A track-and-field coach recorded the length of each student's standing long jump. The data is summarized in the box plot.
Standing Long Jumps
0
+
2
4
+
Feet
6
8
10
Choose all of the statements that can be concluded from this data.
A. The median jump length is 5 feet, which is the average length of a standing long jump for the students represented in the box plot.
B. The median jump length is 5 feet, which is the length of the middle student's long jump if the students were ordered by the length of
their long jump.
C. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 4 feet of the
median.
D. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 2 feet of the
median.
A

Answer:

n = 2.6

Step-by-step explanation:

Hello!

We can create an equation with equivalent fractions. Remember that a ratio can also be represented as a fraction.

We can create two fractions that are equivalent to each other given the ratios.

The value of n is 2.6.

Answer:

Step-by-step explanation:

Distance around = 2*160 + 2*360

= 320 + 720

= 1080 feet.

The distance around the field is 1040 feet.

It is required to find the distance around the field.

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that:

A football field is 160 feet wide and 360 feet in length.

A  football field is in the shape of rectangle.

So, we know that ,

Perimeter of rectangle= 2(length +breadth)

Distance around

= 2(160 + 360)

=2(520)

= 1040 feet.

Hence,  the distance around the field is 1040 feet.

Learn more about  rectangle here:

https://brainly.com/question/28040873

#SPJ2

Answer: 4:3

Step-by-step explanation:

The side length of the triangle is 48/3 = 16.

The side length of the square is 48/4 = 12.

So, the ratio is 16:12 = 4:3.

Answer:

A translation 8 units right and 2 units down

The derivatives of y=[tex]2x^{3}+5x^{2} +4x-9[/tex] is [tex]6x^{2} +10x+4[/tex], derivative of y=[tex]2x^{2} +3x+5[/tex] is 4x+3, derivative of [tex](5x^{2} -9)6[/tex] is 60x.

Given three functions y= [tex]2x^{3}+5x^{2} +4x-9[/tex], y=[tex]2x^{2} +3x+5[/tex], y=[tex](5x^{2} -9)6[/tex].

We have to find the derivative of functions.

Derivative of a function of a real variablemearsures the sensitivity to change of the function value with respect to a chaneg in its argument. Derivatives are a fundamental tool of calculas.

First function: y=[tex]2x^{3}+5x^{2} +4x-9[/tex], derivative can be as under:

dy/dx=2*3[tex]x^{2}[/tex]+2*5x+4             (derivative of x is 1)

(d[tex]x^{n}[/tex]/dx=n[tex]x^{n-1}[/tex])

dy/dx=6[tex]x^{2}[/tex]+10x+4

Second function: y=[tex]2x^{2} +3x+5[/tex], derivative can be as under:

dy/dx=2*2x+3

=4x+3

Third function:y=[tex](5x^{2} -9)6[/tex]

dy/dx=5*2x*6

=10x*6

=60x

Hence the derivative of first function is [tex]6x^{2} +10x+4[/tex], second function is 4x+3, third function is 60x.

Learn more about derivative at https://brainly.com/question/23819325

#SPJ4

The equation that can be used to represent total tickets sales is 2170 = 5s + 2f + 10a

let

Expression for number of students tickets sold;

s = f + 15

Expression for number of faculty tickets sold;

f = 2a

Expression for number of alumni tickets sold;

f = 2a

a = f/2

2170 = 5s + 2f + 10a

Learn more about equation:

https://brainly.com/question/4344214

#SPJ1

Answer:

Step-by-step explanation:

Write it out in expanded form and you will see why Connor is correct.

3^5 means 3x3x3x3x3

6^8 means 6x6x6x6x6x6x6x6

3^9 means 3x3x3x3x3x3x3x3x3

6^10 means 6x6x6x6x6x6x6x6x6x6

These numbers are all multiplied together, so how many of each number do we have?

3x3x3x3x3x6x6x6x6x6x6x6x6x3x3x3x3x3x3x3x3x3x6x6x6x6x6x6x6x6x6x6

3^14 6^18

Answer:

[tex]\dfrac{y^2}{9}=1-\dfrac{x^2}{25}[/tex]

Step-by-step explanation:

When converting parametric equations that involve trig functions to Cartesian equations, use trig identities to eliminate the parameter.

Given parametric equations:

[tex]x=5 \sin \theta, \quad y=3 \cos \theta, \quad 0\leq \theta\leq \pi[/tex]

Square the equation for x:

[tex]\implies x^2=(5 \sin \theta)^2=25 \sin^2 \theta[/tex]

Use the identity [tex]\sin^2 x+\cos^2x =1[/tex] to write [tex]x^2[/tex] in terms of cos:

[tex]\implies x^2=25(1-\cos^2 \theta)[/tex]

Isolate [tex]\cos^2 \theta[/tex] :

[tex]\implies \dfrac{x^2}{25}=1-\cos^2 \theta[/tex]

[tex]\implies \cos^2 \theta=1- \dfrac{x^2}{25}[/tex]

Square the equation for y:

[tex]\implies y^2=(3 \cos \theta)^2=9 \cos ^2 \theta[/tex]

Replace [tex]\cos^2 \theta[/tex] with the found equation involving [tex]x^2[/tex] :

[tex]\implies y^2=9\left(1-\dfrac{x^2}{25}\right)[/tex]

Divide both sides by 9:

[tex]\implies \dfrac{y^2}{9}=1-\dfrac{x^2}{25}, \quad \textsf{with }x\geq 0[/tex]

Answer:

The degree of polynomial is 5.

Step-by-step explanation:

I suppose the polynomial is [tex]\displaystyle{5x^2+8x^3+4-6x^2-3x^5}[/tex]. To find the which degree this polynomial is, we consider the highest exponent of the term which is [tex]\displaystyle{3x^5}[/tex], the 5 is our highest degree of the term and thus, 5 is our highest degree of polynomial.

Answer:

5

Step-by-step explanation:

I'm assuming that the 5 in "3x5​" is supposed to be a exponent. The degree of the polynomial is the greatest of the exponents (powers) of its various terms.

1. The semi inter quartile range is 10

2. The coefficient of quartile deviation is 0.2

1st quartile (Q₁) = (134 + 1) / 4 = 33.75th = 40

3rd quartile (Q₃) = 3 (134 + 1) / 4 = 3 × 33.75 = 101.25th = 60

Semi inter quartile range = (Q₃ - Q₁) / 2

Semi inter quartile range = (60 - 40) / 2

Semi inter quartile range = 10

Coefficient of quartile deviation = (Q₃ - Q₁) / (Q₃ + Q₁)

Coefficient of quartile deviation = (60 - 40) / (60 + 40)

Coefficient of quartile deviation = 0.2

Learn more about statistics:

https://brainly.com/question/8974461

#SPJ1

You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point.

The "slope formula" for a straight line connecting any two locations is another name for the rise over run formula. The rise is the difference between the y-coordinates of the two locations. The run is the difference between the x-coordinates of two locations. Divide the rise by the run to find the slope.

The rise over run formula is also known as the slope formula because the fraction consists of a rise, whether the line is moving up or down, divided by the run, which can be either left or right. The slope of the line dictates the direction of the line as well as its steepness.

Thus, "You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point".

Learn more about the run at

https://brainly.com/question/8460441

#SPJ4

There will be no change to the grass because the exponential of the function remains the same.

According to the questions,

slope = -4 and y-intercept = -5

Equation of straight line y = mx + c

y = -4x - 5

In order to grass line, there will be no change to the grass because the exponential of the function remains the same.

Learn more about exponential here

https://brainly.com/question/1302412

#SPJ4

The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of kite = (product of diagonals)/2

Area of kite = (10 * 14) / 2 = 70 in²

The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

first 35 out of 100 then second person 34 out of 99

Step-by-step explanation:

By applying the basic proportionality theorem (BPT), the length of side SQ is equal to 5 cm.

In order to determine the length of side SQ, we would apply basic proportionality theorem (BPT) as follows:

Since PQ ǁ RS, PT = 16

PT/RP = QT/SQ

16/4 = 20/SQ

Cross-multiplying, we have:

16SQ = 20 × 4

SQ = 80/16

SQ = 5 cm.

Read more on basic proportionality theorem here: https://brainly.com/question/8160153

#SPJ1

Complete Question:

In the figure, PQ is parallel to RS. The length of RP is 4 cm; the length of PT is 16 cm; the length of QT is 20 cm. What is the length of SQ?

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of big sector = (60/360) * π(10)² = (50π /3) cm²

Area of small sector = (60/360) * π(x)² = (x²π /6) cm²

Unshaded area = (x²π /6) cm²

Shaded area = (50π /3) - (x²π /6) = (100π - x²π) /6

Shaded area = unshaded area

(100π - x²π) /6 = (x²π /6) cm²

x = 7.07

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The length of x in the sector is 7.08 cm.

area of a sector = ∅ / 360 × πr²

where

Therefore,

area of a sector = 60 / 360 × π × 10²

area of a sector = 60 / 360 × π × 100

area of a sector = 6000 / 360 π

Hence,

area of the unshaded portion = 6000 / 360 π ÷ 2 = 6000π / 720 =  26.1666666667 = 26.2 cm

Hence,

26.2 = 60 / 360 × 3.14 × x²

x² = 26.2 / 0.52333333333

x = √50.0637261552

x = 7.07557064836

x = 7.08 cm

learn more on sector here: https://brainly.com/question/14129901

#SPJ1

Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input for an exponential growth function.

Verification of Choice

Let us consider the following exponential growth function.

y = Aeˣ ...........................(1)

This equation changes when it is reflected across the y axis and becomes,

y = Ae⁻ˣ ...........................(2)

Here, the set of all x values for which y is defined is known as the domain of this exponential growth function.

Therefore, the domain of exponential growth function 1 is the set of all real numbers, given by, x ∈ [-∞,∞]

The domain of function 2, which is a reflection of function 1, will also consist entirely of real numbers and will be given by x ∈ [-∞,∞ ]

Therefore, between Alissa and himself, Simon is right when he asserts that even if an exponential growth function is reflected across the y-axis, the domain will still consist only of real values.

Learn more on exponential growth function here:

https://brainly.com/question/11487261

#SPJ1

Answer:

[tex]\dfrac{5}{2}\pi[/tex]

Step-by-step explanation:

Rotation about the y-axis

[tex]\textsf{Volume}=\displaystyle \int^b_a \pi x^2\:\text{d}y[/tex]

where:

Given function of y:  [tex]y = 3x^2[/tex]

Rewrite the given function as a function of y:

[tex]\implies x^2=\dfrac{1}{3}y[/tex]

Substitute the values into the formula:

[tex]\implies \displaystyle \int^4_1 \dfrac{1}{3}\pi y\:\:\text{d}y[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ay^n\:\text{d}y=a \int y^n \:\text{d}y$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $y^n$}\\\\$\displaystyle \int y^n\:\text{d}y=\dfrac{y^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Take out the constant and integrate:

[tex]\begin{aligned}\implies \dfrac{1}{3}\pi\displaystyle \int^4_1 y\:\:\text{d}y & = \dfrac{1}{3}\pi \left[\dfrac{1}{2}y^2\right]^4_1\\\\& =\dfrac{1}{3}\pi \left[\dfrac{1}{2}(4)^2-\dfrac{1}{2}(1)^2\right]\\\\&=\dfrac{1}{3}\pi\left[8-\dfrac{1}{2}\right]\\\\&=\dfrac{5}{2}\pi \end{aligned}[/tex]

Therefore, the exact value of the volume of revolution is:

[tex]\dfrac{5}{2}\pi[/tex]

Learn more about integration here:

https://brainly.com/question/27988986

https://brainly.com/question/27805589

Answer:

10 units and 157.84 units

Step-by-step explanation:

4

substitute t = 1 into the equation

h = - 16(1)² + 6 = - 16 + 6 = - 10

the value is negative since the ball travels down

the ball has travelled 10 units after 1 second

5

substitute t = 3.2 into the equation

h = - 16(3.2)² + 6 = - 16(10.24) + 6 = - 163.84 + 6 = - 157.84

the well is 157.84 units deep

Based on the calculations, the true statements are:

A. The angular velocity is 10π rad/sec.

E. The angular velocity is 600π rad/min.

Mathematically, angular velocity can be calculated by using this formula:

ω = θ/t

Where:

Note: 1/2 revolution = 0.5 × 2π = π radians.

Substituting the given parameters into the formula, we have;

ω = θ/t

ω = π/0.1

ω = 10π rad/s.

Next, we would convert the time in seconds to minutes:

ω = 10π × 60

ω = 600π rad/min.

Read more on angular velocity here: https://brainly.com/question/6860269

#SPJ1

Complete Question:

A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true? Check all that apply.

A. The angular velocity is 10π rad/sec.

B. The angular velocity is 10π rad/min.

C. The angular velocity is 60π rad/min.

D. The angular velocity is 600π rad/sec.

E. The angular velocity is 600π rad/min.

Answer:

A,

Step-by-step explanation:

Edge202

The correct option for the inequality is

Week 4 = Week 5. Option B. This is further explained below.

Generally,  the relationship between two expressions that do not have the same value is denoted by a sign such as, which means "not equal to," >, which means "greater than," or, which means "less than."

In conclusion, When converted to decimal form, Week 5's score comes out to -1.8, which is the same as Week 4's score.

Week 4 = Week 5

Read more about inequality

https://brainly.com/question/20383699

#SPJ1

Answer:

The Answer Is B

Step-by-step explanation:

Week 4 = Week 5

The number of lines that the points can make is; 21 lines

We are given that;

- There are 7 points on a Plane

- No 3 points on the plane are on the same line

Thus;

No 3 points are collinear and as such the number of lines that the points can make is found from the combination  formula;

C(7,2);

C(7,2) = 7!/(7 - 2)!*2!

= (7 × 6)/(2 × 1)

= 42/2

=21

Read more about Collinear Points at; https://brainly.com/question/3307641

#SPJ1

Answer:

-5

Step-by-step explanation:

Slope is rise over run. The graph decreases by 5 units every 1 unit to the right, so the slope is -5.

The number which produces a rational number when multiplied by 1/3 is; Choice A; 2.

It follows from the definition of rational number that they can be represented as the quotient a/b of two integers such that b ≠ 0.

On this note, it follows that when 1/3 is multiplied by 2; the result is 2/3 which is a rational number.

Read more on rational numbers;

https://brainly.com/question/1535013

#SPJ1

The vector AB is not related with the vector CD as k is not the same for each pair of components.

In this question we must prove if the vector AB is a multiple of the vector CD, that is:

[tex]\overrightarrow{AB} = k \cdot \overrightarrow {CD}[/tex]

[tex]\vec B - \vec A = k \cdot [\vec D - \vec C][/tex]

(1, 4) - (2, 3) = k · [(- 2, 2) - (1, 3)]

(- 1, 1) = k · (- 3, - 1)

Hence, the vector AB is not related with the vector CD as k is not the same for each pair of components.

To learn more on vectors: https://brainly.com/question/13322477

#SPJ1

Answer:

y = 5x + 2

Step-by-step explanation:

Standard form of Equation of line: y = mx + c

where m = slope or gradient,

c = y-intercept

From the question we know that:

x = - 1

y = - 3

m = 5

We will substitute these values into the equation to find c.

- 3 = (5)(- 1) + c

- 3 = - 5 + c

c = - 3 + 5 = 2

Therefore the equation of this line is: y = 5x + 2

Answer:

[tex]5.5[/tex]

Step-by-step explanation:

Mean:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is

[tex]\mu = \frac{{\sum}x}{N}[/tex]

The formula for the mean of a sample is

[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:

[tex]\frac{55}{10} = 5.5[/tex]

Based on the triangle inequality theorem, the statement that the given segments will form a triangle is TRUE.

If a, b, and c are lengths of a triangle, then,

a + b > c

a + c > b

b + c > a

Given the segments:

AC = 6

CB = 5

BA = 8

6 + 5 > 8 [true]

6 + 8 > 5 [true]

5 + 8 > 6 [true]

Therefore, it is true that the segments given could form a triangle.

Learn more about the triangle inequality theorem on:

https://brainly.com/question/309896

#SPJ1

Answer:

Step-by-step explanation: