When writing expressions for complex numbers, what does i represent?

Answer:

€ 270

Step-by-step explanation:

Since the production cost C(x,y) = 2x² + 5y² + 120 is less than or equal to 250, we have  2x² + 5y² + 120 ≤ 250

The selling price S(x,y) = 40x + 80y

The profit P(x,y) = S(x,y) - C(x,y) = 40x + 80y - 2x² - 5y² - 120

Using the principle of lagrange multipliers, we want to maximize the profit P(x,y) under the condition that C(x.y) ≤ 250.

So, dP/dx = 40 - 4x , dC/dx = 4x, dP/dy = 80 - 10y , dC/dy = 10y

dP/dx + λdC/dx = 0

40 - 4x + 4λx = 0  (1)

4λx = 4x - 40

λ = (x - 10)/x

dP/dy + λdC/dy = 0

80 - 10y + 10λy = 0 (2)

substituting λ into (2), we have

80 - 10y + 10(x - 10)y/x = 0

multiplying through by x, we have

80x - 10xy + 10xy - 100y = 0

80x - 100y = 0

80x = 100y

x = 100y/80

x = 5y/4

substituting x into C(x,y) ≤ 250, we have

2(5y/4)² + 5y² + 120 ≤ 250

25y²/8 + 5y² + 120 ≤ 250

25y² + 40y² + 960 ≤ 2000

65y² ≤ 2000 - 960

65y² ≤ 1040

y² ≤ 1040/65

y² ≤ 16

y ≤ ±√16

y ≤ ± 4 since its quantity, we take the positive value.

So x = 5y/4 = 5(± 4)/4 = ± 5

So, x ≤ ± 5

For the maximum value for the profit, P(x,y), we take the maximum values of x and y which are x = 5 and y = 4. Substituting these values into P(x,y), we have

P(5,4) = 40(5) + 80(4) - 2(5)² - 5(4)² - 120

= 200 + 320 - 50 - 80 - 120

= 520 - 250

= 270

So, the maximum profit obtained is € 270

Answer:

there is significant distinction in opinion regarding abolition of capital punishment.

Step-by-step explanation:

Compute the p cost of 2-proportion for estimating difference. The Minitab output pronounces the p valu eto be 0.000. This is less than the assumed importance degree of alpha = 0.05. Therefore, reject null hypothesis to finish that there is significant distinction in opinion regarding abolition of capital punishment.

The image of the stem-and-leaf plots is in the attachment.

Answer: (a) 31 years; (b) 59 years; (c) 56 years

Step-by-step explanation: Steam and leaf is a table that shows the digits of the data value split into a "stem", which represents the first digit, and a "leaf", which is the last digit.

For example, the first row of the table in the attachment, indicate a "stem" 2 and the first number of a "leaf" is 1, so the actress has 21 years.

(a) According to the table, the youngest actor to win an Oscar has a "stem" 3 and the first "leaf" from the right is 1, so the actor has 31 years.

(b) The oldest actress is 80 and the youngest is 21, so difference is:

80 - 21 = 59

The difference is 59 years.

(c) The oldest age shared by 2 actors is 56 years.

Answer:

c & d

Step-by-step explanation:

the description matches the information in the table

Answer: A, B, C

Step-by-step explanation:

domain = x

range = y

Answer:

y=3x-7

Step-by-step explanation:

lines are parallel hence gradient from the equation in question is the same as the gradient of the equation to be found.. comparing to y=mx+c, eq in question has grad 3... from the formula y-y1=m(x-x1) where (x1,y1) is equal to the point in question

Answer:

Make That Guy Brainliest Now ^^^^^    You can now that there are two answers!

Answer:

37.5

Step-by-step explanation:z

2.0-1.25=0.75

0.75/2.00 x 100

37.5% decrease

Answer:

✅Amanda had a greater percent increase in weight.

Step-by-step explanation:

The percent change in Ryan’s weight was 42/7 or 60%. The percent change in Amanda’s weight was 6.9/6, or 115%. Amanda had a greater percent increase in weight.

IamSugarBee

Answer:

The percent change in Ryan’s weight was 4.2/7, or 60%. The percent change in Amanda’s weight was 6.9/6 , or 115%. Amanda had a greater percent increase in weight.

Step-by-step explanation:

its the sample answer i just did it

Answer:

A. 1.5 seconds

B. 36 feet

C. 0 feet

D. After 3 seconds

Step-by-step explanation:

I graphed it on desmos.

Answer:

Step-by-step explanation:

[tex](x-5)^2+(y-(-3))^2=16[/tex]

Answer:

Step-by-step explanation:

let the height height of the tree be "h"

Hence the tree's height h=9 ft

one year later,let the height of the tree increased by x ft

hence

[tex]9 + x = 16[/tex] --------This is the equation for the growth of the tree

In order to solve for the added height(growth) of the tree we need to solve for x

[tex]9 + x = 16\\x=16-9\\x=7ft[/tex]

Step-by-step explanation:

Hope this helps

Hope this is correct

Answer:

F = 95°

Step-by-step explanation:

[tex]C=\frac{5}{9}(F-32)[/tex] is the formula to convert Fahrenheit to Celsius

If we have C = 35, we just need to plug in this number to its corresponding variable and then solve for F

Answer:

24 ounces of orange juice

Step-by-step explanation:

Given-

          Calories needed=390 calories

    Calories in 8oz juice=130 calorie

Therefore ounces of juice=(390/130)8

                                          =3 x 8

                                          =24 ounces

If Ronald needs a morning breakfast drink that will give him atleast 390 calories. Orange juice has 130 calories in 8oz. Then 24 ounces does he need to drink to reach his calorie goal.

Two or more expressions with an Equal sign is called as Equation.

Ronald needs a morning breakfast drink that will give him at least 390 calories.

Orange juice has 130 calories in 8oz.

We need to find how many ounces does he need to drink to reach his calorie goal

Calories needed=390 calories

Calories in 8oz juice=130 calorie

Three hundred ninety divided by one hundred thirty times of eight.

Therefore ounces of juice=(390/130)8

Three hundred ninety divided by one hundred thirty is three.

=3 x 8

Three times of eight is twenty four.

=24 ounces

Hence 24 ounces of orange juice does he need to drink to reach his calorie goal.

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Answer:

c

Step-by-step explanation:

Answer:

1008

Step-by-step explanation:

to find the number of combinations, just multiply everything. you will get 1008 :)

Answer:

h≤48   h≥30

Step-by-step explanation:

Hey there! I'm happy to help!

We want to find out how much Lana pays per month. Let's dissect each payment we are given so we can find our monthly expense.

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

AUTOMOBILE INSURANCE

$300 for automobile insurance semiannually

The prefix semi- means half. Annual means year. So, she is paying $300 every half year, or six months. So, we can divide 300 by 6 to find how much she pays in one month!

300/6=50

Therefore, she pays $50 a month for automobile insurance.

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

HEALTH INSURANCE

We are told here that she pays $100 every month for health insurance. We don't need do anything else here!

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

LIFE INSURANCE

We see that Lana pays $700 per year on life insurance. We can divide this by 12 to find out how much there is in 1 month!

700/12≈58.33

Therefore, she pays $58.33 every month on life insurance.

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

SOLUTION

Now, we just add all of these monthly totals up to find Lana's monthly expense.

50+100+58.33=208.33

Therefore, Lana's monthly expense is $208.33.

I hope that this helps! Have a wonderful day!

Step-by-step explanation:

1039

This is the correct answer

Answer:

a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

b) We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]  

d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Step-by-step explanation:

Information provided

[tex]\bar X=23400[/tex] represent the sample mean

[tex]s=1412[/tex] represent the sample standard deviation

[tex]n=18[/tex] sample size  

[tex]\mu_o =22100[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Part a

We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

Part b

We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

Part c

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]    

Part d

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Answer:

The correct answer is B (24 units)

Step-by-step explanation:

Answer:

Radius of the circle = 6 units

Step-by-step explanation:

Let the radius of the circle be r

According to the given condition:

Area of the circle = 3 times the circumference of the circle

[tex]\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\[/tex]

Answer:

The age difference between oldest the youngest is of 48 years.

Step-by-step explanation:

We can solve this question using a system of equations.

I am going to say that:

Kissi's age is x.

Esinam's age is y.

Lariba's age is z.

The ratio of the ages of Kissi and Esinam is 3:5

This means that [tex]\frac{x}{y} = \frac{3}{5}[/tex], so [tex]5x = 3y[/tex]

That of Esinam and Lariba is 3:5

This means that [tex]\frac{y}{z} = \frac{3}{5}[/tex], so[tex]5y = 3z[/tex]

The sum of the ages of all 3 is 147 years

This means that [tex]x + y + z = 147[/tex]

What is the age difference between oldest the youngest

z is the oldest

x is the youngest.

First i will find y.

We have that, from the equations above: [tex]x = \frac{3y}{5}[/tex] and [tex]z = \frac{5y}{3}[/tex]

So

[tex]x + y + z = 147[/tex]

[tex]\frac{3y}{5} + y + \frac{5y}{3} = 147[/tex]

The lesser common multiple between 5 and 3 is 15. So

[tex]\frac{3*3y + 15*y + 5*5y}{15} = 147[/tex]

[tex]49y = 147*15[/tex]

[tex]y = \frac{147*15}{49}[/tex]

[tex]y = 45[/tex]

Youngest:

[tex]x = \frac{3y}{5} = \frac{3*45}{5} = 27[/tex]

Oldest:

[tex]z = \frac{5y}{3} = \frac{5*45}{3} = 75[/tex]

Difference:

75 - 27 = 48

The age difference between oldest the youngest is of 48 years.

Answer:

(a) Probability distribution is prepared below.

(b) The probability that two or fewer heads are observed in three tosses is 0.875.

(c) The probability that at least one head is observed in three tosses is 0.875.

(d) The expected value of X is 1.5.

(e) The standard deviation of X is 2.121.

Step-by-step explanation:

The complete question is: A fair coin is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.

(a) Find the probability distribution of X.

(b) Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.)

(c) Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.)

(d) Find the expected value of X. (Round your answer to one decimal place.)

(e) Find the standard deviation of X. (Round your answer to three decimal places.)

Now, firstly the sample space obtained in three tosses of a fair coin is given as;

Sample Space (S) = {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}

(a) The Probability distribution of X is given below;

   Number of Heads (X)         P(X)            [tex]X \times P(X)[/tex]               [tex]X^{2} \times P(X)[/tex]

              0                               [tex]\frac{1}{8}[/tex] = 0.125            0                           0

              1                                [tex]\frac{3}{8}[/tex] = 0.375         0.375                     0.375  

              2                               [tex]\frac{3}{8}[/tex] = 0.375         0.75                          3

              3                               [tex]\frac{1}{8}[/tex] = 0.125          0.375                    3.375

           Total                                                    1.5                        6.75          

(b) The probability that two or fewer heads are observed in three tosses is given by = P(X [tex]\leq[/tex] 2)

      P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)

                     = 0.125 + 0.375 + 0.375

                     = 0.875

(c) The probability that at least one head is observed in three tosses is given by = P(X [tex]\geq[/tex] 1)

      P(X [tex]\geq[/tex] 1) =  1 - P(X = 0)

                    =  1 - 0.125

                    =  0.875

(d) The expected value of X = E(X) =  [tex]\sum (X \times P(X))[/tex]

                                                              =  1.5

(e) The Variance of X = V(X) = [tex]E(X^{2} ) - ( E(X))^{2}[/tex]

                                      =  [tex]\sum (X^{2} \times P(X))- (\sum (X \times P(X)))^{2}[/tex]

                                      =  [tex]6.75 - 1.5^{2}[/tex]  = 4.5

Now, Standard deviation of X = [tex]\sqrt{V(X)}[/tex]

                                                  = [tex]\sqrt{4.5}[/tex]  = 2.121.

Answer:

39 degrees

Step-by-step explanation:

Given

triangle is right angled i.e one angle is 90 degrees

other angle is 51 degrees.

let the third angle be x degrees

we know that sum of angles of any triangle is 180 degrees

thus,

90 + 51+ x = 180

=> 141 + x = 180

=> x = 180 - 141 = 39.

Thus, measure of other small angle is 39 degrees.

Answer:

Step-by-step explanation:

m∠A+m∠B+m∠C = 180

90+51+x1= 180

41+x=180

x=39

Answer:

The difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s

Step-by-step explanation:

⇒ x(x-5) = 50

⇒ x2 - 5x - 50 = 0  

⇒  x2 - 10x + 5x - 50 = 0  

⇒ x (x - 10) + 5 (x - 10) = 0

⇒  (x+5) (x-10) = 0

⇒   (x+5) (x-10) = 0  

⇒ x =  -5 or 10  

⇒ x = 10 (x = -5 , rejected)

Answer:

Step-by-step explanation:

Let P=Mount Peak

Let K=Mount Killimanjaro

The equation should then be

12555=P+K    ...1

P=K+765   ... 2

sub equation 2 into 1

12555=P+P+765

12555=2P+765

12555-765=2P+765-765               (subtracting 765 from both sides)

11790=2P

P=5895, now that we know P

we just make a new equation that was similiar to 1

12555=5895+K

K=6660

the height of Mount K is 6660 Metres

Answer:

Step-by-step explanation:

Corresponding net sales before 1 month and after 1 month form matched pairs.

The data for the test are the differences between the net sales before and after 1 month.

μd = the​ net sales before 1 month minus the​ net sales after 1 month.

Before after diff

57.1 63.5 - 6.4

94.6 101.8 - 7.2

49.2 57.8 - 8.6

77.4 81.2 - 3.8

43.2 41.9 1.3

Sample mean, xd

= (- 6.4 - 7.2 - 8.6 - 3.8 + 1.3)/5 = - 4.94

xd = - 4.94

Standard deviation = √(summation(x - mean)²/n

n = 5

Summation(x - mean)² = (- 6.4 + 4.94)^2 + (- 7.2 + 4.94)^2 + (- 8.6 + 4.94)^2+ (- 3.8 + 4.94)^2 + (1.3 + 4.94)^2 = 60.872

Standard deviation = √(60.872/5

sd = 3.49

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 5 - 1 = 4

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (- 4.94 - 0)/(3.49/√5)

t = - 3.17

We would determine the probability value by using the t test calculator.

p = 0.017

Since alpha, 0.05 > than the p value, 0.017, then we would reject the null hypothesis. Therefore, at 5% significance level, the data indicate that the average net sales improved.

Answer:

The answer is 508

Step-by-step explanation:

Solution

First of all, the proportion of B is exceeds 0.5 in total.

Now,

To find the total of A it we have A =314 +512 = 826

The number of employed that choose B = 356

For us to have the proportion of B to be higher than the 0.5, the unemployed B from what is shown here should exceed the difference between total A and B employed

what this suggest is that the employed B is greater than 826-356 = 470

So,

The respondent that are unemployed that choose B  must be greater than 470

Thus,

We recall that the B proportion among the unemployed respondent is lesser than .50

Thus suggests that the respondent that are unemployed who choose be is lesser than 512

The conditions becomes

470 lesser than the number of unemployed respondents who selected B lesser than 512

Hence  the needed number of the number of unemployed respondents who chose B should be between 470 and 512

So, possible answer here is 508.

Answer:

(3, -1)

Step-by-step explanation:

5-2=3

0-1=-1 (keep 0, change - to a +, flip 1 to a -1)

Answer:

y=[x+1]-3 because it's at the end of the line

Answer:

x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]

Step-by-step explanation:

(x + 6)² = 7

x + 6 = + or - [tex]\sqrt{7}[/tex]

x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]

The solution of the quadratic equation is x = -6 +√7, x = -6 - √7.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant. Finding the maximum or minimum value of the function and when it occurs is one application of completing the square.

Given that the quadratic equation is x² + 12x + 36 = 7.

(x + 6)² = 7

x + 6 = ±√7

x = -6 + √7 , x = -6 - √7

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