To find the Laplace transform of f(t), we use the formula:
L{f(t)} = ∫[0,∞) [tex]e^(-st)[/tex] f(t) dt
where L{f(t)} denotes the Laplace transform of f(t) and u(t) is the unit step function.
Using the linearity of the Laplace transform, we can find the Laplace transform of each term separately and add them up.
L{6u(t-2)} = [tex]6e^(-2s)[/tex] / s (applying the time-shift property)
L{3u(t-5)} = [tex]3e^(-5s)[/tex] / s (applying the time-shift property)
L{-4u(t-6)} = -[tex]4e^(-6s[/tex]) / s (applying the time-shift property)
Therefore, the Laplace transform of f(t) is:
F(s) = L{f(t)} = 6[tex]e^(-2s)[/tex] / s + [tex]3e^(-5s)[/tex] / s - [tex]4e^(-6s)[/tex]/ s
= [tex](6e^(-2s) + 3e^(-5s) - 4e^(-6s)) / s[/tex]
Hence, the Laplace transform of f(t) is F(s) = [tex](6e^(-2s) + 3e^(-5s) - 4e^(-6s)) / s.[/tex]
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What is your net pay after FICA has been taken out if you make $47,000?
Remember that FICA is 7.65%
Answer:
3595.5
Step-by-step explanation:
I used the foil method to expand this but I don’t know what to do after that… a little help?
The expansion of (1+root 2)(3-root 2) is 1 +2√2.
What is distributive property?
The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.
Apply the distributive property
1(3-√2) + √2(3-√2)
Apply distributive property
1.4+ 1(-√2) +√2 (3-√2)
Apply the distributive property
1.3 + 1(-√2) + √2. 3+√2 (-√2)
3+1(−√2)+√2⋅3+ √2(-√2)
Multiply − √2 by 1
3−√2+ √2⋅3+√2(−√2)
Move 3 to the left of √2.3−√2+3⋅√2+√2(−√2)
Multiply √2(−√2)
3−√2+3√2−√2²
Rewrite
√2² as 2.
3−√2+3√2− 1⋅2
Multiply − 1 by 2.
3−√2+3√2−2
Subtract 2 from 3.
1−√2+3√2
Add −√2 and 3√2.
1+2√2
Exact Form:
1 +2√2
Decimal Form:
3.82842712
Therefore, the expansion of (1+root 2)(3-root 2) is 1 +2√2.
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A supplier to a car manufacturer produces a certain valve and seal used in their cars. The sizes of these seals and
valves are closely monitored to ensure the parts actually work. Here are summary statistics on the diameters for
these valves and seals (in millimeters).
Mean
Standard deviation
Valve
Hv = 50
OV = 0. 3
Seal
Ils = 51
Os = 0. 4
Both distributions are approximately normal. A seal properly fits a valve if the seal's diameter is larger than the
valve's diameter, but the difference can't be more than 2 mm. Suppose we choose a valve and seal at random
and calculate the difference between their diameters. We can assume that their diameters are independent.
The probability that a seal properly fits a valve is approximately 0.9332 or 93.32%.
How to find the difference between their diameters?To determine the probability that a seal properly fits a valve, we need to calculate the probability that the difference in diameter between the seal and valve is less than or equal to 2 mm.
Let X be the diameter of the valve and Y be the diameter of the seal. Then, the difference in diameter between the seal and valve can be expressed as Z = Y - X. We want to find P(Z ≤ 2).
We know that X ~ N(50, 0.3²) and Y ~ N(51, 0.4²), and since Z = Y - X, we have:
Z ~ N(51 - 50, √(0.3² + 0.4²)²) = N(1, 0.5²)
To find P(Z ≤ 2), we standardize Z by subtracting the mean and dividing by the standard deviation:
(Z - 1)/0.5 ~ N(0, 1)
P(Z ≤ 2) = P((Z - 1)/0.5 ≤ (2 - 1)/0.5) = P(Z ≤ 1.5)
Using a standard normal table or calculator, we find that P(Z ≤ 1.5) ≈ 0.9332.
Therefore, the probability that a seal properly fits a valve is approximately 0.9332 or 93.32%.
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In a recent poll six hundred adults were asked a series of questions about the state of the economy and their children's future. One question was, "do you expect your children to have a better life than you have had, a worse life, or a life about the same as yours?" Suppose the responses showed 245 better, 311 worse, and 44 about the same. Use the sign test and ???? = 0. 05 to determine whether there is a difference between the number of adults who feel their children will have a better life compared to a worse life. State the null and alternative hypotheses. (Let p = the proportion of adults who feel their children will have a better life. ) H0: p ≠ 0. 50
Null Hypothesis (H0): The proportion of adults who feel their children will have a better life is equal to 0.5.
Alternative Hypothesis (HA): The proportion of adults who feel their children will have a better life is not equal to 0.5.
How to explain the hypothesisThe sign test is a non-parametric statistical test used to test the hypothesis that the median of a population is equal to a specified value.
The critical value is 1.96.
The absolute value of the test statistic is greater than 1.96. Therefore, we reject the null hypothesis and conclude that there is a significant difference between the number of adults who feel their children will have a better life compared to a worse life.
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I have 90 kg of beef and need to add 1. 4 oz of filler to each pound. How many ounces of filler will I add
The ounces of filler will the factory need in order to make meatballs out of this shipment of beef is 56.7 oz of filler.
A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which remains almost unmodified. The avoirdupois ounce, also known as the US customary and British imperial ounce, is equal to one-sixteenth of an avoirdupois pound.
One factory obtained 90 kg of beef from overseas.
They want to add 1.4oz of filler for each pound of beef.
Given is:
0.45 kg = 1 pound
So, 90 kg = 90 x 0.45 = 40.5 pounds
The company want to add 1.4 oz of filler for each pound of beef.
So for 1 pound we have 1.4 oz of filler
So, for 40.5 pounds they will need = x oz of filler.
x = 1.4 x 40.5 = 56.7
Therefore, the company needs 56.7 oz of filler.
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Complete question;
Factories often add filler when making meatballs sold by the bag. One factory obtained 90kg of beef from overseas. They want to add 1.4oz of filler for each pound of beef. How many ounces of filler will the factory need in order to make meatballs out of this shipment of beef?
C C
A student believes that a certain number cube is unfair and is more likely to land with a six facing up. The student rolls
the number cube 45 times and the cube lands with a six facing up 12 times. Assuming the conditions for inference
have been met, what is the 99% confidence interval for the true proportion of times the number cube would land with a
six facing up?
0. 27 2. 58
0. 221-0. 27)
45
0. 7342. 33
0. 731-0. 73)
45
0. 27 2. 33
0. 271 -0. 20)
45
0. 73 +2. 58
0. 73(10. 73)
45
Mix
Save and Exit
we can say with 99% confidence that the true proportion of times the number cube would land with a six facing up is between 0.05 and 0.49.
Find out the confidence interval for the true proportion of time?To find the 99% confidence interval for the true proportion of times the number cube would land with a six facing up, we can use the formula:
CI = p ± zsqrt(p(1-p)/n)
where:
CI is the confidence interval
p is the sample proportion (number of times the cube landed with a six facing up divided by the total number of rolls)
z is the z-score corresponding to the desired confidence level (99% in this case)
n is the sample size (45 in this case)
First, let's calculate the sample proportion:
p = 12/45 = 0.27
Next, we need to find the z-score corresponding to a 99% confidence level. Using a standard normal distribution table or calculator, we find that the z-score is 2.58.
Now we can plug in the values and calculate the confidence interval:
CI = 0.27 ± 2.58sqrt(0.27(1-0.27)/45)
CI = 0.27 ± 0.22
CI = (0.05, 0.49)
The number cube would land with a six facing up between 0.05 and 0.49.
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A circle is drawn with a center point of q. janelle wishes to construct a tangent to the circle that passes through point b. she starts by connecting points q and b to form line segment bq.
what is the best next step when constructing a tangent to the circle?
a
strike an arc on bq with a center of b that has a length the same as the radius of circle q.
b
draw a line straight down from point q to the bottom of the circle.
c
extend bq through the other side of the circle.
d
find the midpoint of bq.
The best step when constructing a tangent to the circle is to strike an arc on bq with a center of b that has a length the same as the radius of circle q. The correct answer is option a.
When constructing a tangent to a circle with a center point of Q that passes through point B, and having already connected points Q and B to form line segment BQ, the best next step is to: A) Strike an arc on BQ with a center of B that has a length the same as the radius of circle Q.
This will help you find the point where the tangent line intersects the circle, allowing you to complete the tangent construction. The tangent line will be perpendicular to the radius at the point of tangency.
Therefore option a is correct.
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Larijah is creating a circular board game with a spinner with four regions that players use to determine what happens on their turns. she wants to meet these requirements: - exactly a quarter of the circle should contain the ""lose a turn"" region. - ""move one space"" should be three times the angle as ""move two spaces"". - ""move two spaces"" should be twice the angle as ""trade places with any opponent"". what is the measure of the ""trade places with any opponent"" region?
The measure of the trade places with any opponent region is 30°
Let the measure of the trade places with any opponent = x
Move two space is twice the angle as trade places with any opponent
Move two space = 2x
Move one space is three times the angle as moving two spaces
Move one space = 3(2x)
Move one space = 6x
Lose your turn is a quarter
Lose your turn = 90°
The sum of a complete angle = 360°
90 + x + 2x + 6x = 360°
9x = 360 - 90
9x = 270
x = 30
The measure of the trade places with any opponent region is 30°
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If the points a,b and c have the coordinates a(5,2) , b(2,-3) and c(-8,3) show that the triangle abc is a right angled triangle
Points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
Define about the right angled triangle:Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees.
The internal 90° angle of right triangles is denoted by a little square in the vertex. The complimentary angles of the other two sides of a right triangle sum up to 90 degrees.The triangle's legs, which are typically denoted by the letters a and b, are the sides that face the complimentary angles.Given coordinates :
a(5,2) , b(2,-3) and c(-8,3).
Find the distance between the points using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
ab = √[(2 - 5)² + (- 3 - 2)²]
ab = √[(-3)² + (- 5)²]
ab = √[9 + 25]
ab = √34
ab² = 34
bc = √[(2 + 8)² + (- 3 - 3)²]
bc = √[(10)² + (- 6)²]
bc = √[100 + 36]
bc = √136
bc² = 136
ac = √[(-8 - 5)² + (3 - 2)²]
ac = √[(-13)² + (1)²]
ac = √[169 + 1]
ac = √170
ac² = 170
Now,
(ac)² = (bc)² + (ab)²
170 = 136 + 24
170 = 170
This, points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
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Find the area of the composite figure.Round Your Answer To The Nearest Hundreth if needed
Answer:
[tex]A = 68.75 \text{ square inches}[/tex]
Step-by-step explanation:
First, we need to identify the trapezoid's dimensions:
base 1 = 16
base 2 = 11.5
height = 5
Then, we can plug these values into the trapezoid area formula:
[tex]A = \dfrac{b_1+b_2}{2} \cdot h[/tex]
[tex]A = \dfrac{16 + 11.5}{2} \cdot 5[/tex]
[tex]A = \dfrac{27.5}{2} \cdot 5[/tex]
[tex]A = \dfrac{137.5}{2}[/tex]
[tex]\boxed{A = 68.75 \text{ square inches}}[/tex]
A theater is selling tickets to a ''preview night'' of their new musical. The tickets cost $12 per adult and $7. 50 per child. Due to limit on seating, they can sell no more than 150 tickets. However, they would like to make at least $675 from ticket sales
it's not possible to sell at least $675 worth of tickets while also staying within the seating limit of 150 tickets. The theater may need to consider raising ticket prices or finding a larger venue to accommodate more audience members.
Let's denote the number of adult tickets sold as "A" and the number of child tickets sold as "C". Then we can set up the following system of equations to represent the given information:
A + C ≤ 150 (limit on seating)
12A + 7.5C ≥ 675 (minimum revenue required)
We want to find the possible values of A and C that satisfy these equations.
One way to solve this system is to graph the inequalities and find the region of overlap. However, since there are only two variables, we can also use substitution or elimination to solve for one variable in terms of the other.
Let's solve for A in terms of C using the first equation:
A ≤ 150 - C
Substitute this expression for A in the second equation:
12(150 - C) + 7.5C ≥ 675
Expand and simplify:
1800 - 12C + 7.5C ≥ 675
-4.5C ≥ -1125
C ≤ 250
So the number of child tickets sold must be less than or equal to 250.
Now we can substitute this inequality into the first equation to find the maximum number of adult tickets sold:
A + 250 ≤ 150
A ≤ -100
This doesn't make sense, since we can't sell negative tickets. Therefore, there is no solution that satisfies the given conditions.
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One can of pumpkin pie mix will make a pie ofdiameter 8 in. if 2 cans 9f pie mix are used to make a larger pie of the same thickness, find the diameter use square root of 2 equals 1. 414
The diameter of the larger pie is 8 x sqrt(2) inches.
How to find the diameter?The area of a circle is proportional to the square of its diameter. If the diameter of a pie made with one can of pumpkin pie mix is 8 inches, then its area is (4 inches)^2 x pi = 16 pi square inches.
If two cans of pie mix are used to make a larger pie of the same thickness, the total area of the pie will be twice that of the smaller pie.
So, the area of the larger pie is 2 x 16 pi = 32 pi square inches.
To find the diameter of the larger pie, we need to solve for d in the equation:
Area of circle = (d/2)^2 x pi
32 pi = (d/2)^2 x pi
32 = (d/2)^2
Taking the square root of both sides, we get:
sqrt(32) = d/2 x sqrt(2)
d/2 = sqrt(32)/sqrt(2)
d/2 = 4 x sqrt(2)
d = 8 x sqrt(2)
Therefore, the diameter of the larger pie is 8 x sqrt(2) inches.
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so if i went to park at 4:30 and it took me 24 minutes , when did i leave home
I must have left home at 4:54 PM in order to arrive at the park at 4:30 PM after 24 minutes of travel time.
When was the time I left home?Given the parameters in the question: if i went to park at 4:30 and it took me 24 minutes
Arrival time = 4 : 30PM
Travel time = 24 minutes
I can determine when i left home by simply subtracting the travel time from the time I arrived.
Hence,
Add the travel time to the time you arrived at the park.
4:30 PM (arrival time) + 24 minutes (travel time) = 4:54 PM
Therefore, I must have left home at 4:54 PM.
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Consider the following. u = 71 + 9j, v = 8i+2j (a) Find the projection of u onto v. (b) Find the vector component of u orthogonal to v.
A. proj_v(u) = (586 / 68) * (8i + 2j) = (293 / 34) * (8i + 2j) ≈ 8.62i + 2.15j
B. u_orthogonal = (71 + 9j) - (8.62i + 2.15j) ≈ 62.38i + 6.85j
(a) To find the projection of vector u onto vector v, we use the formula:
proj_v(u) = (u·v / ||v||^2) * v
where u = 71 + 9j, v = 8i + 2j, "·" represents the dot product, and ||v|| represents the magnitude of v.
First, let's find the dot product u·v:
u·v = (71)(8) + (9)(2) = 568 + 18 = 586
Next, we find the magnitude of v:
||v|| = √((8)^2 + (2)^2) = √(64 + 4) = √68
Now, we find ||v||^2:
||v||^2 = 68
Finally, we can find the projection of u onto v:
proj_v(u) = (586 / 68) * (8i + 2j) = (293 / 34) * (8i + 2j) ≈ 8.62i + 2.15j
(b) To find the vector component of u orthogonal to v, we subtract the projection of u onto v from u:
u_orthogonal = u - proj_v(u)
u_orthogonal = (71 + 9j) - (8.62i + 2.15j) ≈ 62.38i + 6.85j
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Each phrase in the table describes two variables which are strongly correlated. select all phrases that imply correlation without causation.
the number of stuffed animals produced at a factory and the number of newborn babies
the number of hits by a baseball team in a game and the number of runs they score
the number of people at a store and the number of coupons given out
the amount of snow plows on the street and the amount of snowfall
the number of videos rented and the number of new films in theaters
the number of pets in a neighborhood and the amount of grass fields nearby
The phrases that imply correlation without causation are:
The number of stuffed animals produced at a factory and the number of newborn babies.The number of hits by a baseball team in a game and the number of runs they score.The phrases that imply correlation without causation.The number of people at a store and the number of coupons given out.The number of videos rented and the number of new films in theaters.The number of pets in a neighborhood and the amount of grass fields nearby.These correlations do not imply a causal relationship, meaning that an increase or decrease in one variable does not directly cause a corresponding change in the other variable.
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What is the probability of selecting a 2 and then
a number divisible by 4 ?
a.
5/66
b.
1/20
C.
1/24
D.
1/22
Answer: C. 1/24 and that's is your answer to your question
Once Farid spends 15 minutes on a single level in his favorite video game, he loses a life. He has already spent 10 minutes on the level he's playing now.
Let x represent how many more minutes Farid can play on that level without losing a life. Which inequality describes the problem?
A. 10 + x > 15
B. 10 + x < 15
Solve the inequality. Then, complete the sentence to describe the solution.
Farid can play less than _______ more minutes on that level without losing a life
The correct inequality to describe the problem is A. 10 + x > 15, which means that the total time Farid spends on the level (10 + x) must be greater than 15 minutes in order for him to lose a life.
To solve the inequality, we can start by isolating x on one side of the inequality:
10 + x > 15
Subtracting 10 from both sides, we get:
x > 5
This means that Farid can play for up to 5 more minutes on the level without losing a life, since spending a total of 10 + 5 = 15 minutes on the level would cause him to lose a life.
Therefore, the solution to the inequality is "Farid can play less than 5 more minutes on that level without losing a life."
Overall, the correct option is A. 10 + x > 15.
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What is the volume of the composite figure if both the height and the diameter of the cylinder are 2. 5 feet? Give the exact answer and approximate to two decimal places.
Thank you!
19.29 cubic feet is the volume of the composite figure if both the height and the diameter of the cylinder are 2. 5 feet
Without knowing the specific shape of the composite figure, it is impossible to give an exact answer. However, we can provide a general formula for the volume of a cylinder with height h and diameter d, and assume that the composite figure consists of a cylinder and some other shape.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder. The diameter of the cylinder is given as 2.5 feet, which means the radius is 1.25 feet.
If the height of the cylinder is also 2.5 feet, then the volume of the cylinder is:
V_cylinder = π(1.25)^2(2.5) = 6.15π cubic feet (exact)
To approximate to two decimal places, we can use the approximation π ≈ 3.14:
V_cylinder ≈ 6.15(3.14) = 19.29 cubic feet (approximate to two decimal places)
However, since we do not know the specific shape of the composite figure, we cannot give an exact answer for its volume.
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If a+b=3 and ab=4 find the value of a3+b3
Answer:
-9
Step-by-step explanation:
Recall the following relationships about the sum of cubes and a square binomial:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The second factor on the right hand side of equation 1 looks similar to the right hand side of equation 2, but differs slightly.
Carefully choosing to subtract 3ab from both sides of the equation 2, and Combining like terms yields...
[tex](a+b)^2-3ab=a^2-ab+b^2[/tex]
This now matches the second factor on the right hand side of the first equation. So, with substitution, the first equation becomes:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]
Note that all of the parts on the right hand side of the equation are given in the question:
a+b=3 and ab=4
With some substitution and simplification
[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]
[tex]=(3)((3)^2-3(4))[/tex]
[tex]=(3)(9-3(4))[/tex]
[tex]=(3)(9-12)[/tex]
[tex]=(3)(-3)[/tex]
[tex]=-9[/tex]
PLEASE HELP 30 POINTS
Formula for the volume of a cylinder = pi x r^2 x h
---r = radius
---h = height
This problem gives us the diameter. To find the radius from a given diameter, all we need to do is divide the diameter by 2.
radius = 3
height = 22
volume = 3.14 x 3^2 x 22
volume = 3.14 x 9 x 22
volume = 621.72
volume (rounded) = 622
Answer: 622 m^3
Hope this helps!
Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank.
Which statement about the savings plans is true?
Responses
Natalie uses a safer way to save money because she can protect her piggy bank.
Maria's way of saving money allows her to earn interest and make her money grow.
Maria will have less money because she must pay sales tax on her money.
Natalie's method of saving is better because Maria must pay interest on her money.
In a case whereby Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank the statement about the savings plans that is true is B.Maria's way of saving money allows her to earn interest and make her money grow.
What is savings account ?An efficient approach to keep your money safe and earning interest is in a savings account. You can keep your savings in a liquid state with a savings account, which allows you to access your money anytime you need to, while also creating some breathing room between your savings and your daily spending requirements.
Because of their safety, liquidity, and potential for collecting interest, savings accounts are a suitable way to put money set aside for future use. These accounts are perfect for saving for short-term objectives like a trip or home repair or for your emergency fund.
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Find the distance between
the points (4, -3) and (-2, 1)
on the coordinate plane.
Ay
O
X
Answer:no image
Step-by-step explanation:
16 workers will build a house; they can do so in 144 days. if all workers work a the same rate, how many more workers would be needed to build the same house in 96 days
To build a house in 96 days, more workers are required such that the total number of workers becomes 24.
Let W be the number of workers required to build the house in 96 days. Using the work formula, we can write:
(16 workers) x (144 days) = (W workers) x (96 days)
Simplifying the equation, we get:
W = (16 workers x 144 days) / 96 days = 24 workers
Therefore, to build the house in 96 days, 24 workers are required, which is 8 more workers than the original 16. This is because, to complete the work in a shorter time, more workers are needed to contribute their efforts to the work.
The total work done by all the workers remains constant, so if we decrease the time taken to complete the work, we need to increase the number of workers to maintain the same work rate.
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Use the pythagorean Theorem to find the length of a right triangles hypotenuse. The longer sides are 9 cm and 12 cm long
The length of the hypotenuse of the right triangle is 15 cm.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Using this formula, we can calculate the length of the hypotenuse of a right triangle.
Given that the longer sides of the right triangle are 9 cm and 12 cm long, we can assume that one of these sides is the shorter side and the other is the longer side. Let's assume that the shorter side is 9 cm long and the longer side is 12 cm long.
Using the Pythagorean Theorem, we can calculate the length of the hypotenuse as follows:
Hypotenuse² = Shorter side² + Longer side²
Hypotenuse² = 9² + 12²
Hypotenuse² = 81 + 144
Hypotenuse² = 225
Taking the square root of both sides, we get:
Hypotenuse = √225
Hypotenuse = 15
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Write a recursive rule for the sequence [tex]a_{n}[/tex] = 17 - 4n
The recursive sequence are: 17, 13, 9, 5, 1.
The recursive rule for the sequence [tex]a_{n}[/tex] = 17 - 4n is
[tex]a_{1[/tex] = 17
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 4 for n ≥ 2
Using this rule, we can find the first few terms of the sequence
[tex]a_{1[/tex] = 17
[tex]a_{2}[/tex] = [tex]a_{1[/tex] - 4 = 17 - 4 = 13
[tex]a_{3}[/tex] = [tex]a_{2}[/tex] - 4 = 13 - 4 = 9
[tex]a_{4}[/tex] = [tex]a_{3}[/tex] - 4 = 9 - 4 = 5
[tex]a_{5}[/tex] = [tex]a_{4}[/tex] - 4 = 5 - 4 = 1
and so on.
Therefore, the recursive sequence are: 17, 13, 9, 5, 1.
The question is incorrect and correct question is '' Write a recursive sequence that represents the sequence defined by the following explicit formula [tex]a_{n}[/tex] = 17 - 4n and find [tex]a_{1[/tex] and [tex]a_{n}[/tex] ''.
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What is the probability that a student took AP Chemistry, given they did not get into their first-choice college? Enter
your answer as a decimal to the ten thousandths place.
Student
0.25
0.10
0.35
0.30
Chemistry
000
Physics
Env Sci
Biology
0.45
1st choice
Not 1st
0.55
0.55 1st choice
0.45
0.20
0.80
0.30
0.70
Not 1st
1st choice
Not 1st
1st choice
Not 1st
P(Chem and 1st choice) = (0 25)(0.45) = 0.1125
P(Chem and Not 1st) = (0.25)(0.55) = 0.1375
P(Phys and 1st choice) = (0.35)(0.55) = 0.1925
P(Phys and Not 1st) = (0.35)(0.45) = 0.1575
P(ES and 1st Choice) = (0.30)(0.20) = 0.0600
P(ES and Not 1st) = (0.30)(0.80) = 0.2400
P(Bio and 1st choice) = (0.10)(0.30) = 0.0300
P(Bio and Not 1st) = (0.10)(0.70) = 0.0700
The probability that a student took AP Chemistry given they did not get into their first-choice college is 0.0566.
What is the probability?The probability that a student took AP Chemistry given they did not get into their first-choice college is calculated using the formula below:
P(Chem | Not 1st) = P(Not 1st | Chem) * P(Chem) / P(Not 1st)P(Not 1st | Chem) =0.1375
P(Chem) = 0.25
P(Not 1st) = P(Chem and Not 1st) + P(Phys and Not 1st) + P(ES and Not 1st) + P(Bio and Not 1st)
P(Not 1st)= 0.1375 + 0.1575 + 0.2400 + 0.0700
P(Not 1st)= 0.6050
Substituting the values in the formula above:
P(Chem | Not 1st) = 0.1375 * 0.25 / 0.6050
P(Chem | Not 1st) = 0.0566
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Find the value of k. Give your answer in degrees ().
k
84°
Not drawn accurately
Step-by-step explanation:
I had to add some assumed portions to your posted picture. See image.
The yellow boxed angle is 84 degrees (upper LEFT) due to alternate interior angles of parallel lines transected by another line.
then, since the triangle is isosceles ....the other (lower LEFT) angle is 84 degrees also....
that means that k= 12 degrees for the triangle interior angles to sum to 180 degrees .
4) Write the rule for the reflection shown below.
The rule for the reflection shown above is (x, y) → (x, -y).
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).
This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.
Conversely, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
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(a) Find a counterexample which shows that WAT is not true if we replace the closed interval [a,b] with the open interval (a,b).(b) What happens if we replace [a,b] with the closed set [a,\infty). Does the theorem hold?
(a) WAT is not true for the open interval (0,1) with function f(x) = 1/x.
(b) WAT holds for the closed set [a,∞) with any continuous function f(x).
(a) The Weierstrass Approximation Theorem (WAT) is not true if we replace the closed interval [a,b] with the open interval (a,b). A counterexample is the function f(x) = 1/x on the open interval (0,1). This function is continuous on (0,1) but it is not uniformly continuous, so it cannot be uniformly approximated by a polynomial.
(b) The Weierstrass Approximation Theorem holds if we replace [a,b] with the closed set [a,∞). That is, if f(x) is a continuous function on [a,∞), then for any ε > 0, there exists a polynomial p(x) such that |f(x) - p(x)| < ε for all x in [a,∞). The proof is similar to the proof of the original theorem using the Bernstein polynomials.
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The table shows nutrients information for three beverages.
a: which has the most calories per fluid ounce?
b: which has the least sodium per fluid ounce?
bevarage/ serving size/ calorie/ sodium
whole milk/ 1 c/ 146/ 98mg
orange juice/ 1 pt/ 210/ 10mg
apple juice/ 24 fl oz./ 351/ 21mg
Answer:
a) apple juice
b) whole milk
easy pagel