Determine the intervals on which the function is increasing, decreasing, and constant.

A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)

The acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.

Differentiation is a process to find the instantaneous rate of change in function based on one of its variables.

The hypotenuse of a right triangle is growing at a constant rate of a centimeters per second

[tex]\frac{dH}{dt} = a[/tex]

One leg is decreasing at a constant rate of b centimeters per second

[tex]\frac{dy}{dt} = -b[/tex]

From the right triangle

sin θ = [tex]\frac{y}{H}[/tex]           (y is the perpendicular and H is the hypotenuse)

Differentiate both sides with respect to t

cos θ*dθ/dt = (H*dy/dt - y*dH/dt) / H²

cos θ*dθ/dt =  [H(−b)−y(a)] / H²........................(1)

If the both legs are 1 cm.

∴ H= [tex]\sqrt{ 2[/tex],cosθ=sinθ=1/[tex]\sqrt{2}[/tex]

Thus , Equation (1)

cos θ*dθ/dt =  [H(−b)−y(a)] / H²

1/√2*dθ/dt = [√2 (−b)−(a)] / 2

dθ/dt = √2  [(√2 (−b)−(a)) / 2]

Therefore, we can conclude that the acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.

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At x=0

at x=1

at x=2

a=1/2

So correct option is (c).

Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949

Let W be the event that the robot's camera observes a window

It is given that the Probability of observing a window there is no window at its location is given 0.2

P(W/ L1) = 0.2 ( L1 which does not have a window)

Also, probability of observing a window is 0.9

P(W/ L2) = 0.9 ( L2 has window)

Now we have to find updated probabilities for the robot being in L1 i.e:- P(L1/W) & P(L1/w)

w means the camera does not observe a window.

By Bayes Rule,

P(L1/W) = P(L1)P(W/L1)/P(L1)P(W/L1)+P(L2)P(W/L2)

            = (0.7x 0.2)/ (0.7x0.2) + (0.3x0.9)

            = (0.14)/ 0.14+0.27

            ≈0.341 (rounded to 3. decimal places)

Thus  the probability of being in L1 if the camera observes a window is nearly 0.341.

P(L1/w) = P(L1)P(w/L1)/P(L1)P(w/L1)+P(L2)P(w/L2)

As P(W/L1) = 0.2;

P(w/L1) = 1 - P(w/L1) = 1-0.2 = 0.8

Also P(W/L2) = 0.1;

P(w/L2) = 1 - P(w/L2) = 1-0.9 = 0.1

P(L1/w) = (0.7 X 0.8)/ (0.7X0.8) + (0.3X0.1)

           =(0.56)/ (0.56+0.03) = (0.56/ 0.59)

           ≈ 0.949 (rounded to 3 decimal places).

Thus the probability of being in L1 if observe not the window is nearly 0.949.

Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949

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Step 1

Given;

Required; To find the measure of angle F

Step 2

Answer;

Two parallel lines in the coordinate system share the same slope, this means that if you have two parallel lines:

For the given equations, the slopes are:

The slopes are different, so this lines are not parallel.

Two lines are perpendicular, when the slope of one of them is the negative inverse of the first one, this is for the perpendicular lines:

For the given equations, using y=17x-8 as reference, the slope of a line perpendicular to this one must be:

The slope of a perpendicular line to y=17x-8 is different from the slope of the second given line, so you can conclude that these lines are not perpendicular.

The correct choice is Neither

Albert borrowed $17 from his friend.

Given,

Albert brought some items:

Cost of blanket = $32.75

Cost of pillow = $12.75

Cost of glove = $16.25

Amount paid by Albert = 50

Amount borrowed by Albert from his friend = x

Cashier gave back the change = $5.25

We have to find the amount borrowed by Albert from his friend:

This is simply arithmetic operations:

Total cost in shop = 32.75 + 12.75 + 16.25 = $61.75

Total amount given to the cashier = 61.75 + 5.25 = 67

Amount borrowed by Albert from his friend = Total amount given to the cashier - Amount paid by Albert

x = 67 - 50

x = 17

That is,

Albert borrowed $17 from his friend.

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Answer:

The actual area of the warehouse would be:

[tex]72000~\text{feet}^{2}[/tex]

Step-by-step explanation:

Step 1:  Convert all the blueprint lengths into real lengths:

Each inch in the blueprint represents 20 feet in the real world.

So, the real-life length (18 inches in blueprint) would be:

[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times18~\text{inch}= 20\times18~\text{feet}\\18~\text{inch}= 360~\text{feet}\\[/tex]

Similarly, the real-life width would be:

[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times10~\text{inch}= 20\times10~\text{feet}\\10~\text{inch}= 200~\text{feet}\\[/tex]

Step 2: Calculate the area

The area of the warehouse would be given by:

[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]

The length is 360 feet, and the width is 200 feet, so the total area would be:

[tex]\text{Area}=\text{Length}\times \text{Width}\\\\\text{Substitute the values for the length and width}\\\text{Area}= 360\times 200\\\text{Area}=72000[/tex]

a. 2600 ways different samples are possible.

b. 0.11  is the probability that all 3 of the selected students are freshmen.

total student = 26

3 students are randomly selected  on group project

a.   the possible  different sample are

[tex]26 C_{3}[/tex] = [tex]\frac{26}{3 (26-3)}[/tex]

      =  [tex]\frac{26}{3 (23)}[/tex]

     = 2600 ways.

b.  13 students are freshmen  

Pr ( 3  selected students  is freshman)

[tex]\frac{13C_{3} }{26C_{3} }[/tex] = [tex]\frac{286}{2600}[/tex] = 0.11

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Answer: 52

Step-by-step explanation:

a^2+b^2=c^2

x is the hypotenuse (c). You can find the hypotenuse by finding the opposite of the right angle

48^2+20^2=2304+400=2704

√2704=52

x=52

The number of times one needs to use completely filled cone to completely fill the cylinder with water is 24

The volume of cylinder is equal to the product of the area of the circular base and the height of the cylinder.

Given that radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters.

The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.

The volume of cylinder is πr²h

For a volume of cone it is 1⁄3πr²h.

So volume of cylinder = 22/7×(10)2×20=3.142×100×20

=6284

volume of cone it is 1⁄3πr²h=1/3×3.142×(5)^2×10=261.16

Number of times one needs to use the completely filled cone to completely fill the cylinder with water =

= Volume of cylinder/Volume of cone

6284 / 261.16 = 24

Hence the number of times one needs to use completely filled cone to completely fill the cylinder with water is 24

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Answer:

E

Step-by-step explanation:

[tex]\sqrt{144} = 12\\ \frac{234}{3}= 78\\[/tex]

12, 68.12, 78

The given expression: -4f-6(6f-10) in simplified form
is: -40f + 60.

What is an algebraic expression and how is it simplified?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it. Simplifying the algebraic expressions is to carry out operations on the expressions and then clear it out.

Given, the expression for simplification is: y = -4f-6(6f-10)
Working on the expression above, we have:
y = -4f-6(6f-10) = -4f -36f + 60 = -40f + 60
Therefore the given expression: -4f-6(6f-10) in simplified form
is: -40f + 60.

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[tex] \huge\underline\mathcal{Answer \: -} [/tex]

We know that ,

exterior angle equals sum of two interior opposite angles.

therefore ,

[tex]\bold{x + x + 14 = 136\degree} \\ \\ \longrightarrow \: 2x + 14 = 136\degree \\ \\ \longrightarrow \: 2x = 136\degree - 14 \\ \\ \longrightarrow \: 2x = 122\degree \\ \\ \longrightarrow \: x = \cancel\frac{122}{2} \\ \\ \longrightarrow\boxed{ \: x = 61\degree}[/tex]

hence , the first option is correct.

hope helpful ! ;-;

Answer:

First find the last angle of the triangle.

180 - 136 = 44° (sum of angles on a straight line=180)

Form an equation with the unknown angles with the knowledge that sum of angles in a triangle add up to 180°.

x + (x + 14) + 44 = 180

Simplify and solve for x.

2x + 58 = 180

2x = 122

x = 61

Answer:

25 bricks

Step-by-step explanation:

Calculate the volume of one brick:

Volume = (11')(8")(5") = 440 in^3

Divide the volume of a one brick into the volume of concrete that will be used:

(11000 in^3 concrete)/(440 in^3 concrete/brick) = 25 bricks

Answer:

x = 18

The number is 18.

Step-by-step explanation:

Convert the words into an equation.

let x;

( 3x - 10 )( 2 ) + 2 = 5x;

6x - 20 + 2 = 5x;

6x - 18 = 5x;

Subtract both sides by 5x.

6x - 5x - 18 = 5x - 5x;

x - 18 = 0;

Add 18 to both sides.

x - 18 + 18 = 18;

x = 18;

Answer:

Given equation is, x+3y=6

To determine whether each order pair is a solution of the equation

(3,1)

we have that, when x=3 we get y=1

Let us check this in the equation.

Put x=3, we get

Hence (3,1) is the solution of the equation.

(6,0)

Put x=6, we get,

Hence (6,0) is the solution of the equation.

(-2,2/3)

Put x=-2, we get,

Hence (-2,2/3) is not the solution of the equation.

Two hours after depart, the distance between two ships is 39.2 miles and the relative speed of ship A seen by ship B is 19.6 mph heading to 18.4⁰ South of East.

The situation can be depicted on the attached picture.

Let North - South be the y-axis and East - West ne the x-axis.

The velocities vector can be represented as:

Ship A, 20 mph 30⁰ west of north:

vA = - 20 . cos( 60⁰) i + 20 . sin( 60⁰) j

vA = -10 i + 10√3 j

Ship B, 25 mph 20⁰ east of north:

vB = 25 . cos( 70⁰) i + 25 . sin( 70⁰) j

vB = 8.55 i + 23.5 j

b) The speed of ship A relative to ship B is:

vAB = vA - vB

       = ( -10 i + 10√3 j) - (8.55 i + 23.5 j)

       = -18.55 i - 6.18 j

or vAB = sqrt (18.55² + 6.18²) = 19.6 mph with the angle tan⁻¹ (6.18/18.55) = 18.4⁰ South of East.

a) The distance between 2 ships after 2 hours:

d = vAB . 2 hours

d = 19.6 . 2 = 39.2 miles

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Answer:

Step-by-step explanation:

Answer:

29/49

Step-by-step explanation:

x:y = 3:4

let x = 3x , y = 5k

3x+4y/8x+5y

= 3(3k)+4(5k)/8(3k)+5(5k)

= 9k+20k/24k+25k

=29/49

Hello!

Knowing that Alyssa wants to rent a car where the company charges $37.50 per day to rent a car and $0.05 for each mile driven we have to find out how many days she is planning on renting a car for.

Step-by-step explanation:

Using the information we have we can see that it will be an additional $5 based on how many miles she is planning on driving.

If the base cost to rent a car is $37.50 you will have to add an additional $5  for the number of miles she plans to drive making the total $42.50.

Since she has at most $200 to spend on a car rental she can rent a car for a total of 5 days at a total cost of $192.50

[tex]37.50[/tex] × [tex]4=150[/tex] + [tex]42.50[/tex] = [tex]192.50[/tex]

Hope this helps!

The inequality will be 37.5x + (0.05 ×100) ≤ 200, and Alyssa can afford 5.2 days to rent while staying within her budget

Given that the rental car company charges $37.50 per day to rent a car and $0.05 for every mile driven

She plans to drive 100 miles and has at most $200 to spend.

Let x is the number of days, Alyssa can afford to rent while staying within her budget

The inequality can be written as;

37.5x + (0.05 ×100) ≤ 200

Now solve for x:

37.5x + (0.05 ×100) ≤ 200

37.5x + 5 ≤ 200

37.5x  ≤ 200 - 5

37.5x  ≤ 195

x  ≤ 195/37.5

x ≤  5.2

Therefore, she can afford 5.2 days to rent while staying within her budget.

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Given:

Total number of hamburgers and cheeseburgers sold = 439

There were 61 fewer cheeseburgers than hamburgers sold.

Let's determine the number of hamburgers sold.

Let C represent the number of cheeseburgers

Let H represent the number of hamburgers sold.

We have the system of equations:

• H + C = 439

• C = H - 61

Now, let's solve the equations simultaneously using the substitution method.

Substitute (H - 61) for C in the first equation.

We have:

H + (H - 61) = 439

H + H - 61 = 439

2H - 61 = 439

Add 61 to both sides:

2H - 61 + 61 = 439 + 61

2H = 500

Divide both sides by 2:

Therefore, they sold 250 hamburgers on Friday.

ANSWER:

250 hamburgers

The line of the equation which passes through the point (0, 4) and is parallel to the x-axis is 2y = 8.

So, the equation is as:

Then, the equation can be:

(Refer to the graph attached below)

If you solve will become:

Therefore, the line of the equation which passes through the point (0, 4) and is parallel to the x-axis is 2y = 8.

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Answer:  22:2, 33:3 and, 44:4

Step-by-step explanation:

Answer:

Step-by-step explanation:

22 : 2

33 : 3

44 : 4

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

How are polynomials and non-polynomials categorized?

There are two ways to categorize polynomials: by degree and by number of terms. According to degree, polynomials can be classified as zero, linear, quadratic, or cubic. Monomials, binomials, trinomials, etc. are the different types of polynomials based on the quantity of terms.

A polynomial is, in general, an expression containing more than one term and non-negative integral exponents of a variable. A polynomial expression might look like this: ax + by + ca, x3 + 2x + 3, etc.

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Answer:

1/3

Step-by-step explanation:

(4/6) - (1/3)

The denominators need to be the same, so let's convert the second term to (2/6), which is the same as (1/3)

(1/3)*(2/2) = (2/6)

Now we can wite:

(4/6) - (2/6)

This is equal to 2/6 or 1/3

Hello!

The equation [tex]\frac{4}{6} - \frac{1}{3}[/tex] simplified is [tex]\frac{1}{3}[/tex].

Step-by-step explanation:

Begin by giving both equations common denominators in this case we will use 18.

For the first set of fractions we multiply 4 by 3 to get 12 and for the second set of fractions we multiply 1 by 6 to get 6.

Our new set of fractions will look like this [tex]\frac{12}{18}[/tex][tex]- \frac{6}{18}[/tex]

Now we can subtract the numerators since our denominators match.

[tex]12-6=6[/tex] so the new answer will be [tex]\frac{6}{18}[/tex]

It's time to simplify both sets of fractions before we can completely solve the equation. (divide by 2, then 3)

[tex]\frac{6}{18}[/tex] ÷ [tex]2=\frac{3}{9}[/tex] ÷ [tex]3=\frac{1}{3}[/tex]

Since 3 is larger than 1 we are done reducing, time to solve for the final answer.

[tex]\frac{4}{6} -\frac{1}{3} =\frac{1}{3}[/tex]

Hope this helps!

3 equations that can be used to solve the given scenario are:

So, equations that can be used to solve the following scenario are:

Then,

Therefore, 3 equations can be used to solve the given scenario are:

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The solution for the algebraic expression 2 1/3 - 4/7 is 37/21

Given,

The algebraic expression ; 2 1/3 - 4/7

We have to solve this expression;

First lets solve the mixed fraction 2 1/3

2 1/3 = (2 x 3) + 1 / 3 = 6 + 1 / 3 = 7/3

Mixed fraction;

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Now,

7/3 - 4/7 = (7 x 7) / (3 x 7) - (4 x 3) / (7 x 3) = 49/21 - 12/21

That is,

49/21 - 12/21 = (49 - 12) / 21 = 37/21

That is,

The solution for the algebraic expression 2 1/3 - 4/7 is 37/21

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Answer: A. 100/x^2 = h, B. v(x) = x^2*h

Step-by-step explanation:

A. Volume = b * h

100 cm^2 = x^2 * h

100/x^2 = h

B. v(x) = x^2*h

Elijah put $53 in the Bank in the first week .

In the question ,

it is given that Elijah put (2x+3) in the first week .

In the second week Elijah put double the first week savings

that means second week deposit = 2*(2x+3) = 4x+6

in the third week he doubled the amount that was in the bank ,

which means third week deposit = 2*(first week + second week deposit)

= 2*(2x+3+4x+6)

Also given that total amount in the bank = $477

total amount = first week + second week + third week deposit

substituting the values we get

477 = (2x+3) + (4x+6) + 2*(2x+3+4x+6)

477 = 2x+3+4x+6+4x+6+8x+12

477 = 18x + 27

18x = 477-27

18x = 450

x = 450/18

x = 25

the amount deposited in the first week = 2x+3

                                                                  = 2(25)+3

                                                                  = 50+3 = $53

Therefore , Elijah put $53 in the Bank in the first week .

The given question is incomplete , the complete question is

Elijah put 2x+3 dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?

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Answer:

y = -x

Step-by-step explanation:

Answer: Y=-X

Step-by-step explanation: