Suppose a publishing company estimates that its monthly cost is C(x) = 600{x^2} + 300xC(x)=600x 2 +300x and its monthly revenue is R(x) = - 0.4{x^3} + 700{x^2} - 600x + 500R(x)=−0.4x 3 +700x 2 −600x+500, where x is in thousands of books sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?​

Answer: It is a function because at any given time the oven was exactly one temperature.

Step-by-step explanation:

It is given that:

At 5:00 p.m., Antonio turned on the oven.

The oven remained at 400°F for 45 minutes until Antonio turned it off.

It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m.

Answer:

? please explain

Step-by-step explanation:

Answer:128 I think is the answer

Step-by-step explanation:

Answer:

Governor of State B: $120,340; Governor of State A: $169,320

Step-by-step explanation:

For the sake of this problem, let's set the salary of State B's governor as x. That would make the salary of State A's governor equal to x+48980. The following lists out how to solve this problem.

Governor B salary + Governor A salary = $48980

x+x+48980=289660

2x+48980=289660

2x=240680

x=120340

120340+48980=169320

Answer

a. 0.856

b. 0.78071

c. It is not unusual

d. 13.65 years old

Step-by-step explanation:

The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.

We solve this question using z score formula:

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

a. Find the probability that a cat will live to be older than 14 years.

For x > 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x<14) = 0.144

P(x>14) = 1 - P(x<14) = 0.856

b. Find the probability that a cat will live between 14 and 18 years.

For x = 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x = 14) = 0.144

For x = 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x = 18) = 0.92471

The probability that a cat will live between 14 and 18 years is calculated as:

P(x = 18) - P(x = 14)

0.92471 - 0.144

= 0.78071

c. If a cat lives to be over 18 years, would that be unusual? Why or why not?

For x > 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x<18) = 0.92471

P(x>18) = 1 - P(x<18) = 0.075288

Converting this to percentage:

0.075288 × 100 = 7.5288%

Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.

d. How old would a cat have to be to be older than 90% of other cats?

From the question above, 10% of the cats would be older than 90% of other cats.

Hence, we find the z score of the 10th percentile

= -1.282

Hence,

-1.282 = x - 15.7/1.6

Cross Multiply

-1.282 × 1.6 = x - 15.7

- 2.0512 = x - 15.7

x = 15.7 -2.0512

x = 13.6488 years old

Approximately = 13.65 years old

Answer:

x=3y-6

Step-by-step explanation:

x−3y=−6

Step 1: Add 3y to both sides.

x−3y+3y=−6+3y

x=3y−6

Answer:

x=3y−6

Answer:

49

Step-by-step explanation:

49 + 14 = 63

so that means:

x = 49

Answer:

Are directly proportional

Answer:

0.5 ; 0.475 ; 0.689 ; 0.4013

Step-by-step explanation:

Given that:

Rate of production of defective batteries p = 0.05

Number of batteries produced (n) = 10

The expected number of defective batteries = mean = n * p = 10 * 0.05 = 0.5 batteries

Variance of defective batteries :

Var(X) = n * p * q ; q = 1 - p

Hence,

Var(X) = 10 * 0.05 * 0.95 = 0.475

Standard deviation (X) = sqrt(variance) = sqrt(0.475) = 0.689

Probability that atleast 1 battery is defective :

Using the binomial probability function

P(x ≥ 1) = 1 - p(x = 0)

= 1 - q^n

= 1 - 0.95^10

= 1 - 0.59873693923837890625

= 0.40126306076162109375

= 0.4013

Answer:

Step-by-step explanation:

Probability of an event to occur (P) = [tex]\frac{\text{Favorable event}}{\text{Total outcomes}}[/tex]

1). Probability of getting the red crewmate,

   [tex]P_1=\frac{3}{6}=\frac{1}{2}[/tex]

   Probability of getting a chef hat,

   [tex]P_2[/tex] = [tex]\frac{1}{8}[/tex]

  Probability of getting the red crewmate and the chef hat = [tex]P_1\times P_2[/tex]

   = [tex]\frac{1}{2}\times \frac{1}{8}[/tex]

   = [tex]\frac{1}{16}[/tex]

2). Probability of getting blue crewmate,

     [tex]P_1=\frac{2}{6}[/tex]

          [tex]=\frac{1}{3}[/tex]

   Probability of getting an egg hat,

    [tex]P_2=\frac{2}{8}=\frac{1}{4}[/tex]

   Probability to get the blue crewmate and an egg hat = [tex]P_1\times P_2[/tex]

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

    = [tex]\frac{1}{12}[/tex]

3). Probability of getting a green crewmate = [tex]\frac{1}{6}[/tex]

    Probability of getting a banana hat = [tex]\frac{3}{8}[/tex]

    Probability of getting a green crewmate and banana hat

    = [tex]\frac{1}{6}\times \frac{3}{8}[/tex]

    = [tex]\frac{1}{16}[/tex]      

Answer:

[tex]x=38[/tex]

Step-by-step explanation:

[tex]We\ are\ given\ that,\\\angle KLO=134\\\angle OMN= 84\\Hence\ we\ observe\ that,\\\angle KLO\ and\ \angle OLM\ form\ a\ linear\ pair\ and\ hence,\ are\ supplementary.\\Hence,\\\angle KLO\ + \angle OLM=180\\Substituting\ \angle KLO=134,\\134+\angle OLM=180\\\angle OLM=180-134\\\angle OLM=46\\Similarly,[/tex]

[tex]\angle OMN\ and\ \angle OML\ form\ a\ linear\ pair\ and\ hence,\ are\ supplementary.\\Hence,\\\angle OMN\ + \angle OML=180\\Substituting\ \angle OMN=84,\\84+\angle OLM=180\\\angle OLM=180-84\\\angle OLM=96\\[/tex]

[tex]Now\ lets\ consider\ \triangle OML,\\\angle OLM + \angle OML+ \angle LOM=180 [Angle\ Sum\ Property\ Of\ a\ triangle]\\Hence\ substituting\ \angle OLM=46, \angle OML=96, \angle LOM=x\\46+96+x=180\\142+x=180\\x=180-142\\x=38[/tex]

Answer: C

Step-by-step explanation:

Answer:

Store A = 3.17

Store B = 3.25

Step-by-step explanation:

Hope this helps!

Answer:

y = 3x + 5

Step-by-step explanation:

The zero seems to be a place holder to mess you up. Just ignore that it doesn't do anything. Add -3x and -5 to the both sides to create y = 3x + 5

Answer:

a.) 36

b.) 18

c.) 27

Step-by-step explanation:

Answer:

Width  = 166.7 ft

Length = 250 ft.

Step-by-step explanation:

From the diagram at the ATTACHMENT

Let us denote the the length of the rectangular area as "x" and

the width of the rectangular area as "y"

Since, cost of the fence on the western side is shared with a neighbor, we can say  it is $7 per foot. Otherwise, it is $14 per foot. The northern length is not fenced.

From the question, we know that the  cost is not to exceed $7000, therefore we can expressed it as

7y + 14x + 14y = 7000

14x + 21y = 7000

Divide through by 14, we have

(x + 1.5) = 500  ------------- eqn (*)            

But the area of the fenced

= A = (x×y)      -------------- eqn  (**)                    

Substitute (*) into (**) we have

A = (500 - 1.5y)*y

= 500y - 1.5y²

In other to maximize the Area, we can find the differential of A

A'(y) = 500 - 3y

At A'(y) = 0.

500-3y= 0

3y=500

y= 166.67 ft

From eqn(*)

(x+ 1.5) = 500

x = 500 - 1.5y

500-1.5(166.67)

= 250ft

Therefore, the dimensions for the plot that would enclose the most area are

Width  of 166.67 ft and Length = 250 ft.

Answer:

sorry

Step-by-step explanation:

I really don't know answer

Answer:

uhhh

Step-by-step explanation:

Answer:

3.82 x 10

Step-by-step explanation:

divide 4 x 10^4 by 1.1 x 10^3

4 divided by 1.1 is 3.81818181... and you subtract exponents to get 1

Answer:

Step-by-step explanation:

Answer:  The Answer Is A Because if u just add the numbers then divide them

Answer:

Step-by-step explanation:

 U bot. Nub

Answer:

(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))

Step-by-step explanation:

Given that:

NEWER CARS:

Sample size = n1 = 45

Standard deviation s1 = 46

Mean = m1 = 195

OLDER CARS:

Sample size = n2 = 40

Standard DEVIATION s2 = 58

Mean = m2 = 286

Confidence interval at 95% ; α = 1 - 0.95 = 0.05 ; 0.05 / 2 = 0.025

Confidence interval is calculated thus : (newer--older)

(m1 - m2) ± Tcritical * standard error

Mean difference = m1 - m2; (195 - 286)

Tcritical = Tn1+n2-2, α/2 = T(45+40)-2 = T83, 0.025 = 1.99 (T value calculator)

Standard error (E) = sqrt((s1²/n1) + (s2²/n2))

E = sqrt((46^2/45) + (58^2/40))

Hence, confidence interval:

(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))

The 95% confidence interval for estimating the difference in the mean dollar cost of the routine maintenance between newer and older cars is given by:

[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]

The first sample consists of owners of newer cars

The second sample consists of owner of older cars.

95% confidence interval for difference between both samples' means.

Since the sample sizes are > 30, thus we can use the z table for finding the Confidence interval.

The CI is given as:

[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]

For 0.95 probability confidence, we have t at 40+45-3= t at 83 at 0.05/2 is 1.992 (from T tables)

Thus,

[tex]CI=(195-268) \pm 1.992 \sqrt{\dfrac{46^2}{45} + \dfrac{58^2}{40}}[/tex]

Learn more about confidence interval here:

https://brainly.com/question/4249560

Answer:

54 feet.

Step-by-step explanation:

Consider AB and DF. FD is 3 times the size of AB

So if AC = 7 then DG = 3* 7 = 21

The total Perimeter = 15 + 18 + 21 = 54 feet

Answer:

well if the triangle are both equal comparisons just ones a different size then the unknown hunches of the bigger side would probably be 21 so if u add the 15 + 18 + 21 = 54 I think sorry if I'm wrong tho

Answer:

3.6 = a

Step-by-step explanation:

5.4 = a - ( -1.8)

5.4 = a + 1.8

5.4 - 1.8 = a

3.6 = a

Answer:

Following are the solution to this question:

Step-by-step explanation:

For this set, the correlation coefficient is = -0.015.

It shows that financial variables have trust issues. Once a price rises, the other one is decreasing the value of -0,015 shows, that there are several fewer associations in the set of data among x and y and between y values. This interaction also can range between -1 to 1, to 0 being completely unrelated. But you'd never be sure, in this situation, 0.015 is very similar to 0.

It means that your prediction is nothing better than just a wild choice. Its odds of an estimated value being relatively close to the actual result are therefore much smaller as the points are it's hardly the best match.

A. $ 58.50

B. $ 80

C. No, it did not mark up 30%.

Step-by-step explanation:Since,

A. We have,

Mark up percentage = 30%

Actual price = $ 45,

B. We have,

SP = $ 104,

C.  We have,

AP = $ 75,

SP = $100,

Thus, mark up percentage =

= 33.33 %

Hence, store did not mark up the price by 30%.

Answer:

exponential expression:

8ᵇ = 2

log8(2) = 0.333333333 or 1/3

Answer:

log8(2) = 1/3

Step-by-step explanation:

I don't know if they mean this by an exponential expression but:

set x = log8(2), then

8^x = 8^(log8(2))

By logarithmic properties:

8^x = 2.

notice that 8 = 2^3.

By exponential properties:

8^x = (2^3)^x = 2^(3x)

So 2^(3x) = 2 = 2^1.

Comparing exponents gives:

3x = 1 <=> x = 1/3.

So log8(2) = 1/3.