Match the vocabulary terms to the correct definitions.piecewise function

Answer:

The percentage rate of change of a function f(t) is given by:

(Δf / f) x 100

where Δf is the change in f and f is the original value of the function.

To find the largest value of t such that the percentage rate of change equals 100, we need to find the value of t for which:

(Δf / f) x 100 = 100

Simplifying, we get:

Δf / f = 1

This means that the change in f is equal to the original value of f.

So, we need to solve the equation:

f(t + Δt) - f(t) = f(t)

where Δt is the change in t.

Substituting the given function, we get:

[1 - 2(t + Δt) + 4(t + Δt)^2] - [1 - 2t + 4t^2] = 1 - 2t + 4t^2

Simplifying, we get:

-8tΔt + 8Δt^2 = 1

Since we are interested in the largest value of t, we can assume that Δt is a small positive number, such that Δt << t.

Ignoring the term Δt^2, we get:

-8tΔt = 1

Solving for Δt, we get:

Δt = -1 / (8t)

Substituting this value of Δt back into the equation -8tΔt + 8Δt^2 = 1, we get:

-8t(-1 / (8t)) + 8(-1 / (8t))^2 = 1

Simplifying, we get:

1 / t^2 = 1

Solving for t, we get:

t = 1

Therefore, the largest value of t such that the percentage rate of change equals 100 is t = 1.

In response to the question, we may say that  205 adults and 130 kids equation respectively attended the concert, for a total of 205 adults and 130 kids.

The equals symbol (=), which indicates equivalence, connects two statements in a mathematical equation. An algebraic equation's mathematical assertion proves the equality of two mathematical propositions. The equal sign, for instance, places a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. Use a mathematical formula to understand how the two sentences on opposite sides of a letter relate to one another. Usually, the logo corresponds to the particular programmed. An example would be 2x - 4 = 2.

Assume that "x" represents the proportion of adults who attended the performance and "y" represents the proportion of children.

The problem statement informs us that:

x + y = 335 —-(1) (1) (There are 335 persons present in all.)

The total amount of money gathered is $675 (2.5x + 1.25y).

1.25x + 1.25y = 418.75 —-(3) (3)

2.5x - 1.25x = 675 - 418.75

1.25x = 256.25

x = 205

205 + y = 335

y = 130

205 adults and 130 kids respectively attended the concert, for a total of 205 adults and 130 kids.

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Answer:

Step-by-step explanation:

b-y=55

The volume of the resulting block of wood is 576 in³. The correct option is the second option 576 in³

From the question, we are to determine the volume of the resulting block of wood.

From the given information,

The dimensions of the block of wood is 10 in. by 10 in. by 6 in.

First, we will calculate the original volume of the block of wood.

The original block of wood has a volume of

V = 10 x 10 x 6

V = 600 in³

Now, we will determine the volume og the hole that was cut through

The dimensions of the hole is 2 in. by 2 in. by 6 in.

Volume of the hole = 2 x 2 x 6

Volume of the hole = 24 in³

The resulting block would have a volume of

Volume of resulting block = 600 - 24

Volume of resulting block = 576 in³

Hence, the volume is 576 in³.

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After addressing the issue at hand, we can state that Therefore, function  g(-2) = 0 and g(4) = -4.

Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.

When x = -2, g(x) = 0.

When x = 4, g(x) = -4.

Therefore, g(-2) = 0 and g(4) = -4.

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The data in the triangle is not sufficient to find the asked values in the question.

The relationship in between sides and angles for non-right (oblique) triangles is known as the Law of Sines. It simply asserts that for all sides and angles of a given triangle, the ratio of the length of a side to the sine angle opposite this side is the same.

You must know between two angles but one side of the triangle (AAS or ASA) either two sides and an angle opposing one of them in order to employ the Law of Sines (SSA).

g/sinG = h/sinH = f/sinF

Where G, H and F are the angles and g, h and f are the angles' opposing sides.

Put the values:

g/sin136 = 13/sinH = 7/sinF

The three pairs of expression are-

HF/sin136 = 13/sinH ;   13/sinH = 7/sinF and g/sin136 = 7/sinF.

HF = 13*sin136/sinH

HF = 10.97/SinH

From the found 3 expression, each has two missing value.

Thus, the angles F and H is not possible to find.

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Answer:

To determine the flexible budget for the Cutting Department, we need to use the information provided to adjust the original budget for the actual level of production.

First, we need to calculate the variable cost per hour of production:

Variable cost per hour = Direct labor / Hours of production

Variable cost per hour = $37,260 / 4,140 hours

Variable cost per hour = $9

Next, we can use this variable cost per hour to calculate the flexible budget for the actual level of production:

Flexible budget = (Variable cost per hour x Actual hours of production) + Fixed costs

Flexible budget = ($9 x 4,500 hours) + $43,370

Flexible budget = $40,500 + $43,370

Flexible budget = $83,870

Therefore, the flexible budget for the Cutting Department, based on the actual level of production of 4,500 hours, is $83,870.

Answer: 9.60

Step-by-step explanation:

Labeled price = $ 12

Discount = 20% of labeled price = 12 x 20%

= 12 x 2 / 10 = 24 / 10 = $ 2.4

Sale price = Labeled price - Discount.

Sale price = $ 12 - $ 2.40 = $ 9.60

Thus the sale price of the case of soda is 9.60 $

Answer:

in absolute value you consider both the positive and negative side of the expression in the absolute bar.

Answer: y = 4/3x -3

Step-by-step explanation:

Answer:

y = 4

x = 4√2 or 5.66

Step-by-step explanation:

If the △ is a right △ with 1 angle 45o, then the other angle is also 45o. This △ will be isosceles right triangle with y = 4

Pythagorean theorem: c^2 = a^2 + b^2

x^2 = y^2 + 4^2

x^2 = 4^2 + 4^2

x^2 = 32

x = √32 = 4√2 = 5.66

Answer:

See below.

Step-by-step explanation:

For this problem, we are asked to find x, the hypotenuse.

There are a few ways to find the hypotenuse, but an easy way is to use the Pythagorean Theorem.

Represented as;

[tex]a^2 + b^2 = c^2\\(Short \ Leg)^2 + (Long \ Leg)^2 = (Hypotenuse)^2.[/tex]

We have 2 given values, the short leg and the long leg. We can begin solving for the hypotenuse.

Substitute:

[tex]40^2+42^2=c^2[/tex]

[tex]3364 = c^2[/tex]

Square Root the Equation:

[tex]\sqrt{3364} = \sqrt{c^2}[/tex]

[tex]c = 58.[/tex]

The Hypotenuse is 58. Our final answer is Letter D.

The two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.

What is combination ?

Combination refers to the number of ways a selection of items can be made from a larger set of items without regard to their arrangement. In other words, combinations are a way to calculate the total number of possible groups of items that can be formed, regardless of the order in which the items are selected. The formula for calculating the number of combinations is nCr, where n is the total number of items and r is the number of items being selected.

According to the question:
Let's start by finding the possible prices of the pie. Since the price must be an exact number of pence, we can convert the price range to pence by multiplying each value by 100:

£1.30 = 130 pence

£2.99 = 299 pence

We know that the price plus the 24% tip must be an exact number of pence. If we let x be the price of the pie in pence, then we can write this as:

x + 0.24x = 1.24x

Since 1.24 is not divisible by 5 (which we'll need for the change), we need to find two values of x that differ by a multiple of 5. One way to do this is to start with the lower bound and add multiples of 5 until we get a valid value:

x = 130: 1.24x = 161.2

x = 135: 1.24x = 167.4

x = 140: 1.24x = 173.6 (valid)

x = 145: 1.24x = 179.8

x = 150: 1.24x = 186.0 (valid)

x = 155: 1.24x = 192.2

x = 160: 1.24x = 198.4

So the possible prices of the pie are 140p and 150p. To find the possible amounts of change, we need to subtract each price from 500p (the value of the £5 note) and express the result as a combination of coins. For example:

Price = 140p, change = 360p = 3 x £1 + 1 x 50p + 1 x 10p

Price = 150p, change = 350p = 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p

Therefore, the two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.

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Answer:

Step-by-step explanation:

To find the expected difference in height between a child 49 months of age and a child 16 months of age, we need to first find the average height of each child and then find the difference between them.

For a child who is 49 months old, the average height can be found by substituting x = 49 in the given equation:

y1 = 2.9sqrt(49) + 20.1 = 42.7 inches

For a child who is 16 months old, the average height can be found by substituting x = 16 in the given equation:

y2 = 2.9sqrt(16) + 20.1 = 28.9 inches

Therefore, the expected difference in height between the two children would be:

y1 - y2 = 42.7 - 28.9 = 13.8 inches

So we can expect the child who is 49 months old to be, on average, 13.8 inches taller than the child who is 16 months old.

Answer:

the answer is c because every side of a triangle sides are he same so c is your answer

1) The system of inequalities that models this scenario will be:

6x + 3y ≤ 24

6x + 3y ≥ 4

2)
i) the solution for y is y ≤ 5 - 2x.
ii) the solution for y is y ≥ 3 - x.

3) The graph is attached accordingly.

a)
Let's use the variables x and y to represent the number of Mickey pretzels and Mickey bars, respectively, that Mrs. Tobie can buy. We want to ensure that at least four children get one snack each, so the inequality for the total number of snacks should be greater than or equal to 4.

Also, Mrs. Tobie has a budget of S24, so the cost of the snacks should be less than or equal to S24. Putting these together, we get:

6x + 3y ≤ 24 (budget constraint)

6x + 3y ≥ 4 (at least four snacks)

So the system of inequalities that models this scenario is:

6x + 3y ≤ 24

6x + 3y ≥ 4

b)

To solve for y in each inequality, we need to isolate y on one side of the inequality sign.

For the first inequality, we have:

x + y ≥ 3

Subtracting x from both sides, we get:

y ≥ 3 - x

So the solution for y is y ≥ 3 - x.

For the second inequality, we have:

6x + 3y ≤ 15

Dividing both sides by 3, we get:

2x + y ≤ 5

Subtracting 2x from both sides, we get:

y ≤ 5 - 2x

So the solution for y is y ≤ 5 - 2x.

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Step-by-step explanation:

For RIGHT  triangles the cos of an angle = adjacent LEG / hypotenuse

 so for THIS triangle   cos 55°  = x / 9.3

    re-arrange to    9.3 * cos 55° = x    

       use calculator to find x = ~ 5.3 units   (rounded)

Answer:

x = 5.3

Step-by-step explanation:

As triangle XYZ is a right triangle, and we have been given angle X, the side adjacent the angle, and the hypotenuse, we can use the cosine trigonometric ratio to solve for x.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for x:

[tex]\implies \cos 55^{\circ}=\dfrac{x}{9.3}[/tex]

[tex]\implies x=9.3 \cos 55^{\circ}[/tex]

[tex]\implies x=5.3342608...[/tex]

[tex]\implies x=5.3\; \sf (nearest\;tenth)[/tex]

Therefore, the value of x is 5.3 to the nearest tenth.

In this the point (-2,3) on the graph of f multiplied by the corresponding point (-2,2) on the graph of g yields the product (-2,6), which is equal to -8.

A coordinate plane is a two-dimensional surface composed of two number lines, one horizontal (x-axis) and one vertical (y-axis). It is used to graph points, lines, and other shapes. Each point is identified by a pair of numbers which indicate its position along the x and y axes. The x and y axes intersect at the origin and divide the plane into four quadrants.

The graph of fg can be found by first graphing both f and g on the same coordinate plane. From there, the graph of fg can be found by taking each point on the graph of f and multiplying it by the corresponding point on the graph of g. In this example, the point (x,y) on the graph of f is multiplied by the corresponding point (x,y) on the graph of g to form a new point (x,yz). This new point is then placed on the graph of fg.

Using the graphs of f and g provided, we can determine that (fg)(-2) = -8. To find this, first locate the point (-2,3) on the graph of f. Then, locate the corresponding point (-2,2) on the graph of g. The product of these two points is (-2,6). This means that (fg)(-2) = -8.

In summary, to find (fg)(-2) using the graphs of f and g, first graph both f and g on the same coordinate plane. Then, take each point on the graph of f and multiply it by the corresponding point on the graph of g. In this example, the point (-2,3) on the graph of f multiplied by the corresponding point (-2,2) on the graph of g yields the product (-2,6), which is equal to -8.

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That statement that best describes the relationship between x and y in the given equations is: d. In y = 25x, the value of y is 25 times the value of x, and in y = x + 25, the value of y is 25 more than the value of x.

In the equation y = 25x, the value of y is directly proportional to x and is 25 times greater than x. This means that as x increases, y increases by a multiple of 25. For example, if x = 2, then y = 50 (25 x 2), and if x = 4, then y = 100 (25 x 4).

In the equation y = x + 25, the value of y is equal to the value of x plus 25. This means that y is always 25 greater than x, regardless of the value of x. For example, if x = 2, then y = 27 (2 + 25), and if x = 4, then y = 29 (4 + 25).

The answer is option d.

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The width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.

The region contained inside the rectangle's perimeter is referred to as the area of the rectangle. In other terms, the area of a rectangle is the whole area that a rectangle encloses. Depending on the provided dimensions, this may be determined using the area of rectangle formula and a number of other techniques.

Let us suppose the width = x.

Then, length is given as:

l = x + 7

The area of the rectangle is:

A = lw

Substituting the values:

A = (x + 7)x

The perimeter of the rectangle is:

P = 2(l + w)

P = 2(x + 7 + x)

P = 2(2x + 7)

P = 4x + 14

Also, we have:

A = 2P

Substituting the values of area and perimeter:

4x + 14 = (x + 7)x

Simplifying the expression:

x^2 + 7x = 8x + 30

x^2 - x - 30 = 0

(x-6)(x+5) = 0

Since, width cannot be negative value we have:

x = 6.

l = 7 + 6 = 13 inches.

Hence, the width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.

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Using percentage, we can find:

1- 84600

2- 385400

3- 20811.6

4- 7576776

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage. This percent symbol can always be converted to a fraction or decimal equivalent by "dividing by 100".

Now in the question,

Downpayment = 18% of 470000

= 84600

original amount financed =

470000-84600

= 385400

Monthly payment = 5.4% of 385400

= 20811.6

Total payment in 30 years = 7576776

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Answer: 9·9 -36 +4.

Step-by-step explanation: 9x² -12x +4 for x=3. 9·3² -12·3 +4 = 9·9 -36 +4.

As a result, the probability of selecting a 7 and a jack from a regular deck of cards, one at a time and without replacement, is about 0.006 or 0.6%.

Probabilistic theory is a branch of mathematics that evaluates the probability of a certain occurrence or proposition occurring or being true. A danger is a number in the range between 0 and 1, whereas 1 signifies certainty and a probability of around 0 reflects how likely an event seems to be to occur. Probability seems to be a mathematical function for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences between equally as likely possibilities that result in a specific event.

The probability of selecting a 7 and a jack from a regular deck of cards, one at a time and without replacement, is as follows:

As a result, the odds of selecting a jack from the remaining cards are 4/51.

The product of these probabilities is the likelihood of selecting a 7 and a jack in sequence:

P(7) = P(7) x P(jack|7 not picked) = 4/52 x 4/51

When we simplify this expression, we get:

P(Jack and 7) = 16/2652

As a result, the likelihood of selecting a 7 and a jack from a regular deck of cards, one at a time and without replacement, is about 0.006 or 0.6%.

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Answer:

154%

Step-by-step explanation:

First, we need to calculate the increase in size of the privately owned farm:

increase = new value - old value

increase = 432 - 170

increase = 262

Next, we can use the formula to calculate the percent increase:

percent increase = (262 / 170) x 100%

percent increase = 1.54 x 100%

percent increase = 154%

Therefore, the percent increase in the size of privately owned farms in the country is 154%.

The sum of the infinite geometric series is: ²/₅

The formula for the sum of an infinite geometric series is;

[tex]S_{\infty} = \frac{a}{1 - r}[/tex]

where;

a is first term

r is common ratio

The first term is; a = ⁴/₁₅

Common ratio; r = ⁴/₉ ÷ ⁴/₁₅ = ⁵/₃

r = ²⁰/₂₇  ÷  ⁴/₉ = ⁵/₃

Thus;

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ (⁵/₃ - 1)

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ ²/₃

= ²/₅

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Answer:

How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;S_∞ = a/(1 - r)where;a is first termr is common ratioThe first term is; a = 4/15Common ratio; r = (4/9)/(4/15) = 5/3r = (20/27)/(4/9)  = 5/3Thus;S_∞ = (4/15)/((5/3) - 1)S_∞ = (4/15)/(2/3) = 2/5

Answer:

Step-by-step explanation:

(9/4 * 8/7) - (3/8*4/1) =

(72/28) - (12/8)

18/7 - 3/2

36/14 - 21/14

15/14 = 1 1/14

The value of the investment modeled by the function V(t) = 50(0.9)^t Decreases at a decreasing rate, starting with an initial value of 50.

We are given the investment value function V(t) = 50(0.9)^t. This function describes the value of an investment over time, t. Let's analyze the behavior of V(t) and find a statement that is supported by this function.

1. The initial value of the investment is V(0) = 50(0.9)^0 = 50(1) = 50. So, the investment starts with a value of 50.

2. The function V(t) contains a term (0.9)^t, which indicates that as time passes, the investment value decreases. This is because 0.9 is between 0 and 1, so raising it to a power of t (as t increases) results in a smaller value.

3. The rate of decrease is not constant, as the function is exponential, not linear. This means the value of the investment decreases at a decreasing rate over time.

Based on the behavior of V(t), the following statement is supported:

As time passes, the value of the investment modeled by the function V(t) = 50(0.9)^t decreases at a decreasing rate, starting with an initial value of 50.

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Answer:

To multiply polynomials, you can follow these steps:

Distribute each term of the first polynomial to each term of the second polynomial.

Combine like terms.

Simplify the resulting expression.

Here is an example:

(2x + 3)(x - 4)

Distribute:

2x(x - 4) + 3(x - 4)

Combine like terms:

2x^2 - 8x + 3x - 12

Simplify:

2x^2 - 5x - 12

So, (2x + 3)(x - 4) = 2x^2 - 5x - 12.

Step-by-step explanation:

Answer:

Gold ring = 6180

Step-by-step explanation:

Gold ring = ?

I = prt

= 19000 x 6% x 2

= 2180

Amount to be paid= 19000 + 2180

= 21180

gold ring = 21180 - 15000

= 6180

The equation for the logarithmic function that passes through (0,0) and (-5,3) is given as follows:

y = log2(-x + 1)

First we must consider the vertical asymptote of the logarithmic equation, which is given as follows:

x = 1.

As the function is defined for the values to the left of the vertical asymptote, the function was reflected over the y-axis, hence:

y = logb(-x + 1) + d.

When x = -1, y = 1, hence we can have a logarithm of base 2 with a vertical shift of zero, hence:

y = log2(-x + 1)

Which is the logarithmic function for the function graphed in this problem.;

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