What is the change of base property?

The simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12

Given the expression;

5.5(x+6 1/2) - (x+9 1/3) - (19-x)

First, we convert 6 1/2, 9 1/3 and 5.5 to an improper fraction

6 1/2 = 13/2, 9 1/3 = 28/3 and 5.5 = 11/2

So, we have

(11/2)( x + 13/2 ) - ( x + 28/3 ) - ( 19 - x )

Next, we remove the parentheses

11x/2 + 143/4 - x - 28/3 - 19 + x

11x/2 + 143/4 - 28/3 - 19

11x/2 + 317/12 - 19

11x/2 + 89/12

Therefore, the simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12.

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The equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625

The formula for finding the equation of a circle is expressed as:

(x-a)² + (y - b)² = r²

where

(a, b) is the centre

r is the radius

Given the following

(a, b) = (0, 0)

r = 12.5/2 = 6.25

Substitute

(x-0)² + (y - 0)² = 6.25²

x²+y²=39.0625

Hence the equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625

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The function that could represent the price tag's height relative to the table top is  h(t) = 4sin (22) +4

The question is incomplete because the options are not given and hence the correct option is shown below

Which function could represent the price tag's height relative to the table top, h(t), after it has been rolling for e seconds?

A n(t) = 2008(832) +2

B. h(t) =-2005(522) +2

C h(t) = –2sin(572) +2

D. h(t) = 4sin (22) +4

Given diameter is 4 inches and the time given is  5 seconds and

the number of rotations given is 4

We need to find the function that could represent the price tag's height relative to the table top .

Diameter = 4

So, Radius will be D/2 = 4/2

Radius=2

time given is  5 seconds and

the number of rotations given is 4

So ,   5/4 = 2π/w

Therefore ,

W = 8π / 5

Therefore

h(t) = h(t) = 4sin (22) +4

Hence The function that could represent the price tag's height relative to the table top is  h(t) = 4sin (22) +4

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Answer: x=11

Step-by-step explanation:

The lines are parallel, which you can tell by the two arrows. 4x-8 is a corresponding angle to 3x+3, meaning they are congruent.

4x-8 = 3x+3

x=11

Answer:

x = 11

Step-by-step explanation:

these angles are corresponding angles so they are equal to each other.

4x - 8 = 3x + 3 Subtract 2x from both sides

x - 8 = 3   Add 8 to both sides

x = 11

Plug 11 back into the equations find the angle measurements

4(11) -8 = 36 degrees

3(11) + 3 =  36degrees

The smallest possible value of N is 23.

According to the statement

we have given that the sequence {1,2,3.....n}

and the sum is 241. we have to find the smallest value of n.

So, for this purpose we use summation formula of an arithmetic sequence

Sn = n /2 ( a1 +an )

Put the values in it then.

Note that the sum of the first 21 integers  is   21 * 22 /2  =  231...this isn't large enough as compare to given value.

And the sum of the first  22 integers  =   22 * 23 / 2  =   253

So    253 - 241  =  12 = omitted sum.....  

but  the sum of two consecutive integers must be odd

And......the sum of the first 23 integers is  23 * 24 / 2  = 276

So.......276 - 241   =  35    = omitted sum

So....the   consecutive integers omitted must be  17  and 18

So....... the smallest value of n  is   23

So, The smallest possible value of N is 23.

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The equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank is g = 3h + 3; 12 gallon

Check all equation

g = 18 – 2h; 18 gallons

= 18 - 2(3)

= 18 - 6

= 12

g = 18 – 2h; 16 gallons

= 18 - 2(3)

= 18 - 6

= 12

g = 3h + 3; 30 gallons

= 3(3) + 3

= 9 + 3

= 12

g = 3h + 3; 12 gallon

= 3(3) + 3

= 9 + 3

= 12

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The rate at which the distance between the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.

Given length of ladder 39 m and the rate at which the wall is increasing is 101, the bottom of the ladder is 36 m from the wall.

Let bottom is x and the length of wall be y.

We have to find the rate at which the distance between the top of the ladder and the ground at that instant.

we have to find dy/dt.

We have to apply pythagoras theorem first.

[tex]x^{2} +y^{2} =39^{2}[/tex]---------------1

[tex]x^{2} +y^{2} =1521[/tex]

put the value of x=36 in the above equation

[tex]36^{2} +y^{2} =1521[/tex]

[tex]y^{2} =225[/tex]

y=15 m

We have to find the derivative of equation 1 with respect to t.

2x*dx/dt+2y*dy/dt=0

Because it is given that bottom is increasing at 101 meters per minute so dx/dt=101

2x*101+2y*dy/dt=0

put the value of y=15

2x*101+2*15*dy/dt=0

2x*101+2*15*dy/dt=0

dy/dt=-3030/2*36

dy/dt=-42.08

Hence the rate at which the rate at which the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.

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Question is wrong so it includes ladder length be 39 meters and the rate of increasing of bottom of ladder from bottom of wall is 101 meters per minute and the bottomis 36 m from the wall.

Answer:

The answer to your question is C. There a specific quantifiable target that we are interested in or trying to predict.

Step-by-step explanation:

I hope this helps and have a good day!

Answer:

You subtract 249 minus 5

The multiplicative inverse of -13/14 as in the task content is; -14/13.

The multiplicative inverse of a number x is given as; 1/x.

On this same note, it follows that since, the number whose multiplicative inverse is to be found is: -13/14, the multiplicative inverse is; -14/13.

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Answer:

  2.0 km

Step-by-step explanation:

The Law of Cosines can be used to find the third side of a triangle in which two sides and the angle between them are given.

The law of cosines tells us ...

  c² = a² +b² -2ab·cos(C)

Using the given values, we have ...

  c² = 4.2² +4.5² -2(4.2)(4.5)cos(26°)

Simplifying the equation, we get ...

  c² = 37.89 -37.8cos(26°) ≈ 3.91559

  c ≈ 1.979 . . . . km

The width of the strait is about 2.0 km.

The cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3

VAT is an acronym for Value Added Tax. This is a tax attach to goods and products.

Given that the price of a new television is $423. This price includes VAT in 17 1/2%.

a) The cost of the television before VAT was added is calculated below.

Let the initial cost = C

(17.5 + 100)/100 x C = 423

117.5/100 x C = 423

1.175C = 423

C = 423/1.175

C = $360

b. By the end of the year, the value of a television has fallen by 12% of its value at the start of that year. If the value of a television was $423 at the start of the year, the value of the television at the end of the third year will be calculated by using the formula

A = P(1 - R%)^3

Substitute all the parameters

A = 423(1 - 12/100)^3

A = 423 x [tex]0.88^{3}[/tex]

A = 288.3 dollars

Therefore, cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3

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Answer:

The solution for the expression is choice D 26√5 +2√10

Step-by-step explanation:

Hello!

First, apply distributive law: a(b+c)= ab+ac

Step-by-step explanation:

asleep percentage :- ( 8h /24h ) 100 % = 33.33%

awake percentage :- ( 16h / 24h ) 100 % = 66.67%

Answer:

true

-9(z+8)

-9*z +(-9)*8

-9z-72

Answer:

x^7y^9

Step-by-step explanation:

Remembering the laws of indices and applying BODMAS

(x^6y^8)^3/x^2y^2

(x^6 * y^8)^3/x^2 * y^2

opening bracket

we get;

x^6+3 * y^8+3/x^2 * y^2

x^9 * y^11/x^2 * y^2

Applying law of indices at which when the values are the same during division we pick one coefficient and minus the power

therefore;

x^9-2 * y^11-2

x^7 * y^9

=x^7y^9

Answer:

[tex]\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]

Step-by-step explanation:

NOTE :

[tex]x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}[/tex]

………………………………………

f(x) = x² + x +1

     [tex]=x^{2}+2\times \frac{x}{2} +1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]

The correct option is (b) h=0.5cos([tex]\pi[/tex]/6t)+9.5.

The equations can be used to model the height as a function of time, t, in hours is h=0.5cos([tex]\pi[/tex]/6t)+9.5.

The following is a presentation of the cosine function's generic form;

y =  a + cos(bx - c) + d

amplitude = a

b = cycle speed

Calculation for the model height;

The height, h (feet) of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

Obtain amplitude 'a' as

[tex]\begin{aligned}a &=\frac{\text { Maximum value }-\text { Minimum value }}{2} \\a &=\frac{10-9}{2} \\a &=\frac{1}{2} \\a &=0.5\end{aligned}[/tex]

The time 'T' is calculated as-

[tex]\begin{aligned}&\mathrm{T}=\frac{2 \pi}{\mathrm{b}} \\&12=\frac{2 \pi}{\mathrm{b}} \\&\mathrm{b}=\frac{2 \pi}{12} \\&\mathrm{~b}=\frac{\pi}{6}\end{aligned}[/tex]

Now, calculate 'd'

[tex]\begin{aligned}&\mathrm{d}=\frac{\text { Maximum value }+\text { Minimum value }}{2} \\&\mathrm{~d}=\frac{10+9}{2} \\&\mathrm{~d}=\frac{19}{2} \\&\mathrm{~d}=9.5\end{aligned}[/tex]

Therefore, with the height as a function of time, t, expressed in hours, can be modeled by the following equations:

h=0.5cos([tex]\pi[/tex]/6t)+9.5

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The complete question is-

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

A. h=0.5cos([tex]\pi[/tex]/12t)+9.5

B. h=0.5cos([tex]\pi[/tex]/6t)+9.5

C. h=cos([tex]\pi[/tex]/12t)+9

D. h=cos([tex]\pi[/tex]/6t)+9

Answer:4

Step-by-step explanation: 32\8 = 4

IfIf AD BD, the following relationships that can be proved and why is: D. ΔACD ΔBCD, because of SAS.

The relationship that can be proved is ΔACD ΔBCD, because of SAS.

The reason is that m<CDA=M<CDB=90°

CD=CD

AD=BD

Hence, ΔACD=ΔBCD because of SAS. SAS congruence can tend to be proved when the length of the two side correspond and when  the angle between the two side is equal.

Therefore the correct option is D.

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The height of squared pyramid is [tex]\frac{1}{3}h[/tex] unit.

A cube is a solid three-dimensional object with six square faces or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.

Volume of cube [tex]= (side)^3 \ unit^3[/tex]

Given the height of cube is [tex]h[/tex] unit.

Volume of cube is [tex]h^3 \ unit^3[/tex]

Let the height of squared pyramid is [tex]x[/tex] unit

Volume of squared pyramid is [tex]\frac{1}{3} h^{2} \times x \ unit^3[/tex]

According to the question, we have

Volume of cube = [tex]6 \times[/tex] volume of squared pyramid

[tex]\Rightarrow h^3=6 \times \frac{1}{3}h^2 \times x\\\Rightarrow h^3=2 \ h^2 \times x\\\Rightarrow h=2x\\\Rightarrow x= \frac{1}{2}h[/tex]

Therefore, the height of squared pyramid is [tex]\frac{1}{3}h[/tex] unit.

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Answer:

Option C more peaked and more widely spread.

Step-by-step explanation:

15 + 35 + 18 + 30 + 25 + 21 + 32 + 16

80 + 78 + 34

192/8 = 24

24 + 22 + 27 + 28

46 + 55 = 101/4 = 25.2

The possible values of x according to the give. equation are; 0, ±√3i, ±2i, i, -1.

The possible values of x in the equation given in the task content represent the zeroes of the equation and can be determined as follows;

(x²+3) (x³+4x) (x²+x-i-xi) = 0.

Hence, by further factorisation; we have;

x(x²+3) (x²+4) (x-i) (x+1) = 0.

The possible values of x are therefore;

x = 0;

x²+3 = 0; x = ±√3i

x² +4 = 0; x = ±2i

x -i = 0; x = i.

x +1 = 0; x = -1

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Answer:

About 71.77 degrees

Step-by-step explanation:

The starting leg is 2.3 km and the finishing leg is 6.2 km.

Using the law of cosines C^2 = A^2 + B^2 -2AB*cos(c) where A = 2.3 km, B = 6.2 km, C = 5.9 km, and angle c is the opposite angle to side C, we get:

5.9^2 = 2.3^2 + 6.2^2 -2(2.3)(6.2)*cos(c)

cos(c) = -(5.9^2 - 2.3^2 - 6.2^2)/(2*2.3*6.2)

c = 71.77 degrees

Answer:

72°

Step-by-step explanation:

when we have all the sides and need an angle, we use the law of cosine (the extended Pythagoras) :

c² = a² + b² - 2ab×cos(C)

where c is the side opposite of the angle C.

so, since the starting leg is 2.3 km, and the finishing leg is 6.2 km, we know that 5.9 km is the side opposite of the angle between the starting and finishing legs.

so, we have

5.9² = 2.3² + 6.2² - 2×2.3×6.2×cos(C)

34.81 = 5.29 + 38.44 - 28.52×cos(C)

-8.92 = -28.52×cos(C)

cos(C) = -8.92/-28.52 = 0.312762973...

C = 71.77418076...° ≈ 72°

We can to convert the expression  [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression   [tex]\sqrt[5]{9}[/tex].  by using the laws of indices.

A radical expression is an expression of the form ⁿ√x where it is called the nth root of x.

Now, to write [tex](3^{\frac{1}{5} } )^{2}[/tex] as  the radical expression [tex]\sqrt[5]{9}[/tex], we use following laws of indices

So,  [tex](3^{\frac{1}{5} } )^{2} = (3^{2} )^{\frac{1}{5} }[/tex]

  [tex](3^{2} )^{\frac{1}{5} } = 9^{\frac{1}{5} } = \sqrt[5]{9}[/tex]

Thus, we can to convert the expression  [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression   [tex]\sqrt[5]{9}[/tex].  by using the laws of indices.

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The option D is the correct option.

According to the statement

we have to define the sample variance in the words.

So,

The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.

and in the case of the population variance it becomes

The population variance is the average of the squared distances of the measurements on all units in the population from the mean.

This is the method by which we define the sample variance and population variance.

So, The option D is the correct option.

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Answer:

6

Step-by-step explanation:

Substituting in n = 2,

[tex]\frac{3(2)^{2}}{2}=6[/tex]

Let [tex]a,b,c[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% acid solutions, respectively. These quantities then contain [tex]0.20a[/tex], [tex]0.30b[/tex], and [tex]0.60c[/tex] liters of acid.

The chemist wants to end up with a total volume of 54 liters, so

[tex]a + b + c = 54[/tex]

and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so

[tex]0.20a + 0.30b + 0.60c = 24.3[/tex]

He will also use twice as much of the 60% solution as the 30% solution, so

[tex]c = 2b[/tex]

Substitute this into the first two equations and solve for [tex]a,b[/tex].

[tex]\begin{cases} a + 3b = 54 \\ 0.20a + 1.50b = 24.3 \end{cases}[/tex]

Eliminating [tex]b[/tex], we have

[tex](a + 3b) - 2 (0.20a + 1.50b) = 54 - 2(24.3) \implies 0.60a = 5.4 \implies \boxed{a = 9}[/tex]

Solve for [tex]b[/tex].

[tex]9+3b=54 \implies 3b=45 \implies \boxed{b=15}[/tex]

Solve for [tex]c[/tex].

[tex]c = 2(15) \implies \boxed{c=30}[/tex]

a = 9, b = 15 and c = 30 liters of each solution should be used.

According to the question:

Let a, b, and c stand for the relative volumes (in liters) of the 20 percent, 30 percent, and 60 percent acid solutions. The amount of acid in these amounts is 0.20a, 0.30b, and 0.60c liters.

a+b+c = 54 because the chemist wishes to have a final volume of 54 liters.

and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so

0.20a + 0.30b + 0.60c = 24.3

Additionally, he will consume twice as much of the 60% solution as the 30% solution, thus c = 2b.

Substitute this into the first two equations and solve for a,b

a + 3b = 54

0.20a + 1.50b = 24.3

[tex](a+3 b)-2(0.20 a+1.50 b)=54-2(24.3) \\0.60 a=5.4[/tex]

a = 9.

9+3b = 54

3b = 45

b = 15.

c = 2(15)

c = 30.

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The geometric modeling is analyzed below.

Basic shapes are generally created using points, lines, circles, and triangles. Some basic shapes are rectangles, ellipses, triangles, and curves.

In geometric modeling, we make a cad model of parts for virtual analysis. By geometric modeling, one can model, and perform CAE analysis to optimize the product.

The best part is the period of doing all this is very small compared to practical manufacturing and looking at the product. In CAD one can very quickly alter the design and come up with new concepts in a very small span of time.

Here chances of error can be shorted easily and there is no wastage of material hence cost saving is there compared to practically manufacturing the part and altering it.

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