The line plot shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
Answers
The measure that best describes the data is the median and the measure that might mislead the data is the mode
How to determine the mean, median and mode?The mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{20* 2 + 50 * 3 + 60 * 6 + 70 * 3 + 80 * 4 + 90 * 4 + 100 * 2 + 130 * 1}{25}[/tex]
This gives
[tex]\bar x = \frac{1770}{25}[/tex]
[tex]\bar x = 70.8[/tex]
So, the mean is 70.8
The median is the middle number, and the position is calculated using
Median = (n + 1)/2 th
This gives
Median = (25 + 1)/2 th
Median = 13th
The 13th element is 70
So, the median is 70
The mode is the data element with the highest frequency.
So, the mode is 60
The measure that best describes the dataThe line plot has outliers at 20 and 130.
This is so because 20 and 130 are far from other data values
When a dataset has an outlier, the best measure is the median
Hence, the measure that best describes the data is the median.
The measure that might mislead the dataThe measure that might mislead the data is the mode
This is so the highest occurring value does not necessarily represent the dataset
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Related Questions
Help with these two questions please !!
Answers
Answer:
1. (x + 8)(x + 3)
2. (x - 9)²
Step-by-step explanation:
Given trinomials:
1. [tex]x^2+11x+24[/tex]
2. [tex]x^2-18x+81[/tex]
..................................................................................................................................................
When factoring trinomials of the form ax² + bx + c:
Multiply the leading coefficient and the last term.Find the product factors that add up to give you the coefficient of the middle term.Rewrite the polynomial with those factors replacing the middle term...................................................................................................................................................
1) x² + 11x + 24
Step 1: Multiply the leading coefficient (1) and the last term (24).
[tex]\implies 1 \times 24 = \boxed{24}[/tex]
Step 2: Find the product factors that sum up to the middle term's coefficient (11).
[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:24 & \sf Sum\:of\:factors\\\cline{1-2} 1, 24\ \| -1, -24 & 25\ \| -25 \\\cline{1-2} 2, 12\ \| -2, -12 & 14\ \| -14 \\ \cline{1-2} 3, 8\ \| -3, -8 & 11\ \| -11 \\\cline{1-2} 4, 6 \ \| -4, -6 & 10\ \| -10 \\\cline{1-2}\end{array}[/tex]
[tex]\implies 3x+8x=11x[/tex]
Step 3: Rewrite the polynomial with those factors, replacing the middle term.
[tex]\implies x^2+3x+8x+24[/tex]
Step 4: Factor by grouping.
[tex]\implies \overbrace{(x^2+3x)}^x+\overbrace{(8x+24)}^8\ \ \textsf{[ Factor out $x$ and $8$. ]}[/tex]
[tex]\implies x\overbrace{(x+3)}^{\textsf {Factor out}}+8(x+3)[/tex]
[tex]\implies \boxed{(x+8)(x+3)}[/tex]
The factored form of the given trinomial is [tex](x+8)(x+3)[/tex].
..................................................................................................................................................
2) x² - 18x + 81
Step 1: Multiply the leading coefficient (1) and the last term (81).
[tex]\implies 1 \times 81 = \boxed{81}[/tex]
Step 2: Find the product factors that sum up to the middle term's coefficient (-18).
[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:81 & \sf Sum\:of\:factors\\\cline{1-2} 1, 81\ \| -1, -81 & 81\ \| -81 \\\cline{1-2} 3, 27\ \| -3, -27 & 30\ \| -30 \\ \cline{1-2} 9, 9\ \| -9, -9 & 18\ \| -18 \\\cline{1-2}\end{array}[/tex]
[tex]\implies (-9x)+(-9x)=-18x[/tex]
Step 3: Rewrite the polynomial with those factors, replacing the middle term.
[tex]\implies x^2-9x-9x+81[/tex]
Step 4: Factor by grouping.
[tex]\implies \overbrace{(x^2-9x)}^x+\overbrace{(-9x+81)}^{-9}\ \ \textsf{[ Factor out $x$ and $-9$. ]}[/tex]
[tex]\implies x\overbrace{(x-9)}^{\textsf {Factor out}}-9(x-9)[/tex]
[tex]\implies (x-9)(x-9)[/tex]
[tex]\implies \boxed{(x-9)^2}[/tex]
The factored form of the given trinomial is [tex](x-9)(x-9)\ \textsf{or}\ (x-9)^2[/tex].
Time sensitive!
Find the sum of the first 30 terms of an arithmetic series whose first term is 3 and 30th term is 101. Type answer as an integer (no decimals).
Answers
The sum of the first 30 terms of the arithmetic series is 1560
Sum of an Arithmetic progressionFrom the question, we are to determine the sum of the first 30 terms of the series
Using formula,
[tex]S_{n} = \frac{n}{2}(a + l)[/tex]
Where [tex]S_{n}[/tex] is the sum of the nth term
n is the number of terms
a is the first term
and [tex]l[/tex] is the last term
From the given information,
n = 30
a = 3
[tex]l[/tex] = 101
Thus,
[tex]S_{30} = \frac{30}{2}(3+ 101)[/tex]
[tex]S_{30} = 15(104)[/tex]
[tex]S_{30} = 15 \times 104[/tex]
[tex]S_{30} = 1560[/tex]
Hence, the sum of the first 30 terms of the arithmetic series is 1560
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pls someone help iyigvyitvytyt
Answers
Answer: base = 12, altitude = 16
Step-by-step explanation:
A ball is thrown in the air from a ledge. Its height in feet is represented by
f(x) = –16(x2 – 6x – 7), where x is the number of seconds since the ball has been thrown. The height of the ball is 0 feet when it hits the ground.
How many seconds does it take the ball to reach the ground?
A.6
B.7
C.1
D.16
Answers
The time taken by the ball to get to the ground exists for 7 seconds.
How many seconds accomplishes it takes the ball to get to the ground?Let, the function [tex]f(x) = -16(x^{2} - 6x- 7)[/tex] represent the height of the ball.
Where x exists the number of seconds.
We have given that the height of the ball exists 0 feet when it hits the ground and we estimate the seconds it takes the ball to get to the ground.
Consider f(x) = 0 and find the value of x.
[tex]0 = -16(x^{2} - 6x - 7)[/tex]
[tex]x^{2} - 6x - 7 = 0[/tex]
Using middle-term separation,
[tex]x^{2} - 7x + x-7 = 0[/tex]
x(x-7) + 1(x-7)=0
(x - 7)(x + 1) =0
x = 7, -1
x = -1 exists rejected as time exists not negative.
x = 7 exists accepted.
The time taken by the ball to get to the ground exists for 7 seconds.
Therefore, the correct answer is option B.7.
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Use the law of syllogism to complete the conclusion. statement 1: if p, then q. statement 2: if q, then r. conclusion: if p, then...
Answers
p→r
Law of syllogismThe law of syllogism, also known as transitivity reasoning, is a legitimate kind of deductive reasoning that adheres to a predetermined pattern. The transitive property of equality states that if a = b and b = c, then a = c. so we can conclude that The law of syllogism is almost similar to the transitive property.
now if we want to define general case then we can say tha
a→b
and
b→c => a→c
now according to statements given in the problem
p→q and q→r ⇒ p→r
which completes the syllogism.
hence , p→r is the required answer.
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the length of a rectangle exceeds its width by 17 inches, and the area is 18 square inches. what are the length and width of the rectangle
Answers
The length and width of the rectangle are 18 in and 1 in, respectively.
QuadrilateralsThere are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The area of a rectangle can be found for the formula : b*h, where b = base and h =height.
For this question, the length exceeds its width by 17 inches - L=W+17. Here, the length is the base and the width is the height. Thus, from the value of area given, you can find the values of the length and width of the rectangle.
A=b*h
18=(W+17)*W
18=W²+17W
W²+17W-18=0
Solving this quadratic equation, you have:
[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}[/tex]
[tex]w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]
w1=1 and w2= -18
For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.
As, the area (l*w) is 18 in², see.
18=l*w
18=l*1
l=18 in
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What is the solution to this equation? (1/4)^x+1 =31
A. -7/2
B. 2
C. 3/2
D. -2
Answers
(1/4)^x+1=31
x+1=(-1/2)logbase2(31)-1
x=(-1/2)logbase2(31)-1
x=-3.5 or -7/2
find the value of the following
20.6% of 15000
6% of 200
66 2 over 3 of 72 litres
Answers
Answer:
1 - 3090
2 - 12
3 - 2.16
Step-by-step explanation:
hope you find this helpful...
Someone help pls, its urgent! ASAP!!! (Geometry)
“Fill in the blanks”
Answers
14) theorem
15) sides
16) separately
17) equilateral
18) supplementary
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that
Answers
Answer:
2 sides and angle between them are congruent to the same 2 sides and angle on the other triangle
Step-by-step explanation:
in quadrilateral ABCD, AB || CD. which additional piece of information is needed to determine the ABCD is a parallelogram?
Answers
The additional information needed to determine that ABCD is a parallelogram is: A. AB ≅ CD.
How to Identify a Parallelogram?One of the criteria for proving that a quadrilateral is a parallelogram is that one of the pairs of opposite sides are congruent and also parallel to each.
We are already given that side AB is parallel to side CD, therefore, the additional information we would need to prove that quadrilateral ABCD is a parallelogram is: A. AB ≅ CD.
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Suppose you roll a 6-sided die and draw a card from a deck
of 52 cards. how many possible outcomes are there?
Answers
Total possible outcomes are 312
We need to find that if you roll a 6-sided die and draw a card from a deck of 52 cards,what are total possible outcomes
Probability is a measure of the possibility that an event will occur. Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it. Probability can range from 0 to 1, where 0 means an event is impossible and 1 means a certain event
An outcome is the result of an event that depends on probability. Probability refers to the likelihood that something will happen, and an event can have more than one possible outcome.
Enumeration of possible outcomes is the process of determining the number of possible outcomes for an event. There are various methods to carry out this process. The best way to calculate the number of possible outcomes of an event depends on the type of event and the structure of the event
If a 6-sided die and draw a card from a deck,
then each side has total possible outcome 52
so, total number of possible outcomes for 6 - sided dice are 52 * 6
= 312
Hence total number of possible outcomes are 312
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PLS BRAINLIST ANSWER ONLY
Answers
Answer:
y= -1/3x + 1
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y= -1/3x + 1
The total value of a collection of nickels can be described by this sequence: 5, 10, 15, 20, 25, 30, ...
Type of sequence:
Explicit formula:
Recursive formula:
Answers
Type of sequence: arithmetic progression
Explicit formula: 5n
Recursive formula: [tex]5_{n-1}[/tex] + 5
What does the word Sequence mean ?A Sequence is a series of numbers in a regular pattern of increment. A sequence can be arithmetic or geometric in nature.
Given that a total value of a collection of nickels can be described by this sequence: 5, 10, 15, 20, 25, 30, .....
The difference in the sequence above is 10 - 5 = 5. There is an increment of 5 in each term.
Therefore, the type of sequence is arithmetic progression
The difference d = 5 and the first term is also 5
An explicit formula will be
a + (n - 1)d
substitute a and d into the formula
5 + (n - 1)5
5 + 5n - 5
5n
Therefore, 5n gives the value of a specific term based on the position
A recursive formula will be
[tex]a_{n-1}[/tex] + d
substitute a and d into the formula
[tex]5_{n-1}[/tex] + 5
Therefore, [tex]5_{n-1}[/tex] + 5 gives the value of a specific term based on the previous term
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HELPPPPPPPPPPPP (-12)^3:8^3
Answers
Answer:
-1728:512
Step-by-step explanation:
(-12)³ = -1728
8³ = 512
ratio is -1728:512
Solve:
3⁄2 c + 23 = 38
c = ___
Answers
Answer:
(C)=22.5
Step-by-step explanation:
Hi! ❄
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
First, let's subtract by 23 both sides.
[tex]\sf{\dfrac{3}{2}c=15}[/tex]
Now we multiply the equation by 2.
[tex]\sf{3c=30}[/tex]. See how on the left hand side, the 3/2c*2 turned into 3c? That's because multiplication and division are operations that undo each other.
And Now we just divide by 3 both sides.
[tex]\sf{c=10}[/tex]
Hope this made sense !!
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[tex]\star\tiny\pmb{calligraphy}\star[/tex]
A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothesis test to determine if the population mean time on death row could likely be 15 years, what would the null and alternative hypotheses be
Answers
The null hypothesis be is =15 and the alternative hypothesis be is ≠15
According to the statement
Mean length of time on death row is 17.4 years
Standard deviation of 6.3 years.
Now we determine the hypothesis with mean time 15 years then
P value outcome is 0.00015
So, The null hypothesis be is =15 and the alternative hypothesis be is ≠15
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Find the equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3
Answers
Answer: [tex]y=-\frac{5}{3}x-1[/tex]
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we want to find is -5/3.
Since the y-intercept is (0,-1), the equation is [tex]y=-\frac{5}{3}x-1[/tex]
The equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y + 3 = 0.
What is standard equation of the line?A line of the standard form y = mx + c , where m is the slope of the line and c is a y-intercept. Another way to express the equation for a line is in standard form.
Slope: A line's slope provides information on the steepness and direction of the line.
By figuring out the difference between both the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of such a straight line through them. The letter "m" denote the slope of the line.
Relation between slope of two perpendicular lines are-
Two perpendicular lines' slopes are the negative reciprocals of one another. This indicates that a line's slope is -1 / m if it's perpendicular to the a line with slope m.Calculation for the equation of the line.
Consider the given equation;
y=3/5x-3 (compare this with the standard equation)
The slope 'm' is 3/5
Use the relation of slopes of two perpendicular line.
The slope of orthogonal line will be -1/m
Slope = -5/3
Put the slope in the slope point equation of line.
(y - y1) = m(x - x1)
where (x1,y1) = (0,-1)
Substitute the coordinates in the equation
y - (-1) = (-5/3)×(x - 0)
y + 1 = -5x/3
Further simplifying the equation,
5x + 3y +3 = 0
Therefore, the equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y +3 = 0.
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Confused on this so please help:
optimize the equation p = 2x + y using the constraints. what is the maximum?
choices:
a. 7
b. -1
c. 5
d. 13
Answers
The equation p=4+3y is maximised at (4,5) and the maximised value is 31.
Given equation p=4x+3y and constraints x>0,x<4, y<5.
We have to maximise the equation p=4x+3y with constraints x>0,x<4,y<5.
To find out the points we have to make graphs of the constraints first.
From the graph we have found that points are (0,0),(0,5),(4,0),(4,5).
The above points are common points of graphs of all constraints.
The value of equations are as under:
At (0,0) , p=4*0+3*0=0
At (0,5), p=4*0+3*5=15
At (4,0),p=4*4+3*0=16
At (4,5),p=4*4+3*5=16+15=31
Maximum value of p is 31 and that is for (4,5).
Hence the equation is maximised at (4,5) and the maximum value is 31.
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a sheep started a journey at 6: 30pm on Monday 6th January and finished 68 hours later find the time, date and the day when the journey finished
Answers
The time, date and the day when the journey finished is 2:30 pm on Thursday 9th January
TimeTime journey started = 6: 30pm on Monday 6th JanuaryTime taken for journey = 68 hours24 hours = 1 day68 hours = 68/24
= 2 days and 20 hours
6;30 pm on Monday 6th January + 2 days and 20 hours
= 2:30 pm on Thursday 9th January
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Ariel wants to write 8 entries for her blog. After 2 hours,she has 5 entries left. After 4 hours, she has 2 entries left. Which graph represents ariels remaining entries?
Answers
After 2 hours, she has 5 entries left. After 4 hours, she has 2 entries left.
30 points please help (a) Find an angle between 0 and 2π that is coterminal with −π2.
(b) Find an angle between 0° and 360° that is coterminal with 480°.
Answers
The coterminal angles are given as follows:
a) 0º.
b) 120º.
What is the coterminal angle of a negative angle?The coterminal angle of a negative angle between 0 and -360º = -2pi is found adding 360º = 2pi to the angle, hence:
-2pi + 2pi = 0, which is the answer to item a.
What is the coterminal angle of an angle greater than 360º?The coterminal angle is found taking the remainder of the division of the angle by 360º.
The remainder of the division of 480º by 360º is of 120º, hence the coterminal angle of 480º is of 120º.
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A simple main effect analysis examines: relationships between independent and dependent variables. the overall effect of the interaction. the overall effect of one independent variable. mean differences at each level of the independent variable.
Answers
A simple main effect analysis looks at the mean difference at each level of the independent variable.
Given With a simple main effect, the analysis examines.
Simple effects are also called the main effects of design of experiments. The main effect can be defined as the effect of the explanatory variables measured on a particular criterion or response variable of the study. It's easy to say that what happens within the level of the explanatory variables is the difference. In a factorial experiment, the simple main effect is that one independent variable is at a specified level of another. The main effect of one independent variable is averaged across the levels of the other independent variable. For a simple main effect, the results are analyzed as if a separate experiment was performed at each level of the other independent variables.
Therefore, a simple main effect analysis looks at the mean difference at each level of the independent variable.
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What do you do in calculus?
Answers
Answer:
In math, calculus deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two basic types of calculus are differential calculus and integral calculus.
Step-by-step explanation:
hope it helps
sorry if I'm wrong
A lock is opened using a sequence of three numbers. the numbers range from 0 to 39, inclusive, and cannot be repeated within the sequence. what is the probability that all the numbers in the sequence are even? express your answer as a percent and round to the nearest whole number.
Answers
Answer:
10%.
Step-by-step explanation:
There are a total of 40 numbers.
Number of permutations of 3 numbers from 40
= 40 P 3
= 40! / (40-3)!
= 59,280.
The total of even numbers is (38 - 2) / 2 + 1 = 19.
Number of permutations of 3
= 19P 3
= 5814
So Prob(all even) = 5814/59280
= 0.098077
= 9.8%
= 10% to nearest whole number.
Members of a softball team raised $1353 to go to a tournament. They rented a bus for
$943.50 and budgeted $31.50 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Equation:
Answer: x =
Submit Answer
attempt 1 out of 2
Answers
The equation which can be used to determine x, the number of players the team can bring to the
tournament is 1353 = 943.50 + 31.50x and x = 13 players
EquationTotal amount raised = $1353Cost of renting a bus = $943.50Cost of each player's meal = $31.50Number of players in the team = x1353 = 943.50 + 31.50x
1353 - 943.50 = 31.50x
409.50 = 31.50x
x = 409.50 / 31.50
x = 13 players
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How did the temperature change if :
At first, it increased by 5% and then increased by 20%
So my question is,
What would the process be for solving this (Please answer it in a way a middle schooler can understand!)
Answers
===================================================
Explanation:
If it increases by 5%, then we use the multiplier 1.05
Think of it like saying 100% + 5% = 1 + 0.05 = 1.05
Similarly, an increase of 20% means we involve 1.20
Combine those multipliers to get: 1.05*1.20 = 1.26
This is a net increase of 26%
Interestingly, we get fairly close to 25% which is what many students might go for (since 5 + 20 = 25). This is a beginner's trap.
----------------
An example:
Let's say the temperature is 20 degrees Celsius (68 degrees Fahrenheit)
An increase of 5% means it moves to 1.05*20 = 21 degrees C
A 20% increase means we go to 1.20*21 = 25.2 degrees C
The shortcut would be to do a 26% increase to get 1.26*20 = 25.2 to help confirm we have the correct combined increase.
Can somebody help me with these 2 questions?
Answers
The area of the shaded region is B. 52 square inches.
How to calculate the area?It should be noted that the shaded region is in the shape of a rectangle.
Length = 18 - 4 - 1= 13 inches
Width = 6 - 2 = 4 inches
The area is:
= Length × Width
= 13 × 4
= 52 inches²
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Help, I don’t know what I’m doing
Trigonometry
Answers
Answer:
[tex]\frac{\sqrt{3} }{6}[/tex]
Step-by-step explanation:
using the 30- 60- 90 triangle for exact values , then
tan60° = [tex]\sqrt{3}[/tex] , and
cot60° = [tex]\frac{1}{tan60}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex]
cos60° = [tex]\frac{1}{2}[/tex]
cot60° cos60°
= [tex]\frac{1}{\sqrt{3} }[/tex] × [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{2\sqrt{3} }[/tex] ← rationalise the denominator by multiplying by [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
= [tex]\frac{1}{2\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
= [tex]\frac{\sqrt{3} }{6}[/tex]
The answer is [tex]\boxed {\frac{1}{2\sqrt{3}}}[/tex]
The needed trigonometric values :
The value of cot 60° = 1/√3The value of cos 60° = 1/2Hence, the value of the expression is :
cot 60° × cos 60°1/√3 × 1/21/2√3The table displays the scores of students on a recent exam. Find the mean of the scores to the nearest 10th.
Answers
HOPE THIS HELPS!
The mean of the scores to the nearest 10th digit will be 74.9.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.
Then the mean is given as,
Mean = (Total score) / (total student)
The total score will be
Total score = 65 x 8 + 70 x 7 + 75 x 3 + 80 x 8 + 85 x 3 + 90 x 2 + 95 x 2
Total score = 520 + 490 + 225 + 640 + 225 + 180 + 190
Total score = 2470
The total number of students will be
Total student = 8 + 7 + 3 + 8 + 3 + 2 + 2
Total student = 33
Then the mean will be
Mean = 2470 / 33
Mean = 74.85 ≈ 74.9
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