The area A of the minor sector OAC shown below is 180pi cm2. The original circle had a center at O and a radius R measuring 30 cm.


Find the value of ANGLE , the measure of the angle /_AOC.


Give your answer in radians in terms of Pi.

I apologize, but as a text-based AI model, I am unable to provide handwritten answers or show work in form of formulas. To determine annual interest rate of 4.5%, we can use compound interest formula.

To determine how long it will take to double your money with an annual interest rate of 4.5%, we can use the compound interest formula:

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

Where:

A = Final amount (double the initial amount)

P = Principal (initial amount)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Time (in years)

In this case, we want to find the value of t. Let's assume the initial amount is P, and the final amount is 2P (double the initial amount). Substituting these values into the formula, we have:

2P = P(1 + 0.045/n)^(nt)

To solve for t, we can divide both sides of the equation by P and simplify:

2 = (1 + 0.045/n)^(nt)

Taking the natural logarithm (ln) of both sides of the equation:

ln(2) = nt ln(1 + 0.045/n)

Now, we can solve for t:

t = ln(2) / (n ln(1 + 0.045/n))

The value of n will depend on how frequently the interest is compounded (e.g., annually, semi-annually, quarterly, etc.). By substituting the appropriate value for n and evaluating the expression, you can determine the time it will take to double your money.                                              Note: If you provide the specific compounding period, I can assist you in calculating the exact time it takes to double your money.

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The National Archive of Criminal Justice Data (NACJD) is a resource that provides access to criminal justice data for research purposes.

The archive collects and disseminates data from various sources, including federal agencies, state agencies, local agencies, and investigator initiated research projects. However, there is an exception to this list of sources. The NACJD does not source data from investigator-initiated research projects.
Investigator-initiated research projects are research studies that are conducted by researchers who are not affiliated with any law enforcement or criminal justice agency. These researchers may obtain their data from various sources, such as interviews, surveys, or public records. The NACJD does not collect data from these sources because it only provides access to data that is obtained through established criminal justice channels.
The criminal justice data that is available through the NACJD is crucial for researchers to better understand and analyze criminal behavior, crime trends, and policy outcomes. By having access to reliable and valid data, researchers can provide evidence-based recommendations to improve the criminal justice system.

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Answer:y equals 11

Step-by-step explanation:

To solve the equation 2sec^2(x) = 3 - tan(x) in the interval [0, 2π), we can follow these steps:

Rewrite the equation in terms of sine and cosine using the trigonometric identities:

2(1/cos^2(x)) = 3 - sin(x)/cos(x)

Multiply both sides by cos^2(x) to eliminate the denominators:

2 = (3cos^2(x) - sin(x))/cos(x)

Simplify the equation:

2cos(x) = 3cos^2(x) - sin(x)

Rearrange the equation and combine like terms:

3cos^2(x) - 2cos(x) - sin(x) = 0

Unfortunately, this equation cannot be easily solved algebraically to find exact solutions in the given interval [0, 2π). Therefore, the exact solutions for this equation cannot be determined.

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Answer:

a) AE and BC are parallel (as shown by the markings)

b) ED and CD are equal in length (as shown by the markings)

c) 3: AE is perpendicular AB, AB is perpendicular to AE/AC, AC is perpendicular to AB

Answer:

it's C had to double-check really quick sorry

Step-by-step explanation:

Answer:

Step-by-step explanation:

Range: [3, 8]

Answer:

No

Step-by-step explanation:

9.222222 is not a irrational number.

Hope this helps plz hit the crown :D

Answer:

yes it is

Step-by-step explanation:

A box contains five cards lettered A,A,B,C,D. If one card is selected at random from the box and NOT replaced, what is the probability that Jill will draw an A and then a C?​

step 1

Find the probability that Jill draw an A

P=2/5

step 2

Find the probability that jill draw a C

P=1/4

therefore

the probability that Jill will draw an A and then a C is

P=(2/5)(1/4)

P=2/20

Answer:

(i) ∠ABH = 14.46⁰

(ii) The length of AH = 4.6 m

Step-by-step explanation:

From the image uploaded;

Consider △ABC;

the length of b is calculated by applying Pythagoras theorem as follows;

b² = c² - a²

b² = (13.2)² - (6.9)²

b² = 126.63

b = √126.63

b = 11.25 m

Also, ∠ABC is calculated as;

\(Cos \ B = \frac{a^2+c^2-b^2}{2ac} \\\\Cos \ B = \frac{(6.9)^2+(13.2)^2-(11.25)^2}{2(6.9 \times13.2)}\\\\ Cos \ B = \frac{95.288}{182.16} \\\\ Cos \ B = 0.5219 \\\\B = Cos ^{-1} (0.5231)\\\\B = 58.46 ^o\)

Consider △CBH, ∠CBH is calculated as;

∠CBH = 90⁰ - 46⁰ = 44⁰

(i) ∠ABH will be calculated as;

∠ABH = θ

θ + 44⁰ = ∠ABC

θ + 44⁰ = 58.46⁰

θ = 58.46⁰  - 44⁰

θ = 14.46⁰

Thus, ∠ABH = 14.46⁰

(ii) The length of AH

length HC is calculated as;

\(tan \ 46^o =\frac{6.9}{HC} \\\\HC = \frac{6.9}{tan \ 46^o } \\\\HC = 6.66 \ m\)

length of AH = CA - HC

x = b - HC

x = 11.25 - 6.66

x = 4.6 m

length of AH = 4.6 m

Answer:

rounded to the nearest hundredth its 46.21

Step-by-step explanation:

trust im smart

Answer:

D.) x - 4

Step-by-step explanation:

This is a graph of an exponential/quadratic function. There general structure looks like this:

ax² + bx + c

Generally, when finding the zeros these functions, you are told to factor the equation. Once you have factored the equation, you can set the factors equal to zero to find the points where the function touches the x-intercept.

That being said, you can determine the factors without having the entire equation by identifying the zeros on the function. On this graph, there is a zero at (4,0). This means that one of the factors must have been "x - 4". You can check your work by setting the factor equal to zero.

x - 4 = 0

x = 4

Answer:

x*x +4*x-8*x -8*4

x^2+4x-8x-32

x^2-4x-32

Approximately 12 percent of the people in Olde Town own both a goat and a chicken.

Let's assume there are 100 people in Olde Town. According to the given information, 40 percent of people own a goat, which means there are 40 goat owners. Additionally, 35 percent of goat owners also own a chicken, which means there are 35 percent of 40, which is 14 people, who own both a goat and a chicken.

Moreover, it is mentioned that 30 percent of people own a chicken. So, there are 30 chicken owners in Olde Town. However, we have already accounted for 14 of them who also own a goat. Therefore, there are 30 minus 14, which is 16 people who own only a chicken.

To find the number of people who own both a goat and a chicken, we add the number of people who own both to the number of people who own only a chicken: 14 + 16 = 30.

To calculate the percentage, we divide the number of people who own both by the total population of Olde Town (100) and multiply by 100: (30 / 100) * 100 = 30 percent. So, approximately 30 percent of the people in Olde Town own both a goat and a chicken, which is equivalent to 12 people.

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Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

Answer:

The answer is 4 and x-1

Step-by-step explanation:

y= 4

y=x-1

(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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Answer:

6. 8

7. 5

8. 5

9. 17

10. 6

Hope this helps!

The two arbitrary numbers are -14 and 24

Arbitrary numbers:

Basically, the arbitrary numbers refers the numbers that have no special property, other than being large-valued.

Given,

The sum of two arbitrary numbers is 10.

And we need to find if the sum of the squares of the two numbers added to their difference is 62, what are the numbers.

Let us consider x and y be the two arbitrary numbers.

Then according to the given question,

The sum of two arbitrary numbers is 10.

And it ca be written as,

=> x +  y = 10 ------------------------(1)

And then we know that the sum of the squares of the two numbers added to their difference is 62,

Then

=> (x + y)² + (x - y) = 62

Here we have to apply the value of x + y on the equation then we get,

=> 10² + x - y = 62

=> 100 +(x - y) = 62

=> x - y = -38 ------------------(2)

Now, we have to solve the equation (1) and (2), then we get,

The value of x as,

=> 2x = -28

=> x = -14

So, the value of y is calculated as,

=> -y = -38 + 14

=> -y = -24

=> y = 24

Therefore, the value of x is -14 and the value of y is 24.

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Answer:

-7 , -2 , 0 , 5 , 6

Answer:

a. -7,-2,0,5,6

Step-by-step explanation:

The reason this is because the larger the negative interger the less it actually is.

Answer:

8.145

Step-by-step explanation:

Answer:

8128

Step-by-step explanation:

this is because this is the one that when you subject from 8074, it is the lowest number

Answer:

yes, the answer to this question is y=2x

Answer:

Step-by-step explanation:

Answer:

Acute

Step-by-step explanation:

The Pythagorean Theorem refers to \(a^{2} + b^{2} =c^{2}\), no (and only on right angled triangles)? We would have to use the cosine and sine rules to answer this question.

First, lets use the cosine rule to get an angle, then use the sine rule to get another, which would allow us to then determine the third, which will allow us to determine the type of triangle.

\(cosA= \frac{b^2+c^2-a^2}{2bc}\) →  \(cosA= \frac{77^2+56^2-59^2}{2(77)(56)}\) → \(cosA= \frac{5584}{8624}\) → \(cos^{-1}\frac{5584}{8624} = A\) → \(A = 49.65 = 50\)~

Now we can use the sine rule to find the other angles:

\(\frac{sin50}{59} = \frac{sinB}{77}\) → \(77\frac{sin 50}{59} = sin B\) → \(sinB = 0.9997529...\) → \(sin^{-1} 0.9997529... = B = 88.726... = 89\)~

So, if A = 50° and B = 89°, that would mean that the remaining angle is \(180 - 50-89=180-139=41\)

A = 50°

B = 89°

C = 41°

As none of the angles exceed or are equal to 90°, it must be an acute triangle!

Answer:

7(x + 5)

Step-by-step explanation:

7x has the following factors: 1,7,x

35 has the following factors: 1, 5, 7, 35

the greatest common factor is 7

7(x + 5) = 7x + 35

Answer:

38.28 years

Step-by-step explanation:

The computation of the time period is shown below:

Given that

RATE = 6.2%

PV = $500

PMT = $0

FV = $5,000

The formula is shown below:

= NPER(RATE;PMT;-PV;FV;TYPE)

After applying the above formula, the time period is 38.28 years

Hence, in order to save $5,000 it would take 38.28 years

The probability of a car rolling over in a crash is approximately 0.016, or 1.6%, indicating that it is unlikely for a car to roll over in a crash.

We have,

To find the probability that a randomly selected passenger car crash results in a rollover, we divide the number of rollovers by the total number of crashes:

Probability of a rollover = Number of rollovers / Total number of crashes

Probability of a rollover = 83,600 / (83,600 + 5,127,400) ≈ 0.016

The probability of a rollover is approximately 0.016, or 1.6%.

Since the probability is relatively low, it can be considered unlikely for a car to roll over in a crash.

Thus,

The probability of a car rolling over in a crash is approximately 0.016, or 1.6%, indicating that it is unlikely for a car to roll over in a crash.

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Answer:

D= M/V

7.85= M/50

M= 7.85 x 50

392.5 g

Answer:  the value of f′′′(4) is 3/256.

Step-by-step explanation:

Given the third-degree Taylor polynomial:

f(x) = (x−4)³/512 − (x−4)²/64 + (x−4)⁴/2

To find the value of f′′′(4), we need to differentiate the polynomial three times and evaluate it at x = 4.

First derivative:

f'(x) = 3(x−4)²/512 − 2(x−4)/64 + 4(x−4)³/2

Second derivative:

f''(x) = 6(x−4)/512 − 2/64 + 12(x−4)²/2

Third derivative:

f'''(x) = 6/512 + 24(x−4)/2

Now, substitute x = 4 into f'''(x):

f'''(4) = 6/512 + 24(4−4)/2

= 6/512 + 0

= 6/512

= 3/256

Therefore, the value of f′′′(4) is 3/256.