3.2 Provide an example to explain the difference between conceptual knowledge and procedural knowledge. (4)​

The total price of the rollerblades with the discount and a 6% sales tax is $59.63.

Given that a sporting goods store buys pairs of rollerblades for $60 and marks them up 25%.

Then he decides to clear his inventory and sells each pair of rollerblades at a discount of 20%.

Initial Price = $60

Markup = 25% x $60 = 0.25 x 60 = $15

Price after Markup = $60 + $15 = $75

Discount = 20% x $75 = 0.25 x 70 = $18.75

Price after Discount = $75 - $18.75 = $56.25

Sales Tax = 6% x $56.25 - 0.06 x 56.25 = $3.38

Price = $56.25 + $3.38 = $59.63

Hence the total price of the rollerblades with the discount and a 6% sales tax is $59.63.

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Answer:

Step-by-step explanation:

It's given that, The base of a triangle is 1 cm more than the height

Let's assume height of the triangle be x and base of the triangle be 1 + x

Also the area of the triangle is 10 cm².

We know that area of triangle is calculated by,

Putting the values we get ,

[tex] \frac{1}{2} (1 + x) x = 10 \\ \\ (1 + x)x = 10 \times 2 \\ \\ {x}^{2} + x = 20 \\ \\ {x}^{2} + x - 20 = 0[/tex]

Further solving by factorisation,

[tex]x^2 + x-20 = 0 \\ \\ x^2 +5x-4x - 20 = 0 \\ \\ x(x+5)-4(x+5)= 0 \\ \\ (x-4) (x+5) = 0 \\ \\ (x-4) = 0 \: or \: (x+5)=0 \\ \\ { \underline{x= 4 \: or \: x = 5 }}[/tex]

Since value can't be negative.

So, x = 4.

Hence, height of triangle x = 4 cm

base of triangle = x + 1

= 4 + 1

= 5 cm

Therefore the Base of traingle will be 5 cm and Height of the triangle will be 4 cm.

Answer:

P = (1^2)/(2^2) = 1/4 = .25 = 25%

Answer:

A) 13

Step-by-step explanation:

The two given angle measurements are corresponding angles. By definition of corresponding angles, the two given angle measurements are equal. Set the two measurements equal to each other:

[tex]9x + 10 = 127[/tex]

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 10 from both sides of the equation:

[tex]9x + 10 = 127 \\9x + 10 (-10) = 127 (-10)\\9x = 127 - 10\\9x = 117[/tex]

Next, divide 9 from both sides of the equation:

[tex]9x = 117\\\frac{(9x)}{9} = \frac{(117)}{9}\\ x = \frac{117}{9}[/tex]

Simplify:

[tex]x = \frac{117}{9}\\ x = 13[/tex]

~

A) 13 is your answer for x.

~

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The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

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The numbers are 5, 5, 10, 10, 15

To find the value of x, we need to use the fact that the mean of the five numbers is 9. The mean is equal to the sum of all the numbers divided by the total number of numbers. In this case, we have:

(mean) = (sum of all numbers) / (total number of numbers)

We know the mean is 9, and there are 5 numbers, so we can write:

9 = (x + x + 2x + 2x + 3x) / 5

Simplifying the right-hand side, we get:

9 = 9x / 5

Multiplying both sides by 5, we get:

45 = 9x

Dividing both sides by 9, we get:

5 = x

So we now know that the first two numbers are both equal to 5. Using the ratio, we can find the values of the next two numbers:

2x = 2(5) = 10

So the third and fourth numbers are both equal to 10.

Finally, we can use the ratio to find the value of the fifth number:

3x = 3(5) = 15

So the five numbers are:

5, 5, 10, 10, 15

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Yes, the random, 10%, and large counts conditions are all met.

Here, the expected count of players who win a large prize is

np = 100 x 0.10

np = 10

and, the expected count of players who do not win a large prize is

n(1-p) = 100 x 0.90 = 90.

The second prerequisite is also satisfied because both of these anticipated counts are higher than or equal to 10.

The independence criteria is also satisfied if each player's outcome is independent of the results of the other players.

Therefore, Yes, the random, 10%, and large counts conditions are all met.

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The ratios of the identities are;

sin R = 9/15

cos R = 12/15

tan R = 9/15

It is important that we note the different trigonometric identities and their corresponding ratios.

From the information given, we get;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have the parameters given as;

Hypotenuse side = 15

Opposite side = 9

Adjacent side = 12

Now, substitute the values, we have;

sin R = 9/15

cos R = 12/15

tan R = 9/15

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Answer:

There are four possible outcomes for a student who randomly selects a sandwich wrap: chicken and spinach, chicken and tomatoes, turkey and spinach, or turkey and tomatoes. There are two possible outcomes for the meat in a randomly selected wrap: chicken or turkey. There are two possible outcomes for the vegetable in a randomly selected wrap: spinach or tomatoes.

Step-by-step explanation:

1402800 is the number of people who would test positive for the virus

To find the probability for the number who tested positive we divide the positive cases between the total of the covid tests and then mutiply by 100.

P = (8,533/68,811) × 100

P = 12.400, the nearest hundredth of a percent is 12.

11690000 people who live in ohio and the testing results is that 12% of this people would test positive for the virus.

so we need to find percentage 12 for 11690000.

(11690000×12) / 100

Hence, 1402800 is the number of people who would test positive for the virus

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The state of Ohio conducted COVID 19 tests on 68,811 people, and 8,533 tested positive. (6 points)A. What is p for the number who tested positive (round to the nearest hundredth of a percent)?B. Based upon the testing results above, of the 11.69 million people who live in Ohio, what is the bestestimate for the number of people who would test positive for the virus?

Answer:

10.5 cubic feet

(10.5ft³)

Step-by-step explanation:

1.5 x 3.5 = 5.25

5.25 x 2 = 10.5ft³

The solution is:

⇒ 6b = 95.94   (equation to determine cost of one box)

cost of one box 'b' = $`15.99

⇒ 12t = 95.94   (equation to determine cost of per tile)

cost of one tile t = $0.7995.

Given :

Jorge bought a crate of floor tiles for $95.94.

The crate had 6 boxes of floor tiles.

Each box contained 20 floor tiles .

To Find :

Write and solve equation to determine the cost per box'b'.

Write and solve a second equation to determine the cost per tile't'

Solution :

Cost of one box = b

There are 6 boxes

So, cost of 6 boxes = $  6b

Since Jorge bought 1 crate( = 6 boxes) of cost $95.94

⇒     (equation to determine cost of one box)

⇒6b = 95.94

⇒b =15.99

Thus cost of one box = $`15.99

Since 1 box 20 floor tiles

So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles

We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94

Cost of one tile = t

Cost of 120 tiles = $120t

⇒ (equation to determine cost of per tile)

⇒12t = 95.94

⇒t = 0.7995.

Thus cost of one tile t = $0.7995.

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Based on available research and studies, the answer is B: A higher percentage of millennials have at least $100,000 saved for retirement when comparing to Gen X.

According to a report from Fidelity Investments, 30% of millennials have saved at least $100,000 for retirement. In contrast, a 2019 study from the Transamerica Center for Retirement Studies found that 31% of Gen Xers have no retirement savings at all.

This suggests that the fraction of millennials with at least $100,000 saved for retirement is higher than the portion of Gen X people who have no retirement savings.

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The measurement of other two legs of the right triangle is 6.4 and 7.6.

Given is right triangle with hypotenuse equal to 10 units and an acute angle of 40°, we need to find the other two legs,

Here we will use the trigonometric ratios to find the legs,

Let 40° be the reference angle,

So,

Sin 40° = perpendicular / 10

Perpendicular = 6.4

Cos 40° = base / 10

Base = 7.6

Hence the measurement of other two legs of the right triangle is 6.4 and 7.6.

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Answer: $7,000.

Step-by-step explanation:

4% = 0.04. Multiply that by the sales price to calculate commission.

$175,000 x 0.04 = $7,000.

A) For 99% confidence, the critical value (from the table) is approximately 2.576.

48 subjects are required for a 99% confidence level. (Round up to the nearest subject)

B) For 90% confidence, the critical value (from the table) is approximately 1.645.

19 subjects are required for a 90% confidence level. (Round up to the nearest subject)

C) Decreasing the confidence level decreases the sample size needed (option B).

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most usual, but other levels, such 90% or 99%, are occasionally used to generate a confidence range.

How to solve

z for 99%=2.58

z for 95%=1.96

a)sample size= [tex](z*s/E)^2=(2.58*12.6/4)^2=66[/tex]

b)sample size= [tex](z*s/E)^2=(1.96*12.6/4)^2=38[/tex]

decreasing the confidence level decreases the sample size required

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The solution is: the ratio of teenagers to attendees is: 1:2.

Here, we have,

given that,

Out 28 teenagers and adults people 12 adults attend a music concert

now, we need to find the ratio of teenagers to attendees.

so, we have,

12 adults attend a music concert

total  attendees =  28 teenagers and adults people

so, we get,

number of teenagers = 28 -12

                                   = 14

so, the ratio of teenagers to attendees is:

14: 28

=1:2

Hence, The solution is: the ratio of teenagers to attendees is: 1:2.

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The function rule for g(x) is h(x) = (x - 0)² - 7.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex (0, -7) and other points (-3, 2), we can determine the value of a as follows:

f(x) = a(x - h)² + k

2 = a(-3 - 0)² - 7

2 + 7 = 9a

9 = 9a

a = 1

Therefore, the required quadratic function in vertex form is given by:

h(x) = a(x - h)² + k

h(x) = (x - 0)² - 7

h(x) = x² - 7

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Answer:

Without any data or research to draw from, it is impossible to make a reliable conclusion about male and female preferences for veggie pizza. Preferences for food can be influenced by a wide range of factors, including cultural background, personal tastes, dietary restrictions, and individual preferences.

However, if a study were conducted and significant differences were found between male and female preferences for veggie pizza, conclusions could be drawn based on the results of the study. For example, if the study found that a higher proportion of women than men preferred veggie pizza, the marketing team could consider adjusting their marketing strategy to target more women. Alternatively, if the study found that men preferred veggie pizza more than women, the marketing team could consider using this information to develop more effective targeted marketing strategies for male audiences. Ultimately, the conclusions that can be drawn about male and female preferences for veggie pizza (or any other type of food) are dependent on the data and research available.

Step-by-step explanation:

Answer:

To find the surface area of the smaller rectangular prism, we need to use the fact that the two prisms are similar and the ratio of their sides is 2:3. This means that the corresponding sides of the two prisms are in the ratio 2:3.

Let the dimensions of the smaller rectangular prism be 2x, 3x, and y, where x is a constant and y is the height. Then, the dimensions of the larger rectangular prism are 4x, 6x, and 2y.

The surface area of the smaller rectangular prism is given by:

2(2x * 3x) + 2(2x * y) + 2(3x * y) = 12x² + 4xy

We know that the surface area of the larger rectangular prism is 2592 cm², so we can set up the following equation:

2(4x * 6x) + 2(4x * 2y) + 2(6x * 2y) = 2592

Simplifying this equation gives:

72x² + 16xy = 1296

We can solve for y in terms of x by rearranging the terms:

y = (1296 - 72x²) / (16x)

Now we can substitute this expression for y into the equation

Step-by-step explanation:

The blanks are filled using the concept of translation transformation  as follows

Parabola            Equation

Red                       y = x²

Blue                     y = x² + 3

Green                  y = (x - 3)²

Orange                y = x² - 3

Purple                  y = (x + 3)²

Applying translation the graphs are interpreted as follows

y = x²: the parent function

y = x² + 3: shift 3 units up

y = (x - 3)²: shift to the right 3 units

y = x² - 3: shift 3 units down

y = (x + 3)²: a shift 3 units to the left

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The reflection preserves the side lengths and angles of triangle. The dilation preserves angles but not side lengths.

The triangle underwent the following operations:

As a result, while the dilation would only maintain the angles, the reflection would preserve both side lengths and angles.

Thus, Angles are preserved, but side lengths are not.

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The probability of Event A is 1/360 and the probability of Event B is 1/15.

For Event A, we can calculate the probability by considering the order in which the acts are scheduled.

There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.

Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.

Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.

Therefore, the total number of possible ways to schedule all 6 acts is:

6 x 5 x 4 x 3 x 2 x 1 = 720

Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.

There are 2 remaining acts, so there are 2 possible choices for the fifth act.

Only one act remains for the last slot.

Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:

1 x 1 x 1 x 1 x 2 x 1 = 2

Thus, the probability of Event A is:

P(A) = 2/720 = 1/360

For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.

There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.

Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.

Therefore, the total number of possible ways to schedule the first four acts is:

4 x 3 x 2 x 1 = 24

Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.

Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:

24 x 2 = 48

Thus, the probability of Event B is:

P(B) = 48/720 = 1/15

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The domain of f⁻¹(y) is all real numbers greater than or equal to 4. Therefore, option B is the correct answer.

The domain of a function is the set of all possible input values for which the function is defined. In this case, the domain of f(x) is all real numbers, since there are no restrictions given in the problem.

To find the inverse of f(x), we need to solve for x in terms of y.

f(x) = (x-4)^2 + 7

y = (x-4)² + 7

y - 7 = (x-4)²

√(y-7) = x-4

x = √(y-7)+4

The inverse of f(x) is:

f⁻¹(y)=√(y-7)+4

Therefore, option B is the correct answer.

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Answer:

x less than or equal to 4 option c

Step-by-step explanation:

took the test

Answer:

5216.844

Step-by-step explanation:

Let x be the fourth number.

We know that the sum of the four numbers is 20500:

2341.578 + 10690 + x + 2341.578 = 20500

Simplifying and solving for x:

x = 20500 - 2341.578 - 10690 - 2341.578

x = 5216.844

The area of the regular hexagon is A = 166.28 cm²

Given data ,

Let the side length of the hexagon be a = 8 cm

Now , area of hexagon is A = ( 3√3/2 )a²

On simplifying , we get

A = ( 1.5 ) ( √3 ) ( 64 )

A = 96√3

The value of A = 96√3 cm²

On further simplification , we get

A = 166.28 cm²

Therefore , the value of A is A = 166.28 cm²

Hence , the area is A = 166.28 cm²

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Option (A) "Adjust the width of the compass to AB, and draw an arc from point X such that it intersects the arc drawn from N in a point Y" is correct.

We have,

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have a statement:

Steps to construct an angle MNT congruent to angle PQR.

To construct an angle MNT congruent to angle PQR, the steps are as follows:

Step 1: Use a compass to draw an arc from point Q that intersects the side PQ at point A and the side QR at point B.

Step 2: Draw a segment NT, and use the same width of the compass to draw an arc from point N that intersects the segment NT at a point X.

Step 3: Adjust the width of the compass to AB, and draw an arc from point X such that it intersects the arc drawn from N in a point Y.

Step 4: Join points N and Y using a straightedge.

Thus, option (A) "Adjust the width of the compass to AB, and draw an arc from point X such that it intersects the arc drawn from N in a point Y" is correct.

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