What is the sample variance of the following numbers 6 4 2 7 1?

9514 1404 393

Answer:

  boat speed: (7t -95)/(6t² -110t +500)

  stream speed: (37t -345)/(6t² -110t +500)

Step-by-step explanation:

The relation between time, speed, and distance is ...

  time = distance/speed

The boat speed (b) is added to the stream speed (s) going downstream. The stream speed is subtracted going upstream. The given relations tell us ...

  25/(b-s) +44/(b+s) = t

  15/(b-s) +22/(b+s) = 5

This gives us 2 equations in 3 unknowns, so we can only provide a solution in terms of one of the unknowns. Since we are asked for the speeds, they will be provided in terms of t.

Subtracting the first equation from 2 times the second gives ...

  2(15/(b-s) +22/(b+s)) -(25/(b-s) +44/(b+s)) = 2(5) -(t)

  5/(b-s) = 10 -t

  5/(10 -t) = b -s

Substituting for b-s in the second equation gives ...

  15/(5/(10-t)) +22/(b+s) = 5

  30 -3t +22/(b+s) = 5

  22/(b+s) = 3t -25

  22/(3t -25) = b+s

Adding the equations for the sum and difference of speeds, we get ...

  (b-s) +(b+s) = 5/(10-t) +22/(3t -25)

  2b = (5(3t -25) +22(10 -t))/((10-t)(3t-25)) = (95 -7t)/((10-t)(3t-25))

  b = (7t -95)/(6t² -110t +500)

Subtracting the equations for sum and difference of speeds, we get ...

  (b+s) -(b-s) = 22/(3t -25) -5/(10 -t)

  2s = (22(10-t) -5(3t -25))/((10-t)(3t-25))

 s = (37t -345)/(6t² -110t +500)

__

The speed of the boat in still water is (7t -95)/(6t² -110t +500) km/h.

The speed of the stream is (37t -345)/(6t² -110t +500) km/h.

__

Note that these solutions only make sense for values of t between 25/3 and 345/37, approximately 8.33 < t < 9.32. For t=9 hours, the boat speed is 8 km/h and the stream speed is 3 km/h.

Answer:

3 units

Step-by-step explanation:

Here, The distance between two points is 3 units

-TheUnknownScientist

Answer:

141

Step-by-step explanation:

2*3=6

5*9=45

6*15=90

141

Answer:

add all the sides I guess...

Step-by-step explanation:

or you can break that figure into rectangles. then find their areas and later sum up all the areas and you'll have your area of this shape

Answer:

The answer is "[tex]\bold{1920 \ in^2}[/tex]".

Step-by-step explanation:

Please find the graph file.

Rectangular solid area:

Its region comprises four rectangles, each 15 for each case 14 in each.

The rectangle field is the formula [tex]A = lw[/tex]

The four rectangles are therefore covered by a zone: [tex]\to A = 4lw = 4 \times 15 \ in \times 14 \ in = 840 \ in^2.[/tex]

square Pyramids area:

The pyramids in both squares have 8 triangular facets.

Each triangle has a 15-inch basis with a 14-inch base.

The triangle zone formulation is [tex]A = \frac{1}{2}bh[/tex]

That's it. The 8 triangles area is [tex]\to A = 8 \times \frac{1}{2}bh = 4bh = 4 \times 15 \ in \times 18 \ in = 1080 \ in^2[/tex]

Total field surface:

Strong rectangular[tex]= 840 \ in^2[/tex]

Pyramids in the Square[tex]= 1080[/tex]

Overall area [tex]= 1920 \ in^2[/tex]

The number is [tex]1920\ in^2[/tex] for a total area.

9514 1404 393

Answer:

  B.  (2, 1)

Step-by-step explanation:

As a first guess you might say the right angle will be at the point that has the x-coordinate of A (2) and the y-coordinate of B (1).

You notice that the point (2, 1) is on the list of answer choices, so that is a good choice.

The coordinates of C could be (2, 1).

__

Or, you can plot the points and see what forms a right triangle.

Answer:

1/2

Step-by-step explanation:

Even numbers on the dice:

2, 4, 6

Probability of getting even:

3/6

1/2

Answer: 1236

its the answer from deltamath

Answer:

Step-by-step explanation:

1.5

Answer:

A=πr2=π·32≈28.27433ft²

Step-by-step explanation:

Answer:

The mass of the fifth player is 73 kg

Step-by-step explanation:

Since the average mass of the 5 players is 70kg

what this mean is that the total sum of all the masses of the players is equal to the product of 5 and 70 kg

we have this as 5 * 70kg = 350 kg

So, by adding the masses of all the players, we get 350kg

Thus, for us to get the mass of the 5th player, we have to subtract the sum of the remaining 4 from the total 350kg

Mathematically, we have this as;

350 - ( 50 + 62+ 81 + 84) = 73 kg

Answer:

The area of a triangle is 1/2BH, or 1/2 times the base times the height.

If the area = 6, and B and H must both be whole numbers.

The area of the triangle ΔSTU is given by A = 12 units²

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the area of the triangle ΔSTU be represented as A

Now , the area of triangle ΔQTU is 6 square units, and the area of triangle ΔRSU is 6 square units

So , the base of the triangle ΔSTU = 6 units

The height of the triangle ΔSTU = 4 units

So , area of the triangle = ( 1/2 ) x Length x Base

On simplifying , we get

The area of triangle ΔSTU = ( 1/2 ) x 4 x 6

The area of triangle ΔSTU = 12 units²

Therefore , the value of A is 12 units²

Hence , the area of the triangle is 12 units²

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ3

The complete question is attached below :

The area of triangle QTU is 6 square units, and the area of triangle RSU is 6 square units. The dimensions in the figure below are labeled in units. What is the area of triangle STU in square units?

471.2

The 10 is the diameter and you need the radius to do it so you do diameter dived by 2 which gives you the radius then you the radius to the power of 2

so the formula would be (3.14)(5)²(6)

Answer:

decay factor i think

Step-by-step explanation:

Answer:

The answer is "148 ft".

Step-by-step explanation:

Using formula:

Calculating rectangle area:

[tex]A=lw[/tex]

   [tex]=15 \times 8\\\\=120[/tex]

Calculating semicircle area:

[tex]A=\frac{1}{2} \pi r^2\\\\[/tex]

   [tex]=\frac{1}{2} \times \pi \times 7.5^2\\\\=\frac{1}{2} \times \pi \times 56.25\\\\=28.125\ \pi \\\\=28 \ \pi[/tex]

Total area:

[tex]=120+28\\\\=148[/tex]

Answer:

(5+3^2)*4

Step-by-step explanation:

i belive im correct

Olivia ran 56 miles last month.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given,

She ran 5 days during the first week of the month

She ran only 3 days each week for the next 3 weeks.

Number of mile she ran given by expression (5 + 3 * 3) * 4

                                                    = (5 + 9) * 4

                                                     = 1 4 *4  

                                                     = 56

Therefore, Olivia ran 56 miles last month.

Learn more about Expressions here :

brainly.com/question/21751419

#SPJ5

Answer:   B.x^3+4x^2-19x+14 is correct

Step-by-step explanation:

(x + 7)(x2 – 3x + 2)

Multiplying both

x^3-3x^2+2x+7x^2-21x+14

x^3+4x^2-19x+14

After expanding the given equation, the equivalent expression is found to be [tex]x^3 + 4x^2 -19x +14[/tex]

The correct answer is B

Given expression:

[tex](x + 7)(x^2 - 3x + 2)[/tex]

To find:

The given expression can be expanded as follows;

[tex](x + 7)(x^2 - 3x + 2)\\\\remove \ the \ bracket \ by \ multiplying \ through \ with \ "x" \ and \ "7"\\\\x(x^2 - 3x + 2) + 7(x^2 - 3x + 2)\\\\x^3 - 3x^2 + 2x + 7x^2 - 21x+ 14\\\\simplify \ further \ by \ collecting \ similar \ terms \ together\\\\x^3 + (-3x^2 + 7x^2)+ (2x-21x) + 14\\\\x^3 + 4x^2 - 19x+ 14[/tex]

Thus, the equivalent expression of the given equation is [tex]x^3 + 4x^2 -19x +14[/tex]

Learn more here: https://brainly.com/question/21101782

Answer:

1,000

Step-by-step explanation:

1,300,000 ÷ 1,300 = 1,000

Answer:

x=9

Step-by-step explanation:

55+5x=100. -subtract 55 from 100

5x=45. - divide 45 by 5

x=9

Given:

The piecewise function is:

[tex]f(x)=\begin{cases}x+5&x<-2\\x^2+2x+3&x\geq -2\end{cases}[/tex]

To find:

The values of [tex]f(-4),f(-2),f(0),f(3)[/tex].

Solution:

For [tex]x<-2[/tex], the function is

[tex]f(x)=x+5[/tex]

For [tex]x\geq -2[/tex], the function is

[tex]f(x)=x^2+2x+3[/tex]

a) The value of [tex]f(-4)[/tex] is:

[tex]f(-4)=-4+5[/tex]

[tex]f(-4)=1[/tex]

b) The value of [tex]f(-2)[/tex] is:

[tex]f(-2)=(-2)^2+2(-2)+3[/tex]

[tex]f(-2)=4-4+3[/tex]

[tex]f(-2)=3[/tex]

c) The value of [tex]f(0)[/tex] is:

[tex]f(0)=(0)^2+2(0)+3[/tex]

[tex]f(0)=0-0+3[/tex]

[tex]f(0)=3[/tex]

d) The value of [tex]f(3)[/tex] is:

[tex]f(3)=(3)^2+2(3)+3[/tex]

[tex]f(3)=9+6+3[/tex]

[tex]f(3)=18[/tex]

Therefore, the required values are [tex]f(-4)=1,f(-2)=3,f(0)=3,f(3)=18[/tex].

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Statement H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .

Step-by-step explanation:

Given - Gina subtracted 6/8 from 1 and found a difference of 2/8 .

To find - Which statement best describes the difference of 6/8 from 1 is 2/8 ? Statement F : The difference of 2/8 is not reasonable because 1 – 3/4 = 1/4 .

Statement G : The difference of 2/8 is reasonable because 3/4 – 1/4  = 1/2 .

Statement H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .

Statement J : The difference of 2/8 is not reasonable because 3/4 – 1/4 = 1/2 .

Proof -

If we subtract 6/8 from 1 , we get

[tex]1 - \frac{6}{8} = \frac{8 - 6}{8} = \frac{2}{8}[/tex]

So, the difference is 2/8

It is reasonable.

So,

The correct statement is - Statement H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .

Reason -

As we can write

[tex]\frac{6}{8} = \frac{3}{4}[/tex] and [tex]\frac{2}{8} = \frac{1}{4}[/tex]

So,

either we subtract 6/8 from 1 or 3/4 from 1 , we get the same result because both the values are equal

So the correct statement is - H : The difference of 2/8 is reasonable because 1 – 3/4 = 1/4 .

Answer:

The First One

Step-by-step explanation:

Because its dimensions are 5 by 8

Hey there!

4n + 11 - 2n - 5

COMBINE the LIKE TERMS

= (4n - 2n) + (11 - 5)

= 4n - 2n + 11 - 5

= 2n + 6

Therefore, your answer should be:

2n + 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

[tex] \sf \: 2n + 6[/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

Main steps included in solving,

→ Rearranging the expression.

→ Combining the like terms.

The expression is,

→ 4n + 11 - 2n - 5

Let's simplify the expression,

→ 4n + 11 - 2n - 5

→ (4n - 2n) + (11 - 5)

→ (2n) + (6)

→ 2n + 6

Hence, the answer is 2n + 6.

I hope this helps you

1) DC=60

AD=AC=60/2=30

AB=BC=30/2=15

DB=DA+AB=30+15=45

2) RQT is right triangle we can find the side

6^2+8^2=RT^2

36+64=RT^2

RT=10