an art teacher time his students in minutes to see how long it takes them to pain 12 inch canvas he makes a box plot for the data.how long could a student take to paint their canvas if they are slower than 75% of the other students?A-15 minutesB- 25 minutesC- 40 minutesD- 46 minutes

Answer:

Its Spring break pls relax

Step-by-step explanation:

(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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The formula for calculating the mean of a probability distribution is mean = (x * P(x)), where x denotes a potential result and P(x) denotes its probability.

Distribution of Probabilities F(x) = P (X x) is a formula that describes it. Additionally, if the interval (a, b) is semi-closed, the probability distribution function is provided by the equation P(a X b) = F(b) - F (a). The range of a random variable's probability distribution function is always from 0 to 1.

Therefore, the mean for this distribution is: (0 * 0.04) + (1 * 0.24) + (4 * 0.35) + (5 * 0.16) + (7 * 0.21). mean = 0 + 0.24 + 1.4 + 0.8 + 1.47 mean = 4.81

Standard deviation = ((x - mean)2 * P(x)), where x is a conceivable outcome and P(x) is the probability of that outcome, gives the standard deviation of a probability distribution.

This gives us the following standard deviation for this distribution: standard deviation = ((((0 - 4.81)2 * 0.04) + ((1 - 4.81)2 * 0.24) + ((4 - 4.81)2 * 0.35) + ((5 - 4.81)2 * 0.16) + ((7 - 4.81)2 * 0.21)) (23.0461) 4.8114 is the standard deviation.

To two decimal places, round:

mean = 4.81 4.81 is the standard deviation.

Therefore, the provided probability distribution's mean and standard deviation are 4.81 and 4.81, respectively.

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The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.

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The value of x is -3 when value of y = 15 by using the property proportion as x and y are directly related to each other.

What is direct relation?

Two variables x and y are directly related to each other if x increases or decreases the value of y also increases or decreases proportionally.

We are given that value of y is -50 then value of x is 10

We have to find the value of x when y is 15

We solve it using proportion

we have,

10/x = -50/15

On separating the variable from the constant and then simplifying we get,

x=-3

Hence the value of x is -3 when y is 15

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Answer:

\(slope=-\frac{1}{3}\)

Step-by-step explanation:

To find the slope of the two points (1, -1) and (4, -2) we have to use the slope formula.

\(slope=\frac{y_{2}- y_{1} }{x_{2} -x_{1} }\)             \(slope=\frac{(-2)- (-1)}{4 -1}\)      

\(slope=\frac{-1 }{3}=-\frac{1}{3}\)  can also be written as a decimal  \(slope=-0.333333\)

The gap consists of the values 6 and 7.

Check out the dot plot below to see what I mean. We have one cluster on the left from 3 to 5. Then another cluster on the right from 8 to 9.

Answer:

The gap is present around 6 & 7

Step-by-step explanation:

Since there is no evidence of dots above 6 & 7, there must have been a freeze in data around then, called a gap.

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Answer: 5/6, 7/10, 1/2, 1/15

Step-by-step explanation:

5/6=25/30, 7/10=21/30, 1/2=15/30, 1/15=2/30

Step-by-step explanation:

AC B D

AD B C

A BC D

A BD C

hope it's right

Answer:

Var(x)=1

Step-by-step explanation:

x p(x)         x² x*p(x) x²*p(x)

0 1/4     0 0         0

1 1/8     1 1/8             1/8

2 1/2     4 1           2

3 1/8     9 3/8            9/8

Total                      3/2              13/4

The required variance can be computed as

Var(x)=sumx²*p(x)-(sum(x*p(x)))²

Var(x)=13/4-(3/2)²

Var(x)=13/4-9/4

Var(x)=4/4

Var(x)=1

Thus, the required variance is 1.

Answer:

18

Step-by-step explanation:

90 degree angle so

90-54=36

36 / 2 = 18

The equation of a circle that is congruent to circle C and is centered at point P is (x - 5)² + (y - 1)² = 5².

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided, we have the following parameters for the equation of this circle:

By substituting the given parameters, we have:

(x - h)² + (y - k)² = r²

(x - 5)² + (y - 1)² = 5²

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Answer:

461.58

Step-by-step explanation:

Answer:

x ≥ -3

Step-by-step explanation:

The shaded circle means it is equal to as well.

Answer:

Length of the side of a square is 18 sqrt(2)

Step-by-step explanation:

a and b are the sides of square and c is the diagonal.

a^2+b^2=c^2

a^2+b^2= 36^2

As all sides are equal we can take b=a

2a^2=36^2

a^2= (36×36)/2

a^2 = 18×36 = 2×9×9×4

Taking squareroot on both sides we get

a= sqrt(2×9×9×2×2)

a=18 sqrt(2)

Answer:

-1.75

Step-by-step explanation:

add -12 and -5, you get -17, and 4 and 6, get 10, add -17 and 10 to get -7, and divide by 4 and get -1.75

Answer:

200

146- (-54)= 200

or use a number line

Answer:

The average rate of change for the given function, from x = −3 to x = 7 will be:

Step-by-step explanation:

Given the table

x                      f(x)

-3                     50

3                      10

7                       0

As the interval is from x = -3 to x = 7.

so

at x₁ = -3, f(x₁) = 50

at x₂ = 7,  f(x₂) = 0

Using the formula to determine the average rate of change at which the total cost increases will be:

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]

                       = [0 - 50] / [7-(-3)]

                      = [-50] / [7+3]

                      = -50 / 10

                      = -5

Therefore, the average rate of change for the given function, from x = −3 to x = 7 will be:

Answer:

câu này là 500 nhen

Answer:

the answer is monkey epaulets monkey

Step-by-step explanation:

123

Answer:

8111.5

Step-by-step explanation:

Deduct for thousand eleven hundred and a half from twelve thousand twelve hundred and twelve

Rewriting the above question in figure :

4000 + 100 + 0.5 = 5100.5

12000 + 1200 + 12 = 13212

13212 - 5100.5 = 8111.5

= 8111.5

Answer:

f(1)=34 ; f(n)= f(n-1) +6, for n >2

Step-by-step explanation:

arithmetic sequence

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

a) The angles outside the side PQ measure 65° and 25°

The angles outside the side QR measure 85° and 95°

The angles outside the side PR measure 55° and 35°

b) The arc PR, PQ and PR measure 120°

a)

Let us assume that the inscribed square be ABCD and equilateral triangle is PQR.

Let side PR of triangle intersects the quadrilateral at points M and N.

So, we get a triangle DMN outside the equilateral triangle.

Here, ∠DMN = 55°, ∠D = 90°

So, ∠MND = 180 - (90 + 55)

                 = 35°

Similarly,  side PQ of triangle PQR intersects the quadrilateral at points X and Y.

So, we get a triangle AXY outside the equilateral triangle.

From triangle PXM we get the measure of angle PXM which is 65 degrees.

As angle PXM and angle AXY are opposite angles, the measure of angle AXY = 65°

∠A = 90°

So, ∠AYX = 180° - (∠A + ∠AXY )

                 = 180° - (90° + 65°)

                 = 25°

Let the side QR of triangle PQR intersects the quadrilateral at points L and K.

so we get new quadrilateral LKBC

In this quadrilateral ∠B = 90°, ∠C = 90°

From triangle QYL, we get the measure of angle QLY = 95°

So, the measure of ∠KLB = 95° .......(∠QLY and ∠KLB opposite angles)

So, the remaining angle LKC of quadrilateral LKBC would be,

∠LKC = 360° - (∠B + ∠C + ∠KLB)

∠LKC = 360° - (90 °+ 90° + 95°)

∠LKC = 85°

b)

We know that he angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

so, the measure of arc PR = 120°

the measure of arc PQ = 120°

the measure of arc RQ = 120°

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A mean is an arithmetic average of a set of observations. The correct option is B.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

The average pay does not differ significantly since the average wage for subpopulations is not significant. As a result,  the subpopulations of mechanical and civil engineers are Not earning different salaries.

Hence, the correct option is B.

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Step-by-step explanation:

The circumference of a WHOLE circle = pi * d

   you have 1/2 of this  and d = 10 ft

     so   1/2 pi * 10      PLUS the two straight sides + 8+6

       1/2 pi * 10   + 8 + 6

         5 pi + 8 + 6

        5 * 3.14   + 14 = 29.7 ft

Answer:

\(a = - 25.5 \\ b = - 4 \\ c = 12 \\ d = - 8\)

Marking the intersection points on the blueprint with yellow points:

To solve for the intersection points of three lines.

Equation 1: Y = -2X + 14

Equation 2: Y = 3X - 7

Equation 3: Y = 0.5X + 2

To find the intersection point of Equations 1 and 2, use the substitution method.

Substituting Equation 1 into Equation 2:

-2X + 14 = 3X - 7

Adding 2X and subtracting 14 from both sides:

-2X + 2X + 14 = 3X + 2X - 7 - 14

14 = 5X - 21

Adding 21 to both sides:

14 + 21 = 5X

35 = 5X

Dividing both sides by 5:

X = 7

Now substitute X = 7 back into Equation 1 to find the corresponding Y value:

Y = -2(7) + 14

Y = -14 + 14

Y = 0

Therefore, the intersection point of Equations 1 and 2 is (7, 0).

To find the intersection point of Equations 1 and 3, use the same substitution method.

Substituting Equation 1 into Equation 3:

-2X + 14 = 0.5X + 2

Adding 2X and subtracting 14 from both sides:

-2X + 2X + 14 = 0.5X + 2X - 14

14 = 2.5X - 14

Adding 14 to both sides:

14 + 14 = 2.5X

28 = 2.5X

Dividing both sides by 2.5:

X = 11.2

Now substitute X = 11.2 back into Equation 1 to find the corresponding Y value:

Y = -2(11.2) + 14

Y = -22.4 + 14

Y = -8.4

Therefore, the intersection point of Equations 1 and 3 is (11.2, -8.4).

To find the intersection point of Equations 2 and 3, substituting Equation 2 into Equation 3:

3X - 7 = 0.5X + 2

Subtracting 0.5X and adding 7 to both sides:

3X - 0.5X = 0.5X + 2 + 7

2.5X = 9

Dividing both sides by 2.5:

X = 3.6

Now substitute X = 3.6 back into Equation 2 to find the corresponding Y value:

Y = 3(3.6) - 7

Y = 10.8 - 7

Y = 3.8

Therefore, the intersection point of Equations 2 and 3 is (3.6, 3.8).

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\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"v" varies directly with "x"}}{v = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} x=32\\ v=20 \end{cases} \\\\\\ 20=k(32)\implies \cfrac{20}{32}=k\implies \cfrac{5}{8}=k\hspace{8em}\boxed{v=\cfrac{5}{8}x} \\\\\\ \textit{when x = 24, what's v?}\qquad v=\cfrac{5}{8}(24)\implies v=15\)