Which of the following is the best estimate of the direction of the given vector?

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]

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: you have the correct answer hope this helped please mark me the brainlest answer have a good day mate

Answer:

D.

Step-by-step explanation:

A linear function is one that has a constant rate of change.

On table D, we can see that it has a constant rate of +2 as every time x increases by 1, y increases by 2.

Answer:

D

Explanation:

Because linear function is having the same difference or in another way it’s having the same rate of change.

Good luck,!~s

the answer is "Systematic Random Sampling"

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.

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

Answer:

[tex]10.5\ gal[/tex]

Step-by-step explanation:

we know that

[tex]1,000\ cm^{3} =1\ l[/tex]

[tex]1\ l=1.75\ pints[/tex]

[tex]1\ gal=8\ pints[/tex]

we have

[tex]48,000\ cm^{3}[/tex]

step 1

Convert to liters

[tex]48,000\ cm^{3}=48,000/1,000=48\ l[/tex]

step 2

Convert to pints

[tex]48\ l=48*1.75=84\ pints[/tex]

step 3

Convert to gallons

[tex]84\ pints=84/8=10.5\ gal[/tex]

The approximate number of gallons that are equal to 48000cm3 is 12.67 gallons.

1 liter is approximately 1.75 pints, 1 gallon = 8 pints

To convert 48000 cm³ to gallons, first recognize that 1 liter is 1000 cm³.

Therefore, 48000 cm³ is 48 liters.

Next, knowing that 1 gallon is approximately 3.79 liters, divide 48 by 3.79 to get approximately 12.67 gallons.

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

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.

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°.

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.

More about the solution of the equation link is given below.

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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.

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

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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- 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

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!

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:

  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°

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

The answer is y=56.2x-112.4

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:

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:

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:

-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

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

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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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:

The correct answer option is B. Number of Days 120 240 360 480 600 Number of Stories 5 10 15 20 25.

Step-by-step explanation:

We are given some tables showing the number of stories completed in the construction of four different high-rise buildings and the number of days spent working on the building.

We are to determine whether which table represents a linear relationship.

Table B represents a linear relationship since its ratio of number of days to number of stories completed is constant.

Number of Days    120  240  360  480  600  

Number of Stories   5      10     15    20     25

Ratio                        24    24    24    24     24

Answer:

a couple of irrational numbers: -16±4√19, approximately {1.436, -33.436}

Step-by-step explanation:

Your question can be cast as the quadratic equation

  x² +32x -48 = 0

The solutions can be found using the quadratic formula:

  x = (-32 ±√(32² -4(1)(-48)))/(2(1)) = -16±√304 = -16±4√19

_____

Comment on the equation we used

We notice that when p and q are roots, the equation can be written ...

  (x -p)(x -q) = 0 = x² -(p+q)x +pq

You want p+q = -32, pq = -48, so the equation is ...

  x² -(-32)x +(-48) = 0

  x² +32x -48 = 0 . . . . . . with parentheses eliminated