Evan has a loyalty card good for a discount at his local hardware store. The item he
wants to buy is priced at $14, before discount and tax. After the discount, and before
tax, the price is $11.76. Find the percent discount.

While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

Here's a three-column table evaluating how learning takes place according to Piaget, Vygotsky, and Bruner:

Theorist Approach to Learning Key Concepts

Piaget Constructivism 1. Schema: Individuals actively construct their knowledge through assimilation and accommodation, organizing information into mental structures called schemas. 2. Stages of Development: Learning occurs through cognitive development stages, from sensorimotor to formal operational, where individuals progressively acquire more complex mental abilities. 3. Active Exploration: Children learn best through hands-on exploration and interactions with the physical world.

Vygotsky Sociocultural Theory 1. Zone of Proximal Development (ZPD): Learning takes place within the gap between a learner's actual developmental level and their potential level with guidance from a more knowledgeable other. 2. Social Interaction: Learning is facilitated through social interactions with peers and adults, such as cooperative learning and scaffolding. 3. Cultural Tools: The use of language, symbols, and cultural artifacts plays a central role in cognitive development and learning.

Bruner Constructivism 1. Scaffolding: Instruction should provide support and guidance tailored to the learner's current abilities to help them progress to higher levels of understanding. 2. Discovery Learning: Learners construct knowledge by actively exploring and discovering concepts and relationships on their own. 3. Spiral Curriculum: Learning is organized in a spiral manner, revisiting key concepts and building upon previous knowledge in a progressive and interconnected way.

While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

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Answer:

d + 2g

Step-by-step explanation:

Sum of: +

d: d

Twice g: 2 × g = 2g

Sum of d and twice g: d + 2g

Answer:

Not sure if this is right but it might be something like

350,000-4%+1671m

or

3500,000-4%y/1671m

Step-by-step explanation:

The numbers we know are 350,000 4% and 1671 per month

350,000 is the full mortgage

4% is the APR or annual percentage rate like interest

and we know the monthly for the mortgage is 1671 per month

Answer:

No

Step-by-step explanation:

So, you can use the distributive property.

1/2(6x)=3x

1/2(-2)=-1

It is 3x-1, not 3-x

The coordinates A is located at the origin meaning that A(0, 0)

The point M is located at M(4,7)

The slope (m) of the line AM is given by

So, the slope (m) of the line AM is 7/4

Recall that parallel lines have equal slopes.

So, the slope of a line parallel to the line AM is also 7/4

The composite function of (f.g)(x) is 9x^2 + 5 and the other composite function is 3x^2 + 15

In mathematics, function composition is an operation in which takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function.

f(x) = x^2 + 5

g(x) = 3x

The composite function of (f.g)(x) can be calculated as

(f.g)(x) = (3x)^2 + 5

(f.g)(x) = 9x^2 + 5

For the second composite function, (g.f)(x) can be calculated as

(g.f)(x) = 3(x)^2 + (5*3)

(g.f)(x) = 3x^2 + 15.

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Answer:

lesser odd integer =11

Greater odd integer=13

Step-by-step explanation:

let the consecutive odd integers be x,x+2

and  x<x+2

3(x+2)=x+28

3x+6=x+28

3x-x=28-6

2x=22

x=11

x+2=11+3=13

If the size of matrix "M" is 9×10, and a scalar "c" is multiplied by matrix, then the size of "cM"  will be 9×10.

We know that when a scalar is multiplied to a matrix, each element of the matrix gets multiplied by that scalar.

In this case, the scalar "c" is multiplied with the Matrix "M";

So if a scalar "c" is multiplied by a matrix "M" of size 9×10, then the resulting matrix "cM" will also have the same number of rows and columns as the original matrix "M".

Therefore, the size of "cM" will also be 9×10.

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If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

D) 48

Step-by-step explanation:

Let s = Scott

Let j - James

s = 5

s + 43 = j  Substitute 5 for s

5 + 43 = j

48 = j

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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9514 1404 393

Answer:

  10 1/5

Step-by-step explanation:

3 × 3 2/5 = 3(3) +3(2/5) = 9 +6/5 = 9 + 1 1/5

  = 10 1/5

Answer:

  384√3

Step-by-step explanation:

Make use of the commutative and associative properties of multiplication to rearrange the order of operands to something suitable. The square of a square root is the original number.

  \(2\sqrt{8}\cdot4\sqrt{8}\cdot6\cdot\sqrt{3}\\\\=2\cdot4\cdot6\cdot(\sqrt{8})^2\cdot\sqrt{3}\\\\=48\cdot8\cdot\sqrt{3}\\\\=\boxed{384\sqrt{3}}\)

Answer:

To make a box-and-whisker plot, we first need to order the data from smallest to largest:

4, 5, 6, 10, 15, 16, 21

Next, we can find the median, which is the middle value of the ordered data set. In this case, the median is 10.

Then, we can find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set. To find Q1 and Q3, we can split the data set into two halves:

4, 5, 6, 10 and 15, 16, 21

The median of the lower half is (5+6)/2 = 5.5, and the median of the upper half is (16+21)/2 = 18.5. Therefore, Q1 = 5.5 and Q3 = 18.5.

Now we can draw the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom of the box at Q1 (5.5), the top of the box at Q3 (18.5), and the line inside the box at the median (10). The whiskers extend from the box to the smallest and largest values inthe data set that are not outliers. To determine whether there are outliers, we can use the following formula:

Outlier = Q1 - 1.5 * (Q3 - Q1) or Q3 + 1.5 * (Q3 - Q1)

Plugging in the values, we get:

Outlier = 5.5 - 1.5 * (18.5 - 5.5) = -13.25 or Outlier = 18.5 + 1.5 * (18.5 - 5.5) = 37.25

Since there are no values in the data set that are less than -13.25 or greater than 37.25, there are no outliers.

Therefore, the box-and-whisker plot for the given data is:

            |       4

     ___|___

    |              |

    |              |

    |        5.5 |-----  

    |              |      |

    |              |      |

    |------------|  10 |  

    |              |       |

    |      15.5 |------

    |       |      |

     ___|___

            |       21

The box spans from Q1 (5.5) to Q3 (18.5), with the median line inside the box at 10. The whiskers extend from the box to the minimum value of 4 and the maximum value of 21, since there are no outliers.

Hope this helps!

Answer: . x 10^5 miles from the earth. How long does it take light to from a source on earth to reach a reflector on the moon and then return to earth? The speed of light is 3.0 x 10^8 m/s. ... sec. to give us our final answer of 1.28 seconds (the time required for light to travel 2.4 x 105 miles). and the fastest spaceship goes 153,454 miles per hour

Step-by-step explanation:

The number of hours that should be taken to fly to the moon from Earth is 7 hours.

Given that

Now we know that

\(Time = \frac{Distance}{Speed} \\\\= \frac{2.4 \times 10^5 }{3.6 \times 10^4} \\\\= \frac{240}{36}\)

= 6.66 hours

= 7 hours

Therefore we can conclude that The number of hours that should be taken to fly to the moon from Earth is 7 hours.

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We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

The larger circle is, half of the line is used to form one large circle.

What is split in half?

To split or cause to split, especially violently, by cleaving into distinct pieces, typically into two nearly equal ones.

To split into a lesser number of things neatly or equally. The mirror collapsed and broke into three almost identical pieces.

Here, a 100-unit-long line is split in half.

That means a line is divided into two equal part with length 50 unit each.

Also, half of the line is used to form one large circle. The other half forms two identical smaller circles.

From this we can see that  half of the line is used to form one large circle is always a lager circle.

And other half forms two identical smaller circles are the smaller circles.

Hence, the larger circle is, half of the line is used to form one large circle.

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Answer:

36 blues

Step-by-step explanation:

Answer:

36 blue Candies

Step-by-step explanation:

Let

x ----> the number of blue Candies

y ----> the number of yellow Candies

we know that

The ratio of blue candied and yellow candies is 3:5

Step-by-step explanation:

The ratio of blue candied and yellow candies is 3:5

so

x = 3

y 5 -----> equation A

the bag contains 60 yellow Candies

so

y=60 ----> equation B

substitute equation B in equation A

r 3

60 5

solve for x

x=3 (60) = 36

5

The expression for finding the nth term of the given sequence is:

\(n^2 + 21.\)

To find the nth term of a sequence, we need to identify the pattern or rule that generates the sequence.

Looking at the given sequence, we can observe that the difference between consecutive terms is increasing by 1, as follows:

25 - 22 = 3

30 - 25 = 5

37 - 30 = 7

46 - 37 = 9

We can see that the difference between consecutive terms is increasing by 2 each time. This suggests that the sequence is generated by a quadratic equation of the form:

\(an^2 + bn + c\)

where a, b, and c are constants that we need to find. To do this, we can use the first three terms of the sequence to set up a system of equations:

\(a(1)^2 + b(1) + c = 22\)

\(a(2)^2 + b(2) + c = 25\)

\(a(3)^2 + b(3) + c = 30\)

Simplifying these equations, we get:

a + b + c = 22 (equation 1)

4a + 2b + c = 25 (equation 2)

9a + 3b + c = 30 (equation 3)

We can solve this system of equations by subtracting equation 1 from equation 2, and then subtracting equation 2 from equation 3, as follows:

3a + b = 3 (equation 4)

5a + b = 5 (equation 5)

Solving for b in terms of a, we get:

b = 3 - 3a (from equation 4)

b = 5 - 5a (from equation 5)

Setting these two expressions for b equal to each other, we get:

3 - 3a = 5 - 5a

Simplifying this equation, we get:

2a = 2

Therefore, a = 1.

Substituting this value of a into either equation 4 or 5, we get:

b = 0

Substituting a = 1 and b = 0 into equation 1, we get:

c = 21

So the nth term of the sequence is given by:

\(an^2 + bn + c = n^2 + 21\)

Therefore, the expression for finding the nth term of the given sequence is:

\(n^2 + 21.\)

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Answer:

The Answer is 15/4

(Simplied)

Step-by-step explanation:

first make same numerator, so 48/4 and 33/4

48 - 33 = 15

denomater stays same

15/4

Hope this helps!

:)

Answer: 2%

Step-by-step explanation: just bring the decimal point two to the right

Answer:

2%

Step-by-step explanation:

Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

Y=-x+3 is the slope-intercept form equation for the line.

The slope or gradient of a line is a numerical representation of a line's steepness and direction in mathematics. The reason for this usage is unknown, although it first appears in English in O'Brien (1844), who wrote "y = mx + b," and in Todhunter (1888), who wrote "y = mx + c." The letter m is widely used to signify slope.

The slope can be calculated by comparing the "vertical change" to "horizontal change" between any two distinct points on a line. In cases when the ratio is expressed as a quotient ("rise over run").

From the above graph,

The line is passing through the points (-1, 4) and (3, 0)

Let the slope intercept form be

y= mx +c

Slope m=(0-4/3+1)

=-4/4

= -1

y= -x+c

The equation is passing through the point (3, 0)

-3+c=0

c=3

y= -x+3

Therefore, y=-x+3 is the slope-intercept form equation for the line.

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Answer:

y=-1/4x+4

Step-by-step explanation:

The graph starts on 4 so that is your y-intercept

Use slope formula to get the slop (y2-y1 over x2-x1)

Use 2 coordinates for formuls (In your case (0,4) and (4,3))

3-4=-1 4-0=4

slope is -1/4

y= -1/4x+4

Answer:

10.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions to calculate the hypotenuse.

We know the opposite side from the angle labeled 59 degrees.

sin 59 = opp side / hypotenuse

sin 59 = 9.2/x

x = 9.2/ sin 59

x = 10.733

first off, let's take a peek at the picture above

hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.

now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.

\(\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}\)

With the help of simple interest, we conclude that the total amount of money Mrs. Bui will have in the account after 18 months is $5,225.

What is simple interest?

Simple interest is a type of interest that is calculated as a percentage of the principal amount borrowed or invested, without taking into account any additional interest earned on the interest itself.

To solve this problem, we can use the formula for simple interest:

Simple Interest = Principal x Rate x Time

where:

Principal is the amount of money invested

Rate is the annual interest rate (as a decimal)

Time is the time period in years

In this case, the principal is $5,000, the rate is 3% or 0.03, and the time period is 18 months or 1.5 years. We can plug these values into the formula and solve for the simple interest:

Simple Interest = $5,000 x 0.03 x 1.5 = $225

Therefore, the total amount of money Mrs. Bui will have in the account after 18 months is:

Total = Principal + Simple Interest = $5,000 + $225 = $5,225

So the answer is (b) $5,225.

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