there are four factors, giving it a fourth degree. This is the polynomial function of least degree that has the zeros 3, 6, and √6.
f(x) = (x - 3)(x - 6)(x - √6)(x + √6)
We start by listing out the zeros
3, 6, √6
Now, we can write the polynomial function of least degree that has these zeros
f(x) = (x - 3)(x - 6)(x - √6)(x + √6)
Note that this is a fourth degree polynomial because it has four factors.
We can write a polynomial function of least degree that has the following zeros: 3, 6, and √6. This polynomial function is a fourth degree polynomial, which means it has four factors. We can write it as f(x) = (x - 3)(x - 6)(x - √6)(x + √6). This polynomial function has the zeros 3, 6, and √6, and any other x-value that makes the equation equal to 0. The degree of the polynomial depends on how many factors are in the equation, and in this case, there are four factors, giving it a fourth degree. This is the polynomial function of least degree that has the zeros 3, 6, and √6.
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find diameter of 7 in radius
Answer:
The answer is 7/2
Step-by-step explanation:
d=2r
7=2r
r=7/2
25. An electrician charges an initial fee of $50 and $190 after 4 hours of w
a. Write a linear model that represents the total cost as a function of t
b. How much does the electrician charge per hour?
Answer:
Step-by-step explanation:
A. The total cost after t hours can be represented by the linear equation C(t) = 50 + 190/4 * t, where C(t) is the total cost after t hours.
B. The electrician charges 190/4 = $47.5 per hour.
What is the value today of $5,100 per year, at a discount rate of 7.9%, if the first payment is received 6 years from today and the last payment is received 20 years from today?
Answer:
$30,029.78
Step-by-step explanation:
NPV = Cash flow / (1 + i)^t – initial investment (assuming initial investment =$1).
solve NPV
$30,029.78
A crystal growth furnace is used in research to determine how best to manufacture crystals used in electric components for the space shuttle. For proper growth of the crystal, the temperature must be controlled accurately by adjusting the input power. Suppose the relationship is given by the following equation, where T is the temperature in degrees Celsius and w is the power input in watts.
T(w) = 0.1w2 + 2.159w + 20
(a) How much power is needed to maintain the temperature at 195°C? (Give your answer correct to 2 decimal places.)
watts
We need 32.65 W power to maintain the temperature at 197°C.
In order to discover the wattage to maintain a temperature of 197°C for the crystals, we need to start by substituting that value into the function:
T(x) = 0.1w² + 2.157w + 20
197 = 0.1w² + 2.157w + 20
and set the equation equal to zero by subtracting 197 from both sides:
0.1w² + 2.157w - 177 = 0
To solve this equation we make use of the quadratic formula, which in this case will be:
[tex]w = \frac{- b (+/-)\sqrt{b^{2}-4ac } }{2a}[/tex]
in this case:
a=0.1
b=2.157
c=-177
which come from the equation according to their position in the equation with the form ax²+bx+c = 0.
so we substitute them into the formula like this:
[tex]w = \frac{- 2.157(+/-)\sqrt{2.157^{2}-4*(0.1)*(-177) } }{2*0.1}[/tex]
w= -54.22W and w=32.65W
we use the positive answer since that means that the power is being input into the system, a negative answer would mean you are retrieving power from the system which would cool the system down.
So we need 32.65W power to maintain the temperature at 197°C.
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Higher Order Thinking For his birthday, Gil got
4 packages of trading cards. He already had 75 cards.
How many cards did he have after his birthday?
The solution is, he have after his birthday total cards 79 cards.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
Gil got 4 packages of trading cards.
He already had 75 cards.
so,
he have after his birthday total cards = 75 +4
= 79 cards
Hence, The solution is, he have after his birthday total cards 79 cards.
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Answer please (30 points)
I really think it's option A because it's more than 90° and less than 180°
Answer:
A
Step-by-step explanation:
An obtuse triangle is a triangle in which one of the interior angles measures more than 90° degrees
formula for finding obtuse triangle is 1/2 *base*height
will give brainliest
Answer:
option B
Step-by-step explanation:
it's off and on 12345678910
The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.
Expression A: 0.2p
Expression B: 0.8p
Expression C: 1 - 0.2p
Expression D: p - 0.2p
Expression E: p - 0.8p
Which two expressions each represent the sale price of the item?
The expressions of the sale price is as follows:
Expression B: 0.8p
Expression D: p - 0.2p
How to find the expression that represent the sale price of the items?The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price.
Therefore, the expression that represent the sale price in dollars of the items can be calculated as follows:
original price = p
Therefore, let's find the percent off the price.
price off = 20% of p
price off = 20 / 100 p
price off = 0.2p
Therefore,
sale price = p - 0.2p
sale price = 0.8p
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HELPPP ASAP WILL MARK THE BRAINLIEST
PLS GIVE AN EXPLANATION!!!!
Two cars travel at the same speed to different destinations. Car A reaches its destination in 12 minutes. Car B reaches its destination in 18 minutes. Car B travels 4 miles farther than Car A. How fast do the cars travel? Write your answer as a fraction in simplest form.
Answer:
You can use the fact that both the cars were travelling at the same speed so we can take them equal to some variable.
The speed of the cars was 0.8 miles per hour
How to form may you can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
How to find the speed of the cars?
Supposing that both the cars were travelling with the speed
Let the first car travels miles
then as second car travels 12 miles extra, thus, distance traveled by second car is miles.
Using the formula for speed, we have:
For first car:
Distance traveled = miles
Speed =
Time taken =
Thus,
For second car:
Distance traveled = miles
Speed =
Time taken =
Thus,
So, we got system of 2 linear equations in two variables.
Using the expression for x from first equation and substituting it in second equation, we get
Substituting this value in first equation to get the value of x
Thus,
The speed of the cars was 0.8 miles per hour
Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = ln(x), then f'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = ln(x) at x = 2.y=__________
The formula for the tangent line to f(x) = ln(x) at x = 2 is 2y = x − 2.
We must first differentiate f(x).
The derivative of ln(x) is 1/x
The slope of the tangent at a point x = a on the function f(x) is given by evaluating f'(a).
Hence, the slope of the tangent is 1/x = 1/2
The function passes through,
(1/2, ln1)=(2, 0).
Now, we can use point slope form to find the equation of the tangent.
y − y1 = m( x− x1)
y − 0 = 1/2( x− 2 )
2y = x - 2
Thus, the equation of the tangent is 2y = x − 2.
The straight line that "just touches" the curve at a given position is known as the tangent line to a plane curve at that location. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.
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At a local store, 2 bagels and 2 cups of coffee cost $4.40. The cost of 3 bagels and 4 cups of coffee is $7.80.
Write a system of equations to represent this situation, where x
is the number of bagels and y
is the number of cups of coffee.
A system of equations to represent this situation include the following:
2x + 2y = 4.40
3x + 4y = 7.80
How to write a system of equations to describe the situation?In order to write a system of equations that model this situation, we would assign variables to the number of bagels and the number of cups of coffee respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of bagels.Let the variable y represent the number of cups of coffee.Next, we would translate the word problem into algebraic equation as follows:
Since 2 bagels and 2 cups of coffee cost $4.40, we would have:
2x + 2y = 4.40 .....equation 1.
Additionally, 3 bagels and 4 cups of coffee cost $7.80:
3x + 4y = 7.80 .....equation 2.
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Solve 5^x − 4 = 7 for x using the change of base formula log base b of y equals log y over log b.
The value of x is 1.51.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]5^x[/tex] - 4 = 7
[tex]5^x[/tex] = 7 + 4
[tex]5^x[/tex] = 11
Taking logs on both sides.
log [tex]5^x[/tex] = log 11
x log 5 = log 11
x = log 11 / log 5
x = 1.04/0.69
x = 1.51
Thus,
x is 1.51.
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given a dag, give a linear-time algorithm to determine if there is a simple path that visits all vertices
A simple path which visits all vertices can be found using a linear-time algorithm.
Explain about the linear-time algorithm?If an algorithm's time complexity is, then it is said to consume linear time, or time. This essentially indicates that the execution time grows only linearly the with magnitude of the input. In more specific terms, this means that for any input of size n, there exists a constant c where the running time equals at most.How to handle visited vertex is the issue.
The time complexity isn't really linear as you follow because of the many visits.
If not, the following straightforward example will show that your algorithm is flawed:
1 --> 2 -----------> 3 --> 4
\ /
--> 5 -->
After finding 1-2-3-4 in the initial search, the search returns to 2 and finds 1-2-5-3. Now that number 3 has been visited, the search halts and ultimately fails.
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In a research proposal, which of the following sections discusses the types of scales to be used
for data collection?
a) Definition of the target population
b) Sample design
c) Data collection method
d) Specific research instruments e) Definition of the sample size
The correct answer is option C. In a research proposal, the Data Collection method discusses the types of scales to be used for data collection.
The Data Collection Method section of a research proposal is where the various scales for data collection are discussed. The types of scales (such as Likert scales, qualitative scales, etc.) and specific research instruments (such as surveys, interviews, questionnaires, or focus groups) typically are described in this section. that will be applied to the measurement of the variables. The target population and the definition of the sample size might also be discussed in the sample design section.
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which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?
Option (b) is correct. The sample size was not sufficiently large.
The histogram that is shown at the end of the answer shows the results of the simulation. We can clearly see that there are different variations in the population size. There are various reasons which can cause the simulation not to be normal. The main reason for this if the sample size is not big enough. That is because a theory stated that when the sample size taken by a person or researcher is not large or insufficient for the alpha level as well as the analysis one chooses to do, it will limit the statistical power of the study.
Due to the above, we can say that the sample size is not big enough that's why the simulation of the sampling distribution is not approximately normal. So option (b) is correct.
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Your question was incomplete, your most probable question was stated below:
A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation.
Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?
(a) The samples were not selected at random.
(b) The sample size was not sufficiently large.
(c) The population distribution was approximately normal.
(d) The samples were selected without replacement.
(e) The sample means were less than the population means.
Ted bought 2 bags of gravel and a potted tree that weighed 7.4 pounds at Marvin's Garden Shoppe. The total weight of his purchases was 16 pounds. How much did each bag of gravel weigh? Write and Solve Use a bar diagram and an equation to represent the situation. Then solve the equation. Each bag weighed 4.3 pounds.
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If you subtract a rational number from an integer, then the result is always __
Answer:
Rational
Step-by-step explanation:
You will always get a rational number when you add, subtract, multiply, or divide rational numbers with integers.
Hope it helps!
the not the play took in $728 one night. the number of $adult tickets was 14 less than twice the number of $5 child tickets.
Answer:
Let's call the number of $5 child tickets sold "x".
According to the problem, the number of $adult tickets was 14 less than twice the number of child tickets, so the number of $adult tickets sold can be represented as 2x - 14.
The total revenue from ticket sales was $728, so we can set up an equation:
5x + 20(2x - 14) = 728
Expanding the second term on the left side of the equation:
5x + 40x - 280 = 728
Combining like terms:
45x = 1008
Dividing both sides of the equation by 45:
x = 22.4
So the number of child tickets sold was 22 and the number of adult tickets sold was 2 * 22 - 14 = 36.
Use the distance formula to classify each A as scalene, isosceles, or equilateral. triangle ABC with vertices A(- 2, - 2) B(4, 3) and C(3,4)
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{(~~ 4- (-2)~~)^2 + (~~ 3- (-2)~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 6)^2 + ( 5)^2} \implies \boxed{AB=\sqrt{ 61 }} \\\\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill BC=\sqrt{(~~ 3- 4~~)^2 + (~~ 4- 3~~)^2}[/tex]
[tex]~\hfill BC=\sqrt{( -1)^2 + ( 1)^2} \implies \boxed{BC=\sqrt{ 2 }} \\\\\\ C(\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad A(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-2}) ~\hfill CA=\sqrt{(~~ -2- 3~~)^2 + (~~ -2- 4~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -5)^2 + (-6)^2} \implies \boxed{CA=\sqrt{ 61 }} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{two equal sides}}{\textit{\LARGE Isosceles}}~\hfill[/tex]
An ice cream shop has a special on banana splits, and Xing is taking advantage of it. He's astounded at all the options he has in constructing his banana split: He must choose three different flavors of ice cream to place in the asymmetric bowl the banana split is served in. The shop has 20 flavors of ice cream available. Each scoop of ice cream must be topped by a sauce, chosen front six different options. Xing is free to put the same type of sauce on more than one scoop of ice cream. There are 10 sprinkled toppings available, and he must choose three of them to have sprinkled over the entire banana split. (a) How many different ways are there for Xing to construct a banana split at this ice cream shop? (b) Suppose that instead of requiring that Xing choose exactly three sprinkled toppings, he is allowed to choose between zero and three sprinkled toppings In this scenario, how many different ways are there for him to construct a banana spin?
There are 38,400 different ways for Xing to construct a banana split at this ice cream shop if he is allowed to choose between zero and three sprinkled toppings.
a) In order to construct a banana split, Xing needs to select 3 flavors of ice cream, 6 sauces, and 3 sprinkled toppings. Therefore, the formula for the number of ways to construct a banana split is (20 flavors)(6 sauces)(10 toppings)^3. When calculated, this number is 28,800. This means that there are 28,800 different ways for Xing to construct a banana split at this ice cream shop.
b) In this scenario, the formula for the number of ways to construct a banana split is (20 flavors)(6 sauces)(10 toppings)^0 + (20 flavors)(6 sauces)(10 toppings)^1 + (20 flavors)(6 sauces)(10 toppings)^2 + (20 flavors)(6 sauces)(10 toppings)^3. When calculated, this number is 38,400. This means that there are 38,400 different ways for Xing to construct a banana split at this ice cream shop, with the option to choose zero, one, two, or three sprinkled toppings.
Therefore, there are 38,400 different ways for Xing to construct a banana split at this ice cream shop if he is allowed to choose between zero and three sprinkled toppings.
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What’s transformation is happening x,y ( x+2,y-3
The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed.
What is transformation?When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x² up by 3 units, the graph of the function f(x) = x² + 3 is obtained.
Given that the transformation of the coordinate is x,y ( x+2,y-3). Let the coordinate of the point be ( 2, 2 ).
The translation of the point will be:-
( 2 , 2 ) = ( 2 + 2 , 2 - 3 )
( 2 , 2 ) = ( 4 , -1 )
The graph of the translation of the point is attached with the answer below.
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In this figure, h = 6, and r = 8.
What is the exact surface area of the cone?
Enter your answer in the box.
units²
The surface area of Cone is 452.16 unit².
What is Surface area of Cone?The surface area of a cone is equal to the curved surface area plus the area of the base: π r² + πlr
where r is the radius and l is the slant height.
Given:
Radius= 8 unit
height= 6 unit
slant height, l = √8²+6²= √64+36 =√100= 10units
So, the Surface area of Cone
= πr (l +r)
= 3.14 x 8 ( 10 + 8)
= 25.12 x 18
= 452.16 unit²
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CAN SOMEONE HELP WITH THIS QUESTION?
The equation of the velocity is v(t) = 24t² - 24t - 288 and the time where velocity is equal to zero is t = -3 and t = 4.
What is differentiation?Apart from integration, differentiation is one of the two key ideas in calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a process called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation.
The function for the velocity can be found by differentiating the equation for the motion for the particle.
s(t) = 8t³ - 12t² - 288t
v(t) = d/ dt s(t)
v(t) = 24t² - 24t - 288
Velocity is zero for:
v(t) = 0
24t² - 24t - 288 = 0
t² - t - 12 = 0
t² - 4t + 3t -12 = 0
t(t - 4) + 3(t - 4) = 0
(t + 3)(t - 4) = 0
t = -3 and
t = 4
Hence, the equation of the velocity is v(t) = 24t² - 24t - 288 and the time where velocity is equal to zero is t = -3 and t = 4.
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the formula for calculating the ____ of a square is A = Length x Length
Therefore , the solution of the given problem of area comes out to be Formula for Square Area is = length * length.
Describe surface area.Its surface area provides a good estimate of its overall size. When computing a right triangle's squared, the surroundings are taken into consideration. The surface area of everything determines its overall size. The sum of the volumes on each of the six horizontal sides makes up the volume of water inside a cuboid. Utilize the following formula to get the box's dimensions: In 2lh, 2lw, and 2hw, the region is the same (SA). The flexible shape's total area serves as a representation of the area.
Here,
To fill the blank space in the given problem is
Formula for Square Area
We are aware that Side Side equals the area of a square.
7 7 Equals 49 when the side length of 7 cm is substituted.
As a result, the square's area is 49 cm2.
Therefore , the solution of the given problem of area comes out to be Formula for Square Area is = length * length.
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Jeriel goes out to lunch. The bill, before tax and tip, was $9.25. A sales tax of 3% was added on. Jeriel tipped 16% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.
Answer:
(9.25*0.03)+9.25=9.53
(9.53*0.16)+9.53=11.05
Sales tax was $0.28
Step-by-step explanation:
pls help asap !
.
.
.
.
.
Answer:
It's 59 degrees
find the volume common to two spheres, each with radius r, if the distance between their centers is r/2. [hint: it may be helpful to look at the previous question and see how it relates to this one. ]
The volume common to the two spheres is V = 2 * (2/3) * pi * r^3 = (4/3) * pi * r^3.
The volume shared by two spheres with radii r and centers separated by r/2 can be calculated by using the volume of a sphere equation and subtracting the volumes of two smaller spheres cut out by the intersection of the larger spheres.
Assume that the two spheres are centered at (r/2,0,0) and (-r/2,0,0). Finding the points where it intersects with a plane perpendicular to the x-axis and passes through the x-axis at x = r/4.
This plane cuts the spheres at two points, and the smaller spheres have the same radius as the distance between these points.
The radius of these spheres can be found using the Pythagorean theorem:
r = sqrt(r^2 - (r/2)^2) = sqrt(3r^2/4)
The volume of each smaller sphere is given by:
V = (4/3) * pi * (r)^3 = (4/3) * pi * (sqrt(3r^2/4))^3 = (2/3) * pi * r^3
Therefore, the volume common to the two spheres is given by:
V = 2 * (2/3) * pi * r^3 = (4/3) * pi * r^3.
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Which two solid figures have the same volume
americans tend to dine out multiple times per week. the number of times a sample of families dined out last week provides the following data. 7 2 6 4 9 4 1 4 2 4 5 2 3 5 2 0 6 7 4 2 a. compute the mean and median. mean (to decimals) median (to decimal) 4 b. compute the first and third quartiles. round the answers to decimal places, if necessary. first quartile 2 third quartile c. compute the range and interquartile range. round the answers to decimal places, if necessary. range 9 interquartile range d. compute the variance and standard deviation. round the answers to decimal places. variance standard deviation e. the skewness measure for these data is . comment on the shape of this distribution. the data are somewhat skewed to the right. is it the shape you would expect? yes why or why not? the skewness measure indicates the direction of the data skewness. f. compute the lower limit and the upper limit (to decimals and enter negative value as negative number.). lower limit upper limit do the data contain outliers? no, the data do not contain outliers.
The mean of the data is 4, the median is also 4. The range is 9, with an interquartile range of 2. The standard deviation is 2.14 and the skewness measure is 0.38, indicating a slight positive skew. No outliers are present.
(a) [tex]Mean = (7 + 2 + 6 + 4 + 9 + 4 + 1 + 4 + 2 + 4 + 5 + 2 + 3 + 5 + 2 + 0 + 6 + 7 + 4 + 2) / 20 = 4.[/tex]
[tex]Median = 4[/tex] (after sorting the data)
(b) First quartile (Q1) = 2 (after sorting the data and finding the median of the lower half)
Third quartile (Q3) = 6 (after sorting the data and finding the median of the upper half)
(c) Range = 9 - 0 = 9
Interquartile Range (IQR) = Q3 - Q1 = 6 - 2 = 4
(d)[tex]Variance = ((7-4)^2 + (2-4)^2 + (6-4)^2 + (4-4)^2 + (9-4)^2 + (4-4)^2 + (1-4)^2 + (4-4)^2 + (2-4)^2 + (4-4)^2 + (5-4)^2 + (2-4)^2 + (3-4)^2 + (5-4)^2 + (2-4)^2 + (0-4)^2 + (6-4)^2 + (7-4)^2 + (4-4)^2 + (2-4)^2) / 20 = 9.05[/tex]
Standard deviation = √Variance = √9.05 = 3.01
(e) Skewness measure = 0. The data are symmetrically distributed (i.e., not skewed to the left or to the right)
(f) Lower limit = 4 - 3.01 x 1.5 = -1.51
Upper limit = 4 + 3.01 x 1.5 = 8.51
Data does not contain outliers as all values are within the lower and upper limits.
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Part III: If a bottle of dishwashing detergent cost $0.31 in 1950, and if the price of
dishwashing detergent increased at the same rate as the CPI from 1950 to 1970,
what was the CPI to the nearest tenth in 1950?
the CPI to the nearest tenth in 1950 was 24.06.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, a bottle of dishwashing detergent cost $0.31 in 1950 and In 1970, a bottle of dishwashing detergent cost $0.50
Since CPI, Consumer Price Index measures the overall change in consumer prices based on a representative basket of goods and services over time.
The price of dishwashing detergent increased at the same rate as the CPI from 1950 to 1970.
So,
0.50 / 0.31 = CpI for 1970/ CPI for 1950
Since CPI in 1970 is 38.80
CPI in 1950 = 0.62 * 38.80
CPI in 1950 = 24.056
Therefore, the CPI to the nearest tenth in 1950 was 24.06.
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Complete question:
In 1970, a bottle of dishwashing detergent cost $0.50. To answer each of the parts below, assume that the consumer price index (CPI) was 29.6 in 1960, 38.8 in 1970, and 82.4 in 1980.
If the price of dishwashing detergent increased at the same rate as the CPI from 1970 to 1980, how much did a bottle of dishwashing detergent cost in 1980? By how much did the price of a bottle of dishwashing detergent increase from 1970 to 1980?