3

5

of the pupils in Year 9 say their favourite colour is red.

There are 80 pupils in Year 9.

How many students said red is their favourite colour?

4 m/s is the final speed of the 3.0 kg cart.

When two bodies of different masses move together each other and have a head-on collision, they travel in the same or different directions after a collision. This phenomenon is called the conservation of momentum.

The external force is not working here, so the initial momentum is equal to the final momentum. For elastic collision, the final velocities are different for both bodies.

m₁u₁ +m₂u₂ = m₁v₁ +m₂v₂

A 2.0  kg cart moving right at 5.0  m/s on a frictionless track collides with a 3.0 kg cart initially at rest. The 2.0 kg cart has the final speed of 1.0 m/s  to the left.

Substitute the values, m₁ = 2kg, m₂ =3kg, u₁ =5 m/s and u₂ =0 m/s, then the final velocity will be

3x0 +2x5 = -2x1 + 3v₂

v₂ = 4 m/s

Thus, the final velocity 3.0  kg cart is  4 m/s.

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It's worth noting that this form is known as the standard form of a linear equation, where the variables x and y appear only in the first degree and the constant term is on the right side of the equation.

What is the Quadratic Equation?

A quadratic equation is a type of polynomial equation that has the general form of ax^2 + bx + c = 0, where x is the variable, a, b, and c are constants, and a is not equal to zero. The degree of the equation is two, hence the name "quadratic".

x+1/6-y can be rewritten in terms of a,b, and c by using the following equation:

ax + by + c = 0

To get x+1/6-y in the values of a,b, and c we can rewrite the equation as follow:

a = 1, b = -1, c = -1/6

So, x+1/6-y can be written as:

1x - 1y - 1/6 = 0

or

ax + by + c = 0 where a=1, b=-1 and c=-1/6

It's worth noting that this form is known as the standard form of a linear equation, where the variables x and y appear only in the first degree and the constant term is on the right side of the equation.

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This type of data is cross-sectional data.

In statistics and econometrics, cross-sectional data, or a cross-section of a study population, is a type of data gathered by monitoring numerous subjects (such as individuals, firms, countries, or regions) at one point or throughout the course of time. It's also possible that the analysis disregards variations in time. Cross-sectional data analysis often entails contrasting the variations among pre-selected respondents.

Time series data, in which the same small-scale or aggregate entity is seen multiple times in time, differs from cross-sectional data. A different kind of data called panel data (also known as longitudinal data) combines the concepts of cross-sectional and time series data and examines how the topics (firms, people, etc.) develop throughout a time series. Panel data differs from cross-sectional data that has been pooled over time.

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d=2 and (a-1/2)2=2 hence 2a-1=2 hence a=3/2=first term and the common difference=d=2

S1, S2,... Sn can be written as:

A (first term) (first term)

A+r (r is a common difference) (r is a common difference),

A+2r

A+3r

A +(n-1)r

It is possible to calculate the sum as A +A +... +A (n times) + r +2r +3r.... +(n-1)r.

Giving n*A +r*(1+2+3....+n-1)

1+2+3….+n-1= n*(n-1)/2 =n^2 - n/2

The first N terms are added together as follows: n*A + r/2 *n2 - r*n/2

= r/2 *n^2 + (A - r/2)*n

This equals n2 - 2n for any n given the questions, so

A-r/2 = 2 AND r/2 = 1

=> r = 2 and A = 3 with r = 2

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Full question

The sum of the first n terms of an arithmetic sequence is given by Sn= n^2-2n. What are the first term and the common difference?

At store B, they charge $0.09 more for pineapple juice than store A.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, Brody was comparing the price of pineapple juice at two stores.

Equation to represent the cost of pineapple juice at store A is

y=0.7x

Equation to represent the cost of pineapple juice at store B is

From the table, we have (9, 7.11) and (13, 10.27)

Now, slope m= (10.27-7.11)/(13-9)

= 3.16/4

= 0.79

Substitute m=0.79 and (x, y)=(9, 7.11) in y=mx+c, we get

7.11=0.79(9)+c

7.11=7.11+c

c=0

So, the equation is y=0.79x

Cost of 1 bottle juice at store A is $0.7 and Cost of 1 bottle juice at store B is $0.79

Difference in cost =0.79-0.7=$0.09

Therefore, at store B, they charge $0.09 more for pineapple juice than store A.

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Answer: 12

Step-by-step explanation:

x + 9 + 9 = 7x

9 + 9 = 6x

18 = 6x

x = 3

DE = x + 9 = 3 + 9 = 12 :>

Answer:

DE = 12

Step-by-step explanation:

DF = DE + EF

7x = x+9 + 9

7x = x + 18

6x = 18

x = 3

DE = 3 + 9

DE = 12

urrrrrrrrrrrrrrrf mooookoommm

The graph of equations y - 1 = - 3(x - 2) and y = - 3x + 7 is illustrated below with the attached image.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, An equation of a line y - 1 = - 3(x - 2) in point-slope form.

y - 1 = - 3x + 6.

y = - 3x + 7.

The next equation is 3y = x - 9.

y = (1/3)x - 3.

Now, The graph of these two equations can be sketched by assuming two or more arbitrary values of 'x' that correspond to different values of 'y'.

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The equation 12x + 1 = 3(4x + 1) – 2 have infinite solutions

An equation is a mathematical statement that shows that two mathematical expressions are equal. In other terms we say that an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

To solve this problem, we can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.

⇒ 12x + 1 = 3(4x + 1) – 2

⇒ 12x + 1 = 12x + 3 – 2

⇒ 12x + 1 = 12x + 1

So that, The equation have infinite solutions.

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This problem have two question:

1) How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) – 2

2) Which of the following shows the graph of y = –(2)x – 1?

we are giving the answer of question no.1

Answer:

3,271,000

Step-by-step explanation:

There is no explanation for this problem.

Answer: is 3,271,000

a) (i) Working out the value of x2 gives -6

(ii) Working out the value of x3 gives -11

b) Working out the solution to 6 decimal places is undefined.

a) (i) To find the value of x2, we substitute x1 = -1 into the iterative equation:

x2 = ((-1)^(2/3)) - 5 = (-1)^(2/3) - 5 = -1 - 5 = -6

(ii) To find the value of x3, we substitute x2 into the iterative equation:

x3 = ((-6)^(2/3)) - 5 = (-6)^(2/3) - 5 = -6 - 5 = -11

b) To find the solution to 6 decimal places, we would need to continue iterating the process until the desired level of accuracy is reached. But in this case, the equation does not have solution as the equation is not defined for negative values of x. The cube root of a negative number is complex numbers and not real numbers.

Therefore, the values are -6, -11, and undefined respectively.

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By finding the intercept between the graphs of the equations, we can see that the solution is (-1, 3)

Here we have a system of linear equations:

3x - y = -6

y = x + 4

To solve the system of equations graphically, w ejust need to graph both equations on the same coordinate axis and find the point where the lines do intercept.

The graph of the system of equations can be seen on the image at the end.

There you can see that the lines intercept at the point (-1, 3), so that is the solution of the system of equations.

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A line passing between the points (1, 6) and (1, 31) has an undefined slope.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The slope of a line can be found using the formula:

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

where m is the slope of the line, (x1, y1) and (x2, y2) are two points on the line.

In this case, we have (x1, y1) = (1, 6) and (x2, y2) = (1, 31). Plugging these values into the formula:

m = (31 - 6) / (1 - 1)

Hence, the denominator is zero, the slope is undefined. This means that the line is a vertical line and has no slope.

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Answer: B) 2x²-3y=9

Step-by-step explanation:

This is not a linear function because the equation for a linear function is mx+b=y this means that x cannot have an exponent which in B it does.

Answer:

First one is 3^16

Second one is 3^10

Third one is 3^2 * 8^2

Forth one is 3^2/8^2

fifth one is 3^8/3^2

Step-by-step explanation:

The total number of 18,181 bottles should be sold to break the business even based on the investment.

Firstly calculating the profit earned on each soft drink. Based on this, the formula for profit to be used is -

Profit = Selling price - cost price

Keep the values in formula

Profit = 1.20 - 0.65

Performing subtraction on Right Hand Side of the equation

Profit = $0.55

For the business to break even, the total profit earned by company must be equal to the investment. So, let the number of bottles required to break even the business be x.

0.55 × x = 10,000

Performing multiplication on Left Hand Side of the equation

0.55x = 10000

x = 10,000/0.55

Performing division on Right Hand Side of the equation

x = 18181.8

Rounding off = 18181.

Thus, 18,181 bottles need to be sold.

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Answer: 50 cattle for 24500 is cheaper than 18870 for 37 cattle

Step-by-step explanation: divide 24500/50= $490 per cattle

vs

18870/37= $510 per cattle

proving that 24500 for 50 is overall a better deal

Answer: Gabriella's distance from the stadium is modeled by the function G(t) = 550 - 25t.

Ian's distance from the stadium is modeled by the function I(t) = 950 - 50t.

To find the number of hours after noon when Gabriella and Ian are the same distance from the stadium, we need to set the two equations equal to each other and solve for t:

G(t) = 550 - 25t = I(t) = 950 - 50t

Combining like terms we get:

25t = 400

t = 16

So, 16 hours after noon, Gabriella and Ian will be the same distance away from the stadium.

To graph the functions, we can substitute different values of t into the equations to find the corresponding values of G(t) and I(t). Then we can plot the points on a coordinate plane and connect them to form the graph of the two functions.

It is important to note that we are assuming that both Gabriella and Ian don't make any stops, so the speed is constant through the whole trip and no time is wasted.

Step-by-step explanation:

The quantity is a variable is the lowest overnight temperature

In math the term variable is defined as variable is an alphabet which is used to represent the unknown number and this one represents the value.

Here we have know that it rained 0. 5 inches on Tuesday and 0. 2 inches on Wednesday.

And the climate was warmer on Thursday than it was on Friday.

Where the humidity was 15% for 3 days of the week and thus the lowest temperature overnight was 68∘F.

Here we have identified that the temperature is continually falling and it will lead the lowest temperature overnight.

Then the correct option is (c).

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Answer:

Step-by-step explanation: make a table of values, followed be a column for the 1st and another for the 2nd difference

0 0

1 1 -- 1

2 4-- 3 -- 2

3 9 --5 -- 2

4 16 --7 -- 2

5 25 --9 --2

6 36 ------- etc

looks like the 2nd difference is 2

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 1.75\%\to \frac{1.75}{100}\dotfill &0.0175\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.0175)(6) \implies I = 525[/tex]

a) Angular acceleration is 0.53 rad/s^2

b) Tangential acceleration is 2.56 m/s^2

c) Centripetal acceleration is 2.56  rad/s^2

We know that the angular acceleration can be obtained from the equations of circular motion. We know that we have the equation for the circular motion as;

α = ω2 -  ω1/t

α =  angular acceleration

ω2 = final angular velocity

ω1 = initial angular velocity

α = 0.8 - 0/1.5

= 0.53 rad/s^2

b) The tangential acceleration = v^2/r

But V = ωr

V = 0.8 * 4

V = 3.2 m/s

Then;

(3.2)^2/4

= 2.56 m/s^2

c) Centripetal acceleration = ω^2 r

= (0.8)^2 * 4

= 2.56 rad/s^2

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The coordinates of the vertices of quadrilateral A’B’C’D’ after a translation along vector <2, -3> is: A. A' (-2, 5), B' (1, 7), C' (2, 5), D' (1, 3).

In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.

Note: We would move in the opposite direction of the given vector <2, -3>.

By applying a translation to the pre-image of quadrilateral ABCD vertically up by 3 units and horizontally left by 2 unit, the coordinates of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 2, y + 3)

Coordinate A = (0, 2)   →    Coordinate A' (0 - 2, 2 + 3) = (-2, 5)

Coordinate B = (3, 4)   →    Coordinate B' = (3 - 2, 4 + 3) = (1, 7)

Coordinate C = (4, 2)   →   Coordinate C' = (4 - 2, 2 + 3) = (2, 5)

Coordinate D = (3, 0)   →    Coordinate D' = (3 - 2, 0 + 3) = (1, 3)

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An artist draws a stained glass window to scale. The actual window will have a length of 5ft and a width of 2ft. The scale from the drawing to the window is 2in to 1 ft. The width of the drawing is 4 inches.

To find the width of the drawing, we need to determine how much the width of the window has been scaled down on the drawing.

We know that the scale of the drawing is 2 inches to 1 foot, so for every 1 foot in the window, there are 2 inches in the drawing.

Since the width of the window is 2 feet, and the scale is 2 inches to 1 foot, the width of the drawing is (2 inches/foot) * (2 feet) = 4 inches.

Therefore, the correct answer is as given above 4 inches.

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The analysis of the figure, comprising of concentric circles, in the shape of a hollow cylinder cross-section is as follows;

12) Part A; The area of the deck is about 691.15 square feet

Part B; The minimum number of treatment gallons needed is four gallons

Part C; The total cost to cover the patio with weather treatment is $143.8

The cross-sectional area of a hollow cylinder is; A = π·(R² - r²)

Where;

R = The radius of the outer circle of the cylinder

r = The radius of the smaller (open) circle at the center of the cylinder.

Part A

The outside diameter of the deck, D = 32 feet

The radius of the swimming pool = 6 feet

The area of the deck, A = The area of the circle with diameter 32 feet less the area of the swimming pool

A = π·D²/4 - π·r²

A = π × 32²/4 - π × 6² = 220·π ≈ 691.15

Part B

The area covered per gallon of weather treatment = 204.5 square feet per gallon

The minimum number of gallons of weather treatment, n, that will need to be purchased to cover the deck with weather treatment is therefore;

n ≈ 691.15/204.5 ≈ 3.38

Therefore, the minimum number of gallons that needs to be purchased, since 3 gallons is not enough, is four gallons of weather treatment

Part C; The cost per gallon of weather treatment excluding tax = $35.95

The total cost in dollars excluding tax to cover the patio with weather treatment, C, is presented as follows;

C = Number of gallons needed × Cost per gallon

Number of gallons needed to cover the deck = 4 gallons

Cost per gallon = $35.95/gallon

Therefore;

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The numbers that Austin could choose from are: 80, 100 which have 4, 5, and 10 as their multiples

The numbers between 61 and 107 are:

62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106

we will observe that only 70, 80, 90 and 100 have 10 and 5 as their multiple, amongst which, only 80 and 100 have 4 as their multiple.

Therefore, Austin must choose only the two numbers 80 and 100 which have 4, 5, and 10 as their multiples.

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