Yolanda, Kareem, and Jose served a total of 82 orders Monday at the school cafeteria. Kareem served 2 times as many orders as Jose. Yolanda served 6 fewer orders than Jose. How many orders did they each serve?

Check the picture below.

r       = rate of the faster cyclist

r - 7 = rate of the slower cyclist

we know they both met 5 hours later, so the time each one has been cycling has been 5 hours for each.

let's say the faster cyclist on those 5 hours covered "k" kilometers, that means the slower one cover the slack, namely "255 - k" kilometers.

[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{Km s}{distance}&\stackrel{km/h}{rate}&\stackrel{hour}{time}\\ \cline{2-4}&\\ \textit{faster cyclist}&k&r&5\\ \textit{slower cyclist}&255-k&r-7&5 \end{array}\hspace{5em} \begin{cases} k=(r)(5)\\\\ 255-k=(r-7)(5) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{k=5r}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{255-(5r) = (r-7)(5)} \\\\\\ 255-5r=5r-35\implies 255=10r-35\implies 290=10r \\\\\\ \cfrac{290}{10}=r\implies 29=r\hspace{5em}\stackrel{\textit{faster cyclist}}{\text{\LARGE 29}~\frac{km}{h}}\hspace{5em}\stackrel{\textit{slower cyclist}}{\text{\LARGE 22}~\frac{km}{h}}[/tex]

Answer:

Below

Step-by-step explanation:

The equation you need to remember is:

rate X time = distance       re-arrange to

time = distance / rate         sub in the numbers given to get

time =   x / 15  hours

The graph for the piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6 is attached in the solution.

A piecewise function is a function that is defined on a sequence of intervals.

Given is a piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6

Plotting the graph for:

f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6

From the graph, we conclude that:

The graph of the given piecewise function is a straight line with two segments.

The first segment, which lies between x = 0 and x = 6, has a slope of -1/2 and a y-intercept of 6.

The second segment, which lies between x = 0 and x = -∞, has a slope of 1/3 and a y-intercept of -1.

Learn more about piecewise function, click;

https://brainly.com/question/12700952

#SPJ1

Answer:

x ≥ 4

Step-by-step explanation:

Just treat the equation like you would a regular algebraic equation.

10 + x ≥ 14

10 + x - 10 ≥ 14 - 10

x ≥ 4

As for graphing it, I'm not really sure if you want a proper graph or a number line.

For a number line, put a closed dot on a 4

The value of the given indefinite integral is[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]

An integral which is not having any upper and lower limit is known as an indefinite integral. Mathematically, if F(x) is any anti-derivative of f(x) then the most general antiderivative of f(x) is called an indefinite integral and denoted, ∫f(x) dx = F(x) + C.

Given is an indefinite integral, [tex]\int \frac{x-6}{\left(x+3\right)^2+36}dx[/tex]

Solving,

Applying u-subsituition,

[tex]=\int \frac{u-9}{u^2+36}du[/tex]

Expanding,

[tex]=\int \frac{u}{u^2+36}du-\int \frac{9}{u^2+36}du[/tex]

Since, [tex]\int \frac{u}{u^2+36}du = \frac{1}{2} ln|u^2+36|[/tex]

And,

[tex]\int \frac{9}{u^2+36}du = \frac{3}{2} tan^-^1(\frac{u}{6} )[/tex]

Therefore,

[tex]=\int \frac{u}{u^2+36}du-\int \frac{9}{u^2+36}du[/tex] [tex]=\frac{1}{2}\ln \left|u^2+36\right|-\frac{3}{2}\arctan \left(\frac{u}{6}\right)[/tex]

Substitute u = x+3

[tex]=\frac{1}{2}\ln \left|\left(x+3\right)^2+36\right|-\frac{3}{2}\arctan \left(\frac{x+3}{6}\right)[/tex]

[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)[/tex]

Add constant c,

[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]

Hence, the value of the given indefinite integral is

[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]

Learn more about indefinite integral, click;

https://brainly.com/question/29133144

#SPJ1

Answer:

=94

Step-by-step explanation:

Hope itvhelps you↑↑

The total cost of the six fill-ups during winter is $4977.

Word problems are mathematical problems expressed with words that involve the interpretation of mathematical variables and the usage of the appropriate arithmetic operations to solve them.

From the given information;

If the price per gallon is $3.95 and a tank can hold 210 gallons. Then, the price for a single full tank is $3.95 × 210 = $829.5

In addition to that, if Tanis has six fill-ups tanks during the winter, his total cost would be:

= $829.5 × 6

= $4977

Therefore, we can conclude that the total cost of the six fill-ups during winter is $4977.

Learn more about word problems in mathematics here:

https://brainly.com/question/21405634

#SPJ1

Answer:

14ft

Step-by-step explanation:

Perimeter of a square = 4s where s = side length

Here, we are given the perimeter, and we want to find the side length. To do so we plug in the perimeter and solve for s

Perimeter = 56

So 56 = 4s

==> divide both sides by 4

14 = s

A square with a perimeter of 56 feet has a side length of 14 feet

Answer:

3 hours

Step-by-step explanation:

By applying supply and demand concept, it can be concluded that:

a. Point of equilibrium for this market will be reached when p = 20 and q = 50

b. Consumers' surplus for this market when -150 < q < 50

c. Producers' surplus for this market when 50 < q < 130

Demand is the number of goods purchased or requested in the market at a certain price and time, while supply is the number of goods sold or offered in the market at a certain price and time.

Point of equilibrium will be reached when supply and demand are in balance.

We have the following supply and demand functions:

Supply: p = 15 + 0.1q

Demand: p= √(650- 5q)

A. The point of equilibrium occurs when supply and demand are in balance:

                                 15 + 0.1q = √(650- 5q)

                              (15 + 0.1q)² = 650 - 5q

                  225 + 3q + 0.01q² = 650 - 5q

0.01q² + 3q + 5q + 225 - 650 = 0

                    0.01q² + 8q - 425 = 0

                  q² + 800q - 42500 = 0

q² + 800q + 160000 - 202500 = 0

                 (q + 400)² - 202500 = 0

                                  (q + 400)² = 202500

                                     q + 400 = 450

                                                q = 50

As we know q, we can calculate the p:

p = 15 + 0.1q

  = 15 + 0.1 * 50

  = 20

B. The Consumers' surplus when demand > supply:

√(650- 5q) > 15 + 0.1q    ⇔    q < 50

which implies:

√(650- 5q) > 0                ⇔    q < 130

15 + 0.1q > 0                    ⇔    q > -150

So, the Consumers' surplus for this market when -150 < q < 50

C. The Producers' surplus when supply > demand:

15 + 0.1q > √(650- 5q)    ⇔    q > 50

which implies:

√(650- 5q) > 0                ⇔    q < 130

15 + 0.1q > 0                    ⇔    q > -150

So, the Producers' surplus for this market when 50 < q < 130

To learn about supply and demand function, click here: https://brainly.com/question/23029589

#SPJ1

The angle formed 28.42 degree between the slide and the drop.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

length of water slide is 42m. (Hypotenuse)

and length of drop = 20 m (Perpendicular)

Using Trigonometry

sin [tex]\theta[/tex] = P/ H

sin [tex]\theta[/tex] = 20 / 42

sin [tex]\theta[/tex] =  10 /21

sin [tex]\theta[/tex] = 0.476

[tex]\theta[/tex] = [tex]sin ^{-1[/tex] (0.476)

[tex]\theta[/tex] = 28.42 degree.

Hence, the angle is 28.42 degree.

Learn more about Trigonometry here:

https://brainly.com/question/29002217

#SPJ1

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(\dfrac{7}{8})^4}[/tex]

[tex]\mathsf{= \dfrac{7}{8}\times\dfrac{7}{8}\times\dfrac{7}{8}\times\dfrac{7}{8}}[/tex]

[tex]\mathsf{= \dfrac{7\times7\times7\times7}{8\times8\times8\times8}}[/tex]

[tex]\mathsf{= \dfrac{49\times49}{64\times64}}[/tex]

[tex]\mathsf{= \dfrac{2,401}{4,096}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{2,401}{4,096}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: The IV infusion will run for 10 hours.

To find out, you divide the total volume of fluid (1000 mL) by the rate of infusion (100 mL/hr):

1000 mL / 100 mL/hr = 10 hours.

Rounding to the nearest whole number, the IV infusion will run for 10 hours.

Step-by-step explanation:

Answer:

The doctor orders 1000 mL of fluid to run at a rate of 100 mL per hour. To find out how long this IV infusion will run, divide the total volume of fluid by the flow rate:

1000 mL / 100 mL/hr = 10 hours

So, the IV infusion will run for 10 hours.

A second-degree polynomial can be used to fit the three data points by finding the coefficients of the polynomial that pass through the three given points. The general form of a second-degree polynomial is:

p(x) = ax^2 + bx + c

We can use the three data points to solve for the coefficients a, b, and c. Let's use the year 2000 as the reference point and set x = 0. Then, we have:

p(0) = c = 287 million (at x = 0, the population is 287 million)

Next, let's use the data point for 1990, which is 244 million. The year 1990 is 10 years before 2000, so x = -10. Substituting these values into the polynomial, we have:

p(-10) = a * (-10)^2 + b * (-10) + c = 244 million

Solving for a and b using the two equations above, we have:

a = (244 - 287 + 10b) / 100

c = 287

Substituting these values back into the polynomial, we have:

p(x) = (244 - 287 + 10b) / 100 * x^2 + bx + 287

Finally, let's use the data point for 2010, which is 324 million. The year 2010 is 10 years after 2000, so x = 10. Substituting these values into the polynomial, we have:

p(10) = (244 - 287 + 10b) / 100 * 10^2 + b * 10 + 287 = 324 million

Solving for b, we have:

b = (324 - 244 + 287) / 10 - (244 - 287) / 100 * 10^2 = 37

Therefore, the final form of the second-degree polynomial that passes through the three data points is:

p(x) = (244 - 287 + 10 * 37) / 100 * x^2 + 37x + 287 = 7x^2 + 37x + 287

This polynomial can be used to estimate the population of the country for any year close to 1990, 2000, or 2010.

To Know more about Polynomial

https://brainly.com/question/4142886

#SPJ4

The probability that the student was female GIVEN they got a 'B' is 0.194.

It is a branch of mathematics that deals with the occurrence of a random event.

           A        B        C      Total

Male     5       15       20      40

Female 2      14       16       32

Total     7      29      36       72

We have to find the  probability that the student was female GIVEN they got a 'B'

P(Female ∩ B) =  14/72 = 0.1944

Hence, the probability that the student was female GIVEN they got a 'B' is 0.194.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

The correct option is (b)  Regression 2 is a better fit because there appears to be a nonlinear relationship between x and y.

According to the above evidence, it is concluded that Regression 2 is better fit as, in the regression 2, the graph represents to be nonlinear relationship between x and y.

Since all the other concluded ones are not best describe the residential plot of given evidence, Hence, based on the evidence Regression 2 is better than the Regression 1 as it includes the nonlinear relationship between x and y that is exactly shown in the above evidence.

Question:

Which of the following conclusions is best supported by the evidence above?

a) Regression 1 is a better fit because there appears to be a nonlinear relationship between x and y.

b) Regression 2 is a better fit because there appears to be a nonlinear relationship between x and y.

c) Regression 1 is a better fit because there appears to be a linear relationship between x and y.

d)Regression 2 is a better fit because there appears to be a linear relationship between x and y

e) There is a negative correlation between x and y.

To know more about Regression Line:

https://brainly.com/question/17004137

#SPJ4

Answer:

5:2 is the answer of that question.

For the function E(t) = 31 cos (0.11t), the rate at which the number of wolves in the forest is changing at time t = 7 is 22.2549.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function to model the rate at which the number of wolves in a forest is changing is E(t) = 31 cos (0.11t)

Here t is the time measured in weeks.

The time value is given as t = 7

Substitute the value of t in the equation -

E(t) = 31 cos (0.11t)

Apply the arithmetic operation of multiplication -

E(7) = 31 cos (0.11 × 7)

E(7) = 31 cos (0.77)

E(7) = 31 × 0.7179

E(7) = 22.2549

Therefore, the rate value is obtained as 22.2549.

To learn more about function from the given link

https://brainly.com/question/2284360

#SPJ1

Answer:

its 48 lb·in.

I'll give you an example and plug in the numbers:

Given:

6 lb is needed to stretch 4 inches beyond natural length.

Need work done to stretch same string from natural length to 8 inches.

Solution:

string stiffness, K

= Force / stretched distance

= 6 lb / 4 inches

= 1.5 lb/inch

Work done on a string of stiffness K

= (Kx^2)/2 lb-in

= 1.5 lb/in *(8 in)^2)/2

= 48 lb-in.

Answer:

The correct solution is .54

Step-by-step explanation:

Think about this like counting change.

0.54 is the largest amount. Next would be 0.504 (which in change would be close to 0.50 rounded down), lowest amount would be 0.45

The set of whole numbers, the set of integers, and the set of rational numbers are closed under each of the four basic operations.

Whole numbers:

Addition: Yes

Subtraction: No (e.g. 5 - 7 = -2)

Multiplication: Yes

Division: No (e.g. 4 ÷ 2/3 is not a whole number)

Integers:

Addition: Yes

Subtraction: Yes

Multiplication: Yes

Division: No (e.g. 4 ÷ 1/2 is not an integer)

Rational numbers:

Addition: Yes

Subtraction: Yes

Multiplication: Yes

Division: Yes (provided the denominator is non-zero)

Polynomials:

Addition: Yes

Subtraction: Yes

Multiplication: Yes

Division: No (in general, polynomials cannot be divided by other polynomials)

Polynomials are like rational numbers with respect to closure under addition, subtraction, and multiplication.

However, they are not closed under division like rational numbers.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.

For more questions on Number System

https://brainly.com/question/17200227

#SPJ4

Tripling the radius of a circle results in a nine-fold increase in its area.

The radius of a circle is a critical component in determining its size. Tripling the radius of a circle means that the size of the circle has increased three times its original size.

The area of a circle can be calculated using the formula

=> A = πr²,

where A represents the area of the circle, π is Pi, and r is the radius. When the radius of a circle is tripled, the value of r becomes 3 times its original value, meaning the formula becomes

=> A = π(3r)² = π * 9r² = 9πr².

Therefore, the new area of the circle is nine times the original area of the circle.

Complete Question:

The radius of a circle is tripled. Which of the following describes the effect of this change on the area?

To know more about circle here.

https://brainly.com/question/483402

#SPJ4

Step-by-step explanation:

we need to calculate the distances between the points as the side lengths of the triangle.

these side lengths must satisfy the Pythagoras principle :

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle) and the longest of the 3 sides, a and b being the legs.

the distance between 2 points is again calculated via Pythagoras, as the coordinate differences (= the legs) with the distance as Hypotenuse create right-angled triangles.

this is then caked the distance formula, but it is all Pythagoras again.

AB² = (xB - xA)² + (yB - yA)² = (6 - -2)² + (2 - 2)² =

= 8² + 0² = 8²

AB = 8

AC² = (0 - -2)² + (6 - 2)² = 2² + 4² = 4 + 16 = 20

AC = sqrt(20)

BC² = (0 - 6)² + (6 - 2)² = (-6)² + 4² = 36 + 16 = 52

BC = sqrt(52)

as sqrt(20) is a little bit more than 4, and sqrt(52) is a little bit more than 7, 8 is the longest side and Hypotenuse.

if this is a right-angled triangle, then

8² = sqrt(20)² + sqrt(52)²

must be true.

but

64 = 20 + 52 = 72

is wrong.

so, the segments do not form a right-angled triangle.

Answer:

Step-by-step explanation:

Picture?

You didn’t give enough info. Are you able to provide more information? Or a picture?

Answer:

Brhaaliarwoiagsajaidgsiuaaidywlx

Function F(X) is shifted 1 unit left and 1 unit up.

Identify The Parent Function.

Reflect Over X-Axis or Y-Axis.

Shift (Translate) Vertically or Horizontally.

Vertical and Horizontal Stretches/Compressions.

Plug in a couple of your coordinates into the parent function to double check your work.

Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f(x) = x2 + 3 is obtained by just moving the graph of g(x) = x2 by 3 units up.

There are different formulas for different rules of transformation. For vertically transformation the function f(x) is transformed to f(x) + a or f(x) - a. For horizontal transformation the function f(x) is transformed to f(x + a) or f(x - a). Further for stretched or compressed transformation is it f(cx) or cf(x).

To learn more about transformations refers to:

brainly.com/question/27996647

#SPJ1

The correct Set-builder form for the following set written in Roster form       { -4,− 3 , − 2 , − 1 , 0 , 1 } is,

⇒ {x ∈ Z | - 4 ≤ x ≤ 1}

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The set is,

⇒ { -4,− 3 , − 2 , − 1 , 0 , 1 }

Now, The correct Set-builder form for the following set written in Roster form { -4,− 3 , − 2 , − 1 , 0 , 1 } is,

⇒ {x ∈ Z | - 4 ≤ x ≤ 1}

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

In the interval [0, π/2], the function is one-to-one or injective.

The functions which have one-to-one behaviour are called injective functions. An injective function is a function in which every horizontal line in the plane intersects the graph of f at most one point or we can say if f(x) = f(y) then x = y.

First, we need to draw the graph of y = |cos x|. The graph of y = |cos x| is attached.

We can see from the graph that the value of the function is 1 when x = 0 and the value of the function decreases till it takes 0 at x = π/2 and then the value of the function increases again.

In the option [0, π] and [0, 2π] the behaviour of the function is not injective.

In [0, π/4], the function is injective but [0, π/2] is the correct answer as it represents the largest interval starting from 0 on which this function is one-to-one.

To learn more about injective function here:

brainly.com/question/29805748

#SPJ4

To find a pattern in a sequence using differences, we can calculate the difference between consecutive terms and look for a pattern in the differences.

To learn more about sequences refer:

brainly.com/question/6561461

#SPJ1