The volume of the shed ordered by Lorie to hold her gardening supplies is (option a) 1423.5 cubic ft.
Given,
Lorie ordered a shed to hold her gardening supplies.
The length of the shed, l = 18.25 feet
The width of the shed, w = 15 feet
The height of the shed, h = 5 1/5 feet = 26/5 = 5.2 feet
We have to determine the volume of the shed:
From the given data we can assume that the shed is like a cuboid. So to determine the volume, we can use the cuboidal formula.
That is,
Volume = length × width × height
V = l × w × h
V = 18.25 × 15 × 5.2
V = 1423.5 feet
Therefore, the volume of the shed ordered by Lorie to hold her gardening supplies is 1423.5 feet.
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PLEASE PLEASE HELP Explain how to find the average value of a function and contrast this with finding the average rate of change
The average value of function can be calculated using the formula →
[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex] and to find average rate of change of function can be calculated using → f '(x) = [tex]$\frac{f(b)-f(a)}{b-a}[/tex].
We have a function (say f(x)).
We have to find the average value of a function and the average rate of change of function.
What is a function in Mathematics?A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.
According to the question -
PART - A → Finding the Average value of a function.
The average (or the mean) value of f (x) on [a, b] is defined by -
[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]
PART - B → Finding the Average Rate of Change of a function.
The average rate of change of function f(x) is found out as follows -
f '(x) = [tex]$\frac{f(b)-f(a)}{b-a}[/tex]
Hence, to find the average value of function -
[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]
and to find average rate of change of function -
f '(x) = [tex]$\frac{f(b)-f(a)}{b-a}[/tex].
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Which equation represents the ellipse with vertices located at (3,-3) and (3,-13) and foci at (3,-5) and (3,-11)?
The equation of the ellipse in standard form is equal to (y + 8)² / 25 + (x - 3)² / 16 = 1. (Correct choice: D)
How to derive the equation of an ellipseIn this problem we find the case of an ellipse whose center is located at a point distinct of the origin and whose major semiaxis is parallel to the y-axis. The standard form of the equation of the ellipse is:
(y - k)² / a² + (x - h)² / b² = 1
Where:
(h, k) - Center of the ellipse.a - Length of the major semiaxis.b - Length of the minor semiaxis.First, determine the coordinates of the center:
(h, k) = 0.5 · (3, - 3) + 0.5 · (3, - 13)
(h, k) = (3, - 8)
Second, calculate the length of the minor semiaxis:
a = 0.5 · [- 3 - (- 13)]
a = 5
c = 0.5 · [- 5 - (- 11)]
c = 3
b = √(a² - c²)
b = 4
Third, substitute all the parameters in the standard formula:
(y + 8)² / 25 + (x - 3)² / 16 = 1
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identify the postulate or theorem that proves j∥k.
Given: ∠2 and ∠3 are supplementary.
Yes, ∠2 and ∠3 are postulate or theorem that proves the condition is identified as supplementary.
∠1 and ∠2 are supplementary (Linear Pair Theorem)
m∠1 + m∠2 = 180◦ (Definition of supplementary ∠s)
∠1 ≈ ∠3 (Given)
m∠1 = m∠3 (Definition of ≈)
m∠3 + m∠2 = 180◦( Subst . prop . of ≈)
∠2 and ∠3 are supplements (Definition of supplementary ∠s)
An unsubstantiated claim that is assumed to be true is referred to as a postulate. A provable true assertion is referred to as a theorem. A line has at least two points, according to postulate 1. A plane has at least three noncollinear points, according to postulate 2.
Hence, postulate or theorem that proves j∥k and also ∠2 and ∠3 are supplementary.
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Solve the system of equations. Remember: systems with one solution will have an answer in the form of an ordered triplet.
Example: (3, -4, 10)
For systems with infinite solutions or no solutions, write the words ‘infinite solutions’ or ‘no solutions’.
x + 2y -z = 2
2x - 7y + 5z = 3
-4x + y + 2z = 4
The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)
System of Linear EquationsFrom the question, we are to solve the given system of linear equations
The given system of linear equation is
x + 2y - z = 2 ----------- (1)
2x - 7y + 5z = 3 ----------- (2)
-4x + y + 2z = 4 ----------- (3)
From equations (1) and (2), eliminate z
5 × ( x + 2y - z = 2
1 × ( 2x - 7y + 5z = 3
---------------------------------------
5x + 10y -5z = 10
2x -7y + 5z = 3
Add the resulting equations
7x + 3y = 13 ----------- (4)
From equations (2) and (3), eliminate z
2 × ( 2x - 7y + 5z = 3
5 × ( -4x + y + 2z = 4
-----------------------------------
4x - 14y + 10z = 6
-20x + 5y + 10z = 20
Subtract the resulting equations
24x - 19y = -14 ---------- (5)
Now, solve equations (4) and (5) simultaneously
7x + 3y = 13
24x - 19y = -14
Eliminate y
19 × ( 7x + 3y = 13
3 × ( 24x - 19y = -14
---------------------------------
133x + 57y = 247
72x - 57y = -42
Add the resulting equations
205x = 205
x = 205/205
x = 1
Substitute the value of x into equation (4)
7x + 3y = 13
7(1) + 3y = 13
7 + 3y = 13
3y = 13 - 7
3y = 6
c = 6/3
y = 2
Substitute the values of x and y into equation (1)
x + 2y - z = 2
1 + 2(2) - z = 2
1 + 4 - z = 2
1 + 4 - 2 = z
3 = z
z =3
The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)
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Can someone help me with this question? It's due tomorrow :(
The measures of the angles D, F and B are 43°, 105° and 32°, respectively. (Correct choice: C)
What are the values of the missing angles?
Herein we find a geometric system generated by two parallel lines and two lines that pass through the two lines. The values of the missing angles by using triangle properties and concepts of alternating internal angles, supplementary angles and vertical angles. Now we proceed to find the measures of the missing angles:
m ∠ C + m ∠ F + m ∠ D = 180° Sum of the measures of internal angles in a trianglem ∠ D = 180° - 137° = 43° Supplementary anglesm ∠ F = 180° - 32° - 43° = 105° Step 1 / Algebram ∠ F' = 105° Step 3 / Vertical anglesm ∠ B = m ∠ C = 32° Internal alternating anglesTo learn more on angles: https://brainly.com/question/14954407
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Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Can someone pls help me with this question
Domain: (-infinity, 5)
Range; [-3, infinity)
Help please just need to see if I’m doing this right
3x = 3x is true for all values of x.
Hence, x| x is a set all real numbers. ( -∞,∞ )
What is the solution to the given equation?Given the equation in the question;
3(2x + 2) - 3x = 6 + 3xx = ?Remove the parenthesis using the distributive property.
3(2x + 2) - 3x = 6 + 3x
3×2x + 3×2 - 3x = 6 + 3x
6x + 6 - 3x = 6 + 3x
6x - 3x = 6 - 6 + 3x
6x - 3x = 3x
3x = 3x
3x = 3x is true for all values of x.
Hence, x| x is a set all real numbers. ( -∞,∞ )
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Which are numbers are rational?
Answer: D, E, A
Step-by-step explanation: By friend got rejected by them hopefully you don't.
Answer:
F, C, and D
Step-by-step explanation:
Solve this
m−152=3+m10−3
m=?
Answer: -152/9
Step-by-step explanation:
m−152=3+m10−3
m−152=3+10m−3
m−152=10m+3−3
m-152=10m
-152=9m
m=-152/9
Only answer if you are 100%. sure but pls answer quickly
Answer:
It's A, 9.23 × 10⁻⁴
Answer:
A
Step-by-step explanation:
All my work is provided in the attached screenshot!
In the following expression, the 2 distributes to the 3 and to the 4 :
(2)(3)(4) = (2)(3)(2)(4)
True or false?
Person A leaves his home to visit his cousin, person B, who lives 78 miles away. He travels at an average rate of 50 miles per hour. One half-hour later, person B leaves her house to visit person A, traveling at a
average rate of 56 miles per hour. How long after person B leaves will it be before they meet?
Answer:
[tex]\frac{1}{2}[/tex] hour later
Step-by-step explanation:
Since Mr.A has already traveled 25 miles there are 53 miles left to person B's house. In half an hour, Mr. A will have traveled 25 miles, while person b will have traveled 28. 25 + 28 = 53.
Lance is putting a new countertop in his kitchen and is comparing the cost of granite and marble. The cost of granite is $42.78 a square foot. The cost of marble is $57.23 a square foot. If Lance needs 30.25 square feet of countertop, how much more would he pay for the marble countertop than the granite countertop?
Lance would have to pay $437.1125 more for the marble countertop than the granite countertop .
Cost of granite per square feet = $ 42.78
Cost of marble per square feet = $ 57.23
Lance needs 30.25 square feet of countertop,
therefore ,
if he use granite , he would have to pay
30.25 * ( 42.78 ) = $ 1294.095
if he use marble , he would have to pay
30.25 * ( 57.23 ) = $ 1731.2075
Hence , he would have to pay $ 1731.2075 - $ 1294.095 = $437.1125 more for the marble countertop than the granite countertop .
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In a survey of 100 resorts, it was found that
28 had a spa.
44 had a children's club.
11 had a spa and children's club.
9 had all three features.
Complete parts a) through e).
59 had a fitness center.
16 had a spa and a fitness center.
21 had a fitness center and children's club.
a) How many of the resorts surveyed had only a spa?
(Type a whole number.)
Out of 100 resorts surveyed, it was found out that 28 resorts only have spa inside them.
We have a survey of 100 resorts.
We have to determine how many of the resorts surveyed had only a spa.
What are sets ?Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form.
According to the question -
Out of 100 resorts, we have to find the resorts that contain only spa.
The whole number representing the number of resorts that only have spa is 28.
Hence, 28 out of 100 resorts only have spa.
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If a number is 10 more than two-thirds of the same number, then find the number.
Answer:
30
Step-by-step explanation:
Hello!
Let the unknown number be x.
Converting from English to Algebra, we are given the equation:
[tex]x = 10 + \frac23x[/tex]Solve for x by isolating the variable.
Solve for x[tex]x = 10 + \frac23x[/tex] Multiply everything by 3 to remove the fraction[tex]3x = 30 + 2x[/tex] Subtract 2x from both sides[tex]x = 30[/tex]The value of that number is 30.
please help
please hurry
The graph of the function is graph (b)
How to determine the graph of the function?The equation of the graph is given as
f(x) = |x - 3|
The above equation is an absolute value function
An absolute value function is represented as
f(x) = a|x - h| + k
Where the vertex is
Vertex = (h, k)
From the given equation, we have
(h, k) = (3, 0)
a = 1
When a is positive, the graph opens up
From the graphs in the options, we have graph (b) that has the following features
(h, k) = (3, 0) and it opens upward
Hence, the graph of the function is graph (b)
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what is 5 4/5 as in improper fraction
Answer:
29/5
Step-by-step explanation:
5 x 5 +4 = 29
now in fraction form it is 29/5.
Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value.
At a boating and sports store, the cost of renting a personal watercraft is $36.40 per half hour, which includes a 4% sales tax. Determine the cost of a half hour rental before tax.
The equation is _____. The cost of a half hour rental is $____ per half hour.
(Type an equation using x as the variable.)
Answer: $40
Step-by-step explanation:
Given the following :
Total cost of renting a personal water craft = $36.40
Sales tax charged = 4%
Let the pretax cost = y
Therefore,
total cost = pretax cost + tax
$36.40 = y + 4% of y
$36.40 = y + 0.04y
$36.40 = 1.04y
y = $36.40 / 1.04
y = $40
Therefore, the rental cost of a personal watercraft for half an hour before tax is $40
Diego makes an open-top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard is 15 inches by 15 inches. The volumeV(x) in cubic inches of the open-top box is a function of the side length x in inches of the square cutouts.
The volume V(x) in cubic inches of the open-top box is (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])
and side of length x in inches of the square cutouts is
V(1) = 15 - 2 = 13
x ∠ 7.5
The vertical sides were 15 inches before we cut out the corners.
The horizontal sides were 15 inches before we cut out the corners.
So now, if you fold all of the "tabs" up, you get a box that has a height of "x".
The sides are now each missing a length of "x" from each end.
So the longer edges of the box are now (15 - 2x) long.
The shorter edges of the box are now (15 - 2x)
The volume of a box is given by V = (length)(width)(height)
length = 15 - 2x
width and height of the box are equal to x in so
Multiply these together and get:
V(x) = (15 - 2x)(x)(x)
V (x) = (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])
let x = 1
V (x) = (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])
V(1) = 15 - 2 = 13
First x must be greater than 0,
then, we have 2x ∠ 15
x ∠ 7.5
therefore, The volume V(x) in cubic inches of the open-top box is (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])
side of length x in inches of the square cutouts is
V(1) = 15 - 2 = 13
x ∠ 7.5
This unit has two parts:
The surface area of a box, and its volume
The length of the diagonal of a box
Each student should bring an empty cereal box (or some other box) to work on. (The length, width, and height of the box should all be different.)
Formula for the area of the surface
(a) If l, w, and h are the length, width, and height of a box, its surface area is given by surface area = 2*(l*w + l*h + w*h). (Do you see it?)
(b) Measurements
Measurements are made in inches and sixteenths of an inch, but they are recorded as decimals.
1/8 inch = .125 inch, ¼ inch = .25 inch, 3/8 inch = .375 inch, ½ inch = .5 inch, and so on.
Example:
length l = 8.375 inches
width w = 6.125 inches
height = 2.25 inches
(c) How to enter these measurements into a TI-108 calculator to get the surface area:
8.375*6.125 M+ 51.29…
8.375*2.25 M+ 18.84…
6.125*2.25 M+ 13.78…
MRC * 2 = 167.84… square inches
We round this to 168 square inches (more or less)
Part 1b. We can also find the volume of the box:
volume = l*w*h = 8.375*6.125*2.25 = 115.4… cubic inches
If this were a hands-on unit, we would paper the box with square inch paper and fill the box with cubic inch blocks to see whether our computations are confirmed.
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pless i really need help
Perimeter of the parallelogram = 210 in.
Area of parallelogram = 2,484 in.²
What are the Perimeter and Area of a Parallelogram?Perimeter of parallelogram = 2(a + b), where a and b are its sides.
Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.
Given:
a = 51 in.
b = 54 in.
h = 46 in.
Perimeter of the parallelogram = 2(54 + 51) = 210 in.
Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²
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The table shows pricing information for two pizzas. How many toppings would make the cost the same for all pizza
number 13 only
Using linear functions, it is found that 5 toppings would make the cost the same for all pizza.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The cheese pizza price is the intercept.The price per topping is the slope.Hence the cost functions are given as follows:
A(x) = 10 + 1.5x.B(x) = 12.5 + x.The costs will be the same when:
A(x) = B(x)
10 + 1.5x = 12.5 + x
0.5x = 2.5
x = 2.5/0.5
x = 5.
5 toppings would make the cost the same for all pizza.
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Please help with the math problem
Answer:
C
Step-by-step explanation:
For this problem you use the distributive property
the first expression should match the second
Part 1 of 2
The length of a rectangular photograph is 9 in more than the width. If the area is 70 in², what are the dimensions of the photograph?
18
The dimensions of the photograph are the length= 14 in and the width= 5 in.
RectanglesThe rectangle is a quadrilateral. The classification for quadrilaterals is given by the length of sides and angles. For a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).
The area of a rectangle is given by the multiplication between the base and the height.
The question gives:
length (base) = 9 + wwidth (height) = warea = 70 in²Thenm
A= b * h
70 = (9 +w) * w
70= 9w +w²
w²+9w-70=0
[tex]w_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \left(-70\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-9\pm \:19}{2\cdot \:1}[/tex]
Thus, [tex]w_{1}=\frac{-9-\:19}{2\cdot \:1}=\frac{-28}{2}=-14[/tex] and [tex]w_{2}=\frac{-9+\:19}{2\cdot \:1}=\frac{10}{2}=5[/tex]
The dimensions should have positive values, then w=5.
If w=5, the length will be 5+9 = 14. With these dimensions, the area will be 14 * 5 = 70.
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If your total from grocery shopping is 36.73 what would be the final cost with sales tax (3.5%)?
Answer:
$38.02
Step-by-step explanation:
$36.73 × 1.035 = $38.02 (after rounding to two decimal places)
Jonas’s dropped Hey San back from a hot air balloon at a target that is 250 m below the balloon at this moment to sandbagger 75 m below the balloon which of the following expressions represents the distance between the sand bag and the target
Expressions which represent the distance between the sandbag and the target is:
250-75 meters
i.e. 175 meters
Jonas's dropped a sandbag from a hot air balloon at a target that is 250 meters below the balloon.
At this moment, the sandbag is 75 meters below the balloon.
Then, distance between the sandbag and the target is:
250-75 meters
i.e. 175 meters
Hence, expressions which represent the distance between the sandbag and the target is:
250-75 meters
i.e. 175 meters
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Nancy reads 10 pages of her a book a day. How many pages does she read in 4 days?
Answer:
40 pages
Step-by-step explanation:
10 pages per day times 4 days equals forty pages in four days.
Hope this helps! :)
If AB = 63° and BE = 0°, what is the measure of LABE?
The measure of angle ABE is 63 degrees
How to determine the measure of angle ABE?The given parameters are
<AB = 63°
<BE = 0°
The measure of angle ABE is calculated using
<ABE = <AB + <BE
This is so because the angles AB and BE share a common point at B
So, we have
<ABE = 63 + 0
Evaluate the sum
<ABE = 63
Hence, the measure of angle ABE is 63 degrees
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Complete question
If AB = 63° and BE = 0°, what is the measure of <ABE?
SUBTRACT
5 2/5 - (-2 4/15)
Answer:
7.66666666667
Step-by-step explanation:
I looked it up
A football is punted from a starting height of 3ft. With an initial upward velocity of 40 ft/sec. Will the football ever reach a height of 30ft? please explain step by step
Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.
How to determine if the ball will ever reach a height of 30 ft?To determine if the ball will ever reach a hgeight of 30 ft, we need to determine the maximum height of the ball.
What is the maximum height of the ball?Using the equation of motion, v² = u² - 2gh where
v = speed of ball at maximum height = 0 ft/s(since it stops momentarily), u = initial vertical velocity of ball = 40 ft/s, g = acceleration due to gravity = 32 ft/s² and h = maximum height of ball from starting point.So, making h subject of the formula, we have
h = (v² - u²)/-2g
Substituting the values of the variables into the equation, we have
h = (v² - u²)/-2g
h = ((0 ft/s)² - (40 ft/s)²)/-(2 × 32 ft/s²)
h = (0 ft²/s² - 1600 ft²/s²)/-(64 ft/s²)
h = - 1600 ft²/s²/-64 ft/s²
h = 25 ft
Since the ball is released from a height of 3 ft, its maximum height above the ground is H = 3 ft + h
= 3f + 25 ft
= 28 ft
So, we see that H = 28 ft < 30 ft.
Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.
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Kiki And her friends want to go bowling on Friday night but can't decided where to go.Main event charges $3 for bowling shoe rental and $10 per bowling.MaxBowl charges $6 to run bowling shoes and $9 per bowling game.Write and solve an equation that shows how many games can be played for about places to cost the same.
The games that can be played for about places to cost the same is 3 games.
How to calculate the equation?Let the number of games be represented by b.
The event charges $3 for bowling shoe rental and $10 per bowling. This can be represented as:
= 3 + 10b
MaxBowl charges $6 to run bowling shoes and $9 per bowling game. This will be:
= 6 + 9b
We will equate them together:
3 + 10b = 6 + 9b
Collect like terms
10b - 9b = 6 - 3
b = 3
Therefore, the games that can be played for about places to cost the same is 3 games.
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