Using a linear function and the work integral, it is found that the work that was done lifting the sand this far is of 944 ft-lb.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For the weight of the bag of sand in this problem, we have that:
The initial weight of the bag was of 144 lb, hence the y-intercept is of b = 144.When the bag had been lifted 18 ft, 0.5 x 144 = 72 lb were gone, that is, 4 lb were gone for each ft the bag was lifted, hence the slope is of m = -4.Hence the weight of the bag after being lifted x feet is given by:
W(x) = 144 - 4x.
What is the work of a function?The work realized for a function f(x) in an interval [a,b] is given by the following integral:
[tex]W = \int_{a}^{b} f(x) dx[/tex]
For this problem, the function and the bounds of the interval are given as follows:
f(x) = 144 - 4x.a = 0, b = 18.Hence the work is given by:
[tex]W = \int_{a}^{b} (144 - 4x) dx[/tex]
W = 144x - 2x², from x = 0 to x = 18.
Applying the Fundamental Theorem of Calculus:
W = 144(18) - 2(18)² - 144(0) + 2(0)² = 1944 ft-lb.
The work that was done lifting the sand this far is of 944 ft-lb.
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i need help assap dont judge
There is exactly 1 pair of parallel sides in the
following shape.
Base=6 base=8 height=5
What is the area of the shape?
The area of the shape with parallel sides is 35 unit² of trapezoid .
Describe the trapezoid shape?
An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.A = (1/2) * (a + b)h
Where a, b is the length of the parallel sides and h is the height of the trapezoid.
Given that a = 8, b = 6 and h = 5, hence:
A = (1/2) * (8 + 6) * 5 = 35 unit²
The area of the shape with parallel sides is 35 unit².
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Jim began a 86-mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, his bicycle chain broke,
so he finished the trip walking. The whole trip took 4 hours. If Jim walks at a rate of 4 miles per hour and rides at 32
miles per hour, find the amount of time he spent on the bicycle.
The amount of time he spent on the bicycle is; 2.5 hours
How to solve algebra word problems?
The formula that shows the relationship between distance, speed and time is;
distance = velocity * time
Let W = walking time
B = bicycling time
Thus, from the given data we have;
86 = 4W + 32B
W + B = 4
W = 4 - B substitute 6-B for W in 86 = 4W + 32B to get;
86 = 4(4 - B) + 32B
86 = 16 - 4B + 32B
86 = 16 + 28B
70 = 28B
B = 70/28
B = 2.5 hours on the bicycle
W = 4 - 2.5= 1.5 hours walking
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Help help me me me me
Answer:
(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)
Step-by-step explanation:
Answer:
(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)
A scale drawing of a spider is 5 centimeters long. The actual spider is 10
millimeters long.
a. What is the scale of the drawing?
b. What is the scale factor of the drawing?
c. The spiders mate is 8mm, what size should the drawing for it be in cm? Explain how to decide whether to use the scale or scale factor?
(a) The scale of the drawing is in centimeters.
(b) The scale factor of the drawing is 5 mm.
(c) The size of the spider's mate drawing should be 4 cm.
Given scale drawing of a spider is 5 cm long.
The actual spider is 10 mm long
(a) The scale of the drawing is in centimeters because the scale drawing of a spider given is in 5 centimeters,
(b) Scale factor:
The scale factor shows by how much the original model has been multiplied or divided by to get the measurements of the drawing.
In this case, the spider is 10 mm long but the drawing length is 5 cm.
Let’s convert both into the same units
5 cm - 50 mm
Original - 10 mm
Painting -50 mm
X - scale factor
50 = X * 10
X = 50/10 = 5 mm
The spider has been multiplied/ enlarged by a scale factor of 5 mm to draw the painting.
(c) Given the spider's mate is 8mm long.
Now for the drawing, we need to choose the scale factor as above to get the perfect measurement.
So, the 8 mm spider has been enlarged by a scale factor of 5 mm to get the size for drawing.
= 8 * 5
= 40 mm
= 4 cm
The size of the drawing should be 4 cm.
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Your answer is incorrect.
Suppose 2 quarts of pure antifreeze is mixed with 3 quarts of a solution that is 18% antifreeze.
Answer the questions below. Do not do any rounding.
(a) How many quarts of antifreeze are in the resulting mixture?
(b) What percentage of the resulting mixture is antifreeze?
a) There is 2.54 quarts in the resulting mixture (b) The percentage of the resulting mixture is 50.8% antifreeze.
Percentage is defined as parts per hundred. Percentage is calculated by dividing the given amount by the total amount and multiplying by 100.
a) 18% of 3 quarts antifreeze contains (18/100) × 3 quarts of antifreeze.
amount of antifreeze = 0 .18 × 3 = 0.54 quarts
Now to this solution 2 quarts of antifreeze is added.
Therefore total amount of antifreeze in the resulting mixture = 2 + 0.54 = 2.54 quarts.
b) Total amount of the resulting mixture = 2 + 3 = 5 quarts
amount of antifreeze in the mixture = 2.54 quarts
Percentage antifreeze in the mixture = (2.54 / 5) × 100 % = 50.8 % .
Therefore there is 2.54 quarts of antifreeze in the mixture and its percentage is 50.8% of the total mixture.
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Find the equation of the exponential function represented by the table below:
x
0
1
2
3
Y
5
2.5
1.25
0.625
Answer:
x = r ,r is a whole number
y = 5(.5)^r
y=5(.5)
Step-by-step explanation:
The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].
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.
For x=0 for f(0)=(5)[tex](0.5^{0} )[/tex]=5
⇒ x=1 for f(1)=(5)[tex](0.5^{1} )[/tex]=2.5
⇒ x=2 for f(2)=(5)[tex](0.5^{2} )[/tex]=1.25
⇒ x=3 for f(3)=(5)[tex](0.5^{3} )[/tex]= 0.625
Therefore,The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].
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help me me me me me me me
The average price per square foot in 2002 was approximately $85.86.
What is a polynomial function?A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.
Example: a + bx + cx²
We have,
P(t) = 0.019t³ - 0.287t² + 3.073t + 55.130
Where t = number of years.
From 1992 to 2002 we have,
2002 - 1992 = 10 years
Now,
P(10) = 0.019(10)³ - 0.287(10)² + 3.073(10) + 55.130
P(10) = 19 - 28.7 + 30.73 + 55.130
P(10) = 85.86
Thus the average price per square foot in 2002 was approximately $85.86.
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Write a sequence that has the stated property.
The 1st difference of the sequence can be modeled with the expression 8x-5.
The sequence that can be modeled by the expression is T(n+1) = Tn + 8x - 5 where n >= 1
How to determine the sequence that can be modeled by the expression?The expression of the first difference is given as
8x - 5
Rewrite properly as
d = 8x - 5
Where the common difference is represented by d
The common difference of an arithmetic sequence is calculated as
d = T2 - T1
So, we have
T2 - T1 = 8x - 5
Add T1 to both sides of the equation
So, we have
T2 = T1 + 8x - 5
Express 2 as 1 + 1
So, we have
T(1+1) = T1 + 8x - 5
Express 1 as n
So, we have
T(n+1) = Tn + 8x - 5 where n >= 1
Hence, the sequence that can be modeled by the expression is T(n+1) = Tn + 8x - 5 where n >= 1
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help pls i gyg soonn
Answer:
Step-by-step explanation:
8806
1. The soccer team is making pizzas for a fundraiser. They put1/4 of a pound of cheese on each pizza. If they have 12 one-pound packages of cheese, how many pizzas can they make? pizzas ?
2. Dan purchased 3 ½ yards of mulch for his garden. Mulch costs $25 a yard. How much did Dan pay for his mulch? $
3. Mr. Hamilton owns 2 ¾ acres of land. He plans to buy 1 and 1/3 more acres. How many acres will he own? Write your answer as an improper fraction. acres
1) The soccer team can make 48 pizzas using 12 one-pound packages of cheese.
2) The total cost Dan paid for the mulch was $87.50.
3) The number of acres that Mr. Hamilton will own after the planned purchase is 3¹³/₁₂.
How are the values determined?The above values are determined using mathematical operations of addition, division, and multiplication.
For instance, Mr. Hamilton's land increased to 3¹³/₁₂ through the addition of 2¾ and 1¹/₃ acres.
The total cost that Dan paid for the mulch was a multiplication operation.
The number of pizzas the soccer team could make resulted from a division operation.
Data and Calculations:1) Quantity of cheese on each pizza = 1/4 lb
The total quantity of cheese = 12 lb
The number of pizzas to make = 48 (12/1/4) or (12/0.25)
2) The number of yards of mulch purchased = 3¹/₂ yards
Cost of mulch per yard = $25
The total cost for the mulch = $87.50 ($25 x 3¹/₂)
3) Measurement of land owned = 2¾ acres
The planned purchase of additional land = 1¹/₃
The total acres Mr. Hamilton will own = 3¹³/₁₂ (2¾ + 1¹/₃)
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A college has a financial aid formula that applies to applicants whose family's income is below a certain threshold. The financial aid can be determined by the function f(x)=10000+1000x,f(x)=10000+1000x, where xx is the number of siblings (including half siblings and step siblings) that the applicant has living in their household. Find and interpret the given function values and determine an appropriate domain for the function.
The numeric values of the function are given and explained as follows:
f(-2) = 8000, meaning a qualifying applicant with -2 siblings would receive a financial aid of $8,000. This interpretation does not make sense in the context of the problem.f(4) = 14,000, meaning a qualifying applicant with 4 siblings would receive a financial aid of $14,000. This interpretation makes sense in the context of the problem.The domain is: {x is a whole number and x ≥ 0}.How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For this problem, the function is given by:
f(x) = 10000 + 1000x.
In which:
The output f(x) is the financial aid.The input x is the number of siblings in the family.When x = -2, we have that:
f(-2) = 10000 + 1000(-2) = 8000.
Hence:
f(-2) = 8000, meaning a qualifying applicant with -2 siblings would receive a financial aid of $8,000. This interpretation does not make sense in the context of the problem.
When x = 4, we have that:
f(4) = 10000 + 1000(4) = 14,000.
Hence:
f(4) = 14,000, meaning a qualifying applicant with 4 siblings would receive a financial aid of $14,000. This interpretation makes sense in the context of the problem.
The number of siblings is a discrete number, and has to be of at least 0, hence:
The domain is: {x is a whole number and x ≥ 0}.
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Karen must choose a number between 49 and 95 that is a multiple of 2, 8, and 10. Write all the numbers that she could choose. If there is more than one
number, separate them with commas.
Answer:
80
Step-by-step explanation:
80 is the only number that is a multiple of ALL 2, 8 and 10
Answer:
the only answer that is a multiple of 2,8 and 10 between 49 and 95, is 80.
Please help me with 7, 11, 15, 9, 13, 17, . Please explain your answer for each one. I will give an Brainly and extra points.
The truth values of the composite propositions are listed below:
Case 7: T, Case 9: T, Case 11: F, Case 13: T, Case 15: F, Case 17: F
What are the truth values of composite proposition?
Propositions are constructions that contain itself a truth value. This exercise presents a proposition p is false and proposition q is true. Then, we proceed to find the truth value of each composite proposition, that is, a combination of propositions and operators.
Case 7
p → F Given¬ p → T Definition of negation / ResultCase 9
p → F, q → T Givenp ∨ q → T Definition of disjunction / ResultCase 11
p → F, q → T Given¬ q → F Definition of negationp ∨ ¬ q → F Definition of disjunction / ResultCase 13
p → F, q → T Given¬ p → T, ¬ q → F Defintion of negation¬ p ∨ ¬ q → T Definition of disjunction / ResultCase 15
p → F, q → T Givenp ∧ q → T Definition of conjunction¬ (p ∧ q) → F Definition of negation / ResultCase 17
p → F, q → T Given¬ p → T, ¬ q → F Definition of negation ¬ q ∨ p → T Definition of disjunction¬ p ∧ (¬ q ∨ p) → T Definition of conjunction¬ (¬ p ∧ (¬ q ∨ p)) → F Defintion of negation / ResultTo learn more on propositions: https://brainly.com/question/13011669
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20 push-ups in 2days
Answer: ok?
Step-by-step explanation:
PLEASE CAN SOMEONE ANSWER THIS! Thank you pls
Answer: draw a parallelogram like figure A and make it the same area of the unlabeled rectangle.
what is 3 11/12 - 3/4? I have an upcoming test, and I need someone to explain it step-by-step.
Answer:
3 1/6
Step-by-step explanation:
First, we turn 11/12 and 3/4 to have the same denominator
3/4 x 3 is 9/12
11/12- 9/12 is 2/12
Now we add the extra 3 to 2/12 which is 3 2/12
3 2/12 can be simplified to 3 1/6
Based on the graph of z (x), what is the value of z-¹ (-2)?
Answer:
-9
Step-by-step explanation:
[tex]z^{-1}(-2)=k \implies z(k)=-2 \\ \\ k=-9 \implies z^{-1}(-2)=-9[/tex]
Bob sells cars. His income is based on a graduated scale. If he earns %5 commission for the first $50,000 in scales %8 commission for sales over $50,000, then how much would he earn if his total sales were $95,000
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Determine the following geometric probabilities:
A. Tal-mart parking lot is 500 feet by 800 feet. You just parked your car, which is
approximately a rectangle with the dimensions 6 feet by 10 feet. A bird flying
overhead has just relieved himself by having a bowel movement. If the waste
material has an equal chance of landing anywhere in the parking lot then what are
the chances of it hitting your car.
The geometric probability which represents the chances of having the waste material hit the car as described in the task content is; 3/20,000.
What is the probability of having the waste material hit the car?It follows from the task content that the probability which is to be evaluated is the chance of having the waste material hit the car.
First, since the dimension of the parking lot is; 500 by 800 feet. It follows that;
Area of parking lot = 500 × 800 = 400,000.
Also, since the dimension of the rectangular car is approximately 6 by 10. It follows that;
Area occupied by car = 6 ×10 = 60.
Consequently, the chances of the waste material hitting the car is the ratio of desired outcome to the possible outcome and hence is;
P = 60/400,000
P = 3/20,000.
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x^2+48=14x
Show work please
Answer:
Step-by-step explanation:
x^2 - 14x = -48
x^2 +48 -14 x
x^2 - 14x - 48 = 0
a = 1
b = -14
c = 48
x=8, x=6
given line A has a slope of m=-2/5, what is the slope of a line parallel to line A
Given line A has a slope of m = -2/5, the slope of a line parallel to line A is m = -2/5
What is the slope of a line?The slope of a line y = mx + c where
m = slope of line and c = y - interceptIs given by m = Δy/Δx where
Δy = change in y and Δx = change in xHow to find the slope of a line [parallel to another line?Given a line y = mx + c where
m = slope of line and c = y - interceptAlso, given another line y' = m'x + c' where
m' = slope of line and c' = y - intercept.If y is parallel to y' then their slopes are equal. That is m = m'
How to find the slope of the line parallel to line A?Given that line A has a slope of m = -2/5, then by the condition above, the slope of a line paralllel to line A must also equal m.
So, the slope of a line parallel to line A is m = -2/5
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I need help with question!
The equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost?
The total cost based on the equation illustrated as y= 10x is $230.
How to illustrate the information?It should be noted that from the information, the equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost.
Therefore, it should be noted that the total cost when x is 23 will be illustrated thus:
y = 10x
y = 10 (23)
y = 230
Therefore, the total cost based on the equation illustrated as y= 10x is $230.
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The equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost. Calculate the total cost when x is 23.
Write the equation of a line perpendicular to 3x - 8y = - 7 that passes through the point (-3,3).
3y = -8x -27
Solution :
A line equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
Given line: 3x - 8y = -7
-8y = -7 -3x
y=- (-7 -3x)/8
y= 7+3x/8
So, the slope (m1) = 3/8
Let’s consider the slope of the line perpendicular to the given line as m2
Then, m1 x m2 = -1
3/8 x m2 = -1
m2 = -8/3
Now,
The equation of the line perpendicular to the given line and passing through the point (-3, -3) will be
y – y1 = m (x – x1)
y – (-3) = -(8/3) (x – (-3))
y + 3 = (-8/3) (x +3)
3y + 3 = - 8x - 24
3y = -8x -24-3
3y = -8x -27
Thus, the equation of the required line is 3y = -8x -27
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College Level Quantitative Reasoning - See Screenshot
The absolute and relative errors are 0. 8 and 0. 01 respectively.
What is absolute error?Absolute error can be defined as the difference between the inferred or measured value and the actual value of a given quantity.
The formula for absolute error is expressed as;
Absolute error = | VA - VE |
Where;
VA is the actual value = 60. 8 InchesVE is the expected value = 60. 0 InchesSubstitute the values into the formula
Absolute error = | 60. 8 - 60. 0|
Find the difference
Absolute error = | 0. 8|
Absolute error = 0. 8
Relative error = Absolute error/ actual value
Relative error = 0. 8/ 60. 0
Relative error = 0. 01
Thus, the absolute and relative errors are 0. 8 and 0. 01 respectively.
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Find the values of a and b that make f continuous everywhere.
f(x) =
x2 − 4
x − 2 if x < 2
ax2 − bx + 1 if 2 ≤ x < 3
4x − a + b if x ≥ 3
The function is a continuous function. Then the value of variables a and b will be 2.5 and 3.5, respectively.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The piecewise function is given below.
[tex]f\left ( \rm x \right ) = \left\{\begin{matrix} \rm \dfrac{x^2 - 4}{x-2} \ or \ x + 2,& \rm x < 2\\ \rm ax^2 - bx + 1, & \rm 2\leq x < 3\\ \rm 4x - a + b, & \rm x \geq 3\end{matrix}\right.[/tex]
At x = 2, the function is continuous, then we have
2 + 2 = a(2²) - 2b + 1
4a - 2b = 3 ...1
At x = 3, the function is continuous, then we have
a(3²) - 3b + 1 = 4(3) - a + b
10a - 4b = 11 ...2
From equations 1 and 2, we have
8a - 10a = 6 - 11
2a = 5
a = 2.5
Then the value of b will be
10(2.5) - 4b = 11
25 - 4b = 11
4b = 14
b = 3.5
The value of the variable a and b will be 2.5 and 3.5, respectively.
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How many grams are in 0.0564 mol of sodium?
Answer:
1.296623028 grams
Step-by-step explanation:
your answer is 1.296623028 grams because you multiply the given number of moles which was 0.0564 by the molar mass to get the grams
1/4 minus 3/8 in fraction form
Answer: -1/8 is the answer
A total of 52 microphones are to be purchased. Each microphone costs $548. Estimate the total purchase price by using rounded numbers.
The total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A total of 52 microphones are to be purchased. Each microphone costs $548.
Let x be the total purchase price
x = 52x548
x = $28496
Thus, the total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.
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