As a human resources specialist, you keep track of the number of retiring employees for benefits and hiring purposes. You notice that of the current workforce will retire during next month, and an additional of the current workforce will retire the following month. What fraction of the current workforce is scheduled to retire during the next two months?

Part A: the functions are written and evaluated

Part B statement 1 and statement 2 has same result

The statement are written as equation then evaluated

Statement 1 reads f of 2 when function f of x equals two times x plus one,

f(x) = 2x + 1

f(2) = 2 * 2 + 1 = 5

Statement two reads f inverse of four when function f of x equals quantity three times x plus one all divided by four,

f(x) = (3x + 1)/4

let f(x) = y and solving for the inverse

4y = 3x + 1

4y - 1 = 3x

x = (4y - 1)/3

hence f⁻¹(x) = (4y - 1)/3 interchanging y to x i the inverse equation

f⁻¹(x) = (4x - 1)/3

f⁻¹(4) = (4 * 4 - 1)/3 = 5

Statement three reads three times y minus six equals two times y minus 1

3y - 6 = 2(y - 1)

3y - 6 = 2y - 2

3y - 2y = 6 - 2

y = 4

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The revolutions per minute are 83 and angular speed is 522.90 rad/min.

What is angular speed ?

Angular speed measures how fast the central angle of a rotating body changes with respect to time.

Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows:

ω = θ /t

where

θ is the angular displacement, t is the time and ω  

is the angular speed.

Now,

Speed given=45 miles/hour

diameter of wheels = 26 inch ---> radius = 13 inch

total distance covered by wheel in inches in a minute = 45*63360/60

Distance covered in one revolution = 2πr

                                                           = 2*22/7*13

Revolutions/minute=45*63360*7/60*2*22*13

                               =83

Angular speed= θ/t or θf ( f= frequency of revolutions)

                        =360*83 degree/min

                        =360*83*0.0175 rad/min

                       =522.90 rad/min            

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The surface area of a similar cylinder with a diameter 3 cm is  8.4375π cm².

If two figures have the same shape, they are said to be comparable. In more formal terms, two figures are said to be similar if their respective angles are congruent and their corresponding side length ratios are identical.

Given a cylinder with a diameter 8 cm and a surface area 60π cm²

let the radius be  R = dia/2 = 8/2= 4 cm

and let the height be H

total surface area of cylinder  = 2πR(H + R)

60π = 2π(4)(4 + H)

4 + H = 60/8

H = 7.5 - 4

h = 3.5 cm

and a cylinder is similar to given cylinder,

let radius be r and height be h

given dia = 3 cm

r = 3/2 = 1.5 cm

since both cylinders are similar so the ratio of their height to radius is equal,

R/H = r/h

h = Hr/R

h = (3.5)(1.5)/4

h = 1.3125 cm

total surface area of cylinder  = 2πr(h + r)

total surface area of cylinder  = 2π(1.5)(1.5 + 1.3125)

the total surface area of the cylinder  = 8.4375π cm²

Hence the area of a cylinder is 8.4375π cm².

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The distance that lies from where Stefan is and the fish is 15 meters

In order to get Stefan's distance from the fish, we would have to make use of the pythagorean theorem

The formula is given as

a² + b² = c²

where we have the value of a = 12 meters

the value of b = 9 meters

the value of c is unknown

when we input the values we would have:

12² + 9² = c²

144 + 81 = c²

225 = c²

c = √225

c = 15

The distance that lies between Staefan and this fish is given as 15 meters.

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Equation that could be used to determine c is 21.75m + 70.and the equation is s = 16.98m + 99.50.

An equation is a statement that expresses the equality of two expressions. It typically involves a variable, which is a symbol that stands for a number, and operations, such as addition and multiplication, that are performed on the variables. Equations are used to make predictions, describe relationships, and solve problems in mathematics and other fields of study.

c = 21.75m + 70
B. Write an equation that could be used to determine s, the cost for satellite TV for m months.
s = 16.98m + 99.50

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the answer to this math equation is 84.85

To prove that if KB = (p ⇒ q)∧(r ∨s)∧(¬p)∧(¬ ⇒ ¬t)∧(¬q ∨t)∧(¬p ∧r ⇒ u)∧(w ∨t), then KB |= (u ∧ w) using resolution, we can start by assuming the negation of the conclusion, (¬u ∨ ¬w)

To prove that if KB = (p ⇒ q)∧(r ∨s)∧(¬p)∧(¬ ⇒ ¬t)∧(¬q ∨t)∧(¬p ∧r ⇒ u)∧(w ∨t), then KB |= (u ∧ w) using resolution, we can start by assuming the negation of the conclusion, (¬u ∨ ¬w)

Then use the resolution to derive the empty clause, which would mean that our assumption is false and therefore the conclusion is true.

Here is one possible sequence of resolution steps:

step 1: Assume ¬u

step 2: ¬p ∧r ⇒ u (from KB)

step 3: ¬p ∧r (by resolution with step 2)

step 4: ¬p (from KB)

step 5: r (by resolution with step 3)

step 6: ¬q ∨t (from KB)

step 7: t (by resolution with step 5)

step 8: ¬ ⇒ ¬t (from KB)

step 9: (by resolution with step 7)

step 10: p ⇒ q (from KB)

step 11: q (by resolution with step 9)

step 12: ¬q ∨t (by resolution with step 6)

step 13: t (by resolution with step 7)

step 14: w ∨t (from KB)

step 15: w (by resolution with step 13)

step 16: ¬u ∨ w (by resolution with steps 1 and 15)

step 17: (by resolution with steps 10 and 16)

Since we have derived the empty clause, our assumption (¬u ∨ ¬w) is false, and we have proven that KB |= (u ∧ w) by resolution.

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Since KB' contains a contradiction, we know that KB is logically consistent and KB |= (u ∧ w)

Here's how you could prove using resolution that KB |= (u ∧ w):

First, we'll try to find a contradiction in KB by negating our target statement and adding it to KB: KB' = KB ∧ ¬(u ∧ w)

Simplifying the negation: ¬(u ∧ w) = ¬u ∨ ¬w

Adding the negation to KB: KB' = KB ∧ (¬u ∨ ¬w)

Using resolution to simplify the disjunction in KB':

a. Resolve (r∨s) and ¬s to get r.

b. Use (p ⇒ q) to simplify ¬q∨s to ¬p∨s

c. Use (¬p∧r ⇒ u) to simplify ¬p∨r to u

d. Use (¬s ⇒ ¬t) to simplify s to t

e. Use w∨t to simplify t to w

We now have KB' = (p ⇒ q)∧u∧w∧¬w which is a contradiction, since p ⇒ q implies q and ¬w implies w.

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The

equation of tangent and normal

to the surface z^2=4(1+x^2+y^2)at (2,2 ,6)  is

2x+2y+2z-24=0

and

2x+2y+6z-24=0

respectively.

Step-by-step explanation:

To find the equation of the

tangent and normal planes

at the point (2, 2, 6),  we first need to

find the gradient vector of the surface

, which is the vector pointing in the direction of the steepest ascent.

The gradient vector of the surface is grad(z^2)=<2x,2y,2z>

The equation

of the tangent plane

at the point (2, 2, 6) is given by

<2x,2y,2z> . (x-2,y-2,z-6) =0

so the

equation of tangent plane

is 2x+2y+2z-24=0

The

equation of the normal plane

at the point (2, 2, 6) is given by

<x,y,z> . (2,2,6) = constant

so the

equation of normal plane

is 2x+2y+6z-24=0

Note

: The

dot product

of the position vector <x,y,z> and the gradient vector <2x,2y,2z> gives the equation of the tangent plane. The position vector <x,y,z> gives the equation of the normal plane.

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Answer: No solution

Step-by-step explanation:

Expand the left side:

6x - 8 = 8x - 4 - 2x

Combine like terms and get

-8 = -4

No solution

Step-by-step explanation:

a)

g(x) = f(-½ x) - 3

the "-" in the function argument flips the function left-right. everything that was for f(x) on the left side of the origin, is now on the right side. and vice versa.

the 1/2 in the function argument stretches out the function left and right by the factor 2.

the "- 3" at the end shifts the whole function down by 3 units.

the new equation :

[tex]g(x) = \sqrt[3]{ - x \div 2} \: - 3[/tex]

b)

j(x) = 2f(x + 4)

the "+ 4" in the function argument moves the whole function 4 units to the left (everything that happened for f(x) at x happens now 4 units "earlier" - the functional result of f(x + 4) is now created at x).

the factor 2 of f stretches out the whole function up and down (by the factor 2).

the new equation :

[tex]j(x) = 2 \times \sqrt[3]{x + 4} \:[/tex]

c)

h(x) = f(8x - 24)

the "- 24" in the functional argument moves the whole function 24 units to the right (and principle as in b., now f(x - 24) happens only at x and therefore "later").

the factor 8 in the functional argument compresses (or shrinks) the whole function left and right by the factor 8.

the new equation :

[tex]h(x) = \sqrt[3]{8x \: - 24} [/tex]

Answer: 2

Step-by-step explanation:

Volume = Base Area x Height

119 = 3.5 * 17 * Height

    = 59.5 * Height

119/59.5 = 2

The height/thickness of the ream is 2 in

a. The required exponential function f(x) = (11)(3)ˣ which is passes through the points (2,99) and (6, 8019).

b. The required exponential function g(x) = (40)(0.8)ˣ which is passes through the points (-1,50) and (2, 25.6).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

a. Let the formula for an exponential function would be as

⇒ f(x) = abˣ

The exponential function passes through the two points  (2,99) and (6, 8019).

99 = ab²       .....(i)

8019 = ab⁶   .....(ii)

Divided by equation (i), then we get

8019/99 = ab⁶ / ab²  

b⁴ = 81

b = 3

Substitute the value of b = 3 in the equation (i),

99 = a(3)²

a = 11

Substitute the values of a = 11 and b = 3 in the equation f(x) = abˣ

So f(x) = (11)(3)ˣ

Therefore, the required exponential function f(x) = (11)(3)ˣ

b. Similarly let's exponential function g(x) = abˣ  

The exponential function passes through the two points (-1,50) and (2, 25.6).

50 = ab⁻¹

50 = a/b

a = 50b  ....(i)

25.6 = ab²

Substitute the values of a = 50b in the above equation,

25.6 = (50b)b²

25.6 = 50b³

b³ = 25.6/50

b³ = 0.512

b = 0.8

Substitute the value of b = 0.8 in the equation (i),

a = 50(0.8)

a = 40

Substitute the values of a = 40 and b = 0.8 in the equation f(x) = abˣ

So g(x) = (40)(0.8)ˣ

Therefore, the required exponential function g(x) = (40)(0.8)ˣ.

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The 4.5% of cost of home is $20250 which is higher than the estimated.

What is percentage ?

percentage can be defined as the product of ratio of given value, total value and hundred.

Given,

Your estimated closing cost for your $450,000 home were $11,500,

the actual closing cost were 4.5% of the cost of the home.

So,

the 4.5% of cost of home is

= 4.5% of 450,000

= (4.5 / 100) * 450,000

= 45*450

= 20250

Hence, The 4.5% of cost of home is $20250 which is higher than the estimated.

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The best description of the numerical expression 2x - 5 is,

The difference of five and twice a number x.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

The statement to the numerical expression 2x - 5 would be

The difference of five and twice a number x.

As we can not use the statement twice a number x minus five because the term 'minus' can not be used.

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Answer:

a = 24

Step-by-step explanation:

Since the two triangles are similar the ratio of the length of each side of one triangle to the length of the corresponding side of the other triangle must be the same

Looking at the two triangles we see that the side of length a corresponds to the smaller triangle side of length 16

The side of length 15 corresponds to the smaller triangle side of length 10

So we have the ratio equality

[tex]\dfrac{a}{16} = \dfrac{15}{10} \\\\\\a = 16\cdot \dfrac{15}{10} \\\\\\a = 24[/tex]

Answer:

There are two possible answers depending on how you interpret the question. Please read the explanation below carefully and in full

Diagonal distance from top of tower to plane :

[tex]\boxed{d= 12,571\;feet}[/tex]

Horizontal distance from control tower to plane:
[tex]\boxed{h = 10571\;feet}[/tex]

Step-by-step explanation:

Before explanation, I must say the question is confusing. Are they asking for the distance from the top of the tower or the horizontal distance from the location of the tower?

I am giving answers for both. You can ask your professor about this and answer with the right one.

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

This question and explanation can best be understood by drawing a diagram with given information

First, look at the attached Image
A is the top of the control tower 320 feet above the ground

B is the location of the plane 7450' above ground level.

The point C which lies on the vertical line is at the same height from the ground as the top of the control tower i.e. 320 feet

So B

Points ABC form a right triangle with m∠ACB = 90°

m∠ABC = 56° (given)

Since the 3 angles of a triangle add up to 180°, we have

m∠BAC + 56 + 90 = 180°

m∠BAC = 180 - (56 + 90) = 34°

Diagonal distance from top of tower(d)

The objective is to find d.

Use the law of sines which states:

If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of sines states:
[tex]\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]

Looking at the various side lengths and  angles and applying this law we get

[tex]\dfrac{7130}{\sin 34^\circ} = \dfrac{d}{\sin 90^\circ}\\\\\textrm{Since }\sin 90^\circ } = 1\\\\\dfrac{7130}{\sin 34^\circ} = d\\\\d = 12,750.5194 = 12,751 \textrm{ feet rounded to nearest foot}\\\\[/tex]

Horizontal distance from tower

Use the law of sines again.

Without calculating d first, we can use

[tex]\dfrac{h}{\sin 56^\circ} = \dfrac{7130}{\sin 34^\circ}\\\\[/tex]

[tex]h = \dfrac{7130 (\sin 56^\circ)}{\sin 34^\circ} = 10,570.659 = 10,571 \;feet[/tex]

Therefore the possible answers are

Diagonal distance from top of tower to plane :
[tex]\boxed{d= 12,571\;feet}[/tex]

Horizontal distance from control tower to plane:
[tex]\boxed{h = 10571\;feet}[/tex]

It is highly likely that they are looking for the horizontal distance but check with your prof or include both answers

Step-by-step explanation:

(1.2 x 10^8) =120000000

(3 x 10^2). =300

120000000÷300=400000

4×10 in the power of 6

The tutor that will earn more money in a week would be Zhen with the total income of =$1,080.

The total amount collected from pupils tutor by Zhen company = $2400

The 45% of $2400 = 45/100 × 2400

= 108000/100

= $1,080

The total amount collected from pupils Ryder tutored would be = $1080

The 45% of $1080 = 45/100 × 1080

= 48600/100

= $486

Therefore, the tutor that earned higher income is Zhen with an income of $1,080.

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Complete question:

Zhen and Ryder work as tutors at two different test-prep companies. In one week, Zhen earns 45% of the $2400 collected from the pupils tutors. Ryder earns 45% of the $1080 collected from the pupils she tutors the same week. Who earns more money in a week? Explain.

Equations are relationships between two or more variables that are used to determine an unknown variable's value based on the values of other variables that are known.

y = −x − 3

Calculate the slope and y-intercept using the slope-intercept form.

In the slope-intercept form, y = m x + b denotes the slope and the y-intercept, respectively.

y = m x + b

With the use of the formula y = m x + b, determine the values of m and b.

m = − 1 b = − 3

M represents the line's slope, while B represents the y-intercept.

Slope is 1 and the y-intercept is (0, 3).

Two points are all that are required to graph any line. To determine the associated y values, enter two x values into the equation.

Less steps by tapping...

Assign the x and y values to a table.

x    y

0  − 3

1  − 4

The slope and y-intercept, or the points, should be used to graph the line.

Slope: 1 y-intercept: (0, 3 )

x     y

0      3

1      4.

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The way I view this problem is the resultant R is making a 60 degree angle from one of the forces, The two forces are at right angle from each other and they are the x-component Rx and the y- component Ry of the resultant. If the magnitude of Rx = 4N then the angle opposite the side is 30 degrees. The Ry component can be solved using the Pythagorean theorem.

Step 1

one force=4kn

resultant=8kn

degree=60

it can be solved using the Pythagorean theorem.

Step 2

R^2 = Rx^2 + Ry^2

8^2 = 4^2 + Ry^2

64 = 16 + Ry^2

Ry^2 = 64 - 16

Ry^2 = 48

Ry = 6.9282 N

Solving for the direction of Ry

Ry is 90 degrees from Rx

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An equation of the line that passes through the points (-4, -1) and

(6, -1) are  is 0  and  y is 4x - 25.

The slope-intercept version of the equation for the line through point (6, -1) with slope m = 4 is y = 4x - 25.

The line crosses over (4, 1)

Yy 1 = m(xx 1 ) is the equation for a line.

y+1=4 1 (x4) x+4y+4=x4 

x+4y+4=x4 

x+4y+4=x4 

y+4y+4=0

∴x−4y−8=0 is needed to solve a straight line's equation.

y y1 y2-  y1 = x 

x1

The formula for a straight line that connects the coordinates (x1,y1) and (x2,y2) is: y =  y1 y2-  y1 = x  x1 x2 - x1. Now, we may give an example using this formula.

An equation of the line that passes through the points (-4, -1) and

(6, -1) arex−4y−8=0  and  y is 4x - 25.

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Answer: x=2

Step-by-step explanation:

−3x+4=2x−6

Subtract 2x from both sides.

−3x+4−2x=−6

Combine −3x and −2x to get −5x.

−5x+4=−6

Subtract 4 from both sides.

−5x=−6−4

Subtract 4 from −6 to get −10.

−5x=−10

Divide both sides by −5.x=−5−10

​Divide −10 by −5 to get 2

x=2

The fraction of tiles that were painted yellow is 1/8.

What is fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Fraction of tiles that were painted green = 2/8

Fraction of tiles that were painted pink = 5/8

Let the total fraction of tiles be 1.

Then to find the fraction of tiles that were painted yellow -

1 - ( Fraction of tiles that were painted green + Fraction of tiles that were painted pink)

Substituting the values in the expression -

= 1 - [(2/8) + (5/8)]

= 1 - [(2+5)/8]

= 1 - (7/8)

= (8-7)/8

= 1/8

Therefore, the yellow tiles are in fraction 1/8.

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The number of members in the tennis club at the beginning is 1500.

Let's call the original number of members "x". Since 80% of the members were male, we know that 0.8x members were male. Similarly, since 20% of the members were female, we know that 0.2x members were female.

Next, we can use the information about the number of members that left to find the new number of male and female members. We know that the number of male members decreased by 25%, so the new number of male members is 0.8x - 0.25(0.8x) = 0.8x - 0.2x = 0.6x.

Similarly, we know that the number of female members decreased by 50%, so the new number of female members is 0.2x - 0.5(0.2x)

= 0.2x - 0.1x

= 0.1x.

Now we know that the number of members left is 450, so we can set up the equation:

x = 0.6x + 0.1x + 450

Solving for x, we get:

x = 450 / (1 - 0.7) = 450 / 0.3 = 1500

Therefore, the number of members was 1500.

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Answer: Crow can fly 24 miles in 1 hour so 24 miles per hour and for the seagull it is 16 miles per hour

Step-by-step explanation: the graph says it for the crow and for the seagull find the point at which it says 1 hour and look to the y axis for the speed

Answer:

He was there for 1 hour and 17 minutes.

Step-by-step explanation: