FIND THE AREA of this polygon ​

The correct answer is (b) all real numbers except odd multiples of π/2. The domain of validity for cscθ (cosecant) is restricted because cosecant is undefined when the sine of an angle is zero.

In the trigonometric identity cscθ = 1/sinθ, the denominator sinθ becomes zero at odd multiples of π/2 (such as π/2, 3π/2, 5π/2, etc.), resulting in a division by zero error. Therefore, the cosecant function is not defined for these values of θ.

For all other real numbers θ, the sine function is non-zero and well-defined, allowing us to calculate the reciprocal of the sine and determine the value of the cosecant. Hence, the domain of validity for cscθ is all real numbers except odd multiples of π/2, as stated in option (b).

It's important to note that in trigonometry, the domain of validity is determined by avoiding any values that would lead to undefined expressions or division by zero errors.

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The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π, because at these points the sine function equals zero, and division by zero is undefined.

In mathematics, the cosecant function (csc), is defined as the reciprocal of the sine function, or 1/sinθ. The domain of a function are all the possible input values that will yield real numbers (output). For the csc function, its domain includes all real numbers except where the denominator is zero because division by zero is undefined.

In the unit circle context, sine equals zero at 0, π, 2π, ..., and the negative counterparts. Basically, these are the multiples of π. Thus, for the csc function, the domain is all real numbers except multiples of π, which matches option d in your choices.

The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π.

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The approximate size of the cover that Maria will need to buy is 45. 84 square feet

The formula for calculating the circumference of a circle is expressed as;

Circumference = πr²

Where 'r' is the radius of the circle

Now, let's substitute the value of the circumference

24 = 2 × 3. 14 × r

r = 24/6. 28

r = 3. 82 feet

Formula for area = πr²

Substitute value of r

Area = 3. 14 × (3. 82)²

Area = 3. 14 × 14. 59

Area = 45. 84 square feet

Hence, the value is  45. 84 square feet

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The value of $5,000 after 5 years with a 5% interest rate compounded quarterly will be approximately $6,381.41.

To calculate the future value of an investment with compound interest, we can use the formula: FV = P(1 + r/n)^(nt), where FV is the future value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount (P) is $5,000, the interest rate (r) is 5% (or 0.05), the compounding is done quarterly, so n is 4, and the investment period (t) is 5 years. Plugging these values into the formula, we get FV = 5000(1 + 0.05/4)^(4*5) ≈ $6,381.41.

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Answer:

D)  

5

11

This is because there were originally 12 apples and because she did not replace the apple she took out, she has a higher probability of getting a yellow apple.    Hope this helped   :)

Step-by-step explanation:

The results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

Performing the calculation:

(10.52)(0.6721) = 7.0671992

Rounding to the correct number of significant figures, we have:

(10.52)(0.6721) ≈ 7.07

Next, let's calculate (19.09 - 15.347):

(19.09 - 15.347) = 3.743

Rounding to the correct number of significant figures, we have:

(19.09 - 15.347) ≈ 3.74

Therefore, the results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

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Answer:

Slope(m)=-1

Step-by-step explanation:

Answer:

0.8679.

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the z statistic does not lie within the critical region, you cannot reject the null hypothesis but neither can you necessarily accept it.  

What you can do is reject the alternate hypothesis.

The valid conclusion based on the given results is; One can reject the alternate hypothesis.

We are told that;

z-statistic = 2.1

Now, the critical z-values were -1.96 and 1.96

Since our z-statistic does not lie within the critical values region, it means that there is not enough evidence to reject the null hypothesis at the given significance level. However, it means that we can reject the alternate hypothesis.

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Given:

The equation is:

\((x-3)^2+2(x-3)-8=0\)

To find:

The value of x.

Solution:

We have,

\((x-3)^2+2(x-3)-8=0\)

Substitute \(x-3=u\).

\(u^2+2u-8=0\)

Splitting the middle term, we get

\(u^2+4u-2u-8=0\)

\(u(u+4)-2(u+4)=0\)

\((u-2)(u+4)=0\)

Using zero product property, we get

\(u-2=0\text{ and }u+4=0\)

\(u=2\text{ and }u=-4\)

Now, substitute \(u=x-3\).

\(x-3=2\text{ and }x-3=-4\)

\(x=2+3\text{ and }x=-4+3\)

\(x=5\text{ and }x=-1\)

Therefore, the correct option is b.

The solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.

From the question, we are to determine the solution of the given equation

(x - 3)² + 2(x - 3) - 8 = 0

First, we will expand the equation and clear the brackets

\((x - 3)^{2} + 2(x - 3) - 8 = 0\)

\((x - 3)(x - 3) + 2(x - 3) - 8 = 0\)

\(x^{2} -6x + 9 +2x - 6 - 8 = 0\)

Simplifying

\(x^{2} -4x - 5 = 0\)

Factorizing, we get

\(x^{2} -5x +x- 5 = 0\)

\(x(x-5)+1(x- 5) = 0\)

\((x+1)(x-5)= 0\)

Then,

x + 1 = 0 or x - 5 = 0

x = -1 or x = 5

Hence, the solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.

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Answer:

\( - \frac{5 + 5 \sqrt{3} }{2} \)

Option A is the correct option.

Solution,

Multiply and divide by its conjugate.

\( \frac{5}{1 - \sqrt{3} } \times \frac{1 + \sqrt{3} }{1 + \sqrt{3} } \\ = \frac{5(1 + \sqrt{3)} }{(1 - \sqrt{3} )(1 + \sqrt{3)} } \\ = \frac{5 + 5 \sqrt{3} }{ {(1)}^{2} - { (\sqrt{3}) }^{2} } \\ = \frac{5 + 5 \sqrt{3} }{1 - 3} \\ = \frac{5 + 5 \sqrt{3} }{ - 2} \\ = - \frac{5 + 5 \sqrt{3} }{2} \)

hope this helps...

Good luck on your assignment..

To find the point on the surface 6x = y^2 + z^2 where its tangent plane is parallel to a given plane, we need to find a point on the surface and determine the normal vector of the surface at that point.

Then, we can compare the normal vector of the surface to the normal vector of the given plane to check if they are parallel.

Let's first find a point on the surface by substituting a value for either y or z and solving for x. Let's choose y = 0:

6x = 0^2 + z^2

6x = z^2

x = z^2/6

So, one point on the surface is (z^2/6, 0, z).

To find the normal vector of the surface at this point, we can calculate the partial derivatives with respect to x, y, and z:

∂/∂x (6x) = 6

∂/∂y (y^2 + z^2) = 0

∂/∂z (y^2 + z^2) = 2z

The normal vector is then N = (6, 0, 2z) = (6, 0, 2z) / ||(6, 0, 2z)||, where ||N|| represents the magnitude of N.

To determine if the tangent plane is parallel to a given plane, we compare the normal vector of the surface to the normal vector of the given plane. If they are parallel, their direction vectors should be proportional.

If the given plane is parallel to the xy-plane and has a normal vector N_1 = (0, 0, 1), we can compare it to the normal vector of the surface. In this case, we see that the z-component of N (2z) is not proportional to the z-component of N_1 (1). Therefore, the tangent plane of the surface at the chosen point is not parallel to the given plane.

To find a point on the surface where its tangent plane is parallel to the given plane, we would need to choose a different point on the surface such that the normal vector of the surface at that point is parallel to the given plane's normal vector.

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Answer:

Step-by-step explanation:

An isosceles triangle is a one that has two of its sides equal. Hence option (c) is correct because here two sides have length of 11.9.

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Answer:

4x-12

Step-by-step explanation:

factor out the equation

Answer:

4 x-12

Step-by-step explanation:

Distribute

8 − 4 ( − + 5 )

8 + 4 − 2 0

Subtract the numbers

8 + 4 − 2 0

− 1 2 + 4

Rearrange terms

− 1 2 + 4

4 − 1 2

Answer:

the answer 95 degrees

Step-by-step explanation:

9/5*35*+32

Answer:

its D

Step-by-step explanation:

D

Answer:

D. Yes, a 180° rotation about the origin will map ABCD to WXYZ. No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Using number line method:

-8+19=11

11+8=19

Answer:

19 is the answer

19 -8+8=19

17576000 courses can be given unique catalog numbers.

There are three numbers and three English letters.

Each of three numbers can be chosen from 0 to 9, so the ways to choose each number is  = 10

So the total number to choose three numbers = 10*10*10 = 1000

Each of letters can be chosen from A to Z.

Number of choice for the each letter = 26

So, the outcomes of letter combination = 26*26*26 = 17576

Hence the total possible catalog numbers = 1000*17576 = 17576000

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Answer:

The answer is

\(y = - 5\)

Step-by-step explanation:

\(m = 0 \\ y = mx + c \\ y = c \\ y = - 5\)

The predicted number of adults in Oak City whose main source of news is newspapers or the radio is 85

To predict the number of adults in Oak City whose main source of news is newspapers or the radio, we need to add the number of adults who answered "Newspapers" to the number of adults who answered "Radio".

According to the sample data

Number of adults who answered "Newspapers": 64

Number of adults who answered "Radio": 21

Therefore, the predicted number of adults in Oak City whose main source of news is newspapers or the radio we have to use the addition

64 + 21 = 85

Rounding this answer to the nearest whole number, we get

85 ≈ 85

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The given question is incomplete, the complete question is:

There are 44,000 adults living in Oak City. In examining attitudes toward the news, a research group asked a random sample of Oak City adults "What is your main source of news?" The results are shown below. Main Source of News Newspapers Number of Adults 64 Internet 80 Television 126 Radio 21 Other 40 Based on the sample, predict the number of adults in Oak City whose main source of news is newspapers or the radio. Round your answer to the nearest whole number.

The required answers are:

a.The position function for \(0 \leq t \leq 3\)  is \(s(t) = 3016t - (t^3 / 3)\)

b. The position function for\(0 \leq t \leq 3\) is \(s(t) = 3016t - (t^3 / 3)\)

c. At the instant its velocity reaches 300 mi/hr, the airplane has traveled approximately 109,633 miles.

Given that the velocity function is \(v(t) = 3016 - t^2\) min/hr.

a. To determine the position function,  to integrate the velocity function with respect to time, integrate it to find the position function.

\(\int\limits {v(t)} \, dt = \int\limits {3016 - t^2} \, dt\)

Integrating, gives:

\(s(t) = 3016t - (t^3 / 3) + C\)

Since s(0) = 0, substitute t = 0 into the position function:

s(0) = 3016(0) - (0^3 / 3) + C

0 = 0 + 0 + C

C = 0

Therefore, the position function for \(0 \leq t \leq 3\)  is \(s(t) = 3016t - (t^3 / 3)\)

b. To find how far the airplane travels in the first 2 hours, we evaluate the position function at t = 2 and subtract the position at t = 0:

s(2) - s(0) = \((3016(2) - (2^3 / 3)) - (3016(0) - (0^3 / 3))\)

s(2) - s(0) = 6032 - (8 / 3) - 0

s(2) - s(0) = 6024 / 3 ≈ 2008 miles

Therefore, the airplane travels approximately 2008 miles in the first 2 hours.

c. To determine how far the airplane has traveled when its velocity reaches 300 mi/hr, to find the time at which the velocity function v(t) equals 300. We set v(t) = 300 and solve for t:

\(3016 - t^2 = 300\)

\(t^2 = 3016 - 300\)

\(t^2 = 2716\)

\(t = \sqrt{2716} = 52.1\)

Substitute this time value into the position function to find the distance traveled:

\(s(52.1) = 3016(52.1) - (52.1^3 / 3)\)

s(52.1)= 156,837.6 - 47,204.6

s(52.1)≈ 109,633 miles

Therefore, at the instant its velocity reaches 300 mi/hr, the airplane has traveled approximately 109,633 miles.

Hence, the required answers are:

a.The position function for \(0 \leq t \leq 3\)  is \(s(t) = 3016t - (t^3 / 3)\)

b. The position function for\(0 \leq t \leq 3\) is \(s(t) = 3016t - (t^3 / 3)\)

c. At the instant its velocity reaches 300 mi/hr, the airplane has traveled approximately 109,633 miles.

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Answer:

2/1x-12/6

Step-by-step explanation:

Answer:

\(x^{-3} * x^{-3}\)

Answer:

y= -2x^2+4x+126

Step-by-step explanation:

Answer:

as far as he wants. is he walking the diameter, to the store, across the field?

if it is across the field, then about 255 ft

Step-by-step explanation:

Bob will walk for 2512 feet.

The circumference of a circle is basically the perimeter of the circle.

Given that, the stadium has a diameter of 800 ft,

Bob will walk on the perimeter of the stadium, therefore,

circumference = π*diameter

= 800*3.14 = 2512

Hence, Bob will walk for 2512 feet.

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Answer:

Step-by-step explanation:

The length of side length VY is 4z+2

The same as side length WX

Answer:

(0,0)

Step-by-step explanation:

Answer:

15/4 or 3.75.

Step-by-step explanation:

Multiply the numbers as you would in regular math to get 3x5=15. leaving you with 15/4.

The probability, when the two six-sided dice is rolled can be found to be:

P(not 4):

There are 3 combinations that result in a sum of 4: (1, 3), (2, 2), and (3, 1). Thus, there are 36 - 3 = 33 outcomes that do not result in a sum of 4.

P(not 4) = 33 / 36

P(not 4) = 33 / 36 = 11 / 12

P(not 11):

There are 2 combinations that result in a sum of 11: (5, 6) and (6, 5). Thus, there are 36 - 2 = 34 outcomes that do not result in a sum of 11.

P(not 11) = 34 / 36

P(not 11) = 34 / 36 = 17 / 18

So, the probability of not rolling a sum of 4 is 11/12, and the probability of not rolling a sum of 11 is 17/18.

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Answer:

37⁰

Step-by-step explanation:

180⁰ - 106⁰ =74⁰

74⁰ ÷ 2= 37⁰

13 and 13√2 is the value of x and y in the given diagram

The given diagram is a right triangle, we need to determine the value of x and y.

Using the trigonometry identity

tan45 = opposite/adjacent
tan45 = x/13

x = 13tan45
x = 13(1)
x = 13

For the value of y

sin45 = x/y

sin45 = 13/y
y = 13/sin45

y = 13√2
Hence the exact value of x and y from the figure is 13 and 13√2 respectively.

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