The vertex of the graph (3, 0)
What is Vertex of graph?
A vertex or node is the basic building block of a graph in discrete mathematics, and more precisely in graph theory. An undirected graph is made up of a set of vertices and a set of edges, whereas a directed graph is made up of a set of vertices and a set of arcs.
According to question
when f(x) = 0
that's the minimum point, the vertex, or the intersection of two lines, g(x) = 0.25x − 0.75 and h(x) = 0.75 - 0.25x
Therefore
find the intersection of Two line which are
⇒ y = x/4 - 3/4
⇒ 4y = x - 3 → First line
⇒ y = 3/4 - x/4
⇒ 4y = 3 - x → Second line
So x - 3 = 3 - x
2x = 6 ,
x = 3
And y = 0
hence the vertex of f(x) = (3, 0)
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in the morning there were t people at the beach. later at noon, 2/7 of the people left the beach and there were 30 people left on the beach. find t
Answer:
42
Step-by-step explanation:
If 2/7 left that means that 5/7 are still there.
5/7x = 30 Multiple both sides by 7/5
x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]
x = 42
A sinusoidal function whose period is π2
, maximum value is 10, and minimum value is −4 has a y-intercept of 10.
What is the equation of the function described?
Responses
f(x)=7cos(4x)+3
f ( x ) = 7 cos ( 4 x ) + 3
f(x)=7sin(4x)+3
f ( x ) = 7 sin ( 4 x ) + 3
f(x)=7cos(4πx)+3
f ( x ) = 7 cos ( 4 π x ) + 3
f(x)=7sin(4πx)+3
The equation of the function described as; y = 7 sin ( 4x + π/2 ) + 3
The general equation of the sine curve can be written as;
y = a sin ( nx + α ) + b
where : a is the amplitude, n = 2π/period, b = shift in the direction of y
α°= shift in the direction of x
We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.
Thus,
a = (maximum - minimum)/2 = (10 - -4)/2
a = 7
n = 2π/period = 2π/(π/2)
n = 4
b = maximum - a = 10 - 7
b= 3
To find α as y-intercept = 10
y = 10 at x = 0
Substitute in the general function;
y = a sin ( nx + α ) + b
10 = 7 sin ( 4*0 + α ) + 3
Thus, we have;
sin α = 1
α = π/2
So, the equation of the function described is;
y = 7 sin ( 4x + π/2 ) + 3
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You brought popular game on sale for $20 and want to sell it on eBay. You want to mark up the toy 60%. What did you sell it for?
What is the freezing point, in C, of a 2.75 m solution of C8H18 in benzene?
The freezing point of the 2.75 m solution of octane in benzene is -8.56 °C.
The freezing point of a solution is the temperature at which the solution becomes a solid. The freezing point of a solution is lower than the freezing point of the pure solvent because the solute particles interfere with the movement of the solvent molecules, which slows down the freezing process.
To determine the freezing point of a solution, we can use the freezing point depression equation:
ΔTf = Kf x molality
where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent, and molality is the concentration of the solute in the solution expressed in moles of solute per kilogram of solvent.
To find the freezing point of a 2.75 m solution of C8H18 (octane) in benzene, we need to know the freezing point depression constant for benzene, which is 5.12 °C/m. We can then use the equation above to calculate the change in freezing point:
ΔTf = 5.12 °C/m x 2.75 m = 14.06 °C
To find the freezing point of the solution, we need to subtract the change in freezing point from the freezing point of the pure solvent. The freezing point of pure benzene is 5.5 °C, so the freezing point of the 2.75 m solution of octane in benzene is:
5.5 °C - 14.06 °C = -8.56 °C
This means that the freezing point of the 2.75 m solution of octane in benzene is -8.56 °C. At this temperature, the solution will become a solid.
which graph represents the equation y =1/3 x + 2
The graph of the equation y = (1/3)x + 2 is passing through points
(3, 3) and ( -3, 1).
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A linear equation y = (1/3)x + 2.
Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.
When x = 3, y = 3 ⇒ (3, 3).
When x = - 3, y = 1 ⇒( -3, 1).
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Which statement correctly demonstrates using limits to determine a vertical asymptote of g (x) = StartFraction 2 (x + 4) squared Over x squared minus 16 EndFraction
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = negative infinity and limit of g (x) as x approaches 4 plus = infinity
The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
How to find the vertical asymptote of a function?A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.
A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;
In a graph, these vertical asymptotes are given by dashed vertical lines.
An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.
We are given the function;
g(x) = 2(x + 4)²/(x² - 16)
Simplifying the denominator gives;
(x² - 16) = (x + 4)(x - 4)
Thus, our function is;
g(x) = 2(x + 4)²/[(x + 4)(x - 4)]
(x + 4 ) will cancel out to give;
g(x) = 2(x + 4)/(x - 4)
Vertical asymptote:
Point in which the denominator is 0, so:
(x - 4) = 0
x = 4
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What is the fourth root of 625
The required answer is the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
To find the fourth root of 625, we need to determine the number that, when raised to the power of 4, equals 625. Here's the step-by-step process:
Step 1: Start with the number 625.
Step 2: Take the fourth root of 625.
Since we're looking for the fourth root, we need to find a number that, when raised to the power of 4, equals 625.
Step 3: Determine the number that, when raised to the power of 4, equals 625.
To find this number, we can use the concept of exponentiation. Let's denote the unknown number as "x". Mathematically, we have [tex]x^4 = 625[/tex]..
Step 4: Solve the equation [tex]x^4 = 625[/tex].
To solve this equation, we need to find the value of x. Taking the fourth root of both sides of the equation, we have [tex]\sqrt[4]{(x^4)} =\sqrt[4] {625}.[/tex]
The fourth root of 625 is (625)^(1/4).
Step 5: Simplify the expression.
We can simplify [tex]\sqrt[4]{ 625}[/tex] as follows:
[tex]\sqrt[4]{ 625} = \sqrt[4]{ 5^4}= 5^{4/4} = 5^1 = 5.[/tex]
Therefore, the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
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Check the binomial distribution to see whether it can be approximated by the normal distribution. Round p and q to 1 decimal place, as needed. n = 95 P = 0.96 9 -0.04 np - and ng Is a normal approximation appropriate ? Yes No
As per the binomial distribution, the value of the normal approximation is 0.6573
The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.
Here we have given that n = 95 P = 0.96 and q = 0.04
Now, here we have to check the binomial distribution to see whether it can be approximated by the normal distribution.
While we looking into the given question we know that the value of n = 95 P = 0.96.
Then as per the binomial distribution formula, the normal distribution is calculated as,
=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴
When we simplify this one then we get the value as 0.6573
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A line is graphed on the coordinate grid to the right.
Which equation describes the line?
A.y=x/2+1/3
B.y = x/3+1/2
C.y=x/2+15 1/2
D.y=x/3+15 1/2
The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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answer question below
The equations that represent a linear function are :
y = 2x - 94x + y = 7y = 1 / 2 xHow to know a linear function?A linear function is a function that represents a straight line on the coordinate plane. The degree of a linear equation must be 0 or 1 for each of its variables.
A linear function has the following form. y = mx + b.
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
Therefore, linear function can be represented in slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, the linear function of the equations are as follows;
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Type your answers into the boxes.
What are the next two numbers in this sequence?
45.7
46.2
46.7
47.2
Answer:
Step-by-step explanation:
Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7
What is BC?
BC= units?
The value of BC = 25 using properties of triangle.
What are properties of triangle ?
Let us discuss here some of the properties of triangles.
1. A triangle has three sides and three angles.
2. The sum of the angles of a triangle is always 180 degrees.
3. The exterior angles of a triangle always add up to 360 degrees.
4. The sum of consecutive interior and exterior angle is supplementary.
Properties for isosceles:
Isosceles triangles are those triangles that have at least two sides of equal measure.
1. Two equal sides and two equal angles.
2. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.
3. The side opposite the vertex angle is called the base and base angles are equal.
Using 1st property,
in given triangle two angles are equal then opposite side will also be equal.
So, AB = AC
i.e. 4x+4 = 6x-14
4+14 = 6x-4x
18 = 2x
x = 9
Putting value of x in BC
BC = 2*9 +7
= 18+7
= 25.
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Say that we have three voters deciding among seven candidates, a, b, c, d, e, f, g. Their preference orderings are as follows.
1 2 3
(Best) c f g
a b b
e c c
g g d
b a e
d d f
(W orst) f e a
a. Find the top cycle.
b. For each candidate in the top cycle, write down an agenda (a sequence of majority rule
votes) that makes that candidate win (you can write the agenda as a tree).
c. Say that the voters use the Borda count system (each voter gives 6 points to their first
choice, 5 points to their second choice, and so on) to decide among the candidates. Which
candidate wins?
d. Is the Borda count winner also the Condorcet winner?
e. Which candidate does the worst in the Borda count?
f. Say that the person who does worst in the Borda count (your answer in part e. above) is
embarrassed about their poor performance, and tries to convince another candidate to drop
out so that they are no longer the worst person. If a candidate drops out, there would be
six candidates, and hence in the Borda count system, each voter gives 5 points to their first
choice, 4 to their second choice, and so forth. If a candidate drops out, is it possible for the
person who was originally the worst to no longer be the worst? If so, which candidate should
drop out? If not, please explain why not.
A. The top cycle in this case is a -> b -> c -> a.
B. The agenda that wins the candidate is:
First vote:
a vs b -> a wins
Second voice:
versus. c -> a wins
The agenda that Candidate B wins is:
First vote:
b vs c -> b wins
Second Voice:
b vs a -> b wins
The agenda that Candidate C wins is:
First vote:
c vs a -> c wins
Second Voice:
c vs b -> c wins
C. Using the Borda count system, the candidates' scores are as follows:
a:
18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)
b:
18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)
c:
18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)
d:
12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)
e:
12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)
f:
12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)
g:
6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)
Therefore, candidates a, b, and c tie for first place with 18 points each.
D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.
E. The candidate with the worst score in the Borda count is g of 6 points.
F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:
a:
15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)
b:
15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)
c:
15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)
Day:
10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)
e:
10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)
f:
10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)
In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.
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Witch rate is equivalent to 15 milesper hours
Answer: 60 miles per 4 gallons. If that's the question.
Step-by-step explanation:
PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
Answer:
Since YA=AX, XB=BZ, ZC=CY, it follows that A, B and C are the midpoints of the sides TX, XZ, ZY. AB, BC, AC are parallel to the sides and equal to their half. In fact, AB = YC=ZC. Therefore BC=AY.)
Good luck;)
Step-by-step explanation:
Given: ABCD is a parallelogram with AE = 9x−5, AC = 14x + 34. Find AC
The value of AC according to given equation of Parallelogram is 188 units.
What is parallelogram?
In elementary geometry, a parallelogram may be a quadrilateral with 2 pairs of parallel sides. the alternative or facing sides of a quadrangle square {measure} of equal length
Main body:
according to question:
AE = 9X-5
AC = 14X+34
as E is midpoint of AC so , we can say
2AE = AC
2(9x-5)= 14x+34
18x-10= 14x+34
4x = 44
x = 11
Now we need to find AC = 14x+34
= 14*11+34
= 188 units
Hence the value of AC according to given equation of Parallelogram is 188 units.
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I need. Help with this question
Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
What is differentiation?
In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.
Main body:
by using product rule;
Let = u = x² + 4x + 6
⇒ du/dx = 2x + 4 .
Now y = u⁵
⇒ dy/dx = 5u⁴ .
dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)
= 5 * (x² + 4x + 6)⁴ * (2x + 4)
= 5(2x + 4) * (x² + 4x + 6)⁴
hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
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consider the value of t such that 0.05 of the area under the curve is to the right of t. step 2 of 2: assuming the degrees of freedom equals 18, select the t value from the t table.
Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306
Degree of freedom {df}=18
We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t
It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]
As we know, t distribution provides the cumulative probability
As the value of the total area under the t distribution will 1
So, we can write it as:
[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]
Now, using excel, we can easily calculate the t-critical value as follows
=T. INV ( Probability, DF)
Where Probability is the area and DF is the degree of freedom,
Now we will enter these values in excel:
=T. INV (0.95,18)
t-critical value can also be found using t table
Look up for df = 18, in very first column
Now look up for 0.05 in one tail row
Now intersect both of them to get the t-critical value
We will get it as: 2.306
So t-critical value will be =2.306
[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]
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Let f:R→S be a surjective homomorphism of rings with identity.
(a) If R is a PID, prove that every ideal in S is principal.
(b) Show by example that S need not be an integral domain.
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient
Let f:R⇒S be a surjective homomorphism of rings with identity.
We have to find if R is a PID, prove that every ideal in S is principal.
We know that,
Let I be the ideal of S
Since f is sufficient homomorphism.
So, f⁻¹(I) is an ideal of R.
Since R is PID so ∈ r ∈ R such that
f⁻¹(I) = <r>
I = <f(r)>
Therefore,
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
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t=10-x identify to dependent and independent variable
Answer: t is the dependent variable and x the independent variable
Step-by-step explanation: t is the dependent variable it depends upon the values of x that we put in.
x is the independent variable as we can use whatever values we want for x it is not affected by t
1. Which equation describes the line with
slope -4 and y-intercept 2?
A y=-4x+2
B y=-4x-2
C y=4x-2
D y = 4x + 2
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of the line with slope -4 and y-intercept 2 is y = (-4)x + 2.
How could you organize the weighting and grades information differently so that Oscar's and Reagan's final grades are given by WG?
Answer i just need points
Step-by-step explanation: maybe 90
Is there anyone that can help me with a finance question?
Answer:
Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.
Step-by-step explanation:
Select all the points that are on the graph of the line Y=2x+5
Answer:
Some points that are on this line are:
(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)
A train travels at 80 miles per hour. An equation can be written that compares the time (t) with the distance (d). What is the domain and range?
1. The domain is distance (d) and the range is time (t).
2. The domain is time (t) and the range is distance (d).
3. The domain is time (t) and the range is 80.
4. The domain is 80 and the range is time (t).
The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.
What are domain and range?
The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
From the given question, and the above definition of domain and range,
the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value
Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.
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two different two-digit whole numbers are selected at random. what is the probability that their product is less than 200. express your answer as a common fraction. (hints: (l) there are 90 different two-digit numbers, (2) the pair {10, 11} produces the smallest product and the pair {11, 18} produces the largest product less than 200).
The probability that the product of the two two-digit numbers is less than 200 is given as follows:
43/8010.
How to calculate the probability?A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes.
There are 90 different two-digit numbers, hence the number of total outcomes for the product is of:
90 x 89 = 8010.
(the numbers have to be different)
The desired outcomes which result in a product of less than 200 are of given as follows:
10 multiplied by 9 numbers, from 11 to 19.11 multiplied by 10, 12, 13, 14, 15, 16, 17, 18. (8 numbers).12 multiplied by 10, 11, 13, 14, 15, 16. (6 numbers).13 multiplied by 10, 11, 12, 14, 15 (5 numbers).14 multiplied by 10, 11, 12, 13. (4 numbers).15 multiplied by 10, 11, 12, 13. (4 numbers).16 multiplied by 10, 11, 12. (3 numbers).17 multiplied by 10, 11. (2 numbers).18 multiplied by 10, 11. (2 numbers).Hence the number of desired outcomes is given as follows:
9 + 8 + 6 + 5 + 4 + 4 + 3 + 2 + 2 = 43.
Meaning that the probability is of:
43/8010.
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In the last 24 days, it rained 18 days. What is the ratio of rainy days to total days written as a percent?
The ratio of rainy days to total days written as a percent will be 75%.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.
Since in the last 24 days, it rained 18 days.
Number of rainy days = 18.
Number of total days = 24
The ratio of rainy days to total days written as a percent will be:
= Number of rainy days / Total days × 100
= 18/24 × 100
= 3/4 × 100
= 75%
Therefore, the ratio is 3:4 which is 75%.
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according to wine-searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. random ratings of a pinot noir recently produced by a newly established vineyard in follow: excel file: data07-11.xlsx 87 91 86 82 72 91 60 77 80 79 83 96 a. develop a point estimate of mean wine score for this pinot noir (to decimals). 82.00 b. develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals). 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.
Below table showing calculation of Point Estimate of Mean and Standard Deviation:
Score X-X’ (X-X’)^2
87 5 25
91 9 81
86 4 16
82 0 0
72 -10 100
91 9 81
60 -22 484
77 -5 25
80 -2 4
79 -3 9
83 1 1
96 14 196
984 1022
Mean(X’) = Total Score/n
n = Total number = 12
X’ = 984/12 = 82
Standard Deviation (σ) = √∑(X-X’)^2/(n-1)
σ = √1022/(12-1)
σ = √1022/ 11
σ = 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389
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Cylinders A and B are similar solids. The base of cylinder A has a circumference of 47 units. The base of cylinder B
has an area of 97 units.
The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
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The factor that produces the corresponding dimensions of cylinder B is: 3/2.
What are Similar Solids?Similar solids have the same shape but different sizes, and which means the ratio of their corresponding linear measurements are the same.
How to Find the Scale Factor of Similar Solids?To find the scale factor of similar solids, you can use the formula:
scale factor = (size of the similar solid) / (size of the original solid)
For example, if you have two similar solids, one with a volume of 64 cubic units and the other with a volume of 16 cubic units, the scale factor would be:
scale factor = (16 cubic units) / (64 cubic units) = 1/4
This means that the smaller solid is 1/4 the size of the larger solid.
Given the following:
Circumference of the base of cylinder A = 4π units [the radius = 2 units]
Area of the base of cylinder B = 9π units² [the radius = 3 units]
Scale factor = radius of the base of cylinder B / radius of the base of cylinder A
Scale factor = 3/2
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Complete Question:
Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units. The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
URGENT!!!!
Find z such that 7% of the area under the standard normal curve lies to the right of z.
The value of z such that 7% of the area under the standard normal curve lies to the right of z is approximately -0.4
How to find z such that 7% of the area under the standard normal curve lies to the right of z?
To find the value of z such that 7% of the area under the curve lies to the right of z, we need to find the value of z such that 43% of the area lies to the left of z.
This value of z is known as the 43rd percentile of the standard normal curve.
We can use a table of the standard normal distribution, also known as the z-table, to find the value of z corresponding to the 43rd percentile.
According to the z-table, the value of z corresponding to the 43rd percentile is approximately -0.4
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