NEW ASSESSMENT QUESTION:
BASIC EDUCATION CERTIFICATE
SECTION A: OBJECTIVES
1. Divide 2.646 by 0.9. Give your answer to 1
d.p.

The two trapezoids below are similar. The value of Ef will be 6.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Given that there are two trapezoids ABCD and GHEF. The length of EF = x will be calculated as:-

Apply the similarity property in the two trapezoids.

AB / FE = DC / GH

24 / x = 30 / 7.5

x = ( 24 x 7.5 ) / 30

x = ( 1800 / 300 )

x = 6

Hence, the value of the side x = EF = 6.

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Step-by-step explanation:

To find the factor by which the dimensions of cylinder A were multiplied to produce the corresponding dimensions of cylinder B, we can use the fact that they are similar solids. This means that the ratio of corresponding dimensions is the same for both cylinders.

Since the base of cylinder A has a circumference of 4π units and the base of cylinder B has an area of 9π units, we can use these measurements to find the ratio of the radii of the two cylinders.

The circumference of a circle is given by 2πr, where r is the radius, so the radius of cylinder A is 4π/2π = 2 units.

The area of a circle is given by πr^2, so the radius of cylinder B is sqrt(9π/π) = sqrt(9) = 3 units.

The ratio of the radius of cylinder A to cylinder B is 2/3. Since similar solids have the same ratio for all dimensions, this means that the dimensions of cylinder A were multiplied by a factor of 2/3 to produce the corresponding dimensions of cylinder B.

The graph of the polynomial function g(x) = -2x² - 5x³ + 2x² + 7x + 1 is plotted and attached

The zeros are (-1.10, 0), (-0.15, 0) and (1.25, 0) to the nearest hundredth)

Using a graph is potted by written the equation on the plotter , the plotter interprets the equation and presents the graph

Zero of polynomial equation is the point where the y is zero this is solved by equating the polynomial function to zero

From the graph, the zeros are identified by the points where the graph cuts the the x axis.

Examining the graph of the function g(x) = -2x² - 5x³ + 2x² + 7x + 1 the zeros are

(-1.104, 0), (-0.145, 0) and (1.249, 0)

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Answer:

N(-21,-20)

Step-by-step explanation:

We can apply midpoint formula to solve for endpoint (N):

[tex]\displaystyle{\text{Midpoint}= \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)}[/tex]

Let [tex]\displaystyle{x_1 = 1}[/tex], [tex]\displaystyle{y_1 = 12}[/tex] and Midpoint = (-10,-4). Therefore:

[tex]\displaystyle{\left(-10,-4\right)= \left(\dfrac{1+x_2}{2}, \dfrac{12+y_2}{2}\right)}[/tex]

Solve x with -10 and y with -4:

[tex]\displaystyle{\text{N}\left(x_2,y_2\right) = \left(\dfrac{1+x_2}{2}=-10, \dfrac{12+y_2}{2}=-4\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(1+x_2=-20, 12+y_2=-8\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-20-1, y_2=-8-12\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-21, y_2=-20\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right)=\left(-21,-20\right)}[/tex]

Therefore, the coordinate of N is (-21,-20)

The slope of a line perpendicular to the line is 5/4

A straight line of the form

y = mx + c

has its slope as 'm'

It is constant for a line. The more the slope is, the steeper the line is.

Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.

If two lines are perpendicular, their slopes are negative reciprocals, which means that their product is -1

Given;

4x+5y=35

We can write the equation as;

4*x + 5*y - 35  = 0

5*y  = - 4*x  + 35     or    

y  = -(4/5)*x  + 35    

m= -4/5

So, now the slope of this line is -4/5 and line perpendicular slope will be 5/4

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By applying the Golden Ratio rule, the width of the painting is equal to 12.5 inches.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios.

This ultimately implies that, proportions is a mathematical operation which can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying the Golden Ratio rule, the width of the painting can be calculated as follows;

20/x = 8/5

Cross-multiplying, we have the following:

8x = 20 × 5

8x = 100

x = 100/8

x = 12.5 inches.

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The price of the delivery is $15 and the mileage is 40.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that the rosebud flower shop has a basic delivery charge of 5$ plus a rate of 25 cents per mile.

Total cost = basic delivery fee + (rate per mile x number of miles)

=$5 + (0.25 x m)

= $5 + 0.25m

The linear expression that represents the total delivery cost from Rosebud Flower Shop ;

Total cost = basic delivery fee + (rate per mile x number of miles)

=$7 + (0.2 x m)

$7 + 0.2m

When the costs are the same, the two expressions would be;

$7 + 0.2m = $5 + 0.25m

$7 - $5 = 0.25m - 0.20

$2 = 0.05m

m = 2 / 0.05

m = 40

Price = $7 + 0.2(40)

$7 + 8 = $15

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-37. 44 / 4. 8 gives  -7.8 when dividing -37.44 by 4.8 by simple dividing rule whereas after rounding off -37.44 and 4.8 that will be -37 and 5 will be 7.4.

In the given problem Division is = 4. 8 and dividend is = -37. 44, And as per law Division is divided by dividend  (Division/dividend), and the result produced, is called quotient In this case in this case, Quotient is -7.8.

And -37.44 is approximately -37 As .44 is rounded off to .00 (As per law 0-4 is 0 and 5-9 is rounded up to the next digit. And 4.8 could be around off to 5. And now if -37 is divided by 5 estimated will be 7.4.

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Is that a question? You don't seem to have anything linked or a question posted?

Here there is a 10% decrease in the number of streams each week after the song's release. From calculations the number of streams after sixth week is 8,503,056.

Let's look into the data given.

The initial number of streams, X₀ = 16,000,000

The percent decrease is 100- 90 = 10%

So the rate of decrease = 10/100 = 0.10

The period of time, n = 6

The equation to find the final number of streams, X =  X₀ (1-r)ⁿ

                                               = 16,000,000× (1-0.01)⁶

                                               = 8503056.

So the number of streams in the sixth week is 8,503,056

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Answer:

(B) 9,447,840

Step-by-step explanation:

Week         Streams

1                  16,000,000 x 90

2                 14,400,000 x 90

3                 12,960,000 x 90

4                 11,664,000 x 90

5                 10,497,600 x 90

6                 9,447,840 x 90

Therefore, the answer would be 9,447,840

Answer:

32 & 12

Step-by-step explanation:

let age of andy = x

let age of brett = y

x + y = 44        (eq 1)

x= 8 + 2y         (eq 2)

putting the value of x from 2 in 1

8 + 2y + y = 44

3y = 36

y = 12

x = 8 + 2(12)

x = 32

The height of the cube brick is 7 units and the volume is equal to 343 unit³

The volume of a cube is defined as the total number of cubic units occupied by the cube. The formula is given as V = a³ where "a" is the length of edge or sides.

The length of an edge for the cube brick is 7 units which implies the height represented by h is also 7 units and the volume is calculated as follows:

volume of cube brick = 7 units × 7 units × 7 units

volume of cube brick = 343 units ³

Therefore, the height of the cube brick is 7 units and the volume is equal to 343 unit³

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hmmm proofs like these can be a bit circular kinda, let's do some rigamarole on the equations and we'll see if that works for a definition

[tex]\stackrel{\theta \textit{ is always in radian unit}~\hfill }{s=r\theta\implies \cfrac{s}{\theta }=r \hspace{5em}v=\cfrac{s}{t}\implies t=\cfrac{s}{v}\hspace{5em}\omega=\frac{\theta }{t}} \\\\[-0.35em] ~\dotfill\\\\ \omega=\cfrac{\theta }{t}\implies \omega=\cfrac{\theta }{~~ \frac{ s}{v } ~~}\implies \omega=\cfrac{\theta }{1}\cdot \cfrac{v}{s}\implies \omega=\cfrac{\theta v}{s}\implies s\omega=\theta v \\\\\\ \cfrac{s\omega}{\theta }=v\implies \cfrac{s}{\theta }\cdot \omega=v\implies \boxed{r\cdot \omega=v}[/tex]

Liling will end up with four triangles if she starts with two tiny squares of material and cuts them on the diagonal. Knowing the areas of each of the four triangles will help us calculate the size of the larger square quilt block.

We are aware that the area of a square can be calculated by multiplying one side's length by itself (A = s2). Each of the small squares' ensuing triangles has a base and height that are equal to one-half of its side because the small squares were cut on the diagonal. Therefore, each triangle has a surface area of (1/2) x (1/2) x s2 = (1/4) x s2 = (s2)/4.

If the large quilt block is made up of four of these triangles, then the area of the quilt block is 4 x (s^2)/4 = s^2. Since the area of the large quilt block is 36 square inches, we can set up the equation:

s^2 = 36

To find the length of one side of the large quilt block (s), we can take the square root of both sides of the equation:

s = √36

s = 6 inches

So, the length of one side of the large quilt block is 6 inches, and the area of the block is 36 square inches.

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Jetlag is a condition associated with crossing multiple time zones is experienced by sports tourists from Argentina travelling to Japan.

People who travel quickly between different time zones may experience jet lag, a sleep disorder.

Jet lag causes sporadic sleep problems. It occurs when signals from a new time zone cause the body's biological clock to become out of sync. Feeding times and light exposure are two examples of cues.

The term "jet lag" originated from the fact that it was uncommon to travel far and quickly enough to cause desynchronosis prior to the development of passenger jet aircraft. Propeller-driven travel was slower and covered less ground than jet flights, so it had a negligible impact on the issue.

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The price per ounce is given as follows:

$0.15 = 15/100.

The price per ounce is obtained applying the proportions in the context of this problem, dividing the total price by the number of ounces.

The parameters for this problem are given as follows:

Hence the price per ounce is calculated as follows:

2.25/15 = $0.15.

The total price was of $2.25 for 15 ounces, and the problem asks for the price per ounce.

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Mean with frequency represented by the number of times people visits the shop is equal to 1.9.

Let 'v' represents the visits of the people.

'f' represents the frequency that is number of times group of people visits the shop.

To calculate mean results of the table are as follow:

Visits ( v)       frequency ( f)         fv

0                            5                     0

1                             14                   14

2                            18                   36

3                            7                     21

4                            6                     24

Mean of the number of visits

= ( Sum of all the fv ) / ( Sum of all the frequency)

= ( 0 + 14 + 36 + 21 + 24 ) / ( 5 + 14 + 18 + 7 + 6 )

= 95 / 50

= 1.9

Therefore, the mean of the number of visits with the given frequency is equal to 1.9.

The above question is incomplete, the complete question is :

A group of people answer the question:

How many times did you shop at Ascobury's last week?

Here are the results:

Visits ( v)       frequency ( f)         fv

0                           5

1                             14

2                            18

3                            7  

4                             6

Find the mean number of visits.?

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Marcella started with 56 candles during her initial purchase

The given problem can be solved by arithmetic approach

Given,

After 8 weeks she has 160 candles

And also, she buys 13 more candles every week

To find her initial number of candles purchased,

Let her initial number of purchase of candles be 'x'

According to the question,

Initial number of candles + (8 weeks * 13 candles/week) = 160 candles

Substituting x, we get

x+(13*8)=160

or, x+104=160

or, x=160-104

or, x=56

Thus, we can say that initially Marcella had bought 56 candles.

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Graphs (C) and (D) having median value larger than the mean value.

What Is a Histogram?

A histogram is a graphical representation of data points organized into user-specified ranges.

In graphs (C) and (D), the median value is larger than the mean value as the distribution is skewed to the left which means most values are large but there are few exceptionally small values because of which means shift towards the left and thus the mean is less than the median, or we can say that the median value is larger that the mean value.

So, graphs (C) and (D) having median value larger than the mean value.

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Average rate of change of the function F (x ) = 9/ -2 (x)-7. Average rate is -3, 9

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Divide the change in y-values by the change in x-values to determine the average rate of change. In order to determine changes in measurable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.

f (x ) = -2

f (x) = 9/ -2 (-2)-7

      = 9 / 4 - 7

      =9 / -3

      = -3

f (x ) = -4

f (x) = 9/ -2 (4)-7

      = 9 / 8 - 7

      =9 / 1

      = 9

Average rate is -3, 9

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The function is d(t) = 6cos(πt/6 + π/4) + 6. It models the water depth in meters as a cosine function of time after midnight.

The cosine function models the water depth d(t) in meters as a function of time t (in hours after midnight) on a particular day. The amplitude of the cosine curve is the difference between the high and low tide water depths, which is 6 m. The period of the cosine curve is the same as the natural oscillation period, which is 12 hours. The phase shift is π/4, as the high tide occurred at 4:45 a.m. Therefore, the function is d(t) = 6cos(πt/6 + π/4) + 6.

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The volume of the container is 4,500 cm3.

Calculate the volume of the two cubes that make up the container.

For the cube on the left, the volume can be found by multiplying the length (15 cm) by the width (10 cm) by the height (10 cm).

15 cm × 10 cm × 10 cm = 1,500 cm3

For the cube on the right, the volume can be found by multiplying the length (20 cm) by the width (15 cm) by the height (10 cm).

20 cm × 15 cm × 10 cm = 3,000 cm3

Add the two volumes together to find the total volume of the container.

1,500 cm3 + 3,000 cm3 = 4,500 cm3

Therefore, the volume of the container is 4,500 cm3.

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Answer:

the twelve value will produce -3

Step-by-step explanation:

T(12) = 45 - 4(12)

T(12) = 45 - 48

T(12) = -3

Answer: a. $12, b. $12, c. $13, d. $12

Step-by-step explanation:

a. 1+1+1+1+1+1 = 6, 2+2+2=6, 6+6=12

b. 1+1+1+1=4, 2+2+2+2=8, 4+8=12

c. 1+1+1+1+1=5, 2+2+2+2=8, 5+8=13

d. 1+1+1+1+1+1+1+1=8, 2+2=4, 8+4=2

The length of MN for this problem is given as follows:

MN = 12.

The law of sines states that the sine of each angle is proportional to the side length opposite the angle.

The angle opposite to side MN is given as follows:

O.

Which is congruent to angle M, and the side opposite to angle M is:

NO = 12.

Hence the length of MN is also given as follows:

MN = 12.

(as it is opposite to a congruent angle to the opposite side with length of 12).

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Answer:

Step-by-step explanation:

To find the probability that exactly 35 vehicles pass through the drive-thru during the lunch hour rush on a given day, we can use the probability density function of the normal distribution. In this case, the mean is 38 and the standard deviation is 5.7.

The probability of a specific value x in a normal distribution is given by the formula:

P(x) = (1/(σ * √(2π)) * e^((-1/2) * ((x - μ)^2 / σ^2))

Where x is the specific value we are trying to find the probability of, μ is the mean, and σ is the standard deviation.

plugging in the given values, we get:

P(35) = (1/(5.7 * √(2π)) * e^((-1/2) * ((35 - 38)^2 / 5.7^2))

The result is very close to zero, the probability of exactly 35 vehicles passing through the drive-thru during the lunch hour rush is very low, almost impossible.

The hypotenuse of the 45-45-90 triangle measures x / √2 units.Identify the given information. The given information is that the legs of a 45-45-90 triangle each measure x units. The question can be solved by following the steps :

1. Use the Pythagorean Theorem to solve for the hypotenuse. The Pythagorean Theorem states that a2 + b2 = c2 where a and b are the legs of the triangle and c is the hypotenuse. In this case, x2 + x2 = c2.

2. Simplify the equation. When two of the same numbers are added together, the sum is twice that number. Therefore, 2x2 = c2.

3. Solve for c. To solve for c, divide both sides of the equation by 2. This yields x2 = c2 / 2.

4. Take the square root of both sides. Taking the square root of both sides yields x = c / √2.

5.The answer to the question is that the hypotenuse of the 45-45-90 triangle measures x / √2 units.

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The center of dilation if Quadrilateral N' is the image of quadrilateral N under a dilation is; Point C

The center of dilation is defined as a reference point that is used to appropriately scale the dilation of a figure.

Now, if we imagine that the corresponding vertices of the two quadrilaterals are extended, then it will be clear that the extensions intersect at a point C.

Therefore we can conclude that point C is the center of dilation by the fact that corresponding parts of a paragraphic intersect at a point.

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55 rooms should be set aside for full-paying skiers.

Now, According to the question:

Let C represents the contribution that is lost when a reservation is breached.

H represents the loss of opportunity that is associated with not having the availability of anything.

D rep the no- shows with regard to experience in the past

X represents the overbooked number.

All the values here represent the critical probability for yield management.

Let X rep the reserved seats for passengers with full fare

D rep the full fare tickets

F rep the price of full fare

D rep the price of discounted fare

Now, Solving the problem :

P(d< x) < (F -D)/ p × F

= (299 - 109)/0.8 × 299

=  71,012.5

The Z value for 0.71 probability is 0.5

U + Z* standard deviation = 50 + 0.5 *10

= 55 rooms

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