84.78 mm² is area of circle .
What is a circle ?
A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the center.Having no sides or edges, a circle is a figure with a round shape. A closed, two-dimensional curved form is what is meant by the term "circular" in geometry.radius of the circle = 27 mm
area of the circle = πr²
= 3.14 * 27
= 84.78 mm²
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I need help asap thank you..
Step-by-step explanation:
the angle TSW is the total angle and is 73°.
from that total angle, we have one part : angle 1 = 36°.
as angle TSW = angle 1 + angle 2
we have
73 = 36 + angle 2
angle 2 = 73 - 36 = 37°
Help with this math problem
The value of the investment after 3.25 years is $434.93.
What is the interest rate?The amount a lender charges a borrower, expressed as a percentage of the principle, is known as the interest rate.
Given that, the initial investment is P₀ = $400, the interest rate is n = 2.6%, and the time is x = 3.25 years.
The formula for the future value in continuous compounding is:
P(x) = P₀eⁿˣ
Substitute P₀ = 400, n = 2.6%, and x = 3.25 into the equation:
[tex]P(3.25) = (400)e^{2.6\%(3.25)}\\[/tex]
= 434.93
Hence, the value of the investment after 3.25 years is $434.93.
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If X = 32 yards, Y = 60 yards, and Z = 68 yards, what is the sine of ZA?
The sin(x) = 0.88 and sin(y) = 32/68=0.47 in the Trigonometric Functions
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
The given triangle is a right-angled triangle
As Z² = X²+Y²
So sin (x) = 60/68=0.88
and sin(y) = 32/68=0.47
Hence the sin(x) = 0.88 and sin(y) = 32/68=0.47.
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HEEELPPPPPPPP Rearrange the formula v = 2gh for h. A) h = v 2g B) h = 2v g C) h = v2 g D) h = v2 2g
Rearranging the equation, making h the subject of the formula, h = v² / 2g
How to rearrange formula?we rearrange equations and formulas by using inverse operations to make one variable the subject of the formula.
In order to change the subject of, or rearrange, a formula items in the formula need to be arranged so a different variable is the subject.
In our case the the formula needs to be rearrange to make h the subject of the formula.
Therefore,
v = √2gh
square both sides of the equation
v² = (√2gh)²
v² = 2gh
divide both sides by 2g
v² / 2g = 2gh / 2g
h = v² / 2g
Therefore,
h = v² / 2g
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a recipe requires 3/4 cup of water. Nora has a 1 1/2 cup measuring cup. how much of the measuring cup is filled with water?
Answer:
i think it is 15/20
Step-by-step explanation:
because 6/8,9/12,12/16
In the following expression, n is a rational number: Which expression below is equivalent to this expression?
Answer:
none of them
Step-by-step explanation:
which is the correct answer ????
The correct way to replace equation 1 into equation 2 using the substitution method is 2x+(-5x+10) = 7.
According to the question,
We have the following two equations:
Equation 1: y = -5x+10
Equation 2: 2x+y = 7
Now, we will substitute the value of y from equation 1 in equation 2.
So, we have the following expression:
2x+(-5x+10) = 7
(More to know: we can also solve this equation to find the value of x and then the obtained value of x can be put in equation 1 to find the value of y.)
Hence, the correct option is B.
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Find missing side length given two similar triangles
Answer: 49
Step-by-step explanation:
by using triangle ABC and the known values of triangle XYZ, we can divide side XY/AB, 28/4=7. By doing the same with YZ/BC, 56/8=7, we find that the scale factor is 7. With this information, we multiply side CA by the scale factor, 7x7=49.
2x-4y=4
x-2y = 8
Helppppp
Solve for y and graph example;(number,number)
The system of equations has no solutions, meaning that the two lines never intersect, as shown by the image at the end of the answer.
What is a system of equations?A system of equations is a set of equations in the context of a problem, and these equations are solved to find the numeric value of each variable of the problem.
When the system involves linear equations, such as is the case in this problem, the solution is given by the intersection point between these two lines.
In this problem, the equations are given as follows:
2x - 4y = 4.x - 2y = 8.From the second equation, it is found that:
x = 8 + 2y.
Replacing on the first equation, the solution for y can be obtained as follows:
2(8 + 2y) - 4y = 4
16 + 4y - 4y = 4
0y = -12
Which is a contradiction, hence the system has no solutions and the two lines do not intersect.
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Henry invested $1500 into an account that pays 2% interest compounded annually.
How much money will Henry have at the end of 3 years?
Enter your answer in the box. Round to the nearest hundredth.
The compound interest is obtained as $91.81, rounded off to the nearest hundredth.
How is compound interest estimated annually?In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest. The entire compound interest is then obtained by deducting the initial principal.
The equation that results will look like this:
Compound Interest = [tex]P(\left(1+r\right)^{ t}-1)[/tex]
Amount, rate of interest and time is given as $1500, 2% and 3 years respectively.
First, change r as a percent to r as a decimal.
r = R/100
r = 2/100
r = 0.02 rate per year,
Then solve the equation for compound interest.
[tex]\text{Compound Interest}=1500(\left(1+0.02\right)^{3}-1)\\=1500(1.061208-1)\\=15000\cdot 0.061208\\\\=91.81[/tex]
So, the compound interest is obtained as $91.81, rounded off to the nearest hundredth.
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Answer: its 1591.81
Step-by-step explanation:
I took the test and tried with the answer on top and got it wrong.
1. A factory is testing a new machine on its production line that is intended to improve efficiency. Management randomly
selects 12 employees and measures the number of products they complete in one hour when using the new machine. Below
are the results.
Employee 1 2 3 4 5 6 7 8 9 10 11 12
# units 72 68 74 78 75 79 71 69 82 71 73 80
(a) Estimate at the 95% confidence level the average number of units an employee can produce in one hour using the
new machine.
(b) The manufacturer of the machine claims the typical efficiency for a factory worker should be 78 units per hour. What
does the interval suggest about the manufacturer’s claim
(c) An investigation at a similar factory estimates the standard deviation to be 3.91 units. Using this information, what
size sample should we select to estimate the mean number of units produced each hour to within 1.04 units at the
95% confidence level?
a) The confidence interval is given as follows: (71.43, 77.17).
b) The manufacturer's claim is not correct, as 78 is not a part of the interval.
c) A sample of 55 employees is needed to achieve the desired margin of error.
What is a t-distribution confidence interval?The bounds of the t-distribution confidence interval, used when only the standard deviation for the sample is known, are given by the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, considering the 95% confidence level and 12 - 1 = 11 df, is of:
t = 2.201.
The remaining parameters, namely sample mean, sample standard deviation and sample size are given as follows:
[tex]\overline{x} = 74.3, s = 4.52, n = 12[/tex]
(obtained using a calculator from the sample given in this problem).
The bounds of the interval are given as follows:
Lower bound: 74.3 - 2.201 x 4.52/sqrt(12) = 71.43.Upper bound: 74.3 + 2.201 x 4.52/sqrt(12) = 77.17.The interval does not contain the number 78, hence it is not a good estimate for the mean amount.
For item c, the z-distribution is used, as the population standard deviation is used, hence the minimum sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.04 = 1.96\frac{3.91}{\sqrt{n}}[/tex]
[tex]1.04\sqrt{n} = 1.96 \times 3.91[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 3.91}{1.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 3.91}{1.04}\right)^2[/tex]
n = 55. (rounded up, as a sample size of 54 would mean that the margin of error would be slightly above 1.04).
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Determine the length of the line segment shown. graph of line segment from negative 6 comma negative 5 to 0 comma 3 100 units 25 units 10 units 8 units
The length of the line segment will be 10 units.
What is Distance?
The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;
D = √( y₂ - y₁)² + (x₂ - x₁)²
Given that;
Two endpoints of the line segment are (6, -5) and (0, 3).
Now,
The length of the line segment is distance between two endpoints (6, -5) and (0, 3).
So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;
D = √(0 - 6)² + (3 - (-5))²
D = √36 + 64
D = √100
D = 10 units
Thus, The length of the line segment will be 10 units.
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3.
A circular pool of oil grew so that its radius increased by 2 feet. The formula shown can
be used to determine the area of the circle.
A = π (r + 2)²
Which equation is equivalent to the formula solved for r in terms of A?
Or=√1-2
Or=√√√+2
Or=√√4+2
Or-√4-2
Equation which is equivalent to the formula solved for r in term of A is [tex]Or = \sqrt{\frac{A}{r}-2 }[/tex].
What is circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
A circle is also termed as the locus of the points drawn at an equidistant from the centre.
What is radius?
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.
What is circumference?
Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.
Given that;
[tex]A = \pi{({r+2})^{2}}[/tex]
[tex](r+2)^{2} =\frac{A}{\pi}[/tex] (equivalent transformation)
[tex]r + 2 = \sqrt{\frac{A}{\pi} }[/tex]
[tex]r = \sqrt{\frac{A}{\pi} -2}[/tex]
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At the end of an amusement park ride, a boat lands in a pool, splashing out a lot of water. Three inlet pipes, each working alone, can fill the pool in 8 seconds, 12 seconds, and 16 seconds, respectively. How long would it take to fill the pool if all three inlet pipes are used?
The three inlet pipes, each working alone can fill the pool in 8 seconds, 12 seconds, and 16 seconds, respectively. it will take them 3.69 seconds fill the pool
How to determine how long it takes it fill the poolThe problem requires to determine how long it takes to fill the pool when the three pipes are working simultaneously
let the time to fill the the pool when the three pipes are working simultaneously be y, such that
8 seconds pipe fills the pool in y/8 seconds
12 seconds pipe fills the pool in y/12 seconds
16 seconds pipe fills the pool in y/16 seconds
Adding the times together
y/8 + y/12 + y/16 = 1
13y/48 = 1
y = 48/13
y = 3.69 seconds
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Find the X-intercept for this please .
Answer: I believe both the x and y- intercepts are “(0,0)”
Step-by-step explanation: there is only one intercept and it is at the origin (0,0) making both the x and y - intercepts (0,0) :)
In chapters 5-8 of Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm. What causes these feelings
A. A visit from his father
B. A letter from Elizabeth
C. The arrival of Henry Clerval
D. An award for creating the monster
Answer:
C______________4_⁴________
use the figure below to solve for the missing value(s):
The missing values are:
m∠1 = 36°
m∠2 = 122°
m∠3 = 122°
m∠4 = 38°
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The figure has two triangles.
58° and m∠3 is a straight angle.
58 + m∠3 = 180
m∠3 = 180 - 58
m∠3 = 122
Now,
m∠3 + m∠4 + 20 = 180
122 + m∠4 + 20 = 180
m∠4 = 180 - 122 - 20
m∠4 = 180 - 142
m∠4 = 38
m∠3 and m2 are opposite angles.
Opposite angles are equal.
m∠3 = m∠2 = 122
Now,
m∠1 + m∠2 + 22 = 180
m∠1 + 122 + 22 = 180
m∠1 = 180 - 144
m∠1 = 36
Thus,
The missing values are:
m∠1 = 36°
m∠2 = 122°
m∠3 = 122°
m∠4 = 38°
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what is (x+5)……………
……….:…………
Answer:
x+5
Step-by-step explanation:
there are no like terms
Select the correct answer from the drop-down menu.
A new park is adding two new walking paths, as indicated by and , which are measured in meters. The park resembles an isosceles trapezoid.
Figure shows a trapezium ABCD. AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
Determine the length of each path.
A.
The length of each path is
130
meters.
B.
The length of each path is
140
meters.
C.
The length of each path is
120
meters.
D.
The length of each path is
150
meters.
A.The length of each path is 130 meters.
Given:
The park resembles an isosceles trapezoid.
Figure shows a trapezium . AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
we know that:
Diagonals are equal in isosceles trapezoid.
14x + 4 = 11x + 31
14x - 11x = 31 - 4
3x = 27
divide by 3 on both sides
3x/3 = 27/3
x = 9
Diagonal length = 14x + 4.
= 14*9 + 4
= 126 + 4
= 130 meters.
Therefore The length of each path is 130 meters.
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Solve each equation for x. Show all steps.
A) log base 4 (x^2 -12x+48) =2
B) 27^(4x-6) =(1/9)^(2x-7)
A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8
B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2
Solving equations: Determining the value of xFrom the question, we are to solve the given equations
The given equation is log₄(x² - 12x + 48) = 2
From one of the laws of logarithm, we have that
logₐ x = n ⇒ x = aⁿ
Thus,
log₄(x² - 12x + 48) = 2 becomes
(x² - 12x + 48) = 4²
x² - 12x + 48 = 16
x² - 12x + 48 - 16 = 0
x² - 12x + 32 = 0
Solve the quadratic equation
x² - 12x + 32 = 0
x² - 8x - 4x + 32 = 0
x(x - 8) -4(x - 8) = 0
(x - 4)(x - 8) = 0
x - 4 = 0 OR x - 8 = 0
x = 4 OR x = 8
B) 27^(4x-6) =(1/9)^(2x-7)
Solve for x
27^(4x-6) =(1/9)^(2x-7)
Express the bases in index form
3^3(4x-6) =(3)^-2(2x-7)
Equate the powers
3(4x - 6) = -2(2x - 7)
12x - 18 = -4x + 14
12x + 4x = 14 + 18
16x = 32
Divide both sides by 16
16x/16 = 32/16
x = 2
Hence, the value of x is 2
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A famous leaning tower was originally 180.5 feet high At a distance of 125 feet from the base of the tower, the angle of olevation to the top of the tower is found to be 56° Find ZRPQ indicated in the figure. Also find the perpendicular distance from R to PQ
The perpendicular distance from R to PQ is 346 feet.
What are the trigonometric functions?
The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
We have,
consider the sides of leaning tower are,
opposite side of the angle 56° (x) = 180.5 feet.
Adjacent side of the angle 56° (y) = 125 feet.
We know,
[tex]tan\theta =\frac{ opposite \ side}{ adjacent \ side} = \frac{x}{y}[/tex]
[tex]\theta = \ tan^{-1} \left(\frac{ opposite \ side}{ adjacent \ side} \right)[/tex]
The angle of elevation is [tex]\theta = \ tan^{-1} \left(\frac{180.5 }{125} \right)[/tex]
θ = 56°
The perpendicular distance from R to PQ is RQ
[tex]sin\theta = \frac{opposite side}{hypotanous} = \frac{180.5}{y}[/tex]
sin(56) = 180.5/PQ
RQ = 180.5/sin(56)
RQ = - 346.08
RQ = 346 (distance never be negative),
Hence, the perpendicular distance from R to PQ is 346 feet.
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Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
It is a function because the mapping .
(A) Due to the fact that there are no two values in Set B that have only one value in Set A mapped to them, the mapping diagram above represents a function.
(B) A function's very special property is that it associates one output with each input.
(C) Set A represents the domain, whereas Set B represents the range. Therefore, there would be exactly one value in the range that was unique for each value in the domain and would be present for each value in the domain.
What are functions?In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The subsets X and Y are referenced to as the function's domain and codomain, correspondingly. A function is described as a relationship between a group of inputs with one output each. A function is, to describe it simply, a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a codomain, or range. A function is a type of rule that produces one output from one input. Y=X2 is a good illustration of this. Any input for x yields a single output for y.
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Last year, Ivanna opened an investment account with $7500. At the end of the year, the amount in the account had decreased by 7.8%. How much is this
decrease in dollars? How much money was in her account at the end of last year?
0.065=x/5800
x=$377; that is the dollar value of the decrease
The account is now worth $5423.
4/7
of a square is painted green.5/6 of the remainder is painted red. If the green
part is 36 cm² more than the red. find the area of the square.
Answer:
168
Step-by-step explanation:
Let the area of the square be [tex]x[/tex].
[tex]\frac{4}{7}x-\frac{5}{6}\left(\frac{3}{7}x \right)=36 \\ \\ \frac{4}{7}x-\frac{5}{14}x=36 \\ \\ \frac{8}{14}x-\frac{5}{14}x=36 \\ \\ \frac{3}{14}x=36 \\ \\ \frac{1}{14}x=12 \\ \\ x=168[/tex]
Find the perimeter of the shape below. Each grey square has a side
length of 1.
The perimeter of the shape is 38 total unit.
Perimeter of plane shapesThe perimeter of a shape is a measure of the distance round the boundary or edge of the shape.
The given shape comprises of squares of 1 length each, hence to calculate for the perimeter of the shape, we add up each boundary of 1 unit length which will amount to 39 in total.
Therefore by careful observation, the perimeter of the plane shape is calculated to give us 39 total perimeter length.
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PLEASE HELP ME !!!
x² + 12x -
2
8 can be written in the form
(x + a)² + b, where a and b are numbers.
Work out the values of a and b.
Answer:
a = 6 , b = - 44
Step-by-step explanation:
x² + 12x - 8
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² from x² + 12x
x² + 2(6)x + 36 - 36 - 8
= (x + 6)² - 44 ← in the form (x + a)² + b
with a = 6 and b = - 44
(x2 + 3x –9) ÷ (x – 2).
Answer:
Step-by-step explanation:
Creating a Function from a Mapping
The mapping shows a relationship between input and
output values.
Input
Activity
-5
SAING
2
40 Intro
Output
T? 7 NO
-3
-2
2
Which ordered pair could be removed to make this
relation a function?
O (-5,0)
-O (-1, -3)
O (4,-2)
O (6,-1)
Done
The ordered pair could be removed to make this relation a function is (4,-2).
What is an ordered pair?
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
The numeric values in an ordered pair can be integers or fractions.
Here,
A function is when each input has one output. So, for every x there is one y. The x values can not repeat.
But in the given value x is repeating so the ordered pair (4, -2) can be removed.
Hence, the ordered pair could be removed to make this relation a function is (4,-2).
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Emmett is planning a party at an escape room. The escape room will charge Emmett a
booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship.
Answer:
B. After the booking fee the party will cost $20 per person
Which value of x makes the following statement true? 1.4 - x = a positive number
Answer:1.4<x
math math math
Answer:daddy
Step-by-step explanation:gay