A 90% confidence interval will be 82.5% < p < 84.9%
What is the confidence interval in statistics?
A confidence interval is the mean of your estimate plus and minus its variation. Within a certain level of confidence, this is the range of values you expect your estimate to fall between if you redo your test. In statistics, confidence is another word for probability.
We have to find a 90% confidence interval estimate of adults who used at least one prescription medication.
Here, the sample proportion [tex]\hat {p} = 0.837[/tex]
We know that for true population proportion confidence interval is given by
[tex]C.I.= \left( \hat{p}-z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} , \hat{p}+z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)[/tex]
For 90% confidence interval [tex]z_c[/tex] = 1.645 from normal table
[tex]C.I.= \left( 0.837-1.645\sqrt{\frac{0.837(1-0.837)}{3072}} , 0.837+1.645\sqrt{\frac{0.837(1-0.837)}{3072}}\right)[/tex]
[tex]C.I.= \left( 0.837-1.645\sqrt{\frac{0.837(0.163)}{3072}} , 0.837+1.645\sqrt{\frac{0.837(0.163)}{3072}}\right)[/tex]
[tex]C.I.= \left(0.837-1.645\times 0.007 , 0.837+1.645\times 0.007 \right)[/tex]
[tex]C.I.= \left(0.837-0.012 , 0.837+0.012\right)[/tex]
[tex]C.I.= \left(0.825 , 0.849\right)[/tex]
Converting our confidence interval into percentages by multiplying it by 100 we get (82.5%, and 84.9%).
Thus, a 90% confidence interval will be 82.5% < p < 84.9%.
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helpppppppppppppppppppppp plsssss..
Answer:
The function crosses the Y axis (the up down axis) at -1
Step-by-step explanation:
-
12-
Speed
(metres per
second)
0
1
Time (minutes)
5
A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 metres per
second.
It continues at this speed for 1 minute.
It then decelerates for 3 minutes until it stops at the next station.
The diagram shows the speed-time graph for this journey.
Calculate the distance, in metres, between the two stations.
In meters
The value of the total distance between the two stations is 2520m
How to calculate distance in meters ?The train runs with the following acceleration:
v = u + at
12 = 0 + a(120)
a = 0.1 m/s2.
Distance covered by the train in first part:
S = 1/2at^2
S = 1/2×0.1×(120)^2
S = 720m
Distance covered in second part:
S = ut
S = 12×60 = 720m
Train deceleration is given by
v = u+ at
0 = 12+a (180)
a = -1/15
Distance covered by the train in last part:
S = ut- 1/2at^2
S = 12(180) - 1/2(1/15)(180)^2
S = 2160 - 1080
S = 1080m
Therefore, The value of the total distance between the two stations is 720+720+1080 = 2520m.
The complete question is :A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 meters per second. It continues at this speed for 1 minute. It then decelerates for 3 minutes until it stops at the next station .Calculate the distance, in meters, between the two stations.
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Aven wants to buy a car in 4 years and needs a down payment of $2500. If she deposits $2000
now, with interest compounded continuously, what interest rate will she need to get her down
payment in time?
She needs to get her interest rate at will 5.592 %/year.
What is Compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest is applied per time period
t = number of time periods elapsed
Solving for rate r as a decimal
r = n[(A/P)1/nt - 1]
r = 12 × [(2,500.00/2,000.00)1/(12)(4) - 1]
r = 0.0559158
Then convert r to R as a percentage
R = r * 100
R = 0.0559158 * 100
R = 5.592%/year
Hence, she needs to get her interest rate at will 5.592 %/year.
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Eden and Kember are reading the same book. Eden says she has read 1/6 of the book.
Kimber says she has read 32 more pages than Eden. If Kimber is on page 60, how many pages
are there in the book?
In given word problem , number of total pages in the book is 168.
What is word problem?
Word problems in mathematics that concentrate on addition, subtraction, multiplication, and division, among other more precise operations A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Here Eden and Kember are reading the same book.
Here Eden reads 1/6 pages of the book. And Kimber reads,
=> 1/6(total pages)+32 which is 60.
=> 1/6(x)+32=60
=>1/6(x)=60-32=28
=> x = 28*6
=> x = 168.
Therefore total number of page in the book is 168.
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Tulip bulbs are sold in packs of 25 or 40
lily buys a pack of 25 and kiki buys in a pack of 40
what is the smallest number of packs they can each buy so they have the same number of bulbs?
show working please, if solve you will be thanks and marked as the brainliest.
Python py 9.14 lab: triangle area comparison (classes) given class triangle, complete the program to read and set the base and height of triangle1 and triangle2, determine which triangle's area is larger, and output the larger triangle's info, making use of triangle's relevant methods. ex: if the input is: 3.0 4.0 4.0 5.0 where 3.0 is triangle1's base, 4.0 is triangle1's height, 4.0 is triangle2's base, and 5.0 is triangle2's height, the output is: triangle with larger area: base: 4.00 height: 5.00 area: 10.00 code---------------------------------------- class triangle: def __init__(self): self.base = 0 self.height = 0 def set_base(self, user_base): self.base = user_base def set_height(self, user_height): self.height = user_height def get_area(self): area = 0.5 * self.base * self.height return area def print_info(self): print('base: {:.2f}'.format(self.base)) print('height: {:.2f}'.format(self.height)) print('area: {:.2f}'.format(self.get_area())) if __name__ == "__main__": triangle1 = triangle() triangle2 = triangle()
The full Python code is included below as an image, and it sets the base and height of triangles 1 and 2, then calculates the bigger area.
What is Python code?The program sets the bases and heights of both triangle objects using the set base() and set height() methods.The triangle with the largest area is then identified and printed using an if statement. The results of calling both triangles' get area() methods are used to calculate the area information.The print info() method is used to print out details about the triangle with the larger area once the larger area has been obtained.The full Python code is included below as an image, and it sets the base and height of triangles 1 and 2, then calculates the bigger area.To learn more about Python code refer to:
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Which is not a power function?.
A function containing a variable base raised to a fixed power is considered to be a power function.
when a function has a constant base raised to a variable power. This can be called an exponential function, not a power function A power function may be a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number. It is in the form of f(x)=kx^p, where k and p are the real numbers whereas k is the coefficient.
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1) Four cards labeled A, B, C, and D are randomly placed in four boxes labeled A, B, C, and D. Each box receives exactly one card.
In how many ways can the cards be placed in the boxes?
_______ ways
2)four cards labeled A, B, C, and D are randomly placed in four boxes labeled A, B, C, and D. Each box receives exactly one card.
Count the number of elements in the event that no box contains a card with the same letter as the box.
________ elements
If no box has a card with the same letter as the box, then count the number of elements as 24 ways.
Given that,
Four randomly selected cards with the letters A, B, C, and D are placed in the corresponding boxes. There is exactly one card in each box.
We have to find If no box has a card with the same letter as the box, then count the number of elements.
We know that,
What is the permutation?A permutation is a mathematical calculation that establishes the number of possible arrangements for a given set, taking into account the arrangement's order.
From the given information:
The permutation approach can be used to represent the four cards that are randomly placed in the four boxes and can be used to express the following:
=⁴P₄
Since no box contains a card that begins with the same letter as the box, it follows that
Card A can be inserted into a box four different ways,
Card B three different ways,
Card C two ways, and
Card D one way.
The four cards' permutation can then be calculated as follows:
⁴P₄=4!/0!=4×3×2×1/1=24.
Therefore, If no box has a card with the same letter as the box, then count the number of elements as 24 ways.
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3) What is the value of the slope of the line
that passes through the points (3, 10) and
(4, 12)? Show all work.
The slope of the line is 2.
From the question, we have
the slope of the line that passes through two points is given by:
m = (y1 - y2) / (x1 - x2)
=(10-12)/(3-4)
=2
The slope of the line is 2.
Slope of a Line :
The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's slope in mathematics.
Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate.
As a result, the formula for the change in y-coordinate with respect to the change in x-coordinate is m = change in y/change in x = y/x.
where the slope of a line is denoted by "m".
The graph of the equation y = mx + c has a slope of m, an intercept of m, and a y-intercept of c. In the slope-intercept version of the linear equation, m and c are real integer values.
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write 60:52 in the form n:1.
Converted form of ratio 60:52 in form n:1 is 10/7 : 1.
How to write a ratio in n:1 form?
In order that a ratio is written in the form n:1 we must make the right hand side equal to one.
n can be expressed as a decimal or a fraction.
According to the given question:
Convert ratio 60:52 in n:1 form
So, divide both sides of ratio with 52 to get 1 on right side of ratio.
60/52 : 1
10/7 : 1
Hence 10/7 : 1 is the converted form.
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A freight train traveling along a certain route uses 12 units of fuel per mile plus an additional 2.2
units of fuel per mile for each railcar on the train.
Let N represent the number of railcars on the train. What is an expression for f (N), the total number
of units of fuel used per mile?
The total unit of fuel used per mile f (N)= 12+ 2.2N
What is a linear function?A linear function has the following form
y = f (x) = a + bx
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
The graph of a linear function is a straight line.
The train uses 12 unit of fuel per mile and an additional 2.2 unit of fuel per mile for each railcar on the train.
Therefore the unit of fuel used per mile by N railcars is 2.2N
The total number of unit of fuel used per mile = 12+2.2N
therefore f(N)= 12+2.2N
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which of these statements is not true? if the average variance inflation factor is greater than 1 then the regression model might be biased. multicollinearity in the data is shown by a vif (variance inflation factor) greater than 10. tolerance values above 0.2 may indicate multicollinearity in the data. the tolerance is 1 divided by the vif (variance inflation factor).
Point C - Tolerance values above 0.2 may indicate multi collinearity in the data is correct.
Given that
It must be below 0.2, along with VIF above 10.
The remaining options are not correct.
A. If the average variance inflation factor is greater than 1 then the regression model might be biased.
B. Multi collinearity in the data is shown by a VIF (variance inflation factor) greater than 10.
D. The tolerance is 1 divided by the VIF (variance inflation factor).
Hence the answer is Point C - Tolerance values above 0.2 may indicate multi collinearity in the data is correct.
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How do you graph a linear equation that passes through two points?.
The equation of a line that passes through points (a,b) and (c,d) is (c-a)y = (d-b)x+b(c-a)-a(d-b).
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
Let the two points are (a,b) and (c, d)
To find the equation of line,
Use formula y- y₁ = (y₂-y₁/x₂-x₁) (x-x₁)
The equation of line,
y-b = (d-b/c-a)(x-a)
(c-a)(y-b) = (d-b)(x-a)
(c-a)y = (d-b)x+b(c-a)-a(d-b)
The required equation of the line is (c-a)y = (d-b)x+b(c-a)-a(d-b).
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The function g(x) is a transformation of the parent function f(x). Decide how
f(x) was transformed to make g(x).
f(x)
g(x)
x
-2
-1
2
لیا
у
619
9
-13
9
27
81
-2
-1
2
3
4
9
3
110
27
81
OA. Horizontal or vertical stretch
B. Horizontal or vertical shift
C. Horizontal or vertical reflection
D. Reflection across the line y=x
f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
Given that the function g(x) is a transformation of the parent function f(x).
To Decide how f(x) was transformed to make g(x).
The reflection of the point (x,y) across the line y = 1/2 x is the point (y, x).
By the given tables we can see that;
g(x) = 1/2 f (x)
Therefore, f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.
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F(x)= 12x-5 and G(x) = 2x²+3
Find (G-F) (-2) =
The domain of the function is 24.The collection of all potential inputs for a function is known as its domain.
How do you locate the domain?Let y = f(x) be a function with x as the independent variable and y as the dependent variable. A value for x is said to be in the domain of a function f if it can be used to successfully produce a single value, y, using another value for x.The collection of all potential inputs for a function is known as its domain. For instance, the domain of f(x)=x2 is all real numbers, and the domain of g(x)=1/x is all real numbers other than x=0.Determine the input values. Exclude any real numbers that produce a negative value in the radicand since there is an even root. Set the radicand to be bigger than or equal to Calculate x from zero. The area of the function where the solution(s) lie.Explanation:
F(x)= 12x-5 and G(x) = 2x²+3
Find (G-F) (-2) , put x = 0 , 2+3-12-5 = -12.
-12 * -2 = 24.
The domain of the function is 24.
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in a complete undirected graph with five vertices how many cells will contain a value of 1 in an adjacency matrix?
There are 5 1's in the given identity matrix of order 5.
Given, an identity matrix of order 5
we have to find the number of 1 in the given matrix
So, as the matrix is an identity matrix and the order of the matrix is 5
in an identity matrix, the entry is 1 when
i = j i.e. on the diagonal elements.
As, the order of the matrix is 5 then, the number of 1's in the matrix are 5.
Hence, there are 5 1's in the given identity matrix of order 5.
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a trophy company is setting up a nickel plating cell using an electrolyte containing nickel (iii) ions. predict the current required to produce metal at a rate of 5.00 g/min.
The current required to produce metal at a rate of 5.00 g/min is 274A
How to find the current in an electrolyte?The electrolyte ion equation is;
Ni²⁺ (aq) + 2e⁻ → Ni (s)
Faradays constant = 9.65 * 10⁴ C/mol
Molar mass of Nickel = 58.69 g/mol
Number of moles of nickel; n_ni = 5 g/min * 1 mol/58.69 g/mol = 0.0852 mol
n_e = 0.0852 mol * 2/1
n_e = 0.170 mol
I = nF/t
where;
t is in minutes
F is faradays' constant
Thus;
I = (0.17 * 9.65 * 10⁴)/(1 * 60)
I = 274 A
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You are a member of the fund-raiing committee for your chool. The committee i ponoring a fair. Each member of the committee ha agreed to ell 50 ticket to the fair. Student ticket are $3 each and adult ticket are $5 each. Let t repreent the number of tudent ticket that you ell. Write and implify an expreion in term of t for the total amount of money you raie for elling all 50 ticket. Then ue the expreion to determine how much money you will raie if you ell all 50 ticket and 28 of thoe are tudent ticket
The expression that represents the total amount that can be raised from selling 50 tickets is -2t + 250 and the total amount that can be raised is $194.
What is total revenue?
Total revenue is the amount of money earned by a company from the sale of its goods and services. In other words, businesses use this metric to determine how well their core revenue-generating operations are performing. Total revenue is directly related to marginal revenue.
Number of tickets that will be sold = 50
Number of student tickets that will be sold = t
Number of adult tickets that will be sold = 50 - t
The total amount of money that can be raised from selling 50 tickets is the sum of the total amount raised from selling student tickets and adult tickets.
Total revenue = total amount raised from selling students tickets + total amount raised from selling adults tickets
Total revenue = [3 x t] + [(50 -t) x $5]
Total revenue = $3t + $250 - 5t
Total revenue = -2t + 250
Total revenue = -2(28) + 250
Total revenue = -56 + 250 = $194
Hence, the expression that represents the total amount that can be raised from selling 50 tickets is -2t + 250, and the total amount that can be raised is $194.
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If the measures, in degrees, of the three angles of a triangle are x, x + 10, and 2x - 6, the triangle must be isosceles equilateral right scalene
The triangle with angles 44 degrees, 54 degrees, and 82 degrees will be a scalene triangle.
We are given the following:
The measures, in degrees, of the three angles of a triangle are x, x + 10, and 2x - 6.
We know from the triangle angle sum property that the sum of its internal angles is 180 degrees.
Let us find the given angles;
x + x + 10 + 2x - 6 = 180 degrees
4x + 4 = 180 degrees
4x = 180 - 4 degrees
x = 176 / 4 degrees
x = 44 degrees
So,
Angles will be;
x = 44 degrees
x + 10 = 44 + 10 = 54 degrees
2x - 6 = 2 * 44 - 6 = 88 - 6 = 82 degrees
All the angles are different.
Thus, the triangle with angles 44 degrees, 54 degrees, and 82 degrees will be a scalene triangle.
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for each of the following, determine the direction in which the objective function increases: a z 4x1 x2 b z x1 2x2 c z x1 3x2
The direction of increase of the given objective functions is
(a) in the direction of x₁
(b) in the direction of x₂
(c) in the direction of x₂
In the question ,
three objective functions are given ,
we have to find the direction in which the given function increase ,
So ,
Part (a) ,
z = 4x₁ - x₂
According to the signs of the variables given ,
the function z will increase in the direction of x₁ , because x₁ has positive sign and it will decrease in the direction of x₂ as it has a negative sign .
Part(b) ,
z = -x₁ + 2x₂
According to the signs of the variables given ,
the function z will increase in the direction of x₂ , because x₂ has positive sign and it will decrease in the direction of x₁ as it has a negative sign .
Part(c) ,
z = -x₁ + 3x₂
According to the signs of the variables given ,
the function z will increase in the direction of x₂ , because x₂ has positive sign and it will decrease in the direction of x₁ as it has a negative sign .
Therefore , The direction of increase of the given objective functions is
(a) in the direction of x₁
(b) in the direction of x₂
(c) in the direction of x₂ .
The given question is incomplete , the complete question is
For each of the following, determine the direction in which the objective function increases:
(a) z = 4x₁ - x₂
(b) z = -x₁ + 2x₂
(c) z = -x₁ + 3x₂
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(1 point) how many anagrams can be created from the word 'accommodate' if the new words do not need to be meaningful?
The anagrams that can be created from the word accommodate is N=4989600.
What is meant by anagram?An anagram is a word or phrase made by rearranging the letters of another word or phrase, often using all of the original letters exactly once.
The original word or phrase is known as the anagram's subject. An anagram is any word or phrase that exactly duplicates the letters in a different order. An "anagrammatist" is someone who makes anagrams, and the purpose of a serious or expert anagrammatist is to make anagrams that reflect or remark on their subject.
Given word is
'accommodate'
Total number of letters= 11
Number of a = 2
c=2
m=2
0=2
The rest are one each.
Therefore, the number of possible arrangements can be written as;
N = 11!/(2!2!2!2!)
N = 39916800/8
N=4989600
Therefore, the anagrams that can be created from the word accommodate is N=4989600.
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Put these numbers in order from greatest to least.
-0.85
12.45
0.25
-12
Answer:
12.45, 0.25, -0.85, -12
Step-by-step explanation:
The larger the negative the lesser the value, opposite for positive numbers
In a random series, successive observations are probabilistically independent of one another. If this property is violated, the observations are said to be:
If this property is violated, the observations are said to be: autocorrelated
What is Random Series?
The results of an experiment are functions of an integer argument, and the results are described by a random series: U1, U2.. (or, simply, sequences of random values - 1st value, 2nd value, etc).
The term "time series" and, occasionally, "random processes with discrete time" are frequently used to describe random series. The Markov chain exemplifies a crucial category of random series.
In this question, it's asked when the property of independence is violated.
If the consecutive observations are correlated or linearly related, then they are said to be autocorrelated. This denotes that there will be an association of the current time period with the successive and preceding time periods. Violation of the autocorrelation assumption yields inaccurate results.
Hence, The observations are said to be: autocorrelated in the random series.
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If the first and second terms of a geometric sequence are 3 and 12, what is
the expression for the value of the 24th term of the sequence?
Answer:
[tex]3(4)^{23}[/tex]
Step-by-step explanation:
Let the first term be [tex]a[/tex] and the common ratio be [tex]r[/tex].
We know [tex]a=3[/tex] and [tex]ar=12[/tex], meaning [tex]r=4[/tex].
This means the 24th term is [tex]3(4)^{23}[/tex].
What is the solution to the equation 3 m 3 m 3 m/m2 9 m2 9?.
This equation [tex]\frac{3}{m + 3}[/tex] - [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex] has no solution.
Since we have given that
[tex]\frac{3}{m + 3}[/tex] - [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
We need to find the solution of the above equation:
Since is a rational equation so, we will check for its extraneous solution.
[tex]\frac{3}{m + 3}[/tex] - [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]\frac{3}{m + 3}[/tex] + [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]\frac{3(m + 3) + m(m +3)}{m^{2} - 9}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]\frac{3m - 9 + m^{2} +3m }{m^{2}-9 }[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]\frac{m^{2} -9+6m}{m^{2} -9}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]
[tex]m^{2} +6m -9 = m^{2} + 9[/tex]
[tex]6m = 18[/tex]
[tex]m = \frac{18}{6} = 3[/tex]
Hence, the extraneous solution in case of rational equation is 3 , when we put m = 3, it becomes undefined so, it has no solution.
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tom is a big green bay packers and aaron rodgers fan. he claims that aaron rodger's average number of touchdowns per game is 2.45. dave (a hardcore bears fan) believes that tom might be inflating rodgers's statistics. from his debut until november 18, 2019, aaron rodgers has played 175 games! dave does not want to look at all of them. he randomly selects 52 games that rodgers played and finds the sample average number of touchdowns to be 1.942 with a standard deviation of 1.42. do a hypothesis test and state your conclusion. use the significance level
After doing a hypothesis test the conclusion is reject [tex]H_0[/tex] .
Given:
tom is a big green bay packers and aaron rodgers fan. he claims that aaron rodger's average number of touchdowns per game is 2.45. dave (a hardcore bears fan) believes that tom might be inflating rodgers's statistics. from his debut until november 18, 2019, aaron rodgers has played 175 games! dave does not want to look at all of them. he randomly selects 52 games that rodgers played and finds the sample average number of touchdowns to be 1.942 with a standard deviation of 1.42.
here n = 52
σ = 1.42
x = 1.942
μ = 2.45
z = x - μ / σ/√n
= 1.942 - 2.45 / 1.42/√52
= -2.58
p value = 0.0049
[tex]H_0:mean = 2.45[/tex]
[tex]H_a:mean < 2.45[/tex]
Rejection rule:Reject [tex]H_0[/tex] if p value < 0.05
Conclusion Reject [tex]H_0[/tex]
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Is mean absolute deviation the same as mean?.
The Mean absolute deviation and the mean are not same.
Given,
The mean;-
The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Mean absolute deviation;-
The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset contains.
Therefore,
The Mean absolute deviation and the mean are not same.
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What is the approximate average rate of change of the function f(x)=50(1.021)^x over the interval of x=7 to x=10
The average rate of change of the function, f(x)=50(1.021)^x over the interval of x=7 to x=10 is calculated as: 1.24.
How to Find the Average Rate of Change of a Function?The average rate of change = f(b) - f(a) / b - a.
Given the following:
The function is: f(x) = 50(1.021)^x
Interval is: x = 7 to x = 10
Therefore:
a = 7
b = 10
f(a) = f(7) = 50(1.021)^7
f(a) = f(7) = 57.83
f(b) = f(10) = 50(1.021)^10
f(b) = f(10) = 61.55
Therefore:
Average rate of change = (61.55 - 57.83) / 10 - 7
= 1.24.
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How many triangles exist with the given side lengths?.
Exactly one unique triangle exists with the given side lengths, option B is correct.
Here, we are given that the three sides of triangle are- 12, 15 and 18.
According to the triangle inequality theorem- “The sum of the length of any two sides of a triangle should be greater than the third side”. Let us see if this holds in this case-
(12 + 15) > 18
(15 + 18) > 12
(12 + 18) > 15
Thus, we see that the triangle inequality theorem is satisfied. So there is only one triangle possible with the sides of given lengths.
Hence, exactly one unique triangle exists with the given side lengths, option B is correct.
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Your question was incomplete. Check for full content below-
How many triangles exist with the given side lengths?
12 in, 15 in, 18 in
A) No triangle exists with the given side lengths.
B) Exactly one unique triangle exists with the given side lengths.
C) More than one triangle exists with the given side lengths.
Lin wrote a proof to show that diagonal EG is a
line of symmetry for rhombus EFGH. Fill in the
blanks to complete her proof.
Because EFGH is a rhombus, the distance from E to F is the same distance from E to H. Since E is the same distance from F as it is from H, it must lie on the perpendicular bisector of FH. By the same reasoning, G must lie on the perpendicular bisector of FH. Therefore, line EG is the perpendicular bisector of segment FH. So, reflecting rhombus EFGH across line FH will take E to G and G to E (because E and G are on the line of reflection) and F to H and H to F (since FH is perpendicular to the line of reflection, and R and H are the same distance from the line of reflection, on opposite sides). Since the image of rhombus EFGH reflected across EG is rhombus EHGF (the same rhombus), line EG must be a line of symmetry from rhombus EFGH.
