Question 7
Susan bought a car for N$120 000.00. Its value decreased in the ratio 3:5. What is the
value of the car after the decrease?
[2]

Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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Answer:

|2x -18|< 40

|2x|< 40 + 18

|2x|<58

x<|29|

Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

Answer:

S= 45000+2000n

Step-by-step explanation:

The y-intercept of the function is 45000 which represents Daniel's salary when hired.

Answer:

Given:

1 mile = 1.6 km

So, to find how many miles are in 100 km, we need to divide 100km by 1.6km because one single mile contains 1.6km.

100km/1.6km = 62.5 miles

Answer:

\(2\)

Step-by-step explanation:

\(\frac{8}{4}\)

\(\mathrm{Divide\:the\:numbers:}\:\frac{8}{4}=2\\\)

\(=2\)

Answer:

35

Step-by-step explanation:

let x be the number of students in the class

then number of girls = 0.4x , so

x = 21 + 0.4x ( subtract 0.4x from both sides )

0.6x = 21 ( divide both sides by 0.6 )

x = 35

the total number of students is 35

The similarity between the cube and cuboid is that both have 12 edges.

option C.

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

So a cube is a three-dimensional solid figure, having 6 square faces and 12 edges.

A cuboid is a three-dimensional geometric shape that looks like a book or a rectangular box.

A cuboid can be defined as a three-dimensional solid shape that has 12 edges, 8 vertices, and 6 faces and each of its faces is rectangular in shape.

So the similarity between a cube and cuboid is that both have 6 faces and 12 edges.

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The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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Therefore, the value of x that solves the equation is 2/7, after eliminating the fractions and solving the resulting equation.

To eliminate fractions in the equation 6 - 3x + (1/2)x = x + 5, we can multiply each term by a number that will clear the denominators. In this case, the denominator is 2 in the term (1/2)x. The least common multiple (LCM) of 2 is 2 itself, so we can multiply each term by 2 to eliminate the fraction.

By multiplying each term by 2, we get:

2 * (6 - 3x) + 2 * ((1/2)x) = 2 * (x + 5)

Simplifying this expression, we have:

12 - 6x + x = 2x + 10

Now, the equation is free of fractions, and we can proceed to solve it.

Combining like terms, we have:

12 - 5x = 2x + 10

To isolate the variable terms, we can move the 2x term to the left side by subtracting 2x from both sides:

12 - 5x - 2x = 10

Simplifying further:

12 - 7x = 10

Next, we can move the constant term to the right side by subtracting 12 from both sides:

12 - 7x - 12 = 10 - 12

Simplifying again:

-7x = -2

Finally, we solve for x by dividing both sides by -7:

x = (-2) / (-7)

Simplifying the division of -2 by -7 gives us the solution:

x = 2/7

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Answer:

1980 total outcomes are possible.

Step-by-step explanation:

The order in which the candidates are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

How many total outcomes are possible?

2 men, from a set of 11.

2 women, from a set of 9.

So

\(T = C_{11,2}*C_{9,2} = \frac{11!}{2!9!}*\frac{9!}{2!7!} = 1980\)

1980 total outcomes are possible.

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

Answer:

7

Step-by-step explanation:

70% of 10 is 7

-19.99; The line of best fit underpredicts the student's science test score.

So correct option is A.

A prediction is an estimation or forecast about future events or conditions, based on past data and trends, current information, and/or mathematical models. Predictions can be made in various fields, such as finance, weather, sports, social sciences, and natural sciences. The accuracy of predictions depends on many factors, including the quality of the data used, the assumptions made, the complexity of the system being analyzed, and the reliability of the methods used. Predictions are not always accurate and are often subject to revision as new information becomes available.

The predicted science score for the student with IQ 100 can be calculated using the line of best fit:

ŷ = −20.3 + 0.7489 * 100 = 71.59

The residual is the difference between the actual science test score and the predicted science score:

residual = actual score - predicted score = 52.6 - 71.59 = -19.99

So the line of best fit underpredicts the student's science test score by 19.99 points.

Therefore, the residual is:

-19.99; The line of best fit underpredicts the student's science test score.

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Answer:

The product of polynomial \((-2m^3+3m^2-m)(4m^2+m-5)\) is \(\mathbf{-8m^5+10m^4+9m^3-16m^2+5m}\)

Step-by-step explanation:

We need to find the standard form of polynomial that represents the product of \((-2m^3+3m^2-m)(4m^2+m-5)\)

Finding the product of polynomial

\((-2m^3+3m^2-m)(4m^2+m-5)\\=-2m^3(4m^2+m-5)+3m^2(4m^2+m-5)-m(4m^2+m-5)\\=-8m^5-2m^4+10m^3+12m^4+3m^3-15m^2-4m^3-m^2+5m\\Combining\:like\:terms\\=-8m^5-2m^4+12m^4+10m^3+3m^3-4m^3-15m^2-m^2+5m\\=-8m^5+10m^4+9m^3-16m^2+5m\\\)

So, the product of polynomial \((-2m^3+3m^2-m)(4m^2+m-5)\) is \(\mathbf{-8m^5+10m^4+9m^3-16m^2+5m}\)

\({ \huge {\underline {\underline {\mathfrak {\purple{Answer}}}}}}\)

\( \longmapsto{2 {x}^{2} - 5x + 2}\)

\( \longmapsto{2 {x}^{2} - 4x - x + 2}\)

\(\longmapsto{2x(x - 2) - 1(x - 2)}\)

\(\longmapsto{(2x - 1)(x - 2)}\)

\( \boxed{ \huge x = \huge\dfrac{1}{2} \: or \: 2}\)

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

when we use volume formula

v=lenght*width*height

24*18*15=6480cm³

2.1      Solve  :    x2-12 = 0

Add  12  to both sides of the equation :

                     x2 = 12

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 12  

Can  √ 12 be simplified ?

Yes!   The prime factorization of  12   is

  2•2•3

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 12   =  √ 2•2•3   =

               ±  2 • √ 3

The equation has two real solutions  

These solutions are  x = 2 • ± √3 = ± 3.4641 /This is the answer

Answer:

12.5

Step-by-step explanation:

Answer:12.25

Step-by-step explanation:

Therefore , the solution of the given problem of percentage comes out to be $387.704 is the weekly unemployment amount.

In mathematics, a percentage is any amount that can be stated as a proportion of 100. Also occasionally used are the abbreviations "pct.," "pct," or "pc." But the "%" mark is usually used to indicate it. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. A number should be preceded by the percent sign (%) to denote it is a percent.

Here,

Given :

A weekly unemployment amount is calculated using the following three components:

1. Determine the quarterly wage total (consecutive)

2. Multiply the sum by 26.

3.Multiplying by the rate of unemployment

Calculate the total of a quarterly salaries first:

=> (12950.80 + 12250.10) / 26

=>  25,200.9/26

=> 969.26 * 40 %

=> 387.704

Therefore , the solution of the given problem of percentage comes out to be $387.704 is the weekly unemployment amount.

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Answer:

23 degrees

Step-by-step explanation:

We can use basic trigonometric equations to solve for the angle x because we are given a right triangle.

I will use the sin x = opposite / hypotenuse

sin x = 5 / 13

x = sin^-1 (5 / 13)

x = 22.61986 degrees

The question requires us to round to the nearest degree which is 23.

Other alternative methods you can use include the tangent and cosine functions or the law of cosines.

Answer:

x = 23°

Step-by-step explanation:

I will use

\(tanx=opposite/adjacent\)

\(tanx=\frac{5}{12}\)

\(x=tan^{-1} (\frac{5}{12} )=tan^{-1} (0.417)=22.62^{o}\)

rounded to the nearest degree : 23°

Hope this helps

Using the two points you have plotted, draw the parabola. It should look like a downward-facing curve opening at the vertex (0, 7).

What is parabola?

A parabola is a symmetrical, U-shaped curve that is formed by the graph of a quadratic function.

Assuming you meant \(f(x) = -x^2 + 7\), here's how you can graph the parabola using the parabola tool:

Find the vertex

The vertex of the parabola is located at the point (-b/2a, f(-b/2a)), where a is the coefficient of the \(x^2\) term and b is the coefficient of the x term. In this case, a = -1 and b = 0, so the vertex is located at the point (0, 7).

Plot the vertex

Using the parabola tool, plot the vertex at the point (0, 7).

Plot a second point

To plot a second point, you can choose any x value and find the corresponding y value using the quadratic function. For example, if you choose x = 2, then \(f(2) = -2^2 + 7 = 3\). So the second point is located at (2, 3).

Therefore, Using the two points you have plotted, draw the parabola. It should look like a downward-facing curve opening at the vertex (0, 7).

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Complete Question:

Use the parabola tool to graph the quadratic function.

f(x) = -√² +7

Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Given:

An architect has designed two tunnels.

Tunnel A is modeled by:

Tunnel B is modeled by:

Part A: write the equation of tunnel A in standard from

So, we will complete the square for the two variables x, and y as follows:

So, the answer to part A:

The equation will be: (x+15)² + y² = 13²

The conic section is: Circle with canter (-15, 0) and radius = 13 feet

Part B: Write the equation of tunnel B in standard from

So, we will complete the square for the variable x as follows:

So, the answer to part B:

The equation will be: (x-15)² = -4(4)(y-20)

The conic section is: a Parabole with the vertex at (15, 20)

Part C: Determine the maximum height of each tunnel.

Tunnel A:

So, the radius = 13, so, the diameter = 2 * 13 = 26

So, the maximum height = 13 feet

The truck has a height = of 13.5 feet

so, it will not be able to pass through the tunnel A

Tunnel B:

when y = 0, solve for x:

When x = 15, we will find the maximum height

So, the maximum height = 20 feet

the truck will be able to pass through the tunnel

Answer:

1 and 1/2 or 1.5

Step-by-step explanation:

3/8 × 4/1 = 3/2 = 1 and 1/2

Result in decimals: 1.5

Calculation steps:

3/8 × 4/1 = (3 × 4)/(8 × 1) = 12/8

12 ÷ 4 = 3

8 ÷ 4 = 2

= 3/2 = 1 and 1/2