3.1 Complete the following statements so that they are true: 3.1.1The angle between the tangent and chord is ... 3.1.2Opposite angles of a cyclic quadrilateral are ... 3.2In the diagram below, two circles have a common tangent TAB. PT is a tangent to the smaller circle. PAQ, QRT and NAR are straight lines. Let Q = 40°. N B 40° 3.2.1 Determine, with reasons, THREE other angles equal to 40°. 3.2.2 If P₁= A4 prove that PTRN is a parallelogram. ​

Answer:

gradient = [tex]\frac{1}{2}[/tex] , y- intercept = - [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient) and c the y- intercept )

given

x - 2y = 3 ( subtract x from both sides )

- 2y = - x + 3 ( divide through by - 2 )

y = [tex]\frac{-1}{-2}[/tex] x + [tex]\frac{3}{-2}[/tex] = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex] ← in slope- intercept form

with gradient m = [tex]\frac{1}{2}[/tex] and y- intercept c = - [tex]\frac{3}{2}[/tex]

Answer:

Step-by-step explanation:

the radius of convergence (R) is ∞, and the interval of convergence (I) is (-∞, ∞).

To find the radius of convergence (R) and the interval of convergence (I) of the series given by:

∑ 7(-1)^(n-1) n^n x^n

We can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges absolutely if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

Let's apply the ratio test to the given series:

L = lim(n→∞) |(7(-1)^(n-1) (n+1)^(n+1) x^(n+1)) / (7(-1)^(n) n^n x^n)|

Simplifying and canceling out common factors:

L = lim(n→∞) |(7(n+1) x) / (n^n)|

Taking the absolute value:

L = lim(n→∞) |7(n+1) x / n^n|

Now, let's evaluate the limit:

L = |7x| lim(n→∞) (n+1) / n^n

The limit can be further simplified by applying the ratio test for the sequence:

lim(n→∞) (n+1) / n^n = 0

Therefore, the limit L simplifies to:

L = |7x| * 0 = 0

Since L = 0, which is less than 1, the ratio test indicates that the series converges absolutely for all values of x. Thus, the series converges for all x.

For a series that converges for all x, the radius of convergence (R) is infinite (∞), and the interval of convergence (I) is the entire real number line (-∞, ∞).

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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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Answer:

12.8cm

Step-by-step explanation:

radius = 0.5 X diameter

2mm = 0.2cm

volume of circular metal sheet = π r² h = π (24)² (0.2) = 115.2π cm³.

volume, V, of cylindrical bar = π r² L

L = V/(π r²)

 = 115.2π / (π (3)²)

=  115.2/ 9

= 12.8cm

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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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:

- 0.75x - 6y
- 2¼x + ¼y

Step-by-step explanation:

They are asking you to simplify as much as possible.

The experimental probability of rolling a number less than 3 is given as follows:

p = 3/200.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes for this problem is given as follows:

2000.

The desired outcomes are those with a result of 1 or 2, which are numbers less than 3, hence the amount is given as follows:

16 + 14 = 30.

Hence the experimental probability is given as follows:

p = 30/2000

p = 3/200.

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To calculate the odds that the quarterback will complete the next pass he throws, we need to know the ratio of successful outcomes (pass completions) to total outcomes (all passes attempted).

The quarterback has completed 24 out of 37 passes, so the ratio of successful outcomes to total outcomes is:

24/37

To convert this to odds, we divide the ratio of successful outcomes by the ratio of unsuccessful outcomes:

24/37 ÷ 13/37

Simplifying the division gives us:

24/13

Therefore, the odds that the quarterback will complete the next pass he throws are 24 to 13, or approximately 1.85 to 1.

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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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It is most important to have a random sample in inferential statistics, particularly in making statistical inferences about a population based on the sample data.

Random sampling is a critical component of inferential statistics because it helps to ensure that the sample is representative of the population. When a sample is randomly selected, each member of the population has an equal chance of being included in the sample, which reduces the risk of bias in the results. Without a random sample, the results of statistical analyses may not be accurate or generalizable to the population, and the conclusions drawn from the data may be flawed or misleading.

Therefore, random sampling is crucial in making valid statistical inferences about a population.

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Step-by-step explanation:

How to solve a system of equations using substitution:

1. Choose one of the equations and solve for one of the variables in terms of the other variable.

2. Substitute the expression you found in step 1 into the other equation for the variable you solved for.

3. Solve for the remaining variable.

4. Substitute the value you found in step 3 into either of the original equations to find the value of the other variable.

5. Check your solution by plugging in the values you found in both original equations to make sure they are true.

Example:

Solve the system of equations below using substitution:

2x + y = 8

x - y = 2

1. Solve the second equation for x in terms of y:

x = y + 2

2. Substitute the expression for x from step 1 into the first equation:

2(y + 2) + y = 8

3. Simplify and solve for y:

2y + 4 + y = 8

3y = 4

y = 4/3

4. Substitute the value of y into either of the original equations to find x:

x - (4/3) = 2

x = 8/3

5. Check the solution by plugging in both values into both original equations:

2(8/3) + (4/3) = 8 (true)

(8/3) - (4/3) = 2 (true)

Therefore, the solution to the system of equations is (8/3, 4/3).

How to solve a system of equations by graphing:

1. Rewrite each equation in slope-intercept form, y = mx + b.

2. Graph each equation on the same coordinate plane.

3. Find the point of intersection of the two lines. This is the solution to the system of equations.

4. Check your solution by plugging in the values into both original equations to make sure they are true.

Example:

Solve the system of equations below by graphing:

y = 2x - 1

y = -x + 3

1. Rewrite each equation in slope-intercept form:

y = 2x - 1 is already in slope-intercept form.

y = -x + 3 can be rewritten as y = -1x + 3.

2. Graph each equation on the same coordinate plane:

The two lines intersect at the point (1, 1).

3. Check the solution by plugging in both values into both original equations:

y = 2x - 1: 1 = 2(1) - 1 (true)

y = -x + 3: 1 = -(1) + 3 (true)

Therefore, the solution to the system of equations is (1, 1).

Answer:

Substitution:

Solve one of the equations for either variable.

Substitute the expression from Step 1 into the other equation.

Solve the resulting equation.

Substitute the solution in Step 3 into one of the original equations to find the other variable.

Write the solution as an ordered pair.

Check that the ordered pair is a solution to both original equations.

Graphing:

Graph the first equation.

Graph the second equation on the same rectangular coordinate system.

Determine whether the lines intersect, are parallel, or are the same line.

Identify the solution to the system.

If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.

If the lines are parallel, the system has no solution.

If the lines are the same, the system has an infinite number of solutions.

Answer:

8x+11=5x+2

8x-5x=2-11

3x=-9

÷by 3 both sides

x=-3

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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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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Note that the equation in terms of y, volume of air in a person's lungs in mL and t, in seconds, to represent the given context is y = 800 cos (π/2 t) + 1600.

We know that

The function depicted in the graph exhibits a periodic nature, characterized by its oscillation between two extreme points.

The time period of the function is derived as T = 4 seconds,

Given that each complete oscillation occurs between one crest and the subsequent crest or from one through and the subsequent through.

The midline of this function is y = 1300 mL, which denotes its average value.

Furthermore, the amplitude of this function equals half the distance between both extreme values, equivalent to A = 800mL. Given that the function has a period of 4 seconds and that its first crest is located at (3.5, 2600), it follows that we may represent this function with an equation expressed as:

y = A Sin (2π/T ( t-  c)) + 1300

Where:

A = 800

T = 4

3.5, 2600 is a crest

Thus,

1000 = -A + 1300

A = 300

Solving for A, we get

c =3.5 - T/4 = 0.5

replacing those values, we have:

y = 800 sin (π/2 (t - 0.5)) + 1300

This can be simplified further to read

y = 800 cos (π/2 t) + 1300.

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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

Answer:

17

Step-by-step explanation:

A straight angle is 180

180 = 6z + 1 + 77 combine like terms

180 = 6z + 78  Subtract 78 from both sides

180 - 78 = 6z + 78 - 78

102 = 6z  Divide both sides by 6

17 = z

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

what you have to do is

hope this helps!

Answer:

50.26548 Hope that helps

Step-by-step explanation:

v= πr^2

This is a contradiction, which means that our initial assumption that there are n children is incorrect. Therefore, there is no solution to this problem that satisfies the given conditions.

Let's assume that there are n children in the Smith family.

We know that the father is 48 years old, so the sum of the ages of the mother and children is:

Total age = (n + 1) * 20 (as there are n children and 1 father)

And we also know that the average age of the mother and children is 16, so we can write:

Total age / (n + 1) = 16

Combining these two equations, we get:

(n + 1) * 20 / (n + 1) = 16

Simplifying, we get:

20 = 16

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The total distance that she walks over all three days is 8.5 km.

Given that:

Marcia walked 900 meters on Friday.

On Saturday, she walked 4 kilometers.

On Sunday, she walked 3 kilometers and 600 meters.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

The total distance that she walks over all three days is given as,

⇒ 900 m + 4 km + 3 km + 600 m

⇒ 7 km + 1,500/1,000 km

⇒ 7 + 1.5

⇒ 8.5 km

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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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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

The poster width is 21.7 inches.

Given that the original print of the figure is 3.5 inches wide and 5 inches long,

Here we will use the concept of scale factors,

Scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object.

The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.

For example, a rectangle has a length of 5 units and a width of 2 units. Now, if we increase the size of this rectangle by a scale factor of 2, the sides will become 10 units and 4 units, respectively.

Hence, we can use the scale factor to get the dimensions of the changed figures.

The scale factor (k) = ratio of the corresponding sides,

We need to find the width of the poster if it is 6.2 times wider than the photo,

So, the original width = 3.5 in

Therefore, the poster size = 3.5 x 6.2 = 21.7 inches.

Hence the poster width is 21.7 inches.

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When sample observations can be paired or we have dependent samples, treating these as independent samples will reduce the power of the test.

The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false. In other words, it measures the test's ability to detect a significant effect or difference when one actually exists. When we treat dependent samples as independent, we do not take into account the relationship between the paired observations, which can lead to a loss of information and ultimately reduce the test's power.

In summary, when we have dependent samples and treat them as independent, it will reduce the power of the test, leading to an increased chance of a Type II error. This means that we are more likely to fail to detect a true effect or difference when one actually exists. It is important to properly account for the relationship between paired observations in order to maintain the test's power and decrease the likelihood of making errors in our conclusions.

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The values of the conditional probabilities are

From the question, we have the following parameters that can be used in our computation:

Pennies = 15

Nickels = 28

Dimes = 12

Quarters = 20

So, we have the probability formula to be

P(Quarters | Not a penny) = (Quarter and not a penny)/Not a penny

This gives

P(Quarters | Not a penny) =  20/(28 + 12 + 20)

Evaluate

P(Quarters | Not a penny) =  1/3 = 0.33 = 33.33%

Next, we have

P(Dime| Not a nickel) =  12/(15 + 12 + 20)

Evaluate

P(Dime| Not a nickel) =  12/47 = 0.2553 = 25.53%

Lastly, we have

P(Not a quarter| Not a dime) =  (15 + 28)/(15 + 28 + 20)

Evaluate

P(Not a quarter| Not a dime) =  43/63 = 0.6825 = 68,25%

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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

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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The length of the arc subtended by the angle's rays is 0.02 times the radius of the circle

To find the length of the arc subtended by the angle's rays, we need to know the angle measure. Since we know that 1/360th of the circumference is 0.04 cm long, we can find the circumference by multiplying 0.04 cm by 360, which gives us 14.4 cm.

Now, we need to find the angle measure. Since the circle is centered at the vertex of the angle, the angle measures half the arc it subtends. Thus, we can find the angle measure by dividing the circumference by 2 and then multiplying by 1/360.

Angle measure = (14.4/2) x (1/360) = 0.02 radians

Finally, we can find the length of the arc subtended by the angle's rays by multiplying the angle measure by the radius of the circle.

Length of arc = 0.02 x radius


The length of the arc subtended by the angle's rays is 0.02 times the radius of the circle. The given information of 1/360th of the circumference being 0.04 cm long helped us find the circumference and subsequently the angle measure.

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