The Interquartile range i.e 1.5 (IQR) is used to identify outliers in a set of data which is the correct answer would be option (A).
What is the Interquartile range (IQR)?We may build up a "fence" outside of Q1 and Q3 by using the Interquartile range (IQR) method of spotting outliers. Outliers are values that fall outside of this range.
To construct this barrier, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3. This provides us with the lowest and maximum fence posts against which we will compare each observation.
Outliers are observations that are greater than 1.5 IQR below or above Q1. Minitab's default strategy for identifying outliers is this.
Therefore, the Interquartile range (IQR) is used to identify outliers in a set of data.
Hence, the correct answer would be option (A).
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
The answer is 75 degrees
Step-by-step explanation:
Remember that the sum of the three angles of any triangle is 180 degrees.
So, 180=58+47+x
180=105+x
75=x
Need help with writing a rule to describe each transformation
Explanation
By observation, we can see that the transformation from the original to the image, is a rotation of 90 degrees counterclockwise about the origin.
Answer: Option D
The table shows the votes of 900 people in the last elections.
Political
Party
Labour
Conservative
Lib Democrat
Other
Frequency
345
480
60
15
Angle in
Complete the table and draw a pie chart
to represent this information.
Note: Please draw your pie chart in a 'clockwise' direction from the line already drawn
and follow the order from the table (Labour, then Conservative etc...).
The angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.
The table shows the votes of 900 people in the last elections.
Political Party Frequency Angle in
Labour 345
Conservative 480
Lib Democrat 60
Other 15
345 + 480 + 60 + 15 = 900
The total angle in a pie chart is 360
The angle for labour is = 360 (345 / 900) = 138 degree
The angle for Conservative is = 360 (480 / 900) = 192 degree
The angle for Lib democrate is = 360 (60 / 900) = 24 degree
The angle for others is = 360 (15 / 900) = 6 degree
Therefore, the angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.
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2x(x+7) + 35 = (x + 1)x(x+1) -2
Answer:
x= -6
Step-by-step explanation:
1
Distribute
2
Distribute
3
Distribute
4
Multiply by 1
5
Combine like terms
6
Subtract the numbers
7
Move terms to the left side
8
Distribute
9
Add the numbers
10
Combine like terms
11
Multiply by 1
12
Combine like terms
13
Use the quadratic formula
14
Evaluate the exponent
15
Multiply the numbers
16
Subtract the numbers
17
Evaluate the square root
18
Add zero
19
Multiply the numbers
20
Cancel terms that are in both the numerator and denominator
100pts. find the area of these questions below
Answer:
20 feet²Step-by-step explanation:
triangle area formula: A = 1/2 × b × h
Find the base7 +3 = 10 ft
Find Area1/2 10 × 4 =
5 × 4 =
20 feet²
Can you help me find the x and y of this triangle I don’t understand it
Answer: [tex]x=5\sqrt{3}, y=15[/tex]
Step-by-step explanation:
[tex]\sin 60^{\circ}=\frac{x}{10}\\\\x=10 \sin 60^{\circ}\\\\x=5\sqrt{3}\\\\\\\tan 30^{\circ}=\frac{5\sqrt{3}}{y}\\\\\sqrt{3}=\frac{y}{5\sqrt{3}}\\\\y=15[/tex]
graph the linear equation 50 points will mark brainliest
You can see the three points where the result is equal to an integer in the photo below. Good luck!
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a divisor of 6". Find P(A). Outcome Probability 1 0.044 2 0.065 3 0.194 4 0.304 5 0.103 6 0.003 7 0.102 8 0.004 9 0.095 10 0.086
P(A) = P(6) = 0.003
answer: 0.003
there are 100 coins and someone flips them and doesn't tell us the results. i can ask one yes/no question. after the answer i will start guessing the coin flip results. for each correct guess i get 1 dollar and for each wrong guess i lose 1 dollar. what is the best strategy to play this game and what is the maximum expected value of the return.
The answer is not 1 so it is not that simple that you can divide it into 2 equal size subsets and ask whether the final sequence is in there. From what I got through his hints, it should be related to Central Limit theorem.
Given that,
One hundred coins are flipped, but the outcome is kept a secret. I am able to pose one yes/no query. I'll begin speculating on the outcomes of the coin toss following the response. I receive $1 for each accurate guess, and I lose $1 for each unreliable guess.
To find:
What is the most effective gaming approach and what is the highest possible return on investment
By Central Limit Theorem,
It is not straightforward to divide the response into two subsets of equal size and then check to see if the final sequence is present because the answer is not 1. His indications led me to believe that it should be connected to the Central Limit theorem.
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3. Determine the percent of each quantity.
a. 7% of 80
c. 12% of 320
b. 15% of 55
d. 8% of 300
Answer:
a. 5.6
b. 38.4
c. 8.25
d. 24
Step-by-step explanation:
Expand and simplify each polynomial (Answer both problems)
1. (a^2-3a)^2
2. (1/2x^3 +6x)^2
The simplified form of polynomials are:
1. (a² - 3a)² = 3a²
2. (1/2x³ + 6x)² = -12x²
Given,
We have to expand the given polynomials and simplify them.
1. The polynomial: (a² - 3a)²
Here,
The polynomial is in the form of (a - b)²
So,
(a - b)² = a² - 2ab + b²
Then,
(a² - 3a)² = (a²)² - (2 × a² × 3a) + (3a)²
(a² - 3a)² = a⁴ - 6a³ + 9a²
(a² - 3a)² = a²(a² - 6a + 9)
Here,
(a² - 6a + 9) is in quadratic form. Solve using quadratic formula.
a = 1, b = -6 and c = 9
[tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex] = [tex]\frac{6(+-)\sqrt{(-6)^{2}-4(1)(9) } }{2(1)}[/tex] = [tex]\frac{6(+-)\sqrt{36 - 36} }{2}[/tex] = [tex]\frac{6(+-)\sqrt{0} }{2}[/tex] = (6±0) / 2
= 6/2 = 3
Then,
(a² - 3a)² = a²(a² - 6a + 9)
Here,
(a² - 6a + 9) = 3
So,
(a² - 3a)² = 3a²
2. The polynomial: (1/2x³ + 6x)²
Here, the polynomial is in the form (a + b)²
(a + b)² = a² + 2ab + b²
Here,
(1/2x³ + 6x)² = (1/2x³)² + (2 × 1/2x³ × 6x) + (6x)²
(1/2x³ + 6x)² = 1/4x⁶ + 6x⁴ + 36x²
(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)
a = 1/4, b = 6 and c = 36
Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex]
= [tex]\frac{-6(+-)\sqrt{(-6)^{2} -4(1/4)(36)} }{2(1/4)}[/tex] = [tex]\frac{-6(+-)\sqrt{36-36} }{1/2}[/tex] = (-6±0) / (1/2) = -6 × 2 = -12
Therefore,
(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)
Here,
(1/4x⁴ + 6x² + 36) = -12
Then,
(1/2x³ + 6x)² = -12x²
That is,
The simplified form of polynomials are:
1. (a² - 3a)² = 3a²
2. (1/2x³ + 6x)² = -12x²
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The following graph shows a proportional relationship.
What is the constant of proportionality between y and x in the graph?
The constant of proportionality between x and y in the given graph above is determined as: 2.
What is the Constant of Proportionality?The constant of proportionality of a proportional relationship between two variables, x and y, can be defined as the ratio of y to x, which is expressed as, k = y/x, where x and y are the coordinates of one point one the line that represents the proportional relationship.
Using the coordinates of a point on the graph, (2, 4), find the constant of proportionality, k:
Constant of proportionality (k) = y/x = 4/2
Constant of proportionality (k) = 2
Therefore, the constant of proportionality that represents the proportional relationship between the variables, x and y, is calculated as, 2.
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which expression is equivalent to (2x^2+4x-7)(x-3) pls help soon
Answer:
Since you do not have any answer choices, I will step-by-step solve the equation for you. Typically what happens with problems like this is the answer choices will match the work when solving. So, pay attention to my scratch-work and if any answers match the answer choices, then that is most likely the correct answer. (Hint: the solution to the equation is most likely the correct answer)
Write the equation:
(2x^2 + 4x – 7)(x – 3)
Simplify and Distribute:
(2x^2 + 4x – 7)(x – 3)
2(x – 3)^2 + 4x(x – 3) – 7(x – 3)
2x^3 – 6x^2 + 4x
(x – 3) – 7(x – 3)
2x^3 – 6x^2 + 4
x^2 – 12x – 7(x – 3)
2x^3 – 6x^2 + 4
x^2 – 12x – 7x + 21
Combine Like Terms:
2x^3 – 2x^2 – 12x – 7x + 21
2x^3 – 2x^2 – 19x + 21
Solution:
2x^3 – 2x^2 – 19x + 21
Hope that helps! Have an amazing rest of your day! Please consider awarding me the Brainliest! :)
Steve stopped for a drink of water when he had completed 60% of his jog. He had traveled 3 miles. What is the total distance Steve jogged?
2 miles
3 miles
4 miles
5 miles
6 miles
The total distance Steve jogged is 5 miles.
what is percent?The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Given:
Steve completed 60% of the Jog.
Also, he travelled 3 miles.
Let the total distance he travelled be x miles.
Then,
60% of x =3
60/100 x= 3
x= 3 x 100 / 60
x= 300/60
x= 5 miles.
Hence, total he had to jog 5 miles.
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Karl drove 40 miles in 50 minutes. Teresa drove 35 miles in 42 minutes. Who had a higher average speed?
The person that has the higher average speed is Teresa.
How to calculate average speed?The average speed is the total distance travelled by the object in a particular time interval.
Average speed measures the average rate of speed over the extent of a trip.
Therefore,
average speed = distance / time
Hence, Karl drove 40 miles in 50 minutes.
Therefore,
average speed of Karl = 40 / 50
average speed of Karl = 4 / 5 miles per minute
Teresa drove 35 miles in 42 minutes.
Therefore,
average speed of Teresa = 35 / 42
average speed of Teresa = 5 / 6 miles per minutes
Therefore, Teresa had the higher average speed.
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In the accompanying diagram, points A, E, and B are collinear, measure of angle A= 30, measure of angle DEB= 130, and segment AB is perpendicular to segment BC. Find the measure of angle C and the measure of angle D.
Step-by-step explanation:
I assume the points D, E and C are also collinear (are on the same straight line).
that is something your teacher forgot to mention. but it is essential.
we have to remember :
1. the sum of all angles in a triangle is always 180°.
2. the sum of all angles around a single point on one side of a line is also always 180°.
3. the angles at the intersection point of 2 lines are the same on both sides of any of the intersecting lines, but they are left-right mirrored.
so,
angle A = 30°
angle DEB = 130°, so,
angle AED = 180 - DEB = 180 - 130 = 50°.
therefore, angle BEC = AED = 50°
therefore, angle D = 180 - 30 - 50 = 100°.
we know, angle B = 90° (AB is perpendicular to BC).
therefore,
angle C = 180 - 90 - 50 = 40°
Y varies 1/x², when X=2, Y=1. Find the values of X when Y=4/9.
Answer:
x = ± 3
Step-by-step explanation:
given y varies as [tex]\frac{1}{x^2}[/tex] , then
y = k × [tex]\frac{1}{x^2}[/tex] = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k use the condition x = 2 , y = 1
1 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
4 = k
y = [tex]\frac{4}{x^2}[/tex] ← equation of variation
when y = [tex]\frac{4}{9}[/tex] , then
[tex]\frac{4}{9}[/tex] = [tex]\frac{4}{x^2}[/tex] ( cross- multiply )
4x² = 36 ( divide both sides by 4 )
x² = 9 ( take square root of both sides )
x = ± [tex]\sqrt{9}[/tex] = ± 3
f(x) = 3x2 + 2x and g(x) = -2x + 1, what is f g(x)?
Answer:
f g(x) = 12x^2 - 16x +5
Step-by-step explanation:
f(x) = 3x^2 + 2x
g(x) = -2x + 1
f g(x)
f g(x) = 3(-2x + 1)^2 + 2(-2x + 1)
f g(x) = 3(-2x + 1)^2 + -4x + 2
f g(x) = 12x^2 - 12x +3 + -4x + 2
f g(x) = 12x^2 - 16x +5
A pie weighs 500g. jamie cuts it into 4 slices. the largest slice weighs the same as the other 3 combined. what is the weight of the largest piece of pie?
The weight of the largest piece of pie is 250 gram.
How to calculate the weight?Let the weights of others be illustrated as x.
Therefore, the weight of the largest weight is the addition of the others weight. This will be:
= x + x + x = 3x
Therefore, the weights will be:
3x + x + x + x = 500
6x = 500.
Divide
x = 500 / 6
x = 83.33.
The larger weight will be:
= 3x
= 3 × 83.33
= 250
The pie weights 250g.
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IMAGE ATTACHED,please help me with this one please.
Answer:
Step-by-step explanation:
$17.64 for 147 text messages
Therefore 1 text message will cost $17.64 ÷ 147 Text messages = $0.12 per text message
Richard and teo have a combine age of 38 Richard is 11 years okder than twice teo age how old are Richard and teo?
Answer: Richard is 29 and Teo is 9.
Step-by-step explanation: Use Substitution
z + mx = yx Solve for x
Answer:
[tex]X=\frac{-z}{m-y}[/tex]
Step-by-step explanation:
I need this answered please
Answer:
$2,000
Step-by-step explanation:
Amount invested in Fund A = 6000
Profit rate of return = 5%
Amount of profit = 6000 x 5% = 6000 x 0.05 = $300
Let amount invested in Fund B be $x
Profit amount = 0.01x
Total amount invested is 6000 + x
Total profit in $ = 300 + 0.01x
Total profit in percentage = Total Profit/Total investment x 100
= 4 %
So Total Profit/Total investment = 4/ 100 = 0.04
= (300 + 0.01x) / (6000 + x) = 0.04
Multiply both sides by (6000 + x)
=> 300 + 0.01x = 0.04(6000 + x)
=> 300 + 0.01x = 240 + 0.04x
==> 300 - 240 = 0.04x - 0.01x
=> 60 = 0.03x
x = 60/0.03
x = $2,000
Amount invested in Fund B = $2,000
Step-by-step explanation:
Fund A
$6000 returned a 5% profit. that means it had at the end 105% of the original investment
the formally correct way
100% = 6000
1% = 100%/100 = 6000/100 = $60
5% = 1%×5 = 60×5 = $300
in short, if we knew what we are doing, we could have simply calculated 6000 × 0.05 = $300.
and by the way, 6000 × 1.05 = $6300. which is the current balance of the account (investment plus the returned profit). but we don't need this here. this is just FYI.
Fund B
x returned 1% profit.
Fund A + Fund B
6000 + x returned 4% profit.
so, we have
6000×0.05 + x×0.01 = (6000 + x)×0.04
300 + 0.01x = 240 + 0.04x
60 + 0.01x = 0.04x
60 = 0.03x
x = 60/0.03 = $2000
so, he invested $2000 into fund B.
El precio de los boletos para un partido de fútbol es de $19 pesos. Si en total caben 26,472 personas en el estadio, calcula la cantidad aproximada de dinero que se obtiene de la venta de los boletos.
La ganancia aproximada del estadio por concepto de la venta de boletos para un partido de fútbol es $ 502,968.
¿Cuál es la ganancia neta aproximada por la venta de boletos?
En esta pregunta se nos solicita determinar la ganancia aproximada por la venta de boletos para un partido de fútbol en un estadio. La ganancia aproximada es igual al producto del aforo del estadio y el costo de cada boleto. Entonces,
c = ($ 19) · (26,472)
c = $ 502,968
La ganancia aproximada por el partido de fútbol es $ 502,968.
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This is lines , functions and systems. Graphing a line through a given point with a given slope.
The slope of the line is given as -2/3.
We are also given the point (1, 1) in which this line passes through.
Before we can plot the graph of the line, we need to know the equation of the line first.
The values given are more than enough to find the equation of the line.
The formula used to get the equation of the line is given below:
[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ \text{where,} \\ m=\text{slope} \\ _{} \\ x_1,y_1=\text{ The given point} \end{gathered}[/tex]Now, with this formula, let us find the equation of the line.
[tex]\begin{gathered} y_1=1,x_1=1,m=-\frac{2}{3} \\ m=\frac{y-y_1}{x-x_1} \\ \\ -\frac{2}{3}=\frac{y-1}{x-1}\text{ (Cross multiply)} \\ \\ -2\times(x-1)=3(y-1) \\ -2x+2=3y-3 \\ \text{add 3 to both sides} \\ -2x+2+3=3y-3+3 \\ 3y=-2x+5 \end{gathered}[/tex]Thus, the equation of the line is:
[tex]3y=-2x+5[/tex]Now, using a graph calculator, let us plot this equation.
After doing this, the following is the result:
Jenna bought a new car for $29,000. She paid a 10% down payment and financed
the remaining balance for 48 months with an APR of 4.5%. Determine the monthly
payment that Jenna pays.
If the remaining balance for 48 months with an APR of 4.5%. the monthly payment that Jenna pays is: $595.17.
How to find the monthly payment?Using this formula to determine the monthly payment
P = A ×r × ( 1 +r)^n ÷( 1+ r)^n -1
Where:
P = Principal = ?
A = Amount = $29,000 × ( 1- .10) = 26,100
r = Interest rate = 4.5% / 12 = 0.00375
n = number of months = 48 months
Let plug in the formula
P = 26,100 × 0.00375 × ( 1+ 0.00375)^ 48 ÷ ( 1+ 0.00375)^ 48 -1
P = 26,100 × 0.00375 × ( 1.00375)^ 48 ÷ ( 1.00375)^ 48 -1
P = 26,100 × 0.00375 × 1.196814377 ÷ 1.196814377 -1
P = 26,100 × 0.00375 × 1.196814377 ÷ 0.196814377
P = $117.1382456 ÷ 0.196814377
P = $595.17
Therefore $595.17 is the monthly payment.
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a list of 20182018 positive integers has a unique mode, which occurs exactly 1010 times. what is the least number of distinct values that can occur in the list?
The least number of distinct values that can occur in the list is 225.
what is mode?The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode.
The mode appears 10 times. That leaves 2008 numbers.
The least number of distinct values will occur if all but one of the remaining values appears 9 times
= 2008/9
=223 1/9.
So, The list can include a maximum of 225 distinct values, with the mode appearing 10 times, 223 other values nine times, and the last value once.
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t + 4 < 13 solve the inequality of t and simplify your answer as much as possible
Answer:
9
Step-by-step explanation:
t < 13 - 4
t < 9
again as far as it goes
There is a daily fee for renting a moving truck, plus a charge of $0. 50 per mile driven. If driven 48 miles, it cost $64 to rent a truck. Write and solve an equation to find the daily fee
Using concept of Linear equations, we find $40 is the daily fee for renting a moving truck.
Linear equations are generally equations of the first order. The linear equations are defined for the lines in the coordinate system. When the equation having a homogeneous variable of degree 1 (i.e. only one variable), then it is called as a linear equation in one variable. A linear equation can have more than one variables. If the linear equation has two variables, then it is known as linear equations in two variables and so on. Some of the examples of linear equations which are listed here 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.
So, lets suppose daily fee for renting a movie a truck is $x
Then according to question,
Daily fee+ total distance travelled × charge per mile=total cost
=>x+48×0.50=64
On solving x, we get x=40
Hence, daily fee cost is $40 which is required for renting a moving truck.
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A state agency recorded the number of each type of flood that occurred in the state from 2016–2020. The results are as follows. If similar proportions of flood types are predicted for the following year, what is the estimated probability that a flood in 2021 in that state will be a river flood? Round your answer to the nearest percent. A. 7%B. 60%C. 20%
The table shows different flood types and their frequencies.
Total frequency of all flood types = 18 + 6 + 4 + 2 = 30
frequency of river flood = 6
Recall, probability is expressed as
number of favorable outcomes/number of total outcomes
Thus, the estimated probability that a flood in 2021 in that state will be a river flood is
6/30 = 0.2
By changing 0.2 to percentage, we have
0.2 x 100 = 20%
The correct option is C. 20%