- Identify the outlier in the data set {12, 15, 20,
44, 18, 20}, and determine how the outlier
affects the mean, median, mode, and range of
the data.
The outlier in the data set {12, 15, 20, 44, 18, 20} is 44. It significantly increases the mean and range of the data set, but the median and mode are less affected. The outlier highlights sampling variability and induced variability.
The student has asked to identify the outlier in the data set {12, 15, 20, 44, 18, 20} and assess how it affects the mean, median, mode, and range of the data. Considering the provided data, it's apparent that the number 44 is the outlier since it is significantly higher than the rest of the numbers in the set. To confirm, we can calculate the interquartile range (IQR) and use it to detect outliers, but since the data set is small, a visual inspection is sufficient.
Without the outlier (44), the data set is {12, 15, 18, 20, 20}. The mean (or average) is calculated by adding all the numbers and dividing by the count of numbers, which results in a mean of (12 + 15 + 18 + 20 + 20) / 5 = 17. The median, which is the middle number when the data is sorted, is 18. The mode, the number that appears most often, is 20 in this case. As for the range, which is the difference between the largest and smallest number, it's 20 - 12 = 8.
With the outlier included, the mean becomes (12 + 15 + 18 + 20 + 20 + 44) / 6 = 21.5, the median remains 18, the mode is still 20, and the range expands to 44 - 12 = 32. Clearly, the outlier has a significant effect on the mean and range, causing them to increase, while the median and mode are less impacted due to their nature of being more resistant to extreme values. The presence of an outlier shows some degree of sampling variability and may introduce induced variability in the analysis of data.
What is the probability Jane gets a cone with any ice cream and any topping?
1/12
1/4
1/2
2/3
what is -3+1/3=?
what is 5+6+7x+3=
Answer:
-3+1/3=-8/3 or-2.6, 5+6+7x+3=7x+14
Step-by-step explanation:
Answer:
-3+1/3= -2.66666666667
Step-by-step explanation:
a triangular metal plate with a triangular metal plate placed in a box with a regular triangular prism with all the side edges 3 dm. It rests on the edge of the base and is inclined to the bottom of the box at an angle of 60 °. Calculate the area of the plate 0.01 dm2 accuracy. Take a look at how the spacing between planes is measured.
Answer:
6.75 dm²
Step-by-step explanation:
All the side edges in the regular triangular prism are 3 dm long. Then, the base of the triangular plate is 3 dm long, and the other two sides are: √[3² + 3²] = 4.24 dm long (a right triangle is made and Pythagorean theorem is applied).
The height of the triangular plate is: √[4.24² + 1.5²] = 4.5 dm long (again Pythagorean theorem is applied)
Area of the triangular plate is: base*height/2 = 3*4.5/2 = 6.75 dm²
Find the equation of the line that is perpendicular to y = – 1 3 x + 2 and passes though the point (–5, 2)
A) y = 3x + 13
B) y = 3x + 17
C) y = –3x + 13
D) y = –3x + 17
Answer:
y = 3x + 17
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Question 12 (Multiple Choice Worth 5 points)
(05.02 MC)
What is the slope-intercept form equation of the line that passes through (5, 7) and (8, 22)?
Oy= -5x + 18
Oy=5x - 18
Oy=-5x - 18
O y = 5x + 18
Answer:
y = 5x - 18
Step-by-step explanation:
Points:
Equation of the line:
y = ax + b
(5; 7) and (8; 22)
(5; 7)
7 = 5a + b
(8; 22)
22 = 8a + b
a and b are the same values:
{- 5a - b = - 7
{8a + b = 22
3a = 15
a = 5
5a + b = 7
5.5 + b = 7
25 + b = 7
b = 7 - 25
b = - 18
Equation:
y = 5x - 18
I Hope I've helped you.
Final answer:
The slope-intercept form equation of the line that passes through the points (5, 7) and (8, 22) is y = 5x + 18, found by first calculating the slope and then using the point-slope form to solve for y.
Explanation:
To find the slope-intercept form of the equation of the line that passes through the points (5, 7) and (8, 22), we first need to calculate the slope (m). The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using our points, this becomes:
m = (22 - 7) / (8 - 5) = 15 / 3 = 5
Now, we use one point and the slope in the point-slope form of the equation, y - y1 = m(x - x1), which becomes:
y - 7 = 5(x - 5) => y - 7 = 5x - 25
Solving for y to get the slope-intercept form, y = mx + b:
y = 5x + (25 - 7) = 5x + 18
So, the correct slope-intercept form equation of the line is y = 5x + 18.
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Answer: B
Step-by-step explanation:
How is factoring a trinomial different than factoring a number?
Answer:
Hope this answers the question.
Step-by-step explanation:
Factoring a number: If you use the number 10, for example, you have to find all the factors to factor it. 1, 2, 5, 10.
Factoring a trinomial: If you use the trinomial x^2 + 16 + 64, for example, to factor it you need to first find what numbers multiply up to 64 and also add up to 16. In this case, those numbers are 8, and so you get (x + 8)^2.
Final answer:
Factoring a number involves breaking it down into its prime factors, a straightforward process within the real number system. Factoring a trinomial, particularly in algebra, requires finding binomials that, when multiplied, return the original trinomial and can extend to complex numbers, guided by the fundamental theorem of algebra.
Explanation:
Factoring a trinomial and factoring a number are two very different processes within the realm of mathematics. When we talk about factoring a number, we refer to breaking it down into its prime factors, which are the prime numbers that multiply together to give the original number. For instance, factoring the number 10 would give us 2 and 5, since 2 x 5 = 10. This process is straightforward and applies to the number system.
On the other hand, factoring a trinomial involves finding two binomials that, when multiplied together, result in the original trinomial. This is more commonly encountered in algebra, especially when dealing with second-order polynomials (quadratics). For example, factoring the trinomial x² + 5x + 6 involves finding two binomials (x + 2) and (x + 3), since (x + 2)(x + 3) = x² + 5x + 6. Furthermore, factoring trinomials can extend into complex numbers where every nth-order polynomial can be factored into n linear factors in the complex number system, according to the fundamental theorem of algebra.
In summary, factoring a number focuses on prime factorization within the real number system, while factoring a trinomial involves algebraic manipulation that can extend into handling complex numbers and requires an understanding of both real and complex number systems.
Will mark brainliest! Need help (50 points)
Answer:
(-4y,+12y), (z,19z)
Step-by-step explanation:
i got the same question.
Triangle ABC is similar to triangle DEF. What is EF?
Answer:
24
Step-by-step explanation:
First, divide 30.4 by 19 to get your factor.
You get 1.6
Then times 1.6 by 15 to get 24 for EF.
x^2 – 3x – 7 = 0
Solve the quadratic equation using the quadratic formula.
Answer:
x^2-3x-7=0. x2−3x−7=0 x 2 - 3 x - 7 = 0.
Step-by-step explanation:
x^2-3x-7=0. x2−3x−7=0 x 2 - 3 x - 7 = 0. Use the quadratic formula to find the solutions. −b±√b2−4(ac)2a - b ± b 2 - 4 ( a c ) 2 ...
Answer:
x=3/2 ± √37/2
Step-by-step explanation: the answer
Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4. Nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power of 4 to get StartFraction r Superscript negative 20 Baseline s Superscript negative 12 Baseline Over r Superscript 32 Baseline s Superscript 8 Baseline EndFraction. Calvin claims the first step to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4. Who is correct and why? Nadine is incorrect because she should have applied the quotient of powers rule first. Nadine is correct because she correctly applied the power of a product rule. Calvin is incorrect because he should have applied the power of a product rule first. Calvin is correct because he correctly applied the quotient of powers rule.
Answer:
what is the question
Step-by-step explanation:
plsss give brainliest
The correct answer is Calvin is correct because he correctly applied the quotient of powers rule.
The correct option is (D).
Calvin is correct because he correctly applied the quotient of powers rule.
According to the quotient of powers rule, [tex]\( \frac{a^m}{a^n} = a^{m - n} \).[/tex]
So, in this case:
[tex]\[ \frac{r^{-5}s^{-3}}{r^8s^{-2}} = r^{-5 - 8}s^{-3 - (-2)} = r^{-13}s^{-1} \][/tex]
Then, when you raise this expression to the power of -4:
[tex]\[ (r^{-13}s^{-1})^{-4} = r^{-13 \times -4}s^{-1 \times -4} = r^{52}s^4 \][/tex]
Nadine's approach would result in:
[tex]\[ \left( \frac{r^{-5}s^{-3}}{r^8s^{-2}} \right)^{-4} = \left( \frac{e^{-20}s^{-12}}{r^{32}s^8} \right) \][/tex]
Which is incorrect.
So, the correct answer is D. Calvin is correct because he correctly applied the quotient of powers rule.
complete question given below:
Nadine and Calvin are simplifying the expression ( (r^(-5)s^(-3))/r^8s^(-2) ). Nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power (e^(-20)s^(-12))/r^(32)s^8 . Calvin claims the first step to simplify the expression is to apply the quotient of powers to get (r^(-13)s^(-1))^-4.
Who is correct and why?
A.Nadine is incorrect because she should have applied the quotient of powers rule first.
B.Nadine is correct because she correctly applied the power of a product rule.
C.Calvin is incorrect because he should have applied the power of a product rule first.
D.Calvin is correct because he correctly applied the quotient of powers rule
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Betsy's high school is putting on a production of a play as a fundraiser for the school's music programs. A local bank has agreed to allow the school to use a line of credit from which they can withdraw money to pay for the play. Then, any deposits they make at the bank will be applied to the negative balance of the credit account.
The play cost $3,200.00 to produce, and they intend to sell tickets for $10 each. After the play, Betsy will take the ticket proceeds and deposit them with the bank. If 1,007 people attend the play's opening night, what will the balance of the bank account be?
A.
$13,270
B.
$6,870
C.
$10,070
D.
- $3,099
Answer:
B. $6,870
Step-by-step explanation:
Calculate how much money they earned from tickets then subtract the cost of making and that's their balance:
(1007×10)-3200=
10070-3200=
$6,870
B. $6,870
Final answer:
After calculating the total proceeds from selling tickets to 1,007 attendees at $10 each, the balance of the line of credit used to fund the play's production ($3,200) will be a positive $6,870.
Explanation:
The question pertains to a fundraiser calculation for Betsy's high school play. To determine the balance of the bank account after ticket sales, we must calculate the total proceeds from selling tickets to the attendees and then adjust the balance of the line of credit that was originally used to fund the production.
The production cost is $3,200.00, and tickets are sold at $10 each. With 1,007 people attending, the total ticket proceeds will be 1,007 imes $10 = $10,070. Since the school used a line of credit to pay for the play, the proceeds will pay off this balance. Hence, after depositing the ticket sales, the balance is:
Balance after deposit = Ticket proceeds - Production costs
= $10,070 - $3,200
= $6,870 (Credit balance)
The correct balance of the bank account after the play's opening night is therefore $6,870 (Option B).
2/7> b+5/7 what is “B”
Answer:
-3/7 > b
Step-by-step explanation:
2/7> b+5/7
Subtract 5/7 from each side
2/7-5/7> b+5/7-5/7
-3/7 > b
If y=-16 when x=4 find x when y=48
Answer:
x= -12
Step-by-step explanation:
Assuming this is a direct variation
y = kx
When y = -16 x =4 we can find k
-16 = k*4
Divide each side by 4
-16/4 = 4k/4
-4 =k
So
y = -4k
Y = 48
48 = -4x
Divide each side by -4
48/-4 = -4x/-4
-12 =x
PLZZZZZ HELP ME HELP A DUMB CHILD OUT
Answer:
80 inches
Step-by-step explanation:
Pythagorean theorem
In June, Cory begins to save money for a video game and a TV he wants to buy in December.
He starts with $22. Each month he plans to save 10% more than the previous month. How
much money will he have at the end of December?
A) 186.72
B) 208.72
C) 188.56
D) 204.56
Answer: B
Step-by-step explanation:
The answer is 32.2102.
In June, Cory begins to save money for a video game and a TV he wants to buy in December.
He starts with $22. Each month he plans to save 10% more than the previous month.
How to find how much money will he have at the end of December?
the given scenario is an application of a geometric sequence with
a1=$20 and r= 22/2 *100 = 1.1
. Since December is 6 months from June, then to find out the 6th term.
As, a2 = a1 * r = 20 × 1.1 = 22
a3= a2 *r = 22 * 1.1 = 24.2
a4= a3 * r = 24.2 * 1.1 = 26.62
a5=a3 * r = 26.62 *1.1 = 29.282
a6= a4*r = 29.282 * 1.1 = 32.2102.
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To make fruit punch, Tyrone needs 3 3/8 quarts of orange juice and 3 3/4 quarts of cranberry juice.
How many quarts of juice does he need in all?
Calculate the area of the shaded region
Answer:
48π or 150.72
Step-by-step explanation:
The radius of the big circle is 8.
We can use that to find the area of the big circle.
Area is πr^2
π(8)^2
64π
Now, we can find the area of the small circle.
The diameter of that is 8, meaning the radius is 4.
πr^2
π(4)^2
16π
Now we subtract the area of the small circle from the area of the big circle to get the area of the shaded region.
64π-16π=48π
As a decimal: 48*3.14=150.72
Philip shoots an arrow from the top of a hill into the ground. the flight of the arrow can be modeled with the quadratic function y=-5x^2+15x+90, where y represents the vertical height of the arrow, in meters, and x represents the time, in seconds. use factoring to find the positive zero of the function. what does this zero represent? then find the maximum value of the function by completing the square. what does the maximum value represent? explain each step in your answer.
Answer:
(a)Time taken to reach the ground, x=6 seconds
(b)Maximum height of the arrow during its flight =101.25 feet
Step-by-step explanation:
Given the quadratic function which models the flight of the arrow:
[tex]y=-5x^2+15x+90[/tex]
Where:
y represents the vertical height of the arrow, in meters; and x represents the time, in seconds.(a)Positive Zero
[tex]-5x^2+15x+90=0\\-5(x^2-3x-18)=0\\-5(x^2-6x+3x-18)=0\\-5(x(x-6)+3(x-6))=0\\-5(x+3)(x-6)=0\\x+3=0\:or\:x-6=0\\x=-3,x=6[/tex]
In 6 seconds, the arrow will hit the horizontal plane, i.e. the ground.
(b)
[tex]y=-5x^2+15x+90\\y-90=-5(x^2-3x)\\y-90-5(\frac{9}{4}) =-5(x^2-3x+(\frac{3}{2} )^2)\\y-101.25=-5(x-\frac{3}{2} )^2\\y=-5(x-\frac{3}{2} )^2+101.25[/tex]
Comparing with the vertex form:
[tex]y=a(x-h)^2+k[/tex]
Our vertex, (h,k)=(1.5, 101.25)
Maximum Value of y=101.25
The maximum value of y represents the maximum height of the arrow during its flight, which is 101.25 feet.
What is the horizontal distance from the plane’s starting position to its finishing position???? I will mark brainliest
Answer:
The answer would be 13.3.
Step-by-step explanation:
Use the Pythagorean theorem to find the other distances in the 5, 3, x triangle and the 7, 3, y triangle and add those two answers together plus 3 to get your answer.
Answer:
13.3 kilometers
Step-by-step explanation:
You need to use Pythagorean theorem for x+3+y.
The distance you would be looking for is 4+3+6.3=13.3
What are the constant of proportionality on these two?
Answer:
k = y/x
as a fraction for both
A triangle is reduced. A triangle has a base of 16 inches, a height of 12 inches, and a side length of 20 inches. A smaller triangle has a base of 12 inches, a height of 9 inches, and a side length of the blank. Not drawn to scale What is the perimeter of the reduced triangle, in inches?
A.) 15
B.) 21
C.) 36
D.) 48
Answer:
A
Step-by-step explanation:
Answer:
The answer is 15
Step-by-step explanation:
i took the test
Which expression represents the volume, in cubic units, of the composite figure?
Answer:
11.17
Step-by-step explanation:
Someone please help
1.20 Euro
BruhBruhBruh
Answer:
£1.20
Step-by-step explanation:
2/5 on magazine and 1/3 on dance lesson then we need to add these together by converting them to same fraction multiples.
2/5 x 3 = 6/15
1/3 x 5 = 5/15
6/15 +5/15 = 11/15
11/15 of 4.50 is found by division of the multiplier (the denominator)= 15
4.50/15 = 0.3 nb/ 0.3 = 1/15 of the whole 11 we search for
We then can multiply 0.3 x 11 as we have 1/15 and want 11/15
0.3 x 11 = 3.3
£3.30 = value of spending on dance lesson and magazine
0.3 x 4 = 1.2 = value of left over money
£1.20 converted to monetary
Please help me! It would be very much appreciated
Answer:
Answer is x = 100 degrees.
Step-by-step explanation:
Vertically opposite angles are equal.
Then value of x is 100 degrees.
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
Step-by-step explanation:
[tex]x = 100 \: \: degrees[/tex]
(vertically opposite angles)hope this helps
brainliest appreciated
good luck! have a nice day!
2(b+c) (use the distributive property)
Answer:
2b + 2c
Step-by-step explanation:
when distributed, the 2 get multiplied by the b and the c, so you'd have 2b + 2c.
Answer:
Answer is 2b + 2c
Step-by-step explanation:
2(b+c) you multiply 2 with b and then with c
PLEASE HELP!! WILL GIVE BRAINLIEST !!!
Which of the following is true of the data represented by the box plot?
box plot with point at 15, min at 17, Q1 at 51, median at 65, Q3 at 74, max at 90
A) If the outlier is included in the data, the median would not significantly change.
B) If the outlier is included in the data, the mean would increase.
C) If the outlier is included in the data, the box plot would be significantly skewed.
D) If the outlier is included in the data, the length of the tails would change significantly.
Answer:
the outlier is the point at 15
the data is skewed to the bottom because the values below the median are far more spread out; there are more extreme values that are far below the median than above the median.
Step-by-step explanation:
A) If the outlier is included in the data, the median would not significantly change.
Box Plot is a pictorial way of denoting data's distribution on the basis of Quartile 1, Quartile 3, Minimum, Median and Maximum
Outliers are the data observations or points, lying at huge significant difference (distance) from other concentrated data observation points.
A data value below the Box Plot Minimum, or above the Box Plot Maximum is an Outlier.Median is a Positional average, the mid point of data. It divides the data into two equal halves, 50% below it & 50% above it.
Median is not effected by extreme values like Outliers. So, inclusion of outliers doesn't significantly change Median.Mean is an Arithmetic Average. It is effected by extreme values like outliers. However, in this case of presence of Lower Outlier, the mean would decrease rather than increasing.
Skewness or Tail in the data denotes concentration of values in either (lower or higher side). It is not related to outliers.
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1. Without solving, identify whether this equation has a solution that is positive, negative, or zero:
3x – 5 = -3
2. Solve the equation.
x - 5(x - 1) = x - (2x - 3)
Answer:
3
Step-by-step explanation:
The equation will have a positive solution and the value of x will be 2/3.
What is an equation?A mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, x - 5(x - 1) = x - (2x - 3)
On solving,
x-5x+5 = x-2x+3
3x = 2
x = 2/3
Hence, The equation will have a positive solution and the value of x will be 2/3.
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please help me! i’ll give brainliest!