the volume of the cone to be filled up if it has the same radius and height with is 376. 6 cm³
How to determine the volumeTo determine the volume, we need to know the formula for the volume of a cone.
The formula for the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters are expressed as;
V is the volume of the coner is the radius of the coneh is the height of the coneSubstitute the values, we have;
Volume = 3.14 × 6² × 10/3
Find the square value
Multiply the value, we have;
Volume = 1130. 4/3
Divide the values
Volume = 376. 6 cm³
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two buses leave the station at the same time.one travels at 50km/h on a bearing of 046, while the other travels at 90km/h on a bearing of 127.how far apart are they after two hours
The two buses are approximately 141.2 km apart after two hours.
We have,
We can use the Law of Cosines to solve this problem.
Let's call the distance between the two buses "d".
After 2 hours, the first bus will have traveled 100 km (50 km/h x 2 h) and the second bus will have traveled 180 km (90 km/h x 2 h).
Now we can use the Law of Cosines to find d:
d² = 100² + 180² - 2(100)(180)cos(127° - 46°)
d² = 10000 + 32400 - 36000cos(81°)
d² = 42400 - 36000cos(81°)
d ≈ 141.2 km
Therefore,
The two buses are approximately 141.2 km apart after two hours.
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Complete the following, using ordinary interest. (Use Days in a year table.)
Note: Do not round intermediate calculations. Round the "Interest" and "Maturity value" to the nearest cent.
Principal
$
1,350
Interest rate Date borrowed
July 21
8%
Date repaid
January 18
Exact time
Interest
Maturity value
The computation of the interest and the maturity value of the loan, using ordinary interest, is as follows:
Interest = $54.30
Maturity value = $1,404.30.
What is the ordinary interest method?The ordinary interest method is based on the use of 360 days as the ordinary days in a calendar year.
The ordinary interest contrasts with the exact interest, which uses 365 days or the normal calendar days.
Principal = $1,350
Interest rate = 8%
Date borrowed = July 21
Date repaid = January 18
The number of days between July 21 and January 18 = 181 days
Total Interest = Principal x Rate x Time
= $54.30 ($1,350 x 8% x 181/360)
Maturity value = Principal + Total Interest
= $1,404.30 [$1,350 + ($1,350 x 8% x 181/360)]
Thus, based on the ordinary interest method, the maturity value of the loan is $1,404.30.
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X8.8.PS-16
The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to cover
the block entirely with paper. How much paper do you need? Use pencil and paper to explain your
reasoning.
You need cm² of paper.
3mm
(The figure is not to scale)
Answer: 57 cm²
Step-by-step explanation:
To answer this question, we need to find the surface area of the figure.
First, we will find the surface area of the bottom part, the rectangular prism. We will use the given formula. However, we do not count the top side since it is connected to the bottom part. We will subtract this.
SA = 2(wl + hl + hw)
SA = 2((3 cm)(3 cm) + (2 cm)(3 cm) + (2 cm)(3 cm))
SA = 42 cm²
SA = 42 cm² - 9 cm² = 33 cm²
Next, we will find the surface area of the top part, the square pyramid. We know we have four congruent triangles. We will not count the square base since it is connected to the bottom part.
SA = 4 * ([tex]\frac{bh}{2}[/tex])
SA = 2 * (bh)
SA = 2 * ((3 cm)(4 cm))
SA = 2 * (12 cm²)
SA = 24 cm²
Lastly, we will add these two parts together.
33 cm² + 24 cm² = 57 cm²
What is the graph of the function f(x) =⌊x+3⌋
?
The graph of the function f(x) =[x+3] is a linear graph and it is represented on the last graph of the attached image.
Understanding Linear GraphA linear equation can be written in the form:
y = mx + c
where:
y = dependent variable (usually on the vertical axis).
x = independent variable (usually on the horizontal axis).
m = slope of the line, which determines its steepness.
c = y-intercept, which is the point where the line crosses the y-axis.
From our question,
f(x) =[x+3]
y = f(x)
m = 1
c = 3
To plot our graph, we use the range of values of x which are:
x = 0, -1, -2, -3
By substituting the value of x into the equation we have the equivalent y values;
f(0) = [0 + 3] = 3
f(-1) = [-1 + 3] = 2
f(-2) = [-2 + 3] = 1
f(-3) = [-3 + 3] = 0
Plotting x against y will give us the graph attached.
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simplify 2/3 (3x -2) – ¾ (2x -2)
Answer:
Sure, here are the steps on how to simplify 2/3 (3x -2) – ¾ (2x -2):
Multiply the factors in the numerator and denominator of each fraction.
2/3 (3x -2) = (2)(3x -2) / (3)(3) = 6x - 4 / 9
¾ (2x -2) = (3/4)(2x -2) / (3) = 3x - 6 / 12
Subtract the numerators of the two expressions.
6x - 4 / 9 - 3x - 6 / 12 = (6x - 4 - 3x - 6) / (9 * 12) = 3x - 10 / 108
Simplify the fraction by dividing the numerator and denominator by 3.
3x - 10 / 108 = (3x - 10) / (3 * 36) = x - 10 / 36
Therefore, the simplified expression is x - 10 / 36.
Step-by-step explanation:
Credit card A has an APR of 20.8% and an annual fee of $60, while credit card
B has an APR of 24.6% and no annual fee. All else being equal, which of these
equations can be used to solve for the principal, P, the amount at which the
cards offer the same deal over the course of a year? (Assume all interest is
compounded monthly.)
The amount at which the cards offer the same deal over the course of a year is a $2,333.33
Since credit card finance charge is the fee associated with using credit.
Credit card issuers use the finance charges to minimize non-payment risks and earn some profits for extending credit to cardholders.
Data and Calculations:
Card A Credit B
APR 20.8% 24.6%
Annual fee $60 $0
To calculate the balance required, the required equation is
= 22%x + $40 = 24.6%x
Where x = required balance
Thus,
= 0.208x + $60 = 0.246x
= $60 = 0.03x (0.246x- 0.208x )
= 0.03x = $60
x = $60 /0.03
x = $2,333.33
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Find the Value of X.
The measure of the unknown sides is equivalent to 12.6
Circle geometry problemThe given figure is a circle geometry with the perpendicular lines intersecting both segments of the circle.
We need to determine the measure of x. Since the measure of the perpendicular lines are equal, hence the measure of the line of the segments will also be equal.
Hence:
x = 6.3 + 6.3
x = 12.6
Therefore the measure of x from the given diagram is equivalent to 12.6
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
To represent a circle with a diameter of 12 units and a center that lies on the y-axis, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle, and r is the radius.
If the center of the circle lies on the y-axis, then the x-coordinate of the center is 0. Also, since the diameter is 12 units, the radius is 6 units.
Using these values, we can eliminate the equations that do not meet these conditions:
- x2 + (y – 3)2 = 36: This circle has a center at (0, 3), which is not on the y-axis.
- x2 + (y – 5)2 = 6: This circle has a center at (0, 5), which is not on the y-axis.
- (x – 4)² + y² = 36: This circle has a center at (4, 0), which is not on the y-axis.
- (x + 6)² + y² = 144: This circle has a center at (-6, 0), which is not on the y-axis.
- x2 + (y + 8)2 = 36: This circle has a center at (0, -8), which is on the y-axis.
Therefore, the two equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:
- x2 + (y + 8)2 = 36
- x2 + (y - 8)2 = 36
Note that the second equation is also valid, since the center of the circle can also be located at (0, -8).
1 Factor out a monomial NMZ
Learn with an example
Factor out the greatest common factor. If the greatest common factor is 1, just retype the
polynomial.
2x³ - 10
Submit
The greatest common factor of the polynomial 2x³ - 10 is 2.
By extracting the greatest common factor, we obtain:
= 2(x³/2 - 5)
Therefore, the factored form of the polynomial is 2(x³/2 - 5).
Thus, the greatest common factor of the polynomial 2x³ - 10 is 2.
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Megan has two boxes. There are x beads in box A. 7 of these beads are white. The rest of the beads are black. There are x beads in box B. 4 of these beads are white. The rest of the beads are black. She chooses at random a bead from box A. She notes the colour and then places this bead into box B. She then chooses at random a bead from box B. The probability of choosing a white bead from box A and a white bead from box B is 22 Work out the total number of beads in the two boxes:
The total number of beads in the two boxes: is: 20
How to solve Algebra Word problems?The parameters given are:
Number of white beads in box A = 7
Number of black beads in box A = x - 7
Number of white beads in box B = 4
Number of black beads in box B = x - 4
The probability of getting white from both boxes is:
P(W & W) = (7/x) * (4 + 1)/(x + 1)
P(W & W) = 35/(x(x + 1)
We are given that P(W & W) = 7/22
Thus:
35/(x(x + 1) = 7/22
Solving gives x = 10
Thus:
Box A has 10 beads and box B has 10 beads.
Total number of beads = 20 beads
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Jeremiah makes %25, percent of the three-point shots he attempts. For a warm up, Jeremiah likes to shoot three-point shots until he makes one. Let MMM be the number of shots it takes Jeremiah to make his first three-point shot. Assume that the results of each shot are independent. find the probability that it takes Jeremiah more than 6 attempts to make his first shot.
The probability that it takes Jeremiah more than 6 attempts to make his first three-point shot is approximately 0.0479.
The probability that Jeremiah makes a three-point shot is p = 0.25, which means that the probability he misses a shot is q = 1 - p = 0.75.
Let's consider the probability that it takes Jeremiah more than 6 attempts to make his first shot.
This means he must miss the first 6 shots, and make the 7th shot. The probability that he misses a single shot is q = 0.75, so the probability that he misses the first 6 shots is:
P(missing first 6 shots) = q × q × q × q × q × q = (0.75)^6
The probability that he makes the 7th shot is p = 0.25. Therefore, the probability that it takes Jeremiah more than 6 attempts to make his first shot is:
P(MMM > 6) = P(missing first 6 shots) × P(making 7th shot) = (0.75)^6 × 0.25 = 0.0479 (rounded to four decimal places).
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Looking at the paint quantity diagram and using your answer in QUESTION
1.7.2 A make use of different combinations of the tins of paint, then advise Prudence of which combination will be the most cost effective. Include VAT in your calculations.
Option B, three 2-liter tins, is the most cost-effective choice.
How to solve1.7.1: To convert 5 litres to cm³, multiply by 1000 cm³ per litre:
5 litres * 1000 cm³/litre = 5000 cm³.
1.7.2: If 1 litre covers 8m², and you need to paint 14.4m² with three coats: 14.4m² * 3 coats = 43.2m².
Divide by 8m²/litre to find litres needed: 43.2m² / 8m²/litre = 5.4 litres.
To find the most cost-effective combination, consider the options:
A: One 5-liter tin and one 2-litre tin.
B: Three 2-liter tins.
Calculate costs including VAT: A: (1 * 439.99 + 1 * 189) * 1.15 = 723.63, B: (3 * 189) * 1.15 = 651.45.
Option B, three 2-liter tins, is the most cost-effective choice.
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The Complete Question
Paint is sold in different sizes as shown below A B 2 litre tin R189 5 litre tin at 439.99 Prices excludes VAT of 15% 1.7.1 Convert the capacity of a 5-litre tin to its volume in cm³ NOTE: 1 litre 1 000 cm³ 1.7.2
According to a paint specialist one needs at least two coats of pain therefore decided that she will paint three coats just to be sure that covered. Remember that the area that needs to be covered is 14.4 How many litres of paint will be needed if 1 litre of paint covers 8m- Looking at the paint quantity diagram and using your answer in QUI 1.7.2 A make use of different combinations of the tins of paint, ther Prudence of which combination will be the most cost effective. Inclu your calculations. 8,84 cm
Whitney is making a strawberry cake for her brother’s birthday. The cake pan is a right rectangular prism
20
cm
20 cm20, start text, space, c, m, end text wide by
28
cm
28 cm28, start text, space, c, m, end text long. Whitney puts
1848
cm
3
1848 cm
3
1848, start text, space, c, m, end text, cubed of batter into the pan.
How deep is the cake batter?
Answer:
around 3.3 cm
Step-by-step explanation:
The volume of the rectangular prism cake pan can be calculated by multiplying its length, width, and depth:
V = l × w × d
Substituting the given values, we get:
V = 20 cm × 28 cm × d
V = 560d cm³
We are also given that the amount of batter put into the pan is 1848 cm³. So we can set up the following equation:
1848 cm³ = 560d cm³
Solving for d, we get:
d = 1848 cm³ ÷ 560 cm²
d ≈ 3.3 cm
Therefore, the cake batter is about 3.3 cm deep.
In the figure, angle ESY is vertical to angle TSL. Find the value of x given that M angle ESF=125 degrees. Then find m Angle ESY, m Angle TSL, m Angle EST, m Angle YSF, and m Angle FSL.
Find the value of X
The measure of Angle YEA is 70 degrees in the given parallelogram
Given Parallelogram EASY with diagonal ES
∠AES = 40
∠Y = 110
∠ESY = 40 by Z theorem of a parallelogram
∠A = ∠Y by property of parallelogram
∠A = <110 as ∠Y=110
∠YES = 180 - ∠Y
∠YES = 180 - 110 - 40
∠YES = 30
∠YEA = ∠YES + ∠AES
∠YEA = 30 + 40
∠YEA = 70
Hence, the measure of Angle YEA is 70 degrees
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Determine whether the following individual event are independent or dependent. Then find the probability of the combined event.
Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 5 red pieces of candy out of 49 pieces of candy total.
Stuck on this question pls help!!
a) The interval in which the height is increasing is given as follows: (0,2).
b) The interval in which the height is decreasing is given as follows: (4,10), .
c) The interval in which the height is constant is given as follows: (2,4), (10, ∞).
d) The height at 14 seconds is of zero, as when the balloon hits the ground, it does not fly anymore.
When a function is increasing and when it is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when the input variable represented x increases, the output variable represented by y also increases.Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when the input variable represented by x increases, the output variable represented by y decreases.The function is also said to be constant if the graph is a horizontal line.More can be learned about graphs and functions at https://brainly.com/question/12463448
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PLEASE HELP ASAP :) WILL GIVE BRAINLIEST
11 rain jackets were collected. At the end of the the drive, 10 times that number of rain jackets were collected. How many rain jackets were sold
If 11 rain jackets were collected. At the end of the the drive, 10 times that number of rain jackets were collected. The number of rain jackets that were sold is 99.
What is the jackets sold?We must determine the total number of rain jackets gathered at the end of the campaign in order to determine how many were sold.
10 times the original quantity of raincoats gathered is:
= 10 * 11
= 110
So, 110 rain jackets were collected.
Number of raincoats sold:
= 110 - 11
= 99
Therefore 99 rain jackets were sold.
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Click Submit to complete this assessment.
Question 14
The rate of rain on Thursday was two inches every three hours. It rained a total of 11 hours. How much rain fell after 11 hours of consistent rain?
A total of
(If rounding is necessary, round to the nearest hundredth.)
Document56.docx
47°F
Cloudy
inches of rain fell over the course of 11 hours
BE
Search
8
O
A total of 7 33 inches of rain fell over the course of 11 hours
How to find the amount of rain that fellThe rate of rain on thursday was two inches every three hours which means it rained 2/3 inches per hour
After 11 hours of consistent rain the total amount of rain that fell can be calculated by multiplying the rate of rain per hour by the number of hours
total amount of rain = 2/3 inches hour x 11 hours
total amount of rain = 22/3 inches
total amount of rain = 7 33 inches )rounded to the nearest hundredth)
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Can someone help me please
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex] is matrix obtained by multiplying row 3 by 2
[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\6&-5&-2&-3\end{array}\right][/tex] is obtained by interchanging row 3 and row 1
The given augmented matrix is [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]
The first row operation is given that multiply row 3 by 2
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2(2)&5(2)&-6(2)&-4(2)\end{array}\right][/tex]
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]
Now let us find the matrix by interchanging row 3 and row 1
[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\6&-5&-2&-3\end{array}\right][/tex]
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Twice the difference of a number and 9 is 3
Answer:
The number is 10.5-----------------
Let the number be n.
Twice the difference of a number and 9 is 3, set up an equation:
2(n - 9) = 32n - 18 = 32n = 21n = 10.5Hence the number is 10.5.
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line (Each pair of variables has a significant comelation) Then use the regression equation to
predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below
130
360
(a)x= 180 calories
(c)x= 140 calories
Calories, x
Sodium, y
150
430
540
170
480
130
340
+
Find the regression equation
-0.0
(Round to three decimal places as needed)
Choose the correct graph below
540
(a) Predict the value of y for x 180. Choose the correct answer below
OA 396.195
OB. 526.275
OC 623.835
OD. not meaningful
(b) Predict the value of y for x 100. Choose the correct answer below
90
250
180
560
CITTD
ос
(b) x 100 calories
(d) x 210 calories
OD
ŷ= 6.45x + 31.5 is the equation of the regression line for the given data
Here, we have,
to find the equation of the regression line for a given data:
Construct the table of the data as follows:
x >>>> y >>>> x² >>>> y² >>>> xy
1 39 1 1521 39
2 45 4 2025 90
3 52 9 2704 156
4 49 16 2401 196
5 61 25 4096 305
5 72 25 5184 360
................................................................................................
20 318 80 17931 1146
.................................................................................................
∑x = 20, ∑y = 318, ∑x²= 80, ∑xy = 1146, n = 6 (number data points)
The linear regression equation is of the form:
ŷ = ax + b
where a and b are the slope and y-intercept respectively
a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )
a = (6×1146 - 20×318) / ( 6×80-20² )
a = 6876-6360 / 480-400
a = 516 / 80
a = 6.45
x' = ∑x/n
x' = 20/6 = 10/3
y' = ∑y/n
y' = 318/6 = 53
b = y' - ax'
b = 53 - 6.45×(10/3)
b = 53 - 21.5
b = 31.5
ŷ = ax + b
ŷ= 6.45x + 31.5
Thus, the equation of the regression line for the given data is
ŷ= 6.45x + 31.5.
(a) x=3 hours
ŷ= 6.45(3) + 31.5 = 50.85
(b) x=4.5 hours
ŷ= 6.45(4.5) + 31.5 = 60.525
(c) x=13 hours
ŷ= 6.45(13) + 31.5 = 115.35
(d) x=1.5 hours
ŷ= 6.45(1.5) + 31.5 = 41.175
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complete question:
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours
Depot Headquarters has a new promotional payment plan. All purchases can be paid off on
the installment plan with no interest, as long as the total is paid in full within twelve months.
There is a $68 minimum monthly payment required. If the Koslow family buys a hot tub for
$6,283, and they make only the minimum payment for 11 months, how much will they have
to pay in the 12th month?
15–18: INTERPRETING SCATTERPLOTS. Consider the following scatterplots.
a. State whether the diagram shows a positive correlation, a negative correlation, or no correlation. If there is a correlation, is it strong or weak?
b. Summarize any conclusions that you can draw from the graph.
The scatterplot below shows the average points per game and percentage on three-point shots for the leading scorers of the 2020 Women’s National Basketball Association (WNBA). (Source: WNBA Advanced Stats)
In agreement, there is no correlation between the values of the graph because there is no constant that determines the relationship between the average of points and the percentage of failures of three points.
Is there any correlation between the values?Based on the information in the graph, we can infer that there is no correlation between the values in the graph, since neither influences the other (does not modify it). Due to the above, we can establish that the values have no correlation because they are independent and do not depend on each other.
In this case, we can see that the percentage of 35% is in two values: one below 19 and one above 19. This means that there is no correlation because if there were, the values would have an obvious trend.
To conclude we can say that there is no correlation between these values because there is no a constant relationship that determines the location of the points in the graph.
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The equation and the table show two linear functions.
Function A:
x
-6
0
12
y
3
4
6
Function B: y = x +9
What is the rate of change of the function that has the greater rate of change?
h
Answer:
5/2
Step-by-step explanation:
a metallurgist has one alloy containing 32% aluminum and another containing 44% aluminum. How many pounds of each alloy must he use to make 54 pounds of a third alloy containing 36% aluminum?
The number of pounds of each alloy he must use are: 49.33 of 32% aluminum and 4.67 of 44% Alloy
How to solve Algebra Word Problems?X = amount of alloy 1
Y = amount of alloy 2
Thus:
X + Y = 54
X = 54 - Y
0.32X + 0.44Y = 0.36 * 54
0.32X + 0.44Y = 19.44
Plugging in 54 - Y for X gives us:
0.32(59 - Y) + 0.44Y = 19.44
18.88 - 0.32Y + 0.44Y = 19.44
0.12Y = 19.44 - 18.88
Y = 0.56/0.12
Y = 4.67
X = 54 - 4.67
X = 49.33
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Calculati :17,2+1,56-14,4
An Intermediate Phase learner plays around with trapeziums and realises when you put them close to each other they tesselate and they have equal opposite angles. At which level of van Hiele’s levels of geometric thought is this learner?
According to van Hiele's levels of geometric thought, the Intermediate Phase corresponds to level 3, which is called the Informal Deduction stage.
What van Hiele’s level is the learner at ?The learner appears to be at level 3, known as the "Informal Deduction" stage. This is evident from their ability to use geometric properties in their reasoning.
At this phase, students start employing logical thinking to understand the connections and characteristics of geometry, using informal explanations and visual aids. Their ability to draw conclusions from particular instances is evident, though they may face difficulties when attempting to extrapolate their findings to broader contexts.
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Determine the equation of the circle with center (0, -2) containing the point
(√12,-5).
Answer:
i think its
x^2 + (y + 2)^2 = 21.
Step-by-step explanation:
bob said 4x500=200 explain his error using place value
Answer:
The answer is 2000
Step-by-step explanation:
The 2 means hundred and the two zeroes mean tens and ones if he added a zero at the end it would be 2000 making the 2 to be a thousand which is the correct answer.
Hello;
4 x 500 = 500 + 500 + 500 + 500 = 1000 + 1000 = 2000
you want 1000 => 2000/2 = 1000
(4 x 500)/2 = 2 x 500 = 500 + 500 = 1000
not 4 x 500 but 2 x 500
