(X+3)/6=5/4 what is x

Answer:

Hey mate , here is your answer. Hope it helps you

Step-by-step explanation:

Given Zareen has 24min to work on her math homework, and each problem is taking her 2/3 of a minute

As give one problem takes

24*(2/3) minutes = 16

Hence

2/3 divided by 24

Answer:

a. P(x≤9)=0.9999

b. P(x=6)=0.0430

c. P(x≥6)=0.0611

Step-by-step explanation:

The question is incomplete:

a.At most 9 will come to a complete stop?

b.Exactly 6 will come to a complete stop?

c.At least 6 will come to a complete stop?

d.How many of the next 20 drivers do you expect to come to a complete stop?

The amount of drivers from the sample that will come to a complete stop can be modeled by a binomial random variable with n=15 and p=0.2.

The probability that exactly k drivers from the sample come to a complete stop is:

[tex]P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}[/tex]

a. We have to calculate the probability that at most 9 come to a complete stop:

[tex]P(x\leq9)=\sum_{k=0}^9P(x=k)\\\\\\P(x=0) = \dbinom{15}{0} p^{0}q^{15}=1*1*0.0352=0.0352\\\\\\P(x=1) = \dbinom{15}{1} p^{1}q^{14}=15*0.2*0.044=0.1319\\\\\\P(x=2) = \dbinom{15}{2} p^{2}q^{13}=105*0.04*0.055=0.2309\\\\\\P(x=3) = \dbinom{15}{3} p^{3}q^{12}=455*0.008*0.0687=0.2501\\\\\\P(x=4) = \dbinom{15}{4} p^{4}q^{11}=1365*0.0016*0.0859=0.1876\\\\\\P(x=5) = \dbinom{15}{5} p^{5}q^{10}=3003*0.0003*0.1074=0.1032\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\[/tex]

[tex]P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x\leq9)=0.0352+0.1319+0.2309+0.2501+0.1876+0.1032+0.043+0.0138+0.0035+0.0007\\\\P(x\leq9)=0.9999[/tex]

b. We have to calculate the probability that exactly 6 will come to a complete stop:

[tex]P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\[/tex]

c. We have to calculate the probability that at least 6 will come to a complete stop:

[tex]P(x\geq6)=\sum_{k=6}^{15}P(x=k)\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x=10) = \dbinom{15}{10} p^{10}q^{5}=3003*0*0.3277=0.0001\\\\\\P(x=11) = \dbinom{15}{11} p^{11}q^{4}=1365*0*0.4096=0\\\\\\P(x=12) = \dbinom{15}{12} p^{12}q^{3}=455*0*0.512=0\\\\\\[/tex]

[tex]P(x=13) = \dbinom{15}{13} p^{13}q^{2}=105*0*0.64=0\\\\\\P(x=14) = \dbinom{15}{14} p^{14}q^{1}=15*0*0.8=0\\\\\\P(x=15) = \dbinom{15}{15} p^{15}q^{0}=1*0*1=0\\\\\\P(x\geq6)=0.043+0.0138+0.0035+0.0007+0.0001+0+0+0+0\\\\P(x\geq6)=0.0611[/tex]

Answer:

Option 2

Step-by-step explanation:

The question states "the width of the rectangle is 4 less than half the length."  Since we are looking for the value of w, w will be equal to the expression we create.  We start with half the length and than subtract 4 from it.  This is because it says 4 less than half the length, not half of 4-length or another variation.  In many of these problems the best way to solve them is by working backwards.

Answer:

Option 2

Step-by-step explanation:

Translating these words into math, we get w = 1/2l - 4 which is Option 2.

Answer:

The  90% confidence interval for the difference between proportions is (0.115, 0.228).

As the value 0 is not included in the interval, we can conclude that there is significant difference in the proportion of youger adults that use the horn and older adults that use the horn.

Step-by-step explanation:

We want to calculate the bounds of a 90% confidence interval.

For a 90% CI, the critical value for z is z=1.645.

The sample 1 (younger adults) , of size n1=501 has a proportion of p1=0.521.

[tex]p_1=X_1/n_1=261/501=0.5210[/tex]

The sample 2 (older  adults), of size n2=352 has a proportion of p2=0.3494.

[tex]p_2=X_2/n_2=123/352=0.3494[/tex]

The difference between proportions is (p1-p2)=0.1715.

[tex]p_d=p_1-p_2=0.5210-0.3494=0.1715[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{261+123}{501+352}=\dfrac{384}{853}=0.4502[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4502*0.5498}{501}+\dfrac{0.4502*0.5498}{352}}\\\\\\s_{p1-p2}=\sqrt{0.0005+0.0007}=\sqrt{0.0012}=0.0346[/tex]

Then, the margin of error is:

[tex]MOE=z \cdot s_{p1-p2}=1.645\cdot 0.0346=0.0569[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.1715-0.0569=0.115\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.1715+0.0569=0.228[/tex]

The  90% confidence interval for the difference between proportions is (0.115, 0.228).

Answer:

2

Step-by-step explanation:

the vertical axis would be h, the plant's height, and the horizontal axis would be m, the number of months. This would make statement 2 the only valid statement.

statement 1: Incorrect, as the vertical axis is the height

statement 2: correct, as h depends on m

statement 3: incorrect, as the domain is the horizontal and represents the number of months

statement 4: incorrect, as h = f(m)

Answer:-2

Step-by-step explanation:

Ok so I’m assuming the x stands for the multiplication sign

7/2-4.5*3+8

Use pemdas

Multiplication first

7/2-4.5*3+8

-4.5*3

7/2-13.5+8

Then addition

-13.5+8

Lastly subtraction

7/2-5

-2

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:

(0,2)

Step-by-step explanation:

2:4 means one part is 2/(2+4)=1/3 of AB and the other part is 2/3 of AB

Add 1/3 of the distance from -2 to 4. (1/3)(4+2)=2. -2+2=0 The x coordinate is 0

Subtract 1/3 of the distance from 6 to -6, (1/3)6+6)=4 6-4=2 The y coordinate is 2

The point is (0,2)

Answer: the answer is linear pair

Step-by-step explanation:

Answer:

Linear pair postulate

Step-by-step explanation:

Answer:

a) 6

b) 10

Step-by-step explanation:

a) The area of a rhombus is half the product of the diagonals, meaning that the area of the shaded part is 4*3/2=6 square meters.

b) To find the area of the white background, you need to find the area of the full rectangle, and then to find the area of both rhombii. The area of the black rhombus is 2*4/2=4 square meters. The area of the full rectangle is 4*5=20 units. Subtracting the areas of the two rhombii, you get an area for the white background of 20-6-4=10 square meters. Hope this helps!

Answer:

-The total area of a Rectangular Prism:

[tex]A = 366[/tex] [tex]in^{2}[/tex]

Step-by-step explanation:

-To find the total area of a rectangular prism, you need this formula:

[tex]A = 2(l \cdot w + l \cdot h + w \cdot h)[/tex]

[tex]l =[/tex] Length

[tex]w =[/tex] Width

[tex]h =[/tex] Height

-Apply the length, width and height for the formula:

[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]

[tex]l =[/tex] 11 in

[tex]w =[/tex] 8 in

[tex]h =[/tex] 5 in

-Then, solve for the area:

[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]

[tex]A = 2(88 + 55 + 40)[/tex]

[tex]A = 2(143 + 40)[/tex]

[tex]A = 2 \times 183[/tex]

[tex]A = 366[/tex]

So, the total area would be [tex]366[/tex] [tex]in ^{2}[/tex].

Step-by-step explanation:

work is shown and pictured

Answer:

“It is a binomial with a degree of 3”

Step-by-step explanation:

Since it has just two different coefficients, it would be considered “binomial” for that reason. As you can notice, the highest degree is 3. So match those up and the correct answer would be the second choice “It is a binomial with a degree of 3”

Answer:

B

Step-by-step explanation:

Answer:

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Step-by-step explanation:

We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.8}{2} = 0.1[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.5 = 0.9[/tex], so [tex]z = 1.282[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.282*\frac{6}{\sqrt{21}} = 1.68[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.

The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Answer:

[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]

And we can find the probability with this difference and using the normal standard table:

[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]

Step-by-step explanation:

Let X the random variable that represent the wages, and for this case we know the distribution for X is given by:

[tex]X \sim N(17.15,2.25)[/tex]  

Where [tex]\mu=17.15[/tex] and [tex]\sigma=2.25[/tex]

We want to find this probability:

[tex]P(15<X<20)[/tex]

And we can use the z score formula given by:

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

Using this formula we have:

[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]

And we can find the probability with this difference and using the normal standard table:

[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]

Answer:

A. Only the mode makes sense since the data is nominal.

Step-by-step explanation:

Hello!

The objective of the study was to determine if deficiency of carbon dioxide in the soil affects the phenotype of peas.

The variable of study is X: Phenotype of a pea grown in soil with carbon dioxide deficiency.

Possible values of Phenotype codes:

1= smooth-yellow

2= smooth-green

3= wrinkled-yellow

4= wrinkled-green

The absolute frequencies for each phenotype are:

f(1)= 3

f(2)= 4

f(3)= 6

f(4)= 1

n= 14

a) Mean:

X[bar]= (∑xifi)/n= [(1*3)+(2*4)+(3*6)+(4*1)]/14= 33/14= 2.357= 2.36

The average value is always within range of definition of the variable but it does not necessarily correspond to an observation.

b) Median:

To determine the value that corresponds to the median you have to calculate its position:

For even samples the position is:

PosMe= n/2= 14/2= 7

Then you have to arrange the data from least to greatest, in this case, starting from the first category, you have to determine where the seventh observation is within the observed absolute frequencies. The phenotype that corresponds to the 7th observation is 2= smooth-green.

Me= 2= smooth-green.

c) Mode:

The mode corresponds to the most observed category/ value of the variable, i.e. the category with the most observations is 3= wrinkled-yellow

Md= 3= wrinkled-yellow

d) Midrange: (1 + 4)/2= 2.5

e)

As you can see the variable is qualitative and categorical. Even if all central tendency measurements can be calculated, truth is that the only one that shows any valuable information regarding the data set is the mode.

I hope this helps!

Answer:

1. Experimental

2. Correlational

3. Experimental.

Step-by-step explanation:

1. Experimental.

Researches are interested on finding the effects of music on a test.

2. Correlational

Researchers are interested on finding the correlation of the gender and cognition from different samples

3. Experimental

The Researcher wants to know the effects of bedroom light.

Answer:

around 68 minutes 31 seconds.

Step-by-step explanation:

10km = miles = 6.21x11 = 68.31

Answer:

16

Step-by-step explanation:

We can find x using tan 40° which can be represented as x/20. tan 40° is also equal to about 0.8 so that means x / 20 = 0.8 and x = 16.

Answer:

Option D.

Step-by-step explanation:

If a line passing through two points, then the equation of line is

[tex](y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

It is given that  Line f(x) passes through points (-4, 0) and (-3, 1).  So, equation of line f(x) is

[tex](y-0)=\dfrac{1-0}{-3-(-4)}(x-(-4))[/tex]

[tex]y=1(x+4)[/tex]

So, function f(x) is

[tex]f(x)=(x+4)[/tex]    ...(1)

Line g(x) passes through points (-4, 0) and (-3, -3).  So, equation of line f(x) is

[tex](y-0)=\dfrac{-3-0}{-3-(-4)}(x-(-4))[/tex]

[tex]y=-3(x+4)[/tex]

So, function g(x) is

[tex]g(x)=-3(x+4)[/tex]    ...(2)

Using (1) and (2), we get

[tex]g(x)=-3f(x)[/tex]    ...(3)

It is given that

[tex]g(x)=kf(x)[/tex]     ...(4)

On comparing (3) and (4), we get

[tex]k=-3[/tex]

Therefore, the correct option is D.

[tex]answer \\ 9 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

9

Step-by-step explanation:

The ratio of 5 to 5+3 is equivalent to the ratio of 15 to 15+x. This is because when you have a triangle inside of a triangle and both of them share two of the same sides and the third sides are parallel to each other, the side ratios of the triangles are always proportionate.

[tex]\frac{5}{5+3} =\frac{15}{15+x}[/tex]   Starting equation

[tex]\frac{5}{8} =\frac{15}{15+x}[/tex]   Simplify

[tex]5(15+x)=8*(15)[/tex]   Cross multiply

[tex]75+5x=120[/tex]   Distributive Property on left and simplify on right

[tex]5x=45[/tex]   Isolate the variable

[tex]x=9[/tex]   Divide both sides by 5 (Division Property of Equality)

Answer:

The first option is correct.

Parameter because the value is a numerical measurement describing a characteristic of population.

Class width = 12.375

B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit

Step-by-step explanation:

The first option is correct.

Parameter because the value is a numerical measurement describing a characteristic of population.

Parameter is a measure that describes the entire population.

Statistic basically describes a sample of the population.

From the given information , the entire 1700 professors at a college is the population and only  35 % own a television is a characteristic, called parameter, of population.

Another objective we are to find here is:

Use the given minimum and maximum data entries, and the number of classes, to find the class width, .

Class width = Maximum - Minimum /No of classes

Given that :

Maximum = 120

Minimum = 21

number of classes = 8

Then;

Class width = 120 - 21 /8

Class width = 12.375

From the given information :

B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit

Answer:

a. [tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c.  the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e.  86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let  X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability  density function can now be determined as :

[tex]f_X(x) = \dfrac{1}{B-A}A<x<B[/tex]

where A and B  are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

[tex]f_X(x) = \dfrac{1}{12-8.5}8.5<x<12[/tex]

[tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The  probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

[tex]F(x) = \dfrac{x-A}{B-A}[/tex]

[tex]F(10) = \dfrac{10-8.5}{12-8.5}[/tex]

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

[tex]P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx[/tex]

[tex]P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}[/tex]

[tex]P(X\geq11) = {\dfrac{1}{3.5}} (12-11)[/tex]

[tex]P(X\geq11) = {\dfrac{1}{3.5}} (1)[/tex]

[tex]P(X\geq11) = 0.2857[/tex]

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

[tex]P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx[/tex]

[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}[/tex]

[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)[/tex]

[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)[/tex]

[tex]P(9.5 \leq X\leq11.5) =0.2857* (2)[/tex]

[tex]P(9.5 \leq X\leq11.5) =0.5714[/tex]

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

[tex]P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx[/tex]

[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}[/tex]

[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)[/tex]

[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(3)[/tex]

[tex]P(X \geq 9) = 0.2857*}(3)[/tex]

[tex]P(X \geq 9) = 0.8571[/tex]

NOW; The Number of iPad  that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

Answer:

Step-by-step explanation:

2(f^4)^2/8(f^12)

2/8= 1/4

f^16/f^12

f^(16-12)= f^4

f^4/4 is the solution

Answer:

339 bricks.

Step-by-step explanation:

We have the weight of each brick and what the truck can support. Therefore what we must do is pass all to the same unit of measurement to calculate the quantity of bricks.

In this case we will pass everything to pounds.

We have that a 1 pound is 16 ounces, therefore 14 would be:

14 ounces * 1 pound / 16 ounces = 0.875 pounds

In addition we have that 1 ton is 2204.62 pounds, therefore 3/4 would be:

3/4 ton * 2204.62 pounds / 1 ton = 1653.467 pounds

Therefore, in total the brick weighs 4,875 pounds (4 + 0.875) and the truck can support 1653,467 pounds, the number of bricks would be:

1653.467 / 4.875 = 339.17

In other words, it can support about 339 bricks.

Answer:

First we need to calculate 1 part.

Calculate big part first

13*15 = 195

7*12 = 84

195+84=279

279

279 is answer

Answer: 279 yd^2

Step-by-step explanation:

Separate this into two separate rectangles: the larger top rectangle (13 yd x 15 yd) and the smaller bottom rectangle (12 yd x 7 yd).

area of rectangle 1 + area of rectangle 2 = total area of figure

b1(h1) + b2(h2) = total area

13(15) + 7(12) = total area

195 + 84 = total area

279 yd^2 = total area

Answer:

The selection probability to be assigned to each of the package designs is 0.20

Step-by-step explanation:

Firstly, we need to assume that one design is just as likely to be selected by a consumer as any other design

so the probability of selecting any of the design is same and that is 1/5 = 0.20

Thus, what we are trying to say is that each of the package designs have an equal selection probability of 0.20

Answer:

207.24cm

Step-by-step explanation:

Circumference=2pi*r

=2 (3.14)(33)

=207.24cm

The circumference of the circle is 103.62 cm².

Given that, a circle with diameter of 33 cm.

Radius=d/2=16.5 cm.

The formula to find the circumference of the circle is 2πr.

Now, 2×3.14×16.5=103.62 cm².

Therefore, the circumference of the circle is 103.62 cm².

To learn more about the circumference of the circle visit:

https://brainly.com/question/27177006.

#SPJ2

Answer:

radius=7

diameter =2×radius

d=2×7

diameter=14

Answer:

Hello!

The answer is-

Radius: 7

Diameter: 14

Step-by-step explanation:

Diameter:

2*(radius)

d=2(7)

Diameter is 14

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