The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.
According to the statement
we have to find the inverse of the Laplace theorem with the help pf the given theorem in the statement.
So, For this purpose, we know that the
Laplace transformation is a transformation of a function f(x) into the function g(t) that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.
Now, We assume you want to find the inverse transform of [tex]s/(s^2 +3s -4).[/tex]
This can be written in partial fraction form as
[tex]\frac{(4/5)}{(s+4)} + \frac{(1/5)}{(s-1)}[/tex]
which can be found in a table of transforms to be the transform of
[tex]\frac{4}{5} e^{-4t} + \frac{1}{5} e^t[/tex]
There are a number of ways to determine the partial fractions. They all start with factoring the denominator.
[tex]s^2 +3x -4 = (s+4)(s-1)[/tex]
After that, you can postulate the final form and determine the values of the coefficients that make it so.
For example:
[tex]\frac{A}{(s+4)} + \frac{B}{s-1} = (A+B)s + \frac{(4B-A)}{(s^2 +3x -4)}[/tex]
This gives rise to two equations:
(A+B) = 1
(4B-A) = 0.
So, The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) ℒ−1 s s2 + 3s − 4.
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An oblique prism with a square base of edge length x units has a volume of x3 cubic units. which expression represents the height of the prism?x unitsx units2x unitsx units
The expression that represents the height of the oblique prism is: 1/2x.
What is the Volume of a Prism?
The volume of a prism is defined as the total space occupied by the three-dimensional object. Mathematically, it is defined as the product of the area of the base and the length.Prism Volume = base area × height of the prism
Given that the oblique prism has:
Volume = 1/2x³ cubic units
edge length = x units
Therefore,
base area = x²
Thus:
1/2x³ = (x²)(height)
Divide both sides by x²
1/2x³ ÷ x² = height
1/2x³ × 1/x² = height
x³/2 × 1/x² = height
height = x³/2x²
height = x/2
Therefore, the expression that represents the height of the oblique prism is: 1/2x.
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The complete question is -
An oblique prism with a square base of edge length x units has a volume of x3 cubic units. Which expression represents the height of the prism?
Find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative. ) f(x) = x(18x 4)
Answer:
Below in bold.
Step-by-step explanation:
f(x) = x(18x + 4)
f(x) = 18x^2 + 4x
Antiderivative = 18 * (x^2+1)/(2 + 1) -+4x(1+1) / (1+1) + C
= 18x^3 / 3 + 4x^2 / 2 + C
= 6x^3 + 2x^2 + C.
Checking by differentiating:
f'(x) = 6*3 x^(3-1) + 2*2x^(2-1)
= 18x^2 + 4x
= x(18 -+4)
By selling 20 oranges for#1.35 a trader makes a profit of 8% what is the percentage gain or loss if he sells the same 20 oranges for#1.10?
Answer:
12% loss
Step-by-step explanation:
The selling price is the sum of the cost price and the markup. Here, the markup (profit) is expressed as a percentage of the cost price.
Cost priceThe relation between selling price and cost price is ...
selling price = cost price + cost price × markup fraction
selling price = cost price × (1 + markup fraction)
Then the original cost price is ...
cost price = (selling price) / (1 + markup fraction)
cost price = #1.35 / (1 +8%) = #1.25
ProfitAfter the change in selling price, we can find the markup fraction (profit rate) to be ...
1 + markup fraction = (selling price)/(cost price)
markup fraction = (selling price)/(cost price) -1
markup fraction = #1.10/1.25 -1 = 0.88 -1 = -0.12
The trader has a 12% loss when selling the oranges at #1.10.
If you are choosing a single card from a standard deck of playing cards, what is
the probability that you draw a face card or a heart?
Your answer should be in the form of a fraction. Type it like this: 15/52.
Just to review:
• There are 52 cards in a deck.
• There are 4 suits with 13 cards each.
o 2 red suits - hearts and diamonds
o 2 black suites - clubs (look like clovers) and spades
• Each suit has an Ace, numbered cards 2-10, and 3 "face" cards--a Jack, Queen, and King.
Step-by-step explanation:
there are 4 suit with 13 cards each
What is the probability that a five-card poker hand contains the two of diamonds and the three of spades?.
Answer:
1/311875200.
There is exactly 1 way to have all 5 of these cards. For the first card, there are 52 total cards to be had; for the second, 51; for the third, 50; for the fourth, 49; and for the fifth, 48:
(1/52)(1/51)(1/50)(1/49)(1/48) = 1/311875200.
Step-by-step explanation:
When the sample evidence is sufficient to justify rejecting the null hypothesis in a goodness-of-fit test, can you tell exactly how the distribution of observed values over the specified categories differs from the expected distribution? explain your answer.
No, we can only suppose that the observed distribution deviates from the expected distribution when we reject the null hypothesis.
What is a null hypothesis?The null hypothesis exists as a specific mathematical theory that claims that there exists no statistical relationship and significance between two sets of observed data and estimated phenomena for each set of selected, single observable variables. The null hypothesis can be estimated to define whether or not there exists a relationship between two measured phenomena, which creates it useful. It can let the user comprehend if the outcomes exist as the product of random events or intentional manipulation of a phenomenon.
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Solve this system of equations by using the elimination method. x+4y=9 2x-4y=-6
Answer:
[tex]x=6[/tex]
[tex]y=\frac{3}{4}[/tex]
Step-by-step explanation:
Given the following question:
[tex]x+4y=9[/tex]
[tex]2x-4y=9[/tex]
To solve using the elimination method we will add the two equations together to find the two individual values.
[tex]x+2x=3x[/tex]
[tex]4y-4y=0[/tex]
[tex]9+9=18[/tex]
[tex]3x=18[/tex]
[tex]\frac{3x}{3} =x[/tex]
[tex]18\div3=6[/tex]
[tex]x=6[/tex]
[tex]x+4y=9[/tex]
Substitute six in for x:
[tex]x=6[/tex]
[tex]6+4y=9[/tex]
Solve for y:
[tex]6-6=0[/tex]
[tex]9-6=3[/tex]
[tex]\frac{4y}{4} =y[/tex]
[tex]3=\frac{3}{4}[/tex]
[tex]y=\frac{3}{4}[/tex]
x is equal to 6, and y is equal to 3/4.
Hope this helps.
Use 3.14 for pi. ROUND YOUR FINAL ANSWER TO THE NEAREST TENTHS PLACE!
Answer:
379.94
Step-by-step explanation:
3.14 x 11^2 = 379.94
The area of the given circle is 95 square ft.
Calculation for the Area of the Circle:
It is given in the diagram that,
The diameter of the circle, d = 11 ft.
Now, we know that the radius of a circle is equal to half of the diameter.
Therefore, radius of the given circle, r = 11/2 ft.
The formula for the area of the circle is given as follows,
A = π × r²
Substituting the values, π = 3.1, and r = 11/2, we get,
A = (3.14) × (11/2)²
A = (3.14) × 30.25
A = 94.985
A ≈ 95
Hence, the area of the given circle with diameter 11 ft. comes out to be 95 ft².
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subtract 2/9-2/15. enter your answer below as a fraction in lowest terms, using the slash (/) as the fraction bar.
Answer:
2/9 - 2/15
Solution
LCM = 45
45 ÷9 ×2 = 10
45÷ 15 ×2 = 6
10 - 6 = 4
ANSWER = 4/45
Answer:
l
Step-by-step explanation:
take the lcm of 9 and 15. it will be 45 . than continue
algebra 2: help please
a scuba diver enters the water 1m away from her boat. She dives down and then resurfaces 12m away from her boat. Her diving path id in the shape of a quadratic function, where x is the distance away from the boat and y is the distance away from the surface of the water, and negative values of y are below the water. She reaches a maximum depth of 30.25m below the surface of the water.
Her diving partner wants to estimate the diver’s depths at different points away from the boat. What is the diver’s depth when she is 4m away from the boat?
Answer:
24 m depth
Step-by-step explanation:
The quadratic function modeling depth will have zeros at x=1 and x=12, the distances in meters from the boat where the diver is at the surface.
Quadratic functionThe factored form of a quadratic function can be written as ...
y = a(x -p)(x -q)
where p and q are zeros of the function. The value 'a' is a vertical scale factor.
Here, we are given y=0 at the surface, at points where x=1 and x=12. This means the function can be written as ...
y = a(x -1)(x -12)
Scale factorTo find the value of 'a', we can use the maximum depth value. That depth will be halfway between the function zeros, at x = (1+12)/2 = 6.5
-30.25 = a(6.5 -1)(6.5 -12)
30.25 = 5.5²·a = 30.25a ⇒ a=1
Model of depthThen the function modeling the diver's depth in meters is ...
y = (x -1)(x -12)
And the depth at x=4 will be ...
y = (4 -1)(4 -12) = 3(-8) = -24 . . . . meters
The diver's depth is 24 meters when she is 4 m away from the boat.
What is the period of y = 2cos(3x - 2п)?
Answer:
Periodicity of 2cos(3x-2π)=
[tex] \frac{2\pi}{3} [/tex]
Step-by-step explanation:
Greetings![tex]periodicity \: of \: 2 \cos(3x - 2\pi) \\ periodicity \: of \: a. \cos(bx + c) + d = \\ \frac{periodicity \: of \: \cos(x) }{|b|} \\ periodicity \: of \: \cos(x) \: is \: 2\pi = \frac{2\pi}{|3|} \\ simplify = \frac{2\pi}{3} [/tex]
Answer:
[tex]\sf Period=\dfrac{2}{3} \pi[/tex]
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function
f(x) = A cos(B(x + C)) + D
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftGiven function:
y = 2 cos (3x - 2π)
Therefore:
A = 2B = 3C = 2/3D = 0Period of given function:
[tex]\sf \implies Period=\dfrac{2 \pi}{B} = \dfrac{2 \pi}{3}[/tex]
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Towns A, B, and C lie on a straight line, as shown below. Jack and Arthur start at Town B and drive for an hour from Town B to Town C, where they stop for an hour to eat lunch. Which of the following graphs could represent their distance from Town A during these two hours?
Considering the situation described, it can be graphed by the first function.
Which graph models the situation?Cities A, B and C are on a straight line.
On the first hour, they leave town B to town C, moving farther from Town A, hence the distance is increasing on the first hour.On the second hour, they stop for lunch, meaning that the distance remains constant at the point it was at the end of the first hour.Hence, the first graph is the correct one for this problem.
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The degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to:
The degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to 6
How to determine the degrees of freedom applied to a cross-tabulation ?The given parameters are:
Rows = 5
Column = 2
The degrees of freedom is then calculated as:
df = Rows + Column - 1
Substitute the known values in the above equation
df = 5 + 2 - 1
Evaluate the expression
df = 6
Hence, the degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to 6
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The local gym is offering this new promotion: An enrollment fee of $40 and a monthly fee of $30. Which of the following expressions represents the cost of the gym membership for m months?
40+30m=c40 plus 30 m is equal to c
30+40m=c30 plus 40 m is equal to c
40+30m40 plus 30 m
30+40m
The expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The local gym is offering this new promotion:
An enrollment fee of $40 and a monthly fee of $30.
Let m be the total number of months
Total monthly fee = 30m
Total cost(including the enrollment fee of $40) = 40 + 30m
Let the total cost is c:
c = 40 + 30m
If in the linear expression, one variable is present, then the bis known as the linear expression in one variable.
Thus, the expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.
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trevor takes up a test at school and completes it in an hour. the test has two sections. if he takes 35 minutes to complete the first section, how much time does he have left to complete the second section? which equation would you use to answer this problem?
a) x + 2 = 35
b) 2x + 30 = 35
c) 2x + 30 + 60
d) x + 35 = 60
Answer:
I would use equation d
Step-by-step explanation:
because need to find out X which is the second section so you would do 60 subtract 35 which gives 25 so X would be 25 .
I hope this helped . if you need any more help pls ask :)
pls give brainliest if you like my answer :)
if you rolled two dice what is the probability that you would roll a 4 or a 5
what is - 4x +7 > x -13
Answer:
[tex]\huge\boxed{\sf x < 4}[/tex]
Step-by-step explanation:
Given inequality:-4x + 7 > x - 13
Subtract x to both sides
-4x - x + 7 > -13
-5x + 7 > -13
Subtract 7 to both sides
-5x > -13 - 7
-5x > -20
Divide -5 to both sides
x < -20/-5
x < 4[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]x < \bf 4[/tex]
Step-by-step explanation:
[tex]-4x + 7 > x -13[/tex]
We have to make [tex]x[/tex] the subject of the equation:
• Subtract [tex]x[/tex] from both sides:
[tex]-4x - x + 7 > -13[/tex]
⇒ [tex]-5x + 7 > -13[/tex]
• Now subtract 7 from both sides:
[tex]-5x > -13 - 7[/tex]
⇒ [tex]-5x > -20[/tex]
• Next divide both sides by -5, and remember that dividing an inequality by a negative number reverses the inequality symbol:
[tex]x < \frac{-20}{-5}[/tex]
⇒ [tex]x < \frac{20}{5}[/tex]
⇒ [tex]x < \bf 4[/tex]
Find the missing length indicated.
The missing length of given right triangle is equal to 1500.
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: [tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin (x), cos (x) and tan (x) , where:
[tex]sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse} \\ \\ tan (x)= \frac{opposite\ side}{adjacent\ side}[/tex]
There is another important property, where h²=m*n. See the attached image.
From the previous informations presented, you can solve the given question.
Thus, if h²=m*n. You can write:
h²=900*1600
[tex]h=\sqrt{1440000}\\ \\ h=1200[/tex]
If h=1200, you can find x from Pythagorean Theorem.
x²=1200²+900²
x²=1440000+810000
x²=2250000
x=[tex]\sqrt{2250000}[/tex]
x=1500
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Will has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. If Ashley has 30 stamps and she has a third as many as Carlton has, how many stamps are in Will’s collection?
Taking into account the definition of a system of linear equations, 240 stamps are in Will’s collection.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Number of stamps that are in Will’s collectionIn this case, a system of linear equations must be proposed taking into account that:
W: Number of stamps that are in Will’s collectionC: Number of stamps that are in Carlton’s collectionA: Number of stamps that are in Ashley’s collectionOn the other hand, you know that:
Ashley has 30 stamps and she has a third as many as Carlton has → A= [tex]\frac{1}{3}[/tex]C → 30= [tex]\frac{1}{3}[/tex]CWill has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. → W= 2(C + A)So, the system of equations to be solved is
[tex]\left \{ {{30=\frac{1}{3}C } \atop {W=2(C+30)}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Solving the first equation:
30= [tex]\frac{1}{3}[/tex]C
30÷[tex]\frac{1}{3}[/tex]= C
90= C
Substituting the value in the second equation:
W= 2(90 + 30)
W= 2×120
W=240
Finally, 240 stamps are in Will’s collection.
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Kari is preparing for a party and must have the perfect outfit with one
jacket and one jumpsuit. How many possible outcomes can she create if
she has a jean jacket, leather jacket, white jumpsuit, tan jumpsuit, green
jumpsuit, and a black jumpsuit?
Answer:
8
Step-by-step explanation:
Kari has 2 choices for jackets and 4 choices for jumpsuits. We'll multiply those together to find the number of options she has.
Since the numbers are very small, we can grind out this same number (but be organized):
Jean/white
Jean/tan
Jean/green
Jean/black
Leather/white
Leather/tan
Leather/green
Leather/black
These are the eight choices.
A zookeeper is monitoring the population of penguins. the group needs to have exactly two times more males than females for the population to thrive. the zoo only has room for a maximum of 10 female penguins. let x represent the number of female penguins and y represent the number of male penguins. write the constraints that represent the possible number of male and female penguins that can live in a thriving population at the zoo. 0 < x ≤ 10 and 0 < y ≤ 20 x > 0 and y > 0 0 < x ≤ 10 and y > 20 x > 0 and y < 10
Answer:
0 < x ≤ 10 and 0 < y ≤ 20.
Step-by-step explanation:
I did the test and got it right ma bois.
Answer: Its A
Step-by-step explanation:
Can anyone help me solve these linear systems using substitution?
1. 3x-y=4
x+2y=6
2. 2x-y= -39
x+y= -21
3. 2x+y =11
6x-5y =9
Each question should demonstrate step by step on how to do it, as well as each step should show the final given points of each solution (x,y)
Answer:
1. (2,2)
2. (-20, -1)
3. (4,3)
Step-by-step explanation:
See attached images
Answer:
The solutions to the sets of equations may be found by either a substitution process or by graphing and looking for the point that the two lines formed by the quations intersect. Both approaches are described.
The "solution" to these sets of equations is the point at which the two lines intersect each other.
Step-by-step explanation:
1. 3x-y=4 and x+2y=6
x+2y=6
6x-2y=8 We can simply add these two equations since y will disappear, leaving just x.
7x = 14 [result of addition]
x = 2 [Solve]
Since x = 2, [Then use the solution for x to find y]
x+2y=6
(2)+2y=6
2y = 4
y = 2
(2,2) is the solution (where the lines intersect). See attached graph.
2. 2x-y= -39 and x+y= -21
2x-y= -39
x+y= -21 Add the two equations (since the y will be eliminated)
3x = -60
x = -20
Find y:
x+y= -21
(-20)+y= -21
y = -1
Solution is (-20,-1)
3. 2x+y =11 and 6x-5y =9
2x+y =11
-6x+-3y = -33 [Multiply by -3 and then add to other equation. This allows us to eliminate x]
6x - 5y = 9
-8y = - 24
y = 3
2x+y =11
2x+(3) =11
2x = 8
x = 4
Solution is (4,3)
==================
See attached graph for all the graphed solutions.
==================
The substitution process also works if we isolate one of the 2 variables in one equation and then use the resulting value in the second eqaution. For example, in problem 1:
3x-y=4
x+2y=6
Pick either equation and isolate the x or y. I'll pick the second equation and isolate for x:
x = 6-2y
Now use this value of x (6-2y) in the other equation:
3x-y=4
3(6-2y)-y=4
18 - 6y - y = 4
-7y = -14
y = 2
Then use y=2 to fiond x, using either equation:
x+2y=6
x+2(2)=6
x = 2
The solution is (2,2).
This same approach can be used on all these problems. It avoids trying to visualize what can be done to an entire equation to eliminate one of the variables, but it takes a bit more paper.
All solutions are graphed in the attachment.
Sierra found that 15 meters is equivalent to 49.2 feet. Which of the following is an equivalent ratio?
3 to 8.84
5 to 18.22
7 to 22.96
9 to 25.32
Answer:
7 to 22.96
Step-by-step explanation:
Hello!
We can represent each ratio as a fraction:
Original: 15 to 49.2 = [tex]\frac{15}{49.2}[/tex]3 to 8.84 = [tex]\frac{3}{8.84}[/tex]5 to 18.22 = [tex]\frac{5}{18.22}[/tex]7 to 22.96 = [tex]\frac{7}{22.96}[/tex]9 to 25.32 = [tex]\frac{9}{25.32}[/tex]To find equivalent values, we can convert each fraction into a decimal by dividing them.
ConvertOriginal: [tex]\frac{15}{49.2} = 0.304878048780488[/tex][tex]\frac{3}{8.84} = 0.339366515837104[/tex][tex]\frac{5}{18.22} = 0.274423710208562[/tex][tex]\frac{7}{22.96} = 0.304878048780488[/tex][tex]\frac{9}{25.32} = 0.355450236966825[/tex]The ratio of 7 to 22.96 is equivalent to the ratio of 15 to 49.2.
G.CO.5 △ABC undergoes a series of transformations to create △A'B'C'. Which of the following series of transformations will carry △ABC onto △A'B'C'?
Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.
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4x+10=-2x + 4
y - 4 (2y - 5) = -4
Solve the 2 equations
(ignore image)
The solutions to the equations are x = 7/3 and y = 24/7
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
4x + 10 = -2x + 4
y - 4(2y - 5) = -4
Considering the first equation
4x + 10 = -2x + 4
Collect the like terms
4x + 2x = 10 + 4
Evaluate the like terms, by adding them
6x = 14
Divide both sides of the equation by 6
x = 7/3
Considering the second equation
y - 4(2y - 5) = -4
Expand the bracket in the above equation
y - 8y + 20 = -4
Collect the like terms
y - 8y = -20 -4
Evaluate the like terms, by adding them
-7y = -24
Divide both sides of the equation by -7
y = 24/7
Hence, the solutions to the equations are x = 7/3 and y = 24/7
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guys help me please
Answer:
(x + 6, y + 1)
Step-by-step explanation:
Just look at 1 point of ABCD. For example, look at point D.
Point D must become point F.
When you reflect ABCD over the x-axis, point D will end up at (-1, -2).
Now it has to be translated to (5, -1).
For x to go from -1 to 5, you need to add 6.
For y to go from -2 to -1, you need to add 1.
Answer: (x + 6, y + 1)
please help im sorry it is late but please i dont understand
Answer:
416 people
Step-by-step explanation:
The way you get the answer is by adding up the number of people from the sample, which gives you 175 people. After finding that you take the number of people who like pretzels (26) and divide it by 175, giving you 0.16 or 16%.
This means 16% of people will like pretzels, so you apply this to the actual number of people coming, 2600, and find 16% of 2600 (0.16 x 2600) which is 416 people. I hope this makes sense :)
Sloane kicked a soccer ball off the ground at a speed of 56 feet per second. the height of the ball can be represented by the function h(t) = −16t2 56t, where t is the time in seconds. how many seconds did the ball travel before returning the ground? t = 56 seconds t = 16 seconds t = 3.5 seconds t = 0.29 seconds
The time in seconds that it took the ball to travel would be = 0.25 seconds.
Calculation of speed timeSpeed can be defined as the distance covered by an object per unit time.
The speed used to kick the soccer off the ground = 56 feet per second.
The height equation= −16t² + 56t
The time= ?
The formula for speed = distance/time
56= −16t² + 56t/t
56t = −16t² + 56t/t
−16t² = -56t + 56t
−16t² = 0
Make t the subject formula,
t = √1/16
t = 0.25 seconds.
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A local baseball team is struggling this season, and many fans of the team believe it may be time to replace the head coach. to estimate support for firing the current head coach, a television news station provides a link on its website where fans of the team can respond to the question: "do you feel the current head coach should be fired?" after 2,367 votes on the website, 79% of those who responded felt the coach should be fired. which of these describes the type of bias in this survey and a likely direction of the bias in estimating overall support for firing the coach?
This is voluntary response bias. The result overestimates true support for firing the coach.
What is voluntary response bias? When sample participants are self-selected volunteers, as in voluntary samples, voluntary response bias emerges.An illustration would be call-in radio programs that invite listeners to participate in polls on contentious issues (abortion, affirmative action, gun control, etc.).The sample that results tends to overrepresent people with strong opinions. In a random sampling technique, every component of the population has a known, non-zero probability of being chosen, and the selection of the sample unit is dependent only on chance.By removing voluntary response bias and protecting against undercoverage bias, random sampling aids in the production of representative samples.Random sampling underpins all probability sampling techniques.To know more about voluntary response bias with the given link
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The actual length of Lake Superior is 350 miles and the width is 160 miles. What's the length and width of the lake on a map if the scale is "1 cm = 25 miles"?
Answer:
length = 14 cm; width = 6.4 cm
Step-by-step explanation:
We can use proportions to find the length and width.
Thus, for length, l, we have:
[tex]\frac{1}{25}=\frac{l}{350} \\25l=350\\l=14[/tex]
For width, w, we have:
[tex]\frac{1}{25}=\frac{w}{160}\\ 25w=160\\ w=6.4[/tex]
