1/8 of passengers of a train were children. if there were 40 children travelling in the train on a certain day, how many adults were there in the train?

The volume of the regular pyramid is 128 unit³.

Option D) 128 unit³ is the correct answer.

This question is incomplete, the missing image is uploaded along this answer below.

The volume of pyramid is expressed as;

V = ( 1/3 ) × l × w × h

Given that;

We substitute our given values into the equation above.

V = ( 1/3 ) × 8 × 8 × 6

V = 128 unit³

The volume of the regular pyramid is 128 unit³.

Option D) 128 unit³ is the correct answer.

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Answer:

x = [tex]\frac{2}{7}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}[/tex](7x+2) = 2

   7x+2 = 2÷[tex]\frac{1}{2}[/tex]

            = 2×2

            = 4

       7x = 4-2

            = 2

       ∴x = 2÷7

            = [tex]\frac{2}{7}[/tex]

Answer:

[tex]\displaystyle \frac{2}{7} = x[/tex]

Step-by-step explanation:

[tex]\displaystyle 2 = \frac{1}{2}(7x + 2) \Rightarrow 2 = 3\frac{1}{2}x + 1 \hookrightarrow \frac{1}{3\frac{1}{2}} = \frac{3\frac{1}{2}x}{3\frac{1}{2}} \\ \\ \boxed{\frac{2}{7} = x}[/tex]

I am joyous to assist you at any time.

A. 12.08

9 + 2 = 11

(So, 11 across on our x - axis from - 9 to 2)

Then, up 5 from 2 on our x-axis

Join the 2 dots of coordinates, & creating a triangle. Base 11, height 5

Use Pythagoras Theorem, to find that distance between the coordinates (the hypotenuse)

Root 11^2 + 5^2 = 12.083056...

(root means square root)

Hope this helps!

Answer:

Hello! The answer to this question is A. 12.08.

Step-by-step explanation:

The distance formula is:

[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2 }[/tex]

With the distance formula, we can now substitute the values from the points provided:

[tex]\sqrt{(2 - (-9))^2 + (5 - 0)^2} \\= \sqrt{11^2 + 5^2\\\\\\\\= \sqrt{121 + 25} \\=\sqrt{146} \\= 12.08[/tex]

The distance between the points is 12.08.

Option b. The oversight was discovered during the preparation of gators' 2021 financial statements. depreciation expense on this machine for 2021 should be $372,000.

The yearly straight-line devaluation cost for the machine would be $186,000 ($930,000/5). In any case, since no deterioration was perceived in 2020, the collected devaluation toward the start of 2021 would be $0 rather than $186,000. In this manner, the complete devaluation cost for 2021 would be the yearly deterioration of $186,000 in addition to the get up to speed devaluation for 2020 of $186,000, for a sum of $372,000. This make up for lost time devaluation is important to address the blunder made in the earlier year and guarantee that the resource is appropriately recorded on the asset report. Accordingly, the right response is $372,000.

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The complete question is:

On January 1, 2020, Oriole Corp. acquired a machine at a cost of $930000. It is to be depreciated on the straight-line method over a 5-year period with no residual value. Because of a bookkeeping error, no depreciation was recognized in Oriole's 2020 financial statements. The oversight was discovered during the preparation of Oriole's 2021 financial statements. Depreciation expense on this machine for 2021 should be

$232500.

$372000.

$186000.

$0.

Answer:

[tex](x-2)^5 = x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32[/tex]

Step-by-step explanation:

Binomial Theorem

[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]

Given expression:

[tex](x-2)^5[/tex]

Compare with the Binomial Theorem:

[tex]a=x, \quad b=-2, \quad n=5[/tex]

Substitute the values into the formula:

[tex]\begin{aligned}(x-2)^5 & = x^5+\dfrac{5!}{1!4!}x^{4}(-2)+\dfrac{5!}{2!3!}x^{3}(-2)^2+\dfrac{5!}{3!2!}x^{2}(-2)^3+\dfrac{5!}{4!1!}x^{1}(-2)^4+(-2)^5\\\\& =x^5+\dfrac{120}{24}x^{4}(-2)+\dfrac{120}{12}x^{3}(4)+\dfrac{120}{12}x^{2}(-8)+\dfrac{120}{24}x(16)-32\\\\& =x^5-\dfrac{240}{24}x^{4}+\dfrac{480}{12}x^{3}-\dfrac{960}{12}x^{2}+\dfrac{1920}{24}x-32\\\\& =x^5-10x^{4}+40x^{3}-80x^{2}+80x-32\end{aligned}[/tex]

Pascal's Triangle

Pascal's triangle is an arrangement of binomial coefficients in triangular form.  Each row has 1 at both ends, and each remaining number in the row is found by adding together the two numbers directly above it.

[tex]\phantom{-b)))))))}1\\\phantom{-b)))))}1 \:\quad 1\\\phantom{-b)))}1 \:\quad 2\: \quad 1\\\phantom{-b)}1 \:\quad 3\: \quad 3\: \quad 1\\\phantom{))}1 \quad 4 \:\: \quad 6 \quad \;4 \: \quad 1\\1 \quad 5 \quad 10 \quad 10 \quad 5 \quad 1[/tex]

(Note: The initial row with the single number 1 is row zero)

Each term in the binomial expansion using Pascal's triangle is the product of a coefficient, a with an exponent, and b with an exponent.

As we move through each term from left to right, the exponent of a decreases from the exponent of the expression down to zero, and the exponent of b increases from zero up to the exponent of the expression.

The coefficients of each term are the numbers which appear in the number of the row that corresponds with the exponent of the expression.

From the given expression, the power that we are expanding the bracket to is 5, so we need to look at line 5 of Pascal's triangle, which is:

1 5 10 10 5 1

Therefore, the expansion using Pascal's triangle to the power 5 of is:

[tex](a+b)^5=1a^5b^0+5a^4b^1+10a^3b^2+10a^2b^3+5a^1b^4+1a^0b^5[/tex]

Substituting the values of a and b:

[tex]\begin{aligned}(x-2)^5 & = 1x^5(-2)^0 + 5x^4(-2)^1 + 10x^3(-2)^2 + 10x^2(-2)^3 + 5x^1(-2)^4 + 1x^0(-2)^5\\\\ & = x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32\end{aligned}[/tex]

Hello !

Answer:

When x = -3 or x = 3

Step-by-step explanation:

[tex] \frac{ {x}^{2} - 9}{ {x}^{2} + 6x + 8} = 0[/tex]

[tex]\Leftrightarrow \frac{ {x}^{2} - 9 }{ {x}^{2} + 6x + 8} \times ( {x}^{2} + 6x + 8) = 0 \times ( {x}^{2} + 6x + 8)[/tex]

[tex]\Leftrightarrow {x}^{2} - 9 = 0[/tex]

[tex]\Leftrightarrow(x - 3)(x + 3) = 0[/tex]

[tex]\Leftrightarrow \: x - 3= 0 \: or \: x + 3 = 0[/tex]

[tex]\Leftrightarrow \: x = 3 \: or \: x = - 3[/tex]

[tex]\boxed{S = {-3 \: \: or \: \: 3}}[/tex]

Answer:

[tex] < 25 = 56. < { \times 4 \div hwh3 \times }^{?} [/tex]

Answer:

Attached

Step-by-step explanation:

See attached image

They should quote 150 hours so that they can get 98% of the batteries to meet the guarantee.

Given mean of 140 hours and standard deviation of 4 hours with confidence level=98%.

We have to find the lifespan which they should quote to get 98% confident that their batteries meet the guarantee.

We have to use z test for this .

μ=140 hours and σ=4 hours

Z=X-μ/σ

When p value is 0.98 then from z table z value will be 2.58.

Z=X-140/4

2.58=X-140/4

2.58*4=X-140

10.32=X-140

X=150.32

after rounding off we will get 150 hours.

Hence they should quote 150 hours of lifetime on batteries.

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Answer:

132

Step-by-step explanation:

Answer:

x=10, MB=19 CM=16 CB=35

Step-by-step explanation:

Since M is the midpoint of line CB

CM=MB

x+6=2x-4

6+4=2x-x

10=x

The rest is pretty simple, plug 10 in for x

The statements that are true are

From the question, we are to determine the statements that are true

In the given number line,

A =  -2 1/6

B = - 1/2

C = 1/3

D = 1 2/3

B - C = -1/2 - 1/3

B - C = -5/6

∴ B - C ≠ 1/6

A + C = -2 1/6 + 1/3

A + C = -1 5/6

∴ The sum of A and C is negative

A + D = -2 1/6 + 1 2/3

A + D = -1/2

B = -1/2

∴ A + D = B

1 2/3 ÷ - 1/2 = -10/3

∴ The quotient of D and B is -10/3

A×B = -2 1/6 × -1/2

A×B = 13/12

Product of A and C

A×C = -2 1/6 × 1/3

A×C = -13/18

∴ The product of A and B > the product of A and C

|B| = 1/2

|C| = 1/3

|B| > |C|

|B| is NOT less than |C|

Hence, the statements that are true are

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Answer: (1,2)

Step-by-step explanation:

Reflecting across the y-axis means [tex](x,y) \longrightarrow (-x,y)[/tex]

So, [tex](-1,2) \longrightarrow \boxed{(1,2)}[/tex]

Answer:

Below.

Step-by-step explanation:

Standard error  =

standard deviation / √n

=  7.89 / √300

= 0.456 approx.

The equation of the given  line is y=2/3x-6

We have given the graph of the line and also the equation of the line

[tex]y=-6x+\frac{2}{3}[/tex]

[tex]y=\frac{2}{3}x-6[/tex]

[tex]y=-6x+\frac{3}{2}[/tex]

[tex]y=\frac{3}{2}x-6[/tex]

We have to determine which equations graph is given here

We have to draw a graph of the given equation of the line

To find the coordinate of the given line

The equation of the line second is

x=0 then y=-6

and when y=0 then x=9

We get the points (0,-6) and (9,0)

plot this point and we get the given graph of the line.

Therefore the second option is correct.

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Answer:

Hence if the square of binomials needs to be find then we use square of binomial pattern and if the product of conjugate pair needs to determine then we use product of conjugate pattern.

Step-by-step explanation:

Explanation

A) The outcome for Event X or Y is expressed as; X ∪ Y = {D, A, B, E}

B) The outcome of Event X and Y is; X ∩ Y = {A, B, E}

We are given the events;

Event X; The letter selected is found in the word "BEAD"

Event Y; The letter selected comes after D

Thus;

A) The outcome for Event X or Y is expressed as;

X ∪ Y = {D, A, B, E}

B) The outcome of Event X and Y is;

X ∩ Y = {A, B, E}

C) Complement of Event Y is;

Y^(c) = {D}

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The system of equations are x+ y =16 and 2y=x.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions

let the two points shots be x

let the three points shots be y.

According to question,

x+ y =16

and,

2y=x

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The proper sequence of steps in implementing the model in Excel presented in the textbook is option b which is organize the data, represent the decision variables, represent the objective function, represent the constraints and represent the bounds on the decision variables.

Given process of implementing the model in Excel and we have to choose the correct process.

The process of implementing the model in Excel is as under:

1) Organize the data: In excel, to organize the data we have to put similar items in the same column. We have to design the data so that all rows have similar items in the same column. We have to keep a range of data separate and leave at least one blank column and one blank row between a related data range.

2) Represent the decision variables: Now we have to represent the decision variables according to which logical function performs tasks.

3)Represent the objective function: It is important because on the basis of this all the logical function perform tasks.

4) Represent the constraints: In excel when we are using solver we have to now represent the constraints of the objective function.

5) Represents the bounds on the decision variables.

Hence the proper sequence of steps in implementing the model in excel is Organize the data, represent the decision variables, represent the objective function, represent the constraints, and represent the bounds on the decision variables.

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See below for the proof of the trigonometry identity

The identity is given as:

(sin(x) + cos(x))² / sin(2x)= csc (2x) + 1

Start by expanding the numerator

(sin²(x) + cos²(x) + sin(2x)) / sin(2x)= csc (2x) + 1

Express sin²(x) + cos²(x) as 1

(1 + sin(2x)) / sin(2x)= csc (2x) + 1

Expand the fraction

1/sin(2x) + sin(2x)/sin(2x) = csc(2x) + 1

Evaluate the quotient

csc(2x) + 1 = csc(2x) + 1

Hence, the trigonometry identity has been proved

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Answer:

NO

Step-by-step explanation:

Answer:

1/2 log2

Step-by-step explanation:

I hope you understand

Answer:

[tex]x & = \dfrac{1}{2} \ln 2[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x^2+4x\\g(x)=1+e^{2x}\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

Therefore, the given composite function fg(x) means to substitute the function g(x) in place of the x in function f(x):

[tex]\begin{aligned}f[g(x)] & = [g(x)]^2 + 4[g(x)]\\& = \left(1+e^{2x}\right)^2+4\left(1+e^{2x}\right)\\& = 1+2e^{2x}+(e^{2x})^2+4+4e^{2x}\\& = e^{4x}+6e^{2x}+5\end{aligned}[/tex]

[tex]\textsf{Let }u=e^{2x}[/tex]

[tex]\implies e^{4x}+6x^{2x}+5=u^2+6u+5[/tex]

Set the composite function to 21 and factor:

[tex]\begin{aligned}f[g(x)] & = 21\\\implies u^2+6u+5 & = 21\\u^2+6u-16 & = 0\\u^2+8u-2u-16 & = 0\\u(u+8)-2(u+8) & = 0\\(u-2)(u+8) & = 0\\\end{aligned}[/tex]

Apply the zero-product property:

[tex]\implies (u-2)=0 \implies u=2[/tex]

[tex]\implies (u+8)=0 \implies u=-8[/tex]

[tex]\textsf{Substitute back in }u=e^{2x}:[/tex]

[tex]\implies e^{2x}=2[/tex]

[tex]\implies e^{2x}=-8[/tex]

As we cannot take logs of negative numbers, the only solution is:

[tex]\begin{aligned}e^{2x} & = 2\\\ln e^{2x} & = \ln 2\\2x \ln e & = \ln 2\\2x(1) & = \ln 2\\2x & = \ln 2\\\implies x & = \dfrac{1}{2} \ln 2\end{aligned}[/tex]

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Answer:

12.5

30

68.5

Step-by-step explanation:

Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

Given that, ABCD is a quadrilateral, segment AB is congruent to segment CD, ∠1 is congruent to ∠2.

We need to prove that ABCD is a parallelogram.

If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram.

From the given quadrilateral ABCD:

AB=CD (Given)

∠1=∠2 (Given)

AC=AC (Diagonal)

From ASA congruency ΔABC and ΔADC are congruent.

By CPCT, AD=BC and ∠ABC=∠ADC.

Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

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Answer:

x = 2

Step-by-step explanation:

divide both sides by 2

then simplify

Apply exponent rule and vowla theirs your final answer of x = 2

El celular de contado costará 7500 pesos, mientras que el celular a crédito tendrá un costo de 9000 pesos.

7500 / 100 = 75 (valor del 1%)

75 x 20 = 1500 pesos

Celular a contado: El precio no aumenta por lo que el valor sería de 7500 pesos.

Celular a crédito: 7500 + 1500 = 9000 pesos

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Answer:

The graph of [tex]d(x)[/tex] is [tex]f(x)[/tex] shifted right by [tex]27[/tex] units.

The area of the rectangle is 240 square inches

The dimensions are given as:

Length = 15 inches

Width = 4/3 feet

Start by converting feet to inches

Width = 4/3 * 12 inches

Width = 16 inches

The area is then calculated as:

Area = Length * Width

This gives

Area = 15 * 16

Evaluate

Area = 240

Hence, the area of the rectangle is 240 square inches

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Answer:

Correct answer not shown on the options.

y = -(1/2)+1

Step-by-step explanation:

Let's find an equation in the format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

The slope can be calculated as the Rise/Run of the line between the two given points (-6,4) and (-2,2):

Rise = (2 - 4) = -2

Run = (-2 - (-6)) = 4

Slope = Rise/Run = -2/4 or -(1/2)

In fact, the actual full equation is y= -(1/2)x+1  (See attached graph).

None of the options have a slope of -(1/2).  Either the information on the two points or the options are incorrect.

Answer:

y=[tex]-\frac{1}{2}x[/tex]+1

Step-by-step explanation:

y = mx plus c,where m is the gradient.

∴m =[tex]\frac{y2-y1}{x2-x1}[/tex]=[tex]\frac{2-4}{-2-(-6)}[/tex]=[tex]\frac{-2}{4}[/tex]=[tex]-\frac{1}{2}[/tex]

Equation of a line equals

y-y1=m(x-x1) (Using point (-6, 4) for x1 and y1 values)

y-4=[tex]-\frac{1}{2}[/tex](x-(-6))

y-4=[tex]-\frac{1}{2}[/tex](x+6)

y-4=[tex]-\frac{1}{2}[/tex]x-3

2(y-4)=-x-3(2)(multiply through by 2)

2y-8=-x-6

2y=-x+2(divide through by 2)

y=[tex]-\frac{1}{2}x[/tex]+1

∴the equation of the line is y=[tex]-\frac{1}{2}x[/tex]+1

The function that has the given properties below is y = -4sin(x).

It should be noted that a function can be used to illustrate the relationship between variables.

In this case, the domain is the set of all real numbers, the amplitude is 4, and one x-intercept is (2 pi, 0).

The appropriate function is y = -4sin(x).

The graph is attached.

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The average number of points will be 15 points.

It should be noted that average or mean simply means the total added values fall the data in a set which is then divided by the number of data.

Let the assumed points be 10, 12, 24, 15, 23, and 6.

In this case, the average number of points will be:

= (10 + 12 + 24 + 15 + 23 + 6)/6

= 90/6

= 15 points

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A line segment can be made up of the addition of different fractions of the line on a straight path i.e a given line segment can be broken into smaller parts.

Therefore, the required proof that EG = HK is shown below:

Given that: EF = JK

                  FG = HJ

But,

EG = EF + FG .............. 1

and

HK = HJ + JK ............. 2

From equation 1, we have:

EG = EF + FG

     = JK + HJ (since EF = JK, and FG = HJ)

So that,

EG = JK + HJ ........... 3

Also from equation 2, we have:

HK = HJ + JK

     = FG + EF (since EF = JK, and FG = HJ)

So that,

HK = FG + JK ........... 4

Therefore, comparing equations 1, 2, 3, and 4, it can be concluded that;

EG = HK

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