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The period of the sinusoidal function is given as follows:

8 units.

A periodic function is a function that has the behavior repeating in intervals over the domain of the domain.

Then the period of the function is defined as the shortest difference between two points in which the function has the same behavior.

Two consecutive points where the function has the same behavior (same numeric value, increase/decrease and concavity) are given as follows:

x = 4 and x = 12.

Hence the period is of:

12 - 4 = 8 units.

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The error interval for x is given as follows:

27.5 ≤ x < 28.5.

The number x was rounded to the nearest integer.

The rule to round a number to the nearest integer depends on the first decimal digit of the number, as follows:

For both cases, the decimal digit is removed.

Then, considering the two bullet points above, the error interval for x is given as follows:

27.5 ≤ x < 28.5.

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On solving the provided question, we can say that, by Least Common Multiple the amount to buy - 4 packs of buns and 5 packs of hot dogs.

The smallest positive integer that is divisible by both a and b is known as the least common multiple, also known as the least common multiple, or the least common multiple of two numbers a and b. Least Common Multiple is referred to as LCM. The least frequent multiple of two numbers is also the least frequent multiple of both. A number and an integer are combined to create a multiple of that number. For instance, 10 is a multiple of 5, as 10 can be divided by 5, 2, and 5, making it a multiple of 5. The smallest positive integer that can be divided by both 5 and 2 is 10, making it the lowest common multiple of these numbers.

Least Common Multiple (LCM) between 10 and 8 is =  40

Buns is = 10-20-30-40

Hot dogs is =  8-16-24-32-40

So, stock would be equal for both products.

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Answer:

f(x)= (x-3)^2

domain: set= {x| xER}

interval= (-infinity, Infinity)

Step-by-step explanation:

hope this helps

Answer: 4; $1,012.50

Explanation:

The formula to calculate the interest charged on a credit card balance is:

Interest = (Balance * APR) / 12

Where,

Balance = $1,000

APR = 15%

So,

Interest = ($1,000 * 15%) / 12 = $12.50

Therefore, after one month, the total balance on the credit card would be $1,000 + $12.50 = $1,012.50.

The sum of the arithmetic sequence is S = 207 and the summation notation is S = ∑i=1 to 6 ( 5n + 17 )

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic sequence be represented as A

Now , the value of A is

A = 22 + 27 + 32 + 37 + 42 + 47

The number of terms n = 6

So , the value of i ranges from 1 to 6

Now , the summation is represented as ∑i=1 to 6 ( 5n + 17)

when n = 1

S₁ = 5 ( 1 ) + 17 = 22

when n = 2

S₂ = 22 + 5 ( 2 ) + 17

S₂ = 22 + 27

when n = 3

S₃ = 22 + 27 + 5 ( 3 ) + 17

S₃ = 22 + 27 + 32

Hence , the sum of the arithmetic sequence is S = 207

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Option D is the answer.

There are multiple ways to go about this problem, but I'll go over the simplest approach.

From the graph, the line contains the points (0,4), (1,3), (2,2), etc. Calculating for the slope using any of these two points (using rise/run) reveals that the line has a slope of -1.

Out of all four options, option D is the only option that has a slope of -1 as seen by the slope-intercept form [tex]y=mx+b[/tex]. Solving for the inequality entirely provides the same result.

Let me know if you have any questions, thanks!

Answer: To solve the inequality 1/4b−1/5b > 3/10b−1/2, we need to simplify both sides:

1/4b - 1/5b > 3/10b - 1/2

5/20b > 7/20b

Then we isolate b by subtracting 7/20b from both sides:

-2/20b > -7/20

Finally, we divide both sides by -2/20 to get:

b < 35/2

The solution in interval notation is (-∞, 35/2).

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

(n-2)180=900/180

n-2=5

n=5+2=7

n=7

Step-by-step explanation:

Triangle A: Equilateral triangle, all angles are equal (60 degrees) and all sides are equal. Unique.

Triangle B: Isosceles triangle, two sides are equal (6 cm) and two angles are equal. Unique.

Triangle C: Not unique, as different triangles can have two sides of equal length and an included angle of 55 degrees.

Triangle D: Not unique, as different triangles can have a base of 6 cm and base angles of 50 degrees.

Answer:

Step-by-step explanation:

Triangle A and Triangle B

Step-by-step explanation:

I think this is the answer because Triangle A, has a unique that all sides have a measure of 60 degrees. And I also think that Triangle B is unique because It's an Equilateral triangle, which means that all sides have the same length.

So hence, I think the answer is A and B

Always keep more than 2 smiles! You have to share them with people who don't have one too, right??

Thanks!

:D

The expressions defined for all real number are written as for

Information made available in the question include

function s(x) = x - 1

function t(x) = 2x²

rewriting the expression for (s + t) (x)

=  x - 1 +  2x²

= 2x² + x - 1

rewriting the expression for  (s x t) (x)

=  (x - 1) *  2x²

= 2x³ - 2x²

rewriting the expression for  (s - t) (3)

=  (x - 1) - 2x²

= -2x² + x - 1

substituting the value of x = 3

= -2(3)² + 3 - 1

= -6 + 3 - 1

= -4

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Answer:

≈0.785714286

Answer:

207/500

Step-by-step explanation:

Hope it helps! =D

The cost C of renting an economy car as a function of the number x of days used, where 7≤x≤ 14 is C(x) = $24x (if x < 7) and C(x) = $95 + $24(x - 14) (if x > 14).

A function is a mathematical concept that associates each element of a set (called the domain) with exactly one element of another set (called the codomain). The function takes inputs from the domain and assigns to each input a unique output from the codomain.

Functions can be represented in various ways, including by a graph, an equation, or a table of ordered pairs. A function is often denoted by f(x), where x is an element of the domain and f(x) is the corresponding output, or value, in the codomain.

Functions are widely used in mathematics and science to model real-world situations and describe relationships between variables. They can be used to calculate values based on input, to make predictions, and to model complex systems.

Let's call the cost of renting an economy car for x days "C". If x is less than 7, the cost will be $24 per day. If x is between 7 and 14, the cost will be $95 per week. If x is greater than 14, the cost will be $95 per week plus any extra days over 14.

So, the function for the cost of renting an economy car as a function of the number of days used (x) is:

C(x) = $95 (if x >= 7 and x <= 14)

C(x) = $24x (if x < 7)

C(x) = $95 + $24(x - 14) (if x > 14)

Note: This assumes that the cost of the extra days is $24 per day.

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Answer:

30 leaves in one hour

Step-by-step explanation:

[tex]\frac{120}{4}=30[/tex]

13

Step-by-step explanation:

taaaahthyyyyyfffffdddddddddddddddddddddddddddddd

The value of expression after divide is,

⇒ (3x + 18) / (3 + 5x)

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ (x + 6) divided by 3+5x divided by 3.

Now, We can write as;

⇒ (x + 6) ÷ (3 + 5x) ÷ 3

⇒ (x + 6) ÷ (3+ 5x) / 3

⇒ (x + 6) × 3 / (3 + 5x)

⇒ 3 (x + 6) / (3 + 5x)

⇒ (3x + 18) / (3 + 5x)

Thus, The value of expression after divide is,

⇒ (3x + 18) / (3 + 5x)

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The future value of the loan is $5807.65.

It is expressed as a percentage of the amount borrowed and is paid over a specific period of time. The interest rate represents the cost of borrowing money and is one of the key factors in determining the overall cost of a loan. Interest is usually calculated on a yearly basis and can be compounded, meaning that the interest earned on a loan is added to the original principal and the interest rate is then applied to the new, higher amount. This process continues over time, leading to the growth of the original loan amount. The purpose of charging interest is to compensate the lender for the risk they are taking in lending the money and for the opportunity cost of not being able to invest the money elsewhere.

The future value of a loan is equal to the present value plus the interest earned over a specified time period. The formula to calculate the future value of a loan with simple interest is:

FV = PV (1 + rt)

where:

PV is the present value of the loan, which is $5250

r is the interest rate as a decimal, which is 5.3% ÷ 100 = 0.053

t is the time period in years, which is 24 months ÷ 12 months/year = 2 years

Substituting the values into the formula, we get:

FV = $5250 (1 + 0.053 * 2)

FV = $5250 (1.106)

FV = $5807.65

So, the future value of the loan is $5807.65. This is the amount Lynne will have to repay to her grandmother after 24 months, including the interest earned.

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Answer:

Down 2 and a flip with (-1,3)(1,0)(2,3)and(1,4)

Step-by-step explanation:

hope this works

Sequence of transformations that maps quadrilateral ABCD onto quadrilateral A"B"C"D".

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation or dilation.

The translation is moving a function in a specific direction, rotation is spinning the function about a point, reflection is the mirror image of the function, and dilation is the scaling of a function.

Given,

Quadrilateral ABCD and A"B"C"D" in the graph.

Transformation of quadrilateral ABCD to A"B"C"D"

By the graph, Steps of transformation are as follows

Hence,

Reflection of ABCD over Y-axis.

Shift of factor 2 downwards.

are the steps to transform ABCD to A"B"C"D".

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Solution is in the attachment!!

Answer: [tex]\Large\boxed{(0,\:3)}[/tex]

Step-by-step explanation:

Given the system of equations

[tex]1)2x+4y=12[/tex]

[tex]2)3x+y=3[/tex]

Multiply 4 on both sides of the 2) equation

[tex]3x\times (4)+y\times(4)=3\times(4)[/tex]

[tex]12x+4y=12[/tex]

Update the system of equations

[tex]1)2x+4y=12[/tex]

[tex]2)12x+4y=12[/tex]

Subtract the 1) equation from the 2) equation

[tex](12x+4y)-(2x+4y)=(12)-(12)[/tex]

Expand the parenthesis and simplify

[tex]12x+4y-2x-4y=12-12[/tex]

[tex](12x-2x)+(4y-4y)=0[/tex]

[tex]10x+0=0[/tex]

[tex]10x=0[/tex]

Divide 10 on both sides

[tex]10x/10=0/10[/tex]

[tex]x={0}[/tex]

Substitute the x value into one of the equations

[tex]3(0)+y=3[/tex]

[tex]0+y=3[/tex]

[tex]y=3[/tex]

The number of sequences of seven ternary digits containing a single 1 and a single 2 is given as follows:

42.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When elements repeat [tex]n_1, n_2, n_3, \cdots, n_n[/tex] times, the number of arrangements is given as follows:

[tex]A_{n}^{n_1, n_2, n_3, \cdots, n_n} = \frac{n!}{n_1!n_2!n_3! \cdots n_n!}[/tex]

In this problem, we have an arrangement of seven elements, in which:

Hence the number of sequences is given as follows:

N = 7!/(5! x 1! x 1!)

N = 7 x 6

N = 42.

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At this rate, Earl should receive $54 from his grandmother when he turns 18.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

The table shows how much money Earl's grandmother gave him each birthday.

Age   Birthday Money

5       15

8       24

10     30

18       ?.

Here, we find the common ratio,

15/5 = 3,

24/8 = 3.

Hence, r = 3.

Now, the missing value,

= 18 x r

= 18 x 3

= 54.

Therefore, Earl  will receive $54.

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Answer:

Green plants use sunlight and carbon dioxide from the atmosphere to produce carbohydrates by the process of photosynthesis. Since, plants produce food for themselves, they are known as producers.

Step-by-step explanation:

Answer:

32ft

Step-by-step explanation:

Let's convert both the height of the person and the length of their shadow to feet so we can make a comparison.

1 foot = 12 inches

So the person's height in feet is:

5 feet + 6 inches / 12 inches/foot = 5.5 feet

The rule applied here is the concept of similar triangles. If the shadow of the person and the shadow of the flagpole are in the same proportion to their respective heights, then the two triangles formed by their heights and shadows are similar triangles. This means that the ratio of their heights to their shadow lengths is constant.

So, we can set the ratio of the person's height to their shadow length equal to the ratio of the flagpole's height to its shadow length and solve for the flagpole's height. This is done using the formula:

(person's height) / (person's shadow length) = (flagpole's height) / (flagpole's shadow length)

This is known as the proportionality rule, which states that two similar figures have the same ratios of corresponding sides.

Now, we have:

5.5/44 inches = x/16 feet

Cross multiplying, we get:

5.5 * 16 = x * 44

Solving for x:

x = 5.5 * 16 / 44

x = 32 feet

Therefore, the height of the flagpole is 32 feet.

Maureen's pension would be $50,035.20.

What is Percentage?

To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

First, we need to calculate the average of Maureen's three highest salaries:

Average = (107,000 + 107,800 + 108,198) / 3

Average = 322,998 / 3

Average = 107,666

Next, we need to calculate 1.56% of this average:

Percentage = 1.56% * 107,666

Percentage = 1,667.84

Finally, we multiply this percentage by the number of years worked to find the pension:

Pension = 30 * 1,667.84

Pension = 50,035.20

So, Maureen's pension would be $50,035.20.

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The required difference between ratios, rates, and unit rates has been shown.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Ratios, rates, and unit rates are the fraction value of one with respect to the others. the basic difference between the ratios, rates, and unit rates is given as ratios are the fraction between either dependent or non-dependent values, while rates are changes of value with respect to other values. unit rate is a change of value per unit change in the respective value.

Thus, the required difference between ratios, rates, and unit rates has been shown.

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Answer:

a) 8 b) x= 8

Step-by-step explanation:

the coordinate of x is 8 because its a straight line nad the equation is x =8

Angle NOM = 59° because it is vertically opposite angle POQ

Angle STU = 96°

The theorem of triangles refers to various mathematical statements or propositions that describe relationships between the sides and angles of a triangle.  These theorems have various applications in fields such as mathematics, physics, engineering, and computer graphics.

In question 1; Angle NOM = 59° because it is vertically opposite angle POQ

In question 2; Angle UVT = Angle VUT = 42°

Angle UTV = 180 - 2(42)

= 96°

Then;

Angle STU = 96° (The exterior angle of the triangle is equal to the sum of two opposite interior angles).

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12.403 can be expanded in the following manner -

[tex]10 + 2 + \frac{4}{10} + \frac{0}{100} + \frac{3}{1000} \\ [/tex]

hope helpful! ;-;

Answer:

10 + 2 + 4/10 + 3/1000

Step-by-step explanation:

Hope it helps! =D