Find the slope of the line graphed below.

The length of diagonal EK is sqrt(5^2 + 4^2) ≈ 6.403m

Hence perimeter = 2*(12 + 6.403) → 36.8 m (to the nearest tenth of a metre)

The perimeter of the cross-section is 36.8 m.

Given that the length of diagonal EK is

[tex]\sqrt{(5^2 + 4^2) }[/tex]

≈ 6.403m

Thus, the perimeter would be

2*(12 + 6.403)

→ 36.8 m.

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B. 3x+2 is the correct answer

Answer:  The correct option is

(B) [tex]y=3x+2.[/tex]

Step-by-step explanation:  We are given to estimate the line of best fit using the following two points on the line.

(10, 32)  and  (20, 62).

We know that

the slope of a line passing through the points (a, b) and (c, d) is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

So, the slope of the given line will be

[tex]m=\dfrac{62-32}{20-0}=\dfrac{30}{10}=3.[/tex]

Since the line passes through the point (10, 32), so its equation is given by

[tex]y-32=m(x-10)\\\\\Rightarrow y-32=3(x-10)\\\\\Rightarrow y=3x+30+32\\\\\Rightarrow y=3x+2.[/tex]

Thus, the required equation of the line of best fit is [tex]y=3x+2.[/tex]

Option (B) is CORRECT.

Answer:

not geometric

Step-by-step explanation:

A geometric series is one where the nth term is multiplied by a common ratio to get the n+1 term.

1    1/2   1/4     1/8       1/16 .....

is a geometric series. the fourth term (1/8) is multiplied by 1/2 to get 1/16.

The series you have been given is not geometric.  It reduces to

1/3   1/4   1/5    1/6 which does not give you a common number to multiply the nth term to get to the n+1 term.  

Answer:

-0.4

Step-by-step explanation:

z score is:

z = (x - μ) / σ

For x = 28.2, μ = 30, and σ = 4.5:

z = (28.2 - 30) / 4.5

z = -0.4

Answer: -0.4

Step-by-step explanation:

Given: Mean : [tex]\mu=30\text{ inches}[/tex]

Standard deviation : [tex]\sigma=4.5\text{ inches}[/tex]

The formula to calculate z-score is given by :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

For X = 28.2 inches, we have

[tex]z=\dfrac{28.2-30}{4.5}\\\\\Rigahtarrow\ z=-0.4[/tex]

Hence, the z-score of a trout with a length of 28.2 inches.= -0.4

I don’t know what the answer is I wish I could help

The answer is y=56.2x-112.4

The answer is:

The first measurement of volume is equal to 835.23 mL.

Boyle's Law equation can be used when the temperature is kept constant, and it establishes a relation between the pressure and volume, showing that when an ideal gas is kept constant, the pressure and volume are inversely proportional.

So, we Boyle's Law equation states that:

[tex]P_{1}V_{1}=P_{2}V_{2}[/tex]

Where,

[tex]P_1=FirstPressure\\V_1=FirstVolume\\P_2=NewPressure\\V_2=NewVolume[/tex]

Now, if we are looking for the first volume measurement, we need to rewrite the equation as follow:

[tex]P_{1}V_{1}=P_{2}V_{2}\\\\V_{1}=\frac{P_{2}V_{2}}{P_{1}}[/tex]

So, substituting the given information and calculating, we have:

[tex]V_{1}=\frac{8.59atm*527mL}{5.42atm}[/tex]

[tex]V_{1}=\frac{4526.93atm.mL}{5.42atm}=835.23mL[/tex]

Hence, the first measurement of volume is equal 835.23 mL.

Have a nice day!

Answer:

162.43

Step-by-step explanation: I hope its helps it's been a couple of years since I have done geometry

Answer:

the total area of the octagon is 8(20.3 in²), or 162.4 in²

Step-by-step explanation:

A regular octagon has 8 pie-shaped sections.  Each is triangle of height 7 in and base 5.8 in.

Thus, the area of each such section is, by A = (1/2)(b)(h(),

A = (1/2)(5.8 in)(7 in) = 20.3 in².

There are 8 such sections.  

Thus, the total area of the octagon is 8(20.3 in²), or 162.4 in²

Answer:

(√5)/2

Step-by-step explanation:

In the attached figure, we have labeled the circumcenter point D and the incenter point E. The points of tangency of the incircle with sides AB, BC and CA are labeled G, H, and F, respectively.

The distances from any vertex to the two points of tangency from that vertex are the same. So, AG = FA, BG = BH, and CF = CH. If we call the radius of the incircle "r", then we have ...

AG = FA = r, BG = BH = 3-r, CF = CH = 4-r

so the side length BC is ...

BC = BH +CH = (3-r) +(4-r) = 7-2r

We already know that side length BC is 5, so ...

5 = 7 -2r

r = (7 -5)/2 = 1

Of course, the circumcenter of a right triangle is the midpoint of the hypotenuse, so the circumradius "R" is 5/2 = 2.5.

The formula for the distance between the two centers is ...

d = √(R(R -2r)) = √(2.5(2.5 -2)) = √1.25 = (√5)/2

_____

Comment on this answer

We have used a formula for the center-to-center distance found using a web search. The attached diagram shows the coordinates of the two centers, so the distance can be found from those. It is the same.

Answer:

Step-by-step explanation:

The directions tell you what to do and give an example. That work is to be repeated 15 more times. The work is tedious, at best. I found it slightly less tedious to enter the 64 numbers into a spreadsheet and let it do the sums. See the attached for the result.

At the bottom of the array are the sums of columns. At the right are the sums of rows. The upper right and lower left numbers are the sums of the corresponding diagonals.

The "pattern" is that the sums are all -6, which is what you expect from a magic square.

Answer:

  m∠LPM = 60°

Step-by-step explanation:

The measure of the angle facing the marked arcs is the average of the measures of the arcs:

  m∠LPM = (1/2)(40° +80°) = 60°

Answer:

< BCA = 70

Step-by-step explanation:

The complete central angle of a circle is 360 degrees. The given portion is 250 degrees.

What is left over? BOA = 360 - 250 = 110

Tangents always meet the radius at 90 degrees. Since there are two tangents <CAO = <BAO = 90 degrees.

So piecing it all together, the equation becomes

<BAO + CAO + BAO + ACB = 360

110 + 90 + 90 + <ACB = 360

290 + <ACB = 360

<ACB + 290 - 290 = 360 - 290

ACB = 70 degrees

Answer:

first brand 55 gallons

second brand 95 gallons

Step-by-step explanation:

Answer:

S(t) = 2 - 0.25*t

Step-by-step explanation:

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.

When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.

S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).

Therefore the equation formed will be linear.

The equation will be of the form y = mx + b

Here S(t) = mt + b

Here m is the slope which is the rate at which ice is melting.

Putting t = 0

S(t) = 2

Putting t = 3,

S(t) = 1.25

Therefore, m*0 + b = 2 or, b = 2

and 3m + b = 1.25

or, 3m = 1.25 - 2 = -0.75

or, t = -0.25

Hence, function's formula = S(t) = -0.25*t + 2

i.e. S(t) = 2 - 0.25*t

Answer:

y = 2 - 0.25x

Step-by-step explanation:

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.

When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.

S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).

Therefore the equation formed will be linear.

The equation will be of the form y = mx + b

Here S(t) = mt + b

Here m is the slope which is the rate at which ice is melting.

Putting t = 0

S(t) = 2

Putting t = 3,

S(t) = 1.25

Therefore, m*0 + b = 2 or, b = 2

and 3m + b = 1.25

or, 3m = 1.25 - 2 = -0.75

or, t = -0.25

Hence, function's formula = S(t) = -0.25*t + 2

i.e. S(t) = 2 - 0.25*t

- D is the midpoint of AB, E is the midpoint of BC

Answer: A. Given

I left off DB||FC because that's not given.  But we can construct it.

Construct line through C parallel to AB.  Extend DE to intersect and call the meet F.

- DB || FC

By Construction

----

- Angle B congruent to angle FCE

Answer: D. Alternate Interior Angles

We have transversal BC across parallel lines AB and CF, so we get congruent angles ABC and FCB aka FCE

- angle BED congruent to angle CEF

Answer: H. Vertical angles are congruent

When we get lines meeting like this we get the usual congruent and supplementary angles.

- Triangle BED congruent to Triangle CEF

Answer: F. Angle Side Angle

We have BE=CE, DBE=FCE, BED=CEF

- DE congruent to FE and DB congruent to FC

Answer: C. CPTCTF

Corresponding parts ...

- AD congruent to DB and DB congruent to FC therefore AD congruent to FC

Answer: E. Transitive Property of Congruent

Things congruent to the same thing are congruent

- ADFC is a parallelogram

Answer: G.  AD and FC are congruent and parallel

Presumably this is a theorem we have already established.

- DE || AD

Answer: B. Definition of a parallelogram

Answer:

Part A). 20 hours 42 minutes taken by earth to rotate 310°.

Part B). 19 hours 6 minutes taken by earth to rotate 5 radians.

Part C). 2072.4 miles a point on the equator rotate in 2 hours.

Step-by-step explanation:

Given : Earth rotate 360° in 24 hours.

Part A).

Time taken by earth to rotate 360° = 24 hours.

Time taken by earth to rotate 1° = [tex]\frac{24}{360}[/tex] hours.

Time taken by earth to rotate 310° = [tex]\frac{24}{360}\times310[/tex] hours.

                                                   = 20.7 hours = 20 hours 42 minutes (approx.)

Part B).

Time taken by earth to rotate 360° = 24 hours.

We know that 360° = 2π radian

Time taken by earth to rotate 2π radian = 24 hours.

Time taken by earth to rotate 1 radian = [tex]\frac{24}{2\pi}[/tex] hours.

Time taken by earth to rotate 5 = [tex]\frac{24}{2\pi}\times5[/tex] hours.

                                                  = 19.098 hours = 19 hours 6 minutes (approx.)

Part C).

Diameter of Earth = 7920 miles

Radius of Earth, r  = 7920/2 = 3960 miles.

Degree of rotation in 24 hour = 360°

Degree of rotation in 2 hour, [tex]\theta\:=\frac{360}{24}\times2=30^{\circ}[/tex]

Now use Formula used to calculate Length of the arc of the circle.

Length of the Arc = [tex]\frac{\theta}{360}\times2\pi r[/tex]

Length a point on equator moves in 2 hour =  [tex]\frac{\theta}{360}\times2\pi r=\frac{30}{360}\times2\times3.14\times3960=2072.4\:miles[/tex]

Answer: B. 0.45

Step-by-step explanation:

From the given table, the total number of students = 137

The number of students are sophomores =35+42=77

Let A be the event that students are sophomores.

Then probability that students are sophomores is given by  :

[tex]\text{P(A)}=\dfrac{77}{137}[/tex]

The number of sophomores who attended the jazz concert = 35

Let B be the event that students attended the jazz concert .

The probability that students attended the jazz concert and are sophomores is given by  :

[tex]\text{P(A and B)}=\dfrac{35}{137}[/tex]

Now, the probability of that the student attended the jazz concert, given that the students is sophomore is given by :-

[tex]P(B|A)=\dfrac{\text{P(A and B)}}{\text{P(A)}}\\\\=\dfrac{\dfrac{35}{137}}{\dfrac{77}{137}}\\\\\\=\dfrac{35}{77}=0.454545454545\approx0.45[/tex]

The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

y = 4x − 19.4      ...1

y = 0.2x−4.2      ...2

From equations 1 and 2, then we have

4x - 19.4 = 0.2x - 4.2

3.8x = 15.2

x = 4

Then the value of the variable 'y' will be calculated as,

y = 4 (4) - 19.4

y = 16 - 19.4

y = - 3.4

The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

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Answer:

-2(2x +5)² = -8x² -40x -50

Step-by-step explanation:

Evaluate from the inside out, according to the order of operations.

  h(g(f(x))) = h(g(2x +5)) = h((2x +5)²) = -2(2x +5)² = -2(4x² +20x +25)

  = -8x² -40x -50

I personally prefer the factored form, but that is not considered "simplified."

Answer: The answer to your question would be the third graph to your left

Step-by-step explanation: because when you calculate the rate of change from these points:

(50,1)

(100,2)

(150,3)

(200,4)

The rate of change would be 50 miles/ km per hour

Finding the slope formula: [tex]m= y2-y1/ x2-x1[/tex]

And when you take any two points from the graph, for example: (50,1) and (200,4), it would look like this:

[tex]\frac{200-150}{4-1}= 50/1= 50 miles/km per hour[/tex]

The correct graph is 3rd.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Considering the 3rd graph, the coordinates are :-

(50,1)

(100,2)

(150,3)

(200,4)

Finding the slope = (y₂-y₁) / (x₂-x₁)

considering the points (50,1) and (200,4), slope =

slope = 4-1 / 200-50 = 1/50

Since the slope shows the rate, and the rate of change would be 50 miles/ km per hour

Hence, the correct graph is 3rd one.

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Answer:

[tex] 19\sqrt{7} [/tex]

Step-by-step explanation:

[tex] 25\sqrt{7} - 2\sqrt{63} = [/tex]

[tex] = 25\sqrt{7} - 2\sqrt{9 \times 7} [/tex]

[tex] = 25\sqrt{7} - 2\sqrt{9} \sqrt{7} [/tex]

[tex] = 25\sqrt{7} - 2\times 3 \sqrt{7} [/tex]

[tex] = 25\sqrt{7} - 6 \sqrt{7} [/tex]

[tex] = 19\sqrt{7} [/tex]

Part A

The scatterplot is shown the attachment.

Part B

Using a linear regression equation that models Patrick's referrals has a positive slope.

This means that, there is a positive relation between time(number of days),x and  the number of personal recommendations, y.

In other words, as the number of days increases, the number of personal recommendations also increases.

Question 2.

The given functions are:

[tex]y=x^2+3x-5[/tex]

[tex]y=4x+1[/tex]

To find the point where the graphs of these functions intersect,we solve the two equations simultaneously.

We equate the two equations to get:

[tex]x^2+3x-5=4x+1[/tex]

[tex]x^2+3x-4x-5-1=0[/tex]

[tex]x^2-x-6=0[/tex]

Factor to obtain:

[tex](x-3)(x+2)=0[/tex]

x=3 and x=-2

We put x=-2, into [tex]y=4x+1[/tex] to get;

[tex]y=4(-2)+1=-7[/tex]

when x=3 [tex]y=4(3)+1=13[/tex]

Therefore the graphs intersect at (-2,-7) and(3,13).

Yes, solution is correct.

Answer:

What is the area AA of each section of the circle?

Give your answer in terms of pi.

A = 25πm²

Step-by-step explanation:

Given the radius of the circle to be 10

The question is to find area of each sections of the circle .

The formula for calculating the area of a circle is area equals to πr²

A = πr²

Given r = 10m

The next step is to substitute the values into the equations  

A = π (10m)²

A = 100πm²

Since the circle is divided into 4 equal sections, we need to find the area of each sections by dividing the complete area of the circle by 4

Therefore,  

A = 100πm²/4  

A = 25πm²

Answer:

25π[tex]m^{2}[/tex]

Step-by-step explanation:

Final answer:

A rectangle and a rhombus both have opposite sides that are parallel and their interior angles add up to 360 degrees. They differ in that a rectangle has four right angles and a rhombus has four congruent sides, which are not necessarily attributes they share unless they are both squares.

Explanation:

Both a rectangle and a rhombus share some properties as they are both quadrilaterals. Firstly, the opposite sides are parallel in both shapes. Secondly, the angle measures add to 360° which is a property of all quadrilaterals. However, they differ in other aspects; a rectangle has four right angles, whereas a rhombus generally does not unless it's a square. A rhombus has four congruent sides, and a rectangle does not unless it's a square. Therefore, the correct selections based on their commonalities are that the opposite sides are parallel and their angle measures add up to 360°.

Answer:

T T → T

Step-by-step explanation:

A conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 3 + 2 = 5 which is true and 5 + 5 = 10 which is also true.

First convert yards to feet.

1 yard = 3 feet.

100 x 3 = 300 feet long.

53 x 3 = 159 + 1 = 160 feet wide.

Now use the Pythagorean theorem to find the diagonal.

x^2 = 300^3 + 160^2

x^2 = 90000 + 25600

x^2 = 115600

x = √115600

x = 340 feet

1: 107

2: 73

3; 123

4: 62

5: 116

6: 16

7: 92

The missing angle measures in the hexagon are:

∠5 = 116°

∠4 = 62°

∠3 = 123°

∠2 = 73°

∠6 = 16°

∠7 = 92°

∠1 = 107°

A hexagon is a six-sided polygon, whose sum of interior angles equals 720°.

∠5 = 180 - 54 = 116° (supplementary angles)

∠4 = 180 - 118 = 62° (supplementary angles)

∠3 = 180 - 57 = 123° (supplementary angles)

∠6 = 180 - 164 = 16° (supplementary angles)

∠7 = 180 - 88 = 92° (supplementary angles)

∠1 = 720 - 116 - 118 - 123 - 164 - 92 = 107° (sum of interior angles in a hexagon )

∠2 = 180 - 107 = 73° (supplementary angles)

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Answer:

69 feet

Step-by-step explanation:

we have

[tex]h(t)=-16t^{2}+64t+5[/tex]

where

h(t) is the height of the ball

t is the time in seconds

we know that the given equation is a vertical parabola open downward

The vertex is the maximum

so

the y-coordinate of the vertex represent the maximum height of the ball

Convert the quadratic equation into vertex form

The equation in vertex form is equal to

[tex]y=(x-h)^{2}+k[/tex]

where

(h,k) is the vertex of the parabola

[tex]h(t)=-16t^{2}+64t+5[/tex]

[tex]h(t)-5=-16t^{2}+64t[/tex]

[tex]h(t)-5=-16(t^{2}-4t)[/tex]

[tex]h(t)-5-64=-16(t^{2}-4t+4)[/tex]

[tex]h(t)-69=-16(t^{2}-4t+4)[/tex]

[tex]h(t)-69=-16(t-2)^{2}[/tex]

[tex]h(t)=-16(t-2)^{2}+69[/tex]

the vertex is the point (2,69)

therefore

The maximum height is 69 ft

Answer:

Step-by-step explanation:

1. a) spread is the range which is given as Max(S)- Min(S)

Colin =

[tex]3,9,9,14,15,16,17,20,21\\\\range=21-3=18\\\\[/tex]

Jezebel=

[tex]=4,5,8,10,11,14,20,20,26\\\\range=26-4=22[/tex]

Jezebel had a greatest spread.It was 22 while for Colin was 18

2. a) The middle 50% of the game sold is the difference between the third quartile and first quartile of the data

Colin=

[tex]=3,9,9,14,15,16,17,20,21\\\\median=15\\\\lower half=3,9,9,14\\\\\\Q1=(9+9) /2 =9\\\\\\Upper half= 16,17,20,12\\\\\\Q3=(17+20)/2 = 18.5\\[/tex]

⇒The middle 50% = Q3-Q1 = 18.5- 9 = 9.5

Jezebel

[tex]=4,5,8,10,11,14,20,20,26\\\\\\=lower half= 4,5,8,10\\\\\\upper half=14,20,20,26\\\\\\Q1=(5+8)/2 = 6.5\\\\Q3= (20+20)/2 = 20[/tex]

⇒The middle 50% = Q3-Q1 = 20-6.5 = 13.5

Colin had the least spread of 9.5 as compared to Jezebel who had 13.5

c)The answers in part 2a and 2 b tels us that the middle section that contained 50% of the scores was more in Jezebel record than in Colin records.

The answer is D 2,024,657

Answer:

A

Step-by-step explanation:

0.365 x 739,000= 269,735

Answer:

80

Step-by-step explanation:

A = Area of First Rectangle

B = Area of Second Rectangle

w = Width

12(w)=320+B (1st Equation)

8(w) = B (2nd Equation)

w=B/8 (Plug this value of w into the first equation)

12B/8 = 320 +B (you get this)

12B= 2560 + 8B (Simplify)

4B = 2560

B =640 plug this value into the 2nd equation

8(w) = 640

w = 80

To Test This

12x80 = 960

8x80 = 640