Find three consecutive positive integers such that the product of the median and largest integer is 8 times the sum of the smallest and largest interger.

The rule for g(x) = f(x-1)-3 is g(x) = (x-1)⁶-3(x-1)³ - 1

A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable. Based on the information given, we can see that the variables that are illustrated in the question are f and g.

In order to write the rule for g(x) = f(x-1)-3 when f(x) = x⁶ - 3x³ + 2, replace x with x-1 in f(x) and subtract 3. That is:

g(x) =  f(x - 1) - 3

g(x) = (x-1)⁶ - 3(x - 1)³ + 2 - 3

g(x) = (x-1)⁶ - 3(x - 1)³- 1

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On interchanging the logical AND operator with logical OR operator and zeroes with ones,

(B'+C).A = (B'.C) + A

Now, According to the question:

Concept:

Duality theorem states that the dual of the Boolean function is obtained by interchanging the logical AND operator with logical OR operator and zeroes with ones. For every Boolean function, there will be a corresponding Dual function.

Calculation:

On interchanging the logical AND operator with logical OR operator and zeroes with ones,

(B'+C).A = (B'.C) + A

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The complete question is this:

Calculate the dual of the Boolean expression (B' + C).A

Answer:

45 degree

Step-by-step explanation:

45+45 90 +90 180

All triangles will have 180 degrees angle

Answer:

4x-24

Step-by-step explanation:

assume x=Length

perimeter

= x+(x-12)+x+(x-12)

= x+x -12+x+x-12

=4x-24

Both the x- and y-axes have negative values in this quadrant.

The x-axis in the fourth quadrant has positive values, whereas the y-axis has negative numbers.

A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from 1st through 4th and marked by Roman numerals: I (+; +), II (; +), III (; ), and IV (+; ).

The intersection of the x-axis (the horizontal number line) and the y-axis divides the coordinate plane into four equal pieces in the cartesian system (the vertical number line). These four regions are known as quadrants because they each account for one-quarter of the coordinate plane.

The third quadrant, known as Quadrant III, is located in the bottom left quadrant.

The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant.

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Answer:

Yes, a(b)+a(c) is the same as a(b+c)

Step-by-step explanation:

a(b)+a(c) is the same as a(b+c). We call it distributive property in math.

Donald would need to use 5 levels of cubes, So to make p5 he would need 25-12 = 13 more cubes.

A pyramid is a structure with a square or triangular base and four triangular sides that meet at a point, called the apex. Pyramids were built by ancient civilizations, such as the Egyptians, as tombs for pharaohs and their queens.

In the context of building pyramids with wood cubes, it seems like "pyramid levels" refers to the layers of cubes used to construct the pyramid. Each level is a layer of cubes that sits on top of the previous one, and the number of cubes in each level increases as you move up the pyramid. For example, in the case of p4, the base level would use 1 cube, the next level would use 4 cubes, the next level would use 9 cubes, and so on. The top level, which forms the apex of the pyramid, would use the most cubes. So the pyramid levels refer to the different layers of the pyramid and the number of cubes used in each layer.

To make a pyramid labeled p5, Donald would need to use 5 levels of cubes.

Donald uses 1 cube for the base of p4, 4 cubes for the next layer, 9 cubes for the next, 16 cubes for the next and 25 cubes for the top level.

So to make p5 he would need 25-12 = 13 more cubes.

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It would change to about 9. 960 atmospheres

Following the Boyle's law of gases which states that the product of pressure and volume is exactly a constant for an ideal gas.

This is represented as;

PV = K

then,

P₁V₁ = P₂V₂

From the information given, we have that;

Now, substitute the values

8. 9(4. 7) = P₂(4. 2)

mulitply the values

41. 83 = P₂(4. 2)

Divide both sides by 4.2

P₂ = 9. 960 atmospheres

Hence, the value is 9. 960 atmospheres

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Answer:

3

Step-by-step explanation:

Since [tex]\angle A \cong \angle A[/tex] by the reflexive property and [tex]\angle ABC \cong \angle ADE[/tex] since they are both right angles, [tex]\triangle ABC \sim \triangle ADE[/tex] by AA.

It follows that:

[tex]\frac{x}{9}=\frac{5}{9+6} \implies x=3[/tex]

The number of  pastries will be offered in one year could be 26 and the algebraic expression could be  x = 2 + 2y

What is Arithmetic progression ?

Arithmetic progression could be defined as the sequence of number where the difference between two consecutive number is same.

Given,

Mamas bakery just opened and is currently selling only two types of pastry.

Each month mamas bakery will add two more types of pastry to their menu.

let the number of pastries be x.

let y be the given number of pastries.

Hence the algebraic expression could be

x = 2 + 2y

Number of pastries will be offered in one year could be

x = 2 + 2 * 12

x = 26

Hence, the number of  pastries will be offered in one year could be 26 .

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Answer: 1/4 pound (lb) is equal to 4 ounces (oz).

This is because there are 16 ounces in one pound, so you can divide a pound into 16 equal parts, and each part is one ounce. Similarly, you can divide a pound into 4 equal parts , and each part is 1/4 pound. So in order to convert 1/4 pound to ounces, you can multiply 1/4 by 16.

1/4 lb * 16 oz/lb = 4 oz

When converting units, you are essentially multiplying or dividing by a conversion factor. In this case, the conversion factor is 16 oz/lb which tells you that there are 16 ounces in one pound. This factor allows you to convert between pounds and ounces by multiplying or dividing by it.

It's important to pay attention to the units in the conversion factor when using them. Here, the numerator and denominator of the conversion factor have the same unit, but it's not always the case. And the conversion factor helps to cancel out the unwanted unit and yield the desired unit in the end.

Step-by-step explanation:

The term that have the greatest value is

The knowledge of negative and positive number is necessary here.

numbers less than zero are negative while numbers greeter than zero are positive

Negative terms in an odd exponent remains negative hence less than zero in even exponent the negative changes to positive and becomes greater than zero

For the expression aₙ = (-1)ⁿ⁺¹(5)ⁿ the teem that determines whether the expression is greater that zero is  (-1)ⁿ⁺¹. therefore

n + 1 must be even

n must be odd for n + 1 to be even hence the greatest number here is aₙ₊₁₅ a(n+15)

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Answer:

35/4=8.75

Step-by-step explanation:

You and your 3 friends add up to 4 people so you do 35 divided by 4 and get 8.75

Answer:

Step-by-step explanation:

35/3 = p

p = 11.67 per person

After solving, the height in feet of the sixth bounce is 1.892 feet.

In the given question, we ave to find the height, in feet, of the sixth bounce.

From the given question,

Height on the first bounce = 6.7

Subsequent bounce reaches a height of the previous bounce = 81%

Suppose the height is h.

So according to the question:

h(6) = height on the first bounce*(subsequent bounce reaches a height of the previous bounce)^6

h(6) = 6.7*(81%)^6

h(6) = 1.892 feet

So the height of sixth bounce is 1.892 feet.

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No, 10 12 15 is not a Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, and c such that a^2 + b^2 = c^2.

To determine whether 10 12 15 is a Pythagorean triple, we need to calculate a^2 + b^2.

In this case, 10^2 + 12^2 = 100 + 144 = 244. Since 244 ≠ 15^2, 10 12 15 is not a Pythagorean triple. We can also confirm this by plugging 10, 12, and 15 into the Pythagorean Theorem, a^2 + b^2 = c^2.

10^2 + 12^2 = 100 + 144 = 244

244 ≠ 15^2

Therefore, 10 12 15 is not a Pythagorean triple.

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We employ the following equation to get the normal monthly cost:

4m - 8 = 64

Regular monthly expenses amount to $18.

Irma paid for her cats' subscription in advance for a 4-month period.

She saved $8 overall when she utilized a one-time discount.

Irma totaled $64 in payment.

We must identify the equation that can be utilized to calculate m, the average monthly cost.

Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.

When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.

Irma paid a total of $64 according to the problem, thus we can create the following equation:

4m - $8 = $64

We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.

4m = $64 + $8

4m = $72

Finally, divide both sides by 4 to solve for m:

m = $72 / 4

m = $18

So, the regular cost per month, m, is $18.

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Customers older than 45 years are 11 in number. This can be solved using stem-and-leaf plot.

A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.

The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).

The stem and leaf plot represents the age of store patrons. The leaf represents the unit digit, while the stem stands for the tens digit. 45 is not taken into account because the question asks us to determine the percentage of consumers who are over 45.

Customers older than 45 years old include: 48, 50, 50, 51, 55, 56, 62, 64, 65, 65, 73.

So, there are a total of 11 clients.

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The complete question is as follows:

The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store. How many customers were older than 45

bring the variable to the left side and bring all the remaining values to the right side.

Image search results for Write the inequality and solve it. -17 -14 ■ -21 -2 -9 -15

To fix an inequality, use these steps:

Step 1: Remove fractions by multiplying all terms by the fractions’ least common denominator.

Step 2 Simplify the inequality by merging like words on either side.

Step 3 Subtract or add amounts to get the unknown on one side and the digits on the other.

In algebra, the letter “x” is frequently used to represent an unknown value. It is referred to as a “variable” or “unknown” at times. X is a variable in x + 2 = 7, but we can deal with it.

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The information in a table shows that f(x) = 3(2)x  exponential function. An exponential function has the formula y = abx, wherein y and x are variables.

An exponential function is a mathematical function with the following formula: f (x) = 1 x. where an is a fixed sum that serves as the function's basis and x is a variable. The most frequent exponential-function base is the transcendent number e, or around 2.71828. Your function must be exponential if it has the equation y = a b x, or where are constant, a Zero and b > 0 and b 1. You always used functions to the power of 2 while solving quadratic equations. An exponential function's exponent is a variable.

Here,

given:

Using the table's (0, 3):

3 = ab° , a = 3

(2) and (12):

=>12 = ab²

=>12 = 3b²

=>b² = 4

=>b = 2

=>f(x) = 3(2)ˣ

The information in a table shows that the exponential function, f(x), equals 3(2)x.

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In a given study that the null hypothesis asserts the expected value of a phenomenon is 100 resulting in a 95% confidence interval reported as [98.76, 105.24], then we fail to reject the null hypothesis.

Therefore the answer is d) Fail to reject the null hypothesis.

A 95% confidence interval is a range of values that there is a 95% chance that the true value of a population parameter falls within. In this case, the 95% confidence interval is [98.76, 105.24], which includes the expected value of 100 that is stated in the null hypothesis.

Therefore, we fail to reject the null hypothesis because the data does not provide sufficient evidence to suggest that the true value of the population parameter is different from what is stated in the null hypothesis.

It's worth to mention that, Failing to reject the null hypothesis doesn't mean accepting it, it means that we don't have enough evidence to say that the parameter is different from the null hypothesis, it could be due the sample size, or other factors.

--The question is incomplete, complete question is as follows--

"Assume for a given study that the null hypothesis asserts the expected value of a phenomenon is 100. A research study results in a 95% confidence interval reported as [98.76, 105.24]. What decision would you make based on this confidence interval?

a) A decision cannot be made on a confidence interval; a hypothesis test is required.

b) Retain the null hypothesis.

c) Reject the null hypothesis.

d) Fail to reject the null hypothesis."

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The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

what is triangle ?

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

Given, side length, a = 12 units.

the height of equilateral triangle, h = (a√3)/2.

Substituting the value of 'a',

h = (12√3)/2 = 6√3 =

10.39 units.

The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

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A line which is confined between two endpoints is known as a line segment. In other words, we can say that a line segment is a portion of a line that is connected by two points.

The length of the line segment does not vary and the distance between them does not change. The units in which a line can be calculated in centimetres, millimetres, meters, inches, or feet.

The difference between a line segment and a line is that the line segment had two endpoints while the line extends indefinitely. When only one side of the line has an endpoint, it is called a ray or a half-open line segment.

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Answer:

   - A bag of rice is $16.9

   - A bag of flour is $5.20

Step-by-step explanation:

Let R and F stand for the price of a bag of Rice and Flour, respectively.

We can use the information provided to set an equation that will predict the total cost for that restaurant, given the quantities of rice and flour received (Restaurants A and B)

A) 4R + 2F = 78   [4 bags of rice and 2 bags of flour, when multiplied by the prices per bag, R and F, will result in a total cost of $78.

B)  3R + 4F = 71.5  [Now it is 3 bags of rice and 4 of flour, for a total cost of $71.50

We have 2 equations and 2 unknowns.  We can use substitution to find the answers.  Take one of the equations and reorganize it to isolate one of the variables (R or F).  We'll take the equation for A and isolate F

---

A) 4R + 2F = 78

     2F = 78-4R      [subtract 4R from both sides]

       F = 39-2R      [divide both sides by 2]

We've isolated F, and we can use this definition of F in the second equation:

===

B)  3R + 4F = 71.5

3R + 4(39 - 2R) = 71.5  [Use the definition of F derived above.  In this manner, we have legally eliminated one of the two variables.  (Sneaky, effective, and fun)]

3R + 156 - 8R = 71.5   [Multiply, combine like terms, and simplify]

-5R = -84.5                  [Isolate R]

R = $16.9                      A bag of rice costs $16.9

Now use the price of rice (R=$16.9) in one of the equations.  Since the rearranged equation we used above is already conveniently written for F, we'll use it:

F = 39 - 2R

F = 39 - 2(16.9)

F = 39 - 33.8

F = $5.20                     A bag of flour costs $5.20

===

CHECK:

Do these two prices satisfy both equations we first formulated?

Restaurant A:  4R + 2F = 78?

                        4(16.9) + 2(5.20) = 78  YES

Restaurant B:  3R + 4F = 71.5?

                        3(16.9) + 4(5.20) = 71.5  YES

These are the correct answers.

For her research, a geneticist has to raise a stock of fruit flies. She presently has 200 fruit flies in stock;

The mathematical function she may use to calculate is given as

f(n)=log1.38(n/200)

Which function could she use to calculate, the number of days required for her stock to grow to n fruit flies?

Generally, the equation for the final value is mathematically given as

A=Ao(1+u)^t

Therefore

n=200(1+0.38)*t

log(1.38^t)=log(n/200)

t=log1.38(n/200)

In conclusion, The function she could use to calculate is

f(n)=log1.38(n/200)

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In a course of 12 weeks, Perry will be able to play a total of 25 pieces of the piano Leon.

A total of 18 pieces of piano are learnt by Perry in a course of 9 weeks.

By using simple algebra, we can find the number of pieces that will be played by Perry in one week,

So, we can write, The learing speed,

Number of piano pieces learnt = Weeks

19 pieces = 9 weeks

Learning speed = 19/9 Pieces per week

So, the number of pieces learnt in 12 weeks is,

Number of pieces learnt = 19/9 x 12

Number of pieces learnt = 25.22

Number of pieces learnt = 25

So, Perry will be able to play 25 pieces.

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Therefore, Bob must pay $2530 in income tax for last year if Bob made 15,000 in taxable income last year.

The basis of an income tax system is referred to as taxable income. In other words, the amount of revenue that was subject to taxation.

Revenue is the entire amount of money made through the sale of products and services that are essential to the business's core activities.

The first $8000 of Bob's taxable income is taxed at 15%:

Tax on first $8000 = $8000 * 0.15 = $1200

The remaining $7000 of Bob's taxable income is taxed at 19%:

Tax on remaining income = $7000 * 0.19 = $1330

Total tax = $1200 + $1330 = $2530

So Bob must pay $2530 in income tax for last year.

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Answer:

3 3/4 or 3 6/8

Step-by-step explanation:

hope this helps <3

Answer:

68

Step-by-step explanation:

25% of a number is 20, where the number is 80 because 25% times 4 is 100% and 20 times 4 is 80.

We can check by doing 60% of 80 to see if it is 48. Instead of 60%, we can do 10% of 80, which is 8. Since we divided by 6, we multiply 8 by 6 which is 48.

Since we know 80 is the number, we have to find 85% of 80. First, let's find 5% of 80, which is 4 since 4 x 20 is 80 and 5% x 20 is 100%. Now, 85 divided by 5 is 17, let's multiply 17 by 4 to get 85% of 80. 17 x 4 is 68 which is 85% of 80.