The ________ could be used to describe a data set by itself, while ___________ would almost never be used to describe a data set by itself.

The matricial equation of the degenerate parabola is [tex]\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right][/tex].

A parabola is degenerated when its axis of symmetry is not parallel to any orthogonal axis (i.e. x, y). First, we have to find an "equivalent" parabola whose axis of symmetry is parallel to the y-axis and whose vertex is along that axis.

Direction of the degenerate parabola

[tex]\tan \theta = \frac{2 - 1}{2 - 1}[/tex]

tan θ = 1

θ = 45°

This means that the degenerate parabola must be rotated 45° clockwise (- 45°) around the origin with respect to the "equivalent" parabola.

Distance from the vertex to the focus

[tex]p = \sqrt{(2 - 1)^{2}+(2 - 1)^{2}}[/tex]

[tex]p = \sqrt{2}[/tex]

Vertex of the "equivalent" parabola

[tex](h', k') = (0, \sqrt{2})[/tex]

Equation of the "equivalent" parabola

[tex]y = \frac{1}{4\cdot p}\cdot x^{2} + k'[/tex]

[tex]y = \frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}[/tex]

Now we apply following rotation formula:

[tex]\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{cc}\cos (-45^{\circ})&-\sin (-45^{\circ})\\\sin (-45^{\circ})&\cos (-45^{\circ})\end{array}\right] \cdot \left[\begin{array}{c}x\\\frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}} \end{array}\right][/tex]

[tex]\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right][/tex]

A representation of the degenerate parabola is shown in the figure attached below.

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Answer:

x = -8, 1.

Step-by-step explanation:

x^2 + 7x - 8 = 0

(x + 8)(x - 1) = 0

x = -8, 1.

Answer:

-8 and 1

Step-by-step explanation:

Quadratic expression.

A quadratic expression is an expression with 2 as the highest power of the unknown.

Solving the question:

[tex]x {}^{2} + 7x - 8 \\ x {}^{2} + 8x - x - 8 \\ x(x + 8) - 1(x + 8) \\ (x - 1)(x + 8) \\ x = 1 \: or \: x = - 8[/tex]

Point [tex](1,5)[/tex] is a solution of the equation [tex]g(x)=3x+2[/tex] and point [tex](1,5)[/tex] is not a solution of equation [tex]f(x)=|x-1|+1[/tex]

Why point [tex](1,5)[/tex] is solution of the equation [tex]g(x)=3x+2[/tex] ?

If point [tex](1,5)[/tex] is solution of the equation then they must satisfy the equation.

So we need to check one by one

[tex](x,y)=(1,5)[/tex]

equation [tex]g(x)=3x+2[/tex]

We can write as

[tex]y=3x+2\\5=3*1+2\\5=5[/tex]

So  point [tex](1,5)[/tex] is solution of this equation.

Equation [tex]f(x)=|x-1|+1[/tex]

We can write as

[tex]y=|x-1|+1\\5=|1-1|+1\\5=0+1\\5\neq 1[/tex]

So point [tex](1,5)[/tex] is not solution of equation [tex]f(x)=|x-1|+1[/tex]

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Based on the information, Christian would have $5525.5 of annuity.

According to given information, the number of coffees per week is 3 then, per month is 3x4 = 12

For each coffee is $4.5. Then monthly expenditure for coffees is 12 x 4.5 = $54

Rate of interest r = 1.6% = 1.6/100 = 0.016 and for monthly compounding r = 0.016/12 = 0.00133

n = number of payments = 8 x 12 = 96

We can use the formula for finding the future value as below

FV = C x [ ( 1 + r )n-1 ] / ( r )

FV = 54 x [ ( 1 + 0.00133 )96 – 1 ] / (0.00133)

= 54 x [ (1.13609 - 1)] / (0.00133)

= 54 x 0.13609 / (0.00133)

= 54 x 102.3233

= 5525.5

Therefore Christian would have $5525.5 of annuity.

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A binomial probability density function should be used to represent the probability

The given parameters are:

The proportion that plays sport indicates that

68% of the students do not play sport

So, we have two events, which are

When there are two possible events, then the binomial probability density function should be used

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These two should be the points as then 2 points will remain on both sides

Slope

Equation in point slope form

When x=-15

Just above 7

Answer: [tex]x=8, y=2\sqrt 2[/tex]

Step-by-step explanation:

By the Pythagorean theorem, x=8.

So, by the geometric mean theorem,

[tex]y^2 = (6)(2)=8\\\\y=2\sqrt{2}[/tex]

The equation in slope intercept form is y = -4x/3 + 10

The representations are given as:

So, we have:

2 * x + 1.5 * y = 15

Evaluate the product

2x + 1.5y = 15

Subtract 2x from both sides

1.5y = -2x + 15

Divide through by 1.5

y = -4x/3 + 10

Hence, the equation in slope intercept form is y = -4x/3 + 10

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Theo's base salary  using a simultaneous equation approach is $2,996.22 .

In order to determine the base salary of Theo, we can express the two earnings and sales amounts using simultaneous equation, that we would solve to arrive at the base salary

Bear in mind that total earnings are determined as base salary plus commission

Let X be the base salary

Let R be the rate of commission

commission =sales*rate of commission

When earnings were $3,835.25 and sales is $12,850, we have the below equation:

X+(12,850*R)=3,835.25

X+12850R=3,835.25  .................... equation (1)

When earnings were $3,641 and sales is $9,875, we have the below equation:

X+(9,875*R)=3641

X+9875R=3641 .........................  equation (2)

subtract equation 2 from 1

2975R=194.25

R=194.25/2975

R=commission rate=6.52941176470588%

substitute for R in equation 1 to arrive at X(base salary)

X+(12850*6.52941176470588%)=3,835.25

X=3,835.25-(12850*6.52941176470588%)

X=base salary=$2,996.22

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Answer:

[tex]\huge\boxed{\sf 7x + 10\ cm}[/tex]

Step-by-step explanation:

= 5 + 2x + 2x + 5 + 3x

Combine like terms

= 2x + 2x + 3x + 5 + 5

= 7x + 10 cm

[tex]\rule[225]{225}{2}[/tex]

Answer:

7x + 10

Step-by-step explanation:

Perimeter is the sum of all the sides together, the distance around a shape.

3x + 5 + 2x + 2x + 5

Organize so the variables are on one side

3x + 2x + 2x + 5 + 5

Combine like terms:

7x + 10

Your answer would be: 7x + 10

I hope it helps! Have a great day!

bren~

Answer:

Step-by-step explanation:

This is a geometric means problem where the height (length AC of 4) is the geometric mean between the base BC and the base DC. The proportion is

[tex]\frac{12.8}{4} =\frac{4}{CD}[/tex] . Cross multiply to get

12.8CD = 16 and divide both sides by 12.8 to get that

CD = 1.25

That means that the length of the whole thing, BD, is

12.8 + 1.25 = 14.05

The slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

The formula for calculating the slope of a line is expressed as

slope = y2-y1/x2-x1

Given the coordinate points (0, 0) and (-2 , 1), the slope is expressed as:

Slope = 1-0/-2-0

Slope = 1/-2

Slope = -1/2

Hence the slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

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The slope of the line m is - 1 / 2.

The slope a line can be found as follows:

slope = m = y₂ - y₁ / x₂ - x₁

using (0, 0)(2, -1)

hence,

slope = - 1 - 0 / 2 - 0

slope = - 1 / 2

hence,

slope = - 1 / 2

Therefore, the slope of the line m is - 1 / 2.

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If the sales had dropped 23% then music store had sold 551 units in the second quarter.

Given that a music store had sold 715 units in first quarter and sales had dropped by 23%.

We are required to determine the sales in the second quarter.

Percentage is the number or ratio expressed in terms of 100. It is expressed as %.

Sales in first quarter=715 units

Decrease in sales=23%

In units ,decrease=715*23%

=715*23/100

=164.45

Sales of second  quarter=715-164.45

=550.55

After rounding we will get 551.

Hence if the music store sold 715 units in first quarter then the units sold by music store in second quarter 551 units.

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Using the law of sines, it is found that 1 triangle can be formed with the given conditions.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Hence, for this problem, we have that the relation is:

[tex]\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}[/tex]

[tex]\sin{G} = 0.9\sin{64^\circ}[/tex]

[tex]\sin{G} = 0.8089[/tex]

[tex]G = \arcsin{0.8089}[/tex]

G = 54º

A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.

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Step-by-step explanation:

400 is the whole = 100%

20% (= 20 out of 100 equal parts of 100%) are red.

how many are that ?

well, again, 400 = 100%

1% = 100%/100 = 400/100 = 4

20% = 20×1% = 20×4 = 80

when you combine these 2 steps, you see you get 20% by multiplying the 100% by 20/100 or 0.20.

400 × 0.2 = 80

now,

35% are yellow.

35% = 35×1% = 35×4 = 140

or

400×0.35 = 140

red + yellow = 80 + 140 = 220

the rest are green

400 - 220 = 180

we would get this also by seeing that

red + yellow = 20% + 35% = 55%.

so, green has then the remaining 100-55 = 45%

and again

45% = 45×1% = 45×4 = 180

or

400×0.45 = 180

The expression equivalent to -7(y - 2) is -7y + 14

Given the expression; -7(y - 2)

We expand the expression by multiplying each element inside the parentheses the element out i.e -7

-7(y - 2)

[ -7 × y and -7 × -2 ]

-7y + 14

Therefore, the expression equivalent to -7(y - 2) is -7y + 14.

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The equation of the first circle is (x + 1)^2 + (y - 1)^2 = r^2 and the equation of the second circle is (x + 1)² + (y - 1)² = 16

The points are given as:

P(3, 0) and Q(0, 5)

The midpoint of PQ is

Midpoint = 0.5(3 + 0, 0 + 5)

Midpoint = (1.5, 2.5)

Calculate the slope of PQ

m = (y2 - y1)/(x2 - x1)

m = (5 - 0)/(0 - 3)

m = -5/3

A line perpendicular to PQ would have a slope (n) of

n = -1/m

This gives

n = -1/(-5/3)

n = 0.6

The equation is then calculated as:

y = n(x - x1) + y1

Where

(x1, y1) = (1.5, 2.5)

So, we have:

y = 0.6(x - 1.5) + 2.5

y = 0.6x - 0.9 + 2.5

Evaluate the sum

y = 0.6x + 1.6

Hence, the equation of the perpendicular bisector of PQ is y = 0.6x + 1.6

We have:

y = x + 2

Substitute y = x + 2 in y = 0.6x + 1.6

x + 2 = 0.6x + 1.6

Evaluate the like terms

0.4x = -0.4

Divide

x = -1

Substitute x = -1 in y = x + 2

y = -1 + 2

y = 1

Hence, the center of the circle is (-1, 1)

We have:

Center, (a, b) = (-1, 1)

Point, (x, y) = (0, 5) and (3, 0)

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where r represents the radius.

Substitute (a, b) = (-1, 1) in (x - a)^2 + (y - b)^2 = r^2

(x + 1)^2 + (y - 1)^2 = r^2

Substitute (x, y) = (0, 5) in (x + 1)^2 + (y - 1)^2 = r^2

(0 + 1)^2 + (5 - 1)^2 = r^2

This gives

r^2 = 17

Substitute r^2 = 17 in (x + 1)^2 + (y - 1)^2 = r^2

(x + 1)^2 + (y - 1)^2 = r^2

Hence, the circle equation is (x + 1)^2 + (y - 1)^2 = r^2

The equation of the second circle is

2x² + y² + ax + by - 14 = 0

Rewrite as:

2x² + ax + y² + by = 14

For x and y, we use the following assumptions

2x² + ax = 0    and  y² + by = 0

Divide through by 2

x² + 0.5ax = 0    and  y² + by = 0

Take the coefficients of x and y

k = 0.5a                   k = b

Divide by 2

k/2 = 0.25a           k/2 = 0.5b

Square both sides

(k/2)² = 0.0625a²           (k/2)² = 0.25b²

Add the above to both sides of the equations

x² + 0.5ax +0.0625a² = 0.0625a²    and  y² + by + 0.25b² = 0.25b²

Express as perfect squares

(x + 0.25a)² = 0.0625a² and (y + 0.5b)² = 0.25b²

Add both equations

(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²

So, we have:

2x² + ax + y² + by = 14 becomes

(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14

Comparing the above equation and (x + 1)^2 + (y - 1)^2 = r^2, we have:

0.25a = 1 and 0.5b = -1

Solve for a

a = 4 and b = -2

This means that the value of a is 4 and b is -2

We have:

a = 4 and b = -2

Substitute these values in (x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14

This gives

(x + 0.25*4)² + (y - 0.5*2)² = 0.0625*4² + 0.25*(-2)²+ 14

(x + 1)² + (y - 1)² = 16

The equation of the first circle is

(x + 1)² + (y - 1)² = 17

The radii of the first and the second circles are

R = √17

r = √16

√17 is greater than √16

Since they have the same center, and the radius of the first circle exceeds the radius of the second circle, then the second circle lies inside the first circle.

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Answer:

1 1/2

Step-by-step explanation:

When you are subtracting a negative number is is the same as adding a positive.  So the problem is really 5/8 + 7/8, since the denominators are the same, just add the numerators to get 12/8  divide the top and bottom by 4 to get 3/2 or 1 1/2, if I divide 3 by 2.

As a percentage, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.

A relative frequency measures the proportion of events that occur within a class out of the total number of observations.

When using relative frequency, the results are usually displayed in percentages, proportions, and fractions.

Year    State                   Recycled Plastics                 Relative

                                       (thousands of tons)            Frequency

2008  New Mexico                   500                        0.111  (500/4,500)

2008  New York                     1,500                        0.333 (1,500/4,500)

2008  Texas                          2,500                        0.566 (2,500/4,500)

Total                                       4,500                        1

Thus, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.

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Answer: 9%

Step-by-step explanation:

just did the question

The angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

The angle of elevation is says to be the angle made between a horizontal plane and a straight line to a given object that is elevated off the ground.

Therefore, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.

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v = 1.21 m/s is the answer

Kinetic energy of object = 25 J

Mass of object = 34 kg

The formula for the kinetic energy of an object is given by

K.E. = 1/2 m v2.

25 =  1/2 *34* v2.

v2= 25/17

v2 = 1.47

v = 1.21 m/s

In physics, the kinetic energy of an object is the energy that the object has due to its motion. This is defined as the work required to accelerate an object of a given mass from a stationary state to a specified velocity. After the body gains this energy during acceleration, it retains this kinetic energy unless the velocity changes

Everything that moves at home is an example of kinetic energy. This could be a cue ball rolling on a pool table, a fan that circulates air on warm days, or a glass that shatters on the floor after falling off the counter. Electrical equipment that is turned on uses kinetic energy, much like people move around the house.

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the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

A perfect square is the product of a number and itself.

As you can see in the example, 16 is a square number. Then let's try to get 16.

To get 16 we can use the difference:

20 - 4

So the first therm needs to be equal to 20, and the second equal to 4.

To write 20 in scientific notation we have:

[tex]2*10^1[/tex]

To write 4 in in scientific notation:

[tex]4*10^0[/tex]

Then the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

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Answer:

  7.7 km

Step-by-step explanation:

This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.

The Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...

  t/sin(T) = p/sin(P) = j/sin(J)

We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.

We know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:

  7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j

This can be solved in two steps. First, we find angle P, then we use that to find length j.

  sin(P) = 5.2/7.5 × sin(68°) ≈ 0.642847

  P = arcsin(0.642847) ≈ 40.0045°

Now, we can find j:

  j = 7.5 × sin(68° +40.0045°)/sin(68°) ≈ 7.693 . . . km

The distance from the tower to the plane is about 7.7 km.

__

Additional comment

We have used T, P, and J to refer to the vertices at the tower, plane, and jet.

The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.

Answer:

[tex]-\frac{345}{37}[/tex]

Step-by-step explanation:

Just follow the order of operations

210÷[5+16÷2{6−18÷(7+2)}]−15  

= 210÷[5+16÷2{6−18÷9}]−15   (calculate 7+2)

= 210÷[5+16÷2{6−2}]−15 (calculate 18÷9)

= 210÷[5+16÷2{4}]−15  (calculate 6-4)

= 210÷[5+16÷2×4]−15

= 210÷[5+8×4]−15  (calculate 16÷2)

= 210÷[5+32]−15  (calculate 8×4)

= 210÷[37]−15  (calculate 5+32)

= 210÷37−15

= 210÷37−(15×37)÷37  (put on the same denominator)

= 210÷37−555÷37  (calculate 15×37)

= (210−555)÷37

=-345÷37   (calculate 210-555)

Answer:

31

Step-by-step explanation:

C= 2πr  We will used 3.14 for pi and the radius is 5

C = 2(3.14)(5)

C =31.4 Then round to the nearest whole number which would be 31.  31.4 is closer to 31 than 32

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

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

The standard form of a quadratic equation is:

y = ax² + bx + c

The graph of a quadratic equation is a parabola.

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

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The central angle formed between the ends of the ribbon is 98.6°.

The circumference will be:

= πd

= 3.14 × 15 = 47.1

Ribbon = 60 - 47.1 = 12.9

Length of arc = x/360 × πd

12.9 = x/360 × 3.14 × 15

x = 98.6°

The angle is 98.6°

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The property A*B = (A' + A") * ( B'+B") is equal to each other.

According to the statement

We have given that the a and b is the positive integers and we have to prove that the product of all positive divisors of a equals the product of all positive divisors of b.

And in this statement

Now we use Distributive property

Here A and B is the positive integer and

A' and A" are the divisors of A and B' and B" are the divisors of B.

Now,

A = A' + A" and B = B'+B"

Now, Multiply both with each other then

A*B = (A' + A") * ( B'+B")

then

A*B = (A' B'+ A'B") + ( A"B'+A'B")

by this way it is equal to each other

Hence proved.

So, The property A*B = (A' + A") * ( B'+B") is equal to each other.

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