Which of the numbers below is less than 865.473? Select all
that apply.
A) 865.4
B) 865.475
C) 865.471
D) 866

a) The exact circumference of the circle is given as follows: 20π yd.

b) The approximate circumference of the circle is given as follows: 62.8 yd.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius for the circle in this problem is given as follows:

r = 10 yd.

Hence the circumference of the circle is given as follows:

C = 2π x 10

C = 20π yd.

For the approximation, we consider π = 3.14, hence:

C = 20 x 3.14

C = 62.8 yd.

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Answer:

50.26548 Hope that helps

Step-by-step explanation:

v= πr^2

The amplitude of the function is 2, and the period is 2π.

To find the amplitude and period of the function f(x) = -2 sin(x), we can use the standard form of a sine function:

f(x) = A * sin(Bx)

where A represents the amplitude and B represents the reciprocal of the period.

Comparing this with the given function f(x) = -2 sin(x), we can see that A = -2.

Now let's find the period of the function:

The general formula for the period of a sine function is given by:

Period = 2π / |B|

In our case, B = 1, so the period is:

Period = 2π / |1| = 2π

Therefore, the amplitude of the function is 2, and the period is 2π.

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Answer:

1. Circumference of a circle = 2πr or πd (r=radius and d=diameter)

2. Perimeter = 74 feet

3. 2π*5 = 10π

4. π*20 = 20π

Step-by-step explanation:

1. Diameter is equal to radius*2.

2. 25+25+12+12=74

3. Substitute 5 for r in the formula.

4. Substitute 20 for d in the second formula.

To find the margin of error that corresponds to a 95% confidence interval, we first need to calculate the critical value.

For a 95% confidence interval, the critical value is 1.96.  Next, we can use the formula:  Margin of error = Critical value x Standard error
Plugging in the values we have:
Margin of error = 1.96 x 0.022
Margin of error = 0.04312
Therefore, the margin of error that corresponds to a 95% confidence interval is 0.04312. To find the margin of error for a 95% confidence interval, you'll need to use the standard error and the z-score corresponding to the desired confidence level. In this case, the standard error is 0.022, and the z-score for a 95% confidence interval is approximately 1.96.
Margin of Error = Z-score × Standard Error
Margin of Error = 1.96 × 0.022
Margin of Error ≈ 0.04312
So, the margin of error that corresponds to a 95% confidence interval is approximately 0.04312, or 4.312%.

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The bearing of how far east of point G is point H is 51.68 m

Bearing is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass. It is used to describe a particular direction in which an object is traveling.

How to determine this

When point G and point H are 58 m apart

Point H is at a bearing of 63 degrees

i.e At point H = 63°

To calculate how far east of point G is to point H

When North to East is 90°

So, 90° - 63°

= 27°

x meter away from point H to the East

= cos 27° * 58 m

= 0.9114 * 58 m

= 52.86 m

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The length of C'A' is 10 units.

Triangle ABC is dilated by the rule Dy, 5/4

CA = 8

The length of C'A' will be determined by using the formula of scale factor

Scale factor = Dimensions of new figure/ Dimensions of original figure

So, Scale factor = C'A' / CA

(5/4) x CA = C'A'

C'A' = (5/ 4) x 8

C'A' = 10 units

Thus, the length of C'A' is 10 units.

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Answer:

10

Step-by-step explanation:

Edge 2023

Answer:

  the rule for repeated denominator factors applies

Step-by-step explanation:

You want to know why is there not a separate rule in the partial fraction decomposition key idea for what to do if you have a cubic function in the denominator of a rational function.

The rule for repeated denominator factors is that there is a fraction in the partial fraction sum for each power of the denominator factor up to its greatest power.

  A(x)/B(x)^n = a1(x)/B(x) + a2(x)/B(x)^2 + a3(x)/B(x)^3 + ... +an(x)/B(x)^n

This rule applies to cubic factors as well as factors of any other power.

__

Additional comment

The attached calculator display shows an example of a repeated factor.

<95141404393>

There is no separate rule in the partial fraction decomposition key idea for what to do if you have a cubic function in the denominator of a rational function because the general method can be applied to any rational function regardless of the degree of the denominator.

Partial fraction decomposition is the process of decomposing a rational function to a sum of simpler fractions. It is a technique used in the integration and simplification of algebraic expressions. The partial fraction decomposition key idea is a method for separating a rational function into its parts so that it can be more easily manipulated.

1: Factorize the denominator of the rational function into linear factors.

2: Write the partial fraction decomposition of the function as a sum of simpler fractions, with each term having a denominator that matches the factors.

3: Determine the unknown coefficients by equating the coefficients of like terms in the original function and its partial fraction decomposition.

The degree of the denominator does not affect the general method of partial fraction decomposition.

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It will take Isaac 208 months to pay off the mortgage.

A mortgage means to convey (a property) to a creditor as security on a loan.

To calculate the time it will take Isaac to pay off the loan, we can use the formula for the present value of an annuity [tex]PV = PMT * [1 - (1 + r)^-n] / r[/tex]

PV = Present value of the loan

PMT = monthly payment

r = monthly interest rate

n = number of months.

Plugging the value, we get:

[tex]170,000 = 1,050 * [1 - (1 + 0.0025)^{-n} / 0.0025\\(170,000 / 1,050) * 0.0025 = [1 - (1 + 0.0025)^{-n}][/tex]

Using log to solve for n:

[tex]n = -log(1 - (170,000 / 1,050) x 0.0025) / log(1 + 0.0025)\\n = -log0.59523809523 / log 1.0025\\n = 207.776806321\\n = 208.[/tex]

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The missing reasons are

1. Corresponding Angle

2. Alternate Exterior Angle

We know, if a line intersects two parallel lines, the corresponding interior angles on the same side of the transversal will be congruent (equal).

1. Since CL || EK

Then, by the property of parallel line

<BFJ = <ADF (Corresponding Angle)

2. Since CL || EK

Then, by the property of parallel line

<EBH= <LDM (Alternate Exterior Angle)

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There are 84 ways to select 3 lemon drops from the bag.

To arrive at this answer, we can use the combination formula:

nCr = n! / r! (n-r)!

Where n is the total number of items in the bag (15), r is the number of items we want to select (3), and ! represents factorial (the product of all positive integers up to that number).

So, to find the number of ways to select 3 lemon drops, we plug in n=9 and r=3:

9C3 = 9! / 3!(9-3)!
= (9 x 8 x 7) / (3 x 2 x 1)
= 84

Therefore, there are 84 ways to select 3 lemon drops from the bag.

using the combination formula, we can determine the number of ways to select a specific number of items from a larger set. In this case, there are 84 ways to select 3 lemon drops from a bag containing 15 pieces of candy, 9 of which are lemon drops.

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Step-by-step explanation:

If t and w are inversely proportional, it means that as one variable increases, the other variable will decrease by the same factor. In this case, we have the equation t = 4/w, which means that if we multiply w by a certain factor, t will be divided by the same factor.

If we multiply w by 6, the new value of w will be 6 times the original value:

w' = 6w

To find the new value of t, we can substitute w' into the equation:

t' = 4/w'

t' = 4/(6w)

t' = 2/3w

So we see that t has been divided by 6/1 = 6. Therefore, the value of t will decrease by a factor of 6 if the value of w is multiplied by 6.

The final value of the investment after 8 years is approximately $2,346.09.

We can use the formula for compound interest to find the final value of the investment:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the initial investment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = 2000, r = 0.02 (2% expressed as a decimal), n = 4 (compounded quarterly), and t = 8.

Plugging in these values, we get:

A = P(1 + r/n)^(nt)

A = 2,000.00(1 + 0.02/4)(4)(8)

A = 2,000.00(1 + 0.005)(32)

A = $2,346.09

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The curved surface area of cylinder is,

⇒ 90π m²

We have to given that;

the height of the right cylinder is twice it’s diameter.

Hence, We get;

Diameter = 12 / 2 = 6 m

So, Radius = 6 / 2 = 3 m

So, Lateral surface area of cylinder is,

⇒ 2πrh

⇒ 2π × 3 × 12

⇒ 72π m

And, Curved surface area is,

⇒ 2πr²

⇒ 2π × 3²

⇒ 18π m

Thus, The curved surface area is,

⇒ 72π + 18π

⇒ 90π m²

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Answer:

8x+11=5x+2

8x-5x=2-11

3x=-9

÷by 3 both sides

x=-3

Step-by-step explanation:

L side   18  + 10  + 12 = 40

R side = 28

The R side is cut up into lengths of the same ratios as the L

EG =  10 / 40   * 28 =  7

Answer:

m=n + x/p

multiply through by the LCM

which gives

mp=np+x

group like terms and you'll get

mp - np= x

The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;

a) a = 2

b = -2

c = 4

The general equation of a circle is; (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The coordinates of the radius of the circle

The specified equation of a circle is; x² + y² = 9

The coordinates of the center of the circle, is therefore, O = (0, 0)

a) The coordinates of the points P  and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)

((3·√3)/4)/(3/2) = (√3)/2

The specified form of the gradient is; (√3)/a, therefore;

(√3)/a = (√3)/2

a = 2

The value of a is 2

b) The gradient of the tangent to a line that has a gradient of m is -1/m

The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)

The form of the gradient of the tangent at P is b/(√3), therefore;

-2/(√3) = b/(√3)

b = -2

The value of b is; -2

c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates

Slope of the tangent = -2/(√3)

((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)

((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3

(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4

Therefore; c = 4

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The inequality is a < 10

Given that a number a is no more than 10, we need to find the inequality, showing the inequality,

Inequalities are the mathematical expressions in which both sides are not equal.

In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

For example = Olivia is selected in the 12U Softball. How old is Olivia? You don't know the age of Olivia, because it doesn't say "equals". But you do know her age should be less than or equal to 12, so it can be written as Olivia's Age ≤ 12.

This is a practical scenario related to inequalities.

So, the inequality will be =

a < 10

Plotting the inequality,

(check the file attached)

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Answer:

1. 12    2. 3, 4, 7, and 9.     3. 18 and 32

Step-by-step explanation:

To find number 1, you have to find what multiplied by 1/3 is 4. In other words, what divided by 3 is 4. That is 12, so the first is 12, and it can't be anything else. For number 2, you can just put anything less than 12, because 4 would be greater. So, it's 3, 4, 7, and 9. For number 3, you have to imagine what plus 7 is 20, it's 13, but it's not there, so there's nothing for number 3. For number 4, you can put any numbers 13 and greater, because it's a greater or equal sign. So, it's 18 and 32.

Answer:

Step-by-step explanation:

{3, 4, 7, 9, 12, 18, 31}

Question #1: 1/3f = 4

1/3(3) = 1

1/3(4) = 4/3

1/3(7) = 7/3

1/3(9) = 3

1/3(12) = 4

1/3(18) = 6

1/3(31) = 31/3

Question #2: 1/3f < 4

True = 3, 4, 7, 9

False = 12, 18, 31

Question #3: m + 7 = 20

3 + 7 = 10

4 + 7 = 11

7 + 7 = 14

9 + 7 = 16

12 + 7 = 19

18 + 7 = 25

31 + 7 = 38

none of the numbers in the set make the equation true.

Question #4: m + 7 [tex]\geq[/tex] 20

False = 3, 4, 7, 9, 12

True = 18 and 31

There is need to save $3,166.79 each month to build up a 5-month emergency fund over an 18-month period.

To calculate how much you need to save each month to build up a 5-month emergency fund over an 18-month period, follow these steps:

Step 1: Determine your monthly gross income:

Divide your gross annual income by the number of months in a year.

Monthly Gross Income = Gross Annual Income / 12 months

Monthly Gross Income = $52,800 / 12

Monthly Gross Income = $4,400

Step 2: Calculate your monthly savings goal:

Multiply your monthly gross income by the saving percentage allocated for the emergency fund in the 20-50-30 budget model.

Monthly Savings Goal = Monthly Gross Income x Savings Percentage

Monthly Savings Goal = $4,400 * 20%

Monthly Savings Goal = $4,400 * 0.20

Monthly Savings Goal = $880

Step 3: Determine the number of months to save:

Divide the desired number of months to build the emergency fund by the total saving period.

Number of Months to Save = Desired Number of Months / Total Saving Period

Number of Months to Save = 5 months / 18 months

Number of Months to Save = 5 / 18

Number of Months to Save = 0.2778

Step 4: Calculate the monthly saving amount needed:

Divide the monthly savings goal by the number of months to save.

Monthly Saving Amount = Monthly Savings Goal / Number of Months to Save

Monthly Saving Amount = $880 / 0.2778

Monthly Saving Amount ≈ $3,166.79

Therefore, you need to save $3,166.79 each month to build up a 5-month emergency fund over an 18-month period.

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The equation of the parabola graphed is given as follows:

x = 5/9(y + 2)² - 3.

The parabola in the context of this problem is in horizontal form, hence the equation is given as follows:

x = a(y - k)² + h.

In which the parameters are given as follows:

The coordinates of the vertex are given as follows:

(3, -2).

Hence:

x = a(y + 2)² - 3.

When x = 2, y = -5, hence the leading coefficient a is obtained as follows:

2 = a(-5 + 2)² - 3

2 = 9a - 3

9a = 5

a = 5/9

Hence the parabola is:

x = 5/9(y + 2)² - 3.

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Answer:

Dichotomous - Do you think our new line of football shoes are suitable for playing football? (Answer options: Yes Or No)

Rating Scale - On a scale from 1 to 10, how often do you purchase our brand of athletic shoes? (1 being never, 10 being extremely frequently.)

Open-Ended - Which line of our shoes do you find most suitable for playing sports, and why?

Multiple Choice - Which of the follow athletic shoes do you purchase from our company? (Basketball, baseball, football, hiking, or none of the above)

Completion - Fill in the following blank with the type of shoe that best applies to you : I purchase _____ shoes from Athletics Shoe Company.

Answer:

41

Step-by-step explanation:

Use the Pythagorean Theorem to find the hypotenuse.

[tex]a^{2} +b^{2} =c^{2}[/tex]

Plug in the values.

[tex]40^{2} +9^{2} =c^{2}[/tex]

Simplify.

[tex]1600+81=c^{2}[/tex]

Add.

[tex]1681=c^{2}[/tex]

Take the square root of both sides.

[tex]\sqrt{1681}=\sqrt{ c^{2}[/tex]

41=c

A control chart is a visual representation of the various states in a process. The answer is b. True. Control charts are used in quality control and process improvement to monitor and analyze the performance of a process over time.

b. True. A control chart is a graphical tool used to monitor the performance of a process over time. It is a visual representation of the data collected from the process and helps in identifying any patterns or trends that may occur. The chart typically consists of a central line representing the average or target value, and upper and lower control limits representing the acceptable range of values for the process. The data is plotted on the chart, and any points that fall outside the control limits indicate a process that is out of control and may require further investigation. Control charts are commonly used in industries such as manufacturing, healthcare, and finance to ensure that processes are running smoothly and to identify any potential issues early on. Overall, control charts provide a powerful way to monitor and manage processes in a systematic manner.

They help to identify trends, patterns, and variations that may indicate potential issues, allowing for timely corrective actions to be taken.

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Answer:

A and D are true statements.

Explanation:

A: Vertical angles are always congruent. This is a property of vertical angles; they are opposite angles formed by the intersection of two lines and are always congruent.

D: All right angles are congruent. This is a property of right angles, which are defined as angles that measure 90 degrees. All right angles have the same measure, so they are congruent to each other.

B: When a pair of lines are cut by a transversal, the corresponding angles are not always congruent. Corresponding angles are only congruent if the lines are parallel.

C: Inscribed angles that intercept the same arc are not always congruent. The measure of an inscribed angle is half the measure of its intercepted arc, so inscribed angles that intercept the same arc will only be congruent if the arcs have the same measure.

Answer:

There are approximately 163.3 liters in 49 gallons.

Answer:

163.3

Step-by-step explanation:

If each liter is equal to .3 gallons and you need to know how many liters are in 49 gallons

You want to divide 49 by .3 = 163.33333333

The experimental probability of a randomly selected student planning to take auto shop can be found by dividing the number of students.

Who plan to take auto shop (8) by the total number of students surveyed (16):  p(auto shop) = 8/16
Simplifying this fraction, we get: p(auto shop) = 1/2
Therefore, the experimental probability that a randomly selected student plans to take auto shop is 1/2 or 0.5 (as a decimal).

The experimental probability that a randomly selected student plans to take auto shop can be calculated as follows:
P(auto shop) = (number of students planning to take auto shop) / (total number of students surveyed)
P(auto shop) = 8 / 16
By simplifying the fraction, we get: P(auto shop) = 1/2
So, the experimental probability that a randomly selected student plans to take auto shop is 1/2.

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The height of the cylinder whose area is given would be =7.6cm.

To calculate the height of a cylinder, the formula for the area of cylinder should be used and it is given below as follows;

Surface area of cylinder = 2πr²+2πhr

This can also be written as = 2πr(h+r)

surface area = 54cm²

h+r = 9cm

r = ?

54 = 2×2.14×r(9)

54 = 38.52r

r = 54/38.52

r = 1.4

h = 9-1.4 = 7.6cm

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