetryof a regular heptagon are:
It has only one line of reflectional symmetry.
The line of reflectional symmetry passes through the center of the heptagon.
A regular heptagon is a polygon with seven equal sides and angles. Each vertex of the heptagon is equidistant from the center of the heptagon, and the lines connecting the center to the vertices divide the heptagon into seven congruent triangles.
To understand the reflectional symmetry of the regular heptagon, we need to define what it means. Reflectional symmetry is a type of symmetry where a figure is symmetric with respect to a line. In other words, if we fold the figure along this line, one half will coincide with the other half.
In the case of the regular heptagon, we can observe that if we draw a line passing through the center of the heptagon and perpendicular to any of its sides, we obtain a line of reflectional symmetry. This line divides the heptagon into two congruent halves. However, if we draw any other line of reflectional symmetry, it will not coincide with the sides of the heptagon, and therefore, it will not divide the heptagon into congruent halves.
Therefore, we conclude that the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.
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Find the missing side lengths. Leave your answers as radicals in simplest form.
Answer:
Step-by-step explanation:
Rumiya is a saleswoman who receives a base salary of 85000. On top of her base salary, she receives a 10% commission on x dollars of sales she makes for the year. If she aspires 100000 to make over this year, then what minimum amount of sales, , would she need to make?
mx+b>100000
m= b=
Rumiya's total earnings can be represented by the inequality: [tex]85000 + 0.1x > 100000[/tex] and she would need to make sales of at least $150,000 to earn over $100,000 for the year.
What do you mean by commission and inequality ?
A commission is a percentage of sales that a salesperson earns on top of their base salary. In this case, Rumiya earns a 10% commission on sales she makes for the year. An inequality is a statement that compares two values, indicating whether one is greater than, less than, or equal to the other. It is used to represent that Rumiya needs to make sales that exceed a certain amount in order to earn a desired amount.
Finding the minimum amount of sales :
Rumiya's total earnings for the year will be the sum of her base salary and commission on sales. We can represent this as an inequality:
[tex]85000 + 0.1x > 100000[/tex]
To solve for [tex]x[/tex], we first need to isolate the variable on one side of the inequality. We can do this by subtracting 85000 from both sides:
[tex]0.1x > 15000[/tex]
Next, we can solve for [tex]x[/tex] by dividing both sides by 0.1:
[tex]x > 150000[/tex]
Therefore, Rumiya would need to make sales of at least $150,000 to earn over $100,000 for the year. This means that her commission on these sales would be $15,000 (10% of $150,000).
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Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Round your final answer to three decimal places. Intermediate calculations should be rounded to a minimum of four places. n = 15, p = 0.4 a. Find P(2). Round to three decimal places. b. Find P(2 or fewer). Round to the three places.
a. The value of P(2) is 0.022
b. The value of P(2 or fewer) is 0.027
From the question; n = 15, p = 0.4
a. We have to determine P(2).
P(X = x) = ⁿCₓ·Pˣ·(1 - P)ⁿ⁻ˣ
P(X = 2) = ¹⁵C₂·(0.4)²·(1 - 0.4)¹⁵⁻²
We can write ⁿCₓ = [tex]\frac{n!}{x!(n - x)!}[/tex]
P(X = 2) = [tex]\frac{15!}{2!(15 - 2)!}[/tex] · (0.16) · (0.6)¹³
P(X = 2) = [tex]\frac{15\times14\times13!}{2\times1\times13!}[/tex] · (0.16) · (0.6)¹³
P(X = 2) = (15 × 7) · (0.16) · (0.6)¹³
After simplification
P(X = 2) = 0.022(approx)
b. We have to determine P(2 or fewer).
P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)
P(x ≤ 2) = ¹⁵C₀·(0.4)⁰·(1 - 0.4)¹⁵⁻⁰ + ¹⁵C₁·(0.4)¹·(1 - 0.4)¹⁵⁻¹ + ¹⁵C₂·(0.4)²·(1 - 0.4)¹⁵⁻²
After simplification like above
P(x ≤ 2) = 0 + 0.005 + 0.022
P(x ≤ 2) = 0.027
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Mr. Chand is one of the landlords of his town. He buys a land for his daughter spanning over a
area of 480m². He fences the dimensions of the land measuring (x+12) mx (x+16) m. Now he
plans to erect a house with a beautiful garden in the ratio 5:3 respectively. A total of Rs. 5,00,000 is estimated as the budget for the expenses.
1)Give the area of the land purchased in linear polynomial form using algebraic expression
2)Mr. Chand's daughter is ready to share 3/5" of the expenses by her earnings. Express the
fraction in amount.
3)Can you solve the linear equation/polynomial of the area into different factors?
The required answers are 1) [tex]$$A = x^2 + 28x + 192$$[/tex] 2) 300000 3) [tex]$$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$[/tex].
How to deal with area and fractions?area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:
[tex]$$A = (x+12)(x+16)$$[/tex]
Expanding this expression, we get:
[tex]$$A = x^2 + 28x + 192$$[/tex]
Hence, the area of the land purchased is given by the polynomial expression [tex]$x^2 + 28x + 192$[/tex].
The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:
[tex]$\frac{3}{5}=\frac{x}{500000}$$[/tex]
Simplifying this expression, we get:
[tex]$x = \frac{3}{5}\times 500000 = 300000$$[/tex]
Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.
We can solve the polynomial [tex]$x^2 + 28x + 192$[/tex] into different factors by using the quadratic formula:
[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]
Here, the coefficients of the polynomial are:
[tex]$$a = 1, \quad b = 28, \quad c = 192$$[/tex]
Substituting these values in the quadratic formula, we get:
[tex]$x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$[/tex]
Simplifying this expression, we get:
[tex]$$x = -14 \pm 2\sqrt{19}$$[/tex]
Therefore, the polynomial [tex]$x^2 + 28x + 192$[/tex] can be factored as:
[tex]$$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$[/tex]
or
[tex]$$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$[/tex]
So, we have factored the polynomial into two factors.
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PLease soemone help me you would make my life and day just answer true or false. I will give you 20 points just please answer the question with a true or false.
Answer: first 4 are false last one is true
Step-by-step explanation:
tapas and paella that originated in what country
2 Sasha believes her soccer team plays better at away games than at home games. Her team played 12 games at home and 12 games away. She recorded the wins over this season. Based on these results, what is the probability for home and away wins? Is she right about her team playing better away? Show your work. Place: Home Away
Frequency: 8 7
Probability of winning at home is 0.67, Probability of winning away is 0.58.
How to calculate the probabilitiesTo calculate the probability of home and away wins, we need to divide the number of wins by the total number of games played at home and away respectively.
Probability of winning at home = (Number of wins at home) / (Total number of games played at home)
= 8 / 12
= 0.67
Probability of winning away = (Number of wins away) / (Total number of games played away)
= 7 / 12
= 0.58
Based on these results, Sasha's team has a higher probability of winning at home (0.67) compared to away games (0.58).
Therefore, her belief that her team plays better away is not supported by the data.
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Rewrite without absolute value for the given condition: y=|x−3|+|x+2|−|x−5|, if 3 < x < 5
When 3 < x < 5, y can be expressed as y = 3x - 6 without absolute value notation.
What is absolute value notation ?
Absolute value notation is a mathematical notation used to represent the magnitude or distance of a real number from zero. It is denoted by vertical bars or pipes around the number. For example, the absolute value of x is written as |x|.
When 3 < x < 5, the expression |x-3| evaluates to x-3, the expression |x+2| evaluates to x+2, and the expression |x-5| evaluates to 5-x. Therefore, we can rewrite the expression y = |x-3| + |x+2| - |x-5| as:
y = (x-3) + (x+2) - (5-x)
Simplifying this expression, we get:
y = 3x - 6
Therefore, when 3 < x < 5, y can be expressed as y = 3x - 6 without absolute value notation.
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HELP ME ASAP PLEASE!!!!!!!!!
Answer:
See step by step.
Step-by-step explanation:
lets define the events:
A: cuban festival C: tropical Garden
B: street art show D: african festival
a) theoretically the probability is
[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)
b) The experimental probability is given by:
[tex]P(A)= \frac{32}{150} =0.2133[/tex]
[tex]P(B)= \frac{38}{150} =0.2533[/tex]
[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]
c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.
b is the set of odd positive integers less than 11.
(a)list all the elements of b in set notation.
b)state whether each of the followning statements is true or false.
(i)1∈b
Answer:
Step-by-step explanation:
True. 1 is an odd positive integer less than 11 and is an element of set B.
Simplify 3(x+2) + 2x + 5
Answer:
[tex]5x+11[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]3x+6+2x+5[/tex]
Step 2: Add like terms
[tex]5x+11[/tex] < your answer
she works a 35
-hour week earning $17.10
an hour.
How much does she earn in one year? (Use 52
weeks in one year.)
$
Answer:
$31122.00
Step-by-step explanation:
We know
She works 35 hours a week, earning $17.10 an hour.
17.10 x 35 = $598.50 a week
How much does she earn in one year?
We Take
598.50 x 52 = $31122.00
So, she earns $31122.00 one year.
Linda deposits $50,000 into an account that pays 6% interest per year, compounded annually. Bob deposits $50,000 into an account that also pays 6% per year. But it is simple interest. Find the interest Linda and Bob earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits. Year First Second Third Interest Linda earns (Interest compounded annually) Interest Bob earns (Simple interest) Who earns more interest? Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount.
Answer:
Step-by-step explanation:
To calculate the interest earned by Linda for the first year, we can use the formula:
A = P(1 + r/n)^(nt)
Where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
For the first year, we have:
A = $50,000(1 + 0.06/1)^(1*1) = $53,000
So, the interest earned by Linda for the first year is:
Interest = $53,000 - $50,000 = $3,000
For the second year, we can use the same formula with t = 2:
A = $50,000(1 + 0.06/1)^(1*2) = $56,180
Interest = $56,180 - $53,000 = $3,180
For the third year, we can use the same formula with t = 3:
A = $50,000(1 + 0.06/1)^(1*3) = $59,468.80
Interest = $59,468.80 - $56,180 = $3,288.80
Now, to calculate the interest earned by Bob for each of the first three years, we can use the formula:
Interest = Prt
Where P is the principal amount, r is the annual interest rate, and t is the time in years.
For the first year, we have:
Interest = $50,0000.061 = $3,000
For the second year, we have:
Interest = $50,0000.061 = $3,000
For the third year, we have:
Interest = $50,0000.061 = $3,000
As we can see, Linda earns more interest than Bob for each year, as her interest is compounded annually, while Bob's interest is simple interest. Therefore, the answer is:
Linda earns more.
Answer:
Linda earns $9550.8 interest and bob earns $9000 interest
Step-by-step explanation:
Linda takes compound interest: C.I. = Principal (1 + Rate)Time − Principal
interest= 50,000(1+6/100)³
=59550.8 - 50000
Linda earns $9550.8 interest in 3 years.
bob takes simple interest: S.I = prt/100
interest = 50,000*6*3/100
Bob earns $9000 in 3 years.
thus, Linda earns more interest than bob.
Molly has 4 final test to study for. She wants to study an equal amount on each test. If she has 10 hours to study for all her finals, how much time should she study for each test. Record answer in hours and minutes.
Answer:
2.5 hours
Step-by-step explanation:
To find the number of hours for each test,
Divide the number of hours by the number of tests
10 divided by 4
2.5 hours for each test
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An 800 seat multiplex cinema is divided into 3 theatres. There are 270 seats in
Theatre 1, and there are 150 more seats in Theatre 2 than in Theatre 3. How many
seats are in Theatre 2?
Answer:
340 seats in Theatre 2
Step-by-step explanation:
let n be the number of seats in Theatre 3 then the number of seats in theatre 2 is n + 150
summing and equating gives
27 0 + n + 150 + n = 800
420 + 2n = 800 ( subtract 420 from both sides )
2n = 380 ( divide both sides by 2 )
n = 190
then
number of seats in Theatre 2 = n + 150 = 190 + 150 = 340
Answer:
Theatre 3 has 190 seats, and Theatre 2 has 190 + 150 = 340 seats.
Step-by-step explanation:
Let x be the number of seats in Theatre 3.
Then the number of seats in Theatre 2 is x + 150.
And the total number of seats in the multiplex is 270 + x + (x + 150) = 800.
Simplifying the equation, we get
2x + 420 = 800
2x = 380
x = 190
Therefore, Theatre 3 has 190 seats, and Theatre 2 has 190 + 150 = 340 seats.
A doctor collects data on all the men in his practice. They have an average age of 45 years, with a standard deviation of 15 years. They have an average systolic blood pressure of 150 mmHg, with a standard deviation of 10 mmHg. The two variables have correlation r=0.7.
a) Using regression, calculate the predicted systolic blood pressure for a man in the practice who is i) 30 years old ii) 45 years old iii) 50 years old
b) The above predictions all are subject to error. The average size of such errors is about ___ mmHg, and 95% of the predictions we make using regression will be correct to within about ___ mmHg.
c) A man is selected at random from the practice. He is 60 years old, which means that he is ___ SD(s) above the average age of men in the practice. Another way of expressing his relative age is that he is at the ___ percentile of age among all men in the practice.
d) Using regression, we can predict the man from part (c) will have a blood pressure that is ___ SD(s) above average. Therefore, he is predicted to be at the ___ percentile of blood pressure.
(A) This means that the systolic blood pressure 100 is less than average blood pressure and 150is higher than the average blood pressure.
(B) The average size of such errors is about 125 mmHg, and 95% of the predictions we make using regression will be correct to within about 90 mmHg.
(C) He is 60 years old, which means that he is 1.7857 SD(s) above the average age of men in the practice.
(D) The percentile corresponding to -0.6 as27.43. this means that 27.43% of people with blood pressure reading above 125.
(A) We have to find the z statistics of systolic blood pressure 100 and 150.
We have:
z₁₀₀ = 100 -125/14
= -1.7857
And, Z₁₅₀ = 150-125/14
= 1.7857
So, the systolic blood pressure 100 is -1.7857 standard deviation to the left of the mean 125.
And, the systolic blood pressure 150 is 1.7857 standard deviation to the left of the mean 125.
This means that the systolic blood pressure 100 is less than average blood pressure and 150is higher than the average blood pressure.
(B) The above predictions all are subject to error. The average size of such errors is about 125 mmHg, and 95% of the predictions we make using regression will be correct to within about 90 mmHg.
-2.5 = x -125/14
⇒ x = -2.5 × 14 +125
⇒ x = 90.
(C) A man is selected at random from the practice. He is 60 years old, which means that he is 1.7857 SD(s) above the average age of men in the practice. Another way of expressing his relative age is that he is at the 96% percentile of age among all men in the practice.
(D) The z score is: z = 0.6
The percentile corresponding to -0.6 as27.43. this means that 27.43% of people with blood pressure reading above 125.
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Determine the values of A, B, and C when y - 7 = 3(x - 4) is written in standard form, Ax + By = C.
Answer:
To convert the equation y - 7 = 3(x - 4) to standard form Ax + By = C, we need to rearrange it so that it has the form Ax + By = C, where A, B, and C are constants.
y - 7 = 3(x - 4)
y - 7 = 3x - 12 (distribute the 3)
3x - y = 7 - 12 (move y to the left-hand side)
3x - y = -5
Now we have the equation in standard form, where:
A = 3
B = -1
C = -5
Therefore, the values of A, B, and C are 3, -1, and -5, respectively.
Fill in the table using this function rule.
f(x)=√x+5
Simplify your answers as much as possible.
Click "Not a real number" if applicable.
x
-4
0
36
64
f(x)
11
0
0
0
Not a
real
number
Start over
5
Answer:
4
Step-by-step explanation:
(a) What is the expanded form of (a + b) 2? (b) The length of a rectangular mat is 3x-y meter and its breadth is 3-*meter. Find the area of the mat.
Answer: 9x - 3x* - 3y + y* square meters
Step-by-step explanation:
(a) The expanded form of (a + b) 2 is:
(a + b) 2 = a2 + 2ab + b2
(b) The area of the rectangular mat is:
Area = Length × Breadth
Given that the length is 3x - y meters and the breadth is 3 - * meters.
So, the area of the rectangular mat can be calculated as:
Area = (3x - y) × (3 - *)
= 9x - 3x* - 3y + y*
Therefore, the area of the rectangular mat is 9x - 3x* - 3y + y* square meters.
Answer:
Step-by-step explanation:
HEEELLLLPPPPP MEEEEEEEEE
1. Solve.
a. 2/5t = 6
b. -4.5 = a-8
c. 1/2+p=-3
d. 1/2 = x3
e. -12 = -3y
The equation is saying that -12 is equal to -3 multiplied by y. To solve for y, divide both sides by -3. This would give an answer of 4.
What is equation?An equation is a mathematical statement that expresses the equality or inequality of two values or expressions. It consists of two expressions connected by an equals sign, inequality sign or other relational operator. Equations can involve numbers, variables, and operations such as addition, subtraction, multiplication, division and exponentiation. An equation can be used to solve problems related to mathematics, science, engineering, finance, and many other disciplines. Equations can also be used to model and describe real-world phenomena.
t = 30
a = 12.5
p = -5.5
x = 2/3
y = 4.
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a. t = 30/2; To solve this equation, divide both sides by 2/5. The resulting equation is t = 30/2.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions by using an equals sign (=). It states that the two expressions on either side of the equals sign are equal in value. An equation is an example of a mathematical problem, which can be used to solve real-world problems.
b. a = 4.5; To solve this equation, add 8 to both sides. The resulting equation is a = 4.5.
c. p = -7/2; To solve this equation, add 3 to both sides. The resulting equation is p = -7/2.
d. x = 2; To solve this equation, divide both sides by 3. The resulting equation is x = 2.
e. y = 4; To solve this equation, divide both sides by -3. The resulting equation is y = 4.
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francesca bought 27 keychains of two different kinds to make goodie bags for her birthday party. leather keychains were three dollars and beaded keychains for two dollars. she spent $73. how many keychains of each kind did she buy
Answer: Supergirl = 19 and Wonder Woman = 8
Step-by-step explanation:
Let g represent the quantity of Supergirl keychains and w represent the quantity of Wonder Woman keychains.
Qty Cost
Supergirl g $3g
Wonder Woman w $2w
Total 27 $73
Qty: g + w = 27 → -2(g + w = 27) → -2g - 2w = -54
Cost: 3g + 2w = 73 → 1(3g + 2w = 73) → 3g + 2w = 73
g = 19
Input g = 19 into one of the original equations to solve for w:
g + w = 27
(19) + w = 27
w = 8
for each polynomial in factored form show the leading term, the zeros on the x-axis, and the general shape of the polynomial
For the given polynomials in factored form;
(a) the leading term is x³, the zeroes are -2,3 and 5 , the graph will be a cubic function passing through x-axis at -2, 3 and 5.
(b) the leading term is 2x², the zeros are -1, 4 the graph will be a quadratic function passing through x-axis at -1 and 4.
Part(a) : The polynomial in factored form is : f(x) = (x + 2)(x - 3)(x - 5)
The Leading Term is : x³; The Zeros are : -2, 3, 5.
The General Shape: The graph of the polynomial will be a cubic function that passes through the x-axis at -2, 3, and 5.
The function will approach negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.
Part(b) : The Polynomial in factored form is : f(x) = 2(x + 1)(x - 4)
The Leading Term is : 2x²; The Zeros are : -1, 4.
The General Shape: The graph of the polynomial will be a quadratic function that passes through the x-axis at -1 and 4. The function will open upwards since the leading coefficient is positive.
The function will approach negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.
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The given question is incomplete, the complete question is
For each polynomial in factored form show the leading term, the zeros on the x-axis, and the general shape of the polynomial.
(a) f(x) = (x + 2)(x - 3)(x - 5)
(b) f(x) = 2(x + 1)(x - 4).
a circle of radius r centered at (r,0), with r < r, is rotated about the y-axis. find the surface area of the resulting solid.
The surface area of the resulting solid is 4πr².
The surface area of a circle of radius r centered at (r,0), rotated about the y-axis, can be determined by first finding the area of the circle and then adding the area of the cylinder formed by rotating the circle about the y-axis.
The area of the circle is given by A = πr².
The area of the cylinder formed by rotating the circle about the y-axis is equal to the circumference of the circle (2πr) multiplied by the height of the cylinder (2r). Therefore, the total surface area of the rotated circle is equal to the area of the circle (πr²) plus the area of the cylinder (2πr * 2r) which gives a total surface area of 4πr².
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A pipe with the diameter of 2.4 cm discharges water a rate 2.8 m per second. find the volume of water discharges one and a half hour, giving the answer in litres?
Answer: approximately 68,404 liters.
Step-by-step explanation:
To solve the problem, we first need to find the cross-sectional area of the pipe, which we can calculate using the formula for the area of a circle:
A = πr^2
where r is the radius of the pipe, which is half the diameter. So, in this case, the radius is 2.4 cm / 2 = 1.2 cm.
A = π(1.2 cm)^2
A ≈ 4.5239 cm^2
Next, we can use the formula for volume flow rate to find the volume of water that is discharged per second:
Q = Av
where Q is the volume flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the water. In this case, we have:
Q = (4.5239 cm^2)(2.8 m/s)
Q ≈ 0.01266 m^3/s
To find the volume of water discharged in one and a half hours (which is 5400 seconds), we can multiply the volume flow rate by the time:
V = Qt
V = (0.01266 m^3/s)(5400 s)
V ≈ 68.404 m^3
Finally, to convert the volume from cubic meters to liters, we can multiply by 1000:
V = 68.404 m^3 × 1000 L/m^3
V ≈ 68,404 L
Therefore, the volume of water discharged in one and a half hours is approximately 68,404 liters.
Suppose I go on a fishing trip where I visit 4 lakes, lakes L1, L2, L3, and L4. Let C1 be the event that I catch a fish from lake L1. Let C2 be the event that I catch a fish from lake L2. Let
C3
be the event that I catch a fish from lake L3. Let
C4
be the event that I catch a fish from lake L4. I am a poor fisherman, so I am happy if I catch at least one fish. The lakes are far enough apart so that whether I catch a fish in any lake is independent from catching a fish in any other lake. There is a
.3
probability that C1 happens, a .4 probability that C2 happens, a .2 probability that C3 happens and a
.2
probability that C4 happens a. What is the probability I catch fish in all 4 lakes? b. What is the probability I do not catch any fish at all? c. What is the probability that I catch at least one fish? (I am happy.) d. What is the probability that I catch fish in Lake L1 and lake L2? e. What is the probability that I catch fish in lake L1 or lake L2? f. What is the probability that I catch fish in exactly one lake? Add any comments below.
The required probabilities of catching or not catching a fish is given by,
Catching fish in all 4 lakes = 0.0048
Not catching any fish at all = 0.2688
Catching at least one fish = 0.7312
Catching fish in Lake L1 and lake L2 = 0.12
Catching fish in lake L1 or lake L2 = 0.58
Catching fish in exactly one lake = 1.1
Probability of catching fish in all 4 lakes,
Simply multiply the probabilities of catching fish in each lake,
since the events are independent,
P(C1 and C2 and C3 and C4)
= P(C1) x P(C2) x P(C3) x P(C4)
= 0.3 x 0.4 x 0.2 x 0.2
= 0.0048
= 0.48%
Probability of not catching any fish at all,
Probability of the complement of the event of catching at least one fish.
Happy if we catch at least one fish, the probability of not catching any fish is the probability that is not happy,
P(not happy)
= P(not C1 and not C2 and not C3 and not C4)
= (1 - P(C1)) x (1 - P(C2)) x (1 - P(C3)) x (1 - P(C4))
= 0.7 x 0.6 x 0.8 x 0.8
= 0.2688
= 26.88%
Probability of catching at least one fish,
Probability of the complement of the event of not catching any fish and subtract it from 1,
P(at least one fish)
= 1 - P(not happy)
= 1 - 0.2688
= 0.7312
= 73.12%
Probability of catching fish in Lake L1 and lake L2,
Simply multiply the probabilities of catching fish in each lake,
P(C1 and C2)
= P(C1) x P(C2)
= 0.3 x 0.4
= 0.12
= 12%
Probability of catching fish in lake L1 or lake L2,
Add the probabilities of catching fish in each lake,
And then subtract the probability of catching fish in both lakes to avoid double counting,
P(C1 or C2)
= P(C1) + P(C2) - P(C1 and C2)
= 0.3 + 0.4 - 0.12
= 0.58
= 58%
Probability of catching fish in exactly one lake can be broken down into four mutually exclusive events,
Catching fish in L1 only, catching fish in L2 only, catching fish in L3 only, or catching fish in L4 only.
Probabilities of each of these events is,
P(C1 or C2 or C3 or C4)
= P(C1) + P(C2) + P(C3) + P(C4)
= 0.3 + 0.4 + 0.2 + 0.2
= 1.1
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Consider the line that passes through the point and is parallel to the given vector. (4, -1, 9) ‹-1, 4, -2› symmetric equations for the line. -(x - 4) = y+1/ 4 = − z−9 /2 . (b) Find the points in which the line intersects the coordinate planes.
The symmetric equations of the line passing through a point and parallel to a vector are -(x - 4) = y + 1/4 = -(z - 9)/2. The line intersects the xy-, xz-, and yz-planes at (5, -9/4, 0), (15/4, 0, 23/2), and (0, -17/4, 11/2), respectively.
To find the symmetric equations of the line, we first need to find the direction vector of the line. Since the line is parallel to the vector <4, -1, 9>, any scalar multiple of this vector will be a direction vector of the line. So, let's choose the parameter t and write the vector equation of the line:
r = <4, -1, 9> + t<-1, 4, -2>
Expanding this vector equation component-wise, we get:
x = 4 - t
y = -1 + 4t
z = 9 - 2t
These equations can be rearranged to get the symmetric equations of the line:
-(x - 4) = y + 1/4 = -(z - 9)/2
To find the points in which the line intersects the coordinate planes, we substitute the corresponding variables with 0 in the equations for the line.
For the xy-plane, we set z = 0 and solve for x and y:
-(x - 4) = y + 1/4 = -(-9)/2
x = 5, y = -9/4
So, the line intersects the xy-plane at the point (5, -9/4, 0).
For the xz-plane, we set y = 0 and solve for x and z:
-(x - 4) = 0 + 1/4 = -(z - 9)/2
x = 15/4, z = 23/2
So, the line intersects the xz-plane at the point (15/4, 0, 23/2).
For the yz-plane, we set x = 0 and solve for y and z:
-(-4) = y + 1/4 = -(z - 9)/2
y = -17/4, z = 11/2
So, the line intersects the yz-plane at the point (0, -17/4, 11/2).
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Asaad invests $6800 in two different accounts. The first account paid 14 %, the second account paid 11 % in interest. At the end of the first year he had earned $856 in interest. How much was in each account?
Answer:
Step-by-step explanation:
Let x be the amount invested in the first account, which pays 14% interest. Then the amount invested in the second account, which pays 11% interest, is 6800 - x.
The interest earned on the first account is 0.14x, and the interest earned on the second account is 0.11(6800 - x). The total interest earned is the sum of these two amounts, so we have:
0.14x + 0.11(6800 - x) = 856
Simplifying and solving for x, we get:
0.14x + 748 - 0.11x = 856
0.03x = 108
x = 3600
Therefore, Asaad invested $3600 in the first account and $3200 (6800 - 3600) in the second account.
Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, compute the system's impulse response h[n] without using z-transforms.
Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, the impulse response of the system: h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
To compute the impulse response h[n] of a linear time-invariant (LTI) system given its input-output relationship, we can use the convolution sum:
y[n] = x[n] * h[n]
y[n] = (1/2)*(x[n] + 2x[n-1] + 3x[n-2])
y[n] = (1/2)*(δ[n] + 2δ[n-1] + 3δ[n-2])
y[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
Thus, the impulse response of the system is:
h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2],where δ[n] is the impulse signal.
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3. Factor 72x³ +72x² +18x.
The expression's fully factored form is:[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]
Factored value is what?Factored Value, also known as "trended value," is the base annual value plus a yearly inflation factor based on a variation in the cost if live that is not to exceed 2% and is set by the State Agency of Equalization.
What is a factored expression example?Rewriting an expression as the sum of factors is referred to as factor expressions or factoring. For instance, 3x + 12y may be expressed as 3 (x + 4y), which is a straightforward equation. The computations get simpler in this method. Three or (x + 4y) were examples of factors.
We can factor out [tex]18x[/tex] from each term to simplify the expression:
[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{3} + 4x^{2} + 1)[/tex]
An expression enclosed in parentheses can now be calculated by grouping or factoring.
[tex]4x^{3} + 4x^{2} + 1 = (4x^{2} + 1)(x + 1)[/tex]
The expression's properly factored version has the following result,
[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]
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the area of the parallelogram is 40 in2. one base of the parallelogram is 5 in long. the other base is 10 in long find its 2 heights
Step-by-step explanation:
Area of parallelogram = base × height or say b×h
Given: h=8 inches
Area=120 sq.inches
⇒120=8×b
⇒120/8=b
⇒120/8=b = 15
Answer = 15 inches b