Sort each function into the correct category
f(x) = 0.45-1
Linear Functions
Quadratic Functions
Exponential Functions
f(x) = 5
f(x) = 4,5x + 1.8
f(x) = 19x2
f(x) = x2 - 3x + 4
Fx) = 2x - 6

Answer:

7-56n

Step-by-step explanation:

By using the distributive property you multiply the 7 to the 1 which equals 7. Then you distribute the 7 to the -8n which gives you -56n becaus emultiplying a negative and a possitive gives you a negative.

The required solution is -56n+7.

It is required to find the solution.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

Rearrange terms

7(1 - 8n)

=7(-8n+1)

Then distribute by multiplying 7 we get,

-56n+7

Therefore, the required solution is -56n+7.

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Answer:

1/3

Step-by-step explanation:

constant proportionality = x/y

x1/y1 , x2/y2 , x3/y3 , ....

5/15 , 10/30 , 6/18 , 9/27 , 2/6

= 1/3 , 1/3 , 1/3 , 1/3 , 1/3

since in all the cases x/y = 1/3 ,

Therefore, the contant proportionality in the given table is 1/3

Hope it's helpful..

Answer:

50 and 20 that is the answer Thank you

Answer:

12

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

in this case its

\(5^{2}\) + \(b^{2}\) = \(13^{2}\)

25 + \(b^{2}\) = 169 subtract 25 from both sides

\(b^{2}\) = 144 take square root of each side

b = 12

Answer:

\(12\)

Step-by-step explanation:

----------------------------------------

In order to find the missing side of the triangle, we would need to use the Pythagorean theorem: \(a^2+b^2=c^2\)

So,

\(5^2+b^2=13^2\)

\(25+b^2=169\)

\(b^2=144\)

\(b=12\)

--------------------

Hope this helps.

Answer:12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer: no did

Step-by-step explanation:

bwhehe

Answer:

Variable

Step-by-step explanation:

If you can substitute a unknown variable with another expression that is equal, you can then solve for another variable, and with that equal expression, solve for the first variable.

Answer:

30/7 x 1/3 = 1 3/7 cm^3

The degree 3 Taylor polynomial for the function f(x) = (x+5)sin(5x) at x=0 . The degree 3 Taylor polynomial for f(x) at x=0 is \(P(x) = 0 + 25x + (5/2)x^2 + (f"'(0)/3!)x^3.\)

To  find the degree 3 Taylor polynomial for f(x) at x=0, we need to calculate the function and its derivatives.

First, let's find f(0). Plugging x=0 into the function f(x) = (x+5)sin(5x), we have f(0) = (0+5)sin(5(0)) = 0.

Next, we find f'(x) by taking the derivative of f(x) with respect to x. Using the product rule and the chain rule, we get f'(x) = (1)(sin(5x)) + (x+5)(5cos(5x)) = sin(5x) + 5(x+5)cos(5x).

Evaluating f'(x) at x=0 gives us f'(0) = sin(0) + 5(0+5)cos(0) = 0 + 5(5)(1) = 25.

Taking the second derivative, f"(x), we differentiate f'(x) with respect to x, which yields f"(x) = 5cos(5x) + 5(x+5)(-5sin(5x)).  

Evaluating f"(x) at x=0 gives f"(0) = 5cos(0) + 5(0+5)(-5sin(0)) = 5 + 5(5)(0) = 5.

Now that we have the necessary values, we can construct the Taylor polynomial. The general form of a degree 3 Taylor polynomial is P(x) = f(0) + f'(0)x + (f"(0)/2!)x^2 + (f"'(0)/3!)x^3.

Substituting the values we calculated, the degree 3 Taylor polynomial for f(x) at x=0 is  the degree 3 Taylor polynomial for f(x) at x=0 is \(P(x) = 0 + 25x + (5/2)x^2 + (f"'(0)/3!)x^3.\)  

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Answer:

5.436564x^14905

The main factor used to judge the quality of a systematic review (SR) is D. The soundness of the methodology used to conduct it.

A systematic review aims to provide a comprehensive synthesis of available evidence on a specific research question by identifying, evaluating, and summarizing all relevant studies. The quality of a systematic review is heavily dependent on the rigor and transparency of the methodology employed. A well-conducted SR follows a predefined protocol, which includes a clear research question, eligibility criteria for study inclusion, and a comprehensive search strategy.

While the reputation of the professional association that distributes the SR (option a) and the number of studies included in the analysis (option b) can provide some insights into the review's credibility and comprehensiveness, they are not the main factors in judging the SR's quality. Similarly, the use of statistics to combine the findings (option c) is an important aspect of a systematic review but is not the primary factor to determine its quality.

In conclusion, the soundness of the methodology used to conduct a systematic review is the most critical factor in determining its quality. A rigorous and transparent methodology ensures that the review's findings are reliable, valid, and can inform decision-making and policy development. Therefore, the correct option is D.

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Answer:

x = 9

Step-by-step explanation:

5x + 6 = 6x - 3

Simplify from there:

6x - 5x = 6 + 3

x = 9

The mass of the wire is approximately 2.121 units.

To find the mass of the wire, we need to integrate the density over the length of the wire. The length of the wire can be found using the arc length formula

L = ∫[a,b] ||r'(t)|| dt

where r'(t) is the derivative of r(t), ||r'(t)|| is the magnitude of r'(t), and [a,b] is the interval of t values that defines the wire.

In this case, we have

r(t) = (t^2 - 1)j + 2tk

r'(t) = 2tj + 2k

||r'(t)|| = sqrt((2t)^2 + 2^2) = sqrt(4t^2 + 4) = 2sqrt(t^2 + 1)

Therefore, the length of the wire is

L = ∫[0,1] 2sqrt(t^2 + 1) dt

This integral can be evaluated using a trigonometric substitution:

Let t = tan(theta), then dt = sec^2(theta) d(theta), and sqrt(t^2 + 1) = sqrt(sec^2(theta)) = sec(theta)

Substituting, we have

L = ∫[0,π/4] 2sec^2(theta) sec(theta) d(theta)

L = 2 ∫[0,π/4] sec^3(theta) d(theta)

This integral can be evaluated using integration by parts

u = sec(theta), du/d(theta) = sec(theta) tan(theta)

dv/d(theta) = sec^2(theta), v = tan(theta)

∫ sec^3(theta) d(theta) = sec(theta) tan(theta) - ∫ sec(theta) tan^2(theta) d(theta)

Using the identity tan^2(theta) = sec^2(theta) - 1, we have

∫ sec^3(theta) d(theta) = sec(theta) tan(theta) - ∫ sec(theta) (sec^2(theta) - 1) d(theta)

∫ sec^3(theta) d(theta) = sec(theta) tan(theta) + ln|sec(theta) + tan(theta)| + C

where C is the constant of integration.

Substituting back to our original integral, we have

L = 2 [sec(theta) tan(theta) + ln|sec(theta) + tan(theta)|]_0^π/4

L = 2 [1 + ln(1 + sqrt(2))] ≈ 4.885

Now, we can find the mass of the wire using the formula

M = ∫[a,b] δ ||r'(t)|| dt

In this case, δ = 3/2t and [a,b] = [0,1], so we have

M = ∫[0,1] (3/2t) (2sqrt(t^2 + 1)) dt

M = 3 ∫[0,1] t sqrt(t^2 + 1) dt

We can evaluate this integral using a substitution similar to before:

Let t = sinh(u), then dt = cosh(u) du, and sqrt(t^2 + 1) = sqrt(sinh^2(u) + cosh^2(u)) = cosh(u)

Substituting, we have

M = 3 ∫[0,arsinh(1)] sinh(u) cosh^2(u) du

M = 3/2 ∫[0,arsinh(1)] (sinh(2u))' du

M = 3/2 [sinh(2u)]_0^ars

Using the formula for hyperbolic sine, we have:

M = 3/2 [sinh(2arsinh(1))] = 3/2 [sqrt(2^2 + 1^2) - 1] = 3/2 (sqrt(5) - 1) ≈ 2.121

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The given question is incomplete, the complete question is:

Find the mass of a wire that lies along the curve r(t) =(t^2 - 1)j + 2tk, 0<=t<=1, if the density is δ=3/2t.

The median of the following set of numbers  (18, 26, 29, 18, 44) is 26. The correct option to this question is option A

To find median of the following sequence (18, 26, 29, 18, 44) we will arrange them in ascending order

                            18 , 18 , 26 , 29 , 44   . . . . . .  . . . .(1)

Since the number of terms is odd we will apply the formula

                     Median  = \(\frac{(n+1)}{2} th\) term . . . . . . .(2)

       Here n = number of terms

As per question the n = 5

Therefore putting in equation 2 we get

                      Median = \(\frac{(5+1)}{2} th\) term

                      Median = \(\frac{6}{2} th \\\)  term

                      Median = 3 term

Hence the third term from the sequence ( shown in 1 ) we get the median that is 26

Hence the median of the following set of numbers (18, 26, 29, 18, 44) is 26 .

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The median is:

26

Explanation:

First, we will arrange the numbers from least to greatest.

18, 26, 29, 18, 44

Rearrange

18, 18, 26, 29, 44.

Now, the median is the number in the middle, which is 26.

On comparing the left-hand and right-hand derivatives of the given function, we find that they do not exist at x = 0 and they are not equal to each other. The given function is not differentiable at x = 0.

To determine whether the given piecewise-defined function is differentiable at the origin or not, we will calculate the left and right-hand derivatives of the function separately and then compare them. If both the left and right-hand derivatives of the function exist at a point and they are equal to each other, then the function is differentiable at that point. If the left and right-hand derivatives of the function do not exist or they exist but are not equal to each other, then the function is not differentiable at that point.
Given function,

g(x) ={x²/3, x ≥ 0x1/3, x < 0

Left-Hand Derivative: For x < 0; g(x) = x1/3

Now, by applying the power rule of differentiation, we can find the left-hand derivative of the function at x = 0 as follows:

Therefore, the left-hand derivative of the given function at x = 0 does not exist.

Right-Hand Derivative: For x ≥ 0; g(x) = x²/3

Now, by applying the power rule of differentiation, we can find the right-hand derivative of the function at x = 0 as follows:

Therefore, the right-hand derivative of the given function at x = 0 is 0.

On comparing the left-hand and right-hand derivatives of the given function, we find that they do not exist at x = 0 and they are not equal to each other. Therefore, the given function is not differentiable at x = 0.

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Answer: 26

Step-by-step explanation:

26 + 26 = 52

52 + 3 = 55

55 divided by 5 = 11

Hope this helped : )

Answer:

$42.88

Step-by-step explanation:

Let's create a proportion using the following setup:

cost/pounds=cost/pounds

We know that it costs $20.42 for a 10 pound turkey.

$20.42/10 pounds= cost/pounds

We don't know how much a 21 pound turkey costs, so we can say that it costs $x for a 21 pound turkey.

$20.42/ 10 pounds= $x/ 21 pounds

20.42/10=x/21

We want to find x, by getting x by itself.

x is being divided by 21. The inverse of division is multiplication. Multiply both sides by 21.

21*(20.42/10)=(x/21)*21

21* 20.42/10=x

21*2.042=x

42.882=x

Round to the nearest cent, or hundredth.

42.88=x

x= $42.88

A 21 pound turkey costs $42.88

Answer: 28

Step-by-step explanation:

28 is thhe missing number

In this case, Christopher divides the athletes into groups of varsity and junior varsity, which creates the strata. The type of sampling used in this scenario is stratified sampling.

Stratified sampling is a sampling method where the population is divided into homogeneous subgroups or strata, and individuals are randomly selected from each stratum in proportion to their representation in the population. In this case, Christopher divides the athletes into groups of varsity and junior varsity, which creates the strata.

By randomly selecting a proportionate number of individuals from each group, Christopher ensures that both varsity and junior varsity athletes are represented in the sample, maintaining the proportional representation of each group in the population. This method allows for more accurate and representative results by capturing the characteristics of both groups separately.


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Answer:

2 pounds

Step-by-step explanation:

Answer:

A is incorrect

Step-by-step explanation:

when you see -(- it makes the thing plus sign/positive

There is a 3.1% chance of obtaining a sample with a mean of 85 or higher assuming that the true mean sales at the new location are still equal to or less than 75 bowls a day.

What is the P value in statistics?

P value is a part of hypothesis testing. The P value is a measurement used against some data in testing.

Given in question,

    Food Truck in  Old location:

                             Sold =  75 bowls of noodle soup

   New location  Sold =  85 bowls of noodle soup

   p-value = 0.031

there is a 3.1% chance of obtaining a mean with a sample.

similarly, that is we can tell that the true mean sales at the new location will be still equal to or less than 75

  i.e. [P(X=75) ≤ P(X=85)]   bowls a day.

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The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

The trigonometric identity for sin(3x) in terms of sin(nx) and cos(nx) states that sin(3x) can be expressed as 3sin(x)cos²(x) - sin³(x).  

To derive the expression sin(3x) in terms of sin(nx) and cos(nx), we can utilize the angle sum and double angle identities. Starting with the triple-angle identity for sine, sin(3x) = sin(2x + x). Applying the angle sum identity, we get sin(3x) = sin(2x)cos(x) + cos(2x)sin(x).

Now, we express sin(2x) and cos(2x) in terms of sin(nx) and cos(nx). Using the double angle identities, sin(2x) = 2sin(x)cos(x) and cos(2x) = cos²(x) - sin²(x) = cos²(x) - (1 - cos²(x)) = 2cos²(x) - 1.

Substituting these values back into the expression for sin(3x), we have sin(3x) = (2sin(x)cos(x))(cos(x)) + (2cos²(x) - 1)(sin(x)). Simplifying further, sin(3x) = 2sin(x)cos²(x) + 2sin(x)cos²(x) - sin(x) = 3sin(x)cos²(x) - sin³(x). Therefore, sin(3x) can be written in terms of sin(nx) and cos(nx) as 3sin(x)cos²(x) - sin³(x), where n is an arbitrary integer.  

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-4 of the following is the average rate of change over the interval [−3, 0] for the function g(x) = log2(x 4) − 5.

To find the average rate of change over the interval [-3,0] for the function

g(x) = log2(x4) - 5, we can use the formula as shown below;

Average Rate of Change = (g(b) - g(a)) / (b - a)

Where 'b' and 'a' represent the endpoints of the interval [-3,0].

We can therefore plug in these values into the formula as shown below;

Average Rate of Change = [g(0) - g(-3)] / (0 - (-3))

We can then calculate g(0) and g(-3) as follows;

g(0) = log2(04) - 5 = -5g(-3) = log2((-3)4) - 5 = 7

Therefore, the average rate of change over the interval [-3,0] is;

Average Rate of Change = (g(0) - g(-3)) / (0 - (-3)) = (-5 - 7) / (0 + 3) = -12 / 3 = -4

So, the answer is not given in the options provided. Therefore, the correct answer is none of the options.

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Answer:

2/3

Step-by-step explanation:

trust and believe

The answer is: ℎ′(2) = 21 using inverse logic for the given question.

To find ℎ′(2), we first need to find the slope of the tangent line to the graph of ℎ() at the point where = 2. We can use a table of values to do this.

To create a table of values, we choose some values of and calculate the corresponding values of ℎ(). Let's choose a few values of  close to 2:

= 1.8: ℎ(1.8) = 3(1.8) - 23 = -17.4
= 1.9: ℎ(1.9) = 3(1.9) - 23 = -16.3
= 2.0: ℎ(2.0) = 3(2.0) - 23 = -15
= 2.1: ℎ(2.1) = 3(2.1) - 23 = -13.9
= 2.2: ℎ(2.2) = 3(2.2) - 23 = -12.8

Now, we can use these points to estimate the slope of the tangent line at = 2. Specifically, we can use the difference quotient:

[ℎ(2+h) - ℎ(2)]/h

where h is a small number (in this case, h = 0.1). Plugging in the values from our table, we get:

[ℎ(2.1) - ℎ(2)]/0.1 = (-13.9 - (-15))/0.1 = 21

This means that the slope of the tangent line to the graph of ℎ() at = 2 is approximately 21. Therefore, we have:

ℎ′(2) = 21

So, the answer is: ℎ′(2) = 21 in inverse case.

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Answer:

Step-by-step explanation:

American values and social trends are conveyed in The Voyage of Life paintings by Thomas Cole. how did society influence the art