The owner of Cardo Reef Tours found when the price for a tour was $9 US dollars per person
the average number of customers was 1000 per month. When he reduced his price to $7 US dollars
per person the average number of customers increased to 1500 per month. Assuming that his
demand curve was linear, what price should he charge to obtain the largest monthly revenue?
b. If f(x) = 2x
3 − 24x, find the minimum and maximum values of f in the interval [−3,5].

ANSWER

A

[tex]( - \infty , + \infty )

[/tex]

EXPLANATION.

The given function is

[tex]f(x) = 2 {x}^{3} + 21[/tex]

Let

[tex]y= 2 {x}^{3} + 21[/tex]

Solve for x.

[tex]2 {x}^{3} = y - 21[/tex]

[tex] {x}^{3} = \frac{1}{2} y - \frac{21}{2} [/tex]

Take cubic root of both sides,

[tex]x = \sqrt[3]{ \frac{1}{2} y - \frac{21}{2} } [/tex]

x is defined for all real values of y.

The range refers to the values of y, for which x is defined.

Hence the range is all real numbers.

In interval notation, we write this as,

[tex]( - \infty , + \infty )

[/tex]

The correct choice is A.

Answer:

Yes it’s A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

g(x) - h(x)

= 5x² - 10x + 9 - ( - 3x³ + 5x - 6) ← distribute parenthesis by - 1

= 5x² - 10x + 9 + 3x³ - 5x + 6 ← collect like terms

= 3x³ + 5x² - 15x + 15 → B

Answer:

The answer is

g(x) = (x-3)^3

Step-by-step explanation:

We can easily solve this problem by plotting each equation with a graphing tool or calculator.

Please see attached graph

The correct answer is

g(x) = (x-3)^3

Answer:

I think it is 145.20

Step-by-step explanation:

I did 22.45x6=134.70+10.50=145.20

Answer:

$145.04

Step-by-step explanation:

$22.45 * 6 + $10.50 = $145.04

Answer:

1.20 + 1.40x ≥ 5, or $1.20 + $1.40x ≥ $5

Step-by-step explanation:

So since you are only buying 1 soda and you are buying multiple bags of Cheetos so you are able to use you debit card and meet the requirement of at least $5, you can make the inequality:

1.20 + 1.40x ≥ 5, or $1.20 + $1.40x ≥ $5

where x is the number of bags of Cheetos.

The answer is 2. The rate of change between -1 and 0 is 3 and between 0 and -1 is 1. The average between 3 and 1 is 2.

Answer:

- 2

Step-by-step explanation:

The average rate of change in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ - 1, 1 ]

f(b) = f(1) = 1 - 2 = - 1

f(a) = f(- 1) = 1 + 2 = 3

Hence

average rate of change = [tex]\frac{-1-3}{1-(-1)}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

Answer:

15.8

Step-by-step explanation:

Rounding to the nearest tenths means we are focusing on the number 7 and the number after it- 5. Because it is a 5, we will round the number 7, one higher. If it were to be a 4, it would stay a 7.

Answer:

15.8 is the Answer

Step-by-step explanation:

1) 5 in the hundreds place will be turn to 6 due to the fact that in can round up because a 5 is in the thousandth place.

2) Since 6 is 5 and greater than 5 it will round up 7 in the tenths place to 8.

hopes this helps.

For this case we have that the law of cosine is given by:

[tex]c ^ 2 = a ^ 2 + b ^ 2-2 (a) (b) * cos (x)[/tex]

Where:

[tex]c = 12 \ ft\\a = 8 \ ft\\b = 9 \ ft[/tex]

We replace:

[tex]12 ^ 2 = 8 ^ 2 + 9 ^ 2-2 (8) (9) * cos (x)\\144 = 64 + 81-144 * cos (x)\\144 = 145-144 * cos (x)\\-1 = -144cos (x)\\cos (x) = \frac {1} {144}\\x = cos ^ {- 1} (\frac {1} {144})\\x = 89.60 \ degrees[/tex]

Answer:

Option B

Answer:41/8 - 1/3= 115/24

Step-by-step explanation:

Answer:

[tex]\large\boxed{\dfrac{f(3)}{g(2)}=\dfrac{7}{8}}[/tex]

Step-by-step explanation:

[tex]f(x)=2x+1,\ g(x)=3x+2[/tex]

[tex]f(3)\to\text{put x = 3 to the equation of}\ f(x):\\\\f(3)=2(3)+1=6+1=7[/tex]

[tex]g(2)\to\trext{put x = 2 to the equation of}\ g(x):\\\\g(2)=3(2)+2=6+2=8[/tex]

[tex]\dfrac{f(3)}{g(2)}=\dfrac{7}{8}[/tex]

The average distance from the sun to Mars can be found by setting up an equation based on the given information. Subtracting 550 from the average distance to Jupiter gives the average distance to Mars, which is 228 million km.

We know that the average distance from the sun to Jupiter is 778 million km, which is 550 million km more than the distance from the sun to Mars. We could express it in the form of an equation and solve to find the average distance that Mars is from the sun. Let's denote that Mars is 'x' million km from the sun. Then we can write it as:

x + 550 = 778

To find x, we need to subtract 550 from both sides of the equation, which gives us:

x = 778 - 550

And so, the distance from the sun to Mars is x = 228 million km.

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Final answer:

This story problem involves calculating the sales and remaining stock of 40 apples and 17 pears at Ms. Adams' farmer's market stand, applying basic arithmetic operations in a real-life scenario.

Explanation:

Imagine a local farmer's market where Ms. Adams has a stand selling fruits. This particular Saturday, she starts with 40 apples and 17 pears. Throughout the day, customers buy apples and pears at different rates. By midday, half of the apples were sold. An hour later, five customers each bought 2 pears. By the end of the day, Ms. Adams noticed she sold twice as many apples as pears.

Your task is to use this story to calculate:

This problem helps students practice basic subtraction, division, and multiplication within a real-world context, applying arithmetic operations to solve a practical problem.

Answer:

16 to 20 spells

Step-by-step explanation:

4 to 5 spells and you find how much you need to multiply it by and in this case it is 4. Take the 4 and multiply it to 5 and 4 and you will get your answer.

Answer:

25

Step-by-step explanation:

Luna casts 4/5 of the amount of spells that Ginny casts (busy witches), so you take 1/4 of 20 and add it to 20. In other words, add 20 + 5

Since the scuba diver jumps into the water and decreases his altitude by 5.6 meters in one minute, the equation that can be used to represent the divers altitude is [tex]y = -5x + 1.3[/tex]

The standard equation is [tex]y = mx + b[/tex]

y,x = variables

m = rate of change

b = initial value of y.

y = the height of the scuba driver after x minutes.

Given that b = 1.3

m = -5.6(decrease in altitude)

Then the equation can be written as ; [tex]y = -5x + 1.3[/tex]

hence scuba driver height is given by the equation [tex]y = -5x + 1.3[/tex]

Learn more about altitude at;

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missing options;

A.

1.3 + 5.6

= 6.9

B.

-1.3 + 5.6

= 4.3

>

O

C. 1.3+(-5.6) = – 4.3

>

O

D. -1.3+(-5.6) = -6.9

The equation that represents the scuba diver's altitude after jumping into the water is y = 1.3 - 5.6t, where y is in meters and t is in minutes.

Let y represent the diver's altitude in meters relative to sea level after t minutes. Initially, at sea level, we have y(0) = 1.3. Due to the descent in water, the altitude decreases by 5.6 meters per minute, which means the altitude change per minute can be represented by
-5.6t. Thus, the equation that can be used to represent the diver's altitude as a function of time is:

y = 1.3 - 5.6t

where y is in meters and t is in minutes.

Answer:

2160 cm³

Step-by-step explanation:

The volume of a rectangular prism is calculated using the formula

V = lbh ( l is length, b is breadth, h is height )

here l = 18, b = 10 and h = 12, hence

V = 18 × 10 × 12 = 2160 cm³

Volume = l × b × h

= 18 × 10 × 12

= 2160cm³

Answer:

b² - 7b - 18

Step-by-step explanation:

To multiply the factors.

Each term in the second factor is multiplied by each term in the first factor, that is

b(b - 9) + 2(b - 9) ← distribute both parenthesis

= b² - 9b + 2b - 18 ← collect like terms

= b² - 7b - 18

22.26 x 10^7 is the correct answer

Multiply the decimal numbers:

5.3 x 4.2 = 22.26

When multiplying scientific numbers, add the exponents together: 4+3 = 7

So you now have 22.26 x 10^7

Now you need to convert 22.26 to a scientific number, by only having one number to the left of the decimal point.

You need to move the decimal 1 place to the left, which means you need to add 1 more to the exponent.

The final answer would be 2.226 x 10^8

The answer would be Loan A

even though she'll pay more per month, with the others she'll pay be paying more by the time she as payed it off due to having to pay interest over a longer period of time

Answer:

Step-by-step explanation:

The different loan plans are showed in the image attached.

Loan A: 12 months of duration with 9.50%.

Loan B: 24 months of duration with 8.75%.

Loan C: 36 months of duration with 7.75%.

Loan D: 48 months of duration with 6.60%.

Now, all loans are compouneded monthly. Let's the compound interest formula

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Loan A:

[tex]A=2500(1+\frac{0.095}{12} )^{12(1)}\\A=2,748.12[/tex]

Loan B:

[tex]A=2500(1+\frac{0.095}{24} )^{24(2)} \\A=2500(1.004)^{48}\\ A=3,028.02[/tex]

Loan C:

[tex]A=2500(1+\frac{0.095}{36} )^{36(3)} \\A=2500(1.003)^{108}\\ A=3,454.94[/tex]

Loan D:

[tex]A=2500(1+\frac{0.095}{48} )^{48(4)}\\ A=2500(1.002)^{192}\\ A=3,668.95[/tex]

Now, if you compare, you will observe that Loan A offer the cheapest result for Judy.

Therefore, Judy should use the Loan A plan.

Answer:

64

Step-by-step explanation:

20 + 20=40

12 +12 = 24

24+40=64

Answer:

Perimeter = 64ft

Step-by-step explanation:

Perimeter is the sum of the sides i.e.  length and width

Perimeter = 20+20+12+12 = 64

Answer:

See below...

Step-by-step explanation:

Theoretical probability is the probability that something should happen based on the beginning conditions.  Such as having a jar of 30 marbles with 5 being blue.  The probability of pulling out a blue marble when selecting 1 marble is

5/30, or 1/6.  Theoretically you should pull one blue marble out every 6 times you pull a marble out.  

This isn't guaranteed to happen though, that's where experimental probability comes form.

Experimental probability is the number of desired outcomes achieved, divided by the total number of outcomes.  This is based on what actually happened.  Say you selected a marble, and put it back 10 times, recording the color each time and you got 2 blue marbles.  Your experimental probability is

2/10, or 1/5, which doesn't match the theoretical probability.  The more times this experiment is conducted, the closer your result will be to the theoretical probability

Answer:

2.618 in Degrees Celsius is 36.7124 Degrees Fahrenheit. 2.618 in Degrees Fahrenheit is -16.323333 Degrees Celsius.

Answer:

64 oz. were consumed and 16 oz. were left.

Step-by-step explanation:

8*10 = 80 oz. of juice total.

10-2=8 boxes consumed

8*8(number of oz. per box)=64 oz. consumed

2*8=16 oz. left

64+16=80 checks out.

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❖ 9% of 600 = 54

9/100 * 600 = 54

~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡

~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ

9% out of 500

0.09* 500 = 45

45

hope i could helpp!!!!

Answer:

Step-by-step explanation:

[tex]14m-13m=17\\\\(14-13)m=17\\\\1m=17\to\boxed{m=17}[/tex]

[tex]\bold{Hey\ there!}\\ \bold{Simplify\ both\sides\ of\ your \ equation} \\ \bold{Like\downarrow} \\ \bold{14m-13m=17} \\ \bullet{\bold{14m+(-13m)=17}} \\ \\ \\ \bold{Combine\ your\ terms}\\ \bold{Like\downarrow}\\ \bold{14m \ \& -13m} \\ \\ \bold{14m+(-13m)=1} \\ \bold{1=17} \\ \\ \bold{1\times17=17}[/tex]

[tex]\boxed{\boxed{\bold{Answer:m=17}}}\checkmark \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]

-7 and 5. The product would be -35 and the sum -2.

Hope this helps

[tex] {x}^{3} + 7 {x}^{2} + 10x \\ = x( {x}^{2} + 7x + 10) \\ = x( {x}^{2} + 5x + 2x + 10) \\ = x(x + 5)(x + 2)[/tex]

your answer is x(x+2)(x+5)

x3+7x2+10x

x3+7x2+10x

=x(x+2)(x+5)

Answer:

2W=9

Step-by-step explanation:

You must first get the Length, which is 15, and multiply it by 2 and you get 30. You then subtract 30 from 48 and get 18. Since the equation has 2W, you have to divide 18 by 2, which gets you the answer 9.

Answer:

width = 9 feet

Step-by-step explanation:

Here we are given that total length of the wood for the garden is 48 feet only.

The length in represented in the equation given below. In geometry we call it Perimeter.

2l+2w=48

Where l is the length of the garden and the w is width of the garden.

Here also given that , if Manny wants the length to be 15 feet, what will be width of the garden.

In order to find this we put the value of l as 15  in 2l+2w=48 and solve for w

Let us see how

2l+2w=48

2(15)+2w=48

30+2w=48

subtracting 30 from both sides

30+2w-30=48-30

2w=18

Dividing both sides by 2 we get

w=9

Hence the width will be 9 feet

Answer:

it is the subtraction property of equality

Answer:

-3

Step-by-step explanation:

The given expression is:

[tex]\frac{\frac{a-3}{7} }{\frac{3-a}{21} }[/tex]

We can rewrite this as:

[tex]\frac{a-3}{7}\div \frac{3-a}{21}[/tex]

[tex]\frac{a-3}{7}\times \frac{21}{3-a}[/tex]

Factor -1 out of the first numerator:

[tex]\frac{-(3-a)}{7}\times \frac{21}{3-a}[/tex]

Cancel out the common factors;

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

Answer:

-3

Step-by-step explanation:

that's just the way it be.