What are the domain and range of f(x) = 2x-41?

Answer:

D. 24 Units

Step-by-step explanation:

tracing the points given we get a rectangle

the perimeter of a rectangle = 2a+2b

a=length

b= width

in this case a= 8

b= 4

the perimeter of a rectangle = (2*8)+(2*4)

the perimeter of a rectangle = 16+8

the perimeter of a rectangle = 24

Answer:

$17.30

Step-by-step explanation:

So each video game is $2.60 and Brian rented 5 of them.

5 * 2.60 = 13

He spent $13 on just the video games. Now, he also rented 1 DVD, priced at $4.30.

13 + 4.30 = 17.30

Brian spent a total of $17.30 on rentals in the past month.

Stay safe <3

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

Answer:

592 people must be surveyed

When subtracting several quantities, the number of decimal places in the result should match the quantity with the fewest decimal places or the highest level of precision for consistency and accuracy.

When performing subtraction, it is important to maintain consistency in terms of decimal places or precision. The number of decimal places in the result should match the quantity with the fewest decimal places among the numbers being subtracted.

For example, let's consider the following subtraction:

2.4567 - 1.23 = 1.2267

In this case, both numbers have four decimal places, so the result also has four decimal places.

However, if we have a situation like this:

3.45 - 1.236 = 2.214

In this case, the number being subtracted has three decimal places, so the result is rounded to three decimal places to maintain consistency.

The general principle is to consider the number with the fewest decimal places or the highest level of precision when determining the number of decimal places in the result of a subtraction operation. This ensures that the result is presented in a consistent and meaningful manner.

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The value of the smiley face provided in the question is 908.

The first step is to determine the value of each of the shapes.

The value of the rectangle would be determined first. Using the third given equation, let r represent the value of one rectangle.

(4 x r) + (2 x r) - (3 x r) = 15

4r + 2r - 3r = 15

3r = 15

r = 15 / 3 r

r = 5

The next step is to determine the value of the triangle. The second equation would be used. Let t represent the value of the triangle.

(3 x 5) + (4 x t) = 47

15 + 4t = 47

4t = 47 - 15

4t = 32

t = 32 / 4

t = 8

Finally, the value of the star would be determined. Let the value of the star be represented with s. Using the first equation:

5 + (3 x 8) - s = 17

5 + 24 - s = 17

29 - s = 17

s = 29 - 17

s = 12

Now, the value of the smiley face can be determined:

12 x (8  + 12 - 5) + 8(8 . 12 - 5)

12 x (15) + 8(91)

180 + 728 = 908.

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The quotient is 154. The remainder is 3.

What is a divisor?

In division, we multiply one number by any other number to produce a second number. Therefore, the dividend here refers to the number that is being divided. The divisor is the number that divides a given number. The quotient is the sum that we arrive at as a result. The remainder is the number that the divisor leaves after partially dividing the original number.

Given that 927 ÷ 6.

The dividend is 6 and the divisor is 927.

6) 927(100+50+4

   600

______

    327

    300

______

        27

        24

_______

            3

The remainder is 3. The quotient is 154.

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The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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The solutions of the inequality \(2x^{2} + x - 6 = 0\) are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form \(ax^{2} +bx + c = 0\), the solutions are \(x = -b +/-\sqrt{b^{2} -4ac} /2a\).

Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49

Solution 1: x = \(-b + \sqrt{b^{2} -4ac} /2a\) = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2

Solution 2: x = \(-b-\sqrt{b^{2} -4ac} /2a\)= (-1 - √49)/(2×2) = -8/4 = -2

So, the two solutions are 3/2 and -2.

The equation can also be written as,

\(2x^{2} +4x -3x-6=0\)

\(2x(x+2) -3(x+2) = 0\)

\((2x-3)(x+2) = 0\)

x = 3/2, -2

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Answer:

The sequence has '+3' each time, so the next will be 10

Step-by-step explanation:

it is 10 cuz it goes from -5 adding 3

The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).

In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).

"A number": This is represented by the variable x, which can take any value.

"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.

"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).

In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.

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Answer:

8 visits

Step-by-step explanation:

26+8 visits (1 dollar a visit)= 34

Answer:

8

Step-by-step explanation:

The Recurrence Relation T(n) for T(n) = 2n.T(n-1) + 12 2 is:

T(n) = 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0) = 2^n * n! * T(0).

To solve the given recurrence relation T(n) = 2n * T(n-1) + 12, we can use iteration or expansion methods. Let's use the expansion method to find an explicit formula for T(n).

Expanding the recurrence relation, we have:

T(n) = 2n * (2(n-1) * T(n-2) + 12) + 12

= 2n * 2(n-1) * T(n-2) + 2n * 12 + 12

= 2n * 2(n-1) * (2(n-2) * T(n-3) + 12) + 2n * 12 + 12

By continuing this process, we can observe a pattern. Each term in the expansion will be of the form 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0), where T(0) is the initial term.

The number of factors of 2 will depend on the value of n. We can see that for each term, the number of factors of 2 is n! (n factorial). Therefore, the explicit formula for T(n) is:

T(n) = 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0) = 2^n * n! * T(0).

In this case, T(0) represents the initial term of the sequence. Without knowing its value, we cannot provide a specific numerical solution. However, the above formula provides a general expression for T(n) in terms of n and T(0), satisfying the given recurrence relation.

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Answer:

yes .

Step-by-step explanation:

yes because the 7 percent is less than 2 dollars (1.4) , so her 20 dollars will be enough .

Answer:

Step-by-step explanation:

As per diagram, the congruent sides/angles are:

So we have two sides congruent and included angle, this is Side-Angle-Side or SAS

The central limit theorem tells us that the distribution of the sample mean will be approximately normal if the sample size is sufficiently large. This information can be used to calculate the standard error and construct confidence intervals.

The sampling distribution of the sample mean is approximately normally distributed.

This statement is true. When the sample size is large\((n ≥ 30),\) the sampling distribution of the sample mean is approximately normally distributed. The sample mean is the mean of the sample's measurements, while the sampling distribution of the sample mean is the distribution of all possible sample means with a particular sample size.The central limit theorem guarantees that the sampling distribution of the sample mean is approximately normal if the sample size is large enough. This is due to the fact that the distribution of the population is not necessary. This theorem allows us to use the normal distribution in inferential statistics, making it an important theorem in statistics. When the sample size is less than 30, it is appropriate to use the t-distribution instead of the normal distribution because the t-distribution takes into account the extra uncertainty generated by the smaller sample size.The sampling distribution is critical to statistical inference because it helps us estimate population parameters by making inferences based on sample statistics. For instance, suppose we want to know the mean salary of all the employees in a firm. We could take a random sample of employees and calculate their average salary.

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Answer:

a)

There are 6 planes - 5 faces of the pyramid and one base, which overlaps with the plane X.

b)

Collinear points are the points on the same line:

c)

The intersection of planes X and HGD is the line section HG.

a:-

This is a pentagonal pyramid

B:-

C:-

HG is the intersection line

The number of ways to plan her schedule of menus for the 20 school days is 10^20.

To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. To calculate a combination, you will need to calculate a factorial.

For each day, there are ten different choices for what she will cook that day. 20 decisions are made, one for each day with ten different possibilities for each choice.

The complete question is: A school cook plans her calendar for the month of February in which there are 20 school days. She plans exactly one meal per school day. Unfortunately, she only knows how to cook ten different meals.

How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?

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The quadratic function in standard form with zeros -2 and 8 is:

f(x) = (x + 2)(x - 8) = x^2 - 6x - 16

The standard form of a quadratic function is ax^2 + bx + c = 0, where a, b, and c are real numbers. The zeros of a quadratic function are the values of x that make the function equal to 0. In this case, the zeros are -2 and 8.

To find the quadratic function, we can use the following steps:

1. Write the quadratic function in factored form. The factored form of a quadratic function with zeros a and b is (x - a)(x - b). In this case, the zeros are -2 and 8, so the factored form is:

(x + 2)(x - 8)

2. Expand the factored form to get the standard form. Expanding the factored form gives us the standard form:

f(x) = x^2 - 6x - 16

Therefore, the quadratic function in standard form with zeros -2 and 8 is f(x) = x^2 - 6x - 16.

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You can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

To find the slope of the secant line PQ, we need two points on the line: P(x, 4) and Q(3 - x, 3).

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the coordinates of P are (x, 4) and the coordinates of Q are (3 - x, 3). Plugging these values into the slope formula, we have:

slope = (3 - 4) / (3 - x - x)

slope = -1 / (3 - 2x)

To find the slope of the secant line for different values of x, we substitute those values into the expression for the slope.

For example, if x = 1, the slope of the secant line PQ is:

slope = -1 / (3 - 2(1))

slope = -1 / (3 - 2)

slope = -1 / 1

slope = -1

Similarly, you can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

And so on, you can calculate the slope of the secant line for different values of x.

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To calculate the weighted mean of student 40's exam scores with exam 1 weighted twice that of the other 3 exams, you will need to use the weights provided in the spreadsheet. First, locate student 40's scores for all four exams on the second sheet of the spreadsheet. Then, apply the weights provided to each exam score.

To weight exam 1 twice that of the other 3 exams, you will need to multiply the exam 1 score by 2 and leave the other three scores as they are. Once you have adjusted the weights accordingly, you can calculate the weighted mean using the formula:

weighted mean = (weight1 * score1 + weight2 * score2 + weight3 * score3 + weight4 * score4) / (weight1 + weight2 + weight3 + weight4)

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.

The correct answer is option  A: The random variable is discrete. A decibel is a unit of measure used to quantify the loudness or intensity of sound.

From 0 dB (the quietest level of sound) to 140 dB (the loudest level of sound), it is measured on a logarithmic scale (the highest level of sound).

The decibel level of a siren is normally between 110 and 120 dB, which is regarded to be within or close to the threshold of human hearing.

The decibel level of a siren is measured on a logarithmic scale, making it a discrete variable. This indicates that it is measured in whole numbers rather than fractions of a decibel.

For instance, a siren's decibel level can be 110 dB, 111 dB, 112 dB, etc., but it cannot be 110.5 dB or 111.5 dB. Therefore, the decibel level of a siren is a discrete variable.

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The values of a, h and k on the function are given as follows:

The meaning of the transformations is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = 1/x.

Hence the meaning of the transformations is given as follows:

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The distance the bird has flown by the time Alice and Bob meet is 40 feet.

Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.

Distance equals speed multiplied by time.

Distance between Alice and Bob=1000 feet.

Distance between the bird and Bob=1000 feet.

Speed of Alice and Bob=10 feet per second.

The combined speed of Alice and Bob=20 feet per second.

Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)

The time covered at the meeting point=20 second (1000/50)

Speed of the bird=20 feet per second.

The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).

Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.

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 We found the PMF f(x),  calculated the probability of selecting exactly one defective unit, and  determined the probability of selecting more than one defective unit.

To find the probability mass function (PMF) f(x) for the number of defective units, we need to determine the probability of each possible outcome.

Let's assume that the total number of units tested is n. Since it is mentioned that 2% of the units are defective, the probability of selecting a defective unit is 0.02.

The PMF f(x) can be calculated using the binomial distribution formula:
\(f(x) = C(n, x) * (0.02)^x * (0.98)^(n-x)\)

To find p(x=1), we substitute x=1 into the PMF formula:
\(f(1) = C(n, 1) * (0.02)^1 * (0.98)^(n-1)\)

This represents the probability of selecting exactly one defective unit when testing a batch of pedometers.

Similarly, to find p(x>1), we need to sum up the probabilities for x=2, x=3, and so on, up to x=n:
\(p(x>1) = f(2) + f(3) + ... + f(n)\)
This represents the probability of selecting more than one defective unit when testing a batch of pedometers.

To sketch the histogram, we can plot the values of x on the x-axis and the corresponding probabilities f(x) on the y-axis. Each bar's height represents the probability of selecting that many defective units.

In conclusion, we found the PMF f(x), calculated the probability of selecting exactly one defective unit, and  determined the probability of selecting more than one defective unit.

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-17 19 55 91 127 163

36 36 36 36 36

6^2 6^2 6^2 6^2 6^2

It's a second degree sequence

Answer:

y = 4x - 2

y = -x + 3

Step-by-step explanation:

Answer:

the image should be the same size as the reflection

The mandatory orientation and size of the triangle image did not match with the former triangle ABC.

Given that,
Lin tried to reflect triangle ABC across line t. She knows something went wrong because the image isn’t congruent with the original figure.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
The given triangle is ABC,
Lin has to form the image of the reflection of the triangle ABC across the line t. Since the observation shows that the image formed by Lin is oriented and enlarged and does not seems to be congruent with the former triangle.

Thus, the mandatory orientation and size of the triangle image did not match the former triangle ABC.

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