what must be a factor if the polynomial function f(x) graphed ib the coordinate plane below ?
Answers
Solution
The question gives us a graph that crosses the x-axis at 3 points: x = 1, x = 2, and x = -3. We are asked to find which of the factors on the graph is in the options given.
- Whenever a graph crosses the x-axis at a point "a", it implies that x = a is a root of the graph and as a result, (x - a) must be a factor of the graph.
- We can apply this to the question and derive the factors of the graph as follows:
[tex]\begin{gathered} \text{ When }x=-3\colon \\ x=-3 \\ \text{Add 3 to both sides} \\ x+3=0 \\ \\ \text{Thus, }(x+3)\text{ is a factor of the graph.} \\ \\ \\ \text{When }x=1\colon \\ x=1 \\ \text{Subtract 1 from both sides} \\ x-1=0 \\ \\ \text{Thus, }(x-1)\text{ is a factor of the graph} \\ \\ \\ \text{When }x=2\colon \\ x=2 \\ \text{Subtract 2 from both sides} \\ x-2=0 \\ \\ \text{Thus, (}x-2)\text{ is a factor of the graph.} \\ \\ \\ \text{Thus, we can conclude that the 3 factors of the graph are:} \\ (x+3),(x+1),\text{ and }(x-2) \end{gathered}[/tex]- Going through the options, we can see that only (x - 1) is present in the options.
- Thus, (x - 1) is the answer
Final Answer
(x - 1) is the answer (OPTION B)
Related Questions
Which vehicle has the smallest total volume?What is the volume?
Answers
The formula for the volume is,
[tex]V=\text{length}\cdot\text{ width}\cdot\text{ height}[/tex]Determine the volume of Van.
[tex]\begin{gathered} V=10\cdot6\frac{1}{2}\cdot6 \\ =60\cdot\frac{13}{2} \\ =390 \end{gathered}[/tex]Determine the volume of small truck.
[tex]\begin{gathered} V_1=11.3\cdot7.5\cdot6.75 \\ =572.0625 \end{gathered}[/tex]Determine the volume of 2-bedroom moving truck.
[tex]\begin{gathered} V=14\frac{1}{2}\cdot\frac{77}{12}\cdot7\frac{1}{6} \\ =\frac{29}{2}\cdot\frac{77}{12}\cdot\frac{43}{6} \\ =666.798 \end{gathered}[/tex]Determine the volume of 3 bedroom truck.
[tex]\begin{gathered} V=20.5\cdot7.7\cdot8.5 \\ =1341.725 \end{gathered}[/tex]Determine the mega moving truck.
[tex]\begin{gathered} V=22\frac{1}{4}\cdot7\cdot9\frac{1}{3} \\ =1453.666 \end{gathered}[/tex]The smallest volume is equal to
The table of values represents a quadratic function.What is the average rate of change for f(x) from x=−10 to x = 0?Please help me with this problem so that my son can understand better. Enter your answer in the box.xf(x)−10184−5390−654910204
Answers
We are given a quadratic function and the rather than the equation for this function we already have the outputs at each given input as shown in the table provided. This means, for example, for the function given, when the input is -10, the output is 184. Thus the table includes among other values;
[tex]x=-10|f(x)=184[/tex]To calculate the average rate of change we shall apply the formula for the slope (which is also the average rate of change). This is given below;
[tex]\text{Aerage Rate of Change}=\frac{f(b)-f(a)}{b-a}[/tex]Note that the variables are;
[tex]\begin{gathered} f(a)=\text{first input value} \\ f(b)=\text{second input value} \end{gathered}[/tex]The first input value is -10 and the function at that value is 184
The second input value is 0 and the function at that value is -6
We now have;
[tex]\begin{gathered} a=-10,f(a)=184 \\ b=0,f(b)=-6 \end{gathered}[/tex]We can now substitute these into the formula shown nearlier and we'll have;
[tex]\begin{gathered} \text{Ave Rate Of Change}=\frac{f(b)-f(a)}{b-a} \\ =\frac{-6-184}{0-\lbrack-10\rbrack} \end{gathered}[/tex][tex]\begin{gathered} =\frac{-190}{0+10} \\ \end{gathered}[/tex][tex]=\frac{-190}{10}[/tex][tex]\text{Average Rate of Change}=-19[/tex]ANSWER:
The average rate of change over the given interval is -19
used to name a point
Answers
Answer:
It is represented by a dot and named by a capital letter
Step-by-step explanation:
Solve for basic equation x2x+3=-3x-12
Answers
Solution
We have the following equation:
2x +3 = -3x-12
We can solve for x on this way:
5x = -12-3
5x = -15
Dividing both sides by 5 we got:
x= -3
what is the area of the Shaded region used 3.14
Answers
In this problem, the area of the shaded region is equal to the area of the complete square, minus the area of the four circles
so
REmember that
The length side of the complete square is equal to two times the diameter of one circle
A=(2*12)^2-4*pi*(12/2)^2
assume pi=3.14
A=576-4(3.14)(36)
the area of the Shaded region is A=123.84 ft^2For each of the following scenarios state the domain (starting set) show and state the mapping, and decide if it is a function. Be sure to label your set and indicate the direction of the relation.
Answers
Domain: Number of pages
Range:Number of books
Mapping: Number of pages to the number of books.
Explaination: The number of pages is the independent variable and the number of books is the dependent variable.
The given mapping is a function as total number of pages can not have more than two output (number of books).
The following statements "If you are wearing a helmet, you are riding a bike." and "If you are not riding a bike, you are not wearing a helmet." are an example of a _____ statement.Select one:a.inverseb.conversec.contrapositive
Answers
Given:
The given statements are,
"If you are wearing a helmet, you are riding a bike."
"If you are not riding a bike, you are not wearing a helmet."
Required:
To identify the kind of statements.
Explanation:
We have the given statement:
"If you are wearing a helmet, you are riding a bike."
Here, p : you are wearing a helmet
q : you are riding a bike
Thus, taking negation of both the parts of the statement as follows:
If not q, then not p.
Hence, the statement formed is,
"If you are not riding a bike, you are not wearing a helmet."
This is the contrapositive statement.
Final Answer:
Given statements are an example of contrapositive.
Ms wash investdd $22000 in two accounts, one yielding 8% interest and the other yielding 11%. if she recieved a total of $1910 in interest at the end of the year, how much did she invest in each accouny
Answers
Take into account the following formula for the simple interest:
[tex]I=P\cdot r\cdot t[/tex]where:
P: principal investment
r: interest rate
t: time
In order to determine the investments for both accounts, proceed as follow:
-Consider that both investments are represented by P1 and P2 respectively, then, you have:
[tex]\begin{gathered} P_1+P_2=22000 \\ P_2=22000-P_1 \end{gathered}[/tex]- Next, use the given values for parameters r and t for each investment:
8% = 0.08
11% = 0.11
t = 1 year
[tex]\begin{gathered} I_1=P_1\cdot0.08\cdot1=0.08P_1 \\ I_2=P_2\cdot0.11\cdot1=0.11P_2 \end{gathered}[/tex]- Next, consider that the sum of the total earnings is $1910, then:
[tex]I_1+I_2=1910[/tex]- Replace I1 and I2 by the expressions in terms of P1 and P2 and write down the resultant expression in terms of P1, as follow:
[tex]\begin{gathered} 0.08P_1+0.11P_2=1910 \\ 0.08P_1+0.11(22000-P_1)=1910 \\ 0.08P_1+2420-0.11P_1=1910 \\ -0.03P_1=-510 \\ P_1=\frac{510}{0.03}=17000 \end{gathered}[/tex]And for P2:
[tex]\begin{gathered} P_2=22000-P_1 \\ P_2=22000-17000=5000 \end{gathered}[/tex]Hence, the amount of money invested in each account was $5000 and $17000
Which inference about the man is best supported by the events in the text?
Answers
What is the standard form of the equation of a line passing through points (2,3) and (2,-5)?
Answers
Answer:
[tex]x\text{ = 2}[/tex]Explanation:
Here, we want to find the standard form of the equation
We have the standard form as:
[tex]Ax\text{ + By = C}[/tex]We can arrive at this using the two-points form:
This is:
[tex]\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{y-y_1}{x-x_1}[/tex](x1,y1) = (2,3)
(x2,y2) = (2,-5)
Now, as we can see, the line is a vertical line since the x-value is the same
Thus, we have it that:
[tex]x\text{ = c}[/tex]where c will represent the x-intercept
Thus, we have the equation of the line as:
[tex]x\text{ = 2}[/tex]a cyclist rides her bike at a speed of 30 kilometers per hour. what is the speed in miles per hour? how many miles will the cyclist travel in 5 hours?
Answers
Answer:
the answer is 9.321 miles
a scientist need to 6000 calories per day. Based on the percentage of total daily calories and the number of calories needed, how many biscuits, packages of pemmican, butter and coco does a person need each day?
Answers
EXPLANATION:
Given;
We are told that a scientist needs 6000 calories per day.
We are also given a table showing the percentage of daily calories he can get from three types of food.
These are;
[tex]\begin{gathered} Biscuits---40\% \\ pemmican---45\% \\ Butter\text{ }and\text{ }cocoa---15\% \end{gathered}[/tex]Required;
We are required to calculate how many of each type of food he would need to eat each day.
Step-by-step solution;
We shall solve this by first determining how many calories can be gotten from each type of food based on the percentage given. This is calculated below;
[tex]\begin{gathered} Biscuits: \\ 6000\times\frac{40}{100}=2400 \end{gathered}[/tex]This means if he gets 75 calories from one biscuit, then to get 2,400 calories he would have to eat;
[tex]\begin{gathered} 75cal=1b \\ 2400cal=\frac{2400}{75} \\ 2400cal=32 \end{gathered}[/tex]The scientist would have to eat 32 biscuits to get 2400 calories.
[tex]\begin{gathered} Pemmican: \\ 6000\times\frac{45}{100}=2700 \end{gathered}[/tex]This means if he gets 135 calories from one pack of dried meat, then to get 2700 calories he would have to consume;
[tex]\begin{gathered} 135cal=1pack \\ 2700cal=\frac{2700}{135} \\ 2700cal=20 \end{gathered}[/tex]Therefore, the scientist would have to eat 20 packs of pemmican to get 2700 calories
[tex]\begin{gathered} Butter\text{ }and\text{ }Cocoa: \\ 6000\times\frac{15}{100}=900 \end{gathered}[/tex]This means if he eats 1 package of Butter and cocoa he gets 225 calories. To get 900 calories he would have to eat;
[tex]\begin{gathered} 225cal=1pack \\ 900cal=\frac{900}{225} \\ 900cal=4 \end{gathered}[/tex]Therefore, the scientist would have to eat 4 packs of Butter and cocoa.
We now have the summary as follows;
ANSWER:
[tex]\begin{gathered} Biscuits=32 \\ Pemmican=20\text{ }packs \\ Butter\text{ }and\text{ }cocoa=4\text{ }packs \end{gathered}[/tex]Convert 145 to base 4
Answers
Answer:
Converting 145 to base 4 will give;
[tex]2101_4[/tex]Explanation:
We want to convert;
[tex]145_{ten}\text{ to base 4}[/tex]Converting, we have;
[tex]\begin{gathered} 145\text{ }\div\text{ 4 } \\ 36\text{ }\div\text{ 4 R 1} \\ 9\text{ }\div\text{ 4 R 0} \\ 2\text{ }\div\text{ 4 R 1} \\ 0\text{ R 2} \end{gathered}[/tex]Therefore, converting 145 to base 4 will give;
[tex]2101_4[/tex]=
A ball is thrown from a height of 156 feet with an initial downward velocity of 8 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=156-81-161²
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
Answers
The time taken by the ball to hit the ground is 2.88 sec.
What is termed as the distance?Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much surface an object has covered regardless of its starting or closing point.For the given question,
The total height from which the ball is thrown is 156 feet.
Let 'h' be the height after the time 't' sec.
The equation for the relation of the height and the times is;
h = 156 - 8t - 16t²
The initial velocity of the ball is 8 ft/s. .
When the ball hit the ground the height will become zero.
156 - 8t - 16t² = 0.
Divide the equation by -4.
4t² + 2t - 34 = 0
Solve the quadratic equation using the quadratic formula to find the time.
t = 2.88 sec.
Thus, the time taken by the ball to hit the ground is 2.88 sec.
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The correct question is-
A ball is thrown from a height of 156 feet with an initial downward velocity of 8 ft/s . The ball's height h (in feet) after t seconds is given by the following. h=156-8t-16t²
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
Given the zeros of the following polynomial 2 +2i, 3, - 4 select the corresponding factors AND the polynomia O (x + 2i) (2 - 2i) (2 - 3)(x+4) o f(c) = 24 - 23 822 - 42 - 48 0 (2 – 2i) (x + 2i) (2+3)(– 4) 24 – 13 + 82 40 - 48 0 (0 - 2) (+2)(x - 3)(x +4) 24 - 23 - 822 + 4x + 48 1 3 N
Answers
a)
d)
1) Since the zeros of that polynomial were given, then we can write it into the factored form. Note that there are 4 zeros, so we can write:
[tex]\begin{gathered} (x-x_1)(x-x_2)(x-x_3)(x-x_4)=0 \\ (x-(-2i))(x-2i)(x-3)(x-(-4))=0 \\ (x+2i))(x-2i)(x-3)(x+4))=0 \end{gathered}[/tex]2) To find out the corresponding polynomial then we can expand it by rewriting "i" as -1
[tex]\begin{gathered} (x+2i))(x-2i)(x-3)(x+4) \\ (x+2i)(x-2i)=x^2+4 \\ (x-3)(x+4)=x^2+4x-3x-12 \\ (x^2+4)(x^2+x-12) \\ x^4+x^3-8x^2+4x-48 \end{gathered}[/tex]3) Hence, the answers are
a)
d)
[tex]x^4+x^3-8x^2+4x-48[/tex]what is the simplified ratio of 32:24
Answers
Answer:
4/3
Step-by-step explanation:
The simplest form of
32: 24
is 43
Steps to simplifying fractions
Find the GCD (or HCF) of numerator and denominator
GCD of 32 and 24 is 8
Divide both the numerator and denominator by the GCD
32 ÷ 8
24 ÷ 8
Reduced fraction:
4/3
Therefore, 32/24 simplified to lowest terms is 4/3.
For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose isA. 12B. 8C. 4D. 6
Answers
Okay, here we have this:
She can eat the following options:
Sandwich with ham with or without cheese. Two choices.
Sandwich with bologna with or without cheese. Other two choices
This mean that she can eat:
Sandwich with ham with cheese with water or juice. Two options.
Sandwich with ham without cheese with water or juice. Two options.
Sandwich with bologna with cheese with water or juice. Two options.
Sandwich with bologna without cheese with water or juice. Two options.
Finally we obtain a total of: 2+2+2+2=8 options of lunches.
Thw
1. A coat at the Utopian Coat factory cost $99.99. The sales tax is 7%. Find the sales tax and the total cost of the jacket. (Round to the nearest cent).
Answers
The Solution:
Given that a coat costs $99.99 and the sales tax is $75.
We are required to find the actual sales tax and the total cost of the coat.
Step 1:
We shall find the sales tax.
[tex]\begin{gathered} \text{ Cost of the coat=\$99.99} \\ \\ \text{Sales tax of 7\% }=\frac{7}{100}\times99.99=0.07\times99.99 \\ \\ =6.999\approx\text{ \$7.00 (or 700 cent)} \end{gathered}[/tex]Thus, the sales tax is $7.00 or 700 cents.
Step 2:
We shall find the total cost of the coat.
The total cost of the coat is the sum of the coat's cost and the sales tax.
[tex]\text{ The total cost=99.99+6.999=106.989}\approx\text{ \$106.99}[/tex]Therefore, the correct answers are:
Sales tax =$7.00 or 700 cents.
Total cost = $106.99 or 10699 cents..99 or 10699 cents.
Rewrite the following expression so it does not contain any radical term
Answers
Given:
The expression is given as,
[tex]\sqrt[]{36p^{10}m^6}[/tex]The objective is to rewrite the expression without any radical form.
Explanation:
The given expression can be written as,
[tex]\sqrt[]{36p^{10}m^6}=\sqrt[]{6^2p^{10}m^6}\text{ . . . . .(1)}[/tex]In general, the radical form of a square root can be written as,
[tex]\sqrt[]{x}=x^{\frac{1}{2}}[/tex]Then, the equation (1) can be written as
[tex]\sqrt[]{36p^{10}m^6}=(6^2p^{10}m^6)^{\frac{1}{2}}[/tex]On further solving the above expression,
[tex]\begin{gathered} \sqrt[]{36p^{10}m^6}=6^{2\times\frac{1}{2}}p^{10\times\frac{1}{2}}m^{6\times\frac{1}{2}} \\ =6p^5m^3 \end{gathered}[/tex]Hence, the simplified expression of the given term is,
[tex]6p^5m^3[/tex]The nutrition label on Erin's box of animal crackers states that 16 crackers contain 24 grams of carbohydrates. Erin ate 12 animal crackers from the box. What is the number of grams of carbohydrates in 12 animal crackers? A.8 grams B. 12 grams C. 18 gramsD. 20 grams
Answers
16 crackers are proportional to 24 grams of carbohydrates. To find the number of grams of carbohydrates in 12 animal crackers, we can use the next proportion:
[tex]\frac{16\text{ crackers}}{12\text{ crackers}}=\frac{24\text{ grams}}{x\text{ grams}}[/tex]Solving for x,
[tex]\begin{gathered} 16\cdot x=24\cdot12 \\ x=\frac{288}{16} \\ x=18\text{ grams} \end{gathered}[/tex]A family of four went to an amusement park for their vacation. They started the vacation with $426.They spent a total of $198 the first three days.If they divided the remainder of the money evenly between the family members for souvenirs, how much did each person have to spend?
Answers
They started the vacation with $426
After spending $198 the first three days, the remainder is $426 - $198 = $228
Given that there are 4 family members, we have to divide this remainder by 4, that is, $228/4 = $57
Each person has $57 to spend
The graph below shows the number of snowballs, y, needed to make x snowmen.
Number of Snowballs
15
10
S
(1,3)
(3,9)
(4, 12)
+
2
Number of Snowmen
3 4 5
How many snowballs are needed to make 2 snowmen?
Answers
The number of snowballs that are needed to make 2 snowmen is equal to 6.
How to write a proportional equation?Mathematically, a proportional relationship can be represented by the following equation:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:
k = y/x
k = 3/1 = 9/3 = 12/4 = 3
When the number of snowmen, x = 2, the number of snowballs, y is given by:
y = kx
y = 3 × 2
y = 6.
Therefore, the ordered pair is equal to (2, 6).
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100 Points.
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degrees and classifications of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?
Answers
The expression that represents the area of the rectangle is [tex]6x^{2}[/tex]+29x + 35 square units , the degree of the obtained expression is 2.
According to the question,
We have the following information:
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
A) We know that following formula is used to find the area of rectangle:
Area = length*breadth
Area = (3x+7)(2x+5)
Area = [tex]6x^{2}[/tex] + 15x +14x + 35
Area = [tex]6x^{2}[/tex] +29x + 35 square units
B) The degree of an expression is the highest power of the expression. In this case, the highest power is 2. Hence, the degree of the expression obtained is 2.The expression can be classifies as a quadratic polynomial.
C) Part A demonstrates the closure property for the multiplication of polynomials because the expression within the brackets are polynomials and the result obtained is also a polynomial.
Hence, the area of the rectangle is [tex]6x^{2}[/tex] +29x + 35 square units and the degree of the obtained expression is 2.
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What’s the correct answer answer asap for brainlist
Answers
Answer:
Answer is B. Harding, Coolidge, and Hoover
:)
The entire graph of the function h is shown in the figure below.
Write the domain and range of h using interval notation.
(a) domain=
(b) range =
Answers
The Domain is [-2, 5] and Range is [3, -4]
What is Domain and range ?
The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.
a.) Here in graph, see the x-axis for to find Domain
You'll notice that -2 is point where the point is marked as lowest after that there is no line or point is there and the highest it goes up to the blue line is reached is 5 in x-axis.
so, the Domain is [-2, 5]
b.) For the range you to look at y-axis, just observe the highest and lowest point in graph you'll be able to find range.
hence, the Range is [3, -4]
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how much would EZ Excavation charge to haul 40 cubic yards of dirt
Answers
Given the line on the graph, we have that it passes through the points (1,25) and (2,50), then we can find the relation function with the slope-point equation of the line:
[tex]\begin{gathered} \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{50-25}{2-1}=\frac{25}{1}=25 \\ y-y_1=m(x-x_1) \\ \Rightarrow y-25=25(x-1) \\ \Rightarrow y=25x-25+25=25x \\ y=25x \end{gathered}[/tex]we have that the cost of the dirt is given by the equation y=25. To find how much would it be for 40 cubic yards of dirt, we make x=40 and we get the following:
[tex]\begin{gathered} x=40 \\ \Rightarrow y=25\cdot40=1000 \\ y=1000 \end{gathered}[/tex]therefore, the cost to haul 40 cubic yards of dirt is $1000
I know this is something super easy, but I always forget the steps on how to figure this out, I tried to put 30 and number one spot, I tried putting 82 and number two spot, and I tried putting 50 and number one spot but when you add that up that's a lot more than 360. I just need help please
Answers
Anlge directly opposite to 2= 180 - 82= 98
Sum of angles in the triangle (98, 50, x ) = 180
98+50+x = 180
x + 148 = 180
x = 180 - 148= 32
m<1 = x because they are alternate
so m<1 = 32
m<2 + 82 = 180 ( sum of angles in a straight line)
m<2 = 180 - 82 = 98
m< 3 = 50 because they are alternate
Or
m<3 + m<2 + m<1 = 180 ( sum of angles in a triangle)
m< 3 + 98+ 32 = 180
m<3 =180 - 130 =50
Summary
m< 1= 32 degrees
m<2= 98 degrees
m<3 = 50 degrees
For the data values 69, 54, 27, 43, 69, 56, the mean is 53.
Answers
From the table given,
To find the x - mean,
By the summation of all the x - mean
The value of x - mean is
[tex]x-\operatorname{mean}=16+1-26-10+16=-3[/tex]Hence, the value of x - mean is -3
To find the (x - mean)²
By the summation of all the values of (x - mean)²
The value of (x - mean)² is
[tex](x-\operatorname{mean})^2=256+1+676+100+256=1289[/tex]Hence, the value of (x - mean)² is 1289
Crystal's favorite playlist has 80 rock songs, 40 jazz songs, 25 country songs, 30 hip hop songs, and 45 classical music songs. Which of thesestatements is true?
Answers
This problem tests the knowledge of the probability of a random event occuring: of playing a type of song from a variety of different song types
Thus, we have to compute the probability that each type of song is played.
To do this, we need to obtain the total number songs, as follows:
80 + 40 + 25 + 30 + 45 = 220
Thus, the probabilities are now easily computed as follows:
P(rock) = 80/220
P(jazz) = 40/220
P(country) = 25/220
P(hip hop) = 30/220
P(classical) = 45/220
Now:
Option 1 (the first statement in the options) claims that : P(rock) = 2 * P(hip hop)
However, 2 * P(hip hop)
For each level of confidence o below, determine the corresponding normal confidence interval. Assume each confidence interval is constructed for the same sample statistics.Drag each normal confidence interval given above to the level of confidence
Answers
Note that the width of the confidence interval increases as the confidence level increases.
Since the confidence intervals constructed are for the same sample statistic, the higher confidence interval will have a higher width.
The confidence levels have the following widths:
Therefore, the confidence intervals are matched such that the lowest interval has the smallest confidence level and the highest has the largest confidence level. This is shown below: