3 times 2 cubed + 5 squared-18 divided by 6

The definite value of f(x) when x approaching to 3 is 14

What is limit of function ?

In mathematics, limits are the values that a function (or sequence) approaches when an input (or index) approaches a particular value. Limits are essential for calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.

Here, the function given as :

f(x) = x^2+2x-1

and it is to find the value of f(x) when x approaching to 3 that is :

\(\lim_{x \to 3}\) f(x) = \(\lim_{x \to 3}\) x^2+2x-1

Now, substitute x equals to 3 in f(x) to get a definite value of f(x) :

\(\lim_{x \to 3}\) f(x) = 3^2+2 x 3 -1

\(\lim_{x \to 3}\) f(x)  = 9 + 6 -1

\(\lim_{x \to 3}\) f(x) = 14

Therefore, the definite value of f(x) when x approaching to 3 is 14 .

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Answer: 9.7 seconds

Step-by-step explanation:

\(16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)

The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is 18%.

To find the percent of the total area between two z-scores, we need to calculate the area under the standard normal curve between those two z-scores.

Using a standard normal distribution table or a statistical software, we can find the area to the left of each z-score and subtract the smaller area from the larger area to find the area between the z-scores.

For z = -1.5, the area to the left of z = -1.5 is approximately 0.0668.

For z = -0.7, the area to the left of z = -0.7 is approximately 0.2420.

The area between z = -1.5 and z = -0.7 is:

Area between z = -1.5 and z = -0.7 = Area to the left of z = -0.7 - Area to the left of z = -1.5

= 0.2420 - 0.0668

= 0.1752

To convert this area to a percentage, we multiply by 100:

Percentage of the total area between z = -1.5 and z = -0.7 = 0.1752 * 100 ≈ 17.52%

Rounding to the nearest integer, the percent of the total area between z = -1.5 and z = -0.7 is 18%.

The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is approximately 18%.

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Answer:

B. 28 degrees

Step-by-step explanation:

To determine the price the student-athlete should charge for each hot dog to break even, we need to consider the total costs she incurs, including the vendor fee, equipment cost, and the cost per hot dog. By dividing the total costs by the anticipated number of hot dogs sold, we can find the price per hot dog that would allow her to break even.

The total costs for the student-athlete include the vendor fee of $3000 and the equipment cost of $4500, which sums up to $7500 for the season. Additionally, she incurs a cost of $0.35 per hot dog sold. With an anticipation of selling 2000 hot dogs, the total cost for the hot dogs would be 2000 x $0.35 = $700.

To break even, the total revenue from selling the hot dogs should cover the total costs. Therefore, the price per hot dog should be set in such a way that the revenue from selling 2000 hot dogs equals $7500. Dividing the total costs ($7500) by the number of hot dogs (2000), we find that the student-athlete should charge $3.75 per hot dog in order to break even. This price per hot dog would allow her to cover all her expenses and reach the break-even point.

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Cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.

Cyclic Redundancy Checks (CRC) work as an error-detecting method used to ensure data integrity during transmission or storage. The process involves the following steps:

1. A predetermined polynomial (called the generator polynomial) is chosen for the CRC algorithm.

2. Before transmitting data, the sender divides the original data by the generator polynomial, using binary division.

3. The remainder obtained from the division is treated as the CRC value.

4. The sender appends the CRC value to the end of the original data, forming the transmitted message.

5. The receiver, upon receiving the message, performs the same binary division using the same generator polynomial.

6. If the remainder from the receiver's division matches the CRC value sent by the sender, it is assumed that the data is error-free.

7. If the remainder does not match, the receiver knows that an error occurred during transmission and can request the sender to retransmit the data.

In summary, cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.

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Answer:

1. y < -12

2. x > -12

Step-by-step explanation:

Just create a number line with the arrow going towards the direction that the greater/less than symbol is pointing

The slope intercept form of the equation of the line graphed on the coordinate plane below will be y=-3x -1.

As we know, The slope intercept form of a straight line is y=mx + c, where m is the gradient which is the Tanθ where θ is the angle between the line and the x-axis. And C is the interception point on the y-axis.

To find the gradient, we can calculate Δy/Δx. From the graph given we can take two points on the line with the coordinates (1,-4) and (0,-1). From this, we can calculate the gradient :

⇒\(\frac{(y2-y1)}{(x2-x1)}\)

⇒\(\frac{(-1)-(-4)}{0-(1)}\)

⇒-3

And , from the figure we can see the line is intersecting the y-axis -at -1.

So, putting the values in y=mx+c will give us y=-3x -1

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Answer:

D. 29

Step-by-step explanation:

If a = 6 and b = 5, fill in the numbers in place of the variables (letters) in 4a + b

= 4•6 + 5

= 24 + 5

= 29

4a means 4 times a. Multiply first, and then add.

Answer:

5:4, 5 to 4

Explanation:

Given the ratio 5/4, we can also write it in the forms below:

Answer: B

Step-by-step explanation:

 In the systems of equation it already gives you the solution for x  which is -2 so all you have to do is substitute -2 into the first equation and solve for y.

y= 2/3x + 3    

x= -2

Substitute x for -2

y = \(\frac{2}{3}* \frac{-2}1} + 3\)  

y= \(\frac{-4}{3}\) + \(\frac{3}{1}\)    

y = \(\frac{5}{3}\)  

so now you have the solution like this \((-2,\frac{5}{3})\)

Answer:

Pam has 1/2 of the cake and liz has 1/4 of the cake and then sam has 3 1/8 of the cake

Step-by-step explanation:

Try to put it in your own words

The volume of the solid is 0 cubic units.

Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.

The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.

The volume of the solid is given by the definite integral:

V = ∫_\({y=2}^{1} A(y) dy\)

Where A(y) is the area of the cross-section at y. Since the cross-sections are squares, we know that A(y) = \(y^{2}\).

So, the volume is given by:

V = ∫_\({y=2}^{1} y^{2} dy = [\frac{y^{3} }{3} ]_{y=2}^{y=1} = (\frac{8}{3} - (\frac{2^{3} }{3}= (\frac{8}{3}-\frac{8}{3} ) =0\)

The volume of the solid is 0 cubic units.

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We are asked to find the area of the region inside the circle and outside the cardioid. To do so, we will use a double integral to calculate the area of the region.

Answer:

To find the area of the region, we can use a double integral in polar coordinates. The region can be described by the inequalities 0 ≤ r ≤ 4cos(theta) and 1 + cos(theta) ≤ r ≤ 4cos(theta). The limits of integration for theta are 0 ≤ theta ≤ pi/2.

The integral for the area is given by:

A = ∫[0,pi/2] ∫[1+cos(theta),4cos(theta)] r dr dtheta

Solving this integral, we get:

A = ∫[0,pi/2] [1/2(16cos^2(theta) - (1+cos(theta))^2)] dtheta

A = ∫[0,pi/2] [7cos(theta) - 3/2cos^2(theta) - 1/2] dtheta

A = [7sin(theta) - 3/2sin^3(theta) - theta/2] evaluated from 0 to pi/2

A = (7/2) - (3/8) - (pi/4)

A = 15/8 - pi/4

Therefore, the area of the region inside the circle r = 4cos(theta) and outside the cardioid r = 1 + cos(theta) is 15/8 - pi/4 square units.

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The conclusion that can be made given the slopes of the quadrilateral is that: since the slopes of the opposite sides are equal, the opposite sides are parallel, therefore the quadrilateral is a parallelogram. (Option A is correct).

Recall:

The slopes given shows are:

-1/2, 3/2, -1/2, and 3/2

This implies that the quadrilateral has two pairs of equal sides that are parallel to each other.

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Answer:

answer is B

or

[  6  2  |  618  ]

[  1  1  | 165  ]

Step-by-step explanation:

did the test and got it right

The augmented matrix represents the situation is given as, \(\begin{bmatrix}6 & 2 | & 618 \\1 & 1 |& 165 \\\end{bmatrix}\). Then the correct option is B.

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.

Let x be the number of the adults and y be the number of the children.

Adults were charged $6, and children were charged $2.

The total amount of money collected was $618.

6x + 2y = 618

A total of 165 people attended the opening night of a school play.

x + y = 165

The equation can be written in the form of matrix form. Then

\(\begin{bmatrix}6 & 2 | & 618 \\1 & 1 |& 165 \\\end{bmatrix}\)

Then the correct option is B.

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Answer:

its 0 slope

Step-by-step explanation:

Answer:

(x+6)*(x+6)

Step-by-step explanation:

Answer:52

Step-by-step explanation:

Use pemdas :D

10^2+4-18+2-7*5-1

100+4-18+2-(7)(5)-1

104-18+2-(7)(5)-1

86+2-(7)(5)-1

88-(7)(5)-1

88-35-1

53-1

52

THE ANSWER TO YOUR PROBLEM!

52

THE ANSWER TO THE ANSWER TO YOUR PROBLEM!

10^2=100

10^2+14=114

10^2+4-18=86

10^2+4-18+2=88

10^2+4-18+2-7=81

10^2+4-18+2-7*5=83

10^2+4-18+2-7*5-1=52!

Hope i helped!-Animefan28

Answer:

a) 6

b) 37.5

c) 6th term

Step-by-step explanation:

a) plug in 2 for n

3(2)^2/2

6

b) plug in 5 for n

3(5)^2/2

37.5

c) since 5 is 37.5, I am going to check 6

3(6)^2/2

54

The 6th term will be the first to have a value higher than 50

Answer:

y =(2/3)x + 80

Step-by-step explanation:

to get the slope.. change in y/change in x  in two points.

so use the points (0,80) and (30,100) and you get 2/3

you know the intercept, where x=0 (0,80) therefore the equation is 2/3x + 80

Answer:

x+1

if it helps let me know by voting

Step-by-step explanation:

Answer:

3x+(-2x-4)+5 would be one of plenty other possibilities, it would help if we knew what x was equal to

Step-by-step explanation:

The table represents two different functions, where function g(x) is the exponential function

For a function to be an exponential function, the following must be true about the function:

\(r = \frac{y_{n+1}}{y_n}\)

Using the table of values (see attachment), we have:

Function f(x)

r = 12147367/11833485.4 ≈ 1.026525

r = 12464241.8/12147367 ≈ 1.026086

Function g(x)

r = 12112204/11412611 ≈ 1.0613

r = 12854683/12112204 ≈ 1.0613

Notice that the values of r in the function g(x) are the same

Hence, the exponential function is the function g(x)

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None of the wind gusts (17, 22, 8, 13, 19, 36, and 14) fall below -0.5 or above 35.5, there are no outliers in this data set. Therefore, the correct answer is D) none.

To identify any outliers in the data set, we can use a common method called the 1.5 interquartile range (IQR) rule.

The IQR is a measure of statistical dispersion and represents the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. According to the 1.5 IQR rule, any value below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR can be considered an outlier.

To determine if there are any outliers in the given data set of wind gusts (17, 22, 8, 13, 19, 36, and 14), let's follow these steps:

Sort the data set in ascending order: 8, 13, 14, 17, 19, 22, 36.

Calculate the first quartile (Q1) and the third quartile (Q3).

Q1: The median of the lower half of the data set (8, 13, 14) is 13.

Q3: The median of the upper half of the data set (19, 22, 36) is 22.

Calculate the interquartile range (IQR).

IQR = Q3 - Q1 = 22 - 13 = 9.

Step 4: Identify any outliers using the 1.5 IQR rule.

Values below Q1 - 1.5 × IQR = 13 - 1.5 × 9 = 13 - 13.5 = -0.5.

Values above Q3 + 1.5 × IQR = 22 + 1.5 × 9 = 22 + 13.5 = 35.5.

Since none of the wind gusts (17, 22, 8, 13, 19, 36, and 14) fall below -0.5 or above 35.5, there are no outliers in this data set.

Therefore, the correct answer is D) none.

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Step-by-step explanation:

The distance traveled over 9 hours at a speed of 840 km/h is 7,560 km.

Speed can be thought of as the rate at which an object covers distance.

A fast-moving object has a high speed and covers a relatively large distance in a given amount of time, while a slow

moving object covers a relatively small amount of distance in the same amount of time.

To calculate the distance traveled over 9 hours at a speed of 840 km/h, follow these steps:

1. Identify the time and speed given in the student question: 9 hours and 840 km/h.

2. Use the formula for distance:

distance = speed × time.

3. Plug in the values:

distance = 840 km/h × 9 hours.

4. Calculate the distance:

distance = 7,560 km.

So, the distance traveled over 9 hours at a speed of 840 km/h is 7,560 km.

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The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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