Find the circumference and area of the circle identify the radius diameter of the circle use 3.14 for pi

The measure of the arc AT in this problem is given as follows:

mAT = 159º.

The measure of arc AT is obtained applying the two secant theorem, which states the angle measure of intersection of the two secant segments is half the difference of the measure of the far arc by the measure of the near arc.

The parameters for this problem are given as follows:

Hence the measure of the arc AT in this problem is given as follows:

(mAT - 59)/2 = 50

mAT - 59 = 100

mAT = 159º.

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The probability that a car selected at chance is moving at more than 70mi/hr is 0.02

Normal usually refers to the word "normal" in a normal distribution.

The word normal is used when something occurs that has occurred frequently. The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.

Since the speeds of cars are normally distributed, is expressed as

z = (x - µ)/σ

Where x = speeds of cars

µ = mean speed

σ = standard deviation

From the information given,

µ = 60 mi/hr

σ = 5 mi/hr

P(x < 70 )

For x = 70

z = (70 - 60)/5 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02

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The person that is correct among the students is Frank who said the pencils are an example of parallel lines.

Parallel lines are lines that can never meet. These are lines that run a direction that is quite opposite to each other as we can see from the image. It is clear that the lines as shown are not able to meet at any point even if they are extended.

Thus, the person that is correct among the students is Frank who said the pencils are an example of parallel lines.

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The probability that the sum of the pips selected that is at least 11 would be = 1/12.

To determine the probability of the selected events, the formula for problem should be used which is given below;

Probability = possible outcome/sample space

Possible outcome = at least 11 = (5,6),(6,5),(6,6)

= 3

Sample space = 36

Probability = 3/36 = 1/12

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Answer: 3 7 8 ?

Step-by-step explanation:

Answer:

(0,1)

Step-by-step explanation:

the answer is (0,1)

Step-by-step explanation:

Log(x²+8)=log 10+ log x

Log(x²+8)=log(10×x)

x²+8=10x

x² - 10x + 8=0

x is approximately to - 1 and - 8✅

The solutions to the given equation are x = -1 and x = 8.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

Using logarithmic properties, we can simplify the given equation:

logs(x² + 8) = 1 + log g(x)

logs(x² + 8) - log g(x) = 1

log[(x² + 8)/g(x)] = 1

(x² + 8)/g(x) = 10

x² + 8 = 10g(x)

Now we can solve for x by substituting the given answer options and solving for g(x):

For x = -2 and x = -4:

x = -2:

(-2)² + 8 = 12, which is not equal to 10 g(x) for any value of g(x).

So x = -2 is not a solution.

x = -4:

(-4)² + 8 = 24, which is also not equal to 10g(x) for any value of g(x).

So x = -4 is not a solution.

For x = -1 and x = 8:

x = -1:

(-1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = -1 is a solution.

x = 8:

(8)² + 8 = 72, which is equal to 10g(x) when g(x) = 7.2.

So x = 8 is a solution.

For x = 1 and x = -8:

x = 1:

(1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = 1 is a solution.

x = -8:

(-8)² + 8 = 56, which is not equal to 10g(x) for any value of g(x).

So x = -8 is not a solution.

Therefore,

The solutions to the given equation are x = -1 and x = 8.

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Answer:

Step-by-step explanation:

To find the equation of a circle passing through three points, we can make use of the formula for the circumcenter of a triangle, which is the point where the perpendicular bisectors of the sides of the triangle intersect. The circumcenter is the center of the circle, and the distance from the circumcenter to any of the three points is the radius of the circle. Let's follow these steps to find the equation of the circle:

Step 1: Find the midpoint and slope of the line joining two of the points, say (1, 7) and (8, 6). The midpoint of this line is (4.5, 6.5), and the slope is -1/7.Step 2: Find the equation of the perpendicular bisector of the line joining (1, 7) and (8, 6). Since the slope of this line is -1/7, the slope of the perpendicular bisector is 7 (the negative reciprocal of -1/7). The midpoint (4.5, 6.5) lies on the perpendicular bisector, so we can find the equation of the perpendicular bisector in point-slope form:

y - 6.5 = 7(x - 4.5)Simplifying, we get:

y = 7x - 28

Step 3: Repeat steps 1 and 2 for the other two pairs of points, say

(1, 7) and (7, -1), and (8, 6) and (7, -1).  We obtain the equations:

y = 4x + 3, and y = -5x + 46 respectively.

Step 4: Solve the system of equations

y = 7x - 28, y = 4x + 3, and y = -5x + 46

to find the point where the perpendicular bisectors intersect, which is the circumcenter of the triangle formed by the three points. We get the solution x = 5, y = 4. Therefore, the center of the circle is (5, 4), and the radius is the distance from (5, 4) to any of the three points. Let's use (1, 7) to find the radius:

Radius = \(sqrt((5 - 1)^2 + (4 - 7)^2) = sqrt(17)\)The equation of the circle is then\((x - 5)^2 + (y - 4)^2 = 17\).

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The expression could be used to express the width of the rectangular floor is (2x - 3) feet.

What is a rectangular floor?

A rectangular floor is a type of flooring or a floor plan that is rectangular in shape, meaning it has four sides with 90-degree angles and opposite sides that are parallel to each other.

To find the width of the rectangular floor, we need to use the formula for the area of a rectangle, which is:

Area = Length x Width

In this case, we are given the expression for the area, which is 6x² + 3x - 9. We can factor this expression to get:

6x² + 3x - 9 = 3(2x² + x - 3)

Now, we can use the fact that the area is equal to the length times the width to write:

6x² + 3x - 9 = Length x Width

We want to express the width in terms of x, so we can solve for the width by dividing both sides by the length:

Width = (6x² + 3x - 9) / Length

Width = (6x² + 3x - 9) / (3(2x² + x - 3))

Simplifying the expression, we get:

Width = (2x - 3) / (2x² + x - 3)

Therefore, the expression that could be used to express the width of the rectangular floor is (2x - 3) feet.

So the correct option is B. (2x - 3) feet.

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Answer:

Step-by-step explanation:

Given that Ruben's distance from Barstow is d = |210 -60t|, you want to know the time t when he is exactly 90 miles from Barstow.

The absolute value will be 90 when the argument of the function is either -90 or +90.

The question resolves to two equations:

These two-step linear equations can be solved in the usual way:

Then ...

Ruben is 90 miles from Barstow after driving 2 hours, and again after driving 5 hours.

The area of the largest possible Norman window with a perimeter of 34 feet is approximately 13.108 square feet.

What is the area of the rectangle?

If the rectangle has a length of 'l' and the breadth of 'b', then the area of the rectangle is computed by

  Area = l * b

Let's call the width of the rectangle "w" and the height of the rectangle "h". The perimeter of the Norman window is given by:

P = 2w + πw/2 + 2h = 2w + (π/2)w + 2h

Since we want to maximize the area, we need to express the area of the window in terms of just one variable (either "w" or "h"). The area of the window is given by:

A = (1/2)π(w/2)² + wh = (π/8)w² + wh

Now we can use the perimeter equation to solve for one of the variables in terms of the other, substitute it into the area equation, and then find the maximum value using calculus. Alternatively, we can use the perimeter equation to solve for one of the variables and then use the fact that the area is maximized when the window is a square (i.e., w = h). Let's use the second approach:

From the perimeter equation, we have:

2w + (π/2)w + 2h = 34

Simplifying and solving for h, we get:

h = (17 - w - (π/4)w)/2

Substituting this expression for "h" into the area equation, we get:

A = (π/8)w² + w[(17 - w - (π/4)w)/2]

Simplifying, we get:

A = (-π/8)w²+ (17/2)w - (1/4)(w²)

To find the maximum area, we can take the derivative of this expression with respect to "w", set it equal to zero, and solve for "w". Alternatively, we can complete the square to find the vertex of the parabola. Let's use the second approach:

A = (-π/8)(w² - (17/π)w) = (-π/8)(w - (17/(2π)))² + (289π/64)

Therefore, the maximum area occurs when:

w = 17/(2π)

Substituting this value of "w" back into the expression for "h", we get:

h = (17 - w - (π/4)w)/2 = (17 - 17/(2π) - (π/4)(17/(2π)))/2 = (17/2π) - (17/(8π))

Therefore, the maximum area of the Norman window is given by:

A = (π/8)(17/(2π))² + (17/(2π))[17/2π - 17/(8π)] = 4.25 + (289/32π)

Hence, the area of the largest possible Norman window with a perimeter of 34 feet is approximately 13.108 square feet.

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Answer:

1. c 2.  No, its not the original figure. Its 270 degree turn.

Step-by-step explanation:

Answer:

1.) C 2.) choice d flipped left to right.

Answer:

50.13

Step-by-step explanation:

We can easily find the area of our square, so to get that over with, 6*6=36. Now, for our circle, a full circle would be A=pi*r^2, but we only have half a circle. That means our equation will be A= 1/2(pi*r^2). We have our diameter, but we need our radius. Radius is just half the diameter, so 6/2=3. Now, we multiply. 3^3 is 9, and 9*3.14 is 28.26. All we have to do now is divide that by 2. If we do that, we get 14.13. The area of the semi-circle is 14.13. But we still have to add it to the area of the square, which will be our final step. 36+14.13=50.13, which is your area.

Hope this helps!

Answer:

24

Step-by-step explanation:

Answer:

a) Fill in the spaces

The probability of the event "have a Bachelor's Degree" is affected by the occurrence of the event "never married", and the probability of the event "never married" is affected by the occurrence of the event "have a Bachelor's Degree", so the events are not independent.

b) Probability of a woman aged 25 or older having a bachelor's degree and having never married = P(B n NM) = 0.0369

This probability is the probability of the intersect of the two events, 'have bachelor's degree' and 'have never married' for women aged 25 or older.

Step-by-step explanation:

Complete Question

According to a government statistics department, 20.6% of women in a country aged 25 years or older have a Bachelor's Degree; 16.6% of women in the country aged 25 years or older have never married; among women in the country aged 25 years or older who have never married, 22.2% have a Bachelor's Degree; and among women in the country aged 25 years or older who have a Bachelor's Degree, 17.9% have never married. Complete parts a) and (b) below.

(a) Are the events "have a Bachelor's Degree" and "never married"? independent? Explain.

(b) Suppose a woman in the country aged 25 years or older is randomly selected. What is the probability she has a Bachelor's Degree and has never married? Interpret this probability.

Solution

The probability of the event that a woman aged 25 or older has a bachelor's degree = P(B) = 20.6% = 0.206

The probability of the event that a woman aged 25 or older has never married = P(NM) = 16.6% = 0.166

Among women in the country aged 25 years or older who have never married, 22.2% have a Bachelor's Degree.

This means that the probability of having a bachelor's degree given that a woman aged 25 or older have never married is 22.2%.

P(B|NM) = 22.2% = 0.222

And among women in the country aged 25 years or older who have a Bachelor's Degree, 17.9% have never married

This means that the probability of having never married given that a woman aged 25 or older has bachelor's degree is 22.2

P(NM|B) = 17.9% = 0.179

a) To investigate if the two events 'have a bachelor's degree' and 'have never married' are independent for women aged 25 or older.

Two events are said to be independent if the probability of one of them occurring does not depend on the probability of the other occurring. Two events A and B can be proven mathematically to be independent if

P(A|B) = P(A) or P(B|A) = P(B)

For the two events in question,

P(B) = 0.206

P(NM) = 0.166

P(B|NM) = 0.222

P(NM|B) = 0.179

It is evident that

P(B) = 0.206 ≠ 0.222 = P(B|NM)

P(NM) = 0.166 ≠ 0.179 = P(NM|B)

Since the probabilities of the two events do not satisfy the conditions for them to be independent, the two events are not independent.

b) Probability of a woman aged 25 or older having a bachelor's degree and having never married = P(B n NM)

The conditional probability, P(A|B), is given mathematically as

P(A|B) = P(A n B) ÷ P(B)

P(A n B) = P(A|B) × P(B)

or

= P(B|A) × P(A)

Hence,

P(B n NM) = P(NM n B) = P(B|NM) × P(NM) = P(NM|B) × P(B)

P(B|NM) × P(NM) = 0.222 × 0.166 = 0.036852 = 0.0369

P(NM|B) × P(B) = 0.179 × 0.206 = 0.036874 = 0.0369

Hope this Helps!!!

Answer:

the cost of renting the pavilion for 8 hours = $130

Step-by-step explanation:

$50 plus $10 per hour

so 8 hour  = 10 * 8 = $80

$50 + $80 = $130

9514 1404 393

Answer:

  $62.74

Step-by-step explanation:

The annuity formula can be used to find the payment needed. Fill in the known values and solve for the unknown.

The future balance due to a series of payments is given by ...

  A = P(n/r)((1 +r/n)^(nt) -1)

where A is the account balance P is the payment made each period, n is the number of periods per year, r is the annual interest rate, and t is the number of years.

You have A = $20,000, r = 0.041, n = 12, t = 18 and you want to find P

  P = A(r/n)/((1 +r/n)^(nt) -1)

  P = $20,000(0.041/12)/((1 +0.041/12)^(12·18) -1) ≈ $62.74

A monthly payment of $62.74 is required.

The critical values are 0.622, 0.707, 0.789 and 0.834

The sample size is given as:

n = 8

Calculate the degrees of freedom using

df = n - 2

So, we have:

df = 8 - 2

df = 6

Using the table of values of critical values, we have:

Critical values = 0.622, 0.707, 0.789 and 0.834

By comparing the critical values and the linear correlation coefficient, we can conclude that there is no significant linear correlation.

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The probability that you win is 6%, and the two choices are dependent events option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

A standard deck of playing cards contains 52 total cards, 13 of which are "spades".

The probability of the first draw:

Probability = favorable outcomes/total outcomes

First draw: 1/4

For the second draw:

Second draw = 12/51

The probability that you win = (1/4)(12/51) = 3/51

In percent:

= (3/51)x100

= 5.88 = 6%

Thus, the probability that you win is 6%, and the two choices are dependent on events option (B) is correct.

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The solution to the inequality is x >= -2 for inequality 3x-5≥-11

The given inequality is 3x-5≥-11

Three times of x greater than or equal to minus eleven

x is the variable

3x - 5≥ -11:

Adding 5 to both sides, we get:

3x ≥ -6

Dividing both sides by 3, we get:

solution is  x≥-2

Therefore, the solution to the inequality is x >= -2.

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Answer:

32

.......................................

Answer:

 X values make the ordered pair X comma negative to a solution of the system of inequalities represented by the graph below so let's look at this so we're constraining ourselves to all of the points of the form X comma negative 2 which is another way of saying we're going to constrain ourselves to Y equaling negative 2 if we constrain ourselves to Y equaling negative 2 what do what has to be true of X in order for this point to be a solution too.

Answer:

B and C

Explanation:

Only plant cells have a cell wall and chloroplast

Explanation:

To know the volume of the box, we need to identify the number of cu

9514 1404 393

Answer:

Step-by-step explanation:

Solution of the system by the usual means yields the parametric equations ...

  (a², b², c²) = (41 +t, t -7, 2t)

Since we want t-7 to be a perfect square, we can let ...

  t -7 = n²

  t = n² +7

Then the solutions are ...

  (a, b, c) = (±√(n²+48), n, ±√(2(n² +7)))

The only integer solutions are for n=±1 and n=±11. Then the 16 possible triples are ...

  (±7, ±1, ±4) and (±13, ±11, ±16) . . . where the signs can have any combination

Answer:

Equation of parabola:  8*(y - 2) = (x - 3)^2

or

y = (1/8)*(x - 3)^2 + 2

Step-by-step explanation:

focus at (3,4) and its directrix y = 0.

Focus equation:  (h, k + c) = (3, 4)

Directrix equation  y =  k - c = 0

so  h = 3,   k + c = 4,   k - c = 0

Solve  the system :  k + c = 4 and k - c = 0

add the equations together:     k + c + k - c = 4 + 0

2k = 4

k = 2

so   k + c = 4,    2 + c = 4,   c = 2

4c (y - k) = (x -  h)^2

4*2 *(y - 2) = (x - 3)^2

8*(y - 2) = (x - 3)^2

Answer:

-6x^2-18x+1

Step-by-step explanation:

not fully sure but hope this helps!!