The value of a school bus reduces from $512000 to $343000 in 3 years. Find the
uniform rate of depreciation per annum (R).​

The equation of remaining chocolate C  in terms of t is C = 30 - 3t.

A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C = 30 - 3t.

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Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Answer:

Selena's annual intake home salary is $ 26,640.

Step-by-step explanation:

Since Selena's gross annual salary as the content editor of a fashion Magazine is $ 40,000, and she contributes 10% of her salary before she pays taxes to a retirement account, and 25% of her remaining salary is then consumed in state and federal taxes, To determine what is Selena's annual intake home salary if she also has to pay $ 30 for health Insurance each month, the following calculation must be performed:

40,000 - (40,000 x 0.1) - (40,000 x 0.9 x 0.25) - (30 x 12) = X

40,000 - 4,000 - 9,000 - 360 = X

26.640 = X

Therefore, Selena's annual intake home salary is $ 26,640.

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Answer:

  y = x² -8x +13

Step-by-step explanation:

Put the roots in the intercept form and multiply it out. For roots p and q, the quadratic is ...

  y = (x -p)·(x -q)

  y = (x -(4+√3)) · (x -(4 -√3))

  y = ((x -4) -√3) · ((x -4) +√3) = (x -4)² -(√3)² . . . . use the special product form

  y = x² -8x +16 -3 . . . . use the other special product form

  y = x² -8x +13

_____

Comment on the special product

There are a couple of quadratic special products that are useful to remember:

  the difference of squares: (a -b)(a +b) = a² -b²

  the square of a sum: (a + b)² = a² +2ab +b²

When working with quadratics that have complex or radical conjugate roots, the difference of squares form comes in handy sometimes.

Math can be a lot easier if you learn to recognize and use patterns.

The equation of the line is y = x.

To find the equation of a line given its graph, you need to follow the steps below.

Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.

Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.

Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.

Example:Let's say you are given the graph of a line below: .

Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.

Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.

Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.

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The sum of the angles of the triangle expressed in two ways are x + 1/2x + 3/2x and 2x + x + 3x/2

It is important to note that the sum of the angles of a triangle is equal or equivalent to 180 degrees.

We have the angle measurements as;

Substitute the values

x + 1/2 x + 3/2x = 180

Find the lowest common multiple

2x + x + 3x /2 = 180

Add the numerators

6x/2 = 180

cross multiply

6x = 360

x = 60

Hence, the expression is x + 1/2x + 3/2x and 2x + x + 3x/2

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Answer:

Ann traveled 165 miles on 5 gallons of gas

Step-by-step explanation:

First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.

Answer:

a) 376.66

b) Option 2: No, the result from part (a) could not be the actual number of adults who said that rising gas prices are "quite annoying" because a count of people must result in a whole.

c) 377

d) 40.77%

Step-by-step explanation:

a) 37% of 1018 is;

37/100 × 1018 = 376.66

b) Thus, the result in a above is not a whole number. Thus;

No, the result from part (a) could not be the actual number of adults who said that rising gas prices are "quite annoying" because a count of people must result in a whole.

c) from a above a, we got a value of 376.66.

Now the actual number would be preferably an integer. Thus, actual number is approximately 377.

d) percentage of respondents said that cellular phones are not at all harmful = 415/1018 × 100% = 40.77%

a) The experimental probability of landing on blue is approximately 0.184.

b) The theoretical probability of landing on blue is 0.2.

c) The statement that is true is: The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.

(a) To compute the experimental probability of landing on blue, we need to determine the frequency of blue spins out of the total number of spins.

Given that Kira spun the spinner 1000 times and obtained 184 blue spins, we can calculate the experimental probability of landing on blue as:

Experimental probability of blue = Number of blue spins / Total number of spins

Experimental probability of blue = 184 / 1000

Experimental probability of blue ≈ 0.184

Therefore, the experimental probability of landing on blue is approximately 0.184.

(b) Assuming that the spinner is fair, the theoretical probability of landing on blue can be determined by considering the number of blue slices out of the total number of slices.

Theoretical probability of blue = Number of blue slices / Total number of slices

Theoretical probability of blue = 1 / 5

Theoretical probability of blue = 0.2

Therefore, the theoretical probability of landing on blue is 0.2.

(c) The statement that is true is: The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.

As the number of spins increases, the experimental probability tends to converge towards the theoretical probability. This is known as the law of large numbers. With a larger sample size, the experimental results become more representative of the true probabilities. Therefore, as the number of spins increases, the experimental probability is more likely to be close to the theoretical probability.

While there may still be some variation due to random chance, increasing the number of spins improves the likelihood that the experimental probability will closely match the theoretical probability.

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Question

A spinner with 5 equally sized slices has 3 red slices, I yellow slice, and 1 blue slice. Kira spun the chal 1000 times and got the folowing ravilts Answer the following. Round your answers to the nearest thousandths. (a) From Kira's results, compute the experimental. probablity of landing on blue. (b) Assuming that the spinner is fair, compute the theoretical orobability of landing on blue. (c) Assuming that the spinner is fair, choose the statement below that is true. The larger the number of spins, the greater the likelihood that the experimental probability wil be close to the theoretical probability. The experimental probability will never be very close to the theoretical probabilty, no matter the number of spins.

Red has 615 numbers of spins

Yellow has 201 number of spins

Blue has 184 number of spins

Answer: 100

Step-by-step explanation:

This is a straightforward question and easy question. This question simply means that we should find the value of n that will make the equation true.

7.638 × n = 763.8

n = 763.8/7.638

n = 100

Therefore, putting n as 100 will make the equation true.

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Volume is a 3d version of area

i dont know

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

We can use the Polynomial Remainder Theorem. The PRT states that if we have a polynomial \(f(x)\) being divided by a factor in the form of \((x-a)\), then the remainder of the polynomial is given by \(f(a)\).

We have the polynomial:

\(f(x)=3x^{15}-5x^{12}+7x^6-3x^2+12\)

And it is being divided by:

\((x+1)\)

We can rewrite our factor as:

\((x-(-1))\)

Therefore:

\(a=-1\)

Then our remainder will be:

\(f(-1)\)

Evaluate:

\(\begin{aligned} f(-1)&=3(-1)^{15}-5(-1)^{12}+7(-1)^6-3(-1)^2+12\\&=-3-5+7-3+12\\&=8 \end{aligned}\)

So, our remainder will be 8.  

To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.

Using \(\displaystyle\sf \) tags for formatting, the expression becomes:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

First, we simplify the expression within the parentheses:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

\(\displaystyle\sf 5x+15y-18x+4y\)

Next, we can combine the like terms:

\(\displaystyle\sf 5x-18x+15y+4y\)

\(\displaystyle\sf -13x+19y\)

Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

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Answer:

  7) 57.8

  8) 73.8

Step-by-step explanation:

The tangents from a given point are the same length. This means the perimeter can be calculated as twice the length of one side plus twice the length of an opposite tangent.

7) P = 2(22.2 +6.7) = 57.8

8) P = 2(22.9 +14) = 73.8

Answer:

Intelligence Service in the Wisconsin Division of Health, Dr. Butler completed a preventive medicine residency ...

Step-by-step explanation:

..

Answer: you need to add

Step-by-step explanation: I would ask your teacher to help you understand the lesson.  

Answer:

SOMEONE HURRY AND ANSWER THIS

Step-by-step explanation:

Answer:

$648.00 or you can say that you made $48 from simple interest

Step-by-step explanation:

Plug the numbers into the formula A = P(1 + rt)  and solve,

First, convert to a decimal

r = R/100 = 8%/100 = 0.08 per year.

Solving the equation:

A = 600(1 + (0.08 × 1)) = 648

A = $648.00

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

D the last one

Step-by-step explanation:

Answer:

\(\sqrt{130}\) or 11.4

Step-by-step explanation:

Use the distance formula:

d = \(\sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

Plug in the points:

d = \(\sqrt{(-6 - 5)^2 + (0 - 3)^2}\)

Simplify:

d = \(\sqrt{(-11)^2 + (-3)^2}\)

d = \(\sqrt{121 + 9}\)

d = \(\sqrt{130}\)

= approximately 11.4

So, the distance is \(\sqrt{130}\) or approx. 11.4

Answer:

There is enough paint to cover the tank with one layer of paint.

Step-by-step explanation:

Given the cilindrical configuration of the tank and supposing that only external face must be painted, the surface area of the section (lateral wall + lid) can be calculated by the following expression:

\(A_{s} = 2\pi\cdot r\cdot h + \pi\cdot r^{2}\)

Where \(r\) and \(h\) represent the radius and the height of the cube, respectively.

If \(r = 0.55\,m\) (a diameter is two times the length of radius) and \(h = 1.4\,m\), the intended surface area is:

\(A_{s} = 2\pi\cdot (0.55\,m)\cdot (1.1\,m)+\pi\cdot (0.55\,m)^{2}\)

\(A_{s} \approx 4.751\,m^{2}\)

It is known that 250 mL of paint are needed to cover a square meter of the surface area, the needed amount of paint to cover the required area is estimated by simple rule of three:

\(Q = \frac{4.751\,m^{2}}{1\,m^{2}}\times (250\,mL)\)

\(Q = 1187.75\,mL\,(1.188\,L)\)

In consequence, there is enough paint to cover the tank with one layer of paint.

Answer: Number Sense – Understanding Quantity.

Representation – Using Symbols and Words to Represent Numbers.

Shapes and Spatial Relationships (Geometry)

Measurement – Comparing and Communicating about size.

Patterns – Recognizing and Making Patterns.

Problem Solving.

Step-by-step explanation: boom!

Reason:

Negative even integers aren't mentioned, but they are less than 10.

For example, something like -14 is less than 10 and is even.

If the question said "the set of all positive even integers less than 10" then {0,2,4,6,8} would be the correct full solution set, and the statement would be true.

The area of the complex figure is 132 square units

From the information given, we have that the composite shape is a combination of a:

The formula for area of a square is given as:

Area = a ²

Where 'a' is the length of it side

Area = 6²

Area of square = 36 square units

The formula for area of a rectangle is given as:

Area = width × length

Area = 8 × 12

Area of rectangle = 96 square units

Area of the complex figure = Area of square + area of rectangle

= 36 + 96

= 132 square units

Thus, the area of the complex figure is 132 square units

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the equation is:

so we can pass 1245 to the other side as "-1245" and sum the numbers with x, so 15/43+1=58/43

and finally, we can pass the 43 multiplying and the 58 dividings:

So the answer is:

x=-903

Answer: think it’s c 4/28

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.

The point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.

The tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...

  m = y/x = -4/4 = -1

The tangent line's slope is the opposite reciprocal of this:

  m = -1/(-1) = 1

The point-slope form of the equation for the tangent line is ...

  y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)

  y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)

  x -y = 8 . . . . . . . . . . add 4-y to put in standard form

The equation of the tangent line is x - y = 8.

In the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...

  y -0 = -1(x -0)

  y = -x

The equation of the normal line is y = -x.

__

Additional comment

The normal line can also be written as x + y = 0.

The tangent line can also be written as y = x -8.

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