In the spinner below the large wedges are twice the size of the smaller ones. What is true about the probablilty of landing on 6 and the probability of landing on 5

Answer:

  sin θ = 4/5

Step-by-step explanation:

The Pythagorean theorem tells you the distance (h) from the origin to the terminal point:

  h² = (-3)² +(4)² = 25

  h = 5 . . . . . . . . take the square root

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse

For angles other than 1st-quadrant angles, it can sometimes be difficult to identify the relevant sides of the relevant triangle. If the angle were a 1st-quadrant angle, it would be clear that the side opposite the angle is the y-coordinate of the point on the terminal side. That remains the case for all angles. The hypotenuse is always the positive distance from the origin to the terminal point.

So, you have

  sin θ = opposite/hypotenuse = 4/5

Answer:

  √3

Step-by-step explanation:

  cot²(θ) = csc²(θ) -1 . . . . . a relevant identity

  = 1/sin²(θ) -1

  = (1/(1/2))² -1 = 2² -1 = 3

Then ...

  cot(θ) = √3 . . . . . . . . take the square root

Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

It just is

Answer:

mean of sample is 55.7

sample standard deviation is  0.2375

Step-by-step explanation:

given data

population mean  = 55.7

population standard deviation = 3.8

n = 256

to find out

the mean and standard deviation

solution

we know directly mean of sample is mean of population

i.e. mean of sample = 55.7

and standard deviation will be calculate by this formula

sample standard deviation = population standard deviation / [tex]\sqrt{n}[/tex]

sample standard deviation =  3.8 / [tex]\sqrt{256}[/tex]

sample standard deviation =  3.8/ 16

sample standard deviation =  0.2375

so last option is right

(E) μ = 55.7 , σ = 0.2375.

Answer:

108 yards

Step-by-step explanation:

Let circle A be the circle with the 62 yard diameter

Let circle B be the circle whose diameter we are trying to solve for.

Answer:

  D.  y = 3/5x + 13/5

Step-by-step explanation:

The slope of the desired line is the ratio of the difference in y-values to the difference in x-values:

  m = Δy/Δx = (2 -5)/(-1 -4) = -3/-5 = 3/5 . . . . . . eliminates choices B and C

The slope-intercept equation will then be ...

  y = mx + b . . . . . . . generic slope-intercept form

  y = 3/5x + b . . . . . . put in m; true for some b that puts the given points on the line

Using the first point, we have ...

  5 = 3/5×4 + b

  25/5 = 12/5 + b

  13/5 = b . . . . . . . . . subtract 12/5

Then the equation is ...

  y = 3/5x + 13/5

_____

You know as soon as you consider putting a point value in the equation ...

  y = 3/5x + b

that the equation of choice A cannot work. That only leaves choice D.

Answer:

  p² > 4/3(1 -p)

Step-by-step explanation:

Assuming candy selections are independent from one to the next, the probability of getting Coffee Toffee twice in a row will be p². The probability of getting some other selection than Coffee Toffee will be 1-p.

Lisa wants ...

  p² > (4/3)(1 -p)

_____

This has solution p > 2/3.

Answer:

Step-by-step explanation:

The first step in simplifying a mathematical expression, especially those with parentheses, is to eliminate and simplify terms within the parentheses. This involves combining like terms or performing operations according to the order of operations. Subsequent steps may involve factoring and applying algebraic rules to further simplify.

The question is asking for the first step in simplifying a mathematical expression. To begin simplifying any expression, especially when involving parentheses, the first step typically involves eliminating terms within the parentheses wherever possible. This process often involves combining like terms or simplifying the algebraic expression by performing any operations inside the parentheses first, according to the order of operations (PEMDAS/BODMAS).

After simplifying the expression inside the parentheses, you can then apply other algebraic techniques, such as factoring, combining like terms outside the parentheses, and explicit multiplication of terms across the parentheses if needed. Always remember to check the answer to see if it is reasonable and to ensure that no simplification step has been missed.

If the expression involves complex denominators or numerators, applying algebraic rules such as the power rule or the chain rule can further simplify the expression. In cases involving equations, isolating the variable on one side can help in solving for the unknown value.

Answer:

The probability is 2 out of 9 chances to pull a green card.

Step-by-step explanation:

Because your original probability was 3/9 but you removed one so that makes it 2/9 chances to draw one.

If im right may i get brainliest?

Answer: 1/15

Step-by-step explanation:

The odds would be 1/15.

To find these odds, you first have to find the total number of cards.

2 + 3 + 1 + 4 = 10 cards

Then you can find the first set of odd for pulling a green card by placing the goal amount over the total amount.

3 green / 10 total = 3/10

Now, with that green card not being replaced, we have one less green and one less total. This gives us 2 green and 9 total, which helps us find the odds of pulling one again.

2 green / 9 total = 2/9

Now to find the odds of doing both, you need to multiply the two odds together.

3/10 * 2/9 = 6/90 or simplified 1/15

Answer:

In vertex form it's [tex]y=(x+7)^2-9[/tex]

In standard form it's [tex]y=x^2+14x+40[/tex]

Step-by-step explanation:

We can use the vertex form to solve for a in

[tex]y=a(x-h)^2+k[/tex]

"a" is the number out front that dictates the steepness, or lack thereof, in a parabola.  That means that we need h and k (which we have in the vertex) and we need x and y (which we have in the form of one of the zeros).  Filling in using a vertex of (-7, -9) and a coordinate point (-7, 0):

[tex]0=a(-4-(-7))^2-9[/tex] simplifies a bit to

[tex]0=a(-4+7)^2-9[/tex] simplifies a bit more to

[tex]0=a(3)^2-9[/tex] and

[tex]0=a(9)-9[/tex] so

[tex]0=9a-9[/tex],

[tex]9=9a[/tex] and finally,

a = 1

Phew!  So there is the a value.  Now we can simply fill in the formula completely, using the vertex as our guide:

[tex]y=(x+7)^2-9[/tex]

In standard ofrm that is

[tex]y=x^2+14x+40[/tex]

We can check ourselves for accuracy by factoring that standard polynomial using whatever method of factoring you like for quadratics and get that the roots are in fact x = -10, -4

The only reason we needed the zeros is to use one of them as the x and y to solve for a.  

Answer:

The cost of the telegram was 1,270 shilling

Step-by-step explanation:

we know that

The total words-----> 44

The first ten words ----> 10

Extra words----> 44-10=34

so

The total cost is equal to

25(10)+30(34)=1,270 shilling

Answer: 68.86 inches

Step-by-step explanation:

Given : In a survey of women in a certain country having

Mean : [tex]\mu=64.3\text{ inches}[/tex]

Standard deviation : [tex]\sigma=2.77\text{ inches}[/tex]

The z-value corresponds to 0.095 is 1.645.  [Using standard normal distribution table]

The height that represents the 95th percentile is given by :-

[tex]H=z\times\sigma+\mu\\\\=1.6449\times2.77+64.3=68.856373\approx68.86\text{ inches}[/tex]

Hence, the height represents the 95th ​percentile = 68.86 inches.

Answer:

95th ​percentile = 68.86 inches.

Step-by-step explanation:

Just took quiz :)

Answer:

76800 cases

Step-by-step explanation:

The number of cases of new infectious diseases reported last year= 150 cases

Number of cases are going to be double every year

Number of the cases in next or first year=150+150=300

Number of the cases in next or second year=300+300=600

Number of the cases in next or third year=600+600=1200

Number of the cases in next or fourth year=1200+1200=2400

Number of the cases in next or fifth year=2400+2400=4800

Number of the cases in next or sixth year=4800+4800=9600

Number of the cases in next or seventh year=9600+9600=19200

Number of the cases in next or eight year=19200+19200=38400

Number of the cases in next or ninth year=38400+38400=76800

Hence , the total number of cases are 76800 cases

Answer:

38,400

Step-by-step explanation:

The answer above me is wrong

Got it right on the test

Answer:

  The supposition is incorrect.

Step-by-step explanation:

The growth rate of a child is not constant, so height versus time does not look like a straight line. Nothing is wrong with the prediction made using the false assumption. You can conclude anything you like when you start with a false premise.

Answer:

Step-by-step explanation:

Let the time taken by the john to get to his uncle be x.

Let the time taken by the john to get back from his uncle be y.

So,

x+y=12 ------ equation 1

According to the given velocities:

20x=30y

x=3/2y

Put the value x=3/2y in equation 1

3/2y+y =12

3y+2y/2=12

3y+2y=12*2

5y=24

y=24/5

y=4.8h

Now put the value of y in x=3/2y

x=3/2*4.8

x=14.4/2

x=7.2h ....

Answer:

Step-by-step explanation:

Here are some facts you can mention:

1. Parabola.

The equation of a parabola is one where x^2 is the term  of the highest degree. ( the degree being '2' in x^2).  For example y = x^2, y = 2x^2 - 5x,

y = -x^2 + 1 are all parabolas. Also we have the type x = f(y)  - for example

4x = y^2.

The graph looks like a U ( which maybe on its side or upside down The graph of a parabola where  the term coefficient of x^2 is positive opens upwards while if it is negative it open downwards.

It is also a 'conic section' .  A parabola is formed when we  intersect a right cone with a plane surface through the side wall and through the base.

When a projectile  is fired from  a gun at  an angle,  the path it follows is close to a parabola. If fired in a vacuum the path we would be exactly parabolic.

2. Ellipse.

This is another conic section formed when we intersect the cone with a plane surface at an angle  to the base ( not 90 degrees) and the plane passes through both sides walls of the cone.

It is oval shaped.  The path of the planets around our sun form an ellipse.

You can draw an ellipse by fixing 2 pins at a distance apart on a sheet of paper, and tie the ends of a piece of string, longer in length than the distance between the pins, to each pin. We then press a pen or pencil to the string at some point and draw around the 2 pins.

3.   Parametric equations.

A third variable is introduced in a parametric equation. Both x and y  are written in terms of this third variable. This variable is called a parameter , hence the name parametric equation.

Many functions can be written in the form y = f(x) or x = f(y) but there are some that cannot be written this way.  An example is  the circle

x^2 + y^2 = r^2. There are many other such functions. By introducing another variable we are able to identify any point on the graph  and it also makes the calculus work  easier.

The variable used is usually t or  the Greek letter theta (for angles). An example of  parametric equations are the ones for a parabola:   x= at^2, y = 2at,

which are the parametric equation for the parabola y^2 = 4ax.

I hope this helps.

Answer:

Step-by-step explanation:

I have the same problem. Do you still have the answers. I know I'm two years late but just checking.

Answer:

Step-by-step explanation:

____

Good evening ,

_______________

2(7) + 5(1) + 3(-3) = 10

3(7) ­ - (1) + 4(-3) = 8

5(7) - ­ 2(1) + 7(-3) = 12

Then (7,1,-3) is a solution to system

____

:)

Answer:

A.)  Slope of function B = 2 * the slope of Function A.

Step-by-step explanation:

The slope of Function A is 1  ( because of the x  ( = 1x) in the equation).

From the graph, the slope of Function B = 5 / 2.5 = 2.

Answer:

The correct option is A.

Step-by-step explanation:

The slope intercept form of a line is

[tex]y=mx+b[/tex]               .... (1)

where, m is slope and b is y-intercept.

The equation of Function A is

[tex]f(x)=x-9[/tex]      .... (2)

From (1) and (2) we get

[tex]m=1[/tex]

It means slope of Function A is 1.

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

From the given graph it is clear that the line passes through two points (0,-1) and (1,1).

[tex]m=\frac{1-(-1)}{1-0}=2[/tex]

The slope of Function B is 2.

We can say that

Slope of Function B = 2 x Slope of Function A

Therefore the correct option is A.

Answer:

1) 68%

2) 68%

Step-by-step explanation:

We know the mean and the standard deviation.

The mean is:

[tex]\mu=25[/tex]

The standard deviation is:

[tex]\sigma=5[/tex]

The Z-score formula is:

[tex]Z = \frac{x-\mu}{\sigma}[/tex]

For x=20 the Z-score is:

[tex]Z_{20}=\frac{20-25}{5}=-1[/tex]

For x=30 the Z-score is:

[tex]Z_{30}=\frac{30-25}{5}=1[/tex]

Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of the trees are between 20 and 30 years old

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

[tex]\mu=27[/tex]

The standard deviation is:

[tex]\sigma=3[/tex]

The z-score formula is:

[tex]Z = \frac{x-\mu}{\sigma}[/tex]

For x=24 the Z-score is:

[tex]Z_{24}=\frac{24-27}{3}=-1[/tex]

For x=30 the Z-score is:

[tex]Z_{30}=\frac{30-27}{3}=1[/tex]

Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of pizzas are delivered between 24 and 30 minutes

Answer:

a) The portfolio will be at maximum after 12 months (1 year)

b) The maximum value of the portfolio is $5432

Step-by-step explanation:

The function that models Jennifer's stock portfolio (in dollars) is [tex]f(t)=-3t^2+72t+5000[/tex], where t is the time in months since she opened the account.

We complete the square to obtain this function in vertex form:

Factor -3 from the first two terms

[tex]f(t)=-3(t^2-24t)+5000[/tex].

Add the zero pairs -3(+144),-3(-144)

[tex]f(t)=-3(t^2-24t+144)+5000+-3(-144)[/tex].

Factor the perfect square trinomial and simplify.

[tex]f(t)=-3(t-12)^2+5432[/tex].

The vertex of this function is (h,k)=(12,5432)

a) The portfolio will be at maximum when t=12, the h-value of the vertex

b) The maximum value of the portfolio is the k-value of the vertex which is 5432

Jennifer's stock portfolio reaches its maximum value after 12 months, with the maximum value being $5432.

The given function is a quadratic equation in the form f(t) = -3t² + 72t + 5000. This function opens downwards because the coefficient of t2 is negative.

To find the time t when the portfolio is at its maximum, we use the vertex formula for a parabola

t = -b / (2a), where a = -3 and b = 72.

t = -72 / (2 * -3) = 72 / 6 = 12.

So, the portfolio reaches its maximum value at t = 12 months.

To find the maximum value of the portfolio, substitute t = 12 back into the function:

f(12) = -3(12)² + 72 * 12 + 5000.

f(12) = -432 + 864 + 5000 = 5432.

Therefore, Jennifer's stock portfolio will be at its maximum value after 12 months, and the maximum value of the portfolio will be $5432.

Complete Question:

The value of Jennifer's stock portfolio (in dollars) is given by the function f(t) = -3t² +72t + 5000, where t is the time in months since she opened the account. After how many months will her portfolio be at a maximum? What is the maximum value of the portfolio?

Answer:

A).  (7, 0) The time it takes to empty the water in the  pool.

Step-by-step explanation:

If we extend the values we see that they are

x f(x)

5 10

5 5

7 0

So at time 7 minutes the pool is empty.

Answer:

(7, 0); the time it takes to empty the water in the pool

Step-by-step explanation:

The following table shows the amount of water leaking from an inflatable pool as a function of time:

x (time in minutes)    f(x)

0                            35

1                            30

2                            25

3                            20

4                             15

f(x) represents the amount of water in the pool. x intercept is the point where f(x) is 0 .At x intercept the amount of water in the pool is 0.

WE need to find out the point where f(x) becomes 0

F(x) is decreasing by 5. LEts extend the table till we get f(x) becomes 0

Decrease f(x) by 5

x (time in minutes)    f(x)

3                            20

4                             15

5                                  15-5=10

6                                  10-5=5

7                                   5-5=0

When x=7, f(x)=0. (7,0) is the x intercept.

(7, 0); the time it takes to empty the water in the pool

Answer:

A) 420 seconds = 7 minutes

B) 8 times

Step-by-step explanation:

A) After how many second would all three things happen together again?

Solution:

His clock ticked every 5 seconds , a tap was dripping every 7 seconds and     his pet dog snored every 12 seconds. It all happens simultaneously = 5*7*12=420 seconds

B) How many times would all three things happen together again between    midnight and one o'clock

Since all these events happen together after every 420 sec = 7 mins and there are 60 mins between midnight and 1 o'çlock , thus 60/7 = 8 times ....

Answer:

Step-by-step explanation:

These are independent non-ordered events. The faculty members chosen don't affect the students and vice versa. There is no issue with replacement, and the only limitation is the number of people allowed to serve.

12C4*15C5

495*3003=1,486,485 ways

Answer:

1. 2.12 seconds

2. 10 feet

Step-by-step explanation:

1. "Pekka tosses a ball out of a window that is 40 feet in the air.  Its initial velocity is 15 feet per second.  The path of the ball is represented by:

h = -16t² + 15t + 40

How long does it take for the ball to hit the ground (in seconds) rounded to the nearest hundredth?"

When the ball hits the ground, its height is 0:

0 = -16t² + 15t + 40

0 = 16t² − 15t − 40

Solve with quadratic formula:

t = [ -b ± √(b² − 4ac) ] / 2a

t = [ 15 ± √(225 + 2560) ] / 32

t ≈ 2.12 or -1.18

t must be positive, so t = 2.12 seconds.

2. "Tricia bounces a ball in front of her feet.  The path of the ball from the time it hits the ground until it lands on the floor is represented by:

f(x) = -2(x − 3)² + 10

Assuming that Tricia's feet are located at the origin (0, 0), what is the maximum height of the ball (in feet)?"

The function is a parabola.  The vertex of this parabola is at (3, 10).  So the maximum height is 10 feet.

Answer:

She will use:

3 tablespoons of pepper

7 tablespoons of garlic powder

[tex]\frac{1}{4}[/tex] tablespoon of thyme

8 tablespoons of onion powder

Explanation:

To double the amount, Stephanie will need to double the amount of each ingredient used. This means that she will multiply each amount by 2

Therefore:

New amount of any ingredient = old amount of that ingredient x 2

This means that:

New amount of pepper = [tex]1\frac{1}{2}*2= 3[/tex] tablespoons

New amount of garlic powder = [tex]3\frac{2}{4}*2=7[/tex] tablespoons

New amount of thyme = [tex]\frac{1}{8}*2=\frac{1}{4}[/tex] tablespoons

New amount of onion powder = [tex]4*2=8[/tex] tablespoons

Hope this helps :)

Stephanie will need double the original amounts: 3 teaspoons of pepper, 7 1/2 teaspoons of garlic powder, 1/4 teaspoon of thyme, and 8 teaspoons of onion powder when doubling her recipe for the party.

When Stephanie needs to double the recipe for a party, the amount of each ingredient will be doubled as well. Here's the doubled amount for each ingredient:

Pepper: 1 1/2 teaspoons doubled is 3 teaspoons.

Garlic powder: 3 2/4 teaspoons doubled is 7 1/2 teaspoons (since 3 2/4 is equivalent to 3.75 and doubling it gives 7.5).

Thyme: 1/8 teaspoon doubled is 1/4 teaspoon.

Onion powder: 4 teaspoons doubled is 8 teaspoons.

To calculate this, each original amount is multiplied by two. For example, to double 3 2/4 teaspoons of garlic powder, you can first convert the mixed number to a decimal (3 + 2/4 = 3.75) and then multiply by 2 to find that you will need 7.5, which is the same as 7 1/2 teaspoons.

Answer:

The probability that the sample mean will be between 80.54 and 88.9 is 0.951

Step-by-step explanation:

* Lets revise some definition to solve the problem

- The mean of the distribution of sample means is called M

- The standard deviation of the distribution of sample means is

 called σM

- σM = σ/√n , where σ is the standard deviation and n is the sample size

- z-score = (M - μ)/σM, where μ is the mean of the population  

* Lets solve the problem

∵ The sample size n = 36

∵ The sample mean M is between 80.54 and 88.9

∵ The mean of population μ = 84

∵ The standard deviation σ = 12

- Lets find σM to find z-score  

∵ σM = σ/√n

∴ σM = 12/√36 = 12/6 = 2

- Lets find z-score

∵ z-score = (M - μ)/σM

∴ z-score = (80.54 - 84)/2 = -3.46/2 = -1.73

∴ z-score = (88.9 - 84)/2 = 4.9/2 = 2.45

- Use the normal distribution table to find the probability

∵ P(-1.73 < z < 2.45) = P(2.45) - P(-1.73)

∴ P(-1.73 < z < 2.45) = 0.99286 - 0.04182 = 0.95104

∴ P(-1.73 < z < 2.45) = 0.951

* The probability that the sample mean will be between 80.54 and 88.9

  is 0.951

The probability that the sample mean lies between 80.54 and 88.9 is calculated using the Central Limit Theorem and z-scores. The standard error is calculated to convert the measure into a standard normal distribution where probability can be determined.

In order to solve this problem, we use the concept of the Central Limit Theorem in statistics. According to the theorem, as the sample size increases, the sampling distribution tends towards a normal distribution. In this case, the population mean (μ) is 84 and the standard deviation (σ) is 12. If you take a sample of 36 observations, the mean of this sample should theoretically be close to the population mean. The standard deviation of the sampling distribution of the means (also known as Standard Error) is given by σ/√N (√36 in this case).

Now, to find the probability that the sample mean lies between 80.54 and 88.9, you'd first convert these into z-scores, using the formula z = (X - μ)/standard error. Thus, you get two z-scores corresponding to 80.54 and 88.9. The probability that the sample mean lies between these two points is the area under the standard normal distribution between these two z-values, which can be found using standard statistical tables or software.

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Answer:

(-2,3)

Step-by-step explanation:

7x+8y=10

5x+y=-7

To solve this by elimination, we need both equations in the same form.  There are.  They are both in form ax+by=c.

Now we also need for one of the columns with the variables to be opposite or same terms.

I like the way the column with the y's are looking because if I multiply that second y by 8 or -8 I will have sames or opposites.

I'm going to multiply the second equation by -8.

This will give me:

  7x+8y=10

-40x-8y=56

--------------------Add the equations!

-33x+0=66

 -33x   =66

      x    =66/-33

       x  =-2

Now we need to find the other variable. It doesn't matter which equation you use.

I'm going to use 5x+y=-7 where x=-2 to find y.

5(-2)+y=-7

-10+y=-7

Add 10 on both sides

     y=3

The solution is (-2,3)

Answer:

The solution is x = -2, y = 3. As an ordered pair it is (-2, 3).

Step-by-step explanation:

7x +  8y = 10

5x +   y = −7

Multiply the second equation by -8:

-40x - 8y = 56

Add this to the first equation, we get:

-33x = 66

x = -2

Now substitute for x in the second equation:

5(-2) + y = -7

y = -7 + 10

y = 3.

Check these results in the first equation:

7(-2) + 8(3) = -14 + 24 = 10 - so correct.

Answer:

D. 5x2 is the GCF

The greatest common factor of the terms of the given polynomial is 5x². So, option D is correct

To find the GCF of a polynomial,

Given that,

the polynomial is [tex]20x^4-10x^3 + 15x^2[/tex]

Finding factors for all the terms:

[tex]20x^4[/tex] = 2 × 2 × 5 × x × x × x × x

[tex]10x^3[/tex] = 2 × 5 × x × x × x    

[tex]15x^2[/tex] = 3 × 5 × x × x

So, from these three terms, the common factors are 5, x, x

On multiplying them,

⇒ 5 × x × x

∴ GCF = 5x²

Therefore, the greatest common factor of the given polynomial is 5x². So, option D is correct.

Learn more about the GCF of a polynomial here:

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Answer:

He should prepare 260 pounds of first mixture and 0 pounds of second mixture

Step-by-step explanation:

Let x be the total quantity ( in pounds ) of cherries and mints in the first mixture and y be the total quantity in second mixture,

Since, first mixture will contain half cherries and half mints by weight,

That is, in first mixture,

Cherries = [tex]\frac{x}{2}[/tex]

Mints = [tex]\frac{x}{2}[/tex],

While, second mixture will contain one-third cherries and two-thirds mints by weight,

That is, in second mixture,

Cherries = [tex]\frac{y}{3}[/tex]

Mints = [tex]\frac{2y}{3}[/tex]

According to the question,

The manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock,

That is,

[tex]\frac{x}{2}+\frac{y}{3} \leq 130[/tex]

[tex]\frac{x}{2}+\frac{2y}{3}\leq 170[/tex]

Also, pounds can not be negative,

x ≥ 0, y ≥ 0,

Since, the first and second mixture must be sell at the rate of $2.00 per pound and $1.25 per pound respectively,

Hence, the total revenue,

Z = 2.00x + 1.25y

Which is the function that have to maximise,

By plotting the above inequalities,

Vertex of feasible regions are,

(0,255), (180, 120) and (260, 0),

Also, at (260, 0), Z is maximum,

Hence, he should prepare 260 pounds of first mixture and 0 pounds of second mixture in order to maximize his sales revenue.

To maximize sales revenue, the candy manufacturer should prepare one-third cherries and two-thirds mints mixture.

To maximize sales revenue, the candy manufacturer should prepare a mixture that contains one-third cherries and two-thirds mints by weight. Let's assume that he prepares x pounds of this mixture. To calculate the amount of the other mixture, we subtract x from the total weight of the ingredients in stock. So, the amount of the other mixture will be (130 + 170) - x pounds. The candy manufacturer should prepare x pounds of the one-third cherries and two-thirds mints mixture and (130 + 170) - x pounds of the other mixture to maximize his sales revenue.

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Answer:

The correct graph is D (Compare to the graph above)

Answer:

D.

Step-by-step explanation:

You can see it calculating the vertex. the formula of the vertex is

[tex](\frac{-b}{2a}, y(\frac{-b}{2a}))[/tex]

where a = 1/2 and b=2.

[tex](\frac{-2}{1}, \frac{1}{2}(-2)^2+2(-2)-6)[/tex]

[tex](-2, \frac{1}{2}*4-4-6)[/tex]

[tex](-2, 2-4-6)[/tex]

[tex](-2, -8)[/tex]

The only option of graph that has vertex in (-2,-8) is option D.

Answer:

The area of a triangle is given by the formula:

A = bh/2

If the height of the triangle is 3 units more than the base we can say that:

h = b + 3

Therefore, the area of the triangle will be:

A= b(b+3)/2

Where 'b' comes to be the base of the triangle.

Answer:

A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]

Step-by-step explanation:

Given: Height of the triangle is 3 units more than the base.

Let "b" be the base of the triangle.

So, h = b + 3

Area of a triangle A = [tex]\frac{1}{2} base * height[/tex]

Now plug in h = b +3 in the above area of formula, we get

A(b) = [tex]\frac{1}{2} b*(b + 3)[/tex]

Now we can multiply b and (b + 3), we get

A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]

Therefore, the answer is A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]