Which is most likely the correlation coefficient for the set of data shown

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

Find more exercises on  trigonometric identity;

https://brainly.com/question/24377281

#SPJ1

Answer:

  (b)  -4.5

Step-by-step explanation:

Choosing the correct answer here is not the same as knowing what the correct value is.

You know that √30 < √100 = 10, so the sum must be negative. That is, 10 subtracted from a positive number less than 10 will give a negative result.

You know that 25 < 30 < 36, so √25 < √30 <√36. That is, √30 will be between 5 and 6. If we say √30 ≈ 5.5, then the sum is ...

  -10 +√30 ≈ -10 +5.5 = -4.5

__

Additional comment

Of course, a calculator can tell you the value to the desired precision.

Answer:

it is a triangular prism .

Answer:

Triangular Prism

6 vertices

Step-by-step explanation:

The area of the square hole having a side length of 6 inches is 36 inches².

The area of a square is a product of it's any two sides or a product of diagonals divided by two. If side has a length a then diagonal is a√2.

The perimeter of a square is the sum of the lengths of all the sides.

Given, Darius cuts out a square hole that is 6 inches long each side.

We know the area of a square is (side×side).

Therefore, The area of the square hole having a side length of 6 inches is = (6×6) = 36 inch²

learn more about squares here :

https://brainly.com/question/28776767

#SPJ2

Answer:

Step-by-step explanation:

See attachment.

Answer:

65

Step-by-step explanation:

The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65

Answer:

False, True, False, True

Step-by-step explanation:

False - there are twelve

True - 3/4x1/3=3/12=1/4

False - there is one way

True - 3/4x2/3=6/12=1/2

The quantity of each food item that Nathan and Amanda should order for a graduation party with 35 guests, which is a function of ratio, is as follows:

Fried chicken  = 56 pieces

Lasagna = 24.5 lbs

Deli meats = 6.3 lbs

Sliced cheese = 52.5 pounds

Bakery buns = 3.5 dozens

Potato salad = 7 lbs

Ratio of 10 to 35 = 1 : 3.5 (35/10)

Amount of food for 10 party guests:

Fried chicken = 16 pieces

Lasagna = 7 lbs

Deli meats = 1.8 lbs

Sliced cheese = 15 pounds

Bakery buns = 1 dozen

Potato salad = 2 lbs

Fried chicken = 16 pieces x 3.5 = 56 pieces

Lasagna = 7 lbs x 3.5 = 24.5 lbs

Deli meats = 1.8 lbs x 3.5 = 6.3 lbs

Sliced cheese = 15 pounds x 3.5 = 52.5 pounds

Bakery buns = 1 dozen x 3.5 = 3.5 dozens

Potato salad = 2 lbs x 3.5 = 7 lbs

Thus, the quantity of each food item that Nathan and Amanda should order for a graduation party with 35 guests should be based on a ratio of 1:35.

Learn more about ratios at https://brainly.com/question/2914376

#SPJ1

The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

More can be learned about the chords of a circle at brainly.com/question/16636441

#SPJ1

The value of the missing variable x in the given triangle is; x = 15

We know that sum of angles on a straight line is 180 degrees. That means the angle on the horizontal line of (9x + 16)° inside the triangle will be;

180 - (9x + 16)°

Now, we know that sum of angles in a triangle is 180 degrees. Thus;

180 - (9x + 16)° + 5x - 14 = 90

180 - 4x - 30 = 90

150 - 4x = 90

150 - 90 = 4x

60 = 4x

x = 60/4

x = 15

Read more about Missing Angle at; https://brainly.com/question/12522718

#SPJ1

Answer:

a. 5

b. 36

c. 1/3

d. 1/6

Step-by-step explanation:

a. The answer is five because 9 people bike and 4 people walk and 9-4 is equal to 5

b. The is answer is 36 because 12 people walked, 9 people biked, 4 people walked, 6 people used a motorcycle and 5 people used a cab and 12+9+4+6+5=36

c. The answer is 1/3 because 12 people walked to school and there are 36 people in the class so 12/36 people walked to school, which can be simplified to 1/3.

d. The answer is 1/6 because 6 people used a motorcycle to go school and there are 36 people in the class so 6/36 people used a motorcycle which is equal to 1/6

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

To know more about continuous here

https://brainly.com/question/30089268

#SPJ1

Answer:

b = (3V)/h

Step-by-step explanation:

You have to rearrange the equation so that it is equal to b.

V = hb/3

3(V) = (hb/3)(3)

3V = hb

(3V)/h = (hb)/h

b = (3V)/h

zip file, and phrase, angle of applicable. where are u doing now I need to make a sentence, but it was not the same time for changing the full range. uses the nation, angle and phrase, angle. uses a

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

For such more question on Multiply

https://brainly.com/question/29793687

#SPJ8

Answer:

2/5

Step-by-step explanation:

\( \frac{12}{30} = \frac{2 \times 6}{5 \times 6} = \frac{2}{5} \\ \)

Answer:

c.vertical angle is the answer

Answer:

c

Step-by-step explanation:

vertical

correct answer is c

The statements which best defines the mutually exclusive events is two events are mutually exclusive if it is impossible for the two events to occur simultaneously (A).

The two events area said to be mutually exclusive when the cannot be take place simultaneously. For the two events, A and B, to be mutually exclusive,

\(P(A\cap B)=0\)

Properties of mutually exclusive event:

Thus, the statements which best defines the mutually exclusive events is two events are mutually exclusive if it is impossible for the two events to occur simultaneously (A).

Learn more about the mutually exclusive here;

https://brainly.com/question/16632468

#SPJ2

Based on the task content given; the solution to the equation for x 3 1/2(2 1/5x - 4 2/3) - 5 5/6 = 0 is 2 203/231

3 1/2(2 1/5x - 4 2/3) - 5 5/6 = 0

(3 1/2 × 2 1/5x) - (3 1/2 × 4 2/3) - 5 5/6 = 0

(7/2 × 11/5x) - (7/2 × 14/3) - 35/6 = 0

77/10x - 98/6 - 35/6 = 0

77/10x = 98/6 + 35/6

77/10x = 98+35 / 6

77/10x = 133/6

x = 133/6 ÷ 77/10

= 133/6 × 10/77

= 1330/462

x = 2 406/462

= 2 203/231

Learn more about simplification:

https://brainly.com/question/723406

#SPJ1

The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

Read more on volume of a cylinder;

https://brainly.com/question/9554871

#SPJ1

The volume of the rectangular prism is 208cm³

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a rectangular a prism is expressed as base area × height. The base area is a rectangle and the area of a rectangle is Length × width

length = 2cm

width = 13 cm

height = 8cm

base area = 13× 2 = 26cm²

Volume of the prism = 26× 8 = 208cm³

Therefore the volume of the rectangular prism is 208cm³.

learn more about the volume of a rectangular prism from

https://brainly.com/question/24284033

#SPJ1

Answer:

down below

Step-by-step explanation:

5:2=5+2= there are 7 parts altogether

140/7=20 in each 1 part

losing=5

do 20 times 5=100 raffel tickets are losing

2 times 20 is the winning tickets=40 winning tickets

i hope i could help<3

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

For more questions on Function .

https://brainly.com/question/11624077

#SPJ8

Answer: You must rearange 3 3/4 into an improper fraction to make the subtraction easier.

Step-by-step explanation:

(this is a little long bear with me :3)

3 and 3/4ths into a improper fraction would be: 15/4

looking at 15/4 and 7/8 notice how the denominators are 4, and 8. both are common denominators. so we multiply 4x2 to make 4, into 8. and whatever we do to the bottom, we do to the top.

15x2            30

---------- =     ------                                

4x2              8

our new fraction is 30/8.

do the subtraction..

30            7         23

----     -     ---   =    ---   that then turns into a mixed number, which is:

8               8          8

2 7/8.

hope this helped! :)

Answer:

Step-by-step explanation:

because you need to make it same base

\(\\ \sf\longmapsto 2.3\%=0.23\)

\(\\ \sf\longmapsto \sqrt{5}=2.2\)

\(\\ \sf\longmapsto 2\dfrac{3}{16}=\dfrac{35}{16}=2.1\)

\(\\ \sf\longmapsto 2\times 10^2=200\)

\(\\ \sf\longmapsto \pi=3.141\)

Ascending order:-

\(\\ \sf\longmapsto 0.23<2.1<2.2<3.141<200\)

The explicit formula for the sequence 12, 112, 212, 312, 412 is a_n = 100n + 12.

The explicit formula for the given sequence is:

a_n = 100n + 12

In the given sequence, each term is obtained by adding 100 to the previous term. The first term is 12, and each subsequent term is obtained by adding 100 to the previous term.

Using the formula, we can calculate any term in the sequence by substituting the corresponding value of n. For example:

a_1 = 100(1) + 12 = 112

a_2 = 100(2) + 12 = 212

a_3 = 100(3) + 12 = 312

a_4 = 100(4) + 12 = 412

Therefore, the explicit formula for the sequence 12, 112, 212, 312, 412 is a_n = 100n + 12.

for such more question on sequence

https://brainly.com/question/27555792

#SPJ8

Answer:

  B.  y = 4/3x + 1

Step-by-step explanation:

The offered choices are in slope-intercept form:

  y = mx + b

where m represents the slope (rise/run) and b represents the y-intercept.

The graph crosses the y-axis at y=1, so the y-intercept is +1. That eliminates choices A and D.

The slope is greater than 1, so choice C is eliminated. You know the slope is greater than 1 because the line goes up more than 1 unit for a 1-unit change to the right. If you look where the line crosses grid points, you see that it rises 4 units for a run of 3 units to the right. That means ...

  m = rise/run = 4/3

The equation is ...

  y = 4/3x +1 . . . . matches choice B

Answer:

B. y = 4/3x + 1

Step-by-step explanation:

First, find the slope using rise/run (y2 - y1) / (x2 - x1)

Use the points (0, 1) and (3, 5)

Plug in the numbers:

(5 - 1) / (3 - 0)

= 4/3

Looking at the graph, we can see the y intercept is (0, 1) so we can plug in 1 into the equation y = mx + b as b:

y = mx + b

y = 4/3x + 1

Answer:

You need to pay $1,759.50 if you get a 15% discount.

Step-by-step explanation:

100%-15%=85%

0.85x2,070=$1,759.50

The function that best models this scenario is C of x equals 3.75 times x if x is less than 5 and 3.25x plus 5 if x is greater than 6.

Let the number of hours be illustrated as x. In this situation, local city park rents kayaks for $3.75 per hour. This will be:

= 3.75 × x

= 3.75x

Also, customer rents for four or more hours, the cost is only $3.25 per hour, plus a $5 processing fee. This will be illustrated as:

= 5 + (3.25 × x)

= 5 + 3.25x

Learn more about expressions on;

brainly.com/question/723406

#SPJ1