The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder [tex]\frac{x^2}{25} +\frac{y^2}{9}[/tex] is 15π√150 and this can be determined by using the given data.
We are given the two equations are:
10x + 7y + z = 4---------(1)
[tex]\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)[/tex]
equation(1) is written as
z = 4 - 10x - 7y-----------(3)
The surface area is given by the equation:
A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)
compare equation(4) with equation(3) we get the values of ∂f/∂x and
∂f/∂y
∂f/∂x = -10
∂f/∂y = -7
substitute these values in equation(4)
A(S) = ∫∫√[(-10)² + (-7)² + 1]dA
A(S) = ∫∫√[100 + 49 + 1]dA
A(S) = ∫∫√[150]dA
A(S) = √150 ∫∫dA
Where ∫∫dA is the elliptical cylinder
From the general form of an area enclosed by an ellipse with the formula;
comparing x²/a² + y²/b² = 1 with x²/25 + y²/9 = 1, from that we get the values of a and b
a = 5 and b = 3
So, the area of the elliptical cylinder = πab
Thus;
A(S) = √150 × π(5 × 3)
A(S) = 15π√150
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solution of equation 5x / 3 + 2 / 3 = 5
Answer:
x = 13/5 or 2.6
Step-by-step explanation:
First, multiply both sides of the equation by 3.
This leaves us with 5x + 2 = 15.
Next, subtract 2 from both sides to get 5x = 13.
Finally, divide 13 by 5 to get x = 13/5. This cannot be simplified.
Square ABCD is reflected about side BC. Which of the following statements are true? Select three that apply.
Vertex B is the midpoint of AA'.
Side BC is parallel to AA.
The length of CD is equal to the length of C'D'.
Vertex C and vertex C are located at the same point.
Reflection is a type of rigid transformation in which an object is flipped about a reference point or line to produce the required image. The three statements that apply are:Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point
What i Rigid transformation?Rigid transformation is a process in which the size, orientation or position of a given object can be changed by applying some principles. Types of rigid transformation are: reflection, translation, dilation, and rotation.
In the given question, the required statements that apply are:
Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point
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Help pls I put in a photo
Answer:
m∠D = 49°
m∠E = 41°
m∠F = 90°
Step-by-step explanation:
We know a triangle's angles add up to 180, so we can create an equation and solve for x. We also know the little box represents 90 degrees.
Given:
90° + 5x° + 14° + 3x° + 20° = 180°
Combine like terms:
8x° + 124° = 180°
Subtract 124 from both sides of the equation:
8x° = 56°
Divide both sides of the equation by 8:
x = 7
Now, we will plug this value of x back into the angles to solve. Again, the little box represents that Angle F is equal to 90 degrees.
m∠D = 5x° + 14° = 5(7)° + 14° = 49°
m∠E = 3x° + 20° = 3(7)° + 20° = 41°
m∠F = 90°
simplify 5 6/7 + (-2 1/3) + 1 5/6
answer fastttttttttttttttttttttttttttttttt
plssssssssssss 20 points
Solution is 225/42 or 5.35
According to question
5 6/7 + (-2 1/3) + 1 5/6
As it is a mixed fraction we will first solve it
To solve it denominator will get multiplied with the whole number and the solution will be get added to the numerator and the new numerator will get formed.
∴ 41/7 +(-7/3) + 11/6
⇒246-98+77/42. (LCM of 7,3,6 is 42)
⇒225/42
∴5.35
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Mario and hi friend went to a movie on Saturday they left the houe at 5:15 PM. It took one hour and 20 minute to drive to the theater and they arrived 25 minute before the movie tarted. What time did the movie tart?
By applying the algebra concept, we can conclude that the movie that Mario and his friend watched starting at 7 PM
The use of algebra in everyday life.
Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used for financial planning, traveling time calculation, and so on.
In the above problem, we can take some notes as follows:
Departure time (x) = 5:15 PM
Travel time (t) = 1 hour 20 minutes
Arrival time (y) = 25 minutes
If z is the playing time of the movie, then z can be expressed mathematically in the following way:
z = x + t + y
= 5:15 + 1 hour 20 minutes + 25 minutes
= 6:60 PM or generally written 7:00 PM
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It costs a homeowner $6.00 to rent a set of hand tools, plus an additional $2.00 per hour for the rental. The function that models the cost, c, of renting tools for h hours is c = 2h + 6. Identify the solution that has the correct graph and the correct slope.
Answer:
y = 2x + 6
Step-by-step explanation:
The equation c = 2h + 6 represents the cost of renting tools for a given number of hours. The slope of this line is the rate at which the cost of renting the tools increases as the number of hours increases. Since the cost increases by $2.00 for each hour that the tools are rented, the slope of the line is 2.
A graph of this line would be a straight line with a slope of 2 and a y-intercept of 6. This means that the graph would pass through the point (0, 6), which represents the cost of renting the tools for 0 hours. The correct solution is therefore the graph of the equation y = 2x + 6.
list the reasons and statement reasons why line AE ≅ A.F
. Thanks!
Add missing statements and reasons.
Statement Reason
7. FC ≅ EC CPCTC8. AE ≅ A.F. Transitive propertyAn advertisement for a new toothpaste claims that it reduces cavities of children in their cavity-prone years. Cavities per year for this age group are normal with mean 3 and standard deviation 1. A study of 2,500 children who used this toothpaste found an average of 2. 95 cavities per child. Assume that the standard deviation of the number of cavities of a child using this new toothpaste remains equal to 1. (a) are these data strong enough, at the 5 percent level of significance, to establish the claim of the toothpaste advertisement? (b) do the data convince you to switch to this new toothpaste?.
At [tex]$5 \%$[/tex] level, the data is not strong enough to establish the claim of toothpaste advertisement.
It is recommended to switch to new toothpaste.
(a)
The null and alternative hypotheses are,
[tex]$$\begin{aligned}& H_0: \mu=3 \\& H_1: \mu < 3\end{aligned}$$[/tex]
Here, [tex]$\mu$[/tex] is the hypothesized mean.
Let the sample size be [tex]$n=2500$[/tex].
Let the sample mean be [tex]$\bar{x}=2.95$[/tex].
Let the population standard deviation be [tex]$\sigma=1$[/tex].
Since, the population standard deviation is known, one sample z-test is used to test the claim.
The test statistic is,
[tex]$$\begin{aligned}z & =\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \\= & \frac{2.95-3}{\frac{1}{\sqrt{2500}}} \\& =-2.5\end{aligned}$$[/tex]
So, the test statistic is, [tex]$z=-2.5$[/tex].
Let the level of significance be [tex]$\alpha=0.05$[/tex].
Find the critical value.
Using the standard normal distribution area tables, the left tail critical value is,
[tex]$$z_{0.05}=-1.645$$[/tex]
z score table attached at the end of solution.
The test statistic value is falls in the rejection region. Reject the null hypothesis. Therefore, it can be concluded that this does not support the null hypothesis at 5 percent level. So, at [tex]$5 \%$[/tex] level, the data is not strong enough to establish the claim of toothpaste advertisement.
(b)
The value of test statistic is also less than [tex]$-Z_{0.1}=-2.33$[/tex].
So, the claim cannot be established even at 1 percent level. It is recommended to switch to new toothpaste.
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one of two or more numbers that multiply together to form a specific product; a number that divides into another number with no remainder.
one of two or more numbers that multiply together to form a specific product; a number that divides into another number with no remainder is a factor.
What does a factor mean in its simplest form?A component is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, therefore the numbers we are adding are factors of a product because the product is divisible by them.
What types of factors are there?Which of these four main types of factoring are they? The Grouping technique, the Differences in Two Squares, the Total or Difference in Cubes, as well as the Greatest Common Factors (GCF) are the four primary methods of factoring.
Briefing:A factor is a value that completely divides another number. Consequently, the values we are multiplication are factors if multiplying two whole numbers results in a product.
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please help me with this question!! it would be helpful if you drew the rotated shape A on the grid. thank you!! i will vote brainliest to the first person to answer correctly :)
When rotated through 180° anticlockwise or clockwise about the origin, the new position of the above points is.
Rotate shape A [tex]$180^{\circ}$[/tex] about point (1,0) is (-1,0)
How do you rotate a shape about a certain point?
Move each point on a shape the specified number of degrees in a circle centered on the point of rotation to rotate it. Make sure that every new point is located the same amount of time away from the point of rotation as its corresponding original point.
There are 360 degrees in a circle's complete revolution. We discovered that a rotation of 270 degrees is virtually a full circle. We learned that a whole rotation of a circle is divided in half by 180 degrees. 90 degrees, or half of 180, are simple to identify as angles.
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The cash price of a refrigerator is rs 34 500. The hire purchase price is a deposit of Rs 6500 and 10 % simple interest on the outstanding balance,to be paifd in 24 monthly installments.Calculate the amount of each monthly instalment.
Amount of each monthly statement is 1400.
According to question ,
Cash price of refrigerator =34500
Deposit money=6500
Outstanding money=28000
Rate of interest=10%
Time period=24 months or 2 years
∴Simple interest =(principal ×rate of interest×time)÷100
⇒(28000×10×2)÷100
⇒5600
∴The total amount to be paid in 2 years is 28000+5600 =33600
∴Amount to be paid in one month =33600÷24=1400
∴Amount of each monthly statement is 1400.
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What is an equation of the line that passes through the point (-3, -7) and is parallel to the line 2x-3y=24 Please
An equation of the line that passes through the point (-3, -7) and is parallel to the line 2x-3y=24 can be found by taking the slope of the line 2x-3y=24 and using it to write the equation of the line in point-slope form. The slope of the line 2x-3y=24 is 3/2, so an equation of the line that passes through (-3, -7) and is parallel to the line 2x-3y=24 can be written in the form y-y₁ = m(x-x₁), where m is the slope of the line, which is 3/2 in this case. Plugging in the coordinates of the point (-3, -7) and the slope 3/2, we get the equation y-(-7) = (3/2)(x-(-3)), which simplifies to y+7 = 3/2(x+3). Multiplying both sides of the equation by 2/3 to get rid of the fraction on the right-hand side, we get the final equation: 2/3y + 14/3 = x + 3. This is the equation of the line that passes through the point (-3, -7) and is parallel to the line 2x-3y=24.
find a function f such that f '(x) = 3x3 and the line 81x + y = 0 is tangent to the graph of f.
To find the function, we need to find the values of x and y.
In the aforementioned example, x and y are the independent and dependent variables, respectively. A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).
As we know,
fx = 3x to the power 3
f(x) =
[tex]3x {}^{3 } \: dx \: + c \\ \\ fx = 3x { }^{4} \div 4 + c \\ \\ \\ \\ 3x {}^{3} = - 81 \\ \\ x \: = 243 \\ [/tex]
Hence x is 242
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question 1 options: what is the common difference in the sequence 7, 12, 17, 22, 27, ...? put the just the number in the blank.
The common difference in the sequence 7, 12, 17, 22, 27,… is that the difference between two numbers increases by five in the ascending order.
A sequence can be referred to or considered as the set of observations, which usually consists of numbers arranged in such a way that they described a common characteristic between them. A sequence can be exhaustive or inclusive, depending upon the numbers being used in the continuity of the sequence. It can also be said that a sequence is a logical arrangement.
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Complete question
what is the common difference in the sequence 7, 12, 17, 22, 27, ...?
Harry plans to charge $5 for cookies and $10
for cupcakes at the bake sale. He needs to
make a total of $75 to earn a profit. Write an
equation for the number of cookies (x) and
cupcakes (y) that Harry needs to sell at the bake sale.
Answer: 5x + 10y = or > 75
Step-by-step explanation:
make the number of cookies sold = x, and the number of cupcakes sold = y, since we don't know the number.
each cookie is $5 so it is 5 times x, and each cupcake is $10 so it is 10 times y.
add those together, and the sum must equal 75. If you have already learned this, it would be an equal to or greater than sign. if not then just use an equal sign.
find the curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1).
The curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1) is 0.178
In this question we need to find the curvature of r(t) = <3t, t^2, t^3> at the point (3, 1, 1).
The derivative of r(t) with respect to t is:
r'(t) = <3, 2t, 3t^2>
The point (3, 1, 1) corresponds to t = 1,
and r′(1) = <3, 2(1), 3(1)^2>
r'(1) = <3, 2, 3>
|r'(1)| = √(3^2 + 2^2 + 3^2)
|r'(1)| = √(9 + 4 + 9)
|r'(1)| = √(22)
|r'(1)| = 4.69
Now, r''(t) = <0, 2, 6t>
and r′'(1) = <0, 2, 6(1)>
r''(1) = <0, 2, 6>
r′(1) × r′′(1) = <0, 4, 18>
|r′(1) × r′′(1) |
= √(0^2 + 4^2 + 18^2)
= √(16 + 324)
= √340
= 18.44
So, the curvature of r(t) would be,
κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3
k(1) = 18.44 / 4.69³
k(1) = 0.178
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I can’t figure this one out
Answer:
g = 109 degree
h = 71 degree
m = 71 degree
k = 84 degree
Step-by-step explanation:
g= 109 degrees because it is a vertical angle to the 109-degree angle, that is why it is 109 degree
h= 71 degrees because they are supplementary angles which means they add up to 180 degrees. We see that one is 109 degrees, so the other must be 71 degrees.
k = 84 degrees because it is a vertical angle to the 84-degree angle, which is why it is 84 degrees.
m= 71 degrees because m and g must add up to 180 degrees, and we know that g is 109 degrees, so m is 71 degrees!
Help please
A.) (-12,-18)
B.) (18,12)
C.) (-18,-12)
D.) (12,-18)
I think the answer be 12 and -18 D
two groups of friends are taking taxis to a party in yardley. the first taxi leaves from the financial district and travels at 33 miles per hour. at the same time, the other taxi leaves from the marina and travels 45 miles per hour. the two taxis are 5 miles apart and heading directly toward each other. how much time will it take for the taxis meet?
Answer:
3.85 minutes
Step-by-step explanation:
You want to know the time it takes for taxis traveling 33 mph and 45 mph toward each other to meet if they start 5 miles apart.
Closing timeThe speed at which the taxis approach each other is (33 mph +45 mph) = 78 mph. The time it takes to close the 5-mile gap is ...
time = distance/speed
time = (5 mi)/(78 mi/h) = 5/78 h ≈ 0.0641 h
In minutes, the time is ...
(5/78 h)(60 min/h) = 300/78 min ≈ 3.85 minutes
__
Additional comment
That's about 3 minutes 50.8 seconds.
A group of scientists discovered a small creature at the bottom of the ocean that they called a "piknit". When this interesting creature dies, it explodes itself into a number of baby piknits called gogles. The scientists randomly selected 20 piknits from the sea-floor and measured their respective weights in grams. After the piknits died they counted the number of gogles that each piknit produced. They wanted to know if the weight of the piknits can be used to predict the number of gogles. What are the appropriate null and alternative hypotheses?
The weight of the piknits can be used to predict the number of goggles as there is a Linear equation in variables that may be defined as a linear courting among x and y, that is, variables.
In this case, let x is the impartial variable, and y relies upon it, so y is called as the established variable.
linear courting (or linear association) is a statistical period used to explain a straight-line courting among variables. Linear relationships may be expressed both in a graphical layout or as a mathematical equation of the shape y = MX + b.
"There is no linear relationship between the weight and the number of glasses"
"There is a linear relationship.
A. Yes, because the scatterplot shows a linear pattern.
C. Yes, because a random sample was taken from Piknits for the scatterplots of the 4th and 5th residuals.
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an objective function is necessary in a maximization problem but is not required in a minimization problem. true false
False. An objective function is necessary for both maximization and minimization problems.
An objective function is an equation that represents the goal of an optimization problem. It is used to evaluate the performance of a certain set of decisions. Regardless of whether the goal is to maximize or minimize an outcome, the objective function is a necessary component of an optimization problem. In a maximization problem, the objective function is used to determine the highest possible output that can be achieved. In a minimization problem, the objective function is used to determine the lowest possible output that can be achieved. Therefore, an objective function is necessary for both maximization and minimization problems.
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Swimming Pool On a certain hot summer's day, 240 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $510.75. How many children and how many adults swam at the public pool that day?
Answer:
39 children, 201 adults
Step-by-step explanation:
Let c = number of children
a = number of adults
c + a = 240
1.50c + 2.25a = 510.75
--------------------------------
1.50c + 1.50a = 360
1.50c + 2.25a = 510.75
-------------------------------
.75a = 150.75
a = 201, c = 39
I'LL GIVE BRAINLIEST!!
Tom is deciding how many people to take to the movies. The table below shows the cost for different sized groups of people.
The table shows that the cost of going to the movies with a group of people is equal to twice the number of people in the group. For example, if the number of people in the group is 2, the cost is 2 * 2 = $16. Similarly, if the number of people in the group is 4, the cost is 2 * 4 = $32, and if the number of people in the group is 8, the cost is 2 * 8 = $64. Therefore, if Tom wants to go to the movies with a group of n people, the cost will be 2 * n dollars.
15. Robert wants to invest $20,000 in an account
with an annual interest rate of 1.9%. How much
extra will he have after two years if he
compounds continuously, instead of collecting
simple interest monthly? Round answer to the
nearest dollar.
[A] $800
[B] $750
[C] $711
[D] $683
[E] $821
To find the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly, we need to calculate the compound interest on the investment.
The compound interest is calculated by multiplying the principal (the initial amount invested) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 1.9%/12 = 0.158% per month, and there are 12*2 = 24 compounding periods (12 months per year for 2 years).
The compound interest is therefore calculated as follows:
Compound interest = $20,000 * e^(0.158%*24) - $20,000
= $20,000 * e^0.3832 - $20,000
= $20,000 * 1.454 - $20,000
= $4,080 - $20,000
= -$15,920
So the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly is -$15,920. Therefore, the correct answer is [A] $800.
PLS HELP!!! WILL GIVE BRAINLIEST :)
Answer:
1/ We use the SSS method to prove that triangle CBD = triangle ABD
2/ We use the AA method to prove that <CBD equal < ABD
Step-by-step explanation:
1/ SSS, or side side side method, is the method we use to see if triangles are the same or not, and we know that the sides of both triangles are equal; this proves that both triangles are equal!
2/ AA, or Angle Angle method, is the method we use to see if the angles of triangles are the same or not, and we know that there are marks at <C and <A, these marks prove that both angles are equal! So, <CBD equal <ABD
If 5 log 3 3x=15, what is the value of x?
The value of x for the expression 5log(3x) = 15 is 6.7.
What is an expression?The mathematical expression combines 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 denote the logical syntax's operation order and other properties.
Given that the expression is 5log(3x) = 15. The value of x for the expression will be calculated as,
5log(3x) = 15
log(3x) = 15 / 5
log(3x) = 3
3x = e³
x = 20 / 3
x = 6.7
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Plot the piecewise function on the graph.
2x+6,
-5 < x < -2
-2 < x≤2
2
f(x) = { 1,
-3x+10,
What we should do is plot each part of the graph individually.
Step 1: Plot f(x) = 2x + 6 part
We know it starts at x = -5 (noninclusive) and ends at x = -2 (inclusive). Therefore, we can draw a line between the two points (-5, -4) and (-2, 2), with an open point at x = -5 and a closed point at x = -2
Step 2: Plot f(x) = 1 part
We know it starts at x = -2 (noninclusive) and ends at x = 2 (inclusive). Therefore, we can draw a line between the two points (-2, 1) and (2, 1), with an open point at x = -2 and a closed point at x = 2
Step 3: Plot f(x) = -3x + 10 part
We know it starts at x = 2 (noninclusive) and ends at x = 5 (inclusive). Therefore, we can draw a line between the two points (2, 4) and (5, -5), with an open point at x = 2 and a closed point at x = 5
You should end up with a graph that looks like the attached image!
The given function f(x) has been plotted in the graph piecewise with proper endpoints.
How t plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
As per the given piecewise function,
f(x) = [tex]\left \{ {{2x+6 \ \ \ \ -5 < x\leq -2}} \right.[/tex]
f(x) = [tex]\left \{ {{1 \ \ \ \ -2 < x\leq 2}} \right.[/tex]
f(x) = [tex]\left \{ {{-3x+10 \ \ \ \ 2 < x\leq 5}} \right.[/tex]
The function f(x) = 2x + 6 is a linear line with slope 2 and y-intercept 6 shown in red line -5 is excluded while - 2 is included.
The function f(x) = 1 is a constant horizontal line shown in the blue line that -2 excludes while 2 is included.
The function f(x) = -3x + 10 is a linear line with slope -3 and y-intercept 10 shown in the green line 2 is excluded while - 5 is included.
Hence "With the appropriate endpoints, the supplied function f(x) has been piecewise displayed in the graph".
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A random sample of 1012 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1012 adults surveyed, 514 indicated that televisions are a luxury they could do without. Complete parts (a) through (e) below.
(a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.
enter your response here
(Round to three decimal places as needed.)
Part 2
(b) Verify that the requirements for constructing a confidence interval about p are satisfied.
The sample
▼
is stated to be
can be assumed to be
cannot be assumed to be
is stated to not be
a simple random sample, the value of
▼
n
ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis
ModifyingAbove p with caret
n ModifyingAbove p with caret
n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis
is
enter your response here, which is
▼
greater than or equal to
less than
10, and the
▼
population proportion
sample proportion
population size
sample size
▼
cannot be assumed to be
can be assumed to be
is stated to not be
is stated to be
less than or equal to 5% of the
▼
population proportion.
sample size.
sample proportion.
population size.
(Round to three decimal places as needed.)
Part 3
(c) Construct and interpret a % confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without. Select the correct choice below and fill in any answer boxes within your choice.
(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)
A.
There is a
enter your response here% probability the proportion of adults in the country who believe that televisions are a luxury they could do without is between
enter your response here and
enter your response here.
B.
We are
enter your response here% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between
enter your response here and
enter your response here.
Part 4
(d) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?
It is
▼
possible, but not likely
not possible
likely
that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval
▼
does not contain
contains
enter your response here.
(Type an integer or a decimal. Do not round.)
Part 5
(e) Use the results of part (c) to construct a % confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.
Lower bound:
enter your response here, Upper bound:
enter your response here
(Round to three decimal places as needed.)
Answer: (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.
The point estimate for the population proportion is 514 / 1012 = 0.507.
(b) Verify that the requirements for constructing a confidence interval about p are satisfied.
The sample is stated to be a simple random sample.
The value of n * p = 1012 * 0.507 = 514.7796 is greater than or equal to 10.
The value of n * (1 - p) = 1012 * (1 - 0.507) = 497.2204 is greater than or equal to 10.
The population proportion is less than or equal to 5% of the population size.
Therefore, the requirements for constructing a confidence interval are satisfied.
(c) Construct and interpret a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without.
The 95% confidence interval for the population proportion is 0.507 +/- 1.96 * sqrt((0.507 * (1 - 0.507)) / 1012) = 0.507 +/- 0.0245 = (0.4825, 0.5315).
We are 95% confident that the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.4825 and 0.5315.
(d) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?
It is possible that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval contains 60%. However, it is not likely because the confidence interval is relatively narrow and the point estimate is far from 60%.
(e) Use the results of part (c) to construct a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.
The 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is 1 - 0.5315 = 0.4685 to 1 - 0.4825 = 0.5175. Therefore, the 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is (0.4685, 0.5175).
Step-by-step explanation:
Polynomial uing Remainder Theorem and Factor Theorem checking uing ynthetic diviion. X^4 - x^3 - 3x^2 4x 2 ÷ (x 2)
The remainder of the polynomial using the remainder theorem and factor theorem is 6.
Apply the remainder theorem,
When we divide a polynomial
f(x) by (x − c)
f(x) = (x − c)q(x) + r
f(c) = 0 + r
Here,
f(x)=(x−c)q(x)+rf(c)=0+r
and (x−c) is (x−(−2))
Therefore,
f(−2) = [tex](-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2[/tex]
= 16 + 8 − 12 − 8 + 2
= 6
Hence, the remainder of the polynomial using the remainder theorem is 6.
Whereas using the factor theorem and doing synthetic division, we get,
x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide
the coefficients of the polynomial as follows -
-2 | 1 -1 -3 4 2
-2 6 -6 4
-----------------------------------------
1 -3 3 -2 6
Hence, we get that 6 is the remainder when ([tex]x^4-x^3-3x^2+4x+2[/tex]) ÷ (x+2), using the factor theorem.
Read more about factor theorem:
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The complete question is -
Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, [tex]x^4-x^3-3x^2+4x+2[/tex] ÷ (x+2)
(b) consider a set of points that are uniformly distributed on the interval [0,1]. is the statistical notion of an outlier as an infrequently observed value meaningful for this data?
No, the statistical notion of an outlier as an infrequently observed value is not meaningful for this data.
Since the points are uniformly distributed on the interval [0,1], they should all be observed with the same frequency. Therefore, there are no outlier values.The statistical notion of an outlier is an infrequently observed value, meaning that it is an observation that is far away from the rest of the data. For a set of points that are uniformly distributed on the interval [0,1], however, all the points should be observed with the same frequency since they are evenly spaced. Therefore, there is no outlier value and the statistical notion of an outlier is not meaningful for this data.
Learn more about statistics here
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