The 97% confidence interval for the proportion of college freshmen who would report cheating if they witnessed it in class is (0.0728, 0.1482).
The point estimate is the proportion of students who responded "yes" out of the total sample.
In this case, the point estimate is 19/172, which is approximately 0.1105.
b. Margin of Error:
To calculate the margin of error, we need the standard deviation. Since we don't have the population standard deviation, we'll use the formula for the estimated standard deviation of a proportion:
Margin of Error (ME) = z√[(p(1 - p)) / n]
Where z is the z-score corresponding to the desired confidence level. For a 97% confidence level, the z-score is approximately 1.96, p is the point estimate of the proportion and n is the sample size.
Using the given values, we can calculate the margin of error:
ME = 1.96√[(0.1105(1 - 0.1105)) / 172]= 0.0377
c. Confidence Interval:
The confidence interval is calculated by subtracting and adding the margin of error from the point estimate.
Confidence Interval = Point Estimate ± Margin of Error
Confidence Interval = 0.1105 ± 0.0377
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What is the sum of (-2.1x +3.7) and (5 + 4.9x)?
O-7.0x+8.7
-2.8x+8.7
O 2.8x+8.7
O 7.0x+8.7
I will gave brainliest to anyone who answers.
Answer:
To find the sum of (-2.1x + 3.7) and (5 + 4.9x), we need to add the like terms (terms with the same variable and exponent). In this case, the x term is the like term. Therefore:
(-2.1x + 3.7) + (5 + 4.9x) = -2.1x + 4.9x + 3.7 + 5
Combining like terms, we get:
(-2.1x + 4.9x) + (3.7 + 5) = 2.8x + 8.7
Therefore, the sum of (-2.1x + 3.7) and (5 + 4.9x) is 2.8x + 8.7.
So, the answer is: 2.8x+8.7.
Step-by-step explanation:
Solution 2:
The correct answer is 2.8x+8.7.
Here's the solution:
(-2.1x +3.7) + (5 + 4.9x) =
-2.1x + 3.7 + 5 + 4.9x =
-2.1x + 4.9x + 3.7 + 5 =
2.8x + 8.7: answer
The diagram shows a circle inside a square.
Work out the area of the circle.
16 cm
Optional working
The area of the escribed circle is: 201.06 cm²
What is the area of the circle?The formula for the area of a circle is:
A = πr²
where:
A is area
r is radius
From the given diagram, we see that, the side length of the square is 16 cm. Now, we also see that the side length of the square serves as the diameter of the circle and as such:
Radius of circle: r = 16/2 = 8 cm
Thus:
A = π(8²)
A = 201.06 cm²
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I need help right now can someone help me
Step-by-step explanation:
To find the perimeter, we add all side lengths.
Two of the side lengths are given, to find the third side length, we use the following equation based on similarity ratio:
[tex] \frac{kj}{nm} = \frac{kl}{no} [/tex]
[tex] \frac{8}{18.4} = \frac{9}{no} [/tex]
cross multiply fractions.8NO = 165.6
Divide both sides by 8.NO = 20.7
Now we need to find the sum of all sides.20.7 + 23 + 18.4 = 62.1 square units.
You will create an estimate in order to assist your boss in gaining the job!
The equation that is given by the customer for the pool is (units are in feet): x2 + y2 = 81
- Your performance needs to include the following calculations:
- Compute the radius and diameter of the pool.
- Compute the volume of water in the pool using the above calculations and a height of 4 ft.
- Assuming that water costs $0.22 per gallon and that pools cost $185 per foot of radius calculate the total cost of materials for the pool. Keep in mind that there are 7.48 gallons of water per square foot.
- Assuming that a pool will take 2.5 hrs. per foot of radius, compute the total labor hours for the pool.
- If you are to pay someone $19/hr, compute the total cost of labor.
- Find a total cost for the project.
- All of the above is done showing all work.
- A final paragraph that describes your steps and findings.
The solution has been explained below.
We will use the following equation, x² + y² = 81, where x and y are the pool's dimensions in feet, to determine the necessary estimations for the pool project.
1. Calculate the pool's diameter and radius:
We can infer that the radius of the pool is equal to the square root of 81 because the equation depicts a circle. As a result, r = 81 = 9 ft.
The pool's diameter is simply equal to twice its radius, or d = 2r = 18 feet.
2. Calculate the amount of water in the pool:
Since the pool is 4 feet high, we can determine its volume by multiplying the area of its circle-shaped base by the height.
The formula A = πr² can be used to calculate the area of the pool's base,
Therefore, V = Ah = πr²h = 1017.87 cubic feet represents the volume of water in the pool.
3. Determine the pool's total material cost:
There are 7.48 gallons in a cubic foot and a gallon of water costs $0.22.
As a result, Cw = V × 7.48 × 0.22 = 1017.87 × 7.48 × 0.22 = $1,619.72 is the entire cost of water for the pool.
If the radius of the pool is $185 per foot, then the cost of the materials is Cm = r × 185 = 9 × 185 = $1,665.
4. Calculate the pool's total labour hours:
A pool's construction is estimated to take 2.5 hours for every foot of its radius.
So, L = r × 2.5 = 9 × 2.5 = 22.5 hours of labour would be needed to complete this pool.
5. Calculate the total cost of labour for the project:
If you pay someone $19 per hour, Cl = L × 19 = 22.5 × 19 = $427.5.
6. Find the project's overall cost:
The project's overall cost is the product of its labour and material costs:
Cost as a whole equals Cm + Cw + Cl, which is 1,665 + 1,619.72 + 427.5, or $3,712.22.
In conclusion, the pool has an 18-foot diameter and a 9-foot radius according to the supplied equation. There are roughly 1017.87 cubic feet of water in the pool. Water and building supplies are included in the pool's projected material cost of $3,284.72. 22.5 hours of labour in total are needed, with a labour cost estimate of $427.5. Consequently, $3,712.22 is the expected final cost of the pool renovation.
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Which of the following will lower your credit score for a while?(1 point)
You request a copy of your credit report.
A company requests a copy of your report to determine whether they should send you a pre-approved credit card offer.
Your credit card company requests a copy of your credit report as part of a regular review of your account.
You apply for a student loan and the lender requests a copy of your credit report.
The only one that can possibly cause lower your credit score is "You apply for a student loan and the lender requests a copy of your credit report."
The lender normally does a hard inquiry on your credit record when you apply for a new loan or line of credit.
Your credit score may be slightly lowered as a result of this hard inquiry, typically by a few points.
However, the effect is often short-lived, and your credit score should gradually improve.
Hence the correct option is You apply for a student loan and the lender requests a copy of your credit report.
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Find the average rate of change for the function listed below on the interval [2,7].
f(x)=3x^2+2x+4
Answer: 10
Step-by-step explanation:
Someone solve this for me
The solutions to the circle equations in the attached figure are: (5) (x + 2)² + (y - 1)² = 20, (6) x² + y² = 9, (7) (x + 3)² + (y - 1)² = -9 and (8) (x - 4)² + (y - 3)² = -16
Finding the Solution to Equation of CircleEquation of a Circle in the Cartesian coordinate system (x, y) is given by:
(x - h)² + (y - k)² = r²
where
(h, k) = coordinates of the center of the circle
r = radius.
The expression (x - h)² + (y - k)² represents the squared distance between any point (x, y) on the circle and the center point (h, k). By setting this expression equal to the square of the radius, r², we ensure that all points on the circle are equidistant from the center.
You can also expand the equation to get the standard form:
x² - 2hx + h² + y² - 2ky + k² = r².
Using the information above, let us solve the circle equations:
5) y² + 4x - 20 - 2y = -x²
First we need to find the coordinates (h, k) of the circle
x² + 4x + y² - 2y = 20
-2h = 4 => h = -2
-2k = -2 => k = 1
(h,k) = (-2, 1)
Rewrite the equation in a standard circle format
Recall: (x - h)² + (y - k)² = r²
(x - (-2))² + (y - (1))² = 20
(x + 2)² + (y - 1)² = 20
Therefore the solution to the circle equation is: (x + 2)² + (y - 1)² = 20 and the curve is attached.
6) -9 = -y² - x²
First we need to find the coordinates (h, k) of the circle
x² + y² = 9
-2h = 0 => h = 0
-2k = 0 => k = 0
(h, k) = (0, 0)
Rewrite the equation in a standard circle format
Recall: (x - h)² + (y - k)² = r²
(x - (0))² + (y - (0))² = 9
x² + y² = 9
Therefore the solution to the circle equation is: x² + y² = 9 and the curve is attached.
7) 9 = 2y - y² - 6x - x²
First we need to find the coordinates (h, k) of the circle
x² + 6x + y² - 2y = -9
-2h = 6 => h = -3
-2k = -2 => k = 1
(h, k) = (-3, 1)
Rewrite the equation in a standard circle format
Recall: (x - h)² + (y - k)² = r²
(x - (-3))² + (y - (1))² = -9
(x + 3)² + (y - 1)² = -9
Therefore the solution to the circle equation is: (x + 3)² + (y - 1)² = -9 and the curve is attached
8) 16 + x² + y² - 8x - 6y = 0
First we need to find the coordinates (h, k) of the circle
x² - 8x + y² - 6y = -16
-2h = -8 => h = 4
-2k = -6 => k = 3
(h,k) = (4, 3)
Rewrite the equation in a standard circle format
Recall: (x - h)² + (y - k)² = r²
(x - (4))² + (y - (3))² = -16
(x - 4)² + (y - 3)² = -16
Therefore the solution to the circle equation is: (x - 4)² + (y - 3)² = -16 and the curve is attached.
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A cable TV provider charges Nina $99 per month for three services-Internet, land-line phone,
and cable television. In addition, Nina's monthly bill for cell phone calls and text messages
averages $59.70 per month. What is her average cost per day for these four services? Round to
the nearest dollar.
Nina's average cost per day for these four services is $5.
Since, Nina's monthly cost for the cable TV services is $99, and her monthly cost for cell phone calls and text messages is $59.70.
So her total monthly cost is:
$99 + $59.70 = $158.70
Now we need to find the number of days in a month.
Since, There are different ways to do this, but if we assume a month has 30 days,
= $158.70 / 30
= $5.29 (rounded to the nearest cent)
Therefore, Nina's average cost per day for these four services is $5.29. Rounded to the nearest dollar, her average cost per day is $5.
So, Nina's average cost per day for these four services is $5.
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The difference between compound and simple interest on a certain sum of money for
2 years at 8% per annum is Rs. 40. Find the sum.
The sum of money is approximately Rs. 6250.
To find the sum of moneyGiven that the difference is Rs. 40, we must calculate the difference between compound interest and simple interest over a period of two years at an annual rate of 8%.
Assume that P represents the principal amount of money.
The formula for simple interest is: SI = (P * R * T) / 100
The formula for compound interest is: [tex]CI = P * (1 + R/100)^T^ - ^P[/tex]
Where
SI = Simple InterestCI = Compound InterestR = Rate of interest per annumT = Time in yearsThe difference between compound interest and simple interest is Rs. 40. Therefore:
CI - SI = Rs. 40
Substituting the formulas and values into the equation:
[tex](P * (1 + 8/100)^2 - P) - (P * 8 * 2 / 100) = 40[/tex]
Simplifying further:
[tex](P * (1.08^2) - P) - (0.16P) = 40[/tex]
[tex](P * 1.1664 - P) - 0.16P = 40[/tex]
[tex]1.1664P - P - 0.16P = 40[/tex]
[tex]0.0064P = 40[/tex]
[tex]P = 40 / 0.0064[/tex]
[tex]P[/tex] ≈ [tex]6250[/tex]
Therefore, the sum of money is approximately Rs. 6250.
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please help! thank uu ~ :)
Answer:
certain
Step-by-step explanation:
The question says "strawberry OR cherry chew", which means if you have only 17 strawberry and 3 cherry chews, the answer is certain, as you will always pull out one of those options.
Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola:
16.44y = x²
The focus is
The directrix is
The focal diameter is
The vertex is
The axis of symmetry is
As per the given data, Focus: (0, 16.44), Directrix: y = -16.44, Focal Diameter: 32.88, Vertex: (0, 0), and Axis of Symmetry: x = 0 (y-axis).
To determine the focus, directrix, focal diameter, vertex, and axis of symmetry for the given parabola equation, we can rewrite it in standard form, which is of the form [tex](x - h)^2[/tex] = 4p(y - k), where (h, k) represents the vertex.
16.44y = x²
Divide both sides of the equation by 16.44 to isolate y:
y = (1/16.44)x²
Comparing this equation to the standard form, we can see that h = 0 and k = 0.
Therefore, the vertex is (h, k) = (0, 0).
The general equation for a parabola in standard form is given by (x - h)^2 = 4p(y - k), where p is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p can be found using the coefficient of y in the equation (1/4p = 1/16.44).
Thus, p = 16.44.
The focus is located at a distance of p units above the vertex, so the focus is (0, p) = (0, 16.44).
The directrix is located at a distance of p units below the vertex, so the directrix is the horizontal line y = -p, which gives us y = -16.44.
The focal diameter is twice the value of p, so the focal diameter is 2p = 2 * 16.44 = 32.88.
Therefore:
- The focus is (0, 16.44).
- The directrix is y = -16.44.
- The focal diameter is 32.88.
- The vertex is (0, 0).
- The axis of symmetry is the vertical line passing through the vertex, which is the y-axis (x = 0).
Thus, Focus: (0, 16.44), Directrix: y = -16.44, Focal Diameter: 32.88, Vertex: (0, 0), and Axis of Symmetry: x = 0 (y-axis).
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Please answer this question.
Answer:
Step-by-step explanation:
[tex]1c-0.25c=0.75c[/tex]
Find the average value of f(x)….. see the image
The average value of f(x) over the interval [ - 16, 16] is found to be 0.
How do we calculate?The average value of f(x) = 16x over the interval [ - 16, 16] is:
F_average = (1/(b-a)) * ∫(a to b) f(x) dx,
where the value of
a = -16 and b = 16
F_average = (1/(16-(-16))) x ∫(-16 to 16) 16x dx
F_average = (1/32) x [8x²] from -16 to 16
F_average = (1/32) x [8(16² - (-16)²)]
F_average = (1/32) x [8(256 - 256)]
F_average = 0
In concluaion, the average value of f(x) over the interval [ - 16, 16] is determined as 0.
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A box has the shape of a rectangular prism with height 28 cm. If the height is increased by 0.2cm, by how much does the surface area of the box increase? L=13 W=8.7 H=28
The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.
To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.
The formula for the surface area of a rectangular prism is given by:
Surface Area = 2*(length width + length height + width*height)
Initial Surface Area:
Length (L) = 13 cm
Width (W) = 8.7 cm
Height (H) = 28 cm
Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)
Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:
New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm
New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))
To find the increase in surface area, we subtract the initial surface area from the new surface area:
Increase in Surface Area = New Surface Area - Initial Surface Area
Let's calculate the values:
Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²
New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²
Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²
Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.
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NO LINKS!!
Will give brainliest!!!!!
pls help
Answer:
sec B = [tex]\frac{15}{8}[/tex]
Step-by-step explanation:
using the identity
sec B = [tex]\frac{1}{cosB}[/tex]
cos B = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{CD}[/tex] = [tex]\frac{8}{15}[/tex]
then
sec B = [tex]\frac{1}{\frac{8}{15} }[/tex] = [tex]\frac{15}{8}[/tex]
Part II . if f(x)= x-2 and g (x)=-2x+7, what value of x makes f(x)=g(x)?
Part III. Use the substitution method to solve the system of equations. Write your answer as an ordered pair. y=x-2 and y=-2x+7
The value of x is 1/3 and y is -5/3. using substitution method.
We have,
A linear equation has one or two variables.
No variable in a linear equation is raised to a power greater than 1.
No variable is used as the denominator of a fraction.
A linear equation is defined as an equation that is written in the form of ax+by=c.
When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y if x is given.
CALCULATION:-
Y=x-2 -----(1)
y=-2x+7 ---------(2)
putting the value of y in the equation (2)
x-2= -2x+7
x+2x=7+2
3x=9
x=9/3
x=1/9
putting the value of X in equation(1)
Y=x-2 -----(1)
y=1/3-2
y=-5/6
Hence, The value of x is 1/3 and y is -5/3. using substitution method.
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complete question:
Use the substitution method to solve the system of equations write your answer as an ordered pair Y=x-2 and y=-2x+7
Factor x2 − x − 12. (x + 3)(x − 4) (x − 3)(x + 4) (x + 2)(x − 6) (x − 2)(x + 6)
Answer: (x+3)(x-4)
Step-by-step explanation:
What does a positive scatter plot represents y= 2x+0.9
Answer:
Pretty sure the answer is A
Step-by-step explanation:
Of the last 20 trains to pull into Lakeside
Station, 14 were full. What is the
experimental probability that the next
train to pull in will be full?
Write your answer as a fraction or whole
number.
P(full) =
The experimental probability that the next train to pull into Lakeside Station will be full is 7/10.
The experimental probability of the next train to pull into Lakeside Station being full can be calculated by dividing the number of times a full train occurred by the total number of trains observed.
Given that out of the last 20 trains, 14 were full, we can express the experimental probability as a fraction:
P(full) = Number of full trains / Total number of trains observed
P(full) = 14 / 20
Simplifying the fraction, we get:
P(full) = 7 / 10
Therefore, the experimental probability that the next train to pull into Lakeside Station will be full is 7/10.
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22. Find the length of PN if GH = 8 and KP = 4.
Give exact answer.
The length of PN in the circle is 4√2 units.
How to find the radius of a circle?The length of GN in the circle is 8 units and length of KP in the circle is 4.
Therefore, let's find the length PN in the circle as follows:
PM is perpendicular to the chord GH. Therefore, the length KH is equals to the length GK.
Hence,
GH = 8 units
GK = 4 units
KH = 4 units
Therefore,
MP is the radius of the circle just like PN.
PN = MP
Hence, using Pythagoras's theorem,
4² + 4² = PN²
PN = √16 + 16
PN = √32
PN = 4√2 units
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A 25-year-old woman burns 300-60t cal/hr while walking on her treadmill. Her caloric intake from
drinking Gatorade is 140t calories during the tth hour. What is her net decrease in calories after
walking for 5 hours?
The net decrease in calories after walking for 5 hours will be 50 calories.
we have given that the 25-year old woman burns 300-60tcal/hr and Her caloric intake from drinking Gatorade is 110t calories during the t hour.
And we have to find the net decrease in calories after walking for 5 hours.
So, For this purpose,
We know that the
calories burns in one hour = 300-60tt
calories burns in 5 hours = 5(300-60t)
calories burns in 5 hours = 1500- 300t
Now,
Calorie intake in t hours = 110t
And net decrease in calories after walking for 5 hours = 1500- 300t + 140t
the net decrease is 50 cal.
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Research about 5 monuments around the world where Roman numerals are used to depict the year in which they were built explain in 5 sentences about the monument and stick pictures of the same also write the Hindu Arabic form of the Year they were built.
Five monuments around the world where Roman numerals are used to depict the year in which they were built are indicated below.
We have,
the Roman Monuments and the dates they were built:
The roman monuments and the dates they were built are:
Roman Theatre of Merida - 16BC
The White Marble Arch of Septimius Severus - 203 AD
The Pantheon - 125 AD
The colosseum - 70 AD
the Mausoleum of Helena - 28 BC
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9s+13=10s+12 help me out
The answer to the equation 9s + 13 = 10s + 12
We must place the variable s on one side of the equation in order to solve the equation 9s + 13 = 10s + 12. Here's how to accomplish it:
9s + 13 = 10s + 12
First, by taking 9s away from both sides of the equation, let's move all the terms containing s to one side:
9s - 9s + 13 = 10s - 9s + 12
That amounts to:
13 = s + 12
Next, take 12 off of both sides to isolate the variable s:
13 - 12 = s + 12 - 12
1 = s
As a result, s = 1 is the answer to the equation 9s + 13 = 10s + 12
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Find x and the measure of each angle.
Answer:
Solution in attached photo.
Step-by-step explanation:
This question tests on the properties of angles, such as corresponding angles and sum of angles in a straight line.
I need help solving please
The value of slope of line is,
⇒ m = - 1
We have to given that,
Two points on the line are (- 4, 5) and (- 7, 8).
Now, We know that,
Slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is,
m = (y₂ - y₁) / (x₂ - x₁)
Here, Two points on the line are (- 4, 5) and (- 7, 8).
Hence, Slope is,
m = (8 - 5) / (- 7 + 4)
m = 3 / - 3
m = - 1
Therefore, The value of slope of line is,
⇒ m = - 1
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Can you help me solve for x
Applying Pythagoras theorem and trigonometry In the figure the length of x is
18.03 cmHow to determine the side xUsing Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
let y be the required distance
y² = 10² + 15²
y² = 325
y = √18.03
y = 5√13
y = 18.03
To solve for x we use trigonometry tan
tan 45 = 5√3 / x
x = 5√13 / tan 45
x = 5√13
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A square pyramid has a height of 8 inches and a volume of 600 cubic inches. What is the area of the base of the pyramid?
Answer:
Step-by-step explanation:
Si x es un número, un número aumentado en 6
The algebraic expression representing 6 added to x is given as follows:
x + 6.
How to obtain the algebraic expression?The sentence in the context of this problem is given as follows:
"If x is a number, the number added do 6 is given by".
The number is given as follows:
x.
The addition by 6 means that the number 6 is added to the variable x, as follows:
x + 6.
Which is the algebraic expression.
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100 Points! Algebra question. Photo attached. Find the length of the arcs below. Round to the nearest tenth. Please show as much work as possible. Thank you!
The length of the arcs are;
1. s = 6. 4π
2. s = 11. 0π
How to determine the valuesThe formula for calculating the length of an arc is expressed as;
s = rθ
Such that;
s is the length of the arcr is the radius of the circleθ is the central angle in radiansFrom the information given, we have that;
s = 4.25 × 3π/2
Multiply the values, we get
s = 12.75π/2
Divide by the coefficient , we get;
s = 6. 4π
2. The length of the arc would be;
s = 6.62 × 5π/3
Multiply the values, we have;
s = 33. 1π/3
Divide by the value, we get;
s = 11. 0π
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Choose the words to finish the explanation of how to plan a coordinate proof to show that all isosceles right triangles are similar.
The words that has to be kept in the blank space to prove the similarity are (a, 0), (0, a) and scale factor.
Here we have to choose the words to finish the explanation of how to plan a coordinate proof to show that all isosceles right triangles are similar.
Isosceles right triangles are the right triangles which has the two legs of same length.
For that first consider an isosceles right triangle with legs having length "a".
Then if we place the triangle with one of the vertices at origin, then since the length of the legs is "a", the other vertices will be at (a, 0) and (0, a).
If we place another triangle similarly with length of legs "b", then we have to prove that they are similar.
For them to be similar, there must exist a scale factor that maps one triangle on to the other.
Hence the spaces are (a, 0), (0, a) and scale factor.
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