find the definite integral of the function f shown in the graph below, over the limits from 0 to 3.

Answer:Yes,

There is a direct proportional relationship

between the cost of items before tax and the

cost of items after tax.

5.0

Step-by-step explanation:

Given - A city has a 5% sales tax.

To find - Is there a proportional relationship

between the cost of items

before tax and the cost of items after

tax?

Proof

Yes, cost of items before tax is directly

proportional to cost of items after tax.

Reason

With the increase in the sales tax, there is

increase in the cost of items after tax, therefore,

there is a direct relation between cost of items

before tax and cost of items after tax.

Step-by-step explanation:

The exact length of the curve is [tex]\frac{1}{216}[145^{\frac{3}{2} } -1][/tex].

The given equation is [tex]$y=1+8 x^{\frac{3}{2}}$[/tex].

The point is [tex]$$0 \leq x \leq 1$.[/tex]

Arc length: To find the arc length of the function y=f(x), use the power rule. After that use the integration.

Let  f(x)  be a smooth function over the interval [a,b] . Then the arc length of the portion of the graph of  f(x)  from the point (a, f(a))  to the point (b, f(b))  is given by

The formula of the arc length is: [tex]$=\int_0^1 \sqrt{1+\left(y^{\prime}\right)^2}$[/tex]

Differentiate this equation

[tex]$$\begin{aligned}& y^{\prime}=8 \frac{\mathrm{d}\left(x^{\frac{3}{2}}\right)}{\mathrm{d} x} \\& =8 \frac{3}{2} x^{\frac{1}{2}} \\& =12 \sqrt{x}\end{aligned}$$[/tex]

Now, find the arc-length.

[tex]$$\begin{aligned}& \text { Arc-length }=\int_0^1 \sqrt{1+\left(y^{\prime}\right)^2} \\& =\int_0^1 \sqrt{1+144 x}\end{aligned}$$[/tex]

Use the substitution method.

[tex]$$\begin{aligned}& u=1+144 x \\& d x=\frac{1}{144} d u \\& =\frac{1}{144} \int_1^{145} \sqrt{u} d u \\& =\frac{1}{144}\left[\frac{u^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^{145} \\& =\frac{1}{216}\left[145^{\frac{3}{2}}-1\right]\end{aligned}$$[/tex]

Hence, the exact length is [tex]\frac{1}{216}\left[145^{\frac{3}{2}}-1\right][/tex].

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Answer:

177 - 51i

Step-by-step explanation:

[tex](-5+ i)(12- i)(-3).[/tex]

[tex](-5+ i)(12- i)[/tex]

[tex]-5X12-5(-i)[/tex]+[tex](-i)X12+(i)[/tex][tex](-i)[/tex]

[tex]-60+5i+12i-1i^{2}[/tex]

[tex]-60+5i+12i-1(-1)[/tex]

[tex]-59+17i\\(-59+17i)(-3)\\177-51i[/tex]

Hope it helps u:)

Answer:

[tex]177 - 51i[/tex]

Step-by-step explanation:

Given expression:

[tex](-5+i)(12-i)(-3)[/tex]

Use the FOIL method to multiply the first two parentheses:

[tex]\implies \left(-5 \cdot 12 -5 \cdot -i +i \cdot 12 + i \cdot -i\right)(-3)[/tex]

[tex]\implies \left(-60 +5i +12i -i^2\right)(-3)[/tex]

[tex]\implies \left(-60 +17i -i^2\right)(-3)[/tex]

Multiply:

[tex]\implies -60 \cdot -3 +17i \cdot -3 -i^2 \cdot -3[/tex]

[tex]\implies 180-51i+3i^2[/tex]

Apply the imaginary number rule:  i² = -1

[tex]\implies 180-51i+3(-1)[/tex]

Simplify:

[tex]\implies 180-51i-3[/tex]

[tex]\implies 177-51i[/tex]

When the probability distribution of x, where x is the number of times a college graduate changed majors where P(0) = 0.135, P(1) = 0.271, P(2) = 0.271, P(3) = 0.180, P(4) = 0.090, P(5) = 0.036, P(6) = 0.012, P(7) = 0.003 and P(8) = 0.002, the probability that a randomly selected college graduate has changed majors more than two times is 0.323.

Therefore, the answer is 0.323.

The probability that a randomly selected college graduate has changed majors more than two times is obtained by

P( x > 2) = P(3) + P(4) + P(5) + P(6) + P(7) + P(8)

P(x > 2) = 0.180 + 0.090 + 0.036 + 0.012 + 0.003 + 0.002

P(x > 2) = 0.323

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Answer:a=17

Step-by-step explanation:

3(4a-8)=180

4a-8=60

4(a-2)=60

a-2=15

a=17

Hope this help!!!!

The value of x we get from the equation is [tex]\frac{- 10 ±\sqrt{208}}{18}\\[/tex]

The given equation is [tex]9x^{2} + 10x -3=0[/tex]

We know, the quadratic formula is [tex]x=\frac{-b ± \sqrt{b^{2}-4ac}}{2a}[/tex] where [tex]a\neq 0[/tex]

Using the Quadratic Formula where

a = 9, b = 10, and c = -3

We get,

[tex]x=\frac{-b ± \sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x=\frac{- 10± \sqrt{10^{2}-4(9)(-3) }}{2(9)}\\[/tex]

[tex]x=\frac{- 10± \sqrt{100--108 }}{18}\\[/tex]

[tex]x=\frac{- 10± \sqrt{208}}{18}\\[/tex]

The discriminant [tex]b^{2} -4ac[/tex]>0 so, there are two real roots

From this, we get 2 values of x

[tex]x=0.245678[/tex]

[tex]x= -1.35679[/tex]

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Answer:-10±√208÷18

Step-by-step explanation

1) so, there is a formula that is  x= -b±√b²-4ac÷2a, we can use this to solve this equation.

2) put these value in the formula, then we will get

  here, a=9

            b=10

            c=-3

  x=-10±√100-4*9*-3÷2*9

  x=-10±√208÷18

Answer:

-25

Step-by-step explanation:

[tex]-5^2=-25[/tex]

D'après ce que je sais. La pyramide du Louvre (Pyramide du Louvre) est une grande structure de verre et de métal conçue par l'architecte sino-américain I. M. Pei. La pyramide se trouve dans la cour principale (Cour Napoléon) du Palais du Louvre à Paris, entourée de trois pyramides plus petites. La grande pyramide sert d'entrée principale au musée du Louvre. Achevé en 1988 dans le cadre du projet plus large du Grand Louvre, il est devenu un point de repère de la ville de Paris.

The length of the bae of an iocele triangle i x. The length of a leg i 2x-3. The perimeter of the triangle i 44 then x= 10

since the triangle is isosceles then the 2 legs are congruent, that is both 2x - 3

the perimeter is the sum of the 3 sides , that is

x + 2x - 3 + 2x - 3 = 44

5x - 6 = 44 ( add 6 to both sides )

5x = 50 ( divide both sides by 5)

x = 10

hence The length of the bae of an iocele triangle i x. The length of a leg i 2x-3. The perimeter of the triangle i 44 then x= 10

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Answer: -3n + 18

Step-by-step explanation:

When examining the sequence, you can see that every time, it decreases by 3, therefore the first part of your rule should be:

-3n

(Extra note to wow your maths teacher! This is a linear sequence as it decreases/increases by the same amount each time.)

Next, you will need to find the number before the given sequence. As it decreases by 3 every time, to find the number before you need to increase by 3. Therefore, the next part you need is + 18.

Leave a comment if you don't understand anything :)

Answer:

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

Given sequence:

This is an AP, with the first term a = 15 and common difference of - 3, as it is decreasing by 3.

Use nth term equation for an AP:

Answer: The ordered pair that represents the location of vertex A after the dilation is (-40, 35).

Step-by-step explanation:

How do we dilate a figure with the origin as the center of dilation?

To dilate a figure with the origin as the center of dilation, we multiply the coordinates of each point by the scale factor. This has the effect of stretching or shrinking the figure, depending on whether the scale factor is greater than or less than 1.

To dilate a figure by a scale factor of 5 with the origin as the center of dilation, we need to multiply the x- and y-coordinates of each point in the figure by 5.

So, to find the coordinates of vertex A after the dilation, we start with the coordinates of vertex A before the dilation, which are (-8, 7).

Then, we multiply the x-coordinate by 5 to get (-8)5 = -40, and we multiply the y-coordinate by 5 to get (7)5 = 35.

Vertex A is located at (-8, 7). If we multiply these coordinates by 5, we get (-40, 35). Therefore, the coordinates of vertex A after the dilation are (-40, 35).

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After the dilation, the ordered pair that depicts where vertex A is located is (-40, 35).

How can we increase a figure so that the origin serves as the dilation center?

We multiply the coordinates of each point by the scale factor to dilate a figure with the origin as the center of dilation. Depending on whether the scale factor is larger than or less than 1, this has the effect of either expanding or shrinking the figure.

The x- and y-coordinates of each point in the figure must be multiplied by 5 in order to dilate it by a scale factor of 5, with the origin serving as the centre of dilation.

Thus, we begin with the coordinates of vertex A before the dilation, which are, in order to obtain the coordinates of vertex A after the dilation (-8, 7).

The x-coordinate is then multiplied by 5 to get (-8)5 =-40, while the y-coordinate is multiplied by 5 to get (7)5 = 35.

Vertex A can be observed at (-8, 7). These coordinates are multiplied by 5 to get (-40, 35). As a consequence, vertex A's coordinates after dilation are (-40, 35).

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Answer:

1st and 3rd pictures are not functions. 2nd one is a function.

Step-by-step explanation:

Perform the Vertical Line Test by drawing a line in the functions. If they touch the function twice, they are not a functions. However, if the line touches once, it's a function.

The value of the discriminant of f is 0.

There is one distinct real number of zeroes.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 3x² + 24x + 48

This is in the form of ax² + bx + c

a = 3

b = 24

c = 48

The discriminant is given by b² - 4ac.

There are two real solutions when it is greater than 0.

There is one real solution when it is equal to 0.

There are two imaginary solutions when it is less than 0.

Now,

= 24² - 4 x 3 x 48

= 576 - 576

= 0

So,

There is one real solution.

Thus,

The value of the discriminant of f is 0.

There is one distinct real number of zeroes since the discriminant is zero.

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Answer:

Step-by-step explanation:

I plotted this graph on Desmos**

When I plotted the line I got (3,-2) as the point where they intercept.

1st Equation Y=3x-11:
x: 0, 1, 2

y: -11, -8, -5

2nd Equation Y=-2x+4:

x: 0, 1, 2

y: 4, 2, 0

(Hopefully these points are right I went along with the graph I plotted, if wrong, I'm sorry.)

7=x

I hope i read the question right, but use this to help you!

Answer:

x = [tex]\frac{36}{5}[/tex]

Step-by-step explanation:

7 + [tex]\frac{x}{3}[/tex] = 2x - 5 ( subtract 7 from both sides )

[tex]\frac{x}{3}[/tex] = 2x - 12 ( multiply through by 3 to clear the fraction )

x = 6x - 36 ( subtract 6x from both sides )

- 5x = - 36 ( divide both sides by - 5 )

x = [tex]\frac{-36}{-5}[/tex] = [tex]\frac{36}{5}[/tex] = 7.2 ( in decimal form )

The probability that an 11-bit string is a palindrome is 1 in 2048, or 0.00048828125%.

A group of characters known as a palindrome read the same both forward and backward

For an 11-bit string, there are 2048 possible combinations of 0s and 1s. Of those, only one combination is a palindrome. Therefore, the probability of randomly selecting an 11-bit string that is a palindrome is 1 in 2048, or 0.00048828125%.

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The center line, LCL, and UCL for the p chart that would be used for this processing step are 89%, 88.3%, and 89.7%, respectively.

The center line of a p chart is the average yield of good chips during a processing step, and is calculated as follows:

Centerline = average yield of good chips = 89%

The lower control limit (LCL) and upper control limit (UCL) for a p chart are calculated using the following equations:

LCL = average yield of good chips - 3 × standard deviation

UCL = average yield of good chips + 3 × standard deviation

To calculate the standard deviation, we need to know the number of chips per wafer (156 in this case). The standard deviation is calculated using the equation:

standard deviation = √(p × (1 - p) / n)

where p is the average yield of good chips (89% in this case), (1 - p) is the average yield of defective chips (11% in this case), and n is the number of chips per wafer (156 in this case).

Plugging the values for p, (1 - p), and n into the equation gives us:

standard deviation = √(0.89 × 0.11 / 156) = 0.0256

Substituting the standard deviation into the equations for the LCL and UCL gives us:

LCL = 89% - 3 × 0.0256 = 88.3%

UCL = 89% + 3 × 0.0256 = 89.7%

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The option that provides the best description of the relationship between a quadratic parent function and a square root parent function is A. The square root function is the quadratic function reflected across the line y = x, with a limited domain.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

The square root function is the quadratic function reflected across the line y = x, with a limited domain. The graph y=x² and y=√x and y=x. The graph is attached.

In conclusion, the correct option is A.

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[tex]\stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{w}{4}~~ = ~~\cfrac{2}{~~1 \frac{2 }{3 } ~~}\implies \cfrac{w}{4}~~ = ~~\cfrac{2}{~~ \frac{5 }{3 } ~~}\implies \cfrac{w}{4}~~ = ~~\cfrac{\frac{2}{1}}{~~ \frac{5 }{3 } ~~}\implies \cfrac{w}{4}=\cfrac{2}{1}\cdot \cfrac{3}{5} \\\\\\ \cfrac{w}{4}=\cfrac{6}{5}\implies 5w=24\implies w=\cfrac{24}{5}\implies {\Large \begin{array}{llll} w=4\frac{4}{5} \end{array}}[/tex]

Answer:

The lengths of the two pieces are 7 cm and 14 cm.

Step-by-step explanation:

Let x represent the length of the longer piece of the rod. Since the lengths of the two pieces are in the ratio 7:2, the length of the shorter piece is 2x. The total length of the two pieces is therefore 7x + 2x = 9x. Since the total length of the two pieces is 63 cm, we have:

9x = 63

Dividing both sides by 9, we get:

x = 7

Thus, the length of the longer piece is 7 cm, and the length of the shorter piece is 2 * 7 = 14 cm. Therefore, the lengths of the two pieces are 7 cm and 14 cm.

the Utopian treat valuable develop the central idea is the Utopians give valuables to children, who treat them as toys.

The central idea of the above passage is that the Utopians give valuables, such as diamonds and carbuncles to children, who treat them as toys. As such, the Utopians are delighted with these valuables, and glory in them during their childhood but lay them aside when they come to years.

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The equation of a circle with center  (1,-2) and radius 2 is ( x - 1 )² + ( y + 2 )² = 4.

The standard form of the circle is x² + y² = r²

Where r is the radius.

h and k is the horizontal and vertical translation which represent the center of the circle..

Hence, the formula is derived from the distance formula where the distance is between the center and every point on the circle is equal to the length of the radius.

( x - h )² + ( y - k )² = r²

Given that;

Center: (1,-2)

Plug the given values into the equation and simplify.

( x - h )² + ( y - k )² = r²

( x - 1 )² + ( y - (-2) )² = 2²

( x - 1 )² + ( y + 2 )² = 2²

( x - 1 )² + ( y + 2 )² = 4

Therefore, the equation of the circle is ( x - 1 )² + ( y + 2 )² = 4

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The team won 24 games out of the 32 they played.

A ratio is an ordered pair of numbers a and b, written a / b in which b does no longer equal 0. A proportion is an equation wherein two ratios are set the same for every other. In arithmetic, a ratio suggests how commonly one wide variety contains every other. as instance, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is 8 to 6 (this is, eight:6, that is equivalent to the ratio four: three).

The share system is used to depict if two ratios or fractions are the same. we are able to locate the lacking fee by using dividing the given values. the share components can be given as a: b::c : d = a/b = c/d, where a and d are the extreme phrases and b and c, are the suggested phrases.

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g sio2 is always 0.4 mg too high regardless of the weight of the sample taken for analysis. The relative error in parts per thousand would be 400.

This is because the relative error is calculated by taking the difference between the actual value and the measured value, and dividing this by the actual value.

In this case, the actual value is 0.4 mg and the measured value is

0.4 mg + (10% x 0.4 mg) = 0.44 mg. Thus the relative error is

(0.44 – 0.4)/0.4 = 0.1/0.4 = 0.25 = 400 parts per thousand.

The relative error in parts per thousand would be 400.

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Answer:

The ratio is 8:3

Step-by-step explanation:

18 salt shakers and 48 pepper shakers.

Ratio of pepper shakers to salt shakers

48 : 18

Divide each side by 6

48/6 : 18/6

8 : 3

The ratio is 8:3

Answer:

a

Step-by-step explanation:

60 hours in 7 days   =   60/7     hours per day

Answer:

A is correct

Step-by-step explanation:

I got it right on my test

The slope of the line shown in this graph is equal to: B. 1/2.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided in the graph, we have the following points on the line:

Substituting the given points into the formula, we have;

Slope, m = (-2 - (-4))/(2 - (-2))

Slope, m = (-2 + 4)/(2 + 2)

Slope, m = 2/4

Slope, m = 1/2

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The prime factorization of 168 is (d) 2³ × 3 × 7

From the question, we have the following expression that can be used in our computation:

Number = 168

Express 168 as the products of numbers

So, we have the following representation

168 = 2 × 2 × 2 × 3 × 7

Express as exponents

168 = 2³ × 3 × 7

Hence, the prime factorization is 2³ × 3 × 7

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