The two circle graphs show how surveyed employees actually spend their time and how they would prefer to spend their time. Assume that employees have 112 hours a week that are not spent sleeping. Round answers to the nearest tenth of an hour. (a) What is the actual number of hours per week that employees spend on themselves?________ hr/week(b) What is the number of hours that employees would prefer to spend with family and friends? _______ hr/week(c) What is the difference between the number of hours an employee would prefer to spend on their job or career and the actual amount of time the employee spends their on job or career? _______ hr/week

B is the correct answer

Answer:28

Step-by-step explanation:

The area of the square is given as 100 square unit

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

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Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

The Canal's price/earnings ratio is 2.92.

To calculate Canal's price/earnings ratio, we need to find the earnings per share (EPS) first. The EPS can be calculated by dividing the net income by the weighted average number of common shares outstanding.

The weighted average number of common shares outstanding can be calculated as follows:

Weighted average number of common shares outstanding = Total number of common shares - Weighted average number of treasury shares

Weighted average number of common shares outstanding = 24,200 - 4,200 = 20,000

EPS = Net income / Weighted average number of common shares outstanding

EPS = $260,000 / 20,000 = $13

Finally, the price/earnings ratio can be calculated by dividing the market price per share by the EPS:

Price/earnings ratio = Market price per share / EPS

Price/earnings ratio = $38 / $13 = 2.92

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Answer:

The smallest 5 digit number is 10,000 and the greatest 5 digit number is 99,999. There are 90,000 five-digit numbers in all.

Answer: The equation used to find the value of x is 5x - 4 = 3x + 10. The value of x is determined to be 7.

Step-by-step explanation:

Four less than the product of a number (x) and 5 = 5x - 4

8 more than 2 added to 3 times the number = 3x + 2 + 8 = 3x + 10

Four less than the product of a number (x) and 5 is equal to 8 more than 2 added to 3 times the number => 5x - 4 = 3x + 10

                                                         5x - 3x = 10 + 4

                                                         2x = 14

                                                         x = 14/2

                 therefore,                      x = 7

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Answer:

mZCAD=310°

Step-by-step explanation:

M2BAC=1,m2DAE=3 and m-BAE=0 therefore solution will be 310°

a) The minimum height, this is, at the bottom of the Ferris wheel is 13 meters above the ground.

b) The maximum height, this is, at the top of the Ferris wheel is 135 meters above the ground.

c) A seat takes \(\frac{1}{3}\) hours to complete one full rotation.

d) The height of a seat in a Ferris wheel is modeled after \(y(t) = 61\cdot \sin \left(6\pi\cdot t - 0.5\pi\right)+74\), whose graphic representation in time is included below as attachment.

The minimum height, this is, at the bottom of the Ferris wheel is 13 meters above the ground. \(\blacksquare\)

The maximum height, this is, at the top of the Ferris wheel is 135 meters above the ground. \(\blacksquare\)

According to the statement, we know the frequency of rotation, that is, the number of rotations per unit time, this is, one hour. The period (\(T\)), in hours per rotation, is inverse of the frequency (\(f\)), in rotations per hour:

\(T = \frac{1}{f}\) (1)

If we know that \(f = 3\,\frac{rotations}{hour}\), then the period of the Ferris wheel is:

\(T = \frac{1}{3}\,h\)

A seat takes \(\frac{1}{3}\) hours to complete one full rotation. \(\blacksquare\)

Mathematically speaking, a sinusoidal function representing the clockwise rotation of the Ferris wheel is described below:

\(y(t) = \frac{D}{2}\cdot \sin \left(-\frac{2\pi\cdot t}{T} + \phi \right) + \left(y_{min} + \frac{D}{2}\right)\) (2)

Where:

Note - Please notice that the negative sign aside the angular frequency (\(\frac{2\pi\cdot t}{T}\)) represents the counterclockwise rotation of the Ferris wheel.

If we know that \(D = 122\,m\), \(T = \frac{1}{3}\,h\), \(\phi = -\frac{\pi}{2}\,rad\) and \(y_{min} = 13\,m\), then the function of the height of the Ferris wheel is:

\(y(t) = 61\cdot \sin \left(6\pi\cdot t - 0.5\pi\right)+74\) (3)

Now we proceed to graph for \(0 \le h \le \frac{50}{60}\,h\) (1 hour = 60 minutes), of which we present an image attached below. \(\blacksquare\)

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Answer:

226

Step-by-step explanation:

To find the percentage of a given value, firstly convert to a decimal by dividing by 100:

82 ÷ 100 = 0.82

Now, multiply this decimal by the number of tickets:

275 x 0.82 = 225.5

Because you can't sell half a ticket, round up.

This means the total of tickets they need to sell is 226.

Hope this helps!

Answer:

x = 11/2 = 5.5

Step-by-step explanation:

2x-6 = 5

2x = 11

x = 11/2 = 5.5

Answer:

90 degrees

Step-by-step explanation

Answer:

Step-by-step explanation:

The simplified expression is 3a + 5ay - 3y -52 .

(a) There are 4 terms in the simplified expression

(b) there are 2 negative terms in the simplified expression .

In the question ,

the algebraic expression is given as 3a+2y+5ay-2y-52-3y

to simplify it , we first group them in like terms

the expression becomes .

= 3a \(+\) 2y \(+\) 5ay -2y - 52 -3y

= 3a + 5ay + 2y - 2y - 3y - 52

= 3a + 5ay - 3y -52

Part(a)

the number of terms in the simplified expression is 4 ,

Part(b)

as we can see that the terms -3y and  -52 are negative

So , there are 2 negative terms in the expression.

Therefore , (a) There are 4 terms in the simplified expression

(b) there are 2 negative terms in the simplified expression .

The given question is incomplete , the complete question is

Write the expression 3a+2y+5ay-2y-52-3y in simplest form. Then, answer the following questions using complete sentences.

a. How many terms are in the simplified expression?

b. How many of the terms in the simplified expression are negative?

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Given

Alvin runs 2 km to the bus stop, and then rides 4.5 km to school.

the bus is 45 km/h faster than Alvin’s average running speed

entire trip takes 25 min,

Find

how fast does Alvin run?

Explanation

Let r be the running speed of Alvin

so , bus speed = 45 + r

time = distance/speed

run time + ride time = entire time

so ,

on solving this , we get

as we neglect the negative value ,

so , r = 6.0868

Final Answer

Hence , the Alvin speed = 6.0868 approx

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Answer:

C.

Step-by-step explanation:

1) domain is: x≥7; range f(x)≥9.

2) answer C

When θ (the real rate of return) goes down, the equilibrium interest rate also decreases.

Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period.

The economic reason for this is that when the real rate of return is lower, then lenders are less likely to want to lend out their funds for the same rate of return. Since the demand for loans is lower, the equilibrium interest rate decreases to make lending more attractive.

When β (the risk-free rate of return) goes down, the equilibrium interest rate also decreases. The economic reason for this is that when the risk-free rate of return is lower, then lenders are less likely to want to take on additional risk and accept a higher rate of return. Since the demand for loans is lower, the equilibrium interest rate decreases to make lending more attractive.

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Answer:

step back u idiot

Step-by-step explanation:

Answer:

c (88)

Step-by-step explanation:

find angle opposite to the arc BC

A=2 (92)=184

A=360-184

A=176

D=2÷A

D=2÷176

D=88

Answer:

1

Step-by-step explanation:

The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2.  If you look at a graph of

y = sin(x) you can see this.  

Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.

Step-by-step explanation:

Property of Sine function:

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Answer:

i really don't know because i'm only in 7th grade but if this helps then yea

Step-by-step explanation:

Step 1: Set up the synthetic division. ...

Step 2: Bring down the leading coefficient to the bottom row.

Step 3: Multiply c by the value just written on the bottom row. ...

Step 4: Add the column created in step 3.

Answer:

Step-by-step explanation:

Answer:

the greatest common factor is 2

Step-by-step explanation:

none of the other numbers listed can go into 10, 14, and 16.

(a) The inequality follows from the binomial theorem.

\((a - b)^2 = a^2 - 2ab + b^2 \ge 0 \implies a^2 + 2ab + b^2 = (a+b)^2 \ge 4ab \\\\ \implies \dfrac{(a+b)^2}4 \ge ab \\\\ \implies \dfrac{a+b}2 \ge \sqrt{ab} ~~~~~~~~ (1)\)

By the same reasoning,

\(\dfrac{c+d}2 \ge \sqrt{cd}\)

Adding these results together, we have

\(\dfrac{a+b}2 + \dfrac{c+d}2 = \dfrac{a+b+c+d}2 \ge \sqrt{ab} + \sqrt{cd}\)

and since \(\sqrt{ab}\) and \(\sqrt{cd}\) are both positive, they also satisfy the AM-GM inequality,

\(\dfrac{\sqrt{ab} + \sqrt{cd}}2 \ge \sqrt{\sqrt{ab}\times\sqrt{cd}} = \sqrt[4]{abcd}\)

and the 4-variable result follows,

\(\dfrac{a+b+c+d}2 \ge 2\times\dfrac{\sqrt{ab}+\sqrt{cd}}2 \ge 2 \sqrt[4]{abcd} \\\\ \implies \dfrac{a+b+c+d}4 \ge \sqrt[4]{abcd} ~~~~~~~~ (2)\)

(b.i) With \(m=\frac{a+b+c}3\), we have

\(\dfrac{3m}4 = \dfrac{a+b+c}4 \implies m - \dfrac m4 = \dfrac{a+b+c}4 \\\\ \implies m = \dfrac{a+b+c+m}4\)

(b.ii) From (2) it follows that

\(\dfrac{a+b+c+m}4 \ge \sqrt[4]{abcm} = \sqrt[4]{abc\times\dfrac{a+b+c+m}4}\)

Using the result from (b.i), this is equivalent to

\(\dfrac{a+b+c}3 \ge \sqrt[4]{abc\times\dfrac{a+b+c}3}\)

Take 4th powers on both sides.

\(\left(\dfrac{a+b+c}3\right)^4 \ge abc \times \dfrac{a+b+c}3\)

Divide both sides by \(\frac{a+b+c}3\).

\(\left(\dfrac{a+b+c}3\right)^3 \ge abc\)

Finally, take the cube root of both sides.

\(\dfrac{a+b+c}3 \ge \sqrt[3]{abc}\)

as required.

Answer:

C

Step-by-step explanation:

cot²θ = 1/tan²θ

plug this in to get

1/(1/tan²θ + 1)

1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ

we then have

1/((1+tan²θ)/tan²θ)

1/(x/y) = y/x, so this is equal to

tan²θ/(1+tan²θ)

tan²θ = sin²θ/cos²θ, so plug this in to get

(sin²θ/cos²θ)/(1+sin²θ/cos²θ)

1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ

sin²θ + cos²θ = 1, so we have

(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get

(sin²θ/cos²θ)/(1/cos²θ)

(a/b)/(c/d) = (d/c) * (a/b), so we have

(sin²θ/cos²θ)/(1/cos²θ)  = cos²θ/1 * sin²θ/cos²θ = sin²θ

The height of the can of cylinder shape is 9.14 cm.

What is a cylinder?

In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases separated by a curved surface at a specific distance. These bases frequently have a circular shape (like a circle), and an axis connects their respective centres.

We are given the diameter as 4 cm.

So, the radius is 2cm.

Also, it is given that the surface area of the can is 140 square centimeters.

So, using the surface area of cylinder, we get

⇒Area = 2πr (h + r)

⇒140 = 2π * 2 (h + 2)

⇒140 = 4π (h + 2)

⇒140 = 4 * 3.14 * (h + 2)

⇒140 = 12.56 * (h + 2)

⇒11.14 = h + 2

⇒h = 9.14

Hence, the height of the can of cylinder shape is 9.14 cm.

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Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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Answer:

5 units of vertical distance

Step-by-step explanation:

just count

The  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

Given the equation;

8x - 9y = 15

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

8x - 9y = 15

8x - 9(0) = 15

8x = 15

Divide both sides by 8

8x/8 = 15/8

x = 15/8

Next, we find the y-intercept by substituting 0 for x and solve for y.

8x - 9y = 15

8(0) - 9y = 15

- 9y = 15

Divide both sides by -9

- 9y/(-9) = 15/(-9)

y = -15/9

y = -5/3

We list the intercepts;

x-intercept: ( 15/8, 0 )

y-intercept: ( 0, -5/3 )

Therefore, the  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

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ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Geometric terms are terms used for describing geometric objects

The correct responses for the geometric term modeled by each object are as follows:

16. The geometric term modelled by the tip of the needle is a point

17. The figure modelled by he rail track are lines including; Parallel lines and  intersecting lines

18. The figure modelled by the cloth is a plane with points

19. A table cloth models a plane

20. A partially opened newspaper models an angle, and two planes intersecting

21. Woven threads in a piece of cloth models intersecting lines

22.A knot in a string models a point on a line

Required:

To draw and model a figure for each relationship

Solution:

23. The required drawing of the model of line AB intersecting at Q and W is attached

24. The required drawing of the model of point T that lies on \(\overset \longleftrightarrow {WR}\) is attached

25. The required drawing of the model of point Z(4, 2),  R(-4, 2), and collinear point S, with Q, Z, R, and S are not, is attached

26. The given coordinates are; C(-1, 4) and R(6, 4). The point P(3, 2) is the intersection of the lines \(\overset \longleftrightarrow {RS}\) and \(\overset \longleftrightarrow {CD}\)

The required drawing is attached

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