Select the statement that correctly defines continuous and discrete quantitative variables. O A continuous variable has an infinite number of possible values, whereas a discrete variable always has a finite number of possible values. O A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units. O A continuous variable has a countable number of possible values, whereas a discrete variable has an uncountable number of possible values. O A continuous variable has numerical values, whereas a discrete variable serves to group items into categories.

3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).

3.2. it would take approximately 6.67 years to pay off the vehicle through instalments.

A deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit

3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).

3.2 The given information does not explicitly state the number of years for the instalment plan, but it does provide the number of months (80) and the total payment amount (R303,007). Assuming a monthly payment plan, we can calculate the number of years as follows:

Number of years = Number of months / 12

Number of years = 80 / 12

Number of years ≈ 6.67 years

So it would take approximately 6.67 years to pay off the vehicle through instalments.

To calculate the deposit needed, we need to subtract the residual amount from the total cash price. From the given information, the total payment is R303,007 and the residual is R80,180, so:

Cash price = Total payment - Residual

Cash price = R303,007 - R80,180

Cash price = R222,827

So the cash price is slightly higher than the advertised price of R221,180, likely due to financing fees or interest. To determine the deposit needed, we can assume a specific percentage of the cash price that must be paid upfront. For example, if the deposit required is 10% of the cash price, then:

Deposit = 0.1 x Cash price

Deposit = 0.1 x R222,827

Deposit = R22,282.70

So a deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit.

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Answer:

The completely factored form of 15a³bc³ – 6a²b²c³ is 3a²bc³ × (5a - 2b).

Answer:

[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]

Step-by-step explanation:

[tex]15a^{3} bc^{3} - 6a^{2} b^{2} c^{3}[/tex]

[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]

The equation of line is y = -4x + 3 , where the slope is m = -4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -4x + 3   be equation (1)

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = -4

And , the y intercept is 3

The equation of line is plotted on the graph

Hence , the equation of line is y = -4x + 3

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The complete question is :

Which of the following graphs matches the equation y=-4x+3?

On a coordinate plane, a line goes through (0, 3)

On a coordinate plane, a line goes through (-2, 5) and (0, -3).

On a coordinate plane, a line goes through (0, 3) and (3, -1).

Answer:

  (a)  24%

Step-by-step explanation:

You want the percentage of people in the Decades slice of a circle graph if it represents 96 people. The other slices represent 128, 72, 52, 24, and 28 people.

The fraction in the second category is the ratio of the number in that category to the total number. The percent is the fraction multiplied by 100%.

  96/(128 +96 +72 +52 +24 +28) × 100% = 96/400 × 100% = 24%

The Decades slice of the circle would be 24%, choice A.

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To convert inches to yards, we need to divide by 36, since 36 inches make 1 yard. Therefore, to convert the length of the shed and ramp from inches to yards, we can use the following expressions: (12 + 1) / 36 = 0.3611... yards, (12 / 36) + (1 / 36) = 0.3611... yards, 13 / 36 = 0.3611... yards

An expression in mathematics is a grouping of variables, numbers, and actions that can be evaluated to yield a value. A wide range of mathematical notions, from basic arithmetic computations to intricate algebraic formulas and beyond, are represented by expressions.

These components can be used to combine expressions in a wide range of different ways. For instance, we can construct straightforward arithmetic phrases such as "2 + 3" or "5 * 4" or more intricate algebraic expressions such as "3x2 + 2x + 1" or "sin(x) + cos(x)". In each instance, the expression denotes a mathematical idea that may be tested to provide a certain value.

Expressions play a significant role in mathematics and are utilized in a wide range of fields in science, engineering, and finance. By being aware of how expressions work, we can better understand and solve a wide variety of mathematical problems.

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Answer:

  x = 13

Step-by-step explanation:

You want to find x when one half of the diagonal of a parallelogram is 80 and the other half is 6x+2.

The diagonals of a parallelogram bisect each other, so point Y is the midpoint of each. That means ...

  VY = YX

  80 = 6x +2 . . . . . substitute the given values

  78 = 6x . . . . . . . subtract 2

  13 = x . . . . . . . . divide by 6

The value of x is 13.

Answer:

Pole Vault, Discus, 200m, Long Jump

Step-by-step explanation:

Once putting them all as decimals can’t you just sort it our from there? From what I can see, your answers are incorrect, but they might have reset.

In the word problems given above, the results are:

1) Let's call the number we're looking for "x". According to the problem, "three times a number" is the same as 60 minus 21, which is 39. So we can write the equation:

3x + 21 = 60

Subtract 21 from both sides:

3x = 39

Divide by 3:

x = 13

Therefore, the number we're looking for is 13.

2)

Let's call the number we're looking for "x" again. According to the problem, "three times the difference between a number and three" is the same as "four times the number". So we can write the equation:

3(x - 3) = 4x

Simplify:

3x - 9 = 4x

Subtract 3x from both sides:

-9 = x

Therefore, the number we're looking for is -9.

3)

Let's call the first of the three consecutive integers "x". The next two would be x+1 and x+2. According to the problem, their sum is 48, so we can write the equation: x + (x+1) + (x+2) = 48

Simplify:

3x + 3 = 48

Subtract 3 from both sides:

3x = 45

Divide by 3:

x = 15

So the three consecutive integers are 15, 16, and 17. To answer the second part of the question, we can substitute these values into the given expression:

3m - z(1st) = 3(16) - 15(15) = 48 - 225 = -177


4)
Let's call the smallest of the three consecutive odd integers "x". The next two would be x+2 and x+4. According to the problem, twice the smallest is seven more than the largest, so we can write the equation:

2x = (x+4) + 7

Simplify:

2x = x + 11

Subtract x from both sides:

x = 11

So the three consecutive odd integers are 11, 13, and 15. The middle number is 13.


5)
Let's call the width of the rectangle "w". According to the problem, the length is 3 cm more than the width, so the length is w + 3. The perimeter is the sum of all four sides, which is:

P = 2w + 2(w + 3) = 4w + 6

We know that the perimeter is 22 cm, so we can write the equation:

4w + 6 = 22

Subtract 6 from both sides:

4w = 16

Divide by 4:

w = 4

So the width is 4 cm, and the length is 7 cm (since it's 3 cm more than the width). To find the area, we use the formula:

A = (L)(W) = (7)(4) = 28 square cm


6)

Let's denote the length of side a as x. Then we know that side b is 3 times the length of side a, or 3x, and side c is 1 more than twice the length of side a, or 2x+1.

Since the perimeter of the triangle is 43 inches, we can write the equation:

a + b + c = 43

Substituting in our expressions for b and c, we get:

x + 3x + 2x + 1 = 43

Simplifying the left-hand side, we get:

6x + 1 = 43

Subtracting 1 from both sides, we get:

6x = 42

Dividing both sides by 6, we get:

x = 7

thus:

a = 7

b= 3x = 21; na d

c = 2x + 1 = 14+1

c = 15

Thus the sum of sides a and b =
21 + 7
= 28

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Answer:

$150

Step-by-step explanation:

Interest = Principal x Rate x Time (in years)

I = 3000(.05)(1)

I = 150

Answer:

The new slope is 2,

New y-intercept is - 7

Line is flatter since slope has reduced

Step-by-step explanation:

Tony m,ay or may not afford the car insurance

From the question, we have the following parameters that can be used in our computation:

Yearly pay = $8300 (approximated)

Insurance = 1/30 of his rounded yearly pay

Using the above as a guide, we have the following:

Insurance= 1/30 * $8300

Evaluate

Insurance=  $276.7

Additional information about Tony's expenses and financial situation are needed to determine if he can afford the monthly car insurance or not.

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The required trigonometry ratio that would be used to find x is cosine. Option B is correct.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
Consider the triangle ACB, in order to determine the measure of x, we can use the cosine operator of the trigonometric ratio.
So,
cosB = BC/AB
cos37 = 11/x

0.8 = 11/x
x = 11 / 0.8
x = 13.75

Thus, the required trigonometry ratio that would be used to find x is cosine. Option B is correct.

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Answer:57.6^3

thats t

The function can be used to calculate his earnings, 15d + 0.25r + 2h

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

The function that the student can use to calculate his earnings is:

Earnings = 15d + 0.25r + 2h

where:

d = number of days worked

r = number of raffle tickets sold

h = number of hours worked at the game

The first term, 15d, represents the base pay of $15 per day worked.

The second term, 0.25r, represents the additional earnings of $0.25 per raffle ticket sold.

The third term, 2h, represents the additional earnings of $2 per hour worked at the game.

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The amount you made per share is $8.50.

From the question, we have the following parameters that can be used in our computation:

Initial amount = $63.00

Final amount = $71.50

To calculate the profit made, we need to find the difference between the selling price and the buying price per share, and then multiply by the number of shares.

The difference in price per share is:

Difference = $71.50 - $63.00

Evaluate the difference

Difference = $8.50

Hence, the profit per share is $8.50.

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Answer:

  8.5 cm

Step-by-step explanation:

You want to know the length of AB in rectangle ABCD with perimeter 26 cm if BC = PQ, QR = 10 cm, and the area of rectangle PQRS is 45 cm².

The area of rectangle PQRS is ...

  Area = PQ·QR

  45 cm² = PQ·(10 cm)

  PQ = (45 cm²)/(10 cm) = 4.5 cm

The perimeter of rectangle ABCD is ...

  Perimeter = 2(AB +BC)

  26 cm = 2(AB +4.5 cm) . . . . . . . . BC = PQ = 4.5 cm

  13 cm = AB +4.5 cm . . . . . divide by 2

  8.5 cm = AB . . . . . . . . subtract 4.5 cm

The length of AB is 8.5 cm.

<95141404393>

Angles are measured in degrees, with a full circle being 360°, and can be thought of as the amount of rotation that two straight lines or planes undergo.

The class definition of angle changed from a collection of ambiguous expressions, such as “the measurement of all the sides,” “the place where lines meet,” and “the corner of a shape or anything,” to

The equation below can be set up to calculate this.

Tan(angle) = 80 ft / (200 ft – 4 ft)

Solving for the angle, we get:

angle = tan-1(80 ft / 196 ft (ca. 60 m))

angle = tan-1(0.408163265)

Angle = 36.87 degrees (to the nearest hundredth of a degree).

Therefore, The law of tangents indicates that the angle between the subject's eyes and the top of the structure is roughly 36.87 degrees.

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Answer:

5x + 10y = 90

Step-by-step explanation:

x represents the mountain trail which she walked 5 miles

y represents the canal trail which she walked 10 miles

In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:

{x | -8 <= x < 17}

Explanation of set builder notation?

A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | },  where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.

In this case,

the set comprises of all figures higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint

-8 <= x < 17,where x is a real value. This predicts that x must exceed or equal to -8 and must be less than 17 to be a part of the set.

Thus, in set builder form, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows:  {x | -8 <= x < 17}

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The value of the expression represented by |M × N| is 64

from the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

M = 8 i.e.  {m, a, t, h, e, i, c, s}.

N = 8 i.e. {n, e, v, r, t, h, l, s}.

So, we have

|M × N| = 8 * 8

Evaluate

|M × N| = 64

Hence, the value of |M × N| is 64

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Answer: 39%

Step-by-step explanation:

using calculator

1 seat = 0.058%
1700 - 1037 = 663 seats are taken.

0.058% x 663 seats = 39%

Answer:  -1/2

Step-by-step explanation: Down 1 over 2

Answer:

0.392 < p < 0.508

Step-by-step explanation:

[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\CI_{90\%}=0.45\pm 1.645\sqrt{\frac{0.45(1-0.45)}{200}}\\\\CI_{90\%}\approx0.45\pm0.058\\\\CI_{90\%}=\{0.392,0.508\}[/tex]

Thus, we are 90% confident that the true population proportion [tex]\hat{p}[/tex] is between 0.392 and 0.508, assuming conditions are met.

A cross section of a cube that is a regular hexagon can only be obtained if the plane passes through the cube at a 60-degree angle with respect to its edges. If a plane is placed in this manner, it will intersect six of the cube's edges at their midpoints, producing a regular hexagon cross section.

The plane that passes through three edges of a cube to produce a regular hexagonal cross section must intersect the edges of the cube at 60 degree angles. This can be achieved if the plane is aligned with the diagonal of one of the faces of the cube, passing through the opposite vertices of the face.

This configuration of the plane will result in a regular hexagonal cross section of the cube as each vertex of the hexagon will correspond to one of the vertices of the cube, and each side of the hexagon will intersect two edges of the cube at 60 degree angles.

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Answer:

The solution is C. (x+8)² + (y-11)² = 4

Step-by-step explanation:

(x - h)² + (y - k)² = r²

h = -8

k = 11

r = 2

(x + 8)² + (y - 11)² = 2²

(x + 8)² + (y - 11)² = 4

The answer is C. (x+8)² + (y-11)² = 4

Answer:

F = 29

E= 151

D = 90

Step-by-step explanation:

For F:

The angle F is on a 180 degree angle with a degree next to it that is 151. To get the value F subtract 180-151 and you get 29.

For E: If F is 29 then the angle opposite of F is also 29. So again to find the measure of angle E, subtract 180 minus 29 and you get 151.

For D: D is also lying on a 180 degree angle. The angle next to it is 90. To get 180 add 90. 90 is the measure of angle d.

Answer:

-----------------------------------

Angle d is linear pair with a right angle, therefore:

Angle e is vertically opposite with 151° and therefore they are congruent:

Angle f is adjacent with 151° and forming a linear pair, therefore:

The approximate angle of elevation if Brendan looks up at the tower is 20.03°

The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".

We know that, sinθ = opposite/hypotenuse

Here, sinx° = 50/146

sinx° =0.34246575342

x = sin⁻¹(0.34246575342)

x = 20.0271724581

x = 20.03°

Therefore, the approximate angle of elevation if Brendan looks up at the tower is 20.03°

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"Your question is incomplete, probably the complete question/missing part is:"

Amelia and Brendon are both on the ground looking at The top of a tower point D. Amelia is at point A and Brendan is at point B.

What is the approximate angle of elevation in Brendan looks up at the tower explain your reasoning.

The correct answer would be an option (C) y = 5x - 1 is not an exponential function.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

As per option (A), we have

y = 5ˣ

This is an exponential function.

As per option (B), we have

y = 5ˣ - 1

This is an exponential function.

As per option (C), we have

y = 5x - 1

This is not an exponential function because it is a linear function.

As per option (D), we have

D. y = 3.5ˣ

This is an exponential function.

Thus, the correct answer would be an option (C) y = 5x - 1

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The complete question would be as:

Which of the following is not an exponential function?

A. y = 5ˣ

B. y = 5ˣ - 1

C. y = 5x - 1

D. y = 3.5ˣ

Step-by-step explanation:

we know :

sin(2t) = 2×sin(t)×cos(t)

cos(2t) = cos²(t) – sin²(t) = 2×cos²(t) – 1 = 1 – 2×sin²(t)

tan(t) = sin(t)/cos(t)

tan(2t) = sin(2t)/cos(2t) = (2×tan(t))/(1 – tan²(t))

sin²(t) + cos²(t) = 1

as t is in quadrant I, 2t must be in either quadrant I or II.

sin(t) = 7/9

sin²(t) = (7/9)² = 49/81

cos²(t) = 1 - sin²(t) = 1 - 49/81 = 81/81 - 49/81 = 32/81

cos(t) = sqrt(32)/9

sin(2t) = 2×sin(t)×cos(t) = 2×7/9 × sqrt(32)/9 =

= 14×sqrt(32)/81 ≈ 0.98

cos(2t) = cos²(t) - sin²(t) = 32/81 - 49/81 = -17/81 ≈

≈ -0.21

tan(2t) = sin(2t)/cos(2t) =

= 14×sqrt(32)/81 / -17/81 =

= 14×sqrt(32)/81 × -81/17 =

= -14×sqrt(32)/17 ≈ -4.66