The correlation in error terms that arises when the error terms at successive points in time are related is termed _____.

the initial statement is y ∝ x

to convert to an equation multiply by k the constant of variation

[tex]y = kx[/tex]

to find k use the given condition

[tex]y = 27 \\ \\ when \\ \\ x = 3[/tex]

[tex]y = kx \\ \\ k = \frac{y}{x} = \frac{27}{3} = 9[/tex]

equation is y = 9x

when x = 4 then

[tex]y = 9 \times 4 = 36.[/tex]

Answer:

y = 36

Step-by-step explanation:

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 27 when x = 3 , then

27 = 3k ( divide both sides by 3 )

9 = k

y = 9x ← equation of variation

when x = 4 , then

y = 9 × 4 = 36

Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]

      [tex]=142506[/tex]

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]

where;

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]

[tex]\mathbf{^nC_r = 142506}[/tex]

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The shape will have a surface area of 189.25 cm². There are two distinct pieces to the figure: a rectangle and a semicircle.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

The figure is divided into two parts one is a rectangle and the second is a semicircle.

Area of figure = Area of rectangle + Area of a semicircle

Area of figure = L × B + (πr²/2)

A = 10 cm × 15 cm + (3.14 ×(5)^2/2)

A= 189.25 cm²

Hence the area of the shape will be 189.25 cm²

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Answer:

X = 92 degrees

Step-by-step explanation:

the angles of a triangle all add up to 180 degrees, so 40 plus 180-132 = 88

180-88= 92 so X = 92

The Volume and Surface Area of Prism is 294 in² and 114.33 in³.

A large structure built especially in ancient Egypt that usually has a square base and four triangular sides meeting at a point and that contains tombs.

Surface rea of rectangular prism,

= 2( lb +bh +lh)

= 2 ( 7*7 + 7*7+ 7*7)

= 2 ( 49+49+49)

= 2*3*49

= 294 in²

Now, Volume,

= bhl/3

= 7*7*7/3

= 114.33 in³

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The value of x will be 4 ,  Option A is the answer.

A triangle that has one angle as 90 degree is called a Right angled Triangle.

In a right angled triangle

the length of the sides can be determined using Pythagoras Theorem

The length of the side is given in the image attached as

x-2 , x , √20

Hypotenuse ² = Perpendicular² + Base²

(√20)² = x² + (x-2)²

20 = x² + x² +4 -4x

2x²-4x -16 = 0

x² -2x -8 = 0

x² - 4x +2x -8 = 0

x (x-4) +2(x-4) = 0

(x+2)(x-4) = 0

x = -2 , 4

The value of x will be 4 .

Therefore Option A is the answer.

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The radius will be equal to 7.55 centimeters.

The arc length is the curved length on the circumference of a circle suspended by a small angle.

The radius will be calculated as follows:-

r = [tex]\dfrac{Arc}{Angle}[/tex]

r = [tex]\dfrac{\dfrac{26\pi}{9}}{\dfrac{69\times \pi}{180}}[/tex]

r = [tex]\dfrac{9.07}{1.20}[/tex]

r = 7.55 centimeters

Therefore the radius will be equal to 7.55 centimeters.

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Answer:

B

Step-by-step explanation:

Similar to the one you asked earlier.

Given from the table

1 Gallon of gas = $2.15

15 gallons of gas = $2.15 x 15

= $32.25 (B)

Based on the information provided, the table that best matches the data in the scatter plot is shown below.

A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

Based on the information provided, the table that best matches the data in the scatter plot is given by:

Data                       1    2    4    5.5    6.3

Height (cm)            1    2    3     4       5

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Answer:

C

Step-by-step explanation:

= The square root of (5^2+2^2)= The square root of 29 ---> C

[tex] \huge\underline{\underline{\boxed{\color{blueviolet}{ANSWER}}}}[/tex]

★ 15 trucks can carry 26,850 kg weight

★ We've to find the weight carried by one truck

[tex]\huge \pink {\overline{ \quad \quad \quad \quad \quad \quad \quad\quad \quad}}[/tex]

[tex] \sf{Number \: of \: trucks = 15 }[/tex]

[tex] \sf{Weight \: carried \: by \: one \: truck = \frac{26,850Kg}{15} }[/tex]

[tex] \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= 1790Kg[/tex]

Therefore , the weight carried by one truck is 1790 kg

Answer:

A

Step-by-step explanation:

these two triangles are similar

therefore corresping sides are proportionate

12/8=9/x

12x=72

x=72/12=6

Answer:

the answer is 6

Step-by-step explanation:

i hope this is helpful

Answer:

ytyt

Step-by-step explanation:

tyt5667

Area of the rectangle is 96.05 sq.units , The ratio of the areas is 2/3 , Area of rectangle ABEF is 64.03 sq.units.

The complete question is

In the figure, the ratio of the area of rectangle ABEF to the area of rectangle ACDF is(a)_____ . If the coordinates of point A are (0,6), the area of rectangle ABEF is(b)____ square units, and the area of rectangle ACDF is(c)____ square units.  The perimeter of rectangle BCDE is(d)____ units.

A rectangle is a polygon with four sides and for angles and four vertices , Its opposite sides are parallel and equal.

The  area of rectangle ACDF is square units. = ?

The perimeter of rectangle BCDE is units. = ?

[tex]\rm d = \sqrt{ (y_2 -y_1 )^2 + (x_2 -x_1)^2}\\\\\rm d = \sqrt{ (2 - 6 )^2 + (5 - 0)^2}[/tex]

d = 9.605

the length of  [tex]\rm EF[/tex]

[tex]\rm FE[/tex] = 10 units.

and [tex]\rm FD[/tex] = 15 units

Area of a Rectangle [tex]\rm ACDF[/tex] is given by

Length x width

10 * 9.605

Area of the rectangle is 96.05 sq.units

Perimeter of a rectangle is = 2( length + breadth)

ED = FD-FE = 15- 10 = 5 units

Therefore

Perimeter = 2 ( 5 +  √41 )

Perimeter = 22.81 units

Area of rectangle ABEF is 64.03 sq.units

The ratio of the areas

= 64.03/96.05

= 0.666667

= 2/3

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Answer:

-8x²-3x+5

Step-by-step explanation:

First, add like terms.

3-6x-2x²+3x-6x²+2=

= 5-3x-8x²

Put it in standard form. To put in standard form, put the exponent from greatest to least.

-8x²-3x+5.

Hope this helps!

If not, I am sorry.

Answer:

oranges

Step-by-step explanation:

Answer: The oranges.

Step-by-step explanation: I'll set up my work below.

Mangoes: $[tex]49/7=7[/tex] =$7 per mango

Apples: $[tex]24/4=6[/tex]=$6 per apple

Oranges: $[tex]15/3=5[/tex]=$5 per orange

Given this, the cheapest fruit is the orange.

I hope this helps!! Pls mark brainliest :)

The graph is plotted and attached in the attachment. The given equation is a linear equation with the intercept 0.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as y = mx + c.

Given equation;

y + 2 = (x+2)

Rearrange the equation;

y + 2 = x+ 2

y=x

The standard equation for the straight line is;

y = mx + c

Where c is the intercept and m is the slope

After comparing the given equation with the standard equation we get;

m = 1

c =0

Hence,the graph is plotted and attached in the attachment.

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The area of the square is 16 square inches and its perimeter is 16 inches.

What is Area of square ?

A square is a two-dimensional geometric shape with four equal sides and four right angles. The area of a square is the measure of the region enclosed by the square. The area is expressed in square units, such as square inches, square meters, or square feet.

The area of a square is given by the formula:

A = s²

where A is the area and s is the length of a side.

If the side length of the square is 4 inches, the area can be calculated as:

A = 4² = 16 square inches.

The perimeter of a square is given by the formula:

P = 4s

where P is the perimeter and s is the length of a side.

If the side length of the square is 4 inches, the perimeter can be calculated as:

P = 4 x 4 = 16 inches.

Therefore, the area of the square is 16 square inches and its perimeter is 16 inches.

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#Step1

It will result -2x-2y=-8

#2

#3

add

Find x

The exponential function is used. Use x as your variable common ratio.

This is pretty obviously

If it wasn't obvious we can find the common ratio r by dividing successive values:

5/1=5

25/5=5

125/25=5

625/125=5

The common ratio is the number you multiply or divide by at each stage of the sequence. You can find it by dividing two consecutive pairs of terms.

That's the common ratio.  We multiply by the first term, but the first term is one, so that has no effect.

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You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40. How much did each item cost?

First let’s define a shirt as X and pants as Y!

In the first scenario, the equation will be 3X + Y =$32

In the second scenario, the equation will be 2X + 3Y = $40  

Now because we have two different variables (X & Y) let’s solve for one of them (Ex: Y) to simplify the equations!

3X + Y= $32—> subtract 3X on both sides of the equation  

-3X.        - 3X

Net result: Y= 32- 3X

Now we can insert this into the second equation 2X + 3Y = $40 in order to solve for X variable  

2X + 3(32-3X) = $40

2X + 96 - 9X = $40 —> simplify the equation  

-7X + 96 = $40 —> substrate 96 from both sides  

-7X = -56 —> divide both sides by -7  

X= 8  

Now reinsert 8= X into 3X + Y = $32

3(8) + Y = $32

24+ Y = $32 —> substract 24 from both sides

y = 8

ANSWER: X= 8, Y= 8

Answer:

B. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter

As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.

The general form of the cosine function representing the displacement of the rider is:

f(t) = a cos(bt+c) + d, where:

amplitude = |a| which is the distance that travels above and below the midpoint

period = 2 π/|b| which is the time period i.e. time required to complete one cycle

-c/b is the phase shift.

d = vertical displacement of the function

Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.

So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.

The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.

The rider starts from the bottom position, so there will be no phase shift, so c=0

Given that the center of the wheel is 19 m above the ground, so d=19m

Therefore the equation will be

height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter

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One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

As we know;-

1 meter is 100 cm so 0.2 meters will be calculated as:-

1 meter = 100 cm

0.2 meter = 0.2 x 100 = 20 centimeters.

Therefore One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.

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Answer:

[tex]\huge\boxed{\sf 20z\³ + 24z\² - 5z - 6}[/tex]

Step-by-step explanation:

= (5z + 6)(2z + 1)(2x - 1)

= (5z + 6)[(2z)² - (1)²]

= (5z + 6)(4z² - 1)

Distributing

= 5z (4z² - 1) + 6(4z² - 1)

= 20z³ - 5z + 24z² - 6

Arrange

= 20z³ + 24z² - 5z - 6

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

Step-by-step explanation:

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The statements that are true about circle Q are:

The measure of the central angle is 45°.  The measure of the entire circle is 360°.  This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8

To find the area of the shaded sector, this will be:

A = πr² = π(6²) = 36π

1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units.  This is not 4 square units.

The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.

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Answer:

1,3,4

Step-by-step explanation:

Answer:

[tex]x=10[/tex]

Step-by-step explanation:

Here, we can use an angle rule.

We see that angles [tex](8x+50)[/tex]° and 130° are under a sort of F shape, where lines m and n are the horizontal parts of the letter and where the diagonal line is the vertical part of the letter.

This means we can use the rule:

Corresponding angles are equal.

This means that:

[tex]8x + 50 = 130[/tex]

We can now use this equation we have formed to solve for [tex]x[/tex]:

[tex]8x + 50 = 130\\8x = 80\\x = 10[/tex]

Therefore, our final answer is [tex]x=10[/tex].

Answer:

Yes, the relation is proportional because the ratios are equivalent between each pair of values

Step-by-step explanation:

 Proportional relationships are relationships with equal ratios.

Entries in the respective columns are:

        column 1 (Minutes)              column 2 (Blocks)                 Ratios

                   6                                           3                                    1/2                

                   14                                          7                                    1/2

                   20                                         10                                  1/2

  As the ratio of Blocks and Minutes is same for every row,

   the given table represent a proportional relationship.

  hence, option c is correct.

   Yes, because the ratios are equivalent between each pair of values.

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Answer: Yes, the relation is proportional because the ratios are equivalent between each pair of values :)