(f) 3x+0.25x+0.10(2x)+0.05 (x+3)=24.65

Answer:

[tex]\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Increase the power by 1, then divide by the new power.

Given indefinite integral:

[tex]\displaystyle \int x \ln x \:\: \text{d}x[/tex]

To integrate the given integral, use Integration by Parts:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]

[tex]\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]

[tex]\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}[/tex]

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Answer:

  D, E

Step-by-step explanation:

A set of ordered pairs represents a function if no x-value is repeated in the set.

{(-1,6), (4,4), (7, 13), (4,8)} . . . . . not a function

{(3,6), (3, 5), (9, 12), (0, -3)} . . . not a function

{(-5,0), (6, 8), (3,-5), (-5,-3)} . . . . not a function

{(7,9), (8,4), (-2,4),(-3, 14)} . . . . no repeated x-values; is a function

{(8,3), (3, 7), (6,4), (5,4)} . . . . . .no repeated x-values; is a function

Here is conversion chart

1 day=24hr

so the equation to solve this would look like this

(24*11)+7

Therefore the answer is 271 hr

Answer

sum of all 3 digit even number = 247050

The series is 100 + 102 + 104 + .... + 998

which by using formula Sn = N/2 ( a + an)

where N = number of terms

a = first term = 100

an = last term = 998

The ice cube tray can make 200.96 cubic centimeters of ice.

For a sphere of radius R, the volume is:

[tex]V = \frac{4}{3}*3.14*R^3[/tex]

In this case, we have 6 spheres, each one with a radius of 2cm.

Then the total volume of ice that the ice cube tray can make at one time is:

[tex]volume = 6*V = 6*(\frac{4}{3} *3.14*(2cm)^3) = 200.96cm^3[/tex]

The ice cube tray can make 200.96 cubic centimeters of ice.

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The express elevator will go 4 floors per seconds.

We have to find the rate of the express elevator before we can find how many floors one can go in one seconds.

time = 12 3 / 4  = 51 / 4 seconds

number of floor = 51 floors

rate = 51 / 51 / 4

rate = 51 × 4 / 51

rate = 4 floors per seconds

Therefore, the elevator will go 4 floors per seconds.

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The common ratio of the associated geometric sequence is 4

The table of values is given as:

x y

1 9

2 36

3 144

4 576

5 2304

The common ratio is calculated as:

Ratio = y(2)/y(1)

This gives

Ratio = 36/9

Divide

Ratio - 4

Hence, the common ratio is 4

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Answer:

$33.915 for the cd

Step-by-step explanation:

70% of 19.95 = 13.965

19.95 + 13.965= 33.91

The amount you should put is 3846

The given parameters are:

Amount, A = 4000

Rate, r = 8%

Time = 0.5 year i.e. 6 months

The amount on simple interest is calculated as:

A = P(1 + RT)

This gives

4000 = P * (1 + 8% * 0.5)

Evaluate the product

4000 = P * (1 + 0.04)

Evaluate the sum

4000 = P * (1.04)

Divide both sides by 1.04

P= 3846

Hence, the amount you should put is 3846

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Answer:

14) 21.136505024965 m

15) 43.076759215619 km

Step-by-step explanation:

14)

let h be the height of the lighthouse:

tan(41.3) = 18.7/h

Then

h = 18.7÷tan(41.5)

  = 21.136505024965 m

………………………………………

15)

90-71.4 =18.6

Let s be the distance that the plane flew

towards the south:

tan(90 - 71.4) = s/128

Then

tan(18.6) = s/128

Then

s = tan(18.6)×128

  = 43.076759215619 km

14.)

See the diagram below.

Here use tan rule:

[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]

[tex]\sf tan(41+ \frac{30}{60} ) = \dfrac{18.7}{adjacent}[/tex]

[tex]\sf adjacent = \dfrac{18.7}{tan(41.5)}[/tex]

[tex]\sf adjacent = 21.14[/tex]

The height of the lighthouse is 21.14 m.

15.)

See the diagram below.

Here use tan rule:

[tex]\sf tan(x) = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\sf tan(18.6) = \dfrac{opposite}{128}[/tex]

[tex]\sf opposite = 128 tan(18.6)[/tex]

[tex]\sf opposite = 43.08[/tex]

The plane travelled 43.08 km far south.

Answer:

y = (-4/5)x - 7/5

Step-by-step explanation:

The general equation of the line is slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. You have been given the value of the slope (m = -4/5). To find the y-intercept, use the slope and values from the Point (2,-3) to isolate "b".

y = mx + b                                   <----- Slope-intercept form

y = (-4/5)x + b                             <------ Plug -4/5 in "m"

-3 = (-4/5)(2) + b                         <----- Plug in "x" and "y" values from Point

-3 = -8/5 + b                               <------ Multiply -4/5 and 2

-15/5 = -8/5 + b                          <----- Assign common denominator

-7/5 = b                                      <----- Add 8/5 to both sides

Now that you have the slope and y-intercept, you can construct the equation.

y = (-4/5)x - 7/5

Answer:

9x^3-15x

Step-by-step explanation:

The percentage of gold will be equal to 39.7%

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.

1. First find the density of your chain

Density = mass / volume

Volume = displaced water volume

                     = Volume of Final level of water - initial level of water

                     = 20 ml - 15 ml = 5 ml

Mass = 66.7 g

Density = 66.7g / 5 ml = 13.34 g/ml

2. Second, write the density of the chain as the weighted average of the densities of the other metals:

Mass of gold x density of gold + mass of other metals x density of other metals, all divided by the mass of the chain.

Calling x the amount of gold, then the amount of other metals is 66.7 - x:

[(19.3x+(9.7)(66.7-x)] / 66.7 = 13.34

19.3x + 635.66 - 9.7x = 889.778

9.6x = 254.118

x = 26.47

Then, there are 26.47 grams of gold in 66.7 grams of chain, which yields a percentage of:

(26.47 / 66.7) x 100 = 39.7%

Therefore the percentage of gold will be equal to 39.7%

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Answer:

28n+24

Step-by-step explanation:

3 ( 7 n + 5 n + 8 ) - 8 n

combine 7n and 5n to get 12n

3 ( 12n + 8 ) - 8

distribute 3 to 12n +8

36n+24-8n

combine like terms

28n+24

since ypu cant simply any more it stays like thats

*by the way there is an app that helps with equation and explains the process, its Microsoft Math Solver. hope it helped

Answer:

Step-by-step explanation:

let the consecutive even integers be 2x,2x+2

8×2x=7(2x+2)

16x=14x+14

16x-14x=14

2x=14

x=14/2=7

so numbers are 2×7,2×7+2

or

14,16

The equation which represent number of days is 87 ÷ n = 3

It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Here,

total hour practicing = 87 hours

Daily hours for practicing = 3 hours

total number of days = n days

Now, according to question;

n X 3 = 87

87 ÷ n = 3

Thus, the equation which represent number of days is 87 ÷ n = 3.

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The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Let x be the number.

According to the problem.

50% of x = 10

x = 10 ÷ 50%

= 10×(50/100)

= (50÷5)/(100÷5) = 10/20

Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

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If the angles of a convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex] then the smallest angle is 21°.

Given The exterior angles of convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex]

and we have to find the value of smallest angle.

The sum of the  angles of a convex octagon is 360°

so to calculate the smallest angle we need to find out the value of x first and which is calculated by summing up all the exterior angles and put them equal to 360.

(2x+6)+(x+13)+(2x-1)+(2x+12)+(2x-17)+(3x-4)+(3x-10)+4x=360

2x+6+x+13+2x-1+2x+12+2x-17+3x-4+3x-10+4x=360

2x+x+2x+2x+2x+3x+3x+4x+6+13-1+12-17-4-10=360

19x-1=360

19x=360+1

19x=361

x=361/19

x=19

Putting the value of x in all the angles and we will find the following:

2x+6=2*19+6=44

x+13=19+13=32

2x-1=2*19-1=37

2x+12=2*19+12=50

2x-17=2*19-17=21

3x-4=3*19-4=51

3x-10=3*19-10=47

4x=4*19=76

Hence among all the exterior angles the smallest angle is 21°.

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Answer:

[tex]x^2[/tex]

Step-by-step explanation:

Hello!

The HCF or the highest common factor (sometimes also known as the greatest common factor, GCF), is the greatest factor between terms.

First, let's expand both terms:

If we keep them on top of another, we can see that the overlapping variables are [tex]x*x[/tex], meaning that the greatest common factor between them is [tex]x^2[/tex].

Answer:

[tex]2261.9cm^{2}[/tex]

Step-by-step explanation:

Total Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex]

Note: Do not get tricked by the 24cm (taking 24cm as the radius), that is the diameter.

To find r, radius = [tex]\frac{1}{2} d[/tex]

                          =[tex]\frac{1}{2} (24)\\[/tex]

                          = 12cm

Now we know r = 12cm, h = 18cm

Now we substitute r and h into the formula to find the total surface area.

Total Surface Area of Cylinder = [tex]2\pi (12)(18)+2\pi (12)^{2} \\=432\pi +288\pi \\=720\pi cm^{2} \\=2261.9cm^{2}[/tex]

Answer:

The probability that a selected randomly rail bridge will exhibit structural distress given that it is old

= (200/520) * 0.5 * 0.7 * 100

= 0.1346154 * 100

= 13.46154 %

Using a trigonometric identity, it is found that the sine of the angle is given as follows:

[tex]\sin{\theta} = -\frac{4}{5}[/tex].

Considering an angle [tex]\theta[/tex], the identity is given as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem, the cosine is given as follows:

[tex]\cos{\theta} = \frac{3}{5}[/tex]

Hence the sine is found as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

[tex]\sin^2{\theta} + \left(\frac{3}{5}\right)^2{\theta} = 1[/tex]

[tex]\sin^2{\theta} + \frac{9}{25} = 1[/tex]

[tex]\sin^2{\theta} = \frac{16}{25}[/tex]

[tex]\sin{\theta} = \pm \sqrt{\frac{16}{25}}[/tex]

In quadrant IV, the sine is negative, hence:

[tex]\sin{\theta} = -\frac{4}{5}[/tex].

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Duplicate don't answer!

Answer:

Inferential statistics use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects. There are many types of inferential statistics and each is appropriate for a specific research design and sample characteristics

Step-by-step explanation:

hope this helps (﹡ˆ﹀ˆ﹡)♡

Answer:

26

Step-by-step explanation:

[tex]f(x)=3x^{2} -5x+4\\f(-2)=3(-2)^{2} -5(-2)+4\\=3(4)+10+4\\=12+10+4\\=26[/tex]

Answer:

26

Step-by-step explanation:

3(-2)^2 = 12

5(-2) = -10

So 12 - (-10) + 4 = 26

Two or more triangles are said to be congruent if their length of sides and measure of angles are equal. Thus, the required proof expected in the question is option D. <R ≅ <U

When the length of sides or measure of angles of two or more figures is equal, then we say the figures are congruent.

From the given question, the following can be deduced:

RT ≅ US (given: opposite sides are equal)

and TS is a common side for the two triangles.

<TRS  ≅  <RSU (alternate angle property)

<RTS  ≅ <UST (right angle property)

<RTU  ≅  <SUT (alternate angle property)

Therefore it can be observed that the necessary condition to prove that ΔRST ≅ ΔUTS is option D. <R  ≅ <U.

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Answer:

Step-by-step explanation:

Answer: [tex]8\sqrt{5}[/tex]

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]

So, by the Pythagorean theorem,

[tex]8^2 + 16^2 = x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]

The number of cakes Mrs Darby can decorate in a 30-hour week is 22.5 cakes.

Time conversion

1 hour = 60 minutes

1 1/3 hours = 60 × 1 1/3

= 60 × 4/3

= 240/3

= 80 minutes

30 hours = 30 × 60

= 1800 minutes

Number of cakes decorated = 1800 / 80

= 22.5 cakes

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Answer:

Step-by-step explanation:

|√2-y|=|y-√2|

√2-y=±(y-√2)

when √2-y=y-√2

y+y=√2+√2

2y=2√2

y=√2

when √2-y=-(y-√2)

√2-y=-y+√2

or 0=0

it gives no value of y.

so only possible value is y=√2

Hello !

Answer:

[tex]z {}^{ - 6} [/tex]

Step-by-step explanation:

[tex] \frac{z {}^{3} }{z {}^{9} } = z {}^{3 - 9} = z {}^{ - 6} [/tex]