Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks at the bottom.

Hugo is a plumber, and his coworker Oliver is an electrician. Hugo charges customers a fee of $54 just to come to their houses and then $3 per minute that he is there. Oliver also charges a fee of $104 for a home visit, plus an additional $2 per minute. Last week the coworkers went to a job site together, spent the same amount of time working, and earned the same amount. How much did each one earn? How much time did each one spend working?

Hugo and Oliver each earned $__ by working for __ minutes.

To evaluate the surface integral of (x + y + 2) dS, where S is the parallelogram with parametric equations

xu + v, y = u - v, z = 1 + 2u + v, 0 ≤ u ≤ 9, 0 ≤ v ≤ 6

, we need to set up the integral using the given parametric equations and compute the necessary components.

The surface integral is given by the formula:

∬(x + y + 2) dS = ∬(x + y + 2) ||r_u × r_v|| dudv,

where r_u and r_v are the partial derivatives of the position vector r(u, v) with respect to u and v, respectively, and ||r_u × r_v|| is the magnitude of their cross product.

First, we compute the partial derivatives of the position vector:

r_u = ⟨1, 1, 2⟩,

r_v = ⟨1, -1, 1⟩.

Next, we calculate their cross product:

r_u × r_v = ⟨3, -1, -2⟩.

Then, we find the magnitude of the cross product:

||r_u × r_v|| = √(3² + (-1)² + (-2)²) = √14.

Now, we set up the integral using the given parametric equations and the computed components:

∬(x + y + 2) dS = ∬(x + y + 2) √14 dudv.

The limits of integration are

0 ≤ u ≤ 9

and

0 ≤ v ≤ 6

, corresponding to the given range of parameters.

Finally, we evaluate the integral over the parallelogram S with the appropriate limits to find the numerical value of the surface integral.

To learn more about

Surface Integral

brainly.com/question/29851127

#SPJ11

After six​ months, the​ subjects' symptoms are studied and compared. Answer parts​ are given below.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

A pharmaceutical company wants to test the effectiveness of a new allergy drug.

The company identifies 250 females​ 30–35 years old who suffer from severe allergies.

The subjects are randomly assigned into two groups.

One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.

After six​ months, the​ subjects' symptoms are studied and compared.

Here, 30-35 year-old girls are used to test the new allergy medication's effects.

(a)

Females between the ages of 30 and 35 who are the test subjects are the experimental units.

The new allergy medication, whose results are being studied, is the remedy.

It's best to choose C.

(b)

A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.

In this case, choice B is preferable.

(c)

If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.

In this case, choice A is preferable.

Therefore, all the correct choices are given above.

To learn more about the hypothesis;

brainly.com/question/29519577

#SPJ1

The complete question is given in the image.

The amount of gallons of water the Jug can hold is  8.66 gallons.

The water jug is in the shape of a prism the area of the base is 100 square inches and the height is 20 inches.

Therefore, the number of gallons of water the jug can hold can be calculated as follows:

volume of the prism = Bh

where

Therefore,

volume of the prism = 100 × 20

volume of the prism = 2000 inches³

Therefore,

231 inches³ = 1 gallon

2000 inches³  = ?

cross multiply

amount of water the jug can hold = 2000 / 231

amount of water the jug can hold = 8.66 gallons

learn more on prism here: https://brainly.com/question/12791528

#SPJ1

The square root of 225 is 15.

We are ask to simplify the square root of 225.

The square root of a number is the value of power 1/2 of that number.

In other words, a square root of a number is a value that, when multiplied by itself, gives the number.

For example, 3 × 3 = 9, Hence square root of 9 is 3.

Square root is represented with the symbol √.

Therefore, the square root of 225 can be found as follows:

√225 = 15

This is because 15 × 15 = 225

Hence, square root of 225 is 15.

learn more on simplify square roots here:https://brainly.com/question/205331

#SPJ1

Volume is the amount of space in an object. The fraction occupied by the cube is: \(\frac{r\sqrt2}{\pi(r + 2)}\)

First, we calculate the volume of the cube.

\(Volume = Length^3\)

From the figure, we have:

\(Length = r\sqrt 2\)

So:

\(V_1 = (r\sqrt2)^3\)

\(V_1 = (2\sqrt2)r^3\)

Next, the volume of the cylinder

\(Volume=\pi r^2h\)

So, we have:

\(V_2 = \pi r^2 (2r + 4)\)

The fraction (n) occupied by the cube is:

\(n = \frac{V_1}{V_2}\)

So, we have:

\(n = \frac{(2\sqrt2)r^3}{\pi r^2(2r + 4)}\)

Factor out 2 in the denominator

\(n = \frac{(2\sqrt2)r^3}{2\pi r^2(r + 2)}\)

Cancel out common terms

\(n = \frac{r\sqrt2}{\pi(r + 2)}\)

Hence, the fraction occupied by the cube is: \(\frac{r\sqrt2}{\pi(r + 2)}\)

Read more about volumes at:

https://brainly.com/question/15861918

James runs 400m in a day

In a week = 7 days

400m × 7 days = 2800m

To convert 2800m to km

1km = 1000m

So, 2800m/1000m

= 2.8 km

How far are the Town Center and the Park

3.5 km and 650m

650m to km

1km = 1000m

To km  = 0.65km

The distance = 3.5km - 0.65km

= 2.85km

So, they are 2.85km apart

A bottle  = 1.75 liters of lemonade

A can = 330 ml of lemonade

1.75 liters to milliliters

1 liter = 1000 milliliter

= 1.75 × 1000 ml

= 1750 ml

2 bottles of lemonade

1750ml × 2

= 3500 ml

6 cans of lemonade

330ml × 6

= 1980 ml

In total, 3500ml + 1980ml

= 5480 ml

Read more about Word Problem

https://brainly.in/question/12426468

#SPJ1

According to the regression equation, if Camilla scores 100 points higher on her Verbal SAT than her friend, the model predicts her Math SAT score to be 67 points higher than her friend's.

In the given regression equation, the coefficient of the Verbal variable is 0.67, indicating that for every 1-point increase in Verbal SAT score, the predicted Math SAT score increases by 0.67 points.

If Camilla scores 100 points higher on her Verbal SAT than her friend, we can use this information to calculate the predicted difference in their Math SAT scores.

The predicted Math SAT score for Camilla is given by:

(predicted MATH for Camilla) = 210 + 0.67*(Camilla's Verbal)

Similarly, the predicted Math SAT score for her friend is:

(predicted MATH for friend) = 210 + 0.67*(Friend's Verbal)

Subtracting the two equations, we can determine the predicted difference:

(predicted MATH for Camilla) - (predicted MATH for friend) = 0.67*(Camilla's Verbal - Friend's Verbal)

Given that Camilla scores 100 points higher on her Verbal SAT, we substitute the values:

(predicted MATH for Camilla) - (predicted MATH for friend) = 0.67*(100)

Calculating the result, we find that the model predicts Camilla's Math SAT score to be 67 points higher than her friend's.

Learn more about regression equation here:

https://brainly.com/question/32810839

#SPJ11

Answer:

percent of students who have pet = 4/5 × 100%

= 4×20%

So, percent of students who have pet is 80%.

Answer:

70%

Step-by-step explanation:

I'm pretty sure its 70 because write it as a fraction 28/40 when divide them both and you get 0.7 which is 70. I hope that works

The temperature range that a piece of equipment for an oil rig is designed to operate in, when it is capable of functioning in temperatures as low as -30° Celsius and as high as 150° Celsius, is 180° Celsius.

The temperature range that a piece of equipment for an oil rig is designed to operate in can be determined by subtracting the low-temperature limit from the high-temperature limit. The temperature range is therefore equal to the difference between the high temperature and the low temperature:

T range = High temperature - Low temperature

T range = 150°C - (-30°C)T range

= 180°C

Therefore, the temperature range that this piece of equipment is designed to operate in is 180°C.

To know more about temperature visit:

brainly.com/question/11464844

#SPJ11

According to the question and after using the Pythagorean theorem the length of one side of the roof is 7.416 metres.

The Pythagorean Theorem is a mathematical formula used to determine the length of the sides of a right triangle. It is named after the Greek mathematician Pythagoras, who is credited with discovering the formula in the 6th century BC. The theorem states that the sum of the squares of the two shorter sides of the triangle is equal to the square of the hypotenuse (the longest side of the triangle). In equation form, it is expressed as a² + b² = c², where a and b are the lengths of the two shorter sides of the triangle and c is the length of the hypotenuse.

We know that the hypotenuse is 8 metres (the width of the shed) and the two shorter sides are 3 metres (the height of the walls) and y (the length of the side of the roof).
Therefore, using the Pythagorean theorem, we have:
3² + y² = 8²
9 + y² = 64
y² = 55
y = √55
y = 7.416 metres
Therefore, the length of one side of the roof is 7.416 metres.

To learn more about Pythagorean theorem
https://brainly.com/question/231802
#SPJ1

Answer:

92.6 (A-)

Step-by-step explanation:

i used a grade calculator

Answer:

At least be nice about it bruh.

The correct answer to the question is option c) An effect modifier.

A case-control study is a type of observational study that compares two groups of individuals: those who have the disease or outcome under investigation (cases) and those who do not (controls).

It aims to determine if an exposure or risk factor is associated with the development of the disease or outcome.

In this case, the results of the study indicate that there is a difference in the odds ratio (OR) between the two strata, which suggests that the characteristic being studied is an effect modifier.

An effect modifier is a factor that modifies the effect of the exposure on the outcome and leads to different measures of association across different levels of the factor.

Therefore, the characteristic is an effect modifier as it leads to different ORs in the two strata.

Know more about case-control study here,

https://brainly.com/question/30760832

#SPJ11

Answer:

32.7 degress

Step-by-step explanation:

In this question we are to find the value of the angle

The best way to do with the information given is the cosine rule

Mathematically that would be;

y^2 = x^2 + z^2 -2xzCosY

where x = 90 ft , y = 55ft and z = 50 ft

Plugging the values we have;

55^2 = 90^2 + 50^2-2(90)(50)CosY

-7575 = -9000cosY

cosY = 7575/9000

cosY = 0.841666666667

Y = cos^-1 0.841666666667

Y = 32.68 degrees which is 32.7 to the nearest tenth

Answer:

32.7

Step-by-step explanation:

A triangle shape is formed by the cross-section of a triangular pyramid sliced by a plane that is perpendicular to its base

A triangular pyramid is a geometric solid having a triangle for a base and three triangles with the same vertex on each side.  That is, the triangular pyramid is made up of four triangles. Pyramids made of triangles might be straight or inclined. It resembles a pyramid with four triangular faces that meet at one vertex and a triangular base.

Let's first draw the triangular pyramid. Now, mark the base. Then, denote the plane passing perpendicular to the base. From the diagram we can tell, the plane cuts this pyramid to form a triangle cross-section.

To know more about triangular pyramids:

https://brainly.com/question/22213308

#SPJ4

To proceed with this analysis, we assume that the individuals in the sample were randomly selected and that the samples are independent.

Additionally, the sample sizes are large enough to apply the normal approximation to the sampling distribution of the difference in proportions.Using these assumptions, we can calculate the confidence in is 37/77 ≈ 0.481. The proportion of men who follow a regular exercise program is 44/85 ≈ 0.518. The difference between these proportions is 0.518 - 0.481 ≈ 0.037.

The 95% confidence interval for the difference in proportions can be calculated using the formula: difference ± (critical value) * sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)] where p1 and p2 are the proportions of women and men, n1 and n2 are the respective sample sizes, and the critical value corresponds to a 95% confidence level. Performing the calculations, the 95% confidence interval for the difference in proportions is approximately 0.037 ± 0.129, which gives us a range from -0.092 to 0.166.

Interpreting this interval, we can say that with 95% confidence, the true difference between the proportions of women and men who follow a regular exercise program lies within the range of -0.092 to 0.166. This means that there is insufficient evidence to conclude that there is a significant difference in the proportions of women and men who follow a regular exercise program. The interval includes zero, indicating that the difference could be negligible or non-existent.

To learn more about interval click here:

brainly.com/question/17212516

#SPJ11

Answer:

Step-by-step explanation:

Semicircle:

diameter = 6 yd

r = 6/2 = 3 yd

\(Area \ of \ semicircle = \dfrac{1}{2}\pi r^{2}\\\\\)

                                \(=\dfrac{1}{2}*3.14*3*3\\\\= 14.13 \ yd^{2}\)

Triangle:

base = b =6 yd

height = h = 4 yd

\(Area \ of \ triangle = \dfrac{1}{2}bh\\\\\)

                            \(=\dfrac{1}{2}*6*4\\\\\\= 3*4\\\\= 12 \ yd^{2}\)

Area of composite figure =area of semicircle + area of triangle

                                         = 14.13 +12

                                         = 26.13 yd²

        Hence, The Value of:  a^2   +   b^2   is  18

        b  =  1/a  =  1/ 2 + √5

        b  =  1/2 + √5  *   2 - √5/2 - √5

            =     2  - √5/1

        b  =  2  -  √5

       a^2    =  (2  +  √5)^2    =  4  +  4√5  +  5

       b^2    =  (2   -  √5)^2    =  4   -  4√5  +   5

        a^2   +  b^2   =   4  +  4√5  +  5  +  4  -  4√5  +  5

                              =   18  -  3√5

        4    +  5     +  4  +  5

        9    +   4     +   5

       13   +   5   =   18

        a^2  +  b^2       =   18                

        a^2  =  18   -  b^2

        a  =  ± √18  -  b^2

        a  =  √18     -  b^2

        a   =  -√18   -  b^2

        Hence, The Value of:  a^2   +   b^2   is  18

I hope this helps you!

Answer:

84 grams and 5 ounces

Step-by-step explanation:

because one ounce equals 28 grams, that means 3 ounces = 3 * 28 = 84

because 28 grams equals 1 ounce, 140 grams = 140 / 28 = 5 ounces

The radical is 2√21.

The √ symbol that is used to denote square root or nth roots.

Given :

√84

= √2*2*21

=2√21

Hence, the radical is 2√21.

Learn more about radical here:

https://brainly.com/question/14923091

#SPJ1

Answer:

Step-by-step explanation:

Here in this given sequence, -16; -9; -2: _

a=-16

d=-9-(-16)=7

so,The 4th term=

Answer:

given sequence, -16; -9; -2: _

first term(a)=-16

common difference(d)=-9-(-16)=7

next term is 4

so

4th term=a+(n-1)d

=-16+(4-1)7=-16+21=5

c.5

9514 1404 393

Answer:

  x = 60

  y = 30

Step-by-step explanation:

Adjacent angles in a parallelogram total 180°. This relation can be used to form equations to find x and y.

Right Side Angles

  x° +(5x -180)° = 180°

  6x = 360 . . . . . . . . . . . divide by °, add 180

  x = 60 . . . . . . . . divide by 6

__

Left Side Angles

  4y° +2y° = 180°

  6y = 180 . . . . . . . . . divide by °

  y = 30 . . . . . . . divide by 6

Answer:5.97

Step-by-step explanation.  

you have to look at the question.

you have to look around the question

The very last step is you have to answer it  

Answer:

5% of 600 is 30, then you multiply the 30 by the 4 years which gives you 120. then you add the original 600 with the 5 person from the four years which is 120 that comes to 720. so 720 is how much is in salma's account after 4 years.

Comparing the values by subtraction, the chocolates are lighter than the weight stated on the label by 0.0042 pounds.

When comparing two values whether which is greater, compare the digits from left to right.

Comparing 0.384 to 0.3798, where the first digits are both 0, and the digit after the decimal are also the same, compare the hundredth's place.

8 > 7

Hence, the actual weight of the chocolates is less than or lighter than the weight stated on the label.

Using subtraction, two values can also be compared by getting how much one exceeds the other.

Subtracting the two values,

0.384 - 0.3798 = 0.0042 pounds

Learn more about comparing values by subtraction here: brainly.com/question/66864

#SPJ4

Answer:

Yes, they both have a volume of 339.12 inches cubed.

Step-by-step explanation:

To calculate the volume of an oblique cylinder is very simple, we must multiply π (Pi = ~ 3.14) by the radius to the power of two and then multiply by the height. In this case the height forms a 90 degree angle from the opposite base to the position of the base, but outside of it.

Volume = π × Radius² × Height

The formula for the volume of a regular cylinder or an oblique cylinder is the same, if we imagine a stack of poker chips (forming a cylinder), even when we tilt the chips to one side (forming an oblique cylinder) the volume remains the same.

Now using this information, we must find the volumes of both cylinders.

For the oblique cylinder:
Given

Using the formula,

The volume would be 339.29 m³

Now solving for the other cylinder:

V=πr²h=π·32·12≈339.29201

Rounded, the answer would be 33.29 m³

This therefore proves that they both have the same volume.

Answer:

4x + 9x = 52

x = 4

Step-by-step explanation:

Let the unknown number be x

Given: Four times of that number ( 4x ) added to 9 times of that number ( 9x )

equals to 52

4x + 9x = 52

13x = 52

x = 4

So, the number is 4.

If this is correct, please give me brainliest.

Answer:

x + y

Step-by-step explanation:

x + y = - \(\frac{11}{8}\) + (- \(\frac{11}{4}\)) = - \(\frac{11}{8}\) - \(\frac{11}{4}\) = - \(\frac{11}{8}\) - \(\frac{22}{8}\) = - \(\frac{33}{8}\)

x - y = - \(\frac{11}{8}\) - (- \(\frac{11}{4}\) ) = - \(\frac{11}{8}\) + \(\frac{11}{4}\) = - \(\frac{11}{8}\) + \(\frac{22}{8}\) = \(\frac{11}{8}\)

then

x + y < 0 , that is x + y is negative