Which is the inverse of the function f (x) = 1/4x + 1/2

255 number of adults and 355 number of students bought ticket.

Here,  we have,

Let the number of adults bought tickets are x and the number of students that bought tickets is (x + 100).

Since it is given that 100 more students brought tickets than adults.

Now, each adult ticket costs $5 and each student's ticket costs $3.5 and the total collected value of tickets is $2517.5.

So, 5x + 3.5(x + 100) = 2517.5

⇒ 8.5x + 350 = 2517.5

⇒ 8.5x = 2167.5

⇒ x = 255

So, 255 number of adults and (255 + 100) = 355 number of students bought ticket. (Answer)

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Answer:

a) The truth table for F is as follows:

A B C D F

0 0 0 0 1

0 0 0 1 0

0 0 1 0 0

0 0 1 1 1

0 1 0 0 0

0 1 0 1 1

0 1 1 0 1

0 1 1 1 0

1 0 0 0 0

1 0 0 1 1

1 0 1 0 1

1 0 1 1 0

1 1 0 0 1

1 1 0 1 0

1 1 1 0 0

1 1 1 1 1

b) Using the Quine-McCluskey method, we can find the minimal sum-of-products form of F:

F = ¬A ∧ ¬B ∧ D ∨ ¬A ∧ C ∧ D ∨ A ∧ B ∧ ¬C ∧ D ∨ A ∧ ¬B ∧ C ∧ D

c) Using Boolean algebra, we can simplify the Boolean expression of F as follows:

F = (¬A ∧ ¬B ∧ D) ∨ (¬A ∧ C ∧ D) ∨ (A ∧ B ∧ ¬C ∧ D) ∨ (A ∧ ¬B ∧ C ∧ D)

= (¬A ∧ (¬B ∧ D ∨ C ∧ D)) ∨ (A ∧ (B ∧ ¬C ∧ D ∨ ¬B ∧ C ∧ D))

= (¬A ∧ (¬B ∨ C) ∧ D) ∨ (A ∧ ((B ∧ ¬C) ∨ (¬B ∧ C)) ∧ D)

= (¬A ∧ ¬B ∧ C ∧ D) ∨ (¬A ∧ B ∧ ¬C ∧ D) ∨ (A ∧ B ∧ C ∧ D) ∨ (A ∧ ¬B ∧ ¬C ∧ D)

Therefore, the simplified Boolean expression of F in terms of the three variables A, B, and C is:

F = (¬A ∧ ¬B ∧ C ∧ D) ∨ (¬A ∧ B ∧ ¬C ∧ D) ∨ (A ∧ B ∧ C ∧ D) ∨ (A ∧ ¬B ∧ ¬C ∧ D)

Step-by-step explanation:

The approximate height difference between the birdhouse and the tree house is 3 ft.

It is less than the approximate difference in height between the swing set and the tree house.

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

We have:

height of birdhouse = 14[tex]\frac{9}{16}[/tex] ft

height of tree house = 11[tex]\frac{13}{16}[/tex] ft

Thus, the approximate height difference between the birdhouse and the tree house will be:

14[tex]\frac{9}{16}[/tex] ft - 11[tex]\frac{13}{16}[/tex]  = 2[tex]\frac{3}{4}[/tex] ft

                   = 2.75 ft

                  = 3 ft

To determine if it is greater than or less than the approximate difference in height between the swing set and the tree house, we have to find the approximate difference in height between the swing set and the tree house. That is:

height of swing set = 8[tex]\frac{1}{4}[/tex] ft

height of tree house = 11[tex]\frac{13}{16}[/tex] ft

difference = 11[tex]\frac{13}{16}[/tex] - 8[tex]\frac{1}{4}[/tex]

                    = 3[tex]\frac{1}{2}[/tex]

                    = 3.5

                    = 4 ft

Therefore, it is less than the approximate difference in height between the swing set and the tree house

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Answer: 10:22

Step-by-step explanation:

9:55 + :05 = 10:00

10:00+ :22 = 10:22

The area of the triangle in the shaded region is derived to be 29.75 square inches.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

For the triangle in the shaded region;

base = 8.5 inches

height = 7 inches

area of the triangle = 1/2 × 8.5 in × 8.5 in

area of the triangle = (59.5/2) in²

area of the triangle = 29.75 in²

Therefore, the area of the triangle in the shaded region is derived to be 29.75 square inches.

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Answer:

(x - 3)² + (y + 4)² = 29

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

we have the coordinates of the centre but require to find the radius r

the radius is the distance from the centre to a point on the circle.

using the distance formula to find r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (3, - 4 ) centre and (x₂, y₂ ) = (8, - 2) point on circle

r = [tex]\sqrt{(8-3)^2+(-2-(-4))^2}[/tex]

  = [tex]\sqrt{5^2+(-2+4)^2}[/tex]

  = [tex]\sqrt{25+2^2}[/tex]

  = [tex]\sqrt{25+4}[/tex]

  = [tex]\sqrt{29}[/tex]

then equation with centre (3, - 4 ) and r = [tex]\sqrt{29}[/tex] , is

(x - 3)² + (y - (- 4) )² = ([tex]\sqrt{29}[/tex] )² , that is

(x - 3)² + (y + 4)² = 29

The equation is verified, and we have shown that E_0 = cos⁴θ is equivalent to E_0 = E_0 (1/2 + cos2θ/2)².

We have,

To verify the equation

E_θ = E_0 cos^4θ = E_0 (1/2 + cos2θ/2)², we can expand the right-hand side and simplify it.

Starting with the right-hand side of the equation:

E_0 (1/2 + cos2θ/2)²

Expanding the square using the binomial expansion:

E_0 [(1/2)² + 2(1/2)(cos2θ/2) + (cos2θ/2)²]

Simplifying:

E_0 [1/4 + cos2θ + (cos2θ)²/4]

Combining the terms:

E_0 [1/4 + 4cos²θ/4 + (cos²θ)²/4]

Simplifying further:

E_0 [1/4 + 4cos²θ/4 + cos⁴θ/4]

Combining the terms again:

E_0 [1/4 + 4cos²θ/4 + cos⁴θ/4] = E_0 [1/4 + 4cos²θ/4 + cos⁴θ/4]

Simplifying the expression yields:

E_0 cos⁴θ = E_0 cos⁴θ

Therefore,

The equation is verified, and we have shown that E_0 = cos⁴θ is equivalent to E_0 = E_0 (1/2 + cos2θ/2)².

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The center and radius of the circle is (5, -3), and 5 respectively.

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

Given the equation of the circle in the question:

( x - 5 )² + ( y + 3 )² = 25

To identify the center and the radius.

Comparing this equation ( x - 5 )² + ( y + 3 )² = 25 to the standard form of a circle equation, which is (x - h)² + (y - k)² = r², we can easily identify the center and radius of the circle.

( x - 5 )² + ( y + 3 )²

(x - h)² + (y - k)² = r²

The center of the circle is given by the values (h, k), which correspond to the opposite signs of the terms inside the parentheses.

In this case, the center of the circle is (5, -3), as we have (x - 5)² and (y + 3)².

The radius of the circle is the square root of the value on the right side of the equation.

In this case, the radius is √25, which simplifies to 5.

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Answer:

1.3136363636363637

Step-by-step explanation:

Bc u times 17 times 17 devide by 220

Answer:

6 in³

Step-by-step explanation:

volume = width X length X height

= 3 X 1 X 2

= 6 in³

To prove that (secx+tanx)² = (cscx+1)/(cscx-1), we will start with the left-hand side (LHS) of the equation and simplify it step by step until it matches the right-hand side (RHS) of the equation.

LHS: (secx+tanx)²

Using the trigonometric identities secx = 1/cosx and tanx = sinx/cosx, we can rewrite the LHS as:

LHS: (1/cosx + sinx/cosx)²

Now, let's find a common denominator and simplify:

LHS: [(1+sinx)/cosx]²

Expanding the squared term, we get:

LHS: (1+sinx)² / cos²x

Next, we will simplify the denominator:

LHS: (1+sinx)² / (1 - sin²x)

Using the Pythagorean identity sin²x + cos²x = 1, we can replace 1 - sin²x with cos²x:

LHS: (1+sinx)² / cos²x

Now, let's simplify the numerator by expanding it:

LHS: (1+2sinx+sin²x) / cos²x

Next, we will simplify the denominator by using the reciprocal identity cos²x = 1/sin²x:

LHS: (1+2sinx+sin²x) / (1/sin²x)

Now, let's simplify further by multiplying the numerator and denominator by sin²x:

LHS: sin²x(1+2sinx+sin²x) / 1

Expanding the numerator, we get:

LHS: (sin²x + 2sin³x + sin⁴x) / 1

Now, let's simplify the numerator by factoring out sin²x:

LHS: sin²x(1 + 2sinx + sin²x) / 1

Using the fact that sin²x = 1 - cos²x, we can rewrite the numerator:

LHS: sin²x(1 + 2sinx + (1-cos²x)) / 1

Simplifying further, we get:

LHS: sin²x(2sinx + 2 - cos²x) / 1

Using the fact that cos²x = 1 - sin²x, we can rewrite the numerator again:

LHS: sin²x(2sinx + 2 - (1-sin²x)) / 1

Simplifying the numerator, we have:

LHS: sin²x(2sinx + 1 + sin²x) / 1

Now, let's simplify the numerator by expanding it:

LHS: (2sin³x + sin²x + sin²x) / 1

LHS: 2sin³x + 2sin²x / 1

Finally, combining like terms, we get:

LHS: 2sin²x(sin x + 1) / 1

Now, let's simplify the RHS of the equation and see if it matches the LHS:

RHS: (cscx+1) / (cscx-1)

Using the reciprocal identity cscx = 1/sinx, we can rewrite the RHS:

RHS: (1/sinx + 1) / (1/sinx - 1)

Multiplying the numerator and denominator by sinx to simplify, we get:

RHS: (1 + sinx) / (1 - sinx)

Now, we can see that the LHS and RHS are equal:

LHS: 2sin²x(sin x + 1) / 1

RHS: (1 + sinx) / (1 - sinx)

Therefore, we have proven that (secx+tanx)² = (cscx+1)/(cscx-1).

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Answer:

Step-by-step explanation:

we know that,

★ The sum of the angles in a triangle is always 180° ...

__________________________________

Thus, the Value of x is 34°.

Answer:

Step-by-step explanation:

We know that,

Sum of three side of triangle is 180°

so,

100° + 46° + x = 180°

146° + x = 180°

x = 180° - 146°

x = 34°

[tex]\underline{\rule{190pt}{4pt}}[/tex]

The pair of triangles shown can be seen to be similar by SAS.

When comparing two triangles, one way to tell if they are similar is to apply the SAS (Side-Angle-Side) similarity criterion. This criterion states that two triangles are comparable if they have two pairs of corresponding sides in proportion and congruent included angles between those sides.

Triangles must have an equal ratio of their matching sides' lengths. The respective sides' included angles must be equivalent.

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Answer:

the answer is C

Step-by-step explanation:

any negative power is the reciprocal

so m^(-2) = 1/m^2

and so on

1/n^(-3) = n^(3)

Answer:

[1;1;1]

Step-by-step explanation:

try this option; all the details are in the attachment.

Step-by-step explanation:

remember, when we multiply the same base, we add the exponents, when we divide the same base we subtract the exponents.

when we have exponent of exponent, we multiply the exponents.

so,

the expression is

(z^ac / z^bc) × (z^ab / z^ac) × (z^bc / z^ab) = 1

we have in there the commutative and associative properties of multiplication : the sequence of operands do not matter at all.

and therefore we have in there the terms :

z^ac / z^ac

z^bc / z^bc

z^ab / z^ab

all three are 1

and so the main expression is

1 × 1 × 1 = 1

which is true, of course, and therefore the original equation is true.

The statements that complete the function transformations are left, up, stretch and stretch

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

f(x) = (x + 94)²

Also, we have

f(x) = x²

This implies that f(x) = (x + 94)² is obtained by shifting f(x) = x² left by 94 units

Next, we have

f(x) = x² + 94

This implies that f(x) = x² + 94² is obtained by shifting f(x) = x² up by 94 units

Next, we have

f(x) = 94√x from f(x) = √x

This implies that f(x) = 94√x can be obtained from vertically stretching f(x) = √x by a factor of 94

Also, the graph of f(x) = √94x can be obtained from horizontally stretching f(x) = √x by a factor of 1/94

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The basic ratio of minutes of painting to minutes of instruction is 7 : 6

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

Painting = 63 minutes

Instruction = 54 minutes

The ratio can be represented as

Ratio = Painting : Instruction

When the given values are substituted in the above equation, we have the following equation

Painting : Instruction = 63 : 54

Simplify

Painting : Instruction = 21 : 18

Simplify

Painting : Instruction = 7 : 6

This  ratio cannot be simplified

Hence, the solution is 7 : 6

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Step-by-step explanation:

For some side x, we are given two angles so let use law of sines

We don't know the angle opposite of the x side so we using the triangle interior property

[tex]120 + 51 + x = 180[/tex]

[tex]x = 9[/tex]

So the missing angle is 9.

The law of sines formula is that

[tex] \frac{a}{ \sin( \alpha ) } = \frac{b}{ \sin( \beta ) } [/tex]

where a and b are side lengths.

And alpha, and Beta are angles that are OPPOSITE of the side lengths, a and b, respectively

Let a be 25,

therefore alpha is 120

Let b be x,

therefore beta is 9.

[tex] \frac{25}{ \sin(120) } = \frac{x}{ \sin(9) } [/tex]

Solving for x.

[tex]25 \times \frac{ \sin(9) }{ \sin(120) } = x[/tex]

[tex]x = 4.51587[/tex]

Round if needed so our answer is

[tex]x = 4.5[/tex]

a. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4.

b. The coordinates of BTS-4 are (−8,4).

a. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4. A Voronoi cell is a region of space that is closer to a given point than any other point. In this case, the given point is BTS-4. The Voronoi diagram is a partitioning of the plane into Voronoi cells, one for each point.

b. The edge connecting vertices P and Q has the equation y=4, which means that it is a horizontal line that intersects the y-axis at 4. The coordinates of BTS-2 are (−8,6), which means that it is located 8 units to the left of the origin and 6 units above the origin. Therefore, BTS-4 must be located 8 units to the left of the origin and 4 units above the origin, which gives it the coordinates (−8,4).

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The current balance for Jeff's savings account is $317.84.

To find the current balance for Jeff's savings account, we need to calculate the net effect of the deposits, withdrawals, and interest on his initial balance.

Initial balance: $396.80

Deposits: 3 × $15 = $45

Withdrawals: $125

Interest: $1.04

Adding the deposits and interest to the initial balance:

$396.80 + $45 + $1.04 = $442.84

Then, subtracting the withdrawal:

$442.84 - $125 = $317.84

Therefore, the current balance for Jeff's savings account is $317.84.

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In this figure, we have been given a circle. The area of the circle is 314 sq ft.

The number of square units required to fill a circle is known as its area. The region occupied inside the boundaries of a round item or 2d figure is defined as the area in general. The measurement is done in square units, with square metres (m2) being the usual unit.

There are predefined formulas for calculating area for squares, rectangles, circles, triangles, and so on.

Area of a circle = πr²

We have been given r as 10 ft

and the value of π as 3.14, so we will just put it in the formula

Area of circle = 3.14 × 10²

= 3.14 × 100

314 sq ft.

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The expression that is equivalent to the trigonometry ratio (sin²θ + cos²θ)/tan²θ is (a) cot²θ

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

The trigonometry ratio given as

(sin²θ + cos²θ)/tan²θ

In trigonometry,

sin²θ + cos²θ = 1

So, we have the following representation

(sin²θ + cos²θ)/tan²θ = 1/tan²θ

Evaluate the quotient

(sin²θ + cos²θ)/tan²θ = cot²θ

Hence, the expression that is equivalent to the trigonometry ratio is (a) cot²θ

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The row of tiles would be 24 1/2 inches long.

B:The  row of 10 tiles would be 35 inches long.

A 1. To be able to know the length of the row of tiles, one need to multiply the length of one tile by the number of tiles in the said  row.

So, all tile measures 3 1/2 inches on each side, Hence  the length of one tile is 3 1/2 inches.

Based on the fact that there are 7 tiles in a row, we have to multiply the length of one tile by 7:

Length of the row = 3 1/2 inches/tile x 7 tiles

                              = 24 1/2 inches

So, the row of tiles is 24 1/2 inches long.

B 2. Also, to find the length of a row of 10 tiles, we need to multiply the length of one tile by 10.

Note that:

Length of one tile = 3 1/2 inches

Number of tiles in the row = 10

Hence:

Length of the row = 3 1/2 inches/tile x 10 tiles

                               = 35 inches

So, the row of 10 tiles is 35 inches long.

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In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.

The given velocity vector are; 25 and  25√3)

horizontal  components =25

vertical components =25√3

Then the angle

Tan(θ) = {vertical component / horizontal component }

= 25√3 / 25

= √3 / 1

= √3

Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E

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Answer:  2

Step-by-step explanation:

List the factors(numbers that multiply to make that number for each number

6: 1, 2, 3, 6

34: 1, 2, 16, 34

2: 1, 2

Whichever is the factor that is the greatest that they all have in common is your greatest common factor.

2

Answer:

x+1

DOMAIN: x [tex]\neq[/tex] -5

Step-by-step explanation:

We can factor [tex]x^{2}[/tex]+6x+5 as (x+1)(x+5) since this expands to [tex]x^{2}[/tex]+5*x+1*x+5*1, which is [tex]x^{2}[/tex]+6x+5.

Now, we have:

[tex]\frac{(x+1)(x+5)}{(x+5)}[/tex]  

We can cancel out x+5, because this expression is the same as (x+1)*[tex]\frac{x+5}{x+5}[/tex], which is (x+1).

HOWEVER, the denominator cannot be equal to zero because that will make the expression undefined (you can't divide by zero). So, since x+5[tex]\neq[/tex]0, x[tex]\neq[/tex]-5.

Every day, the number of people who receive the email grows by a factor of 3.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided above, an exponential function for the total number of people who received the email is given by;

[tex]P(t) = 4(3)^t[/tex]

By comparison, we have the following parameters;

Initial value, a = 4.

Growth rate, b = 3.

In conclusion, the number of people who receive the email from Elon every day grow by a factor of 3.

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