Therefore , The negative linear equation result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.
A linear equation is precisely what?A straightforward regression graph is created using the equation y=mx+b. The y-intercept is m, and the slope is B. Despite the fact that the line before it contains independent parts, it is repeatedly alluded to as a "mathematical formula combining many factors." Only two factors are present in bivariate linear equations. There are no known solutions to application issues concerning linear equations. Y=mx+b.
Here,
Let H be the number of hot coffee drinks sold yesterday, and I be the number of iced coffee drinks sold yesterday. We know that:
H + I = 100 (since a total of 100 cups were sold)
We also know that the average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00. Therefore, the total revenue from hot coffee drinks is:
3.50H
And the total revenue from iced coffee drinks is:
2.00I
To find the difference in revenue between the hot and iced coffee drinks sold yesterday, we need to subtract the revenue from iced coffee drinks from the revenue from hot coffee drinks:
3.50H - 2.00I
We want this expression to equal zero, so we can set it equal to zero and solve for H:
3.50H - 2.00I = 0
3.50H = 2.00I
H = (2/3.50)I
H ≈ 0.57I
Since H + I = 100, we can substitute 0.57I for H in the equation:
0.57I + I = 100
1.57I = 100
I ≈ 63.7
Rounding to the nearest whole number, we get:
I = 64
Therefore, H = 100 - I = 36
So the difference in revenue between the hot and iced coffee drinks sold yesterday is:
3.50H - 2.00I = 3.50(36) - 2.00(64) = $72 - $128 = -$56
The negative result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.
To know more about linear equation visit:
https://brainly.com/question/11897796
#SPJ1
The complete question is "Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero
A local coffee shop sells iced and hot coffee drinks. Yesterday, the shop sold a total of 100 cups of coffee. The average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00.
What is the difference in revenue between the hot and iced coffee drinks sold yesterday?"
Find the 10th term of the arithmetic sequence 2, 6, 18, 54, ...
With her new company, Annika has a two-year assignment living in a large city. The company will reimburse most of her expenses. Annika is using the Quantitative Reasoning Process to build a budget. Calculate Annika's estimated living expenses for the next two years using the following:
Rent: $1,050 per month, Gym membership: $325 per year with a monthly fee of $35, Renters' insurance: $70 every 6 months, Groceries: $300 per month, and Eating out & entertaining: $150 per week.
Assume 52 weeks in 1 year and 12 months in 1 year.
(Round your answer to the nearest whole dollar)
The solution is, Total estimated living expenses = $53,900.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Estimated expenses for next 2 years:
Rent = 1100 * 12 * 2 = 26,400
Gym membership = 450 * 2 = 900
Gym monthly fee = 40 * 12 * 2 = 960
Renter's insurance = 60 * (12 * 2 / 6) = 240
Groceries = 300 * 12 * 2 = 7200
Eating out & entertainment = 175 * 52 * 2 = 18,200
Total estimated living expenses = $53,900
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ1
Microeconomics
The total cost function of a monopolist is () = 3. The inverse demandfunction for
the monopolist’s products is () = 12 − .
A. find the profit-maximizing level of price and output
B. Find the maximum profit of the firm at an equilibrium price level.
Answer:
aaaaaæaaaaaaaaaaaaaaaaaaaaaa
PLEASE HELP!
Determine the terms and the coefficients of the terms for the
polynomial
x^2-3x+2
Complete the table for the polynomial
Answers in bold
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Term} & \text{Coefficient}\\\cline{1-2}\text{x}^2 & \boldsymbol{1}\\\cline{1-2}\boldsymbol{-3\textbf{x}} & -3\\\cline{1-2}2 & \boldsymbol{2}\\\cline{1-2}\end{array}[/tex]
Explanation:
The given expression [tex]\text{x}^2-3\text{x}+2[/tex] is the same as [tex]\text{x}^2+(-3\text{x})+2[/tex]
This leads to the three terms as shown in the table above. Each term is separated by a plus sign.
The coefficient is the number to the left of the variable. Think of [tex]\text{x}^2[/tex] as [tex]1\text{x}^2[/tex] and think of [tex]2[/tex] as [tex]2\text{x}^0[/tex]
In other words, [tex]\text{x}^2-3\text{x}+2[/tex] is the same as [tex]1\text{x}^2+(-3\text{x})+2\text{x}^0[/tex]
A washer 4mm wide is to be made as indicated in the drawing. Find the area of the washer in term of the outer radius ( in expanded form ).
This question is related to special products. Please help if you can.
The required area of the washer is 8πr - 16π square millimeter.
How to find area of circle?A = π r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit, such as m², cm², in², etc., is the unit of area.
Circle Area Formulas;
Area is equal to π r², where r stands for radius.
Area is equal to ( π /4) d², where d stands for diameter.
Area is equal to C²/4 π where C stands for circumference.
According to question:The area of a washer with outer radius "r" and inner radius "r-4" can be found as follows:
Area = π * (outer radius² - inner radius²)
= π * (r² - (r-4)²)
= π * (r² - r² + 8r - 16)
= 8πr - 16π square millimeter.
Thus, required area of washer is 8πr - 16π,Option(B) is correct.
To know more about Circle visit:
brainly.com/question/12711347
#SPJ1
It was recently estimated that domestic vehicles outnumber foreign vehicles by about seven to five. If there are 4152 vehicles in a county, how many of them are domestic?
In a case whereby It was recently estimated that domestic vehicles out number foreign vehicles by about seven to five. If there are 4152 vehicles in a county, the number of them that are domestic is 2422 domestic vehicles.
How can the number of domestic vehicle be determined?The concept that will be used here is simplification.
From the question, we were told that there are 7x domestic vehicles as well as 5x foreign vehicle.
We can see that the x is the unknown number, which we need to find out,
Then we can make an equation as:
7x + 5x = 4152
12x= 4152
x=4152/12
=346
Hence we can say that there are 7*346 = 2422 domestic vehicles
Learn more about equation at:
https://brainly.com/question/2972832
#SPJ1
Which of the following describes a situation in which it is reasonable to reach a cause-and-effect conclusion based on data from a statistical study?answer choices- The study is based on a random sample from a population of interest.- The study is observational, and the sample used is not a convenience sample.- The study is an experiment that uses random assignment to assign volunteers to experimental conditions (treatments).- It is never reasonable to reach a cause-and-effect conclusion based on data from a statistical study.- It is always reasonable to reach a cause-and-effect conclusion based on data from a statistical study.
The correct answer is: The study is an experiment that uses random assignment to assign volunteers to experimental conditions (treatments).
What is statistical study?A sample is an analytic subset of a larger population in statistics. The utilization of samples enables researchers to conduct investigations with more manageable data and more quickly. Randomly chosen samples exhibit little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.
Here,
A study that uses random assignment to assign volunteers to experimental conditions (treatments) is considered the best design to establish cause-and-effect relationships. In this type of study, researchers can control the variables and minimize extraneous factors that could confound the results. By using random assignment, the volunteers in the experimental and control groups are similar on average, making it more likely that any observed differences between the groups are due to the treatments.
The correct answer is: The research is an experiment in which volunteers are randomly assigned to experimental settings (treatments).
To know more about statistical study,
https://brainly.com/question/27209836
#SPJ4
Similar triangles: To indirectly measure the distance across a river, Madeline stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Madeline draws the diagram below to show the lengths and angles that she measured. Find PR, the distance across the river. Round your answer to the nearest foot.
Answer:
PR = 288.75 feet
Step-by-step explanation:
There are two triangles that we need to consider:
ΔPRE and ΔPOC
These triangles are similar since
m∠PRE = m∠POC = 90°
∠PRE ≅ ∠POC
∠RPE ≅ ∠OPC (common angle)
AA Similarity theorem..
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
∴ ΔPRE ≅ ΔPOC
If two triangles are similar, the ratios of the corresponding sides must be equal
⇒ [tex]\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\[/tex] (1)
PO = PR + RO
PR is the width of the river that is to be determined
Let PR = x
Then
PO = x + 165
OC = 330, RE = 210
[tex]\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\\Rightarrow \dfrac{x + 165}{165} = \dfrac{330}{210}\\\\[/tex]
Left side:
[tex]\dfrac{x+165}{x} = \dfrac{x}{x} + \dfrac{165}{x} = 1 + \dfrac{165}{x}[/tex]
Simplify [tex]\dfrac{330}{210}[/tex] by dividing both numerator and denominator by 30
=>
[tex]\dfrac{330}{210} = \dfrac{11}{7}\\\\[/tex]
Therefore
[tex]\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\\Rightarrow 1 + \dfrac{165}{x} = \dfrac{11}{7}\\[/tex]
Subtract 1 from both sides:
[tex]\dfrac{165}{x} = \dfrac{11}{7} - 1\\\\\dfrac{165}{x} = \dfrac{4}{7}\\\\[/tex]
Cross-multiply
[tex]165 \times 7 = 4x\\\\\Rightarrow 4x = 165 \times 7\\\\\Rightarrow x = \dfrac{165 \times 7 }{4} = 288.75\;feet[/tex]
Company XYZ's Computer can execute a program of an input size n in one minute.
Company ABC claims that their computer runs 100 times faster than XYZ's.
What size input can ABC's computer execute in one minute for each algorithm for the following growth rates?
a.n
b. n^2
c. n^3
d. 2^n
The size input which ABC's computer can execute in one minute for each algorithm for the following growth rates are given below:
a. For a growth rate of "n", ABC's computer can execute an input size of 100n in one minute.b. For a growth rate of "n^2", ABC's computer can execute an input size of (100n)^(1/2) in one minute.c. For a growth rate of "n^3", ABC's computer can execute an input size of (100n)^(1/3) in one minute.d. For a growth rate of "2^n", ABC's computer can execute an input size of log2(100n) in one minute.How are the execution times gotten?For a growth rate of "n", it means the execution time increases linearly with the size of the input. In this case, XYZ's computer takes 1 minute to execute an input size of "n".
Company ABC claims that their computer is 100 times faster, so they can execute an input size of 100n in one minute.
For a growth rate of "2^n", it means the execution time increases exponentially with the size of the input.
In this case, if we double the input size, the execution time increases two times. So, if XYZ's computer takes 1 minute to execute an input size of "n", it would take 2 minutes to execute an input size of "2n".
Company ABC claims that their computer is 100 times faster, so to execute an input size of "2n" in 1 minute, the input size must be log2(100n).
Read more about algorithms here:
https://brainly.com/question/24953880
#SPJ1
given an integer variable timer, write a statement that uses the auto-decrement operator to decrease the value of that variable by 1.
timer--; //This statement uses the auto-decrement operator to decrease the value of the variable timer by 1.
The auto-decrement operator -- is used to decrease the value of a variable by 1. In this case, the variable is called timer. The statement which uses the auto-decrement operator is timer--;. This statement will take the current value of the timer variable and decrease it by 1. For example, if the current value of timer is 5, the statement timer--; will decrease the value to 4. This is a very useful and efficient way to decrease a variable's value by 1. It is also much shorter than having to write out a statement such as timer = timer - 1;. The auto-decrement operator can be used with other types of variables as well, such as strings or characters.
Learn more about variable here
brainly.com/question/29583350
#SPJ4
An animal shelter needs to buy 8 pounds of cat food for every cat
they have. Complete the following table of cats to pounds of cat food.
the food needed for 10 cats will be 80 pounds.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem. Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers
An animal shelter needs to buy 8 pounds of cat food for every cat
they have.
So per pound, it food needed for 10 cats will be 8*10 = 80 pounds.
Hence the food needed for 10 cats will be 80 pounds.
Learn more about arithmetic, by the following link.
https://brainly.com/question/13181427
#SPJ1
Given f(x)=(8/x+13)+2 find the inverse
Answer:
Step-by-step explanation:
da fact that it sometimes get me wrong but it do works ngl
What are the terms a0, a1, a2 and a3 of the sequence {an}, where an equals
a. 2n + n
b. n(n+1)!
c. [n/2]
d. [n/2] + [n/2]
The terms a0, a1, a2, and a3 of the sequence {an} in each case are as follows:
a. a0 = 0, a1 = 3, a2 = 6, a3 = 9
b. a0 = 0, a1 = 2, a2 = 12, a3 = 72
c. a0 = 0, a1 = 0.5, a2 = 1, a3 = 1.5
d. a0 = 0, a1 = 1, a2 = 2, a3 = 3
The sequence {an} is defined asa. 2n + n
a0 = 2*0 + 0 = 0
a1 = 2*1 + 1 = 3
a2 = 2*2 + 2 = 6
a3 = 2*3 + 3 = 9.
b. n(n+1)!
a0 = 0(0+1)! = 0
a1 = 1(1+1)! = 2
a2 = 2*(2+1)! = 12
a3 = 3(3+1)! = 72
c. [n/2]
a0 = [0/2] = 0
a1 = [1/2] = 0.5
a2 = [2/2] = 1
a3 = [3/2] = 1.5
d. [n/2] + [n/2]
a0 = [0/2] + [0/2] = 0
a1 = [1/2] + [1/2] = 1
a2 = [2/2] + [2/2] = 2
a3 = [3/2] + [3/2] = 3
To know more on sequence
https://brainly.com/question/28615767
#SPJ4
Logan says, “140 millilitres is more than 1.2 litres”. Is he right?
A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
First, because we are dealing with different units here, we need to know how many milliliters are in a litre.
1000 milliliter = 1 litreSo, an equation we can use is:
1 litre × 1000 = the amount in millilitersIf we look at 1.2 litres, we can now convert it to milliliters.
1.2 × 1000 = 1200Comparing 1200ml to 140ml, we can see that 1200ml is bigger.
Therefore, 1.2 litres are greater.
3x+4y=6
8x-4y=5
( equation)
On solving the provided question, we can say that the equations are 3x+4y=6 and 8x-4y=5 => x = 1 and y = 3/4
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equations are
3x+4y=6
8x-4y=5
adding both equation
11x = 11
x = 1
y = 3/4
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Your Shadow measures 8 ft your father's Shadow is 9 ft if you are 5.5 ft how tall is your father in inches? I need problem wrote out please.
Check the picture below.
6x^2 − 5x + 6 = 6x + 3
Answer:
x=1/3;3/2
Step-by-step explanation:
6x^2-5x+6 = 6x+3
-6 -6
6x^2 -5x = 6x - 3
+5x +5x
6x^2 = 11x -3
6x^2 + 11x - 3 = 0
(3x-1)(2x-3)=0
3x-1=0
3x=1
x=1/3
2x-3=0
2x=3
x=3/2
please help this is due today :(
Answer:
C
Step-by-step explanation:
Supplementary angles are two angles that equal 180 degrees. An angle is 180 degrees when it's a straight line. As you see, the line with E, A, P, and B is a straight line, making A and B supplementary.
Answer: Supplementary angles because the 2 angles when they are joined they both add up to 180 degrees
Step-by-step explanation:
find the sizes of the lettered angle
[tex]find \: the \: sizes \: of \: the \: lettered \: angle[/tex]
The measures of the angles are:
n = q = j = 57°
m = l = p = k = 123°
How to find the measures of the angles?Remember that vertical angles have the same measure, then:
n = 57°
And if the two horizontal lines are parallel, then the values in the correspondent quadrants are the same ones, then:
q = 57°
j = 57°
And adjacent angles add up to 180°, them:
57° + m = 180°
m = 180° - 57°
m = 123°
Then:
m = l = p = k = 123°
Learn more about vertical angles:
https://brainly.com/question/14362353
#SPJ1
Write the answer is (x,y) form
The translation in the form (x,y) is (-3, -10)
How to determine the translation that maps from T to T'?In geometry, translation is a type of transformation that moves each point of a figure to a new location, while preserving the shape and size of the figure. A translation is defined by a displacement vector, which specifies the direction and magnitude of the movement.
T is the initial position of the object and T' is the image (new position) of the object after translation. We can use this equation:
T + translation = T'
translation = T' - T
translation = (6, -2) - (9, 8)
translation = (6-9, -2-8)
translation = (-3, -10)
Learn more about translation on:
brainly.com/question/12861087
#SPJ1
a triangle has two side lengths of 3.5 inches and 7.75 inches. which of the following could be the length of the third side
The length of the third side could be 5.26 inches.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
There are 2 possible triangles that can arranged one being the 8 the longest side, and another one being the 5 and 8 the sides of the triangle
Given that triangle has two side lengths of 3.5 inches and 7.75 inches.
Using the pythagorean theorem to solve.
3.5² + 7.75² = x²
x² = 12.25 + 15.5
x² = 27.75
x = 5.26
Learn more about Pythagoras theorem;
https://brainly.com/question/343682
#SPJ1
URGENT PLS HELP
stats standard deviation
The sample standard deviation of the given data will be 10.058.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]
The table is given below.
M f Mf M²f
15 8 120 1,800
25 18 450 11,250
35 20 700 22,050
45 13 585 26,325
55 7 385 21,175
The variance is given as,
Var = 1 / (66 - 1) [82600 - 2240² / 66]
Var = 101.16
Then the standard deviation is given as,
SD = √ Var
SD = √101.16
SD = 10.058
The sample standard deviation of the given data will be 10.058.
More about the standard deviation link is given below.
https://brainly.com/question/12402189
#SPJ1
Match each formula on the left side to an equivalent formula on the right side A=BC+D
We can see that matching each formula on the left side to an equivalent formula on the right side, we have:
A = BC + D ------ B = A - D/C
A = B + CD ------ B = A - CD
A = BD - C ------- B = A + C/D
A = CD - B ------- B = CD - A
What is formula?A formula is a mathematical expression that represents a set of instructions for solving a specific problem or calculating a desired value. It often uses symbols and variables to represent values, and can include operations such as addition, subtraction, multiplication, and division.
Formulas can be used in a variety of fields, including physics, chemistry, finance, and engineering.
Learn more about formula on https://brainly.com/question/657646
#SPJ1
Using the region names in the image below, select all regions that represent: A' ∪ B ∩ C'
The region for A' ∪ B ∩ C' is region III.
What is Venn diagram?A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different visually.
Given:
So from the Venn diagram, the item represents the regions four, five, six and seven.
We have to find not A union B intersection not C.
A' is the complement of set A.
So, the region is for not A union B is represented by B.
and, then B ∩ C' gives the region B.
learn more about Venn diagram here:
brainly.com/question/1605100
#SPJ1
Assign a variable solveEquation with a function expression that has three parameters (x, y, and z) and returns the result of evaluating the expression 2 * x * y Z?
The program for assigning variable and solving expression 2 * x * y - z is -
def func1(x, y, z):
return 2*x*y - z
x= int(input("Enter x"))
y= int(input("Enter y"))
z= int(input("Enterz"))
solveEquation=func1(x, y, z)
print (solveEquation)
What is Expression in Code?
Expressions in computer science are written by developers, interpreted by computers, and 'evaluated.' The evaluation yields a result or return. Expressions in code include simple mathematical equations like 2 + 2. They are commonly referred to as arithmetic expressions.
The program for the condition given is -
def func1(x, y, z):
return 2*x*y - z
x= int(input("Enter x"))
y= int(input("Enter y"))
z= int(input("Enterz"))
solveEquation=func1(x, y, z)
print (solveEquation)
Therefore, the coding has been done.
To learn more about Expression in Code, from the given link
brainly.com/question/24661996
#SPJ4
Solve with the box method
Using the box method, the expression is solved as: 4x³ + 8y² - 19y - 35 (see image below).
How to Expand an Algebraic Expression Using the Box Method?The box method, also known as the grid method or area model, is a visual technique for multiplying two expressions or expanding algebraic expressions. Here are the steps to expand an algebraic expression using the box method:
Write the expression to be expanded: Write the algebraic expression that you want to expand.Draw a box: Draw a box, and divide it into smaller boxes, one for each term in the expression.Write the terms: Write each term of the expression on the top of each box.Multiply the terms: Multiply the terms along the sides of the boxes, and write the result in the corresponding smaller box.Combine like terms: Add the products in each box to obtain the expanded expression.The box method shows how the expression has been expanded, thus, combining like terms, we have:
4x³ + 8y² - 19y - 35
Learn more about the box method on:
https://brainly.com/question/29260453
#SPJ1
help
Find an equation of the line that contains the given pair of points.
(25, 26), (6, 7)
Answer:
y = x + 1
Step-by-step explanation:
Since we have two points, we can find the equation of the line in slope-intercept form or y = mx + b, where m is the slope and b is the y-intercept.
We can find the slope using the slope formula, which is:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where y2 and x2 are one point on the line and y1 and x1 are the other point on the line:
Thus, we have:
[tex]m=\frac{7-26}{6-25}\\ m=\frac{-19}{-19}\\ m=1[/tex]
Now that we have the slope, we choose one of the points and plug in the slope to find the y-intercept:
[tex]26=1(25)+b\\26=25+b\\1=b[/tex]
I checked the answer for this question and its. Angle PSR = ⁴⁄₇x = ⁴⁄₇ x 105 = 60°
What I don't understand is how they find the 105°. Could someone write down a step by step explanation answer to this question please?
Answer:
see explanation
Step-by-step explanation:
(a)
let ∠ QRS = x then ∠ PQR = x and
∠ QPS = [tex]\frac{6}{7}[/tex] x and ∠ PSR = [tex]\frac{4}{7}[/tex] x
the sum of the 4 angles in a quadrilateral = 360°
sum the 4 angles and equate to 360
x + x + [tex]\frac{6}{7}[/tex] x + [tex]\frac{4}{7}[/tex] x = 360 ( multiply through by 7 to clear the fractions )
7x + 7x + 6x + 4x = 2520
24x = 2520 ( divide both sides by 24 )
x = 105
then
∠ QRS = 105° , so
∠ PSR = [tex]\frac{4}{7}[/tex] × 105° = 4 × 15° = 60°
(b)
∠ QPS = [tex]\frac{6}{7}[/tex] × 105° = 6 × 15° = 90° ← a right angle
A cylindrical tank has a radius of 20 cm. Water flows out of the tank at .05 liters per second. How fast does the level of water in the tank drop?
Answer:
Step-by-step explanation:
To calculate the rate at which the water level drops, we need to find the volume of water being lost per second and convert that to a height change. The volume of water being lost is given as 0.05 liters per second. The volume of a cylinder with height h and radius r is given by the formula:
V = πr^2h
We can rearrange this formula to solve for h:
h = V / (πr^2)
Substituting the given values, we get:
h = 0.05 / (π * 20^2) = 0.05 / (π * 400) = 0.05 / 1257.0796
So the rate at which the water level is dropping is approximately 0.04 cm per second.
An experienced roofer with Stark Vegas roofing company can install a new roof in 24
hours. Together with a new trainee they can install a new roof in 15 hours. How long
would it take the trainee working by himself to install a new roof? Round to the nearest
tenth.
Answer:
40 hours
Step-by-step explanation:
This is an example of a work-rate-time problem
Since the experienced roofer can finish the job in 24 hours, his rate of work would be 1/24 (of the roof) per hour
Let the time taken by the trainee alone be x hours
His rate of work = [tex]\dfrac{1}{x}[/tex]
Together they finish the roof in 15 hours
So combined work rate = [tex]\dfrac{1}{15}[/tex]
Since combined rate = sum of individual rates we get
[tex]\dfrac{1}{24} +\dfrac{1}{x} = \dfrac{1}{15}[/tex]
Move 1/24 to the right side:
[tex]\dfrac{1}{x} = \dfrac{1}{15} - \dfrac{1}{24}[/tex]
[tex]\dfrac{1}{x} =\dfrac{24 - 15}{24\cdot 15} = \dfrac{9}{360}\\\\[/tex]
Taking reciprocals on both sides
[tex]x = \dfrac{360}{9} = 40 \;hours[/tex]