Which of the equations below represents
this ellipse?
a. x^2/4+y^2/20=1
b. x^2/2+y^2/10=1
c. x^2/100+y^2/4=1
d. x^2/4+y^2/100=1
Answers
The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
What is the equation of the ellipse represented in the graph?
Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:
(x - h)² / a² + (y - k)² / b² = 1 (1)
Where:
(h, k) - Coordinates of the centera, b - Lengths of the semiaxesPlease notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
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Related Questions
Anyone know the anwser to this
Answers
Answer:
4112
Step-by-step explanation:
When you plug in 3 for x you get 6.
Then you just do 4^6 which is 4096.
Then add 16 which gets you 4112.
What is the standard form polynomial representing the volume of this shipping container?
The image shows a blue shipping container with the numbers:
4x2 + 3x(along the length of the bottom)
x2 - 8 (Along the bottom of the 'front')
6x + 15 (going up the length of the 'front')
Answers
The standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x.
What is a Standard Form Polynomial?A standard form polynomial is a polynomial expression written whereby the term with the highest degree or power on a variable is written first in the expression, followed by the least, then the constant of the polynomial comes last.
What is the Volume of a Rectangular Prism?
The Volume of a rectangular prism = (length)(width)(height).
The shipping container is a rectangular prism with the following dimensions:
Length of container = 4x² + 3x
Width of container = x² - 8
Height = 6x + 15
Plug in the values
Volume of container = (4x² + 3x)(x² - 8 )(6x + 15)
Expand
Volume of container = 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x
Thus, using the formula for the volume of a rectangular prism, the standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x.
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Complete the square to transform the expression x2 − 2x − 2 into the form a(x − h)2 k.
Answers
The given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
What is an equivalent function?Two functions are equivalent if they share the same domain and codomain and have the same values for all domain components.To complete the square to transform the expression:
The given expression is [tex]x^{2} -2x-2[/tex].Then the expression can be written as, add and subtract one.Then we have:[tex]x^{2} -2x+1-1-2\\x^{2} -2x+1-3\\(x-1)^{2} -3[/tex]Therefore, the given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
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The correct question is shown below:
Complete the square to transform the expression x^2− 2x − 2 into the form a(x − h)^2+ k.
(A) (x − 1)2 + 3
(B) (x − 1)2 − 3
(C) (x − 2)2 − 3
(D) (x − 2)2 + 3
A man bought a car for 8500 and sold it for 9500. find his percentage gain
Answers
Answer:
11.7647%
Hope this helps!
Carlos went to PetSmart to get his hamster an exercise ball. There was a small one with a 5 inch diameter and a 13 inch ball. How much more space (volume) is in the larger than the smaller? Round to the nearest tenth.
Answers
The amount of space (volume) that is in the larger spherical ball than the smaller = 1,084.8 in.³
What is the Volume of a Sphere/Spherical Solid?To find the volume of a sphere, which is the amount of space the solid contains, the formula used is given as: 4/3 πr³, where r is the radius of the sphere, which is half the measure of the diameter. Volume of sphere (V) = 4/3 πr³.
Diameter of the smaller spherical ball = 5 inches
Radius of the smaller spherical ball = 5/2 = 2.5 inches
Volume of the smaller spherical ball = 4/3 πr³ = 4/3 × π × 2.5³
Volume of the smaller spherical ball ≈ 65.5 in.³
Diameter of the larger spherical ball = 13 inches
Radius of the larger spherical ball = 13/2 = 6.5 inches
Volume of the larger spherical ball = 4/3 πr³ = 4/3 × π × 6.5³
Volume of the larger spherical ball ≈ 1,150.3 in.³
The amount of space (volume) that is in the larger spherical ball than the smaller = 1,150.3 - 65.5
The amount of space (volume) that is in the larger spherical ball than the smaller = 1,084.8 in.³
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A group of friends wants to go to the amusement park. They have $284.25 to spend on parking and admission. Parking is $9.25, and tickets cost $27.50 per person, including tax. How many people can go to the amusement park?
Answers
Answer:
7
Step-by-step explanation:
The start this question by looking at two important things, how much money we have and how much money it costs per person. The friends have a total of $284.25 and we don't know how much it costs per person. To find this we must set up an equation and solve it!
Because each person must pay for parking and a ticket, we can find the cost for one person by adding the parking and ticket cost together.
$9.25 + $27.50 = $36.75
Now that we have solved this equation, we know that it costs $36.75 for one person. To find how many total people can go we dived the total amount of money we have by how much it costs per person. Let's call the number of people that can go 'p'.
p = [tex]\frac{284.25}{36.75}[/tex]
Once we simplify/solve this equation we get 7 [tex]\frac{36}{49}[/tex] so essentially, we get the whole number 7 and a long decimal, but the only important part is the 7. We take the whole number from our answer which is 7.
We now know the answer: 7.
Let's check our work!
7 * 36.75 = 257.75
284.25 - 257.75 = 26.5
26.5 < 36.75 so we are correct!
The final answer is 7!
Have an amazing day!
the weights of cars passing over a bridge have a mean of 3550 pounds and standard deviation of 870 pounds. assume that the weights of the cars passing over the bridge are normally distributed. use a calculator to find the approximate probability that the weight of a randomly selected car passing over a bridge is between 2800 and 4500
Answers
Answer:
Using the usual notations and formulas,
Using the usual notations and formulas,mean, mu = 3550
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculate
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000=1 - P(X < 3000) = 1 - 0.2636 (to 4 decimals) =0.7364 (to 4 decimals)
It costs $0.50 to mail a postcard to Canada and $0.60 to mail a one ounce letter to Canada. Ahmad wrote to 21 friends and spent $12.00 for postage. How many letters and how many postcards did he write?
Answers
It costs $0.50 to mail a postcard to Canada, cost of mailing a one ounce letter to Canada is $0.60 and Ahmad wrote to 21 friends and spent $12.00 for postage. This means that he wrote 15 letters and 6 postcards.
Given Information:
Cost of mailing a postcard = $0.50
Cost of mailing a letter = $0.60
Total number of friends Ahmad wrote to = 21
Total cost of postage = $12.00
Let the number of postcards written by Ahmad be x and that of letters be y.
Then, x + y = 21 ............... (1)
0.50x + 0.60y = 12 ................ (2)
Multiplying equation (1) by 0.50, we get,
0.50x + 0.50y = 10.5 ................. (3)
Subtracting equation (3) from (2), we get,
0.1y = 1.5
⇒ y = 15
From equation (1), x = 21 - y
x = 21 - 15
x = 6
Thus, Ahmad wrote 6 postcards at a mailing cost of $0.50 each and 15 letters at a mailing cost of $0.60 each.
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The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Answers
Here is the five-number summary, range and interquartile range:
Minimum: 9
Lower quartile: 11
Median: 24
Upper quartile: 34
Maximum: 45
Interquartile range: 23
What is the five-number summary?The minimum number is the smallest number in the data. The minimum number is 9. The maximum number is the biggest number in the dataset. The maximum number is 45.
The first quartile, third quartile and the interquartile range are used to measure dispersion.
The first quartile : 1/4(n + 1)
1/4 x (12) = 3rd term = 11
The third quartile : 3/4 x (n + 1)
3/4 x (12) = 9th term = 34
Interquartile range = third quartile - first quartile
34 - 11 = 23
Median can be described as the number that is at the center of the dataset when the number is arranged in either ascending or descending order.
Median = 25
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Find the surface area of the cylinder and round to the nearest tenth. (Use the π button on your calculator)
Answers
The surface area of the cylinder with the given height and radius is 835.2 square inches
How to determine the surface area?The given parameters are
Height, h = 12 inches; this is represented by the distance between the curved surfaces of the cylinderRadius, r = 7 inches; this is represented by the distance between the center of the circle to its circumferenceThe surface area is then calculated using the following formula
A = 2πr² + 2πrh
Substitute the given values in the above equation
So, we have:
A = 2 * 3.14 * 7^2 + 2 * 3.14 * 7 * 12
Evaluate the exponents
A = 2 * 3.14 * 49 + 2 * 3.14 * 7 * 12
Evaluate the products
A = 307.72 + 527.52
Evaluate the sum
A = 835.2
Hence, the surface area of the cylinder with the given height and radius is 835.2 square inches
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2. If P = √2+1 √2-1 and Q = √2-1 √2+1 Find P2 + Q2 + PQ 1
Answers
The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
How to find the value of a expression including elimination of radical in denominators
Herein we have two irrational terms whose denominators are radical expressions, which can be treated by algebraic handling and properties for radical expressions:
P = (√2 + 1) / (√2 - 1)
P = [(√2 + 1) / (√2 - 1)] · [(√2 + 1) / (√2 + 1)]
P = (√2 + 1)² / (2 - 1)
P = (√2 + 1)²
P = 2 + 2√2 + 1
P = 3 + 2√2
Q = (√2 - 1) / (√2 + 1)
Q = [(√2 - 1) / (√2 + 1)] · [(√2 - 1) / (√2 - 1)]
Q = (√2 - 1)²
Q = 2 - 2√2 + 1
Q = 3 - 2√2
Then, the value of P² + Q² + P · Q is:
M = (3 + 2√2)² + (3 - 2√2)² + (3 + 2√2) · (3 - 2√2)
M = 9 + 12√2 + 8 + 9 - 12√2 - 8 + 3 - 8
M = 9 + 8 + 9 - 8 + 3 - 8
M = 21 - 8
M = 13
The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
RemarkThe statement is poorly formatted and reports typing mistakes, correct form is presented below:
If P = (√2 + 1) / (√2 - 1) and Q = (√2 - 1) / (√2 + 1), then find P² + Q² + P · Q.
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Chestnut Hill Coffee Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 46 espressos in all, 26 of which were single-shot. What percentage of the espressos were double-shot? Round to the nearest hundredth.
Answers
Given the number of espresso sold at Chestnut Hill Coffee Cafe as either a single-shot or a double-shot, the percentage of double-shot espressos sold is 43.48%.
What percentage of the espressos were double-shot?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given the data in the question;
Total number of espressos sold or Whole = 46Number of single-shots or Part single = 26Number of double-shots or Part double = 46 - 26 = 20Percentage of double-shot = ?Percentage = ( Part / Whole ) × 100%
Percentage = ( Part double / Whole ) × 100%
Percentage = ( 20 / 46 ) × 100%
Percentage = 0.43 × 100%
Percentage = 43.48%
Given the number of espresso sold at Chestnut Hill Coffee Cafe as either a single-shot or a double-shot, the percentage of double-shot espressos sold is 43.48%.
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Find the critical numbers of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne. ) f(x) = x4/5(x − 8)2
Answers
The critical values of the function are x = 0 and x = 64
The critical values of a function f(x) are the values of x for which f'(x) = 0.
Given,
f(x) = [tex]\frac{x^{4} }{5(x-8)^{2} }[/tex]
The derivative is found as follows, applying the quotient rule:
f'(x) = [tex]\frac{[5(x^{4} )(x-8)^{2}-5x^{4} [(x-8)^{2} ]' }{[5(x-8)^{2} ]^{2} }[/tex]
= [tex]\frac{2x^{3}(x-64) }{5(x-8)^{3} }[/tex]
The zeros of the function are the zeros of the numerator, thus:
[tex]2x^{3} (x-64) =0\\2x^{3} =0-------- > x =0\\[/tex]
x - 64 = 0------------->x = 64
The critical values are x = 0 and x = 64
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What is the surface area of a rectangular prism that has a length of 12 mm, a width of 15 mm, and a height of 16 mm?
Answers
Mark me brainliest
Work out the circumference of this circle.
Take it to be 3. 142 and give your answer to 1 decimal place.
4 cm
Answers
The circumference of the given circle is 25.1 cm.
According to the statement
we have given that the the radius of circle which is 4cm.
And we have to find the circumference of the circle.
So, For this purpose
The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center.To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).
The formula to calculate it is
C = 2(pi)r
So, substitute the values in it then
Here use pi value is 3.14
C = 2 *3.14*4
C = 25.12.
The circumference of the given circle is according to one decimal place is 25.12 cm.
So, The circumference of the given circle is 25.1 cm.
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How many solutions does the equation −3y 3y 4 = 4 have? none infinitely many one four
Answers
A given linear equation has infinitely many solutions.
What is a linear equation?There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that make a linear equation true and plot those values on a coordinate grid.As much as possible, reduce the equation to y = mx + b. Verify the exponents in your equation. It is nonlinear if it has exponents. Your equation is linear if there are no exponents in it.The definition of a linear equation is an equation with a maximum degree of one.Given: −3y 3y 4 = 4
3y+4=3y+4
The given linear equation satisfies any value of 'y'.
So, A given linear equation has infinitely many solutions.
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Does x^-2 equal 2/x?
Answers
Answer:
No,
Step-by-step explanation:
X^-2 is equal to 1/X^2. so any number or letter to negative power, is the same as 1 divided by that number or letter to the positive power..(power remains with denominator
Is (1, 3) a solution to the system of inequalities below?
y> 2x + 1
y <-3x
Why or why not?
Answers
[tex]y > 2x + 1 \\ 3 > 2(1) + 1 \\ 3 > 3 \\ false[/tex]
We can stop here and conclude that ( 1 , 3 ) is not a solution to this system, since it does not even satisfy the first equation, but check for the other one just in case:[tex]y < - 3x \\ 3 < - 3(1) \\3 < - 3 \\ also \: false[/tex]
Assume thst y varies directly with x then solve if y=4 when x=12 find y when x=-24
Answers
Answer:
-8
Step-by-step explanation:
y=(1/3)x
4 = (1/3)12
y=(1/3)(-24)
y= -8
Midpoint of US=
Help me please thanks so much
Answers
Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).
What is the midpoint of line UV?
The midpoint formula is used to find the midpoint of a line segment.
It is expressed as;
[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]
Given the data in the graph,
Point U = ( 3, -1 ) and Point V = ( -3, -4 )
x₁ = 3x₂ = -3y₁ = -1y₂ = -4We substitute into the formular above.
[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]
[ (3 + (-3) )/2 , ( (-1) + (-4) )/2 ]
[ 0/2, (-1-4)/2 ]
[ 0/2, -5 /2 ]
( 0, -5/2 )
Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).
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List the sides in order from the smallest to the largest.
L
K
27°
OA. LJ, KL, JK
OB. LJ, JK, KL
OC. KL, LJ, JK
D. JK, LJ, KL
Reset Selection
78°
75°
Answers
Answer:
A
Step-by-step explanation:
the side opposite of the angle is related to the size of this angle. Smaller angles have less space for the line to "spread out," so it will be shorter. Vice versa, bigger angles will have opposite sides longer because of more space.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
I need to know how to solve this
Answers
To find angle y you subtract the two angles form 180 degrees because it is a straight line. Then you subtract angle y and 72 from 180 because a triangle adds up to 180 degrees and you get angle x.
Hope this helps, ask if you have any more questions!
(x^2-6x+9)^2-15(x^2-6x+10)=1
Answers
Answer:
x = -1, 7, 3 + i, 3 - i.
Step-by-step explanation:
(x^2-6x+9)^2-15(x^2-6x+10)=1
(x^2 - 6x + 9)^2 - 15(x^2 - 6x + 9) - 15*1 = 1
(x^2 - 6x + 9)^2 - 15(x^2 - 6x + 9) - 16 = 0
Let Z = x^2 - 6x + 9, then we have:
Z^2 - 15Z - 16 = 0
(Z - 16)(Z + 1) = 0
Z = 16 or Z = -1
so x^2 - 6x + 9 = -1 or x^2 - 6x + 9 = 16
x^2 - 6x + 9 = -1
---> x^2 - 6x + 10 = 0
Using the Quadratic Formula:
---> x = [6 +/- √((-6)^2 - 4* 1* 10) / 2
---> x = 6/2 +/- √-4/2
---> x = 3 + i , 3 - i.
x^2 - 6x + 9 = 16
---> x^2 - 6x - 7 = 0
---> (x - 7)(x + 1) = 0
---> x = 7, -1.
What is the name for the threshold p-value that determines when the null hypothesis is rejected?.
Answers
Alpha level. the minimum P-value at which we reject the null hypothesis
What is Null hypothesis ?That two options are identical is the null hypothesis. According to the null hypothesis, the observed difference is solely the result of chance. The probability that the null hypothesis is correct can be determined via statistical testing.
What is alpha level?The "significance level," often known as the alpha level, must be established before performing any statistical test. The likelihood of rejecting the null hypothesis when it is true is what is meant by the term "alpha level" in statistics. The likelihood of making a poor decision is what this phrase means.
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Find the surface area of the prism
Answers
The surface area of the prism is 256in².
Given that the sides of the prism is 5in, 12in and 4in.
The total area occupied by the surfaces of an object is called the area.
Here, l=12in, b=5in and h=4in
Firstly, we will find the area of the base, we get
B=l×b
B=12×5
B=60in²
Now, we will find the perimeter of the base, we get
P=2(l+b)
P=2(12+5)
P=2×17
P=34in
Further, we will find the surface area of the prism by using the formula SA=2B+Ph.
Here, we will substitute the values from above, we get
SA=2×60in²+34in×4in
SA=120in²+136in²
SA=256in²
Hence, the surface area of the prism where the sides of the prism is 5in, 12in and 4in is 256in².
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Adrian has a bag full of pebbles that all look about the same. he weighs some of the pebbles and finds that their weights are normally distributed, with a mean of 2.6 grams and a standard deviation of 0.4 grams. what percentage of the pebbles weigh more than 2.1 grams? round to the nearest whole percent.
Answers
89% of pebbles weigh more than 2.1 grams.
What is a percentage?
Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage.Given,
Mean = 2.6
SD = 0.4
As we have to find the percentage of pebbles weighing more than 2.1, we have to find the z-score for 2.1 first.
[tex]z = \frac{x- mean}{SD}[/tex]
[tex]z = \frac{2.1 - 2.6}{0.4}[/tex]
[tex]z = -1.25[/tex]
Now we have to use the z-score table to find the percentage of pebbles weighing less than 2.1
So,
[tex]P ( x < 1.25 ) = 0.10565[/tex]
This gives us the probability of P(z<-1.25) or P(x<2.1)
To find the probability of pebbles weighing more than 2.1
[tex]P ( x > 2.1 ) = 1 - P( x < 2.1 ) = 1 - 0.10565 = 0.89435[/tex]
Converting into percentage
0.89435 × 100 = 89.435 %
Rounding off to nearest percent =89%
Therefore, 89% of pebbles weigh more than 2.1 grams.
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Use theorem 7. 4. 2 to evaluate the given laplace transform. do not evaluate the convolution integral before transforming. (write your answer as a function of s. ) ℒ t et − d 0
Answers
With convolution theorem the equation is proved.
According to the statement
we have given that the equation and we have to evaluate with the convolution theorem.
Then for this purpose, we know that the
A convolution integral is an integral that expresses the amount of overlap of one function as it is shifted over another function.
And the given equation is solved with this given integral.
So, According to this theorem the equation becomes the
[tex]\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{ \mathscr{L} (e^{-\tau} \cos \tau ) }{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{\frac{s+1}{(s+1)^2+1}}{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{1}{s}\left (\frac{s+1}{(s+1)^2+1} \right).[/tex]
Then after solving, it become and with theorem it says that the
[tex]\mathscr{L} \left( \int_{0}^{t} f(\tau) d\tau \right) = \frac{\mathscr{L} ( f(\tau))}{s} .[/tex]
Hence by this way the given equation with convolution theorem is proved.
So, With convolution theorem the equation is proved.
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A day care program has an average daily expense of $75.00. the standard deviation is $5.00. the owner takes a sample of 64 bills. what is the probability the mean of his sample will be between $70.00 and $80.00? step 1. calculate a z-score for $70.00 - step 2. give the probability for step 1. % step 3. calculate the z-score for $80.00 step 4. give the probability for step 3. % step 5. add the probabilities from steps 2
Answers
Answer:
B. 68
Step-by-step explanation:
x is a raw score to be standardized;
μ is the mean of the population;
σ is the standard deviation of the population.
Therefore the mean is zero. Seventy is -1z, or -1 standard deviation.
Step 2: 34.13% of the cases fall between -1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 70 and 75. This, of course, assumes a normal curve.
Step 3: An 80 is +1z or +1 standard deviation assuming a normal curve.
Step 4: Thirty four percent of the cases fall between +1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 75 and 80. This, of course, assumes a normal curve.
Step 5: Score between +1z and -1z, or +1 and -1 standard deviation account for 68.26% of the cases.
Find the value of x if a, b, and c are collinear points and b is between a and c. ab=x 6,bc=3x−5,ac=36−x
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The value of x if a, b, and c are collinear points and b is between a and c : 7
What is collinear points?Collinear points are those that are situated on the same line of sight or within a single line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either close to or far from one another.
According to the given information:
if A, B, and C are col-linear points and B is between A and C
then
AB+BC=AC
AB=x+6
BC=3x-5
AC=36-x
substituting value:(x+6)+(3x-5)=36-x
(x+3x)+(6-5)=36-x
4x+1=36-x
4x+x=36-1
5x=35
x=35/5
x=7
The value of x is 7
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