A person began running due east and covered 15 kilometers in 2.0 hours. What is the average velocity of the person? Show all your work!

The median is 133.5, the first quartile is 128, the third quartile is 139, and the interquartile range is 11.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

To find the median, first we need to order the data set from least to greatest:

106, 127, 129, 132, 135, 138, 140, 158

There are 8 data points, so the median is the average of the 4th and 5th numbers:

Median = (132 + 135) / 2 = 133.5

To find the quartiles, we need to divide the data set into four equal parts. Since there are 8 data points, the first quartile (Q1) is the median of the first half of the data set, and the third quartile (Q3) is the median of the second half of the data set.

Q1 = median of {106, 127, 129, 132} = (127 + 129) / 2 = 128

Q3 = median of {135, 138, 140, 158} = (138 + 140) / 2 = 139

The interquartile range (IQR) is the difference between the third quartile and the first quartile:

IQR = Q3 - Q1 = 139 - 128 = 11

Therefore,

The median is 133.5, the first quartile is 128, the third quartile is 139, and the interquartile range is 11.

Learn more about median here:

https://brainly.com/question/28060453

#SPJ3

Final answer:

The median of the given data set is 133.5, with the first quartile (Q1) at 128 and the third quartile (Q3) at 139. The interquartile range (IQR) is 11, and the range is 52.

Explanation:

To find the median, first quartile (Q1), third quartile (Q3), and interquartile range (IQR) of a set of data, we first need to list the data in ascending order. The given data is: 106, 127, 129, 132, 135, 138, 140, 158.

The median is the middle number when the data set is ordered. Since there are 8 numbers, the median will be the average of the 4th and 5th numbers: (132 + 135) / 2 = 133.5. So the median is 133.5

To find the first quartile, which is the median of the lower half of the data (excluding the median if the number of data points is odd), we look at the first four numbers: 106, 127, 129, 132. The median of this subset is (127 + 129) / 2 = 128. So Q1 is 128.

Similarly, Q3 is the median of the upper half of the data. For the numbers 135, 138, 140, 158, the median is (138 + 140) / 2 = 139. So Q3 is 139.

The IQR is the difference between Q3 and Q1, so IQR = 139 - 128 = 11.

The range of the data is the difference between the max and min values, which is 158 - 106 = 52.

Answer:

3

Step-by-step explanation:

The given function is

[tex]f(x)=-x^2+6x+13[/tex]

The average rate of change is simply the slope of the secant line connecting any two point on the graph of the function.

The average rate of change  of this function over the interval;

[tex]-1\le x\le 5[/tex] is given by:

[tex]\frac{f(5)-f(1)}{5-1}[/tex]

[tex]f(5)=-(5)^2+6(5)+13[/tex]

[tex]f(5)=-25+30+13=18[/tex]

[tex]f(-1)=-(-1)^2+6(-1)+13[/tex]

[tex]f(-1)=-1-6+13=18[/tex]

[tex]f(-1)=6[/tex]

The average rate of change now becomes;

[tex]\frac{18-6}{4}[/tex]

[tex]\frac{12}{4}=3[/tex]

Answer:

Circumference=37.6991 or 38

Step-by-step explanation:

c=2[tex]\pi[/tex]r

c=2[tex]\pi[/tex]6

c=37.6991

Answer:

Step-by-step explanation:

c=2\pir

Let's solve your equation step-by-step.

2x3−5x2+3x+7=x−2

Step 1: Subtract x-2 from both sides.

2x3−5x2+3x+7−(x−2)=x−2−(x−2)

2x3−5x2+2x+9=0

Step 2: Factor left side of equation.

(x+1)(2x2−7x+9)=0

Step 3: Set factors equal to 0.

x+1=0 or 2x2−7x+9=0

x=−1

Answer:

x=−1

The given equation is rearranged into a polynomial equation, and can be solved using methods such as factoring, the quadratic formula, graphing, or completing the square.

To solve this question, you first need to set the equation in order. You should arrange it as a quadratic equation (ax²+bx+c = 0). Given equation is:

2x³ - 5x² + 3x + 7 = x-2

We need to simplify this equation by adding '2' on both sides and subtracting 'x' from both sides:

2x³ - x - 5x² + 3x + 1 = 0

Now, it has been transformed into a polynomial equation with the variable x. Solving this kind of equation requires methods such as factoring, quadratic formula, graphing or completing the square.

https://brainly.com/question/18322830

#SPJ2

Answer:

pk=22

Step-by-step explanation:

3x+23=9x-19

x=7

3x7+23=44

44/2

22

To find PK when PQ = QR, JK = 3x + 23, and LM = 9x - 19, you can add JK and LM together to get PK = 12x + 4.

Given that PQ = QR, JK = 3x + 23, and LM = 9x - 19, we can find PK by adding JK and LM together since they are all part of the same line. So, PK = JK + LM = (3x + 23) + (9x - 19). Now simplify the expression by combining like terms: PK = 3x + 9x + 23 - 19 = 12x + 4.

https://brainly.com/question/32840156

#SPJ3

Do 36 divided by the amount of sides the hexagon has. I think I am not sure

It’s 50 you use the Pythagorean theorem

A^2 + B^2 = C^2

48^2 + 14^2 = C^2

2304 + 196 = C^2

2500= c^2

Then square root 2500 and you get 50

Answer:

A. 16

Step-by-step explanation:

We have to find rate of change of function from x=3 to x=5

The average rate of change for the interval a≤x≤b is given by:

Rate of change=  (f(b)-f(a))/(b-a)

In our question,

a=3

and

b=5

We can see from the table that at x = 3, the value of function is 18

So,

f(a)=18

and

At x=5, the value of function is 50

f(b)=50

Rate of change=(50-18)/(5-3)

=32/2

=16

So the rate of change of function between x=3 and x=5 is 16 ..  

Option A is the correct answer..

Answer:

6720ft^3

Step-by-step explanation:

37²-12² = a²

1225 = a²

√1225 = a

a = 35

35(24²/3) =

35(576/3) =

35•192 = 6720 cm³

The answer is 6720 ft

......................................

ANSWER

B. Domain is (-∞,∞) and Range is (-∞,∞).

The given function is

[tex]f(x) = \sqrt[3]{x - 6} + 5[/tex]

This is function is obtained by shifting the base cubic root function 6 units to the right and 5 units up.

This function is defined for all real values of x.

Therefore the domain is all real numbers.

The range is all real numbers.

The domain for this function becomes the range for the inverse function and the range becomes the domain.

Hence the domain is (-∞,∞) and the range is (-∞,∞).

Answer:

please upload the complete image once again for better understanding.

Step-by-step explanation:

Answer:

The answer is 4/5

Step-by-step explanation:

Answer: About 134% of last years earnings

Step-by-step explanation:

Answer:

Given graph represents function.

Step-by-step explanation:

We have been given a graph. Now we need to find if the given graph represents function or not.

To check if any graph represents function or not, we apply vertical line test. That means if there exists any vertical line that crosses the given graph more than once then the given graph is not a function.

Now if you draw vertical lines then you won't find any such vertical line which crosses graph more than once.

Hence given graph represents function.

Answer:

[tex]f(x=\sqrt{x}-2[/tex].

Step-by-step explanation:

We have been given graph of a function. We are supposed to find the function formula.

Upon looking at our given function, we can see that it is transformed form of a square root function.

We know that square root parent function is in form [tex]f(x)=\sqrt{x}[/tex].

We can see that our given graph is shifted down along y-axis. The rule for shifting a graph down along y-axis is: [tex]f(x)\rightarrow f(x)-a[/tex], where graph of [tex]f(x)[/tex] is shifted down by a units.

So our function will be in form [tex]f(x=\sqrt{x}-a[/tex].

From our attached file, we can see that value of 'a' is 2.

Therefore, our required function would be [tex]f(x=\sqrt{x}-2[/tex].

QUES 1)

Let x denote the gig of data used.

and y denote the monthly charge for use of data

We know that the equation of a line with given slope "m" and y-intercept "c" is given by:

       y=mx+c

Runfast--

The monthly charge is: $ 8

and the cost of per gig of data is: $ 8

Since, the cost per gig represent the slope and fixed monthly charge represent the y-intercept.

Hence, the equation that is given by this set of information is:

             [tex]y=8x+8---------(1)[/tex]

BA & D--

The monthly charge is: $ 15

and the cost of per gig of data is: $ 4

Hence, the equation that is given by this set of information is:

             [tex]y=4x+15-----------(2)[/tex]

QUES 2)

We will substitute the value of y from equation (1) in equation (2) as follows:

 8x+8=4x+15

i.e.  8x-4x=15-8

i.e.   4x=7

i.e.   x=7/4=1.75

and the value of y is:

y=8×1.75+8

i.e.    y=22

Hence, the cost of both the companies are equal when 1.75 gigs of data is used and the cost is: $ 22

( Since , the solution is: (1.75,22)  )

Answer:

1 Goes with A. 2 Goes with C. 3 Goes with B.

Step-by-step explanation:

I counted them lol

ANSWER

Each triangle:40 cm²

Kite : 80cm²

EXPLANATION

The area of a triangle is

[tex] \frac{1}{2}bh[/tex]

The height of the triangle is

[tex] h = \frac{1}{2} (10)=5cm[/tex]

and the base is 16 cm.

The area of each triangle is

[tex] = \frac{1}{2}(16)(5) = 40 {cm}^{2} [/tex]

2. The total area of the kite is 2 times the area of one triangle.

[tex] = 2 \times 40 = 80 {cm}^{2} [/tex]

Answer:

The first answer to your question is B=40

The second answer to your question is B=80

Step-by-step explanation:

Right on ED2021, goodluck!

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y + 8 = - [tex]\frac{1}{9}[/tex] (x - 7) is in this form

with slope = - [tex]\frac{1}{9}[/tex] and (a, b) = (7, - 8)

Answer:

The answer is 7!

Step-by-step explanation:

Step-by-step explanation:

if p = 0.5, then 8p =4

if q =7, then 3q =21

thus 8p + 3q -18 = 4 + 21 -18 = 7

Answer:192^3

Step-by-step explanation:

Multiply the base x width x height (6, 8, 4) and get your answer 192^3.

The volume of composite figure is [tex]76ft^{3}[/tex]

To find the volume of composite figure,

Let us consider that, given figure is complete.

So that, [tex]length=6ft, width=2ft, height=8ft[/tex]

Volume of complete figure,

            [tex]Volume=length*width*height\\\\Volume=6*2*8=96ft^{3}[/tex]

Now find the volume of cut part.

           [tex]Volume=2*2*5=20ft^{3}[/tex]

Volume of composite figure is,

                     [tex]96-20=76ft^{3}[/tex]

Learn more about the Volume here:

https://brainly.com/question/1972490

Answer:

11: b = c - 0.5, where b is the bread and c is the cheese

12: h = b + 2, where h is the height and b is the base

13: p = 25b, where p is the plane ticket and b is the bus ticket

Centi means [tex]10^{-2}=\frac{1}{100}[/tex] that also means you can write 1024 cm as [tex]1024\cdot\frac{1}{100}[/tex] m.

Now we can simplify the above fraction a little bit.

[tex]

1024\cdot\frac{1}{100}=\frac{1024}{100}=\boxed{10.24}

[/tex]

Which means 1024 cm is 10.24 m.

Hope this helps.

r3t40

There are 100 cm in 1 meter so to convert 1024 cm to meters divide 1024 by 100

1024/100 = 10.24

In 1024 cm there are 10.24 meters

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]EH=12\ units[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

ABCD and EFGH are similar

so

CD is proportional to GH

AD is proportional to EH

[tex]\frac{CD}{GH}=\frac{AD}{EH}[/tex]

substitute the given values and solve for EH

[tex]\frac{2}{3}=\frac{8}{EH}[/tex]

[tex]EH=3*8/2=12\ units[/tex]

Step-by-step Answer:

Given:

W=vehicle is White

T=vehicle is a pick-up Truck

P(W and T)=0.06

P(W)=0.25

P(T)=0.15

We need the conditional probability that a vehicle is white, given that it is a pick-up truck:

P(W | T)

= P(W and T) / P(T)

= 0.06 / 0.15

=0.4

Answer:

0.40

Step-by-step explanation:

Answer:

39366

Step-by-step explanation:

Answer:

1. 2

2. 6,

3. 18,

4. 54,

5. 162,

6. 486,

7. 1,456,

8. 4,368

9. 13,104

10. 39,312

Step-by-step explanation:

Answer:

12 5 dollar bills

20 50 dollar bills

Step-by-step explanation:

Let x = number of five dollar bills

Let y = number of fifty dollar bills

We have a total of 32 bills

x+y = 32

The total amount is 1060

5x+50y = 1060

We have 2 equations and 2 unknowns

x+y = 32

5x+50y = 1060

Multiply the first equation by -5 so we can eliminate x

-5x -5y = -5*32

-5x -5y =-160

Add this to the second equation

5x+50y = 1060

-5x -5y =-160

------------------------

45 y    = 900

Divide each side by 45

45y/45 = 900/45

y = 20

There are 20 50 dollar bills

x+y = 32

x+20 = 32

Subtract 20 from each side

x+20-20 = 32-20

x = 12

There are 12 5 dollar bills

What your are going to want to do is look for the average of the number (hope this helps some what!) good luck

Answer:

[tex]x=8\sqrt{2}[/tex] units

Step-by-step explanation:

The given triangle is an isosceles right triangle.

This implies that, the second leg is also x units.

We use the Pythagoras Theorem to obtain:

[tex]x^2+x^2=16^2[/tex]

[tex]2x^2=256[/tex]

Divide both sides by 2; to get

[tex]x^2=128[/tex]

Take positive square root to get:

[tex]x=\sqrt{128}[/tex]

[tex]x=8\sqrt{2}[/tex]

Answer:

x > 12

Answer for 2/3>8

Answer:

x within the domain (-∞,0) ∪ (0,1/12) ∪ (1/6,∞)

Step-by-step explanation:

Let's find the solution by modifying the conditions like this:

First condition:

2/3x > 8

Notice that x needs to be a positive number because if x is negative number the expression 2/3x is always negative, and the given condition will be false. Also, x can't be 0 because dividing by 0 is not allowed.

Multiplying the first condition in both sides by (3x/2) we obtain:

(2/3x)*(3x/2) > 8*(3x/2) equal to:

1 > 12x, which dividing by 12 in both sides is:

1/12 > x, which means a domain: (0,1/12)

Second condition:

2/3x < 4

Notice that if x is negative, the expression (2/3x) is always negative, so the second condition will be always true, so negative numbers are not a problem for this conditions.

Let's find the highest positive number which allows the second condition to be a true statement.

Multiplying the second condition in both sides by (3x/2) we obtain:

(2/3x)*(3x/2) < 4*(3x/2) equal to:

1 < 6x, which dividing by 6 in both sides is:

1/6 < x which means a domain: (-∞,0) ∪ (1/6,∞), notice that 0 is not in the domain because dividing by 0 is not allowed, but also as mentioned before negative numbers makes the statement true.

Notice that the problem uses the word OR (condition one or condition two), which means that we need to create a domain for x which allows that always at least one condition is true.

Adding the x domains for the two conditions we obtain:

(-∞,0) ∪ (0,1/12) ∪ (1/6,∞); notice that all the boundary numbers are not included.

In conclusion, the statement 2/3x>8 or 2/3x<4 is true for x within the domain (-∞,0) ∪ (0,1/12) ∪ (1/6,∞).

Answer:

5 years             I think....

Step-by-step explanation:

B Specie    A Specie      

5000         2000

10000       4000

                 6000

                 8000

                 10000

Answer:

30.54 yrs

Step-by-step explanation:

We have been given the following exponential growth functions;

Species A;

[tex]p=2000e^{0.05t}[/tex]

Species B;

[tex]p=5000e^{0.02t}[/tex]

where t = 0 in 2010.

We are required to determine the number of years it will take for the populations of both species to be equal.

To do this we simply equate the two exponential functions and solve for t;

[tex]2000e^{0.05t}=5000e^{0.02t}\\\\2e^{0.05t}=5e^{0.02t}\\\\\frac{5}{2}=\frac{e^{0.05t} }{e^{0.02t} }\\\\2.5=e^{0.03t}\\\\ln(2.5)=0.03t\\\\t=\frac{ln(2.5)}{0.03}=30.543[/tex]

Answer:

D

Step-by-step explanation:

Answer:

c

Step-by-step explanation: