The area that is swept clean by the wiper is 329.13 inches².
What is the Area of the Sector?The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle. A circle's sector area is the total area contained inside the sector's perimeter.The following formulas can be used to determine a sector's area: Area of a Sector of a Circle = (θ/360°)πr², where r is the circle's diameter and θ is the sector angle, in degrees, that the arc at the center subtends.Given:
Radius of arm(r₁) = 18 inch
Length of wiper blade = 10 inches
Radius of the point at which the blade is mounted(r₂) = 8 inches
Angle of the sector,θ = 145°
Required Area is calculated as,
Area = (θ/360°)πr₁² - (θ/360°)πr₂²
= (θ/360°) (πr₁² - πr₂²)
= (145°/ 360°) π(18² - 8²)
= (145°/ 360°) π(324 - 64)
= 329.13 inches²
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Find the length of side x in simplest radical form with a rational denominator
Length of the side, x = 11/2
radical form, x = √5.5
Define Hypotenuse.The longest side of a right-angled triangle which is the side opposite to the right angle is called hypotenuse. The hypotenuse can be easily found using the Pythagorean theorem. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
As given in question, ∅ = 60°,
Using, Cos ∅ = adjacent/hypotenuse :
Cos 60°= x/11
As we know cos 60° = 1/2
1/2 = x/11
x, length of the side = 11/2= 5.5
radical form = 5.5
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I will give brainliest, like and rating if u solve this right
2) TRUE OR FALSE?
Answer: True
Step-by-step explanation:
Please answer question 6, I will really appreciate it!!
Answer:
z=16
Step-by-step explanation:
1/4 *16=4
and 4 +8=12
Answer:
is that a z or 2?
Members of a softball team raised $1,186.50 to go to a tournament they rented a bus for $842.50 and budgeted $21.50 per player for Meals. write and solve an equation which can be used to determine x the number of players the team can bring to the tournament
If members of a softball team raised $1,186.50 to go to a tournament they rented a bus for $842.50 and budgeted $21.50 per player for Meals. The number of players the team can bring to the tournament is 16.
Number of playersLet x represent the number of players
Formulate an equation
$842.50 + $21.50 × x = $1,186.50
Using the formulated equation to determine the number of players
$842.50 + $21.50 × x = $1,186.50
$842.50 + $21.50 x = $1,186.50
Collect like terms
$21.50 x = $1,186.50 -$842.50
$21.50 x = $344
Divide both side by $21.50 x
x = $344 / $21.50
x = 16 players
Therefore the team can bring 16 players to the tournament.
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Please help I’ll mark you as brainliest if correct !!
Answer:
arithemetic because of the continuos multiplication
Answer:
A. I'm pretty sure would be geometric. and the next numbers would be 729, 2187, 6561
B. is arithmetic and the next numbers would be 46, 55, 64
C.is also arithmetic, and the next numbers would be 32, 36, 40
A trapezoid has coordinates F (−9, 6), G (−6, 9), H (−3, 9), and I (0, 6).
a. Dilate the trapezoid by a scale factor of 1/3 with a center of dilation at the origin.
b. Is the dilation a reduction or an enlargement? Explain your reasoning.
a) the coordinates of the dilated trapezoid is F'(-3, 2), G'(-2, 3), H'(-1, 3), I'(0, 2)
b) Dilation is reduction.
In this question, we have been given a trapezoid has coordinates F (−9, 6), G (−6, 9), H (−3, 9), and I (0, 6).
a. We need to dilate the trapezoid by a scale factor of 1/3 with a center of dilation at the origin.
The scale factor is 1/3
so, the coordinates of the image would be,
F' = 1/3 (-9, 6)
= (-3, 2),
G' = 1/3(-6, 9)
= (-2, 3),
H' = 1/3 (−3, 9)
= (-1, 3),
and I' = 1/3 (0, 6)
= (0, 2)
b. We know that a dilation is a geometric transformation that either enlarges or reduces a figure in size.
As we know, if the scale factor is between 0 to 1 then the image is reduction and if the scale factor is greater than 1 then the image is enlargement.
Here, scale factor is 1/3 which is 0 < 1/3 < 1
So, in this case the dilation is reduction.
Therefore, a) the coordinates of the dilated trapezoid is F'(-3, 2), G'(-2, 3), H'(-1, 3), I'(0, 2)
b) Dilation is reduction.
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Evaluate
-3(7) - (-9) =
The number of hours needed to paint a house, h, varies inversely with the number of painters, n. Four painters need 6 hours to paint a house. Find the equation represents this relationship.
The equation that represents this relationship is h*n = 24.
How do we solve linear equations?
First order equations include all linear equations as a subset. In the coordinate system, lines are defined as having linear equations. A linear equation in one variable is made up of one homogeneous variable of degree one (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.
Given, number of hours needed to paint a house = h
Number of painters needed to paint the house = n
Also, the relation between h and n is inverse, thus:
h*n = k, where k is the proportionality constant.
Therefore, initial equation derived is h*n = k --(i)
Putting h = 6 and n =4 in (i), we can get the value of k as
k = h*n = 6*4 = 24 --(ii)
Comparing (i) and (ii), we get,
h*n = 24, which is the required equation.
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Due to climate change, a certain place experienced an extreme change in weather. The following are the recorded temperatures: 15˚C, 1˚C, -4˚C, 3˚C, -10˚C, -7˚C, and 21˚C. What is the average temperature of all the given days?
The average temperature of all the given days is 19/7˚C or 2.7˚C
The average temperature of all the given days is -19/7˚C or -2.7˚C
The average temperature of all the given days is 61/7˚C or 8.7˚C
The average temperature of all the given days is -61/7˚C or -8.7˚C
Answer: Choice A) The average temp is 19/7 or 2.7 degrees Celsius
=======================================================
Explanation:
Ignore the ˚C and focus on the numbers only
We have this set of values
15, 1, -4, 3, -10, -7, 21
Add them up to get
15+1+(-4)+3+(-10)+(-7)+21 = 19
Then divide that sum over the total number of items in the set, which in this case is 7.
That's how we get to 19/7 which approximates to 2.7 when rounding to one decimal place.
Use implicit differentiation to find ∂z/∂x and ∂z/∂y.
x^4 + y^2 + z^9 = 8xyz
Using implicit differentiation, the derivatives of the function are given as follows:
[tex]\frac{\partial z}{\partial x} = -\frac{4x^3 - 8yz}{9z^8 - 8xy}[/tex][tex]\frac{\partial z}{\partial y} = -\frac{2y - 8xz}{9z^8 - 8xy}[/tex]How does implicit differentiation works?For implicit differentiation, we treat the variables as a function of each other, hence we keep applying the chain rule to find the derivatives.
Supposing a three variable function F(x,y,z) = 0, then the implicit derivatives are given as follows:
[tex]\frac{\partial z}{\partial x} = -\frac{F_x}{F_z}[/tex][tex]\frac{\partial z}{\partial y} = -\frac{F_y}{F_z}[/tex]In standard format, the function is given as follows:
F(x,y,z) = x^4 + y^2 + z^9 - 8xyz.
Hence the partial derivatives are given by:
[tex]F_x = 4x^3 - 8yz[/tex].[tex]F_z = 9z^8 - 8xy[/tex]Then the implicit derivative relative to x is:
[tex]\frac{\partial z}{\partial x} = -\frac{4x^3 - 8yz}{9z^8 - 8xy}[/tex]
The partial derivative relative to y is:
[tex]F_y = 2y - 8xz[/tex]
Then the implicit derivative relative to y is:
[tex]\frac{\partial z}{\partial y} = -\frac{2y - 8xz}{9z^8 - 8xy}[/tex]
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List all the three elements sunsets of the set {1,2,3,4,5}
A list of all the three-element subsets of the given set include the following:
{1, 2, 3} {1, 2, 4} {1, 2, 5} {1, 3, 4} {1, 3, 5} {1, 4, 5}{2, 3, 4} {2, 3, 5} {2, 4, 5}{3, 4, 5}How to determine the three element subsets?In order to determine the three-element subsets from the given set {1, 2, 3, 4, 5}, we would have to calculate the number of ways to choose the three (3) elements by applying a mathematical model referred to as combination.
Mathematically, combination is given by this mathematical equation:
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
Where:
n is the number of elements.r is the number of times of choosing elements.Substituting the given parameters into the formula, we have;
Number of ways = ⁵C₃
Number of ways = 5!/(3! × (5 - 3)!)
Number of ways = 5!/(3! × 2!)
Number of ways = [5 × 4 × 3 × 2 × 1]/[3 × 2 × 2 × 1]
Number of ways = 120/12
Number of ways = 10 ways.
Therefore, there are 10 three-element subsets of this set.
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Complete Question:
List all the three-element subsets of the set {1, 2, 3, 4, 5}
Help IMMEDIATLY please I really need it
Based on the value of the angles in this triangle, the value of x can be found to be 82 degrees
How to find the missing angle?The interior angles of different polygons always add up to a certain number of degrees. For instance, the interior angles of a heptagon add up to 900 degrees.
In triangles, the the interior angles will always add up to 180 degrees. The value of x can then be found by the formula:
180 = 52 + 46 + x
x = 180 - 52 - 46
x = 82 degrees
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K
Some rulers for technical occupations show each inch divided into tenths.
Use the scale drawing below. Change the measurements on the drawing to
decimals and round them to the nearest tenth of an inch.
(a)
(f)
View an example
16
(e)
1.8
3
P
5
16
3
(d)
2
רעון
(c)
1
1
1- in
8
Get more help -
(b)
a) 1.4 to the nearest tenth of the place
b) 1.1 to the nearest tenth of the place
c)0.3 to the nearest tenth of the place
d) 0.5 to the nearest tenth of the place
e) 0.4 to the nearest tenth of the place
f) 0.6 to the nearest tenth of the place
What is decimal ?The full number and the fraction are expressed simultaneously using decimals. By adding a "." (known as a decimal point) in this instance, we will divide the whole number from the fraction. Think about taking an ice cream cone as an illustration. Your purchase of ice cream will cost $2 and 50 cents, the dealer informs you. Currently, you would state that the ice cream cone costs $2.50 if you were to describe this amount in a single number. You may be utilizing decimals unknowingly in a variety of these real-world situations.
a) [tex]1\frac{5}{16} =\frac{22}{16}[/tex]
= 1.375
=1.4 to the nearest tenth of the place
b) [tex]1\frac{1}{8} = \frac{9}{8}[/tex]
=1.125
=1.1 to the nearest tenth of the place
c)[tex]\frac{1}{4}[/tex]
= 0.25
= 0.3 to the nearest tenth of the place
d) [tex]\frac{1}{2}[/tex]
=o.5
=0.5 to the nearest tenth of the place
e) [tex]\frac{3}{8}[/tex]
=0.375
=0.4 to the nearest tenth of the place
f) [tex]\frac{9}{16}[/tex]
=0.5625
= 0.6 to the nearest tenth of the place
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What is the measure of x?
61⁰ 90° 22° 29⁰
X + 7 3x - 5
what is the range? is this relation a function? explain please
Answer:
Range is called a set of possible outputs..in an realtion or function.
Every relation is not function but all function is relation
Actually some specified relations are called function.
Thanks
Here Range= {5}
Three undefined terms in mathematics:
1. Point
II. Line
III. Plane
The undefined terms are parallel lines are line and plane.
What is parallel lines?
Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. In this essay, let's study more about parallel lines. No matter how far we extend a parallel line, it will never meet another parallel line. See the parallel lines in the following illustration. Lines "a" and "b" are parallel, while lines "p" and "q" are also parallel.
Given that,
Parallel lines are two or more lines in a plane that are the same distance apart and will never intersect.
This definition uses two undefined terms, line and plane.
Therefore, undefined terms are parallel lines are line and plane.
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help would be appreciated
We can define the translation of building from location C to location E by the following rule -
(x, y) → (x - 4 , y + 6)
What is translation of graph?
A translation is a movement of the graph either horizontally (parallel to the x -axis) or vertically (parallel to the y -axis) without changing its orientation.
Given is a Building C translated to Building E.
In order to translate the building from location C to location E, we will first shift the building near the x - axis vertically upwards. For this we will shift the y coordinate by -
- 7 + y[s] = - 1
y[s] = -1 + 7
y[s] = 6
So the y - coordinate of the translated graph will be -
(y + 6)
Now, we will shift the x coordinate -
1 + x[s] = -3
x[s] = -3 - 1
x[s] = -4
So the x - coordinate of the translated graph will be -
(x - 4)
Therefore, we can define the translation by the following rule -
(x, y) → (x - 4 , y + 6)
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The rate at which a population of bacteria grows is proportional to the size of the population. At 1:00 PM, the population of a certain strain of bacteria was 5,400. At 1:20 PM, the population was 9,000. At what time will the population of bacteria be 25,000?
The time at which the population of bacteria will be 25,000 is 2:49 pm.
Given that:-
Population of bacteria at 1:00 PM = 5,400
Population of bacteria at 1:20 PM = 9,000
The rate at which a population of bacteria grows is proportional to the size of the population.
We have to find the time at which the population of bacteria will be 25,000.
The rate at which population of bacteria grows = 3600 bacteria/ 20 min = 180 bacteria/min
Let the population of bacteria takes t minutes to become 25,000.
Hence, we can write,
5400 + 180t = 25000
180t = 25000 - 5400
180t = 19600
t = 19600/180
t = 108.889
t = 109 minutes = 1 hour 49 minutes
Hence, the time will be 2:49 pm.
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Somebody, please help me ASAP! I have 2 questions
1. Write, then simplify, an expression for the perimeter of the rectangle below.
3x | 6x +5
2. Write, then simplify, an expression for the perimeter of the figure below.
3x + 2 | x | 2x + 5 | 6x - 17
Please help!!!
Answer: for the first one, there is no picture i need a picture to solve it that's also for the second one.
Step-by-step explanation:
hope that helps
Set up a proportion and solve.
Find the cost of 3 scarves if 2 scarves cost $22.80.
[tex]\begin{array}{ccll} scarves&\$\\ \cline{1-2} 2 & 22.80\\ 3& x \end{array} \implies \cfrac{2}{3}~~=~~\cfrac{22.80}{x} \\\\\\ 2x=3(22.80)\implies x=\cfrac{3(22.80)}{2}\implies x=34.2[/tex]
Answer: $34.20
Step-by-step explanation:
2 scarves = $22.80
22.80 ÷ 2 = $11.40
11.40 x 3 = $34.20
To check your work you could do:
$22.80 + $11.40 = $34.20
or
$34.20 ÷ 3 = $11.40
Nine times the cube of an number
Answer:
9*x³ or 9x³
Step-by-step explanation:
a number = x
cubed = to the power of 3
not really much to explain here
Student A and Student B are disagreeing about how to do the following math problem.
Answer: student A
Step-by-step explanation: in multiplication for powers we use to multiply the digits which are 9 and 2 and add the power which is going to be [tex]18y^{5}[/tex]What is the equation of the line? Please
Answer:
The answer is C.
Step-by-step explanation:
You take 2 values from the graph each for x and y. Use it in finding the gradient:
[tex] gradient = \frac{y2 - y1}{x2 - x1} [/tex]
Your gradient is m. So you replace your answer in the formula:
[tex]y = mx + c[/tex]
where c is the constant
Then you solve solve for x by substituting other values. After finding c, substitute m and c in the equation above but leave x and y like that and you have your equation.
The proportional relationship between the number of hours Lamonte works, h, and his total earnings in dollars and cents, e, can be represented by the equation e=22.5he=22.5h. How much does he make in dollars and cents per hour?
The amount of money Lamonte makes is $22.5 per hour
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let e represent the total earnings in dollars if Lamonte works for h hours. Hence:
e = 22.5h
e/h = $22.5 per hour
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You create gift baskets to sell at the craft show. Small baskets sell for $12, and
large baskets sell for $20. Your goal is to sell $300 worth of baskets at the
upcoming craft show. Write an equation that represents the amounts of the
baskets you have to sell to reach your goal.
If you sell 7 large baskets, how many small baskets will you need to sell to meet or exceed your goal?.
You will need to sell 14 baskets to meet/exceed the goal
How to calculate the number of baskets needed to exceed the goal ?
Small baskets are sold at $12
Large baskets are sold at $20
The goal is to sell $300 worth of baskets at the upcoming craft show
Let x represent the small baskets and let y represent the large baskets
12x + 20y= 300
7 large baskets are sold, the equates to
7 × 20
= 140
The number of small baskets that must be sold to reach the goal can be calculated as follows
300-140
= 160
160/12
13.33
Hence 14 small basket needs to be sold to meet/exceed the goal
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PLEASE HELP ILL GIVE POINTS AND I ATTACHED THE PHOTO
Use measurements to explain why these two figures
are not congruent.
The circle and the elipse in this problem are not congruent because they are of different classes of conics, hence their measures are different.
What are congruent figures?Congruent figures are figures that are exactly the same, having corresponding sides with the same measure.
In this problem, we have two figures that belong to different groups of conics, which are a circle and an elipse.
The circle has one measure, which is it's radius, while the elipse has two measures, the minor axis and the major axis.
It can be seen visually that the elipse has a horizontal major axis and a vertical minor axis, and the major axis is greater than the minor axis. Since these two measures are not equal, the elipse cannot be congruent with any circle, and it is not congruent with circle B given in this problem.
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A My Drive ) CharlotteAnne Hill - Unit6 MYP Project.pdf . Cole thinks they would make the most money if their club supervisor, Mr. Alvarez, invests the $450 they already raised in the stock market. He suggests buying the stock shown in the graph since the value is currently increasing. Do you agree with Cole? Describe what you see in the graph to support your reasoning. 2 points
Looking at the graph
the value is currently increasing, because the slope of the line is positive
so
I agree with Mr. Alvarez reasoning
a tangent or contingent equation for the graph in the picture.......
The graph is about a tangent function.
[tex]y=a\tan (bx-c)+d[/tex]We have to find the parameters a and b.
The period formula is
[tex]P=\frac{\pi}{|b|}[/tex]If we find the period, we can find b.
Remember that the period is the distance between two consecutive asymptotes. In this case, the period is 2pi.
[tex]\begin{gathered} 2\pi=\frac{\pi}{b} \\ 2=\frac{1}{b} \\ b=\frac{1}{2} \end{gathered}[/tex]Write an expression to represent each of the following sketches and give the value of each sketch. - - - + + + ++
a.) The expression of the sketch is:
2 - 1 + 2 - 1 - 1 + 1 = 2
So, the value of the expression is 2.
b.) The expression of the sketch is:
4 - 6 = -2
So, the value of the expression is -2.
c.) The expression of the sketch is:
-1 + 2 - 1 + 1 - 2 + 1 = 0
So, the value of the expression is 0.
d.) The expression of the sketch is:
- 4 + 7 = 3
So, the value of the expression is 3.
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A company has 15 employees with a salary of $21,900, 10 employees with a salary of $24,800, 3 employees with a salary of $31,200, 4 employees with a salary of $37,700 and 1 employee with a salary of $149, 600. Find the mean salary for the employees.The mean salary for the employees is $___.(Type a whole number. Round to the nearest hundred as needed.)
We need to find the mean salary for the employees:
There are
15 employees with a salary of $21,900, 10
10 employees with a salary of $24,800
3 employees with a salary of $31,200
4 employees with a salary of $37,700
1 employee with a salary of $149, 600
33 total of employees:
The mean formula is given by:
[tex]\text{Mean=}\frac{\text{add for all data}}{\text{total number of data}}[/tex]Replacing :
[tex]\text{Mean}=\frac{15(21,900)+10(24,800)+3(31,200)+4(37,700)+1(149,600)}{33}[/tex]Therefore:
[tex]\text{Mean = 70,209}.13[/tex]The result is rounded to the nearest hundred.