TIME SENSITIVE, 50 POINTS, MULTIPLE CHOICE
Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.

Answer:

Set your calculator to Degree mode.

10² = 6.78² + 4² - 2(6.78)(4)(cos x)

100 = 61.9684 - 54.24(cos x)

38.0316 = -54.24(cos x)

cos x = -.701173

[tex]x = {cos}^{ - 1} ( - .701173)[/tex]

x = 134.52°

Answer: 29.9986-----30.0 degrees

Step-by-step explanation:

x = [tex]tan^-^1(5.6/9.7)\\\\toa[/tex]

[tex]\tan(x )=\cfrac{\stackrel{opposite}{5.6}}{\underset{adjacent}{9.7}} \implies \tan^{-1}(~~\tan( x )~~) \approx \tan^{-1}\left( 0.58 \right) \\\\\\ x \approx\tan^{-1}\left( 0.58 \right)\implies x \approx 30.0^o[/tex]

Answer:

[-infinity, 4]

Step-by-step explanation:

-9x + 3 >= -33
-9x >= -36

x<=4 (sign switched because of dividing both sides by a negative integer in an inequality)
Therefore, x is less than or equal to 4

[ - infinity, 4]

Answer:

Step-by-step explanation:

5 minutes is the outlier. It sticks out from the rest.

Answer: 11

Step-by-step explanation:

this is a sequence of odd numbers.

it goes;

1,3,5,7,9,11,13,15,17,19,21,23....

The restricted domain of the function is 0≤s≤25

The equation is a(s) = 37.5s - 1.5s²  models the function represented in the table

a(s) = s(37.5 - 1.5s)

The critical points are s=0 or

37.5 - 1.5s

37.5 = 1.5s

s=25

As area can not be negative, the area should be positive

s< 0 and s>25

Therefore, restricted domain is 0≤s≤25

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Answer:

dört yarım saat 2 saattir

Step-by-step explanation:

Answer:

Refer to the step-by-step.

Step-by-step explanation:

Verify the given identity.

[tex]E_0\cos^4(\theta)=E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2[/tex]

Pick the more complex side to manipulate, in this case it is the R.H.S.

(1) - Apply the following double-angle identity

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Double-Angle Identity:}}\\\\\cos(2A)=1-2\sin^2(A)\end{array}\right}[/tex]

[tex]E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2\\\\\Longrightarrow \boxed{ E_0\Big(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2}\Big )^2}[/tex]

(2) - Split of the right fraction

[tex]E_0(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2} )^2\\\\\Longrightarrow E_0(\frac{1}{2} +\frac{1}{2} -\frac{2\sin^2(\theta)}{2})^2\\\\\Longrightarrow \boxed{E_0(1 -sin^2(\theta))^2}[/tex]

Apply the following Pythagorean identity

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\sin^2(A)=\cos^2(A)\end{array}\right}[/tex]

[tex]E_0(1 -sin^2(\theta))^2\\ \\\Longrightarrow E_0(\cos^2(\theta))^2\\\\\therefore \boxed{E_0\cos^4(\theta)=E_0\cos^4(\theta)}[/tex]

Thus, the identity is verified.

It has been proven and verified that [tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex] below.

In Mathematics and Geometry, the standard equation of a cosine function is represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

In this exercise, you are required to prove that the right-hand side of the cosine function is equal to left-hand side of the cosine function;

[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex]

From the double-angle formulas, we have:

2sin²θ = 1 - cos2θ

cos2θ = 1 - 2sin²θ

Next, we would evaluate the right-hand side of the cosine function by substituting "1 - 2sin²θ" for cos2θ as follows;

[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1-2sin^2 \theta}{2} )^2\\\\E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1}{2} -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -sin^2 \theta)^2\\\\[/tex]

E₀cos⁴θ = E₀(1² - (sin²θ)²)

E₀cos⁴θ = E₀(1 - sin⁴θ)  ⇒ (Verified).

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The height of the equilateral triangle is a = 5√3 inches

Given data ,

Since the triangle is equilateral, all sides are of equal length.

Let's call the length of one side x.

Therefore, the perimeter of the triangle is 3x, which is given to be 30 inches.

On simplifying , we get

3x = 30

x = 10

Now, we know that the height of an equilateral triangle is given by the formula:

height = √3/2 x

Substituting the value of x, we get:

height = √3/2 x 10

height = 5√3 inches

Hence , the height of triangle is 5√3 inches

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Since the difference between the areas of the two rectangles is 64 cm², it has been proven that it is equal to x² - 2x - 35 = 0.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

Area of rectangle M = L × B

Area of rectangle M = (x - 3) × (3x + 4)

Area of rectangle M = 3x² - 5x - 12

Area of rectangle N = L × B

Area of rectangle N = (x + 2) × (x - 3)

Area of rectangle N = x² - x - 6

Difference = Area of rectangle M - Area of rectangle N

Difference = 3x² - 5x - 12 - (x² - x - 6)

Difference = 3x² - 5x - 12 - x² + x + 6

64 = 2x² - 4x - 6

0 = 2x² - 4x - 6 - 64

0 = 2x² - 4x - 70

By dividing all through by 2, we have:

0 = x² - 2x - 35

x² - 2x - 35 = 0 (Proven).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Median, because Sunny Town is symmetric.

09. The total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals.

10. The total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

In order to find the marginal frequencies, we need to calculate the totals for each category separately.

For question 9:

The marginal frequency for "Set Academic Goals - yes" is 64 + 54 = 118. This represents the total number of individuals who answered "yes" to setting academic goals.

The marginal frequency for "Set Academic Goals - no" is 168 + 142 = 310. This represents the total number of individuals who answered "no" to setting academic goals.

The marginal frequency for "Male" is 64 + 168 = 232. This represents the total number of males.

The marginal frequency for "Female" is 54 + 142 = 196. This represents the total number of females.

Interpretation:

The marginal frequencies provide us with the total counts for each category in a contingency table. In this case, we can see that out of the total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals. Additionally, there were 232 males and 196 females in the sample.

For question 10:

The marginal frequency for "Cat - yes" is 104 + 186 = 290. This represents the total number of individuals who have cats.

The marginal frequency for "Cat - no" is 208 + 98 = 306. This represents the total number of individuals who do not have cats.

The marginal frequency for "Dog - yes" is 104 + 208 = 312. This represents the total number of individuals who have dogs.

The marginal frequency for "Dog - no" is 186 + 98 = 284. This represents the total number of individuals who do not have dogs.

Interpretation:

The marginal frequencies reveal the total counts for each category in the contingency table. In this case, we can observe that out of the total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

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After simplification,

(2x + 1)/2(x^2)

Given,

(x/4)+(1/8)/(x^2/4)

Simplifying,

Firstly take LCM of 4 and 8,

LCM of 4 and 8 will be 8.

Then,

(2x +1) /(8) / x^2 /4

Further,

Take reciprocal of the denominator,

(2x +1) /(8) (4/x^2)

(2x + 1)/2(x^2)

Hence after simplification the expression becomes (2x + 1)/2(x^2).

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Answer:

p(3) = 16

Step-by-step explanation:

to evaluate p(3) substitute x = 3 into p(x)

p(3) = 0.5(3 - 5)² + 14

      = 0.5(- 2)² + 14

      = 0.5(4) + 14

      = 2 + 14

      = 16

The measure of <BED = 135 degrees

To determine the value, we need to know the following;

From the information given, we have that;

Angle AED + Angle ACD are on a straight line

Now, susbtitute the values, we have that;

135 + ACD = 180

collect like terms

ACD = 180 - 135

subtract the values

ACD = 45

Then, we have that;

<BED = <ACD + <BEC

Substitute the values

<BED = 45 + 90

<BED = 135 degrees

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Answer:

LN and NK

Step-by-step explanation:

A perpendicular bisector of a line segment divides the line segment into 2 equal halves.

Here, line JM is a perpendicular bisector of line segment LK at point N. So, line JM divides the line segment LK into 2 equal halves.

The two equal halves are segment LN and segment NK.

Therefore, segment LN is congruent to segment NK.

Answer:

The rectangle is 7.9 meters by 2.9 meters.

Step-by-step explanation:

Let l be the length and w be the width

l = w + 5

A = 23 m²

Formula: A = lw

Solve for the dimensions

23 = (w+5)w

23 = w² + 5w

w² + 5w - 23 = 0

Use quadratic formula to find the possible value/s of w

[tex]w = \frac{-b+-\sqrt{b^2-4ac} }{2a}\\ w = \frac{-5+-\sqrt{5^2-4(1)(-23)} }{2(1)} \\w = \frac{-5+-\sqrt{25+92} }{2}\\ w = \frac{-5+-\sqrt{117} }{2} \\w = \frac{-5+-\sqrt{9(13)} }{2} \\w = \frac{-5+-3\sqrt{13} }{2}\\ w = \frac{-5+3\sqrt{13} }{2} = 2.9\\ w = \frac{-5-3\sqrt{13} }{2} = -7.9[/tex]

Since we're dealing with dimensions, take the positive value which is 2.9.

w = 2.9 m

Substitute the value to l = w + 5

l = 2.9 + 5

l = 7.9 m

x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex], we can use the Factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).the remainder when we divide [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex] by x-7 is 4054.

To check if x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$,[/tex] we can use the factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).

To check if x-7 is a factor, we evaluate the polynomial at x=7:

[tex]f(7) = 7^5+5\cdot7^4-2\cdot7^3+4\cdot7^2+8\cdot7+3976 = 384004$.[/tex]

Since [tex]$f(7)\neq 0$[/tex], we can conclude that x-7 is not a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$.[/tex]

To find the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$[/tex]by x-7, we can use polynomial long division or synthetic division. Using polynomial long division, we get:

  [tex]x^4 + 12x^3 + 82x^2 + 578x + 4046\\x-7 | x^5 + 5x^4 - 2x^3 + 4x^2 + 8x + 3976\\- x^5 + 7x^4[/tex]

    ------------

      [tex]12x^4 - 2x^3 + 4x^2 + 8x\\ 12x^4 - 84x^3[/tex]

          -------------

                     [tex]82x^3 + 4x^2 + 8x\\ 82x^3 - 574x^2[/tex]

                      --------------

                                  [tex]578x^2 + 8x\\ 578x^2 - 4046[/tex]

                                    ------------

                                              4054

Therefore, the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$ by $x-7$ is $4054$.[/tex]

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The required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.

Given that the heights of adult parrots are normally distributed with a mean height of 34 cm and standard deviation of 8 cm.

The formula used to calculate the z-score for the height of 18 cm is

z = (x - mean) / standard deviation

By substituting the value of mean and standard deviation gives,

z = (18 - 34) / 8.

On simplification of numerator gives,

z= -16 / 8 = -2.

To find the proportion of parrots more than 18 cm tall by calculating the area under the standard normal curve to the right of z = -2 by the standard normal distribution table.

That implies, proportion = area to right of z = -2 is approximately equal to 0.9772.

The formula used to calculate the number of parrots that is more than 18 cm tall is  proportion × total number of parrots.

That implies, the number of parrots out of 400 birds which are more than 18 cm tall is 0.9772 × 400 = 390.88 ≈ 391.

Therefore, the required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.

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Answer:

the answer is 10.63km/L.

The horizontal transformations are defined as follows:

cos(ax).

They are classified as follows:

The vertical transformations are defined as follows:

acos(x).

They are classified as follows:

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The solution is:

20/29 is the probability that a student chosen randomly from the class plays golf or soccer.

0 is the probability that a student chosen randomly from the class plays golf and soccer.

Here, we have,

given that,

In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer.

There are 9 students who play neither.

Number of students that play = 20

let, students play golf = A

students play soccer = B

so, given that,

n ( A) = 6 and, n ( B) = 14

so, total sample space = 29

now, P(A) = 6/29

P(B) = 14/29

and, P(students who play neither) = 9/29

we get, 6/29 + 14/ 29 + 9/29 = 29/29 = 1

i.e. there are no students who play both golf and soccer = 0

all the events are independent.

so, we have,

the probability that a student chosen randomly from the class plays golf or soccer = P(A) + P(B)

               = 6/29 + 14/ 29

               = 20/29

and, the probability that a student chosen randomly from the class plays golf and soccer = 0.

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Hello!

m     dm    cm    mm

5   ,   0        0

500cm = 5m

The population of the town 12 years later will be 224,800 if the current population is 28,100 and the population doubles every 4 years.

Since the population doubles every 4 years, we can use the formula:

P = P0 x [tex]2^{t/4}[/tex]

where P0 is the initial population, t is the time elapsed in years, and P is the population after time t.

In this case, the initial population P0 is 28,100, and we want to know the population after 12 years, so t = 12. Substituting these values into the formula, we get:

P = 28,100  2^(12/4)

  = 28,100 x 2³

  = 28,100 * 8 = 224,800

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The correct statements are:

When a point is reflected across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. Therefore, statement A) is true.

When a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate changes sign. Therefore, statement C) is true.

It should be noted that to represent the reflection of point A (1,-2) across the y-axis, we flip the sign of the x-coordinate to obtain the image point A' (-1,-2). Therefore, statement D) is true.

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The value of given expression is 57.

We are given that;

|—15u| + |3v| + 3

u=3, v = 3

Now,

To evaluate the expression, you need to substitute the values of u and v and simplify. The absolute value of a number is the distance from zero on the number line, so it is always positive or zero. You can write your solution as:

|—15u| + |3v| + 3 = |—15(3)| + |3(3)| + 3 = |—45| + |9| + 3 = 45 + 9 + 3 = 57

Therefore, by the given expression the answer will be 57.

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The graph of the modulus function is plotted

Given data ,

Let the modulus function be represented as A

Now , the value of A is

| x | + 1 < 3

On simplifying the inequality , we get

Subtracting 1 on both sides , we get

| x | < 2

When x is positive or zero: In this case, the absolute value of x is equal to x itself. Therefore, we have x < 2

When x is negative: In this case, the absolute value of x is equal to -x. Therefore, we have -x < 2

Hence , the graph of function is plotted

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Part A: The equation of the circle in standard form is x² + (y - 7)² = 2².

Part B: Center: (h, k) = (0, 7), Radius: 2

Part C: Please check the attachment.

In this problem we find the definition of the equation of a circle in general form, whose standard form must be found:

(x - h)² + (y - k)² = r²

Where:

This can be done by completing the square. First, write the equation of the circle:

x² + y² = 14 · y - 45

Second, complete the square by algebra properties:

x² + y² - 14 · y + 45 = 0

x² + (y² - 14 · y + 49) = 4

x² + (y - 7)² = 2² (PART A)

Third, write the coordinates of the center and the radius of the circle:

Center: (h, k) = (0, 7), Radius: 2 (PART B)

Finally, we proceed to graph the resulting expression.

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Answer:

0.0909

Step-by-step explanation:

4 blue + 5 red + 3 black = 12 chips in total.

p=probability

1st draw:

p (blue) = 4/12

there are now 11 chips in the bag, 4-1 =3 are blue.

2nd draw?

p (blue) = 3/11

probability of pulling one blue chip followed by another blue chip is:

(4/12) X (3/11) = (4X3)/12X11)

= (12)/(132)

= 1/11

0.0909