Given the function : h(x) = 5. e^(-x^2/10) Determine the horizontal asymptote, the y-intercept, and the type of symmetry (if any) of the function.
Answers
The horizontal asymptote of the function h(x) = 5e^(-x^2/10) is y = 0. The y-intercept is (0, 5), and the function exhibits even symmetry.
As x approaches positive or negative infinity, the exponential term e^(-x^2/10) approaches 0, since the exponent becomes increasingly negative. As a result, the overall function approaches the value of 5 multiplied by 0, which is 0. Therefore, the horizontal asymptote of the function is y = 0. To find the y-intercept, we substitute x = 0 into the function h(x). Plugging in x = 0 gives us h(0) = 5e^(0) = 5 * 1 = 5. Thus, the y-intercept of the function is (0, 5).
The function h(x) = 5e^(-x^2/10) exhibits even symmetry. This symmetry can be observed by noticing that the exponential term e^(-x^2/10) is an even function, meaning it remains unchanged when x is replaced by -x. Consequently, the function h(x) is symmetric about the y-axis, indicating even symmetry.
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Related Questions
Find the new amount increase
700 by 40%
Answers
40% of 700 is 280, you then add that to 700.
PLZ IM ON A TEST AND HAVE 2 MIN LEFT
Which equation does NOT represent a direct variation?
1.-3x+2y=0
2.-2y=x
3.y=50x
4. 5x+2y=10
Answers
Answer:
2.-2y=x
Step-by-step explanation:-2y=x
y=kx for constant k
x - 11 / 3 = - 4 / 5 x + 5 / 6
Answers
Answer:
SOLVE FOR X
x=2
Step-by-step explanation:
Answer:
5/2
Step-by-step explanation:
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Evaluate the following expression if x=3: 2^x *
Answers
Answer:
x = 8
Step-by-step explanation:
This question is pretty simple. You already know the value of x, we substitute what x equals and find the number 2 cubed.
2^3 = ?
2x2x2 = 8
Convert (xy)⁸ = 3 to an equation in polar coordinates. ___=r¹⁶
Note: use "t" for ø
Answers
The equation (xy)⁸ = 3 can be converted to an equation in polar coordinates as r¹⁶ = 3. Here, "r" represents the radial distance from the origin, and "t" represents the angle ø.
To convert the given equation to polar coordinates, we need to express "x" and "y" in terms of the polar variables "r" and "t". In polar coordinates, "x" can be expressed as r * cos(t), and "y" can be expressed as r sin(t). Substituting these values into the given equation, we get (r cos(t) r sin(t))⁸ = 3.
Simplifying the equation, we have (r² cos(t) * sin(t))⁸ = 3. Since cos(t) sin(t) = (1/2) * sin(2t), we can rewrite the equation as (r² * (1/2) * sin(2t))⁸ = 3.
Further simplifying, we get (r¹⁶ sin⁸(2t)) = 3. Therefore, the equation in polar coordinates is r¹⁶ = 3, where "r" represents the radial distance from the origin and "t" represents the angle ø.
Note that the value "3" remains the same in the converted equation, while the expression (xy)⁸ is equivalent to r¹⁶ in polar coordinates.
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Have to finish these by the 23rd :(
Answers
Answer:
5/6
Step-by-step explanation:
x²- 3x + 7 / x + 4
when [x = 2]
Putting the value of x,
2² - 3(2) + 7 / 2 + 4
= 4 - 6 + 7 / 6
=5 / 6
Please answer these for me
Answers
Answer:
1 is D
2 is A
if cost price rs 50 and selling price =rs 80 is there a profit or loss find the value of profit or loss
Answers
The sum of twelve and a number is twenty
Answers
Answer:
12 + Y = 20 _ _ 12+8=20
Step-by-step explanation:
Y represents a number
Y= 8
A triangular prism is 18.8 meters long. It has a triangular face with a height of 9 meters. The volume of the prism is 1,353.6 cubic meters. What is the base length of its triangular face?
Answers
1) Gathering the data
width = 18.8
height = 9 m
V = 1353.6 m³
2) Let's use the formula of the Volume, derived from the Base Area and the height:
\(undefined\)The path of a kicked soccer ball can be
modeled by the equation y = 3x2. State
whether the equation represents a linear or a
nonlinear function.
Answers
Answer:
Step-by-step explanation:
There is an x², so the equation is a parabola, not a line.
Frank wrote these ratios to describe the number of votes each candidate received compared to the total. Which one is wrong, and why?
Answers
Answer:The right answer is (B)
Step-by-step explanation:
Your welcome
Answer:
B) The numbers in the ratio 344 to 111 are written in the wrong order.
Step-by-step explanation:
Edg 2020
are the trianlges congruent. am I right?
Answers
Answer:
The triangles are congruent.
Step-by-step explanation:
Don't let those little lines mess up. Both triangles have the same shape and size. They are congruent.
Hi, could you please solve in a clear handwriting showing exactly step by step how to solve it? Thanks
The management of a company analyzes the dependence of sales of the company's main product on investments. Information on investments (X variable, thousand Euro) and the main product's sales for the last 12 years (Y variable, thousand Euro) are the following:
ΣΧi = 22, ΣΥi = 66, ΣΧ i2= 45.8, ΣΥi2 = 369.94, EXiYi = 126.54
1) Calculate the correlation coefficient and make conclusions about the closeness of the linear relationship.
2) Find the linear regression from variable Y to the X and forecast the sales volume if the investment volume is planned to be 30 thousand Euro.
Answers
The forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.
Let's solve this problem step by step:
Calculate the correlation coefficient (r) using the formula:
r = (ΣXY - (ΣX)(ΣY)/n) / sqrt([(ΣX^2 - (ΣX)^2/n)(ΣY^2 - (ΣY)^2/n)])
Plug in the given values into the formula:
r = (126.54 - (22)(66)/12) / sqrt([(45.8 - (22)^2/12)(369.94 - (66)^2/12)])
Simplify the formula and solve for r:
r = (126.54 - 121) / sqrt([(45.8 - 40.333)(369.94 - 363)])
r = 5.54 / sqrt[(5.467)(6.94)]
r = 5.54 / 4.967
r = 1.115
Make conclusions about the closeness of the linear relationship based on the value of r:
Since the value of r is close to 1, this indicates a strong positive linear relationship between the investments (X variable) and the main product's sales (Y variable).
Find the linear regression from variable Y to the X using the formula:
Y = a + bX
Calculate the slope (b) using the formula:
b = (ΣXY - (ΣX)(ΣY)/n) / (ΣX^2 - (ΣX)^2/n)
Plug in the given values into the formula and solve for b:
b = (126.54 - (22)(66)/12) / (45.8 - (22)^2/12)
b = 5.54 / 5.467
b = 1.013
Calculate the intercept (a) using the formula:
a = (ΣY - b(ΣX))/n
Plug in the given values into the formula and solve for a:
a = (66 - 1.013(22))/12
a = 44.714/12
a = 3.726
Plug in the values of a and b into the linear regression formula:
Y = 3.726 + 1.013X
Forecast the sales volume if the investment volume is planned to be 30 thousand Euro by plugging in the value of X into the linear regression formula:
Y = 3.726 + 1.013(30)
Y = 3.726 + 30.39
Y = 34.116
Therefore, the forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.
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the lengths of the sides of a triangle with positive area are $\log {10}12$, $\log {10}75$, and $\log {10}n$, where $n$ is a positive integer. find the number of possible values for $n$.
Answers
The number of possible values for n is infinite since the logarithm function is continuous and can take on any positive real value.
In this case, the lengths of the sides of the triangle are given as logarithms of different numbers. The logarithm function is continuous and defined for all positive real numbers. It maps each positive real number to a unique value on the logarithmic scale.
Since the lengths of the sides are given as logarithms, it means that the actual lengths of the sides can be any positive real numbers corresponding to those logarithmic values. Therefore, there are infinitely many possible values for n, as the logarithm function can take on any positive real value.
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PLEASE OMG I CANT DO THIS PLEASE JUST HELP OMG!!!!
Answers
Then use vertical angle theorem to make it adjacent to (9x+19)
Use supplementary angle theorem to make them equal to 180
Solve for x
62+9x+19=180
9x+19=118
9x=99
X=11
20 pts!!!!!!!!!!!
what is (-1678 / 345) +64
Answers
The value of (-1678 / 345) + 64 will be -60.86.
What is PEDMAS?In this situation, it's important to use PEDMAS. This implies that the parentheses will be solved first.
The value of (-1678 / 345) +64 is illustrated thus:
= (-1678 / 345) + 64
= -4.86 + 64
= -60.86
In this case, the concept was to solve the numbers in the parentheses before addition
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Let f(x) be the probability density function for a normal distribution N(68,5). Answer the following: (a) At what x value does f(x) reach a maximum? Maximum height: x (b)Does f(x) touch the x-axis at μ±30 ? No Yes
Answers
The probability density function for a normal distribution N(68, 5) reaches its maximum height at x = 68, which is the mean of the distribution. The function does not touch the x-axis at μ±30.
The probability density function (PDF) for a normal distribution is bell-shaped and symmetrical around its mean. In this case, the mean (μ) is 68, and the standard deviation (σ) is 5.
(a) To find the x value at which the PDF reaches a maximum, we look at the mean of the distribution, which is 68. The PDF is highest at the mean, and as we move away from the mean in either direction, the height of the PDF decreases. Therefore, the x value at which f(x) reaches a maximum is x = 68.
(b) The PDF of a normal distribution does not touch the x-axis at μ±30. The x-axis represents the values of x, and the PDF represents the likelihood of those values occurring. In a normal distribution, the PDF is continuous and never touches the x-axis. However, the PDF becomes close to zero as the values move further away from the mean. Therefore, the probability of obtaining values μ±30, which are 38 and 98 in this case, is very low but not zero. So, the PDF does not touch the x-axis at μ±30, but the probability of obtaining values in that range is extremely small.
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during december the average daily temperature in a town is -1.7.the average daily temperature in the same town is 3.2 lower in january what is the average daily temperature in january?
Answers
Answer:
the average daily temperature in January is -4.9
Which statement best explains how the author develops the points of view of Samantha
and Melinda?
• 1. The author uses physical details
to show that Samantha is confused about Melinda's project ideas.
2. The author uses a flashback to
show why Samantha is worried about Melinda's idea for the project.
• 3.
The author uses
dialogue to suggest that Samantha may be interested in Melinda's proposed project.
4. The author uses foreshadowing to show why Samantha senses that Melinda's project will not succeed.
Answers
The best statement that explains how the author develops the points of view of Samantha and Melinda is option 2.
The author uses a flashback to show why Samantha is worried about Melinda's idea for the project. By incorporating a flashback, the author provides background information on the two characters and their relationship. The flashback allows the reader to understand why Samantha is concerned about Melinda's project idea and gives insight into their past interactions. This method of development allows the author to create a more well-rounded understanding of the characters and their motivations. Additionally, the use of physical details and dialogue further adds to the development of the characters' perspectives and personalities. However, the use of foreshadowing does not seem to be present in the given information and is not relevant to the question.
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Random variable X has a normal distribution with mean u and standard deviation 2. The pdf f(x) of X satisfies the following conditions: (A) f6 > f(16), (B) f(1)
Answers
we have:
P(X > 6) < 0.0668
We can use the standard normal distribution to find probabilities for a normal distribution with mean u and standard deviation 2. Let Z = (X - u)/2 be the standard normal variable corresponding to X.
(A) Since f(6) > f(16), we have P(X < 6) > P(X < 16). Using the standard normal distribution, we can write this as:
P(Z < (6 - u)/2) > P(Z < (16 - u)/2)
Multiplying both sides by -1 and using the symmetry of the standard normal distribution, we get:
P(Z > (u - 6)/2) < P(Z > (u - 16)/2)
Looking up the standard normal distribution table, we can find the values of the right-hand side probabilities for different values of the argument. For example, if we use a table with z-scores and look up the probability corresponding to z = 1.5, we find that P(Z > 1.5) = 0.0668 (rounded to four decimal places).
Therefore, we have:
P(X > 6) < 0.0668
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Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. 30% of adults will have an IQ score higher than what value?
Answers
Step-by-step explanation:
Use z-score table to find the z-score that corresponds to .7000 ( 70%)
approx .525 s.d. above the mean
.525 * 10 = 5.25 points above 100 = 105.25
What number is 9 more than 1/4 of itself?
(A) 8
(B) 9
(C) 10
(D) 12
(E) 14
Answers
Answer:
letter c
Step-by-step explanation:
.............
The value of the unknown number will be 12. The correct option is D.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that the number is 9 more than 1/4 of itself. Let the unknown number be x. Form the equation and solve.
( x / 4 ) + 9 = x
9 = x - ( x / 4 )
9 = 3x / 4
3 = x / 4
x = 12
Therefore, the value of the unknown number will be 12. The correct option is D.
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After Lois picks a value for b, Clark must solve the equation 2x + 7 - x = 4x + 2b – 3x - 3b.
Clark uses Lois's b, then tries to solve the equation by repeatedly guessing values of x until he guesses
the right one. However, for every x he picks, the left side is always 3 more than the right side. What
value of b did Lois give Clark?
Answers
The value of b Lois gave to Clark to satisfy the given equation is -7.
The given parameters;
2x + 7 - x = 4x + 2b – 3x - 3b
To obtain the value of b, simplify the equation as follows;
2x + 7 - x = 4x + 2b – 3x - 3b
collect similar terms together
(2x - x) + 7 = (4x - 3x) + (2b - 3b)
x + 7 = x - b
(x - x) + 7 = -b
0 + 7 = -b
7 = -b
-7 = b
b = -7
Thus, the value of b Lois gave to Clark to satisfy the given equation is -7.
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Amistad Middle School is hosting "Amistad got Talent" show for a fundraiser to earn money for an upcoming field trip. Ms. G is in charge of selling the tickets. There goal is to earn $500. Identify the Independent (x) and dependent (y) variables. Represent your answer as - IV(x)- Tickets/Money DV(y)- Tickets/Money *
Answers
The middle school will host a Talent show.
The goal of the tickets sale is to earn $500
To reach this goal Ms G has to sell a determined number of tickets.
This means that the earnings depend directly on the number of tickets sold.
So the independent/ explanatory variable is the number of tickets sold, and the dependent/ response variable is the money earned
x → Tickets sold
y → Money earned
Is (8, 3) a solution to the system?
- 2 + 4y = 4
- 2 + 3y = 1
Answers
Answer:
No, it's not a solution.
Step-by-step explanation:
-2 + 4(3) = 4
-2 + 12 = 10
-2 + 3(3) = 1
-2 + 9 = 7
The surface area of a rectangular prism that has height of 4 inches, width of 9 inches and length of 3 inches
Answers
The surface area of a rectangular prism is found as 150 square inches.
What is rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces make up a rectangular prism, and each face has a rectangle shape and twelve edges.
Actually, prisms get their name from the way their faces are shaped. Therefore, a rectangular prism is just a prism with rectangular faces. Although it is a closed, three-dimensional object, two rectangles serve as its foundation.
Calculation for the surface area of rectangular prism-
Height of a rectangular prism => H = 4 inches
Width of a rectangular prism => B = 9 inches
Length of a rectangular prism => L = 3 inches
Surface area of a rectangular prism = 2(LB + BH + HL)
= 2(9×3 + 9×4 + 4×3)
= 150
Therefore, the surface area of a rectangular prism is found as 150 square inches.
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Question 5 of 5
Mrs. Gomez is buying a triangular table for the corner of her classroom. The
side lengths of the table are 4 feet, 3 feet, and 2 feet.
Is this triangular table a right triangle?
OA. Yes, because 2² + 3² = 4².
OB. No, because 2² +3² > 4².
OC. No, because 2² + 3² +4²
OD. Yes, because 2+ 3+ 4.
SUBMIT
Answers
The triangular table does not represent a right triangle.
b) The Pythagorean theorem asserts that the total of the square of both of the shorter sides of a right triangle equals the square of the side that is longest (the hypotenuse). The side lengths in this example are 4 feet, 3 feet, and 2 feet. To see if the Pythagorean theorem is true with these side lengths, we can apply it.
Taking each square of side lengths: 42 = 16 32 = 9 22 = 4
If the table were a right a triangle, the total of the squares of the two smaller sides (9 + 4 = 13) should equal the square of the side that is longest (16), according to the Pythagoras theorem. In this situation, however, 13 does not equal 16.
As a result, the triangular tables does not meet the Pythagorean theorem criteria, showing that it is not a triangle with a right angle.
c) You can find out more regarding the Pythagorean theorem
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Mrs Gomez is buying a triangular table for the corner of her classroom. The side lengths of the table are 4 feet, 3 feet, and 2 feet. The triangular table is not a right triangle since the sum of the squares of the two shorter sides (9 + 4 = 13) does not equal the square on the longest side (16), proving that the triangle is not a right triangle. Thus Option B. is the correct answer.
In order to determine whether or not the triangular table is a right triangle, we must first see if the Pythagorean theorem holds true for the specified side lengths. According to the Pythagorean theorem, the square of the hypotenuse, the longest side of a right triangle, equals the sum of the squares of the lengths of the other two sides.
Let's compute the squares of the side lengths given:
2² = 4
3² = 9
4² = 16
Let's now evaluate the available options for answers:
OA. Yes, because 2² + 3² = 4².
4 + 9 = 16
This option is incorrect since the squares of the two shorter sides do not add up to the square of the longest side.
OB. No, because 2² + 3² > 4².
2² + 3² = 4 + 9
2² + 3² = 13
4² = 16
This option is correct since 13 does not equal 16. Hence, the triangular table is not a right triangle
OC. No, because 2² + 3² + 4².
This option seems to be incomplete because to decide whether it is a right triangle or not, there is no comparison or equation.
OD. Yes, because 2 + 3 + 4.
This option is incorrect because it just adds the side lengths without taking the Pythagorean theorem into account.
Therefore, Option B is the correct answer.
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Nicholas is saving $232 per month. If their account earns a 3.7% interest rate, how many years will it take before they can buy a $27,000 car? Lauren recently inherited $1,930,000, which they immediately invested in an equity index mutual fund. If they plan to withdraw $7,000 per month from their account, what annual interest rate must they earn in order to have $251,000 left after 27 years?
Answers
a. It will take Nicholas approximately 9.69 years to save enough to buy a $27,000 car. b. Lauren needs to earn an annual interest rate of 5.02% in order to have $251,000 left after 27 years.
To calculate the time it will take for Nicholas to save enough for a $27,000 car, we can use the formula for compound interest. The formula is given by:
Future Value = \(Present Value * (1 + interest rate)^{(number of periods)}\)
In this case, Nicholas is saving $232 per month, so the future value (FV) is $27,000 and the interest rate (r) is 3.7% per year. We need to find the number of periods (t) in years. Rearranging the formula, we get:
t = log(FV / PV) / log(1 + r)
Plugging in the values, we have:
t = log(27000 / (232 * 12)) / log(1 + 0.037)
≈ 9.69 years
Therefore, it will take Nicholas approximately 9.69 years to save enough to buy a $27,000 car.
To calculate the required annual interest rate for Lauren, we can use the formula for future value with regular withdrawals. The formula is given by:
\(Future Value = Withdrawal Amount * ((1 + interest rate)^{t - 1} / interest rate\)
In this case, the future value (FV) is $251,000, the withdrawal amount is $7,000 per month, and the time (t) is 27 years. We need to find the interest rate (r). Rearranging the formula, we have:
\(r = ((FV * interest rate) / Withdrawal Amount + 1)^{(1 / t) - 1}\)
Plugging in the values, we get:
\(r = ((251000 * r) / 7000 + 1)^{1 / 2}\)7) - 1
Solving this equation, we find that Lauren needs to earn an annual interest rate of approximately 5.02% to have $251,000 left after 27 years.
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Tiffany makes 35% commission on the websites he sells to businesses. If he sells $3500 worth of websites, what is his commission?
Answers
Answer:
1225
Step-by-step explanation:
.35 x 3500 = 1225 im late though