4.) What is the exact value of sinθ when θ lies in Quadrant II and cosθ=−513
Fill in the blanks.
___/___

10.) Suppose that a laser light, positioned 100 ft from the base of a flag pole, illuminates a flag that is 85 ft above the ground.

What is the angle of inclination (angle of elevation) of the light beam?

Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.

11.)

Suppose that a man standing at the edge of a cliff near the North Rim of the Grand Canyon is looking downward towards a campground inside the canyon. The elevation of the North Rim is 5389 ft and the elevation of the campground is 2405 ft. The man's range finder indicates that his line of sight distance to the campground is 3044 ft.

What is the angle of depression of the man's line of sight to the campground?

Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.

12.) What is the exact value of arcsin(0.5)?
Determine the value in degrees.

13.) Determine the exact value in degrees:
What is the exact value of arcsin−2√2

1: 107

2: 73

3; 123

4: 62

5: 116

6: 16

7: 92

The missing angle measures in the hexagon are:

∠5 = 116°

∠4 = 62°

∠3 = 123°

∠2 = 73°

∠6 = 16°

∠7 = 92°

∠1 = 107°

A hexagon is a six-sided polygon, whose sum of interior angles equals 720°.

∠5 = 180 - 54 = 116° (supplementary angles)

∠4 = 180 - 118 = 62° (supplementary angles)

∠3 = 180 - 57 = 123° (supplementary angles)

∠6 = 180 - 164 = 16° (supplementary angles)

∠7 = 180 - 88 = 92° (supplementary angles)

∠1 = 720 - 116 - 118 - 123 - 164 - 92 = 107° (sum of interior angles in a hexagon )

∠2 = 180 - 107 = 73° (supplementary angles)

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Answer: B. 0.45

Step-by-step explanation:

From the given table, the total number of students = 137

The number of students are sophomores =35+42=77

Let A be the event that students are sophomores.

Then probability that students are sophomores is given by  :

[tex]\text{P(A)}=\dfrac{77}{137}[/tex]

The number of sophomores who attended the jazz concert = 35

Let B be the event that students attended the jazz concert .

The probability that students attended the jazz concert and are sophomores is given by  :

[tex]\text{P(A and B)}=\dfrac{35}{137}[/tex]

Now, the probability of that the student attended the jazz concert, given that the students is sophomore is given by :-

[tex]P(B|A)=\dfrac{\text{P(A and B)}}{\text{P(A)}}\\\\=\dfrac{\dfrac{35}{137}}{\dfrac{77}{137}}\\\\\\=\dfrac{35}{77}=0.454545454545\approx0.45[/tex]

The answer is D 2,024,657

Answer:

A

Step-by-step explanation:

0.365 x 739,000= 269,735

Answer:

162.43

Step-by-step explanation: I hope its helps it's been a couple of years since I have done geometry

Answer:

the total area of the octagon is 8(20.3 in²), or 162.4 in²

Step-by-step explanation:

A regular octagon has 8 pie-shaped sections.  Each is triangle of height 7 in and base 5.8 in.

Thus, the area of each such section is, by A = (1/2)(b)(h(),

A = (1/2)(5.8 in)(7 in) = 20.3 in².

There are 8 such sections.  

Thus, the total area of the octagon is 8(20.3 in²), or 162.4 in²

The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

y = 4x − 19.4      ...1

y = 0.2x−4.2      ...2

From equations 1 and 2, then we have

4x - 19.4 = 0.2x - 4.2

3.8x = 15.2

x = 4

Then the value of the variable 'y' will be calculated as,

y = 4 (4) - 19.4

y = 16 - 19.4

y = - 3.4

The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

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Answer:

What is the area AA of each section of the circle?

Give your answer in terms of pi.

A = 25πm²

Step-by-step explanation:

Given the radius of the circle to be 10

The question is to find area of each sections of the circle .

The formula for calculating the area of a circle is area equals to πr²

A = πr²

Given r = 10m

The next step is to substitute the values into the equations  

A = π (10m)²

A = 100πm²

Since the circle is divided into 4 equal sections, we need to find the area of each sections by dividing the complete area of the circle by 4

Therefore,  

A = 100πm²/4  

A = 25πm²

Answer:

25π[tex]m^{2}[/tex]

Step-by-step explanation:

Answer:

< BCA = 70

Step-by-step explanation:

The complete central angle of a circle is 360 degrees. The given portion is 250 degrees.

What is left over? BOA = 360 - 250 = 110

Tangents always meet the radius at 90 degrees. Since there are two tangents <CAO = <BAO = 90 degrees.

So piecing it all together, the equation becomes

<BAO + CAO + BAO + ACB = 360

110 + 90 + 90 + <ACB = 360

290 + <ACB = 360

<ACB + 290 - 290 = 360 - 290

ACB = 70 degrees

[tex]\bf \textit{vertex of a horizonal parabola, using f(y) for "x"} \\\\ x=\stackrel{\stackrel{a}{\downarrow }}{a}y^2\stackrel{\stackrel{b}{\downarrow }}{+b}y\stackrel{\stackrel{c}{\downarrow }}{+c} \qquad \left(f\left(-\cfrac{ b}{2 a}\right)~~~~ ,~~~~ -\cfrac{ b}{2 a} \right) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 2x+y^2=0\implies 2x=-y^2\implies x=\cfrac{-y^2}{2}\implies x=\stackrel{\stackrel{a}{\downarrow }}{-\cfrac{1}{2}}y^2\stackrel{\stackrel{b}{\downarrow }}{+0}y\stackrel{\stackrel{c}{\downarrow }}{+0} \\\\\\ -\cfrac{b}{2a}\implies -\cfrac{0}{2\left(-\frac{1}{2} \right)}\implies 0\qquad therefore\qquad (f(0)~~,~~0)\implies \stackrel{vertex}{(0,0)}[/tex]

you can see it this way, x = -(1/2)y² is just a horizontal parabola opening to the left-hand-side, the -1/2 is just a stretch transformation of the parent function x = y², but as much as it stretches, their vertex is the same, at the origin.

Answer:

S(t) = 2 - 0.25*t

Step-by-step explanation:

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.

When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.

S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).

Therefore the equation formed will be linear.

The equation will be of the form y = mx + b

Here S(t) = mt + b

Here m is the slope which is the rate at which ice is melting.

Putting t = 0

S(t) = 2

Putting t = 3,

S(t) = 1.25

Therefore, m*0 + b = 2 or, b = 2

and 3m + b = 1.25

or, 3m = 1.25 - 2 = -0.75

or, t = -0.25

Hence, function's formula = S(t) = -0.25*t + 2

i.e. S(t) = 2 - 0.25*t

Answer:

y = 2 - 0.25x

Step-by-step explanation:

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.

When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.

S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).

Therefore the equation formed will be linear.

The equation will be of the form y = mx + b

Here S(t) = mt + b

Here m is the slope which is the rate at which ice is melting.

Putting t = 0

S(t) = 2

Putting t = 3,

S(t) = 1.25

Therefore, m*0 + b = 2 or, b = 2

and 3m + b = 1.25

or, 3m = 1.25 - 2 = -0.75

or, t = -0.25

Hence, function's formula = S(t) = -0.25*t + 2

i.e. S(t) = 2 - 0.25*t

Answer:

not geometric

Step-by-step explanation:

A geometric series is one where the nth term is multiplied by a common ratio to get the n+1 term.

1    1/2   1/4     1/8       1/16 .....

is a geometric series. the fourth term (1/8) is multiplied by 1/2 to get 1/16.

The series you have been given is not geometric.  It reduces to

1/3   1/4   1/5    1/6 which does not give you a common number to multiply the nth term to get to the n+1 term.  

Answer:

at the most 308 pounds

Step-by-step explanation:

Given

Weight of each sack = 364 pounds

Weight of Kevin = w = 150 pounds

Weight that lift can take = 2000 pounds

In order to find the weight of sacks that can be put into the elevator we have to subtract the weight of Kevin from the capacity of the lift.

So, actual weight of sacks that can be taken =[tex]2000-150[/tex]

= 1850 pounds

As 6 sacks have to be taken, to find the weight of one sack

Required weight of one sack = [tex]\frac{1850}{6}[/tex]

= 308.33 pounds

So, each sack has to weigh at the most 308 pounds ..

The correct option is a. at the most 308 pounds. Each sack should weigh at most 308 pounds to ensure that the elevator's weight limit is not exceeded when Kevin is in the elevator with six sacks.

To determine the weight each sack can be so that the elevator capacity is not exceeded, we must consider the total weight limit of the elevator and the weight of Kevin.

 The elevator has a capacity of 2,000 pounds. Kevin weighs 150 pounds, and he will be riding the elevator with the sacks. Therefore, the total weight available for the sacks is:

 2,000 pounds (elevator capacity) - 150 pounds (Kevin's weight) = 1,850 pounds.

 If six sacks are to be taken at a time, we divide the total available weight by the number of sacks to find the maximum weight each sack can have:

1,850 pounds / 6 sacks = 308.333... pounds.

Since the weight of each sack must be a whole number, we round down to the nearest whole number, which is 308 pounds. This ensures that the elevator's capacity is not exceeded.

Therefore, This allows for a small margin of error in the weight of the sacks, which is safer and more practical than having the sacks weigh exactly 308 pounds each.

First convert yards to feet.

1 yard = 3 feet.

100 x 3 = 300 feet long.

53 x 3 = 159 + 1 = 160 feet wide.

Now use the Pythagorean theorem to find the diagonal.

x^2 = 300^3 + 160^2

x^2 = 90000 + 25600

x^2 = 115600

x = √115600

x = 340 feet

Answer:

  m∠LPM = 60°

Step-by-step explanation:

The measure of the angle facing the marked arcs is the average of the measures of the arcs:

  m∠LPM = (1/2)(40° +80°) = 60°

Answer:

x = 3

Step-by-step explanation:

By rearranging the equations,

y = 6 - 3x

y = x - 6

x - 6 = 6 - 3x

4x - 6 = 6

4x = 12

x = 3

Answer:

x = 3

Step-by-step explanation:

Follow the elimination method like so:

3x + y = 6            The Ys cross each other out.

x - y = 6               Add to get:

4x = 12

4x = 12               Divide to get:

4       4

x = 3

Hope this helps! :)

Answer:

[tex] 19\sqrt{7} [/tex]

Step-by-step explanation:

[tex] 25\sqrt{7} - 2\sqrt{63} = [/tex]

[tex] = 25\sqrt{7} - 2\sqrt{9 \times 7} [/tex]

[tex] = 25\sqrt{7} - 2\sqrt{9} \sqrt{7} [/tex]

[tex] = 25\sqrt{7} - 2\times 3 \sqrt{7} [/tex]

[tex] = 25\sqrt{7} - 6 \sqrt{7} [/tex]

[tex] = 19\sqrt{7} [/tex]

Answer:

Step-by-step explanation:

The directions tell you what to do and give an example. That work is to be repeated 15 more times. The work is tedious, at best. I found it slightly less tedious to enter the 64 numbers into a spreadsheet and let it do the sums. See the attached for the result.

At the bottom of the array are the sums of columns. At the right are the sums of rows. The upper right and lower left numbers are the sums of the corresponding diagonals.

The "pattern" is that the sums are all -6, which is what you expect from a magic square.

Answer:

first brand 55 gallons

second brand 95 gallons

Step-by-step explanation:

The length of diagonal EK is sqrt(5^2 + 4^2) ≈ 6.403m

Hence perimeter = 2*(12 + 6.403) → 36.8 m (to the nearest tenth of a metre)

The perimeter of the cross-section is 36.8 m.

Given that the length of diagonal EK is

[tex]\sqrt{(5^2 + 4^2) }[/tex]

≈ 6.403m

Thus, the perimeter would be

2*(12 + 6.403)

→ 36.8 m.

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- D is the midpoint of AB, E is the midpoint of BC

Answer: A. Given

I left off DB||FC because that's not given.  But we can construct it.

Construct line through C parallel to AB.  Extend DE to intersect and call the meet F.

- DB || FC

By Construction

----

- Angle B congruent to angle FCE

Answer: D. Alternate Interior Angles

We have transversal BC across parallel lines AB and CF, so we get congruent angles ABC and FCB aka FCE

- angle BED congruent to angle CEF

Answer: H. Vertical angles are congruent

When we get lines meeting like this we get the usual congruent and supplementary angles.

- Triangle BED congruent to Triangle CEF

Answer: F. Angle Side Angle

We have BE=CE, DBE=FCE, BED=CEF

- DE congruent to FE and DB congruent to FC

Answer: C. CPTCTF

Corresponding parts ...

- AD congruent to DB and DB congruent to FC therefore AD congruent to FC

Answer: E. Transitive Property of Congruent

Things congruent to the same thing are congruent

- ADFC is a parallelogram

Answer: G.  AD and FC are congruent and parallel

Presumably this is a theorem we have already established.

- DE || AD

Answer: B. Definition of a parallelogram

Answer:

(√5)/2

Step-by-step explanation:

In the attached figure, we have labeled the circumcenter point D and the incenter point E. The points of tangency of the incircle with sides AB, BC and CA are labeled G, H, and F, respectively.

The distances from any vertex to the two points of tangency from that vertex are the same. So, AG = FA, BG = BH, and CF = CH. If we call the radius of the incircle "r", then we have ...

AG = FA = r, BG = BH = 3-r, CF = CH = 4-r

so the side length BC is ...

BC = BH +CH = (3-r) +(4-r) = 7-2r

We already know that side length BC is 5, so ...

5 = 7 -2r

r = (7 -5)/2 = 1

Of course, the circumcenter of a right triangle is the midpoint of the hypotenuse, so the circumradius "R" is 5/2 = 2.5.

The formula for the distance between the two centers is ...

d = √(R(R -2r)) = √(2.5(2.5 -2)) = √1.25 = (√5)/2

_____

Comment on this answer

We have used a formula for the center-to-center distance found using a web search. The attached diagram shows the coordinates of the two centers, so the distance can be found from those. It is the same.

Answer:

Step-by-step explanation:

1. a) spread is the range which is given as Max(S)- Min(S)

Colin =

[tex]3,9,9,14,15,16,17,20,21\\\\range=21-3=18\\\\[/tex]

Jezebel=

[tex]=4,5,8,10,11,14,20,20,26\\\\range=26-4=22[/tex]

Jezebel had a greatest spread.It was 22 while for Colin was 18

2. a) The middle 50% of the game sold is the difference between the third quartile and first quartile of the data

Colin=

[tex]=3,9,9,14,15,16,17,20,21\\\\median=15\\\\lower half=3,9,9,14\\\\\\Q1=(9+9) /2 =9\\\\\\Upper half= 16,17,20,12\\\\\\Q3=(17+20)/2 = 18.5\\[/tex]

⇒The middle 50% = Q3-Q1 = 18.5- 9 = 9.5

Jezebel

[tex]=4,5,8,10,11,14,20,20,26\\\\\\=lower half= 4,5,8,10\\\\\\upper half=14,20,20,26\\\\\\Q1=(5+8)/2 = 6.5\\\\Q3= (20+20)/2 = 20[/tex]

⇒The middle 50% = Q3-Q1 = 20-6.5 = 13.5

Colin had the least spread of 9.5 as compared to Jezebel who had 13.5

c)The answers in part 2a and 2 b tels us that the middle section that contained 50% of the scores was more in Jezebel record than in Colin records.

Part A

The scatterplot is shown the attachment.

Part B

Using a linear regression equation that models Patrick's referrals has a positive slope.

This means that, there is a positive relation between time(number of days),x and  the number of personal recommendations, y.

In other words, as the number of days increases, the number of personal recommendations also increases.

Question 2.

The given functions are:

[tex]y=x^2+3x-5[/tex]

[tex]y=4x+1[/tex]

To find the point where the graphs of these functions intersect,we solve the two equations simultaneously.

We equate the two equations to get:

[tex]x^2+3x-5=4x+1[/tex]

[tex]x^2+3x-4x-5-1=0[/tex]

[tex]x^2-x-6=0[/tex]

Factor to obtain:

[tex](x-3)(x+2)=0[/tex]

x=3 and x=-2

We put x=-2, into [tex]y=4x+1[/tex] to get;

[tex]y=4(-2)+1=-7[/tex]

when x=3 [tex]y=4(3)+1=13[/tex]

Therefore the graphs intersect at (-2,-7) and(3,13).

Yes, solution is correct.

Answer:

T T → T

Step-by-step explanation:

A conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 3 + 2 = 5 which is true and 5 + 5 = 10 which is also true.

Answer: The answer to your question would be the third graph to your left

Step-by-step explanation: because when you calculate the rate of change from these points:

(50,1)

(100,2)

(150,3)

(200,4)

The rate of change would be 50 miles/ km per hour

Finding the slope formula: [tex]m= y2-y1/ x2-x1[/tex]

And when you take any two points from the graph, for example: (50,1) and (200,4), it would look like this:

[tex]\frac{200-150}{4-1}= 50/1= 50 miles/km per hour[/tex]

The correct graph is 3rd.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Considering the 3rd graph, the coordinates are :-

(50,1)

(100,2)

(150,3)

(200,4)

Finding the slope = (y₂-y₁) / (x₂-x₁)

considering the points (50,1) and (200,4), slope =

slope = 4-1 / 200-50 = 1/50

Since the slope shows the rate, and the rate of change would be 50 miles/ km per hour

Hence, the correct graph is 3rd one.

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Answer:

C [tex]x=\frac{4}{3}[/tex]

Step-by-step explanation:

The given logarithmic equation is:

[tex]\log_{3x+4}(4096)=4[/tex]

We rewrite in exponential form; to get;

[tex]4096=(3x+4)^4[/tex]

We rewrite the LHS as a certain natural number exponent 4.

[tex]8^4=(3x+4)^4[/tex]

The exponents are the same, hence the bases must also be the same.

[tex]\implies 3x+4=8[/tex]

[tex]\implies 3x=8-4[/tex]

[tex]\implies 3x=4[/tex]

Divide both sides by 3;

[tex]\implie x=\frac{4}{3}[/tex]

The correct answer is C

Answer:

-2(2x +5)² = -8x² -40x -50

Step-by-step explanation:

Evaluate from the inside out, according to the order of operations.

  h(g(f(x))) = h(g(2x +5)) = h((2x +5)²) = -2(2x +5)² = -2(4x² +20x +25)

  = -8x² -40x -50

I personally prefer the factored form, but that is not considered "simplified."

Final answer:

A rectangle and a rhombus both have opposite sides that are parallel and their interior angles add up to 360 degrees. They differ in that a rectangle has four right angles and a rhombus has four congruent sides, which are not necessarily attributes they share unless they are both squares.

Explanation:

Both a rectangle and a rhombus share some properties as they are both quadrilaterals. Firstly, the opposite sides are parallel in both shapes. Secondly, the angle measures add to 360° which is a property of all quadrilaterals. However, they differ in other aspects; a rectangle has four right angles, whereas a rhombus generally does not unless it's a square. A rhombus has four congruent sides, and a rectangle does not unless it's a square. Therefore, the correct selections based on their commonalities are that the opposite sides are parallel and their angle measures add up to 360°.

Answer:

(0.55, 0.75)

Step-by-step explanation:

The range can be estimated to be 6 standard deviations wide.  Therefore, the standard deviation is:

σ = (0.72 - 0.42) / 6

σ = 0.05

The margin of error is ±2σ, so:

ME = ±0.10

Therefore, the interval estimate is:

(0.65 - 0.10, 0.65 + 0.10)

(0.55, 0.75)

The standard deviation is a measure of a collection of values' variance or dispersion. The interval estimate of the true population proportion is (0.55, 0.75).

The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

A.) The range is around 6 standard deviations broad. As a result, the standard deviation is:

σ = (0.72 - 0.42) / 6

σ = 0.05

B.) Because the margin of error is ±2σ, therefore, we can write,

Margin Of Error = (±0.05)×2 = ±0.10

C.) The interval can be estimated as,

Interval = 0.65±0.10

             = 0.65-0.10, 0.65+0.10

             = 0.55, 0.75

Hence, the interval estimate of the true population proportion is (0.55, 0.75).

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I don’t know what the answer is I wish I could help

The answer is y=56.2x-112.4

Answer:

67.1

Step-by-step explanation:

we need to use trig to work this out

(Soh Cah Toa)

The answer will be 67.11461952384143

to nearest tenth its

67.1

Answer:

x = 67.1°

Step-by-step explanation:

Cos(x) = Adj./Hypo.

Cos(x) = 28/72

Cos(x) = 0.3889

x = 67.1°