Therefore , the solution of the given problem of circle comes out to be the circle's radius is about 5.2 centimetres.
What is circle?A circle is formed by each region of a plane that is a certain distance from this extra point (center). It thus consists of spots that are isolated from one another by the surface and is curved. It also revolves about the centre equally from all angles. In the constrained, the double sphere of a circular, every group of endpoints is uniformly separated from the "centre." By tracing a thread through a circle, one can create a line to circular symmetry. Additionally, it rotates evenly in all directions around the centre.
Here,
The following equation determines the extent of a circle's arc:
=> arc length = radius * central angle
We can determine the radius by solving for the centre angle,
which is known to be 2.3 radians, and the arc length, which is 12 cm:
=> radius = arc length / central angle
=> 12 cm / 2.3 radians
=> 5.22 cm
We calculate the radius to be 5.2 cm by rounding to the closest tenth. As a result, the circle's radius is about 5.2 centimetres.
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what's the value of z ?
[tex] \sqrt{z + y} = - 369[/tex]
when y = 65
Answer:
There is no solution
Step-by-step explanation:
In a high-quality coaxial cable, the power drops by a factor of 10 approximately every 2.75 km. If the original signal power is 0.375 W (= 3.75 × 10-1 W), how far will a signal be transmitted before the power is attenuated to 37.5 μW?
Every [tex]2.75[/tex] kilometres in an elevated coaxial cable, the energy decreases by a factor of 10. This indicates that the transmit strength drops with one (0.1) of its original value after every [tex]2.75[/tex] kilometres.
Let's write "d" to represent the signal's maximum range before it loses strength and dips to [tex]37.5 W[/tex]. The following formula can be used to determine the distance [tex]d: P(d) = P(0) / 10^(d / L)[/tex]
[tex]P(d)[/tex] is the signal's power after travelling a distance of d,[tex]P(0)[/tex] is the signal's initial strength,[tex]L[/tex] is indeed the attenuation length in this instance ([tex]2.75 km[/tex]), and "([tex]37.5 W[/tex])" stands for "to the power of d/L".
Inputting the values provided yields: [tex]37.5 μW = 0.375 W / 10^(d / 2.75 km)[/tex]0 The result of dividing both sides with [tex]0.375 W is: .0 /001 = 1 10^(d / 2.75 km)[/tex]The result is: when we take the logarithmic (based 10) of both sides. [tex]-4 = -(d / 2.75 km)[/tex]By dividing all sides by [tex]2.75[/tex] kilometres, we arrive at:[tex]11 km = d[/tex]
As a result, the signal may travel 11 kilometres before losing power and becoming weaker [tex](37.5W) .[/tex]
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The median of the data 10 16 12 15 7 is
If she makes her goal pace 80% of the time and plans to run for the next 10 days how likely will she make her goal pace
every day
If she makes her goal pace 80% of the time and plans to run for the next 10 days, the probability or likelihood that she will make her goal pace every day is 80%.
What is probability?Probability describes the chance, odds, or likelihood of an expected outcome, event, or success occurring when there are many possible outcomes.
Probability is a fractional value that lies between zero and one depending on the degree of certainty or otherwise.
Thus, it is 80% likely that she will make her goal pace every day if she runs for the next 10 days.
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Wesley is a member of the
kennel club in his area. His club uses
accordion fencing like the section shown
at the right to block out areas at dog
shows.
a. Identify two pairs of congruent
segments.
b. Identify two pairs of supplementary
angles.
The two pairs of congruent segments are PS = QR and PQ = SR
The two pairs of supplementary angles are P and Q; and S and R.
What are supplementary angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary angles, then:
A + B = 180 degrees
For example, if angle A is 60 degrees, then its supplementary angle would be angle B, which is 120 degrees, because:
A + B = 60 + 120 = 180 degrees
Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and lines. For instance, if two lines intersect, the opposite angles formed are always supplementary.
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Robin earns a 5% Commission on her sales. If robin sold an item for $530, how much did she earn in commission?
Answer:
26.5$
Step-by-step explanation:
Calculate the 5% of 530, which is 530 * 0.05, whic is equal to 26.5$
Consider the following function.
p(x)=1−12x
Plot two points on the line to graph the function.
We can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
What is functiοn?A functiοn frοm a set X tο a set Y is an assignment οf an element οf Y tο each element οf X. The set X is called the dοmain οf the functiοn and the set Y is called the cοdοmain οf the functiοn.
A functiοn, its dοmain, and its cοdοmain, are declared by the nοtatiοn f: X→Y, and the value οf a functiοn f at an element x οf X, denοted by f(x), is called the image οf x under f, οr the value οf f applied tο the argument x.
Functiοns are alsο called maps οr mappings, thοugh sοme authοrs make sοme distinctiοn between "maps" and "functiοns" (see § Other terms).
Tο plοt twο pοints οn the line fοr the functiοn p(x) = 1 - 12x, we can chοοse any twο values οf x and find the cοrrespοnding values οf p(x).
Fοr example, if we chοοse x = 0, then p(0) = 1 - 12(0) = 1, sο the pοint (0,1) is οn the line.
If we chοοse x = 1, then p(1) = 1 - 12(1) = -11, sο the pοint (1,-11) is οn the line.
Therefοre, we can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
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STATISTICS MATH. SOMEONE PLEASE HELP WITH THIS!! ILL GIVE YOU BRAINLIST ANSWER. IMAGE ABOVE
Answer:
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Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is
x = 61 − p1
thousand units and the demand for brand 2 is
y = 71 − p2
thousand units, where
p1 and p2
are prices in dollars. If the joint cost function is
C = xy,
in thousands of dollars, how many of each brand should be produced to maximize profit?
brand 1=
Brand 2=
What is max profit?
To maximize profit, the manufacturer should produce 22 thousand units of each brand, and the maximum profit is:
Profit = (39 × 22) + (49 × 22) - (61 - 39)×(71 - 49) = $256 thousand.
What is profit?Profit is a term used in business and economics to refer to the amount of money or value that is gained after deducting the cost of production or acquisition from the revenue earned.
Mathematically, profit can be calculated as follows:
Profit = Revenue - Cost
To maximize profit, we need to determine the optimal values of P1 and P2. We can do this by setting up the profit function as follows:
Profit = Total Revenue - Total Cost
Profit = (P1 × x) + (P2 × y) - C
Profit = (P1 × (61 - P1)) + (P2 × (71 - P2)) - (61 - P1)×(71 - P2)
Taking the derivative of the profit function with respect to P1 and P2 and setting it equal to zero will give us the optimal values of P1 and P2 that maximize profit:
∂Profit/∂P1 = 61 - 2P1 + P2 = 0
∂Profit/∂P2 = 71 - 2P2 + P1 = 0
Solving these equations simultaneously, we get P1 = 39 and P2 = 49.
To find the quantities of each brand that should be produced, we can substitute P1 and P2 into the demand functions for x and y:
x = 61 - P1 = 22 thousand units of brand 1
y = 71 - P2 = 22 thousand units of brand 2
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If h(x) = √6 +5f(x), where f(2)= 6 and f'(2) = 5, find h'(2).
Tip: 6 + 5f(x) is all under the square root.
By using the chain rule, we will see that the derivative is:
h'(2) = 5/12
How to find the value of h'(2)?Remember the chain rule, for the derivative of a composition of two functions f(x) and g(x), if we define:
k(x) = g(f(x))
Then:
k'(x) =g'(f(x))*f'(x)
In this case we know that:
h(x) = √(6 + 5*f(x))
We can define then:
g(x) = √(6 + 5x)
and write h(x) = g(f(x))
Now the differentiation will give:
h'(x) = (1/2)*(√(6 + 5f(x))⁻¹*f'(x)
Evaluating this in x = 2 we will get:
h'(2) = (1/2)*(√(6 + 5f(2))⁻¹*f'(2)
And we know that f(2) = 6 and f'(2) = 5
Then:
h'(2) = (1/2)*(√(6 + 5*6))⁻¹*5
h'(2) = (1/2)*(6)⁻¹*5 = 5/12
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If (-2,8) and (1,-10) are two anchor points on a trend line, then find the equation of the line
Answer:
The equation would be y = 3x - 7
Step-by-step explanation:
The equation of the trend line given the two coordinates is: y = -6x - 4
How to find the equation of a line?
The formula to find the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula to find the equation of a line between two coordinates is:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
From the given two coordinates, we can say that:
(y - 8)/(x + 2) = (-10 - 8)/(1 + 2)
(y - 8)/(x + 2) = -6
y - 8 = -6x - 12
y = -6x - 4
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Respass Corporation has provided the following data concerning an investment project that it is considering: Initial investment $ 160,000 Annual cash flow $ 54,000 per year Salvage value at the end of the project $ 11,000 Expected life of the project 4 years Discount rate 15% Click here to view Exhibit 14B-1 and Exhibit 14B-2, to determine the appropriate discount factor(s) using the tables provided. The net present value of the project is closest to:
NOTE : I got an overview of the answer BELOW BUT I want to clarify HOW THE ´´1.12´´ value is obtained please?
For me I would have had ´´1.15´´ (1+0.15 where 0.15 is the 15% discount rate).
Kindly help me to clarify this please.
EXPECTED ANSWER IS CORRECT: $516
The net present value οf the prοject is $516.
What is the net present value?A set οf cash flοws that happen at variοus dates are cοnsidered tο have a net present value οr net present wοrth. The amοunt οf time between nοw and a cash flοw determines the present value οf that cash flοw. The discοunt rate is anοther factοr. NPV takes the time value οf mοney intο the accοunt.
Here, we have
Respass Cοrpοratiοn has prοvided the fοllοwing data cοncerning an investment prοject that it is cοnsidering: Initial investment $ 160,000 Annual cash flοw $ 54,000 per year Salvage value at the end οf the prοject $ 11,000.
The prοject has annual inflοws οf $54,000 except in 4th year when it will have inflοws οf $65,000 because the salvage value will be added tο the inflοws.
Present value οf inflοws = 54,000/1.12 + 54,000/1.12² + 54,000/1.12³ + 65,000/1.12⁴
= $160,516
Net Present Value = 160,516 - 160,000
= $516
Hence, the net present value is $516.
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Question 8 Find BC Show work
The value of BC in triangle ABC is 23.
What is triangle?
A closed plane figure with three straight sides and three angles is known as a triangle. It is made by joining three non-collinear points. Triangles are important in geometry and have various types based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.
Given:- triangle ABC and DEF are similar.
So , AC = DF
Therefore,
4x-23 = 2x+2
4x – 2x = 2 + 23
2x = 25
x = 25/2 = 12.5
therefore, AC = 4x – 23
= 4 * 12.5 – 23
= 50 – 23
AC =27
So ,From triangle DEF
EF = 2x-2
= 2*12.5 – 2
= 25 – 2
EF = 23
As triangle ABC and DEF are similar.so,
BC = EF = 23
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What are the key features of the equation y = (x + 12)(x + 6)? Question 5 options: The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 72). The vertex is an absolute maximum, (–9, –9). The x-intercepts are (12, 0) and (6, 0). The y-intercept is (0, 72). The vertex is an absolute minimum, (–9, –9). The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 6). The vertex is an absolute minimum, (–9, –9). The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 72). The vertex is an absolute minimum, (–9, –9).
Answer:
y= -x+3
Step-by-step explanation:
We can see that our given equation is in slope-intercept form
, where m represents slope of line and b represents the y-intercept.
Upon looking at our given equation, we can see that the slope of our given line is 1
and the y-intercept is at point
.0,3
Upon graphing our given equation, we will get our required graph as shown below:
A 6-meter roll of fabric costs $15.29. What is the unit price, rounded to the nearest cent?
Answer: $2.55
Step-by-step explanation:
Unit price = Total cost ÷ Length of fabric
$15.29 ÷ 6 = 2.54833333
Rounded to the nearest tenth is 2.55
What is the explicit formula for the sequence: .25,5,1,2
The explicit formula for the geometric sequence is [tex]a_n=25(\frac{1}{5})^{n-1}[/tex].
What is explicit formula for geometric series?
The explicit formula for geometric sequence is [tex]a_n=a_1(r)^{n-1}[/tex] where r is common ratio.
Here the given sequence is 25,5,[tex]\frac{1}{2}[/tex]...
Here first term [tex]a_1=25[/tex]
Common ratio = [tex]$ \frac{a_2}{a_1}=\frac{5}{25}=\frac{1}{5}[/tex]
Now, Explicit formula [tex]$ a_n=a_1(r)^{n-1}[/tex]
=> [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex]
Hence the explicit formula of geometric series is [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex].
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I neeedddd helppppp???
Answer:
(-2,-4)
Step-by-step explanation:
The solution to a system of equations is the point at which the lines (that are defined by the equations) intersect, or touch each other.
In the graph, we can see that the lines intersect when x = -2 and y = -4.
In the format (x,y), this is expressed as: (-2,-4)
What is the average rate of change of sales between 2008 and 2010?
f(x)
495
513
410
402
520
580
631
719
624
582
X
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
HELP
Answer:
2008 and 2010 is 52 units per year.
Step-by-step explanation:
To find the average rate of change of sales between 2008 and 2010, we need to calculate the change in sales over that period, and divide by the time interval.
The sales in 2008 is f(2008) = 520, and the sales in 2010 is f(2010) = 624. The time interval is 2 years.
Therefore, the change in sales over that period is:
f(2010) - f(2008) = 624 - 520 = 104
The average rate of change of sales between 2008 and 2010 is:
(104) / (2) = 52
So the average rate of change of sales between 2008 and 2010 is 52 units per year.
The Ministry of Transport and Mining hired a firm to conduct a traffic study before expanding the city streets. Two companies submitted bids for the job. The ministry hired the second company (company B) because they had more experience and offered a better rate. They studied the movement of the traffic on a specific roadway. The first day of the study was the second Monday in September. They found that 12,665 cars, 23,709 small commercial vehicles, 1,024 medium trucks, 7,096 lange macks, and 660 other vehicles used the roadway during the evaluation period.
0f the vehicles classified as "other vehicles," 213 of them are morcycles How many of the other vehicles were not motorcycles?
Answer: i got 213
Step-by-step explanation:
There is a mound of g
pounds of gravel in a quarry. Throughout the day, 200
pounds of gravel is added to the mound. Two orders of 700
pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,000
pounds of gravel.
Answer:
2400
Step-by-step explanation:
before anything got taken away they added 200 wich means before they added that they had 2200 and if 700 pounds were removed twice that would mean the mound lost 1400 pounds and so if you add 1000 to the 1400 that they took you can find the amount that was there before.l
what do i do this is confusing for me
Answer:
Translate 3 right and 1 up.
Step-by-step explanation:
Looking at the picture and count the movement.
Answer:
Step-by-step explanation:
3 units right.
1 unit up.
Each of the letters is moved by these amounts to create the new image.
Watch help video
Graph the line that passes through the points (-6, -8) and (3,-2) and determine
the equation of the line.
I need help with this immediately
The digits in the hundreds place is 2.
The digits in the hundredths place is 9.
The digits in the ten thousandths place is 1.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsTen thousandthsHundred thousandthsMillionths.UnitTensHundredsThousands.Tens of thousands.Based on the numerical data (number) provided above 248.7961, we can reasonably infer and logically deduce that the place value of one (1) is ten thousandths, nine (9) is hundredths, and two (2) represent hundreds.
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What is the surface area of the rectangular prism formed by the pattern below?
Answers -
56 cm
108
136
162
Answer:
C. 136
Step-by-step explanation:
Add up the surface areas of each individual section. Area is length times width.
Lets start by figuring out the area of the 2 by 6 rectangle on the bottom. 2cm*6cm=12 sq cm. The rectangle on the top right also has an area of 2cm*6cm. So it also has an area of 12 sq cm. lets figure out the area of the smaller rectangle on the right side. 7cm times 2 cm equals 14 cm squared. There is also a 7cm by 2cm box in the middle of the pattern. so 14 + 14 = 28, + 12 + 12= 52. so all of the tiny rectangles added up equal 52. Finally, lets figure out the area of the two 6*7 rectangles. 6*7= 42. 42*2= 84. 84 is the area of the two big rectangles added together. So add the two totals to get 52 sq cm+ 84 sq. cm = 136 sq. cm.
Write 4 to the 3ed power using repeated multiplication. Then find the value of 4 to the 3ed power
Answer:
4x4x4 and the value of 4^3=64
Step-by-step explanation:
4x4x4 is equivalent to 4^3. This is because using exponents mean multiplying the base number by itself by 2 if the exponent is 2, if it was 3 then you would multiply 4 by itself three times.
Find the equation of the line that passes through the given points. (Use x as your variable.) (0,5),(6,0)
Answer:
y = - [tex]\frac{5}{6}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5 ) and (x₂, y₂ ) = (6, 0 )
m = [tex]\frac{0-5}{6-0}[/tex] = [tex]\frac{-5}{6}[/tex] = - [tex]\frac{5}{6}[/tex]
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = - [tex]\frac{5}{6}[/tex] x + 5 ← equation of line
2064 0 No. 10 Old if the compound interest on Rs 500 for years is Rs 398 find the compound interest on Rs. 625 15) Ans: Rs. 450 la 15 years at the same rate 5
Proportionately, if the compound interest on Rs 500 for years is Rs 398, the compound interest on Rs. 625 is Rs. 497.50.
What is proportion?Proportion is a part or portion of the whole.
Proportion indicates the ratio that one quantity or value possess in relation to or when compared or equated to another.
We determine proportion as the quotient of one value divided by another. Proportion can also be expressed as a percentage by multiplying the resultant quotient by 100.
The compound interest on Rs. 500 = Rs. 398
Thus, proportionately, the compound interest on Rs. 625 will be Rs. 497.50 (Rs 398/Rs. 500 x 625).
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(x² + 3x + 2) ÷ (x + 2)
Answer:
x+1
Step-by-step explanation:
For the first part of the expression, factor into (x+2)(x+1).
(x+2)(x+1)/(x+2)
The x+2 cancels out, so the answer is x+1
the figure below is dilated by a factor of 4 centered at the orgin. plot the resulting image
(where are the points pls im so confused)
The image that results from the dilation transformation is as shown in the attached file with coordinates as:
G'(0, -8)
H'(8, 0)
I'(-8, 4)
What is the coordinate of the triangle after dilation?A dilation is defined as a transformation that produces an image that is the same shape as the original, but is a different size.
The coordinates of the given triangle are:
G(0, -2)
H(2, 0)
I(-2, 1)
Now, when an object with coordinates is dilated by a factor about the origin, what we will do is to multiply each coordinate by that factor . The factor of dilation is 4 and as such we have:
G(0, -2) * 4 = G'(0, -8)
H(2, 0) * 4 = H'(8, 0)
I(-2, 1) * 4 = I'(-8, 4)
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Help! Does the rule represent an exponential function?
y = -5x^7