Please help asap and break it down please so I may learn

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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(a) The domain of g(x, y) is the disk D = {(x, y) : x² + y² ≤ 16}.

(b) The total differential of g is dg = -x/(√(16 - x² - y²))dx - y/(√(16 - x² - y²))dy.

The domain of g(x, y) is the set of all values of x and y that satisfy the condition inside the square root to be non-negative.

16 - x² - y² ≥ 0

- x² - y² ≥ -16

x² + y² ≤ 16

The total differential dg of g(x, y), is calculated as follows;

dg = (∂g/∂x)dx + (∂g/∂y)dy

Using the chain rule, we have;

∂g/∂x = (1/2)(16 - x² - y²)^(-1/2)(-2x)

∂g/∂x = -x/(√(16 - x² - y²))

∂g/∂y = (1/2)(16 - x² - y²)^(-1/2)(-2y)

∂g/∂y = -y/(√(16 - x² - y²))

dg = -x/(√(16 - x² - y²))dx - y/(√(16 - x² - y²))dy.

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Answer:

A

Step-by-step explanation:

Answer :

Step-by-step explanation:

A.

[tex] \rightarrow \bigg(\dfrac{1}{3} \bigg )\bigg(\dfrac{ - 1}{2} \bigg ) \\ \\ \rightarrow \bigg(\dfrac{ - 1}{6} \bigg )[/tex]

B.

[tex] \rightarrow\bigg(\dfrac{ - 1}{4} \bigg )\bigg(\dfrac{ - 2}{3} \bigg ) \\ \\ \rightarrow\bigg(\dfrac{ 2}{12} \bigg ) \\ \\ \rightarrow \dfrac{1}{6} [/tex]

C.

[tex]\rightarrow\bigg(\dfrac{ - 12}{7} \bigg )\bigg(\dfrac{ - 2}{7} \bigg ) \\ \\ \rightarrow\dfrac{ - 12}{7} \times \dfrac{ - 7 }{2} \\ \\ \rightarrow 6[/tex]

D.

[tex]\rightarrow\bigg(\dfrac{ 12}{7} \bigg )\bigg(\dfrac{ - 2}{ 7} \bigg ) \\ \\ \rightarrow\dfrac{ 12}{ \cancel{7} } \times \dfrac{ \cancel{ 7 }}{ - 2} \\ \\ \rightarrow - 6[/tex]

Hence, Option D is the answer.

The volume of the square pyramid is 191.25 cm³

The volume of a square pyramid refers to the space enclosed between its five faces. The volume of a square pyramid is one-third of the product of the area of the base and the height of the pyramid. Thus, volume = (1/3) × (Base Area) × (Height).

We can write this mathematically as;

v = a² * (h/3)

v = 1/3 * 7.5² * 10.2

v = 765/4

v = 191.25 cm³

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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 : 1/4 is the fraction which is equivalent to the shaded area of the rectangle.

Here, we have,

Since the rectangle is divided into 8 equal parts and two parts are shaded, this simply means that 2 out of 8 parts are shaded which is 2/8.

The fraction that's equivalent to the shaded area of the rectangle will be:

2/8 = (2 × 1) / (2 × 4)

      = 1/4

The equivalent fraction is 1/4

Hence, The solution is : 1/4 is the fraction which is equivalent to the shaded area of the rectangle.

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complete question:

A rectangle is divided into 8 equal parts. Two parts are shaded. What fraction is equivalent to the shaded area of the rectangle.

Answer:

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

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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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:

The Probability of drawing a card higher than an 8 from a regular 52-card deck is 5/13, or approximately 0.3846 (rounded to four decimal places).

There are a total of 52 cards in a regular deck, with 4 cards of each rank (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 13 cards in each suit (hearts, diamonds, clubs, spades).

To determine the probability of drawing a card higher than an 8, we need to count the number of cards that satisfy this condition and divide it by the total number of cards in the deck.

There are 4 cards of each rank that are higher than an 8: 9, 10, Jack, Queen, King, and Ace. Therefore, there are a total of 5 x 4 = 20 cards that are higher than an 8 in the deck.

So, the probability of drawing a card higher than an 8 is:

P(higher than 8) = number of cards higher than 8 / total number of cards

P(higher than 8) = 20 / 52

Simplifying the fraction by dividing both the numerator and denominator by 4, we get:

P(higher than 8) = 5 / 13

Therefore, the probability of drawing a card higher than an 8 from a regular 52-card deck is 5/13, or approximately 0.3846 (rounded to four decimal places).

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The area of the triangle is 17 cm square

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

The triangle

Where we have

Base = 5 cm

Height = 6.8 cm

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

Area = 1/2 * Base * Heigt

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 5 * 6.8

Evaluate

Area = 17 cm square

hence, the area is 17 cm square

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The value of k from the given trigonometric equation is 1.

Given that, sec²θ(1+sinθ)(1-sinθ)=k

Here, sec²θ(1-sin²θ)=k (∵(a+b)(a-b)=a²-b²)

sec²θ×cos²θ=k  (∵1-sin²θ=cos²θ)

We know that, secθ=1/cosθ

1/cos²θ ×cos²θ=k

k=1

Therefore, the value of k from the given trigonometric equation is 1.

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The value of slope of the secant line is, 6

We have to given that;

The graph of line are shown in figure.

Now, Take two points on the secant line is,

⇒ (0, 0) and (0.1, 0.6)

Hence, The slope of the secant line is,

m = (0.6 - 0) / (0.1 - 0)

m = 0.6 / 0.1

m = 6/1

m = 6

Thus, The value of slope of the secant line is, 6

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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 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 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

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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[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{12}\\ o=\stackrel{opposite}{7} \end{cases} \\\\\\ x=\sqrt{ 12^2 + 7^2}\implies x=\sqrt{ 144 + 49 } \implies x=\sqrt{ 193 }\implies x\approx 13.9[/tex]

Answer: The plane travelled 144 miles in 0.4 hours

Step-by-step explanation:

The plane travels at a speed of 360 miles/hour.

The speed is 360/60=6 miles per minute.

0.4 hours will be 0.4*60=24 minutes. To calculate how much the plane travels in 24 minutes, 24 will be multiplied by 6.

24*6= 144 miles.

Answer: 144

Step-by-step explanation: To solve this problem, we can use the formula:

distance = rate x times

where distance is the entire distance covered, rate denotes the plane's speed, and time denotes the length of the trip.

We can state that the plane is moving at a speed of 360 miles per hour (360 mph) given that it can fly 360 miles in an hour.

We need only enter the following variables into the formula and do a distance calculation to determine how far the plane can travel in 0.4 hours:

distance = rate × time

distance = 360 mph × 0.4 hours

distance = 144 miles

As a result, the aircraft can fly 360 miles per hour for 144 miles in 0.4 hours.

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:

The ratio or the proportion is solved

Given data ,

A ratio is a comparison of two quantities by division. It expresses the relative size or amount of one quantity in comparison to another.

Ratios are often written as a fraction, with a colon, or with the word "to".

For example, if we have a bowl of fruit that contains 6 apples and 2 oranges, the ratio of apples to oranges is 6:2, which can be simplified to 3:1. This means that for every 3 apples, there is 1 orange in the bowl.

Hence , the proportion is solved

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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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You will have $50,000 in your account after 50 years.

We have,

Simple interest formula is given by:

I = Prt

Where:

I = interest earned

P = principal amount (initial investment)

r = interest rate

t = time (in years)

Here,

P = $10,000

r = 8%

t = 50 years

So, the interest earned after 50 years will be:

I = Prt

= 10000 x 0.08 x 50

= $40,000

The total amount in the account after 50 years will be the initial investment plus the interest earned:

Total amount = $10,000 + $40,000 = $50,000

Therefore,

You will have $50,000 in your account after 50 years.

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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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The value of x is 3[tex]\sqrt{5}[/tex].

Labeling the given figure,

AC = 6

AB  =  3

BC =  x

Since Pythagorean theorem states,

(Hypotenuse)²= (Perpendicular)² + (Base)²

Therefore,

(x)²= (6)² + (3)²

(x)²= 45

Squaring both sides,

Hence x = 3[tex]\sqrt{5}[/tex]

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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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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: