An example of a boundary value problem is the Sturm-Liouville problem, which entails determining the eigenvalues and eigenfunctions of a differential equation that complies with specific boundary requirements.
The general formula for the Sturm-Liouville problem's solution in x is y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the differential equation's eigenfunctions. When the differential equation and boundary conditions are solved, the eigenvalues and eigenfunctions are discovered.
For instance, if the differential equation has the following form: -y" + q(x)y = lambda* w(x)y where y is the dependent variable, y" is the second derivative of y, q(x) and w(x) are functions of x, and lambda is the eigenvalue, the boundary conditions can be of the following
form: where L is the length of the interval on which the differential equation is defined, y(0) = 0, and y(L) = 0.
The general solution in x can be expressed in the form: y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the eigenfunctions of the differential equation. The eigenvalues and eigenfunctions can be discovered by solving this differential equation and the boundary conditions.
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Linear function k has a zero at 3 and a y-intercept of 9 . Which graph best represents k ?
In the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.
In the given question, linear function k has a zero at 3 and a y-intercept of 9.
We have to choose which graph best represents k.
As we know that;
A linear equation represent the relationship between the two unknown variable. The equation of linear equation is of one degree.
The simplest linear equation shows the correlation between (x,y), which may then be used to make a table or a graph on the coordinate plane or to assess at a specific x or y value.
We represent linear function in the form of y=mx+c.
where m is the slope of the line, c is the y intercept of the line, x is independent variable and y is the dependent variable.
As we see the y intercept in the graph crosses the y axis.
Here y intercept is 9.
The zeros of the linear function is that where y value is zero.
As in the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.
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Write this set using interval notation.
Please help me!!!
Answer:
Step-by-step explanation:
The set {x | x < 0 or x > 3 } can be written in interval notation as (-∞, 0) ∪ (3, ∞).
The set {x | x < 0 or x > 3 } consists of all real numbers that are either less than 0 or greater than 3. This set can be represented as the union of the set of all numbers less than 0, which can be written as (-∞, 0), and the set of all numbers greater than 3, which can be written as (3, ∞).
Therefore, the set {x | x < 0 or x > 3 } can be written in interval notation as (-∞, 0) ∪ (3, ∞).
a line that includes the point (17,2) and has a slope of 1. what is its equation in slope-intercept form?
Answer:
y = x - 15
Step-by-step explanation:
y-2 = 1(x-17)
y-2 = x - 17
y = x -17 + 2
y = x - 15
Which ordered pair is NOT a point on the graph of f(x)=1/2. x-7
(1,-61/2)
(2,8)
(-2,-8)
(0,-7)
The ordered pair that is NOT a point on the graph of f(x) = (1/2)*x - 7 is (2,8) , the correct option is (b) .
In the question ,
it is given that ,
the function is given as ;
f(x) = (1/2)*x - 7 ,
Option(a) ,
the ordered pair is (1 , [tex]-6\frac{1}{2}[/tex] )
To satisfy the function f(x) , on putting x = 1 , we should get y = [tex]-6\frac{1}{2}[/tex] .
f(1) = (1/2) - 7 = (1 - 14)/2 = -13/2 .
So , this point lies on graph of f(x) .
Option(b) ,
the ordered pair is (2,8) ,
f(2) = (1/2)*2 - 7 = 1 - 7 = -6 ≠ 8 .
So , this point does not lie on graph of f(x) .
Option(c) ,
the ordered pair is (-2,-8) ,
f(-2) = (1/2)*(-2) - 7 = -1 - 7 = -8 = -8 .
So , this point lies on graph of f(x) .
Option(d) ,
the ordered pair is (0,-7) ,
f(2) = (1/2)*0 - 7 = - 7 = -7 .
So , this point lies on graph of f(x) .
Therefore , the ordered pair (2,8) is not on the graph .
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Please help will mark Brainly
The range of the function will be 0 ≤ y ≤ 960
Range of a FunctionThe range of a function is the set of all its outputs. Example: Let us consider the function f: A→ B, where f(x) = 16x and each of A and B = {set of natural numbers}. Here we say A is the domain and B is the co-domain. Then the output of this function becomes the range. The range = {set of even natural numbers}.
Generally, the range of a function is the possible values of y in the that function and can be from -negative infinity to positive infinity.
In the given question, the function y = 16x models the situation and the capacity of the the container is 960 ounces
The range will fall between 0 ≤ y ≤ 960
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A set of 3 consecutive even integers adds up to 6. What are the integers?
NO LINKS!! Please help me with this statement Part 6 ll
Answer:
C) Domain: all real numbers x except x = ±2
E) f(x) → ∞ as x → -2⁻ and as x → 2⁺, f(x) → -∞ as x → -2⁺ and as x → 2⁻
Step-by-step explanation:
Given function:
[tex]f(x)=\dfrac{3x^2}{x^2-4}[/tex]
The domain of a function is the set of all possible input values (x-values).
A rational function is undefined when the denominator is equal to zero.
The denominator of the given function is zero when:
[tex]\implies x^2-4=0[/tex]
[tex]\implies x^2=4[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{4}[/tex]
[tex]\implies x= \pm 2[/tex]
Therefore the domain of the function is:
all real numbers x except x = ±2The excluded x-values are x = -2 and x = 2.
To find the behaviour of the function near the excluded x-values, input values of x that are very near either side of excluded values:
[tex]x \rightarrow -2^-: \quad f(-2.001)=\dfrac{3(-2.001)^2}{(-2.001)^2-4}=3002.250...[/tex]
[tex]x \rightarrow -2^+: \quad f(-1.999)=\dfrac{3(-1.999)^2}{(-1.999)^2-4}=-2997,750...[/tex]
[tex]x \rightarrow 2^-: \quad f(1.999)=\dfrac{3(1.999)^2}{(1.999)^2-4}=-2997.750...[/tex]
[tex]x \rightarrow -2^+: \quad f(2.001)=\dfrac{3(2.001)^2}{(2.001)^2-4}=3002.250...[/tex]
Therefore, the behaviour of the function near the excluded x-values:
f(x) → +∞ as x → -2⁻f(x) → -∞ as x → -2⁺f(x) → -∞ as x → 2⁻f(x) → +∞ as x → 2⁺find the equation for the line containing the points (-4,-2) and (-3,5)
Answer:
Step-by-step explanation:
Given the points
(4, 2)
(3, 5)
We know that the slope-intercept form of the line equation is
where m is the slope and b is the y-intercept
substituting m=-3 and the point (4, 2) to get the y-intercept i.e. b
2=(-3)4 + b
2 = -12 + b
b = 2+12
b = 14
Now, substituting b=14 and m=-3 in the slope-intercept form to determine the equation of a line in the slope-intercept.
y=(-3)x+(14)
y=-3x+14
Thus, the equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:
y=-3x+14
Solve the system of linear equations
Answer:
Below
Step-by-step explanation:
I'll do the first one....you can then do the second one
-4x-2y = -12
4x+8y = -24 add these two equations together ( this will eliminate 'x')
6y = -36
y = - 6 use this value in either equation to compute x = 6
HINT: On the next one....multiply either equation by -1 then add together
Point M is the midpoint of PQ, and LM is the perpendicular bisector of PQ. Write a two-column proof to show that LP = LQ.
The two column proof below has shown us that the LP ≅ LQ by definition of segment congruence.
How to write a two column proof?We are told that Point M is the midpoint of PQ, and LM is the perpendicular bisector of PQ. Thus, the two-column proof to show that LP = LQ is as follows;
Statement 1; PM ≅ QM, LM ⊥ PQ
Reason 1; Given
Statement 2; LM ≅ LM
Reason 2; Reflexive Property of Congruence
Statement 3; ∠PML ≅ ∠QML
Reason 3; Right angle congruence theorem
Statement 4; ΔPML ≅ ΔQML
Reason 4; SAS congruence theorem
Statement 5; ∠PML ≅ ∠QML
Reason 5; Corresponding parts of congruent triangles are congruent
Statement 6; LP ≅ LQ
Reason 6; Definition of segment congruence
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If loan Amy is 89000 monthly payment is 479.66 rate is 4.2 what is the interest principal and balance for month 1 and month2
The amount of money an account with simple interest at an annual rate of 4.2% would be $3738 after 1 month and 7476 dollar after 2 month.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.
Simple Interest = (Principal × Rate × Time) / 100
Given that loan Amy is 89000 monthly payment is 479.66 rate is 4.2
Amount = $89000
Rate = 4.2 %
Time = 1 month
Therefore, Simple Interest = (Principal × Rate × Time) / 100
Simple Interest = 89000 × 4.2% × 1
Simple Interest = 3738
Also,
Simple Interest = 89000 × 4.2% × 2
Simple Interest = 7476
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Solve for the lengths of XZ and YZ
a bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed v/2. Thependulum bob is suspended by a stiff rod of length and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle?
Sell Order 5: Price: $20, Quantity: 400
Since this order has the same price as Sell Order 2, it will be executed fifth.
1: Sell Order 3: Price: $30, Quantity: 300
2: Sell Order 1: Price: $25, Quantity: 500
3: Sell Order 4: Price: $25, Quantity: 100
4: Sell Order 2: Price: $20, Quantity: 200
5: Sell Order 5: Price: $20, Quantity: 400
1: Sell Order 3: Price: $30, Quantity: 300
Since this order has the highest price, it will be executed first.
2: Sell Order 1: Price: $25, Quantity: 500
Since this order has the second highest price, it will be executed second.
3: Sell Order 4: Price: $25, Quantity: 100
Since this order has the same price as Sell Order 1, it will be executed third.
4: Sell Order 2: Price: $20, Quantity: 200
Since this order has the third highest price, it will be executed fourth.
5: Sell Order 5: Price: $20, Quantity: 400
Since this order has the same price as Sell Order 2, it will be executed fifth.
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Of the animals on a farm 60% are cows and the rest are sheep. When 260 more cows and sheep are added to the farm, the percent of cows increases by 20% and the number of sheep doubles. Find the number of sheep originally on the farm.
The number of sheep originally on the farm will be equal to 200.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from.
Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Let the number of animals originally at the farm is x.
60% of the animals are cows.
So, 0.6x are cows.
If there are 60% cows, then there are 40% of sheep.
So, 0.4x are sheep.
The quantity of sheep multiplies when many cows and sheep were introduced to the property.
As a result, the farm now has the same amount of sheep that it did before.
Number of sheep added = 0.4x
There are total 260 animals added to the farm.
So,
Number of sheep added = 260-0.4x
Total number of animals = x + 260
The percentage of cows increased to 20%.
Initial number of cows at farm + cows added = Initial number of cows at farm + 20% of the total cows initially at the farm.
0.6x + (260-0.4x) = 0.6x + 0.2(0.6x)
0.6x+260-0.4x = 0.6x+0.12x
0.2x+260 = 0.6x+0.12x
0.2x+260 = 0.72x
260 = 0.52x
x = 260/0.52
x = 500
Thus, the farm's initial animal population was 500.
0.6x = the amount of cows that were first on the farm= 0.6(500) = 300 cows
0.4x = the amount of sheep that were initially on the farm = 0.4(500) = 200 sheep
0.4x = Sheep added = 200
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the quality-control manager of a large factory is concerned about the number of defective items produced by workers. thirty workers at the factory agree to participate in a study of three different incentive plans to help reduce the number of defective items produced. the plans will be randomly assigned to the workers so that 10 workers received each plan. the reduction in the number of defective items produced by each worker will be recorded two weeks after the plans are implemented. which of the following best describes why a completely randomized design is an appropriate design to use in this situation? responses
A completely randomized design is an appropriate design to use in this situation because There is no blocking variable, and incentive plans will be randomly assigned to the workers.
A completely randomized design (CRD) is the simplest design for comparative experiments because it employs only two basic experimental design principles: randomization and replication.
By randomization, we mean that the experimental units' run sequence is determined at random.
Treatments are assigned to experimental units or plots in a completely random manner in CRDs. CRD can be used for either single-factor or multifactor experiments.
According to the question,
The quality control manager of a large factory wants to find out the number of defective items . For that 10 workers are selected Randomly and these worker will work on item according 3 incentive plans Means Replication is 3.
Hence , A completely randomized design is an appropriate design to use in this situation because There is no blocking variable, and incentive plans will be randomly assigned to the workers.
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Situation:
An archaelogist in Turkey discovers a
spear head that contains 55% of its
original amount of C-14.
PLS HELP AHHHHH
The age of the spear head to the nearest year is 8 years.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since the archaelogist in Turkey discovers a spear head that contains 55% of its original amount of C-14. The amount will be:
= 55% × 14
= 0.55 × 14
= 7.7
The age of the spear will be 8 years.
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Complete question
An archaelogist in Turkey discovers a spear head that contains 55% of its original amount of C-14. Find the age of the spear head to the nearest year.
you are managing a portfolio of $1 million. your target duration is 10 years, and you can invest in two bonds, a zero-coupon bond with maturity of five years and a perpetuity, each currently yielding 7.8%.
40% percentage of your portfolio in the zero-coupon bond with a maturity of 5 years and 60% of your portfolio in the perpetuity. This would result in an overall duration of 10 years.
To achieve your target duration of 10 years, you would need to allocate your investments in a way that has an overall duration of 10 years. You could do this by investing 40% of your portfolio in the zero-coupon bond with a maturity of 5 years and 60% percentage of your portfolio in the perpetuity. This would result in an overall duration of 10 years.
Duration of zero-coupon bond = 5 years
Duration of perpetuity = infinity
Weighted duration of portfolio = (0.4 x 5) + (0.6 x infinity) = 10 years.
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The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y).
Temp 170 172 173 174 174 175 176 177 Ratio 0.76 1.27 1.48 0.99 0.99 1.02 1.12 1.70 Temp. 180 180 180 180 180 181 181 182 Ratio 1.43 1.50 1.57 2.15 2.11 0.88 1.33 0.84 Temp. 182 182 182 184 184 185 186 188 Ratio 1.73 2.04 2.70 1.59 2.62 3.10 1.89 3.18 (a) Determine the equation of the estimated regression line. (Round all numerical values to five decimal places.) y = . 1017x-16.592 レ 19174x (b) Calculate a point estimate for true average efficiency ratio when tank temperature is 182. (Round your answer to four decimal places.) 1.9174 (c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 182. (Round your answers to four decimal places.) (182, 0.84) 1581 (182, 1.73) (182, 2.04) (182, 2.70)
The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate.
a) The equation of the estimated regression line is ŷ = - 16.592 + 0.1017x.
b) A point estimate is 1.9174 for true average efficiency ratio when tank temperature is 182.
c) The values of the residuals from the least squares line for the four observations for which temperature is 182 are -1.0774, -0.1874, 0.1226, 0.7826..
We have given the accompanying data on tank temperature (x) and efficiency ratio (y).
a) We have to find out the equation of the estimated regression line. Consider the calculations shown in the above table:
ΣΧ= 4308 ; ΣΥ= 39.99 ; ΣΧΥ = 7229.47 ;
ΣX² = 773790
Determine the slope and intercepts using the following formulas,
Slope b₁ = (n ΣΧΥ - ΣX ΣΥ)/(nΣΧ² - (ΣX)²)
=> b₁ = [24 (7229.47) - (4308) (39.99)]/(24(773790)-(4308)²)
=> b₁ = 1230.36/12096 = 0.10171626984
=> b₁ ≈ 0.1017
Intercept, b₀ = ΣY /n - b₁ΣΧ /n
=> b₀ = 39.99/24 - 0.1017×4308/24
= -16.592
Thus, the estimated regression equation of the form, ŷ = b₀ + b₁ x
ŷ = - 16.592 + 0.1017x
b) Calculate the point estimate for true average efficiency ratio when tank temperature is 182.
y = -16.592 + 0.1017x
=> y= -16.592 +0.1017 (182)
=> y= 1.9174
Therefore, the point estimate for true average efficiency ratio when tank temperature is 182 is 1.9174..
c)We have to find out the values of the residuals from the least squares line for the four observations for which temperature is 182.
From part (b), the value of ŷ is 1.9174.
The table below shows the residuals.
Vi ŷ e = y₁ - y
0.84 1.9174 -1.0774
1.73 1.9174 -0.1874
2.04 1.9174 0.1226
2.70 1.9174. 0.7826
Hence, we got all the required values.
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What is the rule that describes the translation ABC → A' B' C' ?
The rule that describes the translation will be as T<-3, 2>
Given,
Translation;-
Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same.
Here,
In order to move from A = (-3,3) to A' = (-6, 5), we must first move 3 units to the left and 2 units up.
Step 1's change causes x to become x-3.
Step 2's change causes y to become y+2.
When you combine these, (x, y) becomes (x-3, y+2).
That is equivalent to writing T<-3, 2>.
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Compute the orthogonal projection of [-2 2] onto the line through [ -1 5] and the origin. The orthogonal projection is [ __ __ ]
the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75] using unit vector.
First, we need to calculate the unit vector of the line. This can be done by subtracting the two given points and dividing the result by the magnitude of the vector:
[-1 5] - [0 0]
= [-1 5]
|[-1 5]| = sqrt(1^2 + 5^2) = sqrt(26) = 5.1
Unit vector = [-1/5.1 5/5.1] = [-0.196 0.980]
Next, we need to calculate the dot product of the vector [-2 2] and the unit vector [-0.196 0.980]. This will give us the scalar projection.
(-2)(-0.196) + (2)(0.980) = -0.392 + 1.960 = 1.568
Finally, we can calculate the orthogonal projection by multiplying the scalar projection by the unit vector.
[-0.196 0.980] (1.568) = [-0.301 1.527]
Rounding to two decimal places, the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75].
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Use the given information to prove that ∠QPR ≅ ∠SPR.
Given: QR ≅ SR
PQ ≅ PS
Prove: ∠QPR ≅ ∠SPR
By SSS rule of congruence
∠QPR ≅ ∠SPR
"Information available from the question"
In the question:
Use the given information to prove that ∠QPR ≅ ∠SPR.
Given: QR ≅ SR
PQ ≅ PS
Prove: ∠QPR ≅ ∠SPR
Now, According to the question:
In triangle PQR and triangle PRS
We can see that
QR ≅ SR (given)
PQ ≅ PS (given)
PR = PR (Common line)
By SSS rule of congruence
When all the sides of two triangles are congruent, the angles of those triangles must also be congruent. This method is called side-side-side, or SSS for short.
Hence, ∠QPR ≅ ∠SPR
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I need help with this question. I know the answer I jsut don't know how to get there. Please help!
The graph of f(x)=x2 is shown.
Use the parabola tool to graph g(x).
g(x)=(x+2)2−1
(Answer is (-2,-1) and (-3,0) )
Answer:
The graph of f(x) = x^2 is shown.
Use the parabola tool to graph g(x).
9(x)= (1 + x)^2 – 2
graph the parabola by first plotting its vertex and then plotting a second point on the parabola
Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
The value of the other points in the number line for each case are;
a) M = -2¹/₂
N = -1
R = 4
b) M = -1
P = 1
R = 1.6
c) M = -125
P = 125
N = -50
d) N = -6
P = 15
R = 24
How to interpret Number Lines?a) We are given that P = 2¹/₂
From the point 0 of the number line to point P is 5 units and as such;
Each unit = 2¹/₂/5 = ¹/₂
Thus;
M = -2¹/₂
N = -1
R = 4
b) We are given that N = -0.4
From the point 0 of the number line to point N is 2 units and as such;
Each unit = 0.4/2 = 0.2
Thus;
M = -1
P = 1
R = 1.6
C) We are given that R = 200
From the point 0 of the number line to point R is 8 units and as such;
Each unit = 200/8 = 25
Thus;
M = -125
P = 125
N = -50
D) We are given that M = -15
From the point 0 of the number line to point N is 5 units and as such;
Each unit = 15/5 = 3
Thus;
N = -6
P = 15
R = 24
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The sum of the first 15 terms of the sequences 7, -14, 28, -56, 112,...
The sum of the first 15 terms of the geometric sequences will be 76,456.33.
What is the sum of a geometric sequence?The aggregate to boundless GP implies, the number of terms in a limitless GP.
Let a₁ be the first term, n be the total number term, and r be a common ratio.
Then the sum of the geometric sequence will be
Sₙ = [a₁ (1 - rⁿ)] / (1 - r)
The geometric sequence is given below.
7, -14, 28, -56, 112,...
The first term of the geometric sequence is 7 and the common ratio of the geometric sequence is given as,
r = - 14 / 7
r = - 2
Then the sum of the first 15 terms of the sequences will be given as,
S₁₅ = [7 (1 - (-2)¹⁵)] / (1 - (-2))
S₁₅ = [7(1 + 32,768)] / 3
S₁₅ = -229,369 / 3
S₁₅ = 76,456.33
The sum of the first 15 terms of the geometric sequences will be 76,456.33.
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The sides of AUVW are UV = 8x-19,
VW = 5x-5, and UW = 9x -22. If the
perimeter of AUVW is 86, list the angles in order from largest to smallest.
Solve the equation.
9(z + 3) = 45
Answer:
Step-by-step explanation:
9z + 27 = 45
9z= 18
z= 18/9
z = 2
Answer:
[tex]z=2[/tex]
Step-by-step explanation:
[tex]9(z+3)=45\\9z+27=45\\9z=45-27\\9z=18\\z=\frac{18}{9}\\ z=2[/tex]
Hope it helps you
-3x+2y=9 X-3y=4 solve this system of equations by using the scientific method, the ordered pair of solutions is written in the format (x,y)
The ordered pairs of the solution to the system of equation are (-5, -3).
How to solve system of equation?System of equation can be solved using methods like substitution method, elimination method and graphical method.
Let's solve the system of equation by substitution method.
Therefore,
-3x + 2y = 9
x - 3y = 4
Hence,
x = 3y + 4
Substitute the value of x in equation(i)
-3x + 2y = 9
-3(3y + 4) + 2y = 9
-9y - 12 + 2y = 9
-7y = 9 + 12
-7y = 21
y = 21 / -7
y = -3
Let's find x using equation(ii)
x = 4 + 3y
x = 4 + 3(-3)
x = 4 - 9
x = -5
Hence, x = -5 and y = -3
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i need help it's hard
The teeth on the key are busted and now they must be readjusted and the code is 12y×2x^2.
What is code?Coding in Math is a series of the independent, standalone modules to that is use coding to reinforcement and extended by to the students' understandings of to the math.! As students learning major programming is concepts, they will development math-related to the projects that is demonstrate their proficiency by math and to the computer science.
18xy^2z^2=2xy^2 z×9xz
20xy^2z= 2xy^2z×10x^2
11xy^z=xyz^2×11
180y=9y×2x
24xy =12y×2x^2
(Take the greatest common factor)
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A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured? А Bimodal B Uniform SO с Approximately normal D Strongly skewed to the left E) Strongly skewed to the right 11 8 GA N TALK ESTU MacBook Pro esc O F3 090 F FS FO aa E7 DI TO DO F9 F10 ! 1 $ % A 12. 2 3 4 C 5 & 7 6 3 0 * 8 9 ВЫ В ㅉ ㅈ CC C 77 u i Q W E R E T Y U HHHH 0 Р L o
The best description of the shape of the sampling distribution is C. Approximately normal.
The sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.
A sampling distribution is the distribution of a statistic calculated from a random sample of data. In this case, the statistic is the sample proportion of those who will be cured with the skin cream.
The Central Limit Theorem states that the sampling distribution of a statistic will be approximately normal if the sample size is large enough, regardless of the shape of the underlying distribution.
Since the sample size of 100 people is large enough, the sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.
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The question is -
Certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured? А. Bimodal B. Uniform C. Approximately normal D. Strongly skewed to the left E. Strongly skewed to the right.
Given that events A and B are independent with
P(A) = 0.42 and P(B) = 0.05, determine the value
of P(AN B), rounding to the nearest thousandth, if
necessary.
Answer
P(A∩B) = 0.021
Step-by-step explanation:
For independent events P(A∩B) is the same as P(A)*P(B) so for this 0.42*0.05 = 0.021