A function is given.
g(t) = t4 − t3 + t2; t = −6, t = 6
(a) Determine the net change between the given values of the variable.


(b) Determine the average rate of change between the given values of the variable.

The absolute value inequalities for the different lengths are

1) 4.19 ≤  x ≤  4.21

2) 3.3 ≤  x ≤  3.7

What is an absolute value inequality?

The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|.

An expression using absolute functions and inequality signs is known as an absolute value inequality. One example of an absolute value inequality with a larger than symbol is the statement |x + 3| > 1.

1)  length x = 4.2 cm with a tolerance of 0.01 cm

Absolute value inequality is:

|x - 4.2| ≤ 0.01

This can be written as:

           x ≤ 4.21

            x ≥ 4.19

2)  length x =  3.5 cm with a tolerance of 0.2 cm

Absolute value inequality is:

|x - 3.5| ≤ 0.2

This can be written as:

           x ≤ 3.7

            x ≥ 3.3

Therefore the absolute value inequalities for the different lengths are

1) 4.19 ≤  x ≤  4.21

2) 3.3 ≤  x ≤  3.7

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The probability that the sum of the ticket is 5, expressed as a percentage is 30%

The probability that an event will occur can be found by the ratio of the number of times the event occurs to the number of all possible events.

The five tickets in the box = 1, 2, 3, 4, 3

The tickets that sum to 5 are; 1 and 4, 2 and 3

The probability that the first ticket picked is 1 = 1/5

The probability that the next ticket picked is a 4 = 1/(5-1) = 1/4

Therefore, the probability of picking a 1 and 4 = (1/5) × (1/4) = 1/20

Similarly, the probability of picking a 4 and then a 1 is 1/20

The probability of picking tickets with numbers 1 and 4 in either order therefore = 2 × 1/20 = 1/10

The probability that the first ticket drawn is 2 = 1/5

The probability that the next ticket picked is a 3 = 2/(5-1) = 1/2

Therefore, the probability to draw a 2 and 3 = (1/5) × (1/2) = 1/10

The probability that the first ticket picked is 3 = 2/5

The probability that the next ticket picked is a 2 = 1/(5-1) = 1/4

Therefore, the probability of picking a 3 and 2 = (2/5) × (1/4) = 2/20 = 1/10

The probability of picking a 2 and a 3 in either order is therefore;

1/10 + 1/10 = 2/10 = 1/5

The probability that the sum of the ticket is 5, is the sum of the probabilities of picking a 1 and a 4 and the probability of picking a 2 and a 3, which is; 1/10 + 1/5 = 3/10 = 0.3

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Answer:

Below

Step-by-step explanation:

r = 1/2 diameter = 4 x^2 y^2

Volume = pi  r^2 h =

            pi  (4 x^2 y^2 )^2   * ( 12 x^2 y^2 ) =

               16 x^4 y^4   *  12 x^2 y^2  * pi

             =  192 x^(4+2) y^(4+2)  pi

             = 192 x^6 y^6  pi

The graph of the linear function h has slope the function h in the form

h(x) = 8x + 9.

Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.

As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.

Since f(x) = axe + b is the typical slope-intercept form of a linear function,

an is the slope (rate of change), and b is the y-intercept (initial value).

g = -12x + 100 is the necessary linear function, which is what has been presented.

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Answer:

y = |x - 3| - 1

Step-by-step explanation:

The vertex of the absolute value function graphed is (3, -1). The formula for absolute value is y = a |x - h| + k, where (h, k) is the vertex. The a stretches the graph, although this graph isn't stretched. So a is 1, which is the same as multiplying by 1. Plugging 3 as h and -1 as k into the formula results in y = |x - 3| - 1.

Find the value of day/dx when X = 1 and when Y = 1. I would like to answer correct but Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.

The solution set to the given inequality is (−∞, 2.5].

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is 8(2x-3) ≤ 20-4.

Here, 8(2x-3) ≤ 16

Divide 8 on both the sides of an inequality, we get

2x-3≤2

Add 3 on both the sides of an inequality, we get

2x≤5

Divide 2 on both the sides of an inequality, we get

x≤2.5

Convert the inequality to interval notation.

(−∞, 2.5]

Therefore, the solution set is (−∞, 2.5].

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Answer:

Let's call the number of white boards that Mr. Kelso purchased "W", the number of sharpies "S", and the number of glue sticks "G". We know the following information:

W = 5G

S = G + 10

And we also know the total cost of the items:

0.79W + 1.56S + 0.85G = 91.92

We can use the first equation to substitute for W in the second equation:

0.79(5G) + 1.56(G + 10) + 0.85G = 91.92

Expanding and simplifying the equation:

4.95G + 1.56G + 16.6 + 0.85G = 91.92

7.36G + 16.6 = 91.92

7.36G = 75.32

G = 10.25

So Mr. Kelso purchased 10 glue sticks. Using the first equation, we can find that he purchased 5 * 10.25 = 51 white boards. And using the second equation, we can find that he purchased 10.25 + 10 = 20.25 sharpies.

Since the number of each item must be a whole number, we round up or down to the nearest integer. In this case, it would make sense to round up the number of sharpies to 21. So Mr. Kelso purchased 51 white boards, 21 sharpies, and 10 glue sticks.

Answer: a) 1.57 m .

b) 637.79 turns

Step-by-step explanation:

a) The circumference of the wheel can be used to determine how far the vehicle has travelled after making one full turn.

Circumference = 2πr = 50π

C = 157 cm

b)By dividing the entire distance traveled by the diameter of the wheel, we can determine how many times the wheel will turn over a ride of 1 km (1000 meters): 1000 m / 1.57 m = 637.79 turns.

The ratio that is equivalent to the greatest fraction is B. 8:4.

A ratio is a relative size or value contained in another quantity.  It is computed as the quotient of the smaller and larger values.

Ratios are fractional values, which we can depict as fractions, decimals, or percentages.

Ratios are also depicted using the ratio symbol (:), describing the numerical relationship between two or more values or variables.

The sum of ratios = 8

5/8 = 0.625

The sum of ratios = 12

8/12 = 0.67

The sum of ratios = 9

2/9 = 0.22

The sum of ratios = 14

9/14 = 0.64

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The required paragraphs regarding with given expression f(x) = x²-2x+1/4x+5 have been explained later in the section.

A rational expression is a fraction in which the numerator and denominator are polynomials.

Here,
a) To determine the values of x that make the rational function f(x) equal to 0, we need to solve the equation:

x² - 2x + 1 = 0

Next, we can factor the quadratic on the left-hand side of the equation:

(x - 1)(x - 1) = 0

The quadratic is a perfect square, and we can see that it is equal to 0 when x = 1. So, the value of x that makes the rational function 0 is x = 1.

b) To determine the values of x where the rational function f(x) is undefined, we need to look for values of x that would make the denominator, 4x+5, equal to 0. If the denominator is equal to 0, then we would be dividing by 0, which is undefined.

So, we set the denominator equal to 0,

4x + 5 = 0

4x = -5

x = -5/4

Therefore, the value of x where the rational function is undefined is x = -5/4.

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Answer:

do it yourself

Step-by-step explanation:

Answer:

A. The transformation preserves distances and angles between points.

B. The transformation preserves the orientation of the figure.

C. The transformation involves a sliding of the figure in a fixed direction.

D. The transformation results in a change of size or shape of the figure.

E. The transformation results in a reflection of the figure.

For the transformation to be a translation, statements A, B, C and E are not true, while statement D is true.

Step-by-step explanation:

The solution is, x =48.6

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have,

Since this is a right triangle, we can use trig functions

sin theta = opp side / hypotenuse

sin x = 54 /72

Taking the inverse sin of each side

sin ^ -1( sin x) =sin ^-1 ( 54/72)

x = 48.59037789

To the nearest tenth

x =48.6

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25+25=50,4+4=8;50+8=58

In this exercise we have to use the knowledge of excel to explain some functions that can be used, as:

In excel cell a division formula can be written as: =(A4+B4+C4+D4+E4)/5

If you track your daily earnings in an Excel spreadsheet, you can use the same spreadsheet to estimate your forecasted earnings for any period of time. You can use Excel's AVERAGE function to find out your average daily income. Multiply your average daily sales by the number of days specified to estimate how much profit you could make over time.

In mathematics, the average of a list of data represents the central value of the set of data. Mathematically defined as the ratio of the sum of all data and the number of items in the list. In statistics, the mean of a particular set of numerical data is also called the mean. For example, the average of 2, 3, 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the center value of 2, 3, and 4. So the meaning of average is to find the average of a group of numbers.

mean = sum of values ​​/ number of values

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Answer:

Step-by-step explanation:

a) The second stop is the third floor:

The first stop is the first floor, so the probability of going up from the first floor is 3/4.

The next stop is the third floor, so the probability of going up from the second floor (which is the first floor in this scenario) to the third floor is 3/4.

The probability of both events happening is the product of the individual probabilities: (3/4) * (3/4) = 9/16.

b) The third stop is the fourth floor:

The first stop is the first floor, so the probability of going up from the first floor is 3/4.

The next stop is the third floor, so the probability of going up from the first floor to the third floor is 3/4.

The next stop is the fourth floor, so the probability of going down from the third floor to the fourth floor is 1/4.

The probability of all three events happening is the product of the individual probabilities: (3/4) * (3/4) * (1/4) = 3/16.

c) The fourth stop is the first floor:

The first stop is the first floor, so the probability of going up from the first floor is 3/4.

The next stop is the third floor, so the probability of going up from the first floor to the third floor is 3/4.

The next stop is the fourth floor, so the probability of going down from the third floor to the fourth floor is 1/4.

The next stop is the first floor, so the probability of going down from the fourth floor to the first floor is 3/4.

The probability of all four events happening is the product of the individual probabilities: (3/4) * (3/4) * (1/4) * (3/4) = 9/64.

The expression represents a quintic polynomial with 4 terms. The constant term is -6, the leading term is x⁵/2, and the leading coefficient is 1/2.

A polynomial expression is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.

From the polynomial expression given:

[tex]\dfrac{1}{2}x^5 - 6 - x^4 -5x^2[/tex]

The degree of a polynomial is the highest degree of its terms which helps us to determine the type of polynomial (quintic polynomial). The constant term is -6.

The leading term in a polynomial is the term with the highest degree = x⁵/2. The leading coefficient of a polynomial is the coefficient of the leading term is 1/2.

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Answer:

quadrinomial, 4, -6, 1/2x^5, 1/2

Step-by-step explanation:

quadrinomials are polynomials with 4 terms

constant is the number with no variable

leading term is the term at the beginning

leading coefficient is the number at the beginning

If a TCP receiver advertises a window size of 6,353 bytes, and with a link transmission rate 10 Mbps an end-to-end propagation delay of 14.4 ms, then the utilization is 0.4%.

What is Round trip time?

The round-trip time (RTT) is the time it takes from when a browser submits a request to when it receives a response from a server, measured in milliseconds.

The time it takes for a segment to be transmitted over the link is:

time per segment = 1,126 bytes / 10 Mbps = 0.00009008 seconds

The end-to-end propagation delay is 14.4 ms, or 0.0144 seconds.

The time it takes for an ACK to be sent back from the receiver is the propagation delay plus the time it takes for the ACK segment to be transmitted over the link:

time for ack = 0.0144 seconds + (1 segment / 10 Mbps) = 0.014508 seconds

The time it takes for the sender to receive an ACK after sending a segment is the time it takes for the segment to be transmitted, plus the time it takes for the ACK to be sent back:

round trip time = time per segment + time for ack = 0.00009008 + 0.014508 = 0.0145

The number of segments that can be in flight at any given time is the window size divided by the segment size:

segments in flight = 6,353 bytes / 1,126 bytes = 5.645 segments

We can now calculate the maximum sending rate of the sender by dividing the number of segments in flight by the round-trip time:

max sending rate = segments in flight / round trip time = 387.165 segments per second

The utilization of the link is the sending rate divided by the link rate, multiplied by 100 to get a percentage:

utilization = (max sending rate / 10 Mbps) * 100 = 0.00387165 * 100 = 0.387165%

Rounding to one decimal place, the utilization is 0.4%.

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The value of the expression represented by |M × N| is 64

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

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

M = 8 i.e.  {m, a, t, h, e, i, c, s}.

N = 8 i.e. {n, e, v, r, t, h, l, s}.

So, we have

|M × N| = 8 * 8

Evaluate

|M × N| = 64

Hence, the value of |M × N| is 64

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The solution is, he is now 21 yrs old.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

William is 6 years older than Camila.

Nine years ago he was twice Camila’s age.

let, he is now = x yrs

Camila’s age = y yrs.

so, we get,

x-y = 6 .....(1)

and, x-9 = 2(y-9) ....(2)

solving we get,

x-9 = 2(x-6-9)

or, x = 21

Hence, The solution is, he is now 21 yrs old.

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place g(x) as the value x, into p(x)

to gain p(g(x)) = (1 / SqrRt(x) )² - 4

simplify = ( 1 / x ) - 4

find domain

x =/= 0 (undefined) & (1/4)

The constant of proportionality in the equation is 0.3.

Firstly, there is proportional relationship.

Two values x  and  y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called constant of proportionality.

WE are given that number of candies sold can be determined by the equation: T = 0.3c, where T is number of candies and c is the number of children.

0.3 = constant of proportionality

0.3 = p / n

which is the ratio of p to n

The constant of proportionality is the ratio between the two quantities that are directly proportional.

Therefore,

0.3 is the constant of proportionality in the equation.

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The data in the table represents a linear function, as when x is increased by one, y is subtracted by a constant amount of 9.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

For this problem, the function is classified as linear, as the difference between consecutive terms is 9, while the ratios are different.

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Answer:

The correct answer is D.

Step-by-step explanation:

D. y = 0.8x + 4.

Answer:

It would be C.

Step-by-step explanation:

It would be C.

JKP, the smaller triangle, needs to be turned into J'K'P' to show proof the the triangles are similar. So the first thing you would have to do, because J'K'P' is exactly 2 times bigger than JKP, is multiply the x and the y by 2. However, this shifts the triangle, and we need the triangles to overlap to prove they are also the same size. So comparing the x and y values after we increase the sides of JKP, we would see we need to subtract the x value by 3, and the y value by 2.

Answer:

2570 is ten times smaller than 25700

Step-by-step explanation:

The table to represents the total cost for the different numbers of books ordered is:

Number of books     Spending     Total cost

1                                     $41            $44

2                                    $65           $71

3                                    $125          $134

An expression is written with one or more terms with addition, subtraction, multiplication, and division.

Example:

2.2 + 3x + 4y = 7 is an expression.

3 + 5x = 9 is an expression.

We have,

The book cost = $3

Now,

Spendings = $41, $65, or $125

Now,

Table:

Number of books     Spending     Total cost

1                                     $41            41 + 3 = $44

2                                    $65           65 + 6 = $71

3                                    $125          125 + 9 = $134

Thus,

The table for the total cost is given above.

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Answer:

Step-by-step explanation:

its 11

ignore bllllllllllldjbjddddddddddddddddddddddddd

Answer:yo no se como ablar ingles

Step-by-step explanation: perdoname

Answer:

12 [tex]in^{3}[/tex]

Step-by-step explanation:

Volume is the length x  the width x the height

The rectangle of the bottom would be

(4)(2)(1) = 8

The rectangle on the top would be

(1)(2)(2) = 4

8 + 4 = 12 [tex]in^{3}[/tex]