Find the value of each variable.
Simplify your answers as much as possible.
If necessary, you may learn what the markings on a figure indicate.

a) The graph of f(x) is as shown below.

b)

The domain of f(x) is: [-4, 4]

The range of function f(x) is [-2, 6]  

In this question we have been given a piecewise function [tex]f(x)=\left \{ {{\frac{-(x+2)}{2} ~~~-4\leq x\leq 2} \atop {4x-10}~~~~2 < x\leq 4} \right.[/tex]

We need to graph the given function.

The table of (x, f(x)) values is as shown below.

  x             f(x)

 -2             0

 -4              1

  0             -1

  2             -2

 2.5           0

  3.5          4

  4             6

The graph of f(x) is as shown below.

The domain of f(x) is: [-4, 4]

The range of function f(x) is [-2, 6]          

Therefore, for given piecewise function,

a) The graph of f(x) is as shown below.

b)

The domain of f(x) is: [-4, 4]

The range of function f(x) is [-2, 6]  

Learn more about the function here:

https://brainly.com/question/28193995

#SPJ1

There is a modest rise in arrival rates as compared to the prior arrival because the value is bigger than 0.05. It is a minuscule rise.

Given that,

The Message is arrive at an electronic mall server at the average

rate is 4 messages for every 5 minutes. Then the average

number of message is said to be a and mean is 4 to 5 interval.

Therefore ,we can use poission's approximation  to binomial  distribution in this case,

λ=4/5 min

( a ) Then , The Number of messages arrived in 1 hour

4x 12 = 48 . , So 48 messages per hour.

Now , our New arrival rate of messages , λ =48

By using possion's distribution ,

θ = time/rate

= 60/48= 1.25

NOW

probability density function of X is given as

f (x ) = θ e^-θx

for X>0

Given , the probability of new message arrival during given frame

equal is 0.05

p (X > x ) = 0.05

Now , of θ ∫e^-θx dx  = 0. 05 .

then, e^-θx =0.05

Apply logarithm on both sides , then

In( e^-θx) = In 0.05

By solving,

1- 25

X = 2. 39658

(b) Now , probability of arrival of 50 messages in 60 minutes

p (X>2.39658 ) = 0.05

Now arrival gap is θ = 60/50 = 1.2

P(x> 2.39658 ) =e^-θx

=e^- 1- 2 * 2.39658 = 0.0564

NOW ,

p(x>2- 39658) = 0.0564.

It is greater than 0.05 , so it is called there is slight increase in arrival rates as compared to the previous arrival. It is very small increase .

Learn more about probability density function here:

brainly.com/question/14410995

#SPJ4

For the given infinite geometric sequence,

(a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]

(b) The two possible values of m are -8 and 5.

(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]

What are Geometric Series?

What is the Common Ratio of an Infinite Geometric Sequence?

In the question, the first three terms of an infinite geometric sequence are given as, m-1, 6, m+8

[tex]\implies a_{0} =m-1, a_{1}=6,[/tex] and [tex]a_{2}=m+8[/tex]

So, the common ratio is calculated as,

[tex]r=\frac{6}{m-1}=\frac{m+8}{6}[/tex]

Here, there are two expressions,

[tex]r=\frac{6}{m-1}[/tex]    ------(1), and  [tex]r= \frac{m+8}{6}[/tex]  ------(2)

Simplifying (1), we get

[tex]r(m-1)=6[/tex]  -----(3)

Simplifying (2), we get

[tex]6r=m+8\\\implies r= \frac{m}{6}+\frac{8}{6}[/tex]   ------(4)

Now, substituting the values of (4) in (3), we get

[tex](\frac{m}{6}+\frac{8}{6})(m-1)=6\\\implies \frac{m^{2} }{6}-\frac{m}{6} +\frac{2m}{3}-\frac{2}{3} =6\\\implies m^{2}+3m-4=36\\[/tex]

Solving further, we get

[tex]\implies m^{2}+3m-40=0\\\implies m=5, m=-8[/tex]

So, when [tex]m=5, r=\frac{6}{5-1}=\frac{3}{2}[/tex]

Also, when [tex]m=-8, r=\frac{6}{-8-1}=-\frac{2}{3}[/tex]

Therefore, (a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]

(b) The two possible values of m are -8 and 5.

(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]

To learn more about common ratio from the given link

https://brainly.com/question/24643676

#SPJ1

The area of an L-shaped room is calculated by cutting off the Leg of the L and finding the area of the rectangles separately.

Area of the floor space occupied by an objected which is measured in unit squares.

A rectangle is an object which is bounded by four sides, four vertices

The area (A) of a rectangle is;

A=Length x Width

The Area of the L-shaped room is calculated by

A = Area of the Vertical rectangle + Area of the Leg

A = LW + lw

where

learn more about a rectangle on brainly.com/question/15019502

#SPJ1

Converting the given equations from standard form to slope intercept form gives

Information given in the question include

-2x+3y=-6

Standard form of linear equations is of the form Ax + By = C

The slope intercept form is y = mx + c

rearranging the equation

-2x + 3y = -6

3y = 2x - 6

y = 2x/3 - 2

The equation of the line in slope intercept form is y = 2x/3 - 2

Learn more about linear functions at:

https://brainly.com/question/29356636

#SPJ1

Answer:

[tex]f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)[/tex]

Step-by-step explanation:

The root -2 has a multiplicity of 2, and corresponds to a factor of [tex](x+2)^2[/tex].

The root 1 has a multiplicity of 1, and corresponds to a factor of [tex](x-1)[/tex].

The root 3 has a multiplicity of 1, and corresponds to a factor of [tex](x-3)[/tex].

So, [tex]f(x)=a(x+2)^2(x-1)(x-3)[/tex].

Since [tex]f(0)=10[/tex],

[tex]10=a(0+2)^2(0-1)(0-3) \\ \\ 10=12a \\ \\ a=\frac{5}{6} \\ \\ \therefore f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)[/tex]

Answer:

X = -3, y = -8

Please see the link to view the Graph:

Answer:

It's D.

Step-by-step explanation:

I know I can't see that option, but it's D. If you use A for the first one, you get 4(-4) which is -16 and you add 3 to that, it's -12, so that's not 2 so it can't be A. If you use B for the first one, you get 2(-4) which is -8, and if you add 3, you get -5, not 2, so it can't be that either. If you use C, you get 0.5(-4) which is -2, and if you add 3 to that, you just get 1, so it can't be C either. I assume there is fourth option, so it's D.

The probability that a car buyer bought an alarm system or bucket seats is 0.50.

Probability of ,

Alarm system p(A) = 40/100 = 0.40

Bucket seat p(B) = 30/100 = 0.30

Alarm system and bucket seat p(A and B) = 20/100 = 0.20

Probability of alarm system or bucket seat is :

= p(A)+p(B)-p(A and B)

= 0.40+0.30-0.20

= 0.50

In mathematics, probability is the likelihood of an event occurring. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is to occur. A simple example is the tossing of a coin, where the probability of either head or tail is 1/2.

Learn more about probability at : https://brainly.com/question/11234923

#SPJ4

Check the picture below.

Answer:

Exterior angle: 86°

Base angle: 43°

Base angle: 43°

Third angle: 94°

Step-by-step explanation:

First we'll find x, then calculate all the angles.

There is a mark on two of the sides of the triangle. Two sides are the same. This is an isosceles triangle. So that means the base angles are the same also. One is marked 5x - 12, so the other base angle is also 5x - 12.

The marked exterior angle has a special relationship with the two remote interior angles.

If you add the two remote interior angles it equals the exterior angle.

8x-2 = 5x-12 + 5x-12

Combine like terms.

8x - 2 = 10x - 24

Subtract 8x.

-2 = 2x - 24

Add 24.

22 = 2x

Divide by 2.

11 = x

Now we can find all the angles.

The exterior angle is 8x - 2

= 8(11) - 2

= 88 - 2

= 86°

Base angle is 5x - 12

= 5(11) - 12

= 55 - 12

= 43°

The last angle in the triangle is a linear pair with the exterior angle. Or (Also,) the three angles in the triangle add up to 180°.

Angle+43°+43°=180°

Angle + 86 = 180

Angle = 94°

The total cost of your trip to the movie theater is $43.50.

The total cost will be the sum of money spent on ticket and soda and popcorn.

Ticket cost for or cost price of Ticket for:

         5 years old brother = $4.25

          Grandparents = $6.00 × 2 = $ 12.00

           For self= $7.25

Total cost of tickets = $4.25 + $ 12.00 + $ 7.25

                                 = $ 23.50

Total Money spent = Cost of ticket + cost of soda and popcorn

                                = $ 23.50 + $20

                                = $ 43.50

Learn more about Total Cost:

https://brainly.ph/question/6284625

#SPJ4

Answer:

No because their ratios are not the same

Step-by-step explanation:

The scalar from 5 to 10 is 2 but from 3 to 4, its 4/3.

After simplifying the equation, the chemist used 18 liters of 20% solution, 12 liters of 35% solution and 24 liters of 80% solution.

From the given question,

Let that chemist used x, y, z liters of 20%, 35% and 80% solution respectively.

Then according to the given information,

x+y+z=54..........(1)

As we know that in x liters having 20% acid, in y liters having 35% acid, in z liters having 80% acid and in total mixture having 50% acid.

So the equation should be

x ×20%+y×35%+z×80%=54×50%

On simplifying we get

20x+35y+80z=2700

4x+7y+16z=540...............(2)

As given that the number of 80% solution used in 2 times the number of liters of 35% solution used.

So z=2y

Now putting the value of z in equation (1)

x+y+2y=54

x+3y=54

Subtract 3y on both side

x+3y−3y=54−3y

x=54−3y

Now putting the value of x and z in equation (2)

4(54−3y)+7y+16×2y=540

Simplifying

216−12y+7y+32y=540

216+27y=540

Subtract 216 on both side

216+27y−216=540−216

27y=324

Divide by 27 on both side

27/27 y=324/27

y=12

Now putting the value of y in x=54−3y to find the value of x

x=54−3×12

x=54−36

x=18

Now putting the value of y in z=2y to find the value of z

z=2×12

z=24

Hence, the chemist used 18 liters of 20% solution, 12 liters of 35% solution and 24 liters of 80% solution.

To learn more about simplification of equation link is here

brainly.com/question/17350733

#SPJ1

The dimensions of the rectangle are either 10cm x 24cm or

24cm x 10cm having perimeter 68 cm.

What is Pythagorean theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

A rectangle has 4 angles measure of each is 90°.

A diagonal of rectangle divides it into two right angled triangles.

Pythagorean theorem can be applied on these triangles to get the desired values.

According to the given question:  

Let the length and breadth of rectangle be  x  and  y .

Perimeter:  2x + 2y = 68 (Given)

Using Pythagorean theorem diagonal:  [tex]x^2+y^2=26^2[/tex]

Using perimeter,  x + y = 34

∴ x = 34 - y

Substituting this is the equation for diagonal

[tex](34-y)^2 +y^2=26^2\\1156 - 68y + 2y^2 = 676\\2y^2 - 68y + 480 = 0\\y^2 - 34y + 240 = 0\\(y - 10)(y - 24) = 0[/tex]

Therefore dimensions of rectangle are either 10cm x 24cm or

24cm x 10cm.

To know more about Pythagorean theorem visit

https://brainly.com/question/3346664

#SPJ1

The minimum number of swaps required to flip the list is 2.

Array : Generally, in the field of applied sciences, knowledge structures called arrays and typically regarded as just arrays, each containing at least one array-index award or key. Arrays are stored so that formulas can use each component's index tuple to determine the placement of that component within the array.

Given an array with values 5, 10, 15, 20,25

swap reverses the array:

25, 10, 15, 20, 5

25, 20, 15, 10, 5

So, for reversing the number of swaps required list is 2 ..

This may be the smallest variation possible.

Hence, the minimum exchange required to achieve list reversal is two.

To learn more about Array, visit:

brainly.com/question/19570024

#SPJ4

Let's call the price before the VAT "x".

Then x plus that 20% VAT totals 14400.

The VAT is calculated as 20% of the original price, so 20% of x or 0.20x.

This gives us x + 0.20x = 14400.

Simplifying, we get 1.2x = 14400.

Dividing by 1.2 on both sides, we get x = 14400/1.2 = 12000.

Answer:

£18000

Step-by-step explanation:

[tex]x[/tex] x 80/100=14400

80x=1440000

x=1440000/80

x=£18000

Check the picture below.

if the segment AD is an angle bisector, that means it makes two twin angles, and let's also keep in mind that the side AG is shared by both triangles, so is not shorter or longer for either, is the same for both, which means Andrea rules!!!

Answer:5.76

Step-by-step explanation:

-2 2/5=-2.4

(-2.4)^2=5.76

The strategies that would eliminate a variable to help solve the system of equations are

B. Multiply the first equation by -2 and add it to the second equation

C. Multiply the first equation by 1/3 and add it to the second equation

D. Multiply the second equation by 3 and add it to the first equation

From the question we are to determine the strategies that would eliminate a variable to help solve the system of equations.

The given system of equations is

12x + 5y = 7

-4x + 10y = -7

To eliminate y,

Multiply the first equation by -2 and add it to the second equation

-2 × [12x + 5y = 7]

-24x - 10y = -14

Now add to the second equation

 -24x - 10y = -14

+ (-4x + 10y = -7

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

-28x = -21

To eliminate x

Multiply the first equation by 1/3 and add it to the second equation

1/3 × [12x + 5y = 7

4x + 5/3y = 7/3

Now, add it to the second equation

   4x + 5/3y = 7/3

+ (-4x + 10y = -7

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

5/3y + 10y = 7/3 + (-7)

Also, to eliminate x

Multiply the second equation by 3 and add it to the first equation

3 × [-4x + 10y = -7

-12x + 30y = -21

Now, add to the first equation

  -12x + 30y = -21

+ (12x + 5y = 7

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

35y = -14

Hence, the required strategies are the ones explained above.

Learn more on Solving system of equations by elimination here: https://brainly.com/question/29334172

#SPJ1

In triangle ABC, the value of angle A  is 60°.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the triangle ABC,

b=5cm, c=10cm

And by using Pythagoreans theorem,

a²=c²-b²

a²=10²-5²

a²=75

Use cosine rule to determine the angle A,

cosA=b²+c²-a²/2bc

cosA=25+100-75/2×5×10

cosA=50/100

cosA=1/2

cosA=cos60

⇒A=60°

To know more about Triangle on:

https://brainly.com/question/2773823

#SPJ1

The function will return the data type double.

Simply put, a function is a "chunk" of code that you can reuse repeatedly rather than having to write it out several times. Programmers can divide a problem into smaller, more manageable chunks, each of which can carry out a specific task, using functions.

Function declaration type will be as follows in general,

return type function name(argument 1, argument 2,...)

In the given question the declaration is double numbers (int x).

The return type is double, the name of the function is numbers and it has one argument which in an integer.

Hence, the return type of the function is double.

To learn more on function here:

brainly.com/question/5975436

#SPJ4

The volume of the fully inflated balloon is 267.95 cubic inches, the volume of half-inflated balloon is 133.97 cubic inches and it's radius is 3.17in

The volume of sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.

The formula of a sphere is given as

v = 4/3πr³

But diameter = 2 * radius

radius = diameter / 2

radius = 8/2

radius = 4in

The volume of the fully inflated balloon will be

v = 4/3πr³

v = 4/3 * 3.14 * 4³

v = 267.95in³

The volume of the fully inflated balloon is 267.95in³

b) The volume of the half-inflated balloon will half the size of the current volume

v = 267.95in³ / 2 = 133.97in³

c) v = 4/3πr³

133.97 = 4/3 * 3.14 * r³

r = 3.17in

Learn more on volume of a sphere here;

https://brainly.in/question/30880094

#SPJ1

Poncho ha recorrido más trayecto de la carrera de bicicletas, con una fracción de 3/4 del recorrido.

Problema de comparación de fracciones:

Carmen lleva: 3/5 del trayecto

Memo: 4/7

Poncho: 3/4

Jocelyn: 1/2

Una forma de comparar las fracciones es usando un mismo denominador, esto es posible con el Mínimo Común Múltiplo (MCM):

MCM(2,4,5,7) = 2² · 5 · 7 = 140

Fracciones con mismo denominador:

3/5 = (3 · 7 · 4)/(5 · 7 · 4) = 84/140

4/7 = (4 · 5 · 4)/(7 · 5 · 4) = 80/140

3/4 = (3 · 5 · 7)/(4 · 5 · 7) = 105/140

1/2 = (1 · 2 · 5 · 7)/(2 · 2 · 5 · 7) = 70/140

Comparando:

70/140 < 80/140 < 84/140 < 105/140

  1/2     <     4/7  <     3/5    <     3/4

To learn more about trayecto visit: https://brainly.com/question/20802079

#SPJ1

a) The sampling proportion's mean value is 0.25. 0.016 is the standard deviation. The form resembles a bell.

b) There is a 10% possibility of getting this number, p=0.27 or more, given a sample proportion, so I wouldn't be surprised.

c) Since there is no chance that the sample fraction of 0.31 will occur, I would be shocked if it did.

Given,

a) The null hypothesis proportion would be the middle of the sampling distribution (p-0.25). So, p=0.25 is the sampling proportion's mean value.

This would be the standard deviation:

σp = √(p (1 - p) / n) = √(0.25 × 0.75/731) = 0.016

The distribution would resemble a binomial distribution, hence the form would be bell-shaped.

b) By calculating the z-value and checking for its probability in the standard normal distribution, we may determine the likelihood of a value p=0.27 in this distribution.

z = (p - π) / σp = (0.27 - 0.25) / 0.016 = 0.02/0.016  = 1.25

p(z > 1.25) = 0.106

There is a 10% probability of achieving this value, p=0.27 or more, for a sample proportion, so I wouldn't be surprised.

c) We repeat the calculation for p=0.31

z = (p - π) / σp = (0.31 - 0.25) / 0.016 = 0.06/0.016  = 5

p(z > 5) = 0.000

I would be astonished to see that value because the probability of this sample fraction occurring at p=0.31 is zero.

Learn more about probability here;

https://brainly.com/question/15727765

#SPJ4

The measure of the line segment AB is  36cm .

In the question ,

it is given that ,

The triangle ABC is a isosceles triangle ,

that means side AB = side BC ,

and the length of base AC = 24 cm .

given the perimeter of the triangle is 96 cm .

So ,

AB + BC + AC = 96

AB + AB + AC = 96       .....because AB = BC

2AB + AC = 96

Substituting the value of AC = 24 cm

2AB + 24 = 96

Subtracting 24 from both the sides , we get

2AB = 96 - 24

2AB = 72

Dividing both sides by 2 ,

we get ,

AB = 72/2 = 36 .

Therefore , The measure of the line segment AB is  36cm .

The given question is incomplete , the complete question is

Isosceles triangle ABC has a perimeter of 96 centimeters. The base of the triangle is Line segment A C and measures 24 centimeters.

What is the measure of Line segment AB ?

Learn more about Triangle here

https://brainly.com/question/13938498

#SPJ4

The prime factorization of the number 68 is 2×2×17 and least prime number is 2 and greatest prime number is 17.

A number system is defined as a system of writing to express numbers.

We need to find the prime factorization of the number 68

Prime factorization is a process of writing all numbers as a product of primes.

The prime factorization of 68 is 2×2×17

The prime factors of 68 are 2 and 17.

The least prime number is 2 and greatest prime number is 17.

Hence the prime factorization of the number 68 is 2×2×17 and least prime number is 2 and greatest prime number is 17.

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ1

Answer: 10

Step-by-step explanation:

Set the equal angles as x, as shown below.

Then, [tex]sin(x)=\frac{x+4}{8}[/tex] and [tex]sin(x)=\frac{2x+1}{12}[/tex]. Set them equal to each other and solve for x:

[tex]\frac{x+4}{8} =\frac{2x+1}{12} \\ \\12(x+4)=8(2x+1)\\12x+48=16x+8\\48-8=16x-12x\\4x=40\\x=10[/tex]

This is assuming those two triangles are right triangles. I'm actually not sure if they're right triangles.

The given equation is a combined variation.

We have been given an equation is

[tex]\frac{xy}{z}[/tex]

This is an equation in which we have three variables and one constant.

This can not be the case of direct or inverse variation because in direct or inverse variation we have only two variables. Whereas, here we have three variables.

So, Direct and inverse options are discarded.

So, either It can be joint or combined

In joint variation both the variables are directly proportional

Hence, given equation is not joint because if we rewrite the equation we will get [tex]y = \frac{cz}{x}[/tex] both the variables are not directly proportional.

In combined, one variable is directly proportional and the other one is inversely proportional.

From [tex]y = \frac{cz}{x}[/tex]  we can see that z is directly proportional and x is inversely proportional.

Hence the answer is, the given equation is combined variation.

To learn more about variations click here https://brainly.com/question/2375770

#SPJ9

Answer:

If you use y = mx + b, your equation would be y = -4x + 20

Step-by-step explanation:

M is always the slope, and to find the x-intercept, you just set y = 0 and in this case it would be 0 = -4x + 20. If you subtract 20 from both sides you get -20 = -4x and to find x, you just divide by -4 and get -20/-4, which equals 5. You're welcome :)

We need to determine the value of the y-intercept for this equation. Let's start by finding all other information about the x-intercept.

If the x-intercept is x = 5, f(5) = 0. So, now let's solve for b.

f(5) = -4(5) + b
0 = -4(5) + b
0 = -20 + b
0 + 20 = -20 + 20 + b
b = 20

We have m and b now, so:

y = -4x + 20