An equation for this linear function that describes how height varies with age is y = 1/5(x) + 2.
The predicted height at 9 is 3.8 feet.
The predicted height at 31 is 8.2 feet.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Conversion:
1 feet = 12 inches
24 inches = 24/12 = 2 feet.
Next, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 2)/(10 - 0)
Slope (m) = 2/10
Slope (m) = 1/5
At data point (0, 2) and a slope of 1/5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 1/5(x - 0)
y = 1/5(x) + 2
When x = 9, the predicted height is given by;
y = 1/5(9) + 2
y = 3.8 feet.
When x = 31, the predicted height is given by;
y = 1/5(31) + 2
y = 8.2 feet.
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Imagine Math simple interest
The simple interest which has the least amount of interest is investment of $ 2000 at 10 % for 3 years
Given data ,
SI is the simple interest, P is the principal amount, r is the annual interest rate, and t is the time in years.
Given that P = 2000, r = 10% = 0.1, and t = 3 years, we can calculate the simple interest as:
SI = 2000 x 0.1 x 3 = 600
Hence , the simple interest earned on an investment of $2000 for 10% at SI for 3 years is $600
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Apply the United States rule to determine the balance at maturity and the total interest paid if the borrower makes two partial payments and the remainder of the loan is paid at maturity.
Principal $1450
Interest Rate % 15.0
Loan Length (Days) 280
Partial Payment
$5800.00
$4350.00
Payment on Day #
112
196
Answer: The United States rule is a method for calculating interest and balances on loans that have partial payments during their term. The rule assumes that each partial payment is applied to the interest first, then to the principal. Here's how to use the United States rule to calculate the balance and interest for this loan:
Calculate the daily interest rate by dividing the annual interest rate by 360 (the number of days in a standard year for most loans).
Daily Interest Rate = 15.0% / 360 = 0.04167%
Calculate the interest due for the first partial payment of $5800 made on day 112. Since this payment is larger than the remaining principal, it will pay off the loan entirely and no interest will accrue beyond this date.
Days between start of loan and first payment = 112 daysInterest due on first payment = (1450 x 0.04167% x 112) = $8.10Principal remaining after first payment = $0.00
Calculate the interest due for the second partial payment of $4350 made on day 196.
Days between first payment and second payment = 84 daysInterest due on second payment = (0 x 0.04167% x 84) = $0.00Principal remaining after second payment = $0.00
Calculate the interest due on the remaining principal at maturity (day 280).
Days between second payment and maturity = 84 daysInterest due at maturity = (0 x 0.04167% x 84) = $0.00
Add up the interest due from each period to get the total interest paid over the life of the loan.
Total interest paid = $8.10 + $0.00 + $0.00 = $8.10
Add up the principal amounts from each payment to get the total amount paid.
Total amount paid = $5800.00 + $4350.00 = $10,150.00
Subtract the total amount paid from the original principal to get the balance at maturity.
Balance at maturity = $1450.00 - $10,150.00 = -$8700.00 (which means the lender owes the borrower this amount)
Therefore, the balance at maturity is -$8700.00 (meaning the lender owes the borrower this amount) and the total interest paid over the life of the loan is $8.10.
Consider the five points
(0,0),(0,5),(6,0),(3,4),(−1,8)
in
R
2
and name them
(x
i
,y
i
)
for
i=1,…,5
. The objective is to find two coefficients
a,b∈R
such that the boundary of the ellipse
ax
2
+by
2
=1
is as close to the above 5 points as possible. To this end, we define the error function: \[ f(a, b)=\sum_{i=1}^{5}\left(a x_{i}^{2}+b y_{i}^{2}-1\right)^{2} \] Calculate the optimal values of
(a,b)
by finding the local minima of the error function
f(a,b)
.
The optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
To find the optimal values of (a,b), we need to minimize the error function f(a,b). We can do this by taking partial derivatives of f(a,b) with respect to both a and b, and then setting them equal to zero:
∂f/∂a = 2∑([tex]x_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex]+ b [tex]y_{i}^{2}[/tex] - 1) = 0
∂f/∂b = 2∑([tex]y_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex] + b [tex]y_{i}^{2}[/tex] - 1) = 0
We can simplify these equations by defining the following sums:
Sxx = ∑[tex]x_{i}^{4}[/tex]
Syy = ∑[tex]y_{i}^{4}[/tex]
Sxy = ∑[tex]x_{i}^{2}y_{i}^{2}[/tex]
Sx = ∑[tex]x_{i}^{2}[/tex]
Sy = ∑[tex]y_{i}^{2}[/tex]
Using these sums, we can rewrite the partial derivatives as:
∂f/∂a = 2(aSx² + bSxy² - Sx)
∂f/∂b = 2(aSxy² + bSy² - Sy)
Setting these equal to zero and solving for a and b, we get:
a = (SySx - Sxy²) / (SxSyy - Sxy²)
b = (SxSy - Sxy²) / (SxSyy - Sxy²)
Plugging in the values for Sxx, Syy, Sxy, Sx, and Sy, we get:
a = 0.7205
b = 0.5369
Therefore, the optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).
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cost function definition
Please if you know the answer tel me thank you.
Answer:
Step-by-step explanation:
(a) currently the mode is pink. Mode means which one occurs the most.
If you take a pink out. Now P=3 G=3 and Y=3
(a) PINK
(b) Yellow, you want yellow to be the most/mode so they put a yellow back in
can someone help me please
The matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]
What is a matrix row operationRow operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.
performing the row operation 4R₁ + R₂ — R₂ on M, we have;
4(1) + (-5) = -1 {row 2 column 1}
4(0) + 2 = 2 {row 2 column 2}
4(3) + (-2) = 10 {row 2 column 3}
Therefore, the matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]
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Suppose that you are taking a course that has 4 tests. The first three tests are each worth 20% of your final grade, and the fourth test is worth 40% of the final grade. To get a B in the course, you must have an average of at least 80 percent on the 4 tests. Your scores on the first 3 tests were 63.5 %, 76 %, and 87 %. What is the minimum score you need on the fourth test to get a B for the course?. Don't round your answer.
Answer:
86.75
Step-by-step explanation:
Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.
Course gradeThe grade for the course, with fourth test score x, will be ...
0.20(63.5 +76 +87) +0.40x = 80
0.40x +45.3 = 80
Solving for x, we get ...
0.40x = 34.7 . . . . subtract 45.3
x = 86.75 . . . . . . . divide by 0.4
The minimum score you need on the fourth test is 86.75.
<95141404393>
In a class of students, the following data table summarizes how many students have a
brother or a sister. What is the probability that a student chosen randomly from the
class has a brother?
The probability that a student chosen randomly from the class has a brother is 57%.
Given is a data table summarizes how many students have a brother or a sister.
We need to find the probability that a student chosen randomly from the class has a brother,
So, we know, probability = favorable outcome / total outcome
Here, favorable outcome = having a brother = 12 + 4 = 16
Total outcomes = all the students = 12+4+10+2 = 28
So,
P(having a brother) = 16/28 = 0.57 = 57%
Hence the probability that a student chosen randomly from the class has a brother is 57%.
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find x, y, and z
will give brainly
Answers:
[tex]z=12\sqrt{3} \\y=12\\x=12\sqrt2[/tex]
Please help me with this
An example of a function that models a linear relationship between two quantities, x and y is y = mx + b
How to explain the functionWe need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:
y = mx + b
In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.
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Stephanie bought two rugs. One rug is 15 feet long, and the other rug is 142 feet long. Each rug has a width of 10 feet.
What is the total area in square feet of the two rugs?
A 175 ft²
B 155 ft²
C 147.5 ft²
D 302.5 ft²
*please help me
The total area of the two rugs in square feet is calculated as: 1570 ft² (none of the options are correct).
How to Find the Total Area of the Rug?To find the total area of the two rugs, we first need to calculate the area of each rug by multiplying its length and width.
Area of the first rug = 15 ft x 10 ft = 150 ft²
Area of the second rug = 142 ft x 10 ft = 1420 ft²
Now, we can find the total area by adding the area of both rugs:
Total area = 150 ft² + 1420 ft² = 1570 ft²
Therefore, the answer is not one of the options provided.
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A company that sells paper has a tiered pricing model based on how much paper you buy. If you buy less than 10 reams, they charge you $7 per ream and a shipping cost of $8. If you buy 10 or more reams but less than 20 reams, they charge you $6 per ream and a shipping cost of $16. If you buy 20 or more reams, they charge you $6 per ream and shipping is free.
a. Write a function that models the price in terms of the number of reams bought.
b. What is the domain of the function?
c. What is the range of the function?
d. How much will it cost to buy 25 reams of paper?
f. How much paper can you buy for $60?
The function can be defined as price = 6x
It will cost $150 to buy 25 reams of paper.
How to explain the functionThe domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.
The range of the function is all non-negative real numbers, since the price cannot be negative.
Fir 25 items, price = 6(25) = $150
It will cost $150 to buy 25 reams of paper.
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Find the sine, cosine, and the tangent of the acute angle A of the triangle. Express each answer as a fraction in simplest form.
Answer:
Step-by-step explanation:
sina=12/20=0.6
cosa=16/20=0.8
tana=0.6/0.8=0.75
Need help with these!!
The decimal used to figure the price of their clothing is 2.1
The improvement in Larry's test score written as a decimal is 1.52
How to write in decimals?Markup = 210%
= 210/100
= 21/10
= 2.1
Larry's increased test score percentage = 152%
= 152/100
= 1.52
In conclusion, the price of clothing and Larry's test score in decimals is 2.1 and 1.52 respectively.
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5. The Smiths took out a $155,500, 30-year mortgage. The
monthly payment was $992. What will be their total interest
charges after 30 years?
Question 6
3 pts
Answer:
$176420
Step-by-step explanation:
Monthly payment = $992
Yearly payment = 992 × 12 = $11064
Total payment = 11064 × 30 = $331920
Interest = 331920 - 155500 = $176420. The interest seems too much, are you sure there's no mistake in the question? Maybe the monthly payment is more than what you've written here?
1. Rachel has $60 to spend
on lunches this week. On
Monday she spent $5, and
on Tuesday she spent $7.
Which inequality can be
used to find, x, the amount
of money she can spend
the rest of the week?
WY is a midsegment of AVXZ.
If VZ = 5t + 51 and WY = 11t, what is VZ?
VZ is 92.5. WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.
what is midsegment ?
A midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle. It is also known as a midline. The midsegment of a triangle is parallel to the third side of the triangle, and its length is half the length of the third side.
In the given question,
Since WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.
Let's call the length of AX as L. Then, we have:
WY = 11t = 1/2 L
Multiplying both sides by 2, we get:
22t = L
Now, we can use this information to find VZ. Since WY is also parallel to VZ, we have:
WV = VZ
Substituting WV = L/2 and VZ = 5t + 51, we get:
L/2 = 5t + 51
Substituting L = 22t, we get:
22t/2 = 5t + 51
11t = 5t + 51
6t = 51
t = 8.5
Substituting t = 8.5 in the equation for VZ, we get:
VZ = 5t + 51 = 5(8.5) + 51 = 92.5
Therefore, VZ is 92.5.
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QUESTION 6·1 POINT
A medical experiment on tumor growth gives the following data table.
x y
81 25
90 36
92 41
103 59
151 60
The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 914.8 and the sum of squares of regression (SSR) was 568.5. Calculate R2, rounded to three decimal places.
Provide your answer below:
The calculated R2 value is 0.621, indicating that 62.1% of the variability in tumor growth can be explained by the linear regression model.
In statistics, the coefficient of determination, denoted by R2, is a measure of how well the regression line fits the data. It represents the proportion of the variance in the dependent variable (y) that is predictable from the independent variable (x).
To calculate R2, we use the formula R2 = SSR/SST, where SSR is the sum of squares of regression and SST is the total sum of squares.
From the given data, SSR = 568.5 and SST = 914.8. Thus, R2 = 568.5/914.8 = 0.621, rounded to three decimal places.
This means that 62.1% of the variability in the tumor growth can be explained by the linear regression model. The remaining 37.9% of the variability is unexplained and may be due to other factors not included in the model.
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A triangle is shown in the image 28 inches 32 inches 8 inches what is the area of the triangle
The area of the triangle is 128 square inches.
How to find the area of the triangle
To find the area of a triangle, you can use the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is 32 inches and the height is 8 inches.
Plugging these values into the formula, we get:
Area = (1/2) * 32 * 8
Area = 16 * 8
Area = 128 in²
So, the area of the triangle is 128 square inches.
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A triangle is shown in the image. A triangle with a height of 8 inches. The height is perpendicular to the base labeled 32 inches. The side from the top of the perpendicular side to the base is labeled 28 inches. What is the area of the triangle? 256 in2 224 in2 128 in2 112 in2
Which linear equation is represented in the graph?
*If correct giving brainlyest*
A. y = 2x – 1
B. y = –2x – 1
C. y = –2x + 1
D. y = 2x + 1
Answer:
C
x1=2
-2(2)+1=3
which is the answer for y1
Answer this pleaseeee
The solution of the trigonometric equation on the interval (, 360) is
x = 90° or x = 126.87° or x = 216.87 What is a trigonometric equation?A trigonometric equation is an equation that contains trigonometric ratios.
Given the trigonometric equation
2sinx = 1 - cosx, we proceed to solve for x as follows.
Since 2sinx = 1 - cosx
Using sin²x = 1 - cos²x
⇒ sinx = √(1 - cos²x )
Substituting this into the equation, we have that
2sinx = 1 - cosx
2√(1 - cos²x ) = 1 - cosx
Squaring both sides, we have that
[2√(1 - cos²x )]² = (1 - cosx)²
4(1 - cos²x ) = (1 - cosx)²
4 - 4cos²x = 1 - 2cosx + cos²x
Collecting similar terms, we have that
1 - 4 - 2cosx + 4cos²x + cos²x = 0
- 3 - 2cosx + 5cos²x = 0
Re-arranging the equation, we have that
5cos²x - 2cosx - 3 = 0
Let cosx = y
So, we have that
5y² - 2y - 3 = 0
Factorizing, we have that
5y² - 2y - 3 = 0
5y² - 5y + 3y - 3 = 0
5y(y - 1) + 3(y - 1) = 0
(5y + 3)(y - 1) = 0
⇒ 5y + 3 = 0 or y - 1 = 0
⇒ 5y = -3 or y = 1
⇒ y = -3/5 or y = 1
Since y = cosx, we have that
cosx = -3/5 or cosx = 1
cos(180° - x) = 3/5 or cos(270° - x) = 3/5 or cosx = 1
Taking inverse cosine, we have that
180° - x = cos⁻¹(3/5) or 270° - x = cos⁻¹(3/5) or x = cos⁻¹(1)
180° - x = 53.13° or 270° - x = 53.13° or x = 90°
x = 180° - 53.13° or x = 270° - 53.13° or x = 90°
x = 126.87° or x = 216.87 or x = 90°
So, the solution is
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Duante is wrapping a present that is 1 foot wide, 10 inches long, and 8 inches high. What is the minimum amount of
wrapping paper he will need?
592 square inches is the minimum amount of wrapping paper Duante needed.
Duante will need a minimum of 592 square inches of wrapping paper.
Lets convert the dimensions to the same units.
Since there are 12 inches in a foot, the dimensions are:
Width = 1 foot = 12 inches
Length = 10 inches
Height = 8 inches
The rectangular box is known as a cube
The surface area of a b=cuboid is given by SA = 2lw + 2lh + 2wh
where l is length, w is width and and h is the height of the cuboid
Substituting the given values, we get:
SA = 2(10)(12) + 2(10)(8) + 2(12)(8)
= 240 + 160 + 192
= 592
Therefore, Duante will need a minimum of 592 square inches of wrapping paper.
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100 Points! Algebra question. Please show as much work as possible. Thank you!
The first term a₁ of the geometric series is equal to 121.5
How to evaluate for a₁ of the geometric seriesFor a geometric series when the common ratio |r| > 1, then we use the formula for the sum of nth term:
Sₙ = a(rⁿ - 1)/(r - 1)...(1)
The nth term aₙ = arⁿ⁻¹
Thus for Sₙ = 4860 and aₙ = 3280.5, the value of a₁ can be derived as follows:
aₙ = arⁿ⁻¹
aₙ = arⁿ/r = 3280.5
rⁿ = a(r × 3280.5)/a
rⁿ = 9841.5/a
putting 9841.5/a for rⁿ in equation (1) we have;
Sₙ = a[(9841.5/a) - 1]/(r - 1)
Sₙ = (9841.5 - a)/(r - 1)
recall Sₙ = 4860 and r = 3 so;
(9841.5 - a)/2 = 4860
a = 9841.5 - 2(4860)
a = 121.5
Therefore, the first term a₁ of the geometric series is equal to 121.5
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ACTIVITY 3: Solve the following equations.
The value of x in each expressions are:
1) 6
2) 1
3) -3
4) -21
5) -4
We have,
The expressions are:
1)
[tex]3^x = 9^3[/tex]
And,
9³ = (3²)³ = [tex]3^6[/tex]
So,
[tex]3^x = 3^6[/tex]
And,
x = 6
2)
[tex]4^{x + 1}[/tex] = 16
16 = 4²
So,
x + 1 = 2
x = 2 - 1
x = 1
3)
[tex](1/3)^x[/tex] = 27
27 = 3³
So,
[tex]3^{-1x}[/tex] = 3³
-x = 3
x = -3
4)
[tex]5^{3x}[/tex] = [tex]25^{x - 1}[/tex] =
[tex]5^{3x}[/tex] = [tex]5^{2x - 21}[/tex]
3x = 2x - 21
3x - 2x = -21
x = -21
5)
[tex]2^{-x}[/tex] = 16
16 = [tex]2^4[/tex]
So,
-x = 4
x = -4
Thus,
The value of x in each expression are:
1) 6
2) 1
3) -3
4) -21
5) -4
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if you have the answer please reply im having trouble need the steps.
Over a given period of time, Seth sold more water bottles than Hayden.
To compare the number of water bottles sold by Seth and Hayden, we need to find out the equation for Seth's sales rate. Looking at the graph, we can see that Seth sold 10 bottles on day 1, 20 bottles on day 2, 30 bottles on day 3, and 40 bottles on day 4.
We can find the average daily sales rate for Seth by dividing the total bottles sold by the number of days:
Average daily sales rate for Seth = (10+20+30+40)/4 = 25
The equation given for Hayden's sales rate is y = 11x, where y represents the number of bottles sold and x represents the number of days. This equation shows that Hayden sells 11 bottles per day.
Comparing the two sales rates, we can see that Seth sold more water bottles. On average, Seth sold 25 bottles per day, while Hayden sold only 11 bottles per day. Therefore, over a given period of time, Seth sold more water bottles than Hayden.
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I can’t figure out what is correct to get about 8
Step-by-step explanation:
Going down the list :
8.98 rounds to 9
6.64 rounds to 7
7.03 rounds to 7
8.52 rounds to 9
7.59 rounds to 8
If the first number past the decimal point >= 5 round the units up
o/w leave the units as they are
Danielle got 23 out of 25 points on her math test. What percent of questions did she get correct?
To calculate the percentage of questions Danielle got correct on her math test, we can divide the number of questions she got correct by the total number of questions on the test and then multiply by 100. In this case, Danielle got 23 out of 25 questions correct, so we can calculate her percentage as follows: (23/25) * 100 = 92%. Therefore, Danielle got 92% of the questions correct on her math test.
Percent = amount per 100
23/25 = amount per 25
25 x 4 = 100
23 x 4 = 92
92/100 = 92%
Answer = 92%
Hope this helps!
If I save 300 a week how much will I have at the end of the year?
15,653 much will I have at the end of the year in linear equation.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
Earning $300 a week equals $15,587 a year. This result is obtained by multiplying the base salary by the number of hours, weeks, and months worked in a year, assuming a 40-hour work week.
15,653 much will I have at the end of the year in.
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The questions I need answered are in the picture… help plsss
The graph of the linear equation y = (1/2)*x + 3 can be seen in the image at the end.
How to graph the linear equation?Here we want to graph the linear equation:
y = (1/2)*x + 3
To graph it we need to find a few points on the line, graph them on a coordinate axis and then draw a line that connects them.
The first point that we can use is the y-intercept, it is what we get when we evaluate in x = 0.
y = (1/2)*0 + 3
The point is (0, 3)
Then we can get other points by evaluating in different values of x, for example, if x = 2
y = (1/2)*2 + 3 = 1+ 3 =4
If x = 4
y = (1/2)*4 + 3 = 2 + 3 = 5
So we have the points (2, 4) and (4, 5)
Now just graph all these points on a cordinate axis and connect them with a line, you will get a graph like the one in the image below.
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The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 3.
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 3.
The median is the best measure of center, and it equals 19.
An appropriate measure of center for the data, and its value include the following: D. The median is the best measure of center, and it equals 19.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 12.
First quartile (Q₁) = 17.
Median (Med) = 19.
Third quartile (Q₃) = 20.
Maximum (Max) = 24.
In conclusion, the best measure of center is the median and it is equal to 19.
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