The bookstore reduced all items by 20% for the spring sale. After the sale, it increased the prices to 20% above the sale price. Were these prices the same as the original prices? Explain.
8 a. You have an item that costs $40 that is 25% off. At the register they take an additional 30% off because of a daily coupon. What do you pay?
b. Some people might assume that 25% off followed by 30% off is 55% off. Why might people think that? How would you convince them it's not? What is the overall percentage when you take 25% off followed by 30% off?
9. You buy something priced at 20% off. You use a coupon for 10% off. Does the order in which the discounts are taken matter? Why or why not?

Answer:

\(30 \div 5\)

Way A

• 5 divided by 0 is 0.

• 5 divided by 3 is 0.6, flip the number, and you get 6.

Way B

• Divide 30 by 5 to get 6.

The dilation which represented by the line is enlargement and the scale factor of dilation is 2.

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

The distance from O to A is 3. Therefore,

\(OA=3\)

The distance from A to A prime is 3. Therefore,

\(AA'=3\)

Here, the new length of the line segment is,

\(OA'=OA+AA'\\OA'=3+3\\OA'=6\)

The scale factor of dilation is,

\(r=\dfrac{OA'}{OA}\\r=\dfrac{6}{3}\\r=2\)

The scale factor is 2 and the image is enlarged.

Hence, the dilation which represented by the line is enlargement and the scale factor of dilation is 2.

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Answer:

enlargement

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Discussion

Note: I think the length is supposed to be the height of 1 cookie.

The volume of the 12 cookies (1 dozen=12) is 176,715 in^3

The area of 1 cookie is 5 in

Area = pi * r^2

Area  of one cookie = 3.14 * 5^2

Area of one cookie = 78.5 in ^2 Note this is also the area of the base of the container.

Height of the 12 cookies = Volume / Area of one cookie

Height of the 12 cookies = 176.715/78,5

Height of the 12 cookies = 2.25 inches.

Answer

Thickness (height) of one cookie = 2.25/12

Thickness (height) of one cookie = .188 inches.

To determine the maximum number of 2/0 AWG THW aluminum compact conductors permitted in a 2½-inch PVC conduit, Schedule 80, we need to consult the applicable electrical code or standards.

The number of conductors allowed in a conduit is typically governed by factors such as fill capacity and heat dissipation.

The specific requirements may vary depending on the jurisdiction and the electrical code being followed. It is recommended to consult the local electrical code or a qualified electrician to ensure compliance with the regulations in your area.

They will be able to provide the precise guidelines and restrictions for conductor fill capacity based on the conduit size, type, and the specific application.

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Trigonometric functions values of a 60-degree angle and a 30-degree angle are related to each other. The values of the sine, cosine, and tangent functions of a 60-degree angle are the same as the values of a 30-degree angle. However, the values of cosecant, secant, and cotangent functions of 60 degrees angle are opposite of 30 degrees angle.

This is because, in a right-angled triangle, the side opposite the 60-degree angle is twice the length of the side opposite the 30-degree angle. The six trigonometric functions values of an angle can be defined as ratios of the side lengths in a right-angled triangle with respect to the angle. A right-angled triangle can be used to understand and calculate the values of the six trigonometric functions.

For any given acute angle, the six trigonometric functions of the angle will always have the same ratio, regardless of the size of the triangle or the length of its sides. However, the values of the six trigonometric functions vary depending on the angle.In the case of a 60-degree angle and a 30-degree angle, these two angles are commonly used in trigonometry because they can be easily evaluated using special triangles. In a right-angled triangle with a 30-degree angle, the side opposite to the angle is half the length of the hypotenuse. Whereas, in a right-angled triangle with a 60-degree angle, the side opposite to the angle is twice the length of the side opposite to the 30-degree angle.In the special triangle, if the length of the shorter leg is 1, then the length of the hypotenuse is 2 and the length of the longer leg is √3. These are the ratios for a 30-degree angle and the same ratios for a 60-degree angle are: sin 60° = sin 30° = 1/2, cos 60° = cos 30° = √3/2, and tan 60° = tan 30° = √3/3. However, the values of cosecant, secant, and cotangent functions of 60 degrees angle are opposite of 30 degrees angle.

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The lengths of the sides of the triangle with vertices A(2,-1,4), B(-2,3,9), and C(6,4,8) are approximately 10.63, 7.07, and 7.81 units.

To find the lengths of the sides of the triangle, we can use the distance formula in three-dimensional space. The distance formula is derived from the Pythagorean theorem, where the distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is given by:

d(PQ) = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

Applying this formula to our triangle, we can calculate the lengths of the sides as follows:

1. Side AB:

  AB = √((-2 - 2)² + (3 - (-1))² + (9 - 4)²)

     = √((-4)² + (4)² + (5)²)

     ≈ √(16 + 16 + 25)

     ≈ √57

     ≈ 7.55 units (rounded to two decimal places)

2. Side BC:

  BC = √((6 - (-2))² + (4 - 3)² + (8 - 9)²)

     = √((8)² + (1)² + (-1)²)

     ≈ √(64 + 1 + 1)

     ≈ √66

     ≈ 8.12 units (rounded to two decimal places)

3. Side CA:

  CA = √((6 - 2)² + (4 - (-1))² + (8 - 4)²)

     = √((4)² + (5)² + (4)²)

     ≈ √(16 + 25 + 16)

     ≈ √57

     ≈ 7.55 units (rounded to two decimal places)

Therefore, the lengths of the sides of the triangle ABC are approximately 7.55, 8.12, and 7.55 units.

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The AC in Rhombus ABCD is 16 cm.

Here, we have,

In question it is not given that what is E, so, let suppose that E is intersecting point of diagonals AC and BD of rhombus with side AB, BC, CD and DA.

Rhombus :

Rhombus is a parallelogram with four equal sides and sometimes one with no right angles.

As it is given that AE =8 cm.  

And, we know that AC is diagonal rhombus,

so, as E is middle point of diagonal AC

Then,    AC  = 2 × AE

           AC  = 2 × 8

Hence,  AC  = 16 cm.

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complete question:

ABCD is a Rhombus. Solve the following problems. If AE = 8, then find AC

Answer:

Type: Quartic

Fourth-degree polynomials are also known as quartic polynomials.

Constant Term: \(\frac{1}{9}\)

Number Of Terms: 4

Leading Term: \(-x^{4}\)

Leading Coefficient: -1

The most simplified expression for \((5y)^2(16y^4)^{\frac{1}{2}\) is \(100y^4\)

The given expression is:

\((5y)^2(16y^4)^{\frac{1}{2}\)

Expand the expression using the laws of indices

\(5^2y^2 \times 16^{\frac{1}{2}}y^{\frac{4}{2}\\\\\)

\(25y^2 \times 4y^2\)

Multiply like terms

\((25 \times 4)y^{2+2}\)

The resulting expression is:

\(100y^4\)

Therefore, the most simplified expression for \((5y)^2(16y^4)^{\frac{1}{2}\) is \(100y^4\)

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Answer:

bro got you

x>-6

Step-by-step explanation:

 \(\bold{x}\) ≥ \(\bold{-6}\)

______________________________

  - We have to get rid of both numbers on each side, so to do so, we do the opposite of what we see: Since we have a negative 7, we add 7 on each side.

Equation at the end of Step 1:

 -  We have to get rid of numbers on each side, so do to so, we do the opposite of what we see. Since we have a negative 3 being multiplied, we divide by -3 instead.  

 - Since -3 is negative, the inequality direction is changed as well.

Equation at the end of Step 2:

______________________________

The inverse function of f(x) is; f-¹(x) = x³ + 5

To find the inverse of the function;

We should represent f(x) as y.

Now we have;

By taking the cube of both sides;

y³ = x - 5

By solving for x;

x = y³ + 5

By swapping x and y; we have;

y = x³ + 5

f-¹(x) = x³ + 5.

The inverse function of f(x) is; f-¹(x) = x³ + 5.

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Answer:

16 square units

Step-by-step explanation:

→ Find the area of the whole triangle

0.5 × ( 5 + 4 ) × 8 = 36

→ Find the area of the small triangle

0.5 × 5 × 8 = 20

→ Minus the area's of the triangles

36 - 20 = 16 square units

The experimental probability of John passing the quiz is 1.

To find the experimental probability that John passed the quiz, the recorded results are used.

Given:

John answered the questions randomly.

He generated random numbers from 1 to 100 using a calculator.

Odd numbers represent True (T) and even numbers represent False (F).

The correct answers are T, T, F, F, and T.

The recorded results are given below:

Recorded Results:

True (T)

False (F)

True (T)

False (F)

True (T)

From the recorded results, John answered 3 out of 5 questions correctly.

Since John needs at least 3 correct answers to pass the quiz, it can e concluded that he passed the quiz based on the experimental data.

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Answer:

0.46 feet

Step-by-step explanation:

Length = 5/6 feet (or 0.254 m)

Width = 3/8 feet (or 0.114 m)

(5/6 - 3/8) feet = 11/24 feet or 0.46 feet (0.140 m)

The region enclosed by the curves. y = 5x³, y = 5x is sketched below.

The equation of the curves are : y = 5x³, y = 5x,

To sketch the region enclosed by these curves, we first need to intersection point of these curves,

So, the intersection-point can be calculated as :

5x³ = 5x,

x³ - x = 0,

(x - 1)(x)(x + 1) = 0,

So, the values of x are x = -1, x = 0 and x = 1,

Substituting the values, in both the curve equation,

We get, the intersection point as : (-1,-5), (0,0) and (1,5);

The graph of y = 5x³ is a cubic function that passes through the origin (0, 0) and has a positive slope.

The graph of y = 5x is a linear function with a positive slope. It also passes through the origin and increases steadily as x increases.

So, The graph of these curves, with the intersection-point (-1,-5), (0,0) and (1,5) is sketched below.

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The given question is incomplete, the complete question is

Sketch the region enclosed by the given curves. y = 5x³, y = 5x.

Answer:8sqrt 2 or sqrt 128

Step-by-step explanation:

We can use the Pythagorean Theorem. Since the ladder is leaning against the wall, it is the hypotenuse. It is also 4 feet away from the wall so 12^2-4^2=b^2 b^2=128 so b=8sqrt 2 or sqrt 128.

The total monthly cost of the phone bill is represented by y and the total number of minutes is represented by x. Then, a sample piece-wise function to describe their relationship is written as \(y(x)=\begin{cases} {{\$35\;&\mathrm{if}\;0\leq x \leq300} \\ {\$[35+(x-300)]\;&\mathrm{if}\;x > 300}} \end{cases}\)

A function that is produced from bits of multiple functions over various periods is known as a piecewise function. By providing the input value, one can produce this function that operates differently.

Given the total cost of the phone bill is represented by y and the total number of minutes is represented by x. To write a piecewise function, let's consider an example of this.

For $35 per month, 300 minutes are included in a cell phone package. $0.25 will be charged for each additional minute. Then, the piecewise function for this is represented by,

\(y(x)=\begin{cases} {{\$35\;&\mathrm{if}\;0\leq x \leq300} \\ {\$[35+(x-300)]\;&\mathrm{if}\;x > 300}} \end{cases}\)

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Answer:

Asking four boys and four girls from each first period class which type of cake they prefer.

Step-by-step explanation:

cant really explain it just knew it off the top of my head.

You can use the fact that whenever bases are same, the product of such quantities end up getting their exponents added.

The product result of given expression is \(^5\sqrt{(2x)^4}\)

Suppose you've got two values to multiply with each other and you have got both value's bases same, then the multiplication will end up with result being that base raised with sum of the exponents of both the initial values.

For example:

\(a^b \times ^c =a^{b+c}\)

You can convert the roots to powers. Then you can use the fact that the bases are same and thus the powers will add.

Remember that if you've got xth root, then the power would be 1/x.

For our case, it will go like this:

\(^5\sqrt{4x^2} \times ^5\sqrt{4x^2} = \: ^5\sqrt{(2x)^2} \times ^5\sqrt{(2x)^2} = {((2x)^2)}^{\frac{1}{5}} \times {((2x)^2)}^{\frac{1}{5}} = (2x)^{\frac{2}{5}} \times (2x)^{\frac{2}{5}}\\\\ ^5\sqrt{4x^2} \times ^5\sqrt{4x^2} = (2x)^{\frac{2}{5} + \frac{2}{5}} = (2x)^{\frac{4}{5}} = \: ^5\sqrt{(2x)^4}\)

Thus, the final product result will be written as \(^5\sqrt{(2x)^4}\)

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Answer:

x = 10/9

Step-by-step explanation:

Solve for x:

(4 x)/5 + 4/3 = 2 x

Put each term in (4 x)/5 + 4/3 over the common denominator 15: (4 x)/5 + 4/3 = (12 x)/15 + 20/15:

(12 x)/15 + 20/15 = 2 x

(12 x)/15 + 20/15 = (12 x + 20)/15:

(12 x + 20)/15 = 2 x

Multiply both sides by 15:

(15 (12 x + 20))/15 = 15×2 x

(15 (12 x + 20))/15 = 15/15×(12 x + 20) = 12 x + 20:

12 x + 20 = 15×2 x

15×2 = 30:

12 x + 20 = 30 x

Subtract 30 x from both sides:

(12 x - 30 x) + 20 = 30 x - 30 x

12 x - 30 x = -18 x:

-18 x + 20 = 30 x - 30 x

30 x - 30 x = 0:

20 - 18 x = 0

Subtract 20 from both sides:

(20 - 20) - 18 x = -20

20 - 20 = 0:

-18 x = -20

Divide both sides of -18 x = -20 by -18:

(-18 x)/(-18) = (-20)/(-18)

(-18)/(-18) = 1:

x = (-20)/(-18)

The gcd of 20 and -18 is 2, so (-20)/(-18) = (-(2×10))/(2 (-9)) = 2/2×(-10)/(-9) = (-10)/(-9):

x = (-10)/(-9)

Multiply numerator and denominator of (-10)/(-9) by -1:

Answer: x = 10/9

The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

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Answer:

4

Step-by-step explanation:

7h-15h+40=-72

-8h=-32

h=4

Answer:

One sec

Step-by-step explanation:

There is a significant difference between the average numbers of traffic accident related emergency room admissions between Friday the 6th and Friday the 13th.

To conduct a hypothesis test to evaluate if there is a difference between the average numbers of traffic accident related emergency room admissions between Friday the 6th and Friday the 13th, we can use a paired t-test. The null hypothesis would be that there is no difference between the means of the two populations, while the alternative hypothesis would be that there is a difference.

We can calculate the paired differences by subtracting the number of admissions on Friday the 6th from the number of admissions on Friday the 13th. Then we can calculate the mean and standard deviation of these differences. Using the given data, the mean of the differences is 10.83 - 7.5 = 3.33 and the standard deviation of the differences is 3.6.

Next, we can calculate the t-statistic by dividing the mean difference by the standard deviation of the differences and multiplying by the square root of the sample size. Using the given data, the t-statistic is (3.33 - 0) / (3.6 / sqrt(6)) = 3.07.

We can look up the critical value for a two-tailed test with 5 degrees of freedom (n-1) at a significance level of 0.05. The critical value is 2.571.

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Answer:

c) ab/14

Step-by-step explanation:

\(\frac{a}{7} * \frac{b}{2} =\frac{ab}{14}\)

multipling fractions rule is to multiply nominators and denominators separately

Answer:

1260

hope this helps

have a good day :)

Step-by-step explanation:

Step-by-step explanation:

2 x 2 x 3 x 3 x 5 x 13

= 2340

................