Find all angles, 0 ≤C<360 that satisfy the equation below, to the nearest tenth of a degree.

Answer:

[tex]\displaystyle \sin{\frac{\theta}{2}} = \frac{5\sqrt{26}}{26}\approx 0.196[/tex].

Step-by-step explanation:

[tex]\displaystyle \theta\in \left(\pi, \frac{3\pi}{2}\right)[/tex],

such that

[tex]\displaystyle \frac{\theta}{2} \in \left(\frac{\pi}{2}, \frac{3\pi}{4}\right)[/tex].

As a result,

[tex]\displaystyle \tan{\frac{\theta}{2}} = \frac{\sin{\displaystyle \frac{\theta}{2}}}{\displaystyle \cos{\frac{\theta}{2}}}[/tex],

such that

Let

[tex]\displaystyle t = \tan{\frac{\theta}{2}}[/tex].

[tex]t < 0[/tex].

By the double angle identity for tangents.

[tex]\displaystyle \frac{\displaystyle 2\tan{\frac{\theta}{2}}}{1-\displaystyle \left(\tan{\frac{\theta}{2}}\right)^{2}} = \tan{\theta}[/tex].

[tex]\displaystyle \frac{2t}{1 - t^{2}} = \frac{5}{12}[/tex].

[tex]24t = 5 - 5t^{2}[/tex].

Solve this quadratic equation for [tex]t[/tex]:

Discard [tex]t_1[/tex] for it is not smaller than zero.

Let [tex]\displaystyle s = \sin{\frac{\theta}{2}}[/tex].

[tex]0 < s <1[/tex].

By the definition of tangents:

[tex]\displaystyle \tan{\frac{\theta}{2}} = \frac{\displaystyle \sin{\frac{\theta}{2}}}{\displaystyle \cos{\frac{\theta}{2}}}[/tex].

Apply the Pythagorean Algorithm to express the cosine of [tex]\displaystyle \frac{\theta}{2}[/tex] in terms of [tex]s[/tex]. Note that [tex]\displaystyle \cos{\frac{\theta}{2}}[/tex] is expected to be smaller than zero.

[tex]\displaystyle \cos{\frac{\theta}{2}} = -\sqrt{1 - \left(\sin{\frac{\theta}{2}}\right)^{2}}= - \sqrt{1 - s^{2}}[/tex].

Solve for [tex]s[/tex]:

[tex]\displaystyle \frac{s}{- \sqrt{1 - s^{2}}} = -5[/tex].

[tex]s^{2} =25(1 - s^{2})[/tex].

[tex]\displaystyle s = \sqrt{\frac{25}{26}} = \frac{5\sqrt{26}}{26}[/tex].

Therefore

[tex]\displaystyle \sin{\frac{\theta}{2}} = \frac{5\sqrt{26}}{26}\approx 0.196[/tex].

Answer:

  the three angle measures are 35°, 29°, 26°

Step-by-step explanation:

The sum of the angle measures will be 90°, assuming the sections do not overlap. Then ...

  ( 7x - 49) + ( 2/3x + 21) + ( 3/4x + 17) = 90

  (8 5/12)x -11 = 90 . . . . . simplify

  x = 101/(8 5/12) = 12 . . . divide by the coefficient of x

Then the angles are ...

  7x -49 = 7·12 -49 = 35

  2/3x + 21 = 2/3·12 +21 = 29

  3/4x +17 = 3/4·12 +17 = 26

The angle measures are 35°, 29°, 26°.

_____

Check

  35 +29 +26 = 90 . . . . the sum of the covered section angles is 90°

_____

We assume you can manage addition of fractions and division by a mixed number or improper fraction. If not, convert all of the coefficients of x to multiples of 1/12. Instead of dividing by the coefficient of x, multiply by the inverse of the coefficient of x.

To find the angle measures of each of the three sections at home plate, the equation (7x - 49) + (2/3x + 21) + (3/4x + 17) = 90 is solved to find that x equals 12. Substituting 12 for x, the angle measures are calculated to be 35 degrees, 29 degrees, and 26 degrees.

Since the angle at home plate is 90 degrees, the sum of the angles for the sections must also be 90 degrees. This allows us to set up the following equation:

(7x - 49) + (2/3x + 21) + (3/4x + 17) = 90

To solve this equation, we combine like terms. First, find a common denominator for the x terms, which is 12. So, we convert all terms into twelfths:

Combining these we get:

(101/12)x - 11 = 90

Add 11 to both sides to isolate the variable term:

(101/12)x = 101

Now, divide both sides by (101/12):

x = 12

Now we will substitute this value for x into the original expressions to get the angle measures:

Therefore, the angle measures for the sections are 35 degrees, 29 degrees, and 26 degrees.

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

The Answer is 7.88

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

Answer:

The answer here would be 7.88

Hope this helps!

Answer:

A

120

Step-by-step explanation:

With all the parallel lines involved, the central figure is a parallelogram.  These 4 sided figures have the odd property of having their opposite angles equal.

What that means, in plain English is that <NRL = <NML

Both of these angles = 120

Here's the cruncher. <NRL and <PRK are vertically opposite. They are therefore equal.

The answer to your question is 120 which is A

the answer is A good luck !

Answer:

A.) 19.5

Step-by-step explanation:

Answer: 6 pounds of apples

Step-by-step explanation:

See photo attached. (:

Answer:

64 sq feet

Step-by-step explanation:

Given:

Rectangle Length = 10 feet

Rectangle Width = 6 feet

Triangle Base = 4 feet

Triangle Height = 2 feet

Area of rectangle = Length x Width = 10 x 6 = 60 sq feet

Area of triangle = [tex]\frac{1}{2}[/tex] x Base x Height = [tex]\frac{1}{2}[/tex] x 4 x 2 = 4 sq feet

Total area

= Area of Rectangle + Area of Triangle

= 60 + 4 = 64 sq feet

Answer:

64 ft^2

Step-by-step explanation:

The rectangular area is 10 ft by 6 ft, which comes to 60 ft².

The triangular area is A = (1/2)(base)(height) = (1/2)(4 ft)(2 ft) = 4 ft²  

The total area of tile will be 4 ft² + 60 ft², or 64 ft².

Her first visit and follow up 60 mins + 30 mins

The limit is 8 follow ups per day

The hospital has 8 hrs available for appointments

Her first visit cost $120 (60 mins) as her follow up was $70 (30 mins)

X = Visits

Y = Follow-ups

And since her first visit and follow up equals to an hour and 30 mins, meaning for it to all add up into the 8 hrs for the appointment, it'll be... 1 hr, 30 mins/ 3 hrs/ 4 hrs, 30 mins/ 6 hrs/ 7 hrs, 30 mins/ 9 hrs

Eight hours is the limit so that means it equals to 5 visits and 6 follow ups, due to if you want it to be the whole 8 hours.

Claude is so Brainy his brain's nickname is Brainly

Answer:

I believe it is SSS

Step-by-step explanation:

because all the sides are exactly the same length

Answer:

10/3

Step-by-step explanation:

|x+3|=4x-7

So |-(x+3)|=|x+3|

We are going to try out two cases:

-(x+3)=4x-7                              and    x+3=4x-7

-x-3=4x-7                                               3=3x-7

 -3=5x-7                                               10=3x

  4=5x                                                   x=10/3

  x=4/5

We are going to test out both because we could something that isn't actually a solution, this is called extraneous.

First thing I'm going to check is 4x-7 for it being positive.

4(4/5)-7=20/5-7=-15/5=-3 so 4/5 will not work because absolute value result can't be negative

4(10/3)-7=40/3-7=19/3 which is positive

checking |x+3| to see if is 19/3 for x=10/3 we see that is so that is the answer

Answer:

  see below

Step-by-step explanation:

The answer is a list of arcs. That means you can ignore the answer choices that are lists of angles or line segments.

The only requirement is that the end points of the arc lie on the circle. Points M, N, P, Q, R are all on the circle, and all are at the end of line segments that intercept them. Any combination of these letters will define an intercepted arc.

Answer:

Two lines are shown intersecting on ordered pair 3, 7.

Step-by-step explanation:

The first of the two lines has a slope of -4 and a y-intercept of 19 (off the top of the graph). It will decrease 4 units for each 1 unit to the right.

The second of the two lines has a slope of +2 and a y-intercept of +1. It will increase 2 units for each 1 unit to the right.

These two lines must intersect in the first quadrant at a point with an x-value less than 5, eliminating the first and last two choices, leaving only the second choice you have listed here.

You would have to examine the graphs to see which has the lines with proper slope and intercept.

My graphing calculator's solution is attached.

two lines are shown intersecting on ordered pair 3, 7.

Answer:

7/17

Step-by-step explanation:

16 inches of concrete plus 4 inches of limestone come to 20 inches of concrete and limestone combined.  Subtracting 20 inches from 34 inches yields 14 inches.  14 inches of the total wall thickness (34 inches) is brick.  This fraction is 14/34, or 7/17.

The fraction of the wall made up of brick is found by subtracting the concrete and limestone widths from the total width of the wall. The fraction is 14/34, which simplifies to 7/17.

The question is asking us to find the fraction of the wall made up of brick. The total width of the wall is 34 inches. Substrating the concrete and limestone widths from the total width (34 inches - 16 inches for concrete - 4 inches for limestone) we get a result of 14 inches for the brick portion. To express this as a fraction of wall's total width, we place the number 14 (the width of the brick portion) over 34 (the total width of the wall). Therefore, the fraction of the wall that is brick is 14/34, which simplifies to 7/17 when reduced to lowest terms.

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Answer:

Option D.  18.75 cm3

Step-by-step explanation:

we know that

The Boyle's law (Ideal gas law) states that Where temperature remains constant, the pressure is inversely proportional to volume.

so

[tex]P1 *V1 = P2 *V2[/tex]  

In this problem we have

P1=150 kPa

P2=200 kPa

V1=25 cm³

substitute and solve for V2

[tex](150)(25)= 200*V2[/tex]

[tex]V2=(150)(25)/200=18.75\ cm^{3}[/tex]    

Answer:

Option D.  18.75 cm3

Step-by-step explanation:

MARK ME PLS

Answer:

A rectangle is a parallelogram with at least one right angle is the best choice ⇒ answer A

Step-by-step explanation:

* Lets revise the properties of the rectangle

# Each two opposite sides are parallel

# Each two opposite sides are equal in length

# Its two diagonals bisect each other  and equal each other

# Its four angles are right angles

- The parallelogram can be a rectangle if:

# Two adjacent sides are perpendicular to each other means one

  angle of its four angles is a right angle

- OR

# Its two diagonals are equal in length

* Lets solve the problem

- We will study the answers to chose the best one

# Answer A

- A rectangle is a parallelogram with at least one right angle

∵ Each tow opposite angles are equal in the rectangle

∵ One of the is right angle means its measure is 90°

∴ The measure of the opposite angle is also 90°

∵ The sum of the measures of the four angles is 360°

∴ The sum of the measures of the other two angles is;

   360 - (90 + 90) = 180°

∵ They are equal to each other (opposite angles)

∴ The measure of each one = 180 ÷ 2 = 90°

∴ The measure of the four angles are 90°

∴ The four angles of the rectangle are right angles

* A rectangle is a parallelogram with at least one right angle is the

 best choice

Answer:it is A

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

[tex]\cos x+\sqrt{2}=-\cos x \\ 2\cos x = -\sqrt 2 \\ \cos x = -\dfrac{\sqrt 2}{2}\\ \\ \Rightarrow x = \pm \arccos\Big(-\dfrac{\sqrt 2}{2}\Big)+2k\pi,\quad x\in \mathbb{Z}\\ \Rightarrow x =\pm\dfrac{3\pi}{4}+2k\pi\\ \\ \\k = -1 \Rightarrow x < 0\\\\ k=0 \Rightarrow x<0 \quad \text{or}\quad \boxed{x = \dfrac{3\pi}{4}} \\ \\k = 1 \Rightarrow x=-\dfrac{3\pi}{4}+2\pi \Rightarrow \boxed{x= \dfrac{5\pi}{4}}\quad \text{or}\quad x > 2\pi[/tex]

Answer:

C

Step-by-step explanation:

Given

cos x + [tex]\sqrt{2}[/tex] = - cosx ( add cosx to both sides )

2cosx +[tex]\sqrt{2}[/tex] = 0 (subtract [tex]\sqrt{2}[/tex] from both sides )

2cosx = - [tex]\sqrt{2}[/tex] ( divide both sides by 2 )

cosx = - [tex]\frac{\sqrt{2} }{2}[/tex]

Since cosx < 0 then x is in the second/ third quadrant

x = [tex]cos^{-1}[/tex] ( [tex]\frac{\sqrt{2} }{2}[/tex] )

  = [tex]\frac{\pi }{4}[/tex] ← related acute angle

Hence

x = π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{3\pi }{4}[/tex] ← second quadrant

or

x = π + [tex]\frac{\pi }{4}[/tex] = [tex]\frac{5\pi }{4}[/tex] ← third quadrant

The best and most correct answer among the choices provided by the question is 3.) radius. Hope this helps :)

Answer:

3.radius.

Step-by-step explanation:

The area of a circle is the space enclosed by the circle.

The circumference is the total length of the circle when stretched.

The diameter is a line that divides the circle into 2 halves or semicircles.

The radius of a circle is the line drawn from the center of the circle to any part of the circumference or any point on the circle.

The right answer is 3.radius.

Answer:

d.

Step-by-step explanation:

The goal of course is to solve for x.  Right now there are 2 of them, one on each side of the equals sign, and they are both in exponential positions.  We have to get them out of that position.  The way we do that is by taking the natural log of both sides.  The power rule then says we can move the exponents down in front.

[tex]ln(2^x)=ln(3^{x+1})[/tex] becomes, after following the power rule:

x ln(2) = (x + 1) ln(3).  We will distribute on the right side to get

x ln(2) = x ln(3) + 1 ln(3).  The goal is to solve for x, so we will get both of them on the same side:

x ln(2) - x ln(3) = ln(3).  We can now factor out the common x on the left to get:

x(ln2 - ln3) = ln3.  The rule that "undoes" that division is the quotient rule backwards.  Before that was a subtraction problem it was a division, so we put it back that way and get:

[tex]x(\frac{ln(2)}{ln(3)})=ln(3)[/tex].  We can factor out the ln from the left to simplify a bit:

[tex]x[ln(\frac{2}{3})]=ln(3)[/tex].  Divide both sides by ln(2/3) to get the x all alone:

[tex]x=\frac{ln(3)}{ln(\frac{2}{3}) }[/tex]

On your calculator, you will find that this is approximately -2.709

Answer:

In brief, apply the pythagorean theorem to show that the distance between the point [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] and the origin is [tex]1[/tex].

Step-by-step explanation:

The pythagorean theorem can give the distance between two points on a plane if their coordinates are known.

A point is on a circle if its distance from the center of the circle is the same as the radius of the circle.

On a cartesian plane, the unit circle is a circle  

Therefore, to show that the point [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] is on the unit circle, show that the distance between [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] and [tex](0,0)[/tex] equals to [tex]1[/tex].

What's the distance between [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] and [tex](0,0)[/tex]?

[tex]\displaystyle \sqrt{\left(\frac{\sqrt{2}}{2}-0}\right)^{2} + \left(\frac{\sqrt{2}}{2}-0\right)^{2}} = \sqrt{\frac{1}{2} + \frac{1}{2}}= \sqrt{1}= 1[/tex].

By the pythagorean theorem, the distance between [tex](\sqrt{2}/2,\sqrt{2}/2) [/tex] and the center of the unit circle, [tex](0,0)[/tex], is the same as the radius of the unit circle, [tex]1[/tex]. As a result, the point [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] is on the unit circle.

Answer:

D

Step-by-step explanation:

Don't be scared off by this problem. Just read the numbers.

Those A + = 264

Those RH- = 111

The total = 375

Total of everyone typed is 740

Probability = 375 / 740 = 0.50675

Probability = 0.507 to the nearest thousandth.

Answer:

6 hours and 40 minutes

Step-by-step explanation:

10 taps = 4 hours

( ÷ 10 )         ( × 10 )

1 taps = 40 hours

( × 6 )       ( ÷ 6 )

6 taps = 6.66666666667 hours / 400 minutes

Final answer:

To fill an aquarium initially using 10 taps in 4 hours, using 6 taps would take 6 hours and 40 minutes.

Explanation:

The time it takes to fill the aquarium initially can be calculated by:

Determine the rate of filling using all 10 taps: 1/4 of the aquarium per hour (as 4 hours to fill).

Calculate the rate using 6 taps: 6/10 of the original rate.

Divide the time taken initially (4 hours) by the reduced rate to find the new time.

Therefore, the time it would take to fill the aquarium using only 6 taps is 6.67 hours or 6 hours and 40 minutes.

Answer:

horizontal compression by factor 3, vertical stretch by factor 2, then reflection across the x-axis ⇒ answer A

Step-by-step explanation:

* Lets revise some transformation

- A vertical stretching is the stretching of the graph away from

 the x-axis

# If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

  by multiplying each of its y-coordinates by k.

# If k should be negative, the vertical stretch is followed by a reflection

  across the x-axis.  

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

# If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally

  compressed by dividing each of its x-coordinates by k.

* Lets solve the problem

∵ y = cos x

∵ y = -2 cos 3x

- At first cos x multiplied by -2

∵ y multiplied by -2

∵ 2 > 1

∴ y = cos x is stretched vertically by factor 2

∵ The factor 2 is negative

∴ y = cos x reflected across the x-axis

∴ The function y = cos x stretched vertically with factor 2 and then

  reflected across the x-axis ⇒ (1)

∵ cos x changed to cos 3x

∵ x multiplied by 3

∵ 3 > 1

∴ y = cos x compressed horizontally by factor 3

∴ The function y = cos x compressed horizontally by factor 3 ⇒ (2)

- From (1) and (2)

* The function y = cos x has horizontal compression by factor 3,

  vertical stretch by factor 2, then reflection across the x-axis to

  produce y = -2 cos 3x

Answer:

It is A

Step-by-step explanation:

AP3x

Answer:

C

Step-by-step explanation:

y=x is a line that has slope 1 meaning it go ups (increases) from left to right.

So that puts us at choice A or C.

Both A or C differ by the numerator for the other function.

We can find the x-intercept for A and C by setting the numerator equal to 0 and solving for x.

Let's do that:

A:  -x-10=0                           C.  -x+10=0

     -x=10                                    -x=-10

      x=-10                                    x=10

A says x-intercept -10

C says x-intercept 10

Your graph intercepts the x-axis at 10 so the answer is C.

[tex]\bf \cfrac{5x+50}{x+5}\cdot \cfrac{1}{x+10}\implies \cfrac{5~~\begin{matrix} (x+10) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{x+5}\cdot \cfrac{1}{~~\begin{matrix} x+10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \cfrac{5}{x+5}[/tex]

Answer:

The correct answer option is C. [tex] \frac { 5 } { x + 5 } [/tex].

Step-by-step explanation:

We are given the following expression and we are to simplify it:

[tex] \frac { 5 x + 5 0 } { x + 5 } . \frac { 1 } { x + 1 0 } [/tex]

We would take the common terms out and then cancel any like terms present in the expression to get the simplest form.

[tex] \frac { 5 ( x + 1 0 ) } { x + 5 } . \frac { 1 } { x + 1 0 } [/tex]

[tex] \frac { 5 } { x + 5 } [/tex]

Therefore, the correct answer option is C. [tex] \frac { 5 } { x + 5 } [/tex].

Answer:

Random Sampling

Step-by-step explanation:

Random sampling is when people are chose at random from a population.

Population is the chits that have been put up on the dart board.

Blindly throwing darts to select 5 names is selecting randomly. In this case, there will be no bias involved in it as names are chosen blindly.

!!

Answer: Random sampling method.

Step-by-step explanation:

A random sampling is a sampling technique in which a researcher randomly picks participants for the sample such that the chances for each participants to get selected is equal.

Given : In a study, the sample is chosen by putting people's names on a dartboard, and blindly throwing darts to select 5 names.

Here , the probability to throw dart on any any name is equal because they throwing it blindly.

Thus, this sampling method is a random sampling method.

Answer:

the middle set of points

Step-by-step explanation:

A translation < 3, - 4 > means add 3 to the x- coordinate and subtract 4 from the y- coordinate.

Under a reflection in the x- axis

a point (x, y ) → (x, - y )

Hence

X(0, - 2) → X'(0 + 3, - 2 - 4) → X'(3, - 6) → X''(3, 6)

Y(1, 4) → Y'(1 + 3, 4 - 4) → Y'(4, 0) → Y''(4, 0)

Z(5, 3) → Z' (5 + 3, 3 - 4) → Z'(8, - 1) → Z''(8, 1 )

Answer:

12

Step-by-step explanation:

12-3>8and 12+1<14

9>8 and 13<14

Answer:

$50/day

Step-by-step explanation:

If 90% of 150 beds are occupied, the .90 × 150 are occupied, or 135 beds.  The total expenses for ALL the residents for the month is 202,500.  We need the cost per day for all the residents, then when we know that we can find the cost per day of one resident.

202,500 ÷ 30 = $6750 for one day for ALL residents

$6750 ÷ 135 = $50 for one day for a single resident

To find the average cost per resident per day for a facility with an average 90% occupancy rate, multiply the number of beds by the occupancy rate to find the average daily occupancy, then multiply by the number of days in the month to get total resident-days. Finally, divide the total monthly expenses by the total resident-days to get the average daily cost per resident.

To calculate the average cost per resident per day in a 150 bed facility with a 90% average occupancy rate over a 30-day month with total expenses of $202,500, we can follow these steps:

So, first we find the average number of occupied beds per day:
150 beds × 90% = 135 occupied beds per day.

Next, we calculate the total number of resident-days for the month:
135 occupied beds × 30 days = 4050 resident-days.

Finally, we find the average cost per resident per day:
$202,500 total expenses ÷ 4050 resident-days = $50 per resident per day.

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From the graph, when x = 1, y = 57,000.

Replace x with 1 in the equations and see if any of the Y 's equal 57,000 :

y = -2610.82(1) + 47860.82 = 45,250

y = 219(1)^2 - 6,506.78(1) + 59,385 = 219 - 6506.78 + 59385 = 53,097.22

y = 54041.5(0.9)^1 =  48,637.35

y = 10,504.6 (1.1)^1 = 11,555.06

The second equation is the closest. so try another x value to see if it is close to the Y value:

Let's try x = 14:

y = 219(14)^2 - 6506.78(14) + 59,385 = 42924 - 91094.92 + 59385 = 11,214.08

This is close to Y = 12,00 shown on the graph

SO the closest equitation is y = 219x^2 - 6506.78x + 59385

A - rolling exactly one six

[tex]P(A)=\dfrac{1}{5}\cdot\dfrac{4}{5}+\dfrac{4}{5}\cdot\dfrac{1}{5}=\dfrac{4}{25}\cdot \dfrac{4}{25}=\dfrac{16}{625}[/tex]