The volume of copper needed to make such pot is 20πrh + 10πr² [tex](cm)^{3}[/tex]
What is surface area?The surface area of a three-dimensional object is the total area of all its faces. In real-life we use the concept of surface areas of different objects when we want to wrap something, paint something, and eventually while building things to get the best possible design.
The quantity of copper she needs to make such pot is same as the volume of copper need for such pot.
Volume = surface Area x thickness
Surface area had beemn given as 2πrh + πr²
thickness as 1mm = 10cm
Volume = 10(2πrh + πr²)
volume = 20πrh + 10πr² [tex](cm)^{3}[/tex]
In conclusion, the quantity of copper needed for the pot is 20πrh + 10πr² [tex](cm)^{3}[/tex]
Learn more about surface area of solids shapes: https://brainly.com/question/27176049
#SPJ1
Julio says, "If you subtract 17 from my number and multiply the difference by -3, the result is -9." What is Julio's number?
Answer:
23
Step-by-step explanation:
Taking an algebraic approach
let the number be n, then (n - 17) is 17 subtracted from the number, and -2(n - 17) = - 12 ( divide both sides by - 2 )n - 17 = 6 ( add 17 to both sides ) which is n=23
What is the solution to the equation One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x?
x = negative 5
x = negative 4
x = 4
x = 5
The solution to the equation represented by One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x is (b) x = negative 4
How to determine the solution to the equation?The statement in the question is given as
One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x
Mathematically, this statement can be represented as
1/4x - 1/8 = 7/8 + 1/2x
Multiply through the equation by 8
So, we have:
2x - 1 = 7 + 4x
Collect the like terms
4x - 2x = -1 - 7
Evaluate the like terms
2x = -8
Divide both sides by 2
x = -4
Hence, the solution is -4
Read more about equation at
https://brainly.com/question/2476251
#SPJ1
After the consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function C(t) = 1. 35te−2. 802t † models the average BAC, measured in mg/mL, of a group of eight male subjects t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink). A. What is the maximum average BAC during the first 3 hours? (Round your answer to three decimal places. ) mg/mL b. When does it occur? (Round your answer to two decimal places. ) h
The maximum average BAC during the first 6 hours is about 0.177 mg/ml.
What is average ?
The middle number in a group of numbers is the average value, which is determined by dividing the sum of all the values by the variety of values.
When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
The maximum is found where the derivative of C(t) is zero.
dC/dt = 1.35e^(-2.802t) -(1.35t)2.802e^(-2.802t) = 0
Solving for t gives ...
t = 1/2.802
So, the maximum C(t) is ...
C(1/2.802) = 1.35/2.802e^(-1) ≈ 0.177 . . . . . mg/mL
The maximum average BAC during the first 6 hours is about 0.177 mg/mL.
Learn more about average
brainly.com/question/24057012
#SPJ4
The points A, B, and C, shown on the number line, have weights 1, 1,
and 3 respectively.
A=2 B=4 C=7
What is the weighted average of points A, B, and C?
O 1.33
O 4.33
O 5.4
O 9.0
Answer:
4.33
Step-by-step explanation:
See picture attachment.
The weighted average of points is M = 5.4
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the weighted average be represented as M
Now , the value of M is
The points A, B, and C, shown on the number line, have weights 1, 1,
and 3 respectively.
A = 2 , B = 4 and C = 7
To find the weighted average of points A, B, and C with the given weights, we need to use the formula:
The weighted average M = (weight of A * value of A + weight of B * value of B + weight of C * value of C) / (total weight)
Plugging in the given values, we get:
The weighted average M = (1 * 2 + 1 * 4 + 3 * 7) / (1 + 1 + 3)
The weighted average M = (2 + 4 + 21) / 5
The weighted average M = 27 / 5
The weighted average M = 5.4 (rounded to one decimal place)
Hence , the weighted average of points A, B, and C with the given weights is 5.4
To learn more about average or mean click :
https://brainly.com/question/15526777
#SPJ2
A linear function is shown on the graph. What is the domain of the function?
{x | −4 < x < 6}
{x | −4 < x ≤ 6}
{y | −1 < y < 4}
{y | −1 < y ≤ 4}
The domain of the function is{x | −4 < x < 6}.
What is domain ?A function's domain is the set of all potential inputs.
For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
What is range?
The statistical difference between the highest and lowest values for a given data collection is called the range.
For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. It is possible to think of the range as the distance between the highest and lowest observation as a result.
the domain of the function is{x | −4 < x < 6} because
there is no restriction on x domain and range both are the set of real numbers.
To know more about domain visit:
https://brainly.com/question/28135761
#SPJ1
Write an equation for a rational function with:
Vertical asymptotes at x = -5 and x = -2
x intercepts at x = -1 and x = 6
y intercept at 4
y =
The rational equation with the desired asymptotes and intercepts is given by: f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].
What are the asymptotes of a function f(x)?Vertical asymptotes are x values that are outside the domain and, in a fraction, are the denominator zeroes.
As long as this value differs from infinity, the horizontal asymptote is the value of f(x) as x approaches infinity.
The vertical asymptotes are related to the denominator roots, so:
f(x) = a / ( x + 5)( x + 2 )
f(x) = a / ( x² + 7x + 10 )
The x-intercepts are related to the function's numerator, so:
f(x) = [a( x + 1 )( x - 6) ] / [x² + 7x + 10 ]
The y-intercept is to find a, hence, when x = 0, y = 5, thus:
4 = a(-6)/ 10
a = (-40/6)
a = -20 / 3
The equation will be written as,
f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].
To know more about asymptotes follow
https://brainly.com/question/28184934
#SPJ1
Examine the table, which represents a linear function.
Input (x) Output (y)
−3 14
0 7
3 0
6 −7
What is the initial value of the function?
Responses
3
−3
77
0
The initial value of the function obtained from the table of values for the linear function is; 7
What is a linear function?A linear function is a function that when plotted, produces a straight line on the coordinate plane.
The initial value of a function is the value of the function, when the input value is 0.
The initial value indicates the point where the graph intersects the y-axis, which is the y-intercept. It the point the graph enters quadrant I, where the x and y-values are positive.
From the initial value, and to the right of the x-axis, the input variable (x) is positive, such that the values of the function for natural value input, such as time can be found, and the initial value then represents the start of the measurement of the output values of the function.
The data in the table indicates that when the input variable x = 0, the output variable, y = 7
Therefore:
The initial value of the function is 7Which indicates that at the initial point of the positive value inputs of the function, the output is 7
Question details are:
Please find the table of the linear function, which is to be examined, presented as follows:
[tex]\begin{array}{|c|c|}In put (x) & Out put (y)\\-3 &14 \\0 & 7 \\3 & 0 \\6 & -7 \\\end{vmatrix}[/tex]
The initial value of the function that the above table represents is required.
Learn more about linear functions in mathematics here:
https://brainly.com/question/4025726
#SPJ1
On the 5th grade class picnic , 50 students share 75 sandwiches equally. How many sandwiches does each student get
Answer:
75÷50
Step-by-step explanation:
1.5 or 3÷2 is the correct answer
The volume of this cone is 83.7 cubic meters. With a height of 5m. Find the DIAMETER. SHOW ALL WORK
The volume of this cone is 83.7 cubic meters and the given height 5m then diameter 3.99 m.
What is Volume?
Volume is a measurement of three-dimensional space that is occupied. Numerous imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch).
Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.
Given that ;
volume of cone = [tex]\pi r^{2} \frac{h}{3}[/tex]
volume of cone = 83.7 [tex]m^3[/tex]
height = 5m
to find diameter :
[tex]d = \sqrt{\frac{3\times V}{\pi \times h} }[/tex]
[tex]d=\sqrt{\frac{3\times 83.7}{3.14\times 5} }[/tex]
[tex]d = \sqrt{\frac{251.1}{15.7} }[/tex]
[tex]d = \sqrt{15.993}[/tex]
d = 3.99 m
Learn more about Volume click here:
https://brainly.com/question/1082469
#SPJ1
the sum of two number 12 when three times the first number is added to 5 times the second number the results is 44
Answer:
one number is 8 and other is 4
Step-by-step explanation:
So we can say x+y=12.
And 3x+5y=44
For x+y=12, we can subtract x to get: y=12-x
Plug that in to get 3x+5(12-x)=44
3x+60-5x=44
Subtract 44: -2x+16=0
2x=16
x=8
12-8=4.
What is the slope of the line?
to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{4 +3}{3 +1} \implies {\Large \begin{array}{llll} \cfrac{7 }{ 4 } \end{array}}[/tex]
Composition of functions worksheet
using f(x) = 8x squared and g(x) (2x+8), find:
The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.
We have,
i] f(x) = 8x and
g(x) = (2x+8)
(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16
(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) = 8x.
(f ∘ g) (x) = 8(2x+8)
= 16x + 64
ii] f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2
= 6x - 28
g [f(3)] = (6x + 2 ) - 5
= -30x - 10
Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
To learn more about the composition of the function visit,
https://brainly.com/question/10687170
#SPJ1
A game consists of drawing three cards at random from a deck of playing cards. You win $3 for each red card that is drawn. It costs $2 to play. For one play of this game, the sample space S for the net amount you win (after deducting the cost of play) is
Select one:
a. S = {$0, $1, $2, $3}
b. S = {$0, $3, $6, $9}
c. S = {-$2, $1, $4, $7}
The sample space S for the net amount you win (after deducting the cost of pay) is S = {-$2, $1, $4, $7}.
What is cost?
A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to obtain it.
Let, a game consists of drawing three cards at random from a deck of playing cards.
You win $3 for each red card that is drawn.
It costs $2 to play.
After deducting the cost of pay the amount will start from -$2.
For first red card drawn you win $3.
So, the amount becomes, -$2 + $3 = $1.
For second red card drawn you again win $3.
So, the next amount becomes $1 + $3 = $4.
For third red card drawn the amount becomes,
$4 + $3 = $7.
Hence, the sample space S for the net amount you win is
S = {-$2, $1, $4, $7}.
To know more about the cost, click on the link
https://brainly.com/question/25109150
#SPJ4
visit your local library: on a recent saturday, a total of 1343 people visited a local library. of these people, 253 were under age 10, 466 were aged 10-18, 174 were aged 19-30, and the rest were more than 30 years old. one person is sampled at random. (a) what is the probability that the person is less than 19 years old? (b) what is the probability that the person is more than 10 years old? part 1 of 2 (a) what is the probability that the person is less than 19 years old? round your answer to four decimal places.
Probability of people less than 19 year old = 0.5343
Probability of people greater than 10 year old = 0.8116
What is probability?
Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.
People under age 10 = 253
People between the age of 10-18 = 466
People between the age of 19-30 = 174
People above the age of 30 = 450
Total no. of people = 1343
a) people less than 19 years old = 253+466 = 719
probability of people<19 year old = P(age<19) = 719/1343 = 0.5354
b) people of age greater than 10 = 466+174+450 = 1090
probability of people >10 year old = P(age>10) = 1090/1343 = 0.8116
To learn more about probability:
https://brainly.com/question/13604758
#SPJ4
Write the equation of the given line in slope intercept form
The equation of the line in slope-intercept form is: y = 5/2x.
What is the Slope-intercept Form of a Line?If the value of the slope of the line is represented by m, and y-intercept of the line is b, therefore, the equation of the line in slope-intercept form can be written as: y = mx + b.
The slope of the line (m) = rise/run = 5/2
m = 5/2
The line intercepts the y-axis at 0. The y-intercept therefore is b = 0.
To write the equation of the line, substitute m = 5/2 and b = 0 into y = mx + b:
y = 5/2x + 0
y = 5/2x
Learn more about the slope-intercept form on:
https://brainly.com/question/25826868
#SPJ1
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!
Time intervals = 14/7 = 2
Final Amount = 40(1/2)² = 10
Choose the equation for the line in slope-intercept form. A graph of a diagonal line on a coordinate plane going up and to the right. The line passes through the points zero comma negative 3 and 2 comma negative 2. y=2x+3 y=12x+3 y=12x−3 y=−12x−3
will the line y=4x+1 pass through the point (2,9)?
Answer: Yes
Step-by-step explanation:
y=4x+1
(2,9) 2 is x, 9 is y
9=4(2)+1
9=8+1
9=9
Which statement best explains whether the equation y = 2x − 4 represents a linear or nonlinear function?
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because its graph contains the points (0, 2), (2, 3), and (4, 4), which are not on a straight line.
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
What is linear equation?
Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.
Given, the equation y = 2x -4
Which is linear function and have y a dependent variable and x be the independent variable,
because value of y depends upon the value of x.
Hence, a is the correct answer.
To know more about linear equation, visit:
https://brainly.com/question/11367265
#SPJ1
Answer: A
Step-by-step explanation: Trust me
suppose you are performing a hypothesis test with σ unknown, n=22, α=0.05, and the following hypotheses: h0: μ = 24 h1: μ ≠ 24 what is the decision rule?
Reject H0 if the test statistic is less than -1.321 or greater than 1.321 .
What is a hypothesis simple definition?
A tested assertion regarding the relationship between two or more variables .
a theory put out to explain an observed occurrence is referred to as a hypothesis (plural: hypotheses) in a scientific context.
Reject H0 if the test statistic is less than -1.321 or greater than 1.321 .
Learn more about hypothesis
brainly.com/question/29519577
#SPJ4
Which expression is equivalent to (6x^-9x) - (2x - 3)?
The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3
What is an equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.
To find equivalent expression we can simplify the expression.
Therefore,
(6x² - 9x) - (2x -3)
open the brackets
6x² - 9x - 2x + 3
combine like terms
Therefore,
(6x² - 9x) - (2x -3) = 6x² - 11x + 3
learn more on equivalent expression here: https://brainly.com/question/6997280
#SPJ1
Find the difference 4 3/12 - 2 8/12
Answer:19/12 or 1 7/12
Step-by-step explanation:
51/12 - 32/12=19/12
1 7/12
Answer:
1 7/12
Step-by-step explanation:
4 3/12 - 2 8/12
First, subtract the integers:
2 3/12 - 8/12
Since 3/12 cannot subtract 8/12, we can take 1 from the 2 and turn it to 12/12 to add to our 3/12:
1 15/12 - 8/12
Simplify:
1 7/12
PLEASE MARK AS BRAINLIEST!Has the marrying age of a man changed over the years? the united states bureau of the census takes a formal count of everyone in the u. S. Every 10 years and has provided the following data that gives the median age of an american man at the time of his first marriage. Year 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 median age 25. 1 24. 6 24. 3 24. 3 22. 8 22. 8 23. 2 24. 7 26. 1 26. 8 determine the average rate of change in median age per year from 1950 to 1990.
The average rate of change in median age per year from 1950 to 1990 is 0.085 years of age per year.
The median is the mid-value in a set of data. to find it we first arrange the data set from smallest to largest, then pick the middle value which divides the data set in half.
From the given table,
The median age at the time of the first marriage in 1950 = 22.8 years,
While the median age in 1990 = 26.1 years,
Hence, the average rate of change in median age per year from 1950 to 1990
= (22.8-26.1)/(1950-1990)
= (-3.3)/(-40)
= 0.0825 years of age per year.
Read more about Median:
brainly.com/question/26177250
#SPJ4
a punch recipe calls for 1 1/2 quarts of sparkling water and 3/4 of a quart of grape juice. how much of each ingredient would you need to make 75 quarts of punch?
50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.
The ratio of sparkling water to grape juice is,
1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) = 2 : 1
The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is
2/3 · 75quarts = 50 quarts
Then the grape juice content is,
1/3 · 75 quarts = 25 quarts
Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.
To know more about ratios and proportions follow
https://brainly.com/question/2914376
#SPJ1
Bob bad $50. he spent $28.67 for a new backpack. How much money does he have left?
Answer: $21.33
Step-by-step explanation: 50 - 28.67 = 21.33
Simplify an expression for the perimeter of the rectangle.
Answer:
P = 16w - 4
Step-by-step explanation:
P = (5w-2 + 3w)2
P = (8w-2)2
P = 16w - 4
Use a calculator to perform the indicated operations. Round the result to two decimal places.
[tex]
19.42-34.8(19.3)+10.23+5.78
[/tex]
Using PEMDAS to solve the mathematical expression, the result is -637.947
Mathematical OperationThe mathematical operation refers to calculating a value using operands and a math operator. The symbol of the math operator has predefined rules to be applied to the given operands or numbers.
In this kind of problem, we need to use the PEDMAS rule which is
Parenthesis, Exponents, Division, Multiplication, Addition and Subtraction.
The order in which this must be prioritized is from parenthesis and the least is subtraction.
Applying PEMDAS to this mathematical operation, we would have
19.42 - 34.89(19.3) + 10.23 + 5.78
Using a calculator which follows this rule, we would have;
19.42 - 34.89(19.3) + 10.23 + 5.78 = -637.947
Learn more on mathematical operation here;
https://brainly.com/question/550188
#SPJ1
The interior angles of a polygon are the angles formed inside a polygon by two adjacent sides. The sum S of the measures of the interior angles of a polygon with n sides can be found using the formula S = 180(n - 2). The sum of a polygon’s interior angle measures is 1260°. How many sides does the polygon have?
The number of sides in the polygon that has 1,260° as the sum of the interior angles, found using the formula for the sum of the interior angles in the polygon, S = 180·(n - 2) is 9 sides
What is a polygon in geometry?A polygon is a figure consisting of a specified number of straight sides such that they form a closed loop. The number of sides in a polygon are three or more.
The formula for the sum of the interior angles of a polygon, S, can be be used to find the number of sides in the polygon as follows;
S = 180·(n - 2)
Where;
n = The number of sides the polygon has
The sum of the interior angles in the specified polygon = 1,260°
The number of sides in the polygon can be found by equating the formula for S to 1,260° as follows;
When S = 1.260°, we get;
1,260 = 180·(n - 2)
Which indicates;
n - 2 = 1,260 ÷ 180 = 7
Therefore; n - 2 + 2 = 7 + 2 = 9
n = 9
The number of sides in the polygon that has a sum of the interior angles as 1,260° is therefore, n = 9 sidesLearn more about polygons here:
https://brainly.com/question/12291395
#SPJ1
Two numbers that end with 376 are multiplied. What 3-digit number do the last three digits of the result make?
Answer:
376
Step-by-step explanation:
which of the following functions of xx is guaranteed by the extreme value theorem to have an absolute maximum on the interval [0,4][0,4] ?
X=pi/2 only in the interval 0 to 4 . We have the maximum value of f(x) = sinx = 1
What is function interval ?
If the value of the function f (x) grows with an increase in the value of x, the function interval is said to be positive.
The function interval, on the other hand, is said to be negative if the value of the function f (x) decreases as the value of x increases.
First of all to apply the extreme value theorem function must be countions at the interval 0 to 4.
F(x)=(x^2-16)/(x^2+x-20) is countinious int the given interval .
Now we find
F'(x)= d(F(x))/dx=1/(x+5)^2 so here we don't have in critical point therefore this choice is incorrect
Similarly if we take
F(x)= sinx
F'(x) = cosx
For critical point ,
Cosx =0
X=pi/2 only in the interval 0 to 4
And this point we have the maximum value of f(x) = sinx = 1
Learn more about function interval
brainly.com/question/17238753
#SPJ4
