find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, three yellow, and four red marbles.

The solution of the trigonometric equation is x = 26.57° or 153.43°

A trigonometric equation is an equation that contains the trigonometric ratios.

Given the trigonometric equation 2cos x - sin x = 3/(2cos x + sin x)

We solve for x in the equation. We proceed as follows.

Since 2cos x - sin x = 3/(2cos x + sin x)

Multiplying both sides by (2cos x + sin x), we have that

(2cos x - sin x)(2cos x + sin x) = 3

Now, we know that (a² - b² = (a + b)(a - b)

Applying this where a = 2cosx and b = sinx, we have that

(2cos x - sin x)(2cos x + sin x) = 3

(2cos x)² - (sin x)² = 3

4cos² x - sin² x = 3

Since sin²x = 1 - cos²x, substituting this into the equation, we have that

4cos² x - sin² x = 3

4cos² x - (1 - cos²x) = 3

4cos² x - 1 + cos²x = 3

4cos² x + cos²x  = 3 + 1

5cos²x  = 4

cos²x  = 4/5

Taking square root of both sides, we have that

cosx  = ±√(4/5)

cosx  = ±2/√5)

cosx  = ±2/√5 × √5/√5

cosx  = ±2√5/5

Taking inverse cosine of both sides, we have

x = cos⁻¹(±2√5/5)

x = cos⁻¹(±0.8944)

x = cos⁻¹(0.8944) or x = cos⁻¹(-0.8944)

x = 26.57° or (180 - 26.57)°

x = 26.57° or 153.43°

So, the solution is x = 26.57° or 153.43°

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The unit rate is 2 servings per package

From the question, we have the following parameters that can be used in our computation:

Packages Servings

3                 6

13.5             27

The unit rate is calculated as

The unit rate = Servings/Packages

Substitute the known values in the above equation, so, we have the following representation

The unit rate = 6/3

Evaluate

The unit rate = 2

Hence, the unit rate is 2

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In exchange for a $300 million fixed commitment line of credit, your firm had agreed to pay an up-front commitment fee of .130 percent of the amount of the line.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent.

Here,

Your company had agreed to pay an upfront commitment fee equal to.13% of the line's value in exchange for a $300 million fixed commitment line of credit.

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Answer: y = 1x + 5

Step-by-step explanation:

This is where the equation; y=mx+b comes in handy.

We are given m, 1.

And we are given a coordinate to plug in.

2=1(-3)+b

2=-3+b

b=5

y = 1x + 5

Answer:

Step-by-step explanation:

The standard form of a line is Ax+By=C.  To solve this problem, begin with the point-slope form [tex]y-y_1=m(x-x_1)[/tex].  For this problem, let

[tex](x_1,y_1)=(-3,2)\\m=1[/tex]

Input these values into the point-slope form equation and convert to slope-intercept form,

[tex]y-(2)=(1)[x-(-3)]\\y-2=x+3\\y-2+2=x+3+2\\y=x+5[/tex]

Next, convert slope-intercept form to standard form:

y=x+5

-x+y=5

For standard form, A must be positive.  So,

-(x-y)=5

x-y=-5

The equation use to determine the value of [tex]x[/tex] is [tex](2x+5)+3(2x+5)=92[/tex].

The measures of [tex]\angle A, \angle B[/tex] are [tex]23^\circ, 69^\circ.[/tex]

Let us assume the measures of [tex]\angle A, \angle B[/tex] are [tex]z, y[/tex].

Now according to the question, we can write the relation between [tex]\angle A, \angle B[/tex] is [tex]y=3z....(i)[/tex].

We know, the measure of [tex]\angle A[/tex] is [tex]2x+5[/tex] so [tex]2x+5=z....(ii)[/tex]. Now, we will substitute the value of [tex]z[/tex] from equation [tex](ii)[/tex] in equation [tex](i)[/tex].

[tex]y=3z\\= 3 \times (2x+5)\\=6x+15[/tex]

So, the final equation will be [tex](2x+5)+3(2x+5)=92[/tex]

⇒ [tex]6x+15+2x+5=92[/tex]

⇒ [tex]8x+20=92[/tex]

⇒ [tex]8x=72[/tex]

⇒ [tex]x=9[/tex]

[tex]\therefore[/tex] measure of [tex]\angle A[/tex] is [tex]2x+5=(2 \times 9)+1=25[/tex] and measure of [tex]\angle B[/tex] is [tex]2 \times 23 = 69[/tex].

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Answer:

18

Step-by-step explanation:

awwww this is so sweet of you! you see this is the type of people we need in the world, kind people like you just wanting to help, thats why I answer questions on brainly not for the points and popularity but to help people out, thank you! <33333

Answer:

If the x is a Times then its 18 but if its not its 3x4+6

Step-by-step explanation:

Answer: x[tex]\geq[/tex]1

Step-by-step explanation:

x is all the numbers equal to or less than 1. The closed dot means its less than or equal to and the dot is on 1. It cant be more than 1, because the arrow shows that all those numbers are greater than one and cant be x.

i hope you understand cause i can write on a screen

The converse of statement is “If dangerous to your health then walking in front of a moving car”.

The inverse of statement is “If not dangerous to your health then not walking in front of a moving car”.

The contrapositive of statement is “if not walking in front of a moving car then not dangerous to your health."

The definition of a conditional statement refers to its two essential parts, the hypothesis (if) and the conclusion (then).

The given conditional statement is

"walking in front of a moving car is dangerous to your health."

The converse is “If dangerous to your health then walking in front of a moving car”.

The inverse is “If not dangerous to your health then not walking in front of a moving car”.

The contrapositive is “if not walking in front of a moving car then not dangerous to your health."

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Answer:

15

Step-by-step explanation:

To find the total number of combinations you can make with these four coins, we have to do 2 to the power of the total amount of coins. This because each coin has two choices: to be included in the combination or not. There are 4 total coins, and 2^4 is 16. There are 16 total combinations. But since one of those possibilities are that none of the coins are included, we subtract 1 from the total, and get 15. There are 15 combinations with 1 or more coins, which each give us different amounts.

Answer:

a. 2664 Explanation: 543 + 534 + 453 + 435 + 354 + 345 = 2664

Step-by-step explanation:

Answer:

m = 40

Step-by-step explanation:

m% = 40%

135x40% = 54

Answer: yes, her luggage is under limit

Step-by-step explanation:

1 kg = 2.2 pounds

Take 55 divided by 2.2 = 25 kg

25 < 30

Her luggage is under the limit

Answer: 8x + 2

Step-by-step explanation:

Answer:

8x+2

Step-by-step explanation:

x3+2x2+x+2

=3x+4x+x+2

=8x+2

The equation of a line perpendicular to y=4/24x that pass through the point (-8, -4) is -6x-4y=16 where x-intercept is -6 and y-intercept is -4.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables.

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

Given line ;

y=1x/6

now comparing it with y=mx+c to find the value of m and we found;

m1=1/6

now if two lines are perpendicular then,

m1.m2=-1

m2=-6

now finding the equation of line passing through the point (-8, -4)

x1=-8

y1=-4

(y−y1)=m(x−x1)

Y+4=(-6)(x+4)

Y+4=(-6x/4)

Y=(-6x/4)-4

Y=(-6x-16)/4

4y=-6x-16

rearrange;

-6x-4y=16

this is our required value.

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Using mathematical operations, we know that 27/4 pounds of Ham are still left with M.D.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Most people believe that addition, subtraction, multiplication, and division are the four basic operations in mathematics.

So, we know that:
M.D. bought 8½ pounds of Ham.

He gave 1¾ pounds to Mr. Chavir.

Remaining Ham with M.D.:

8½ - 1¾

16+1/2 - 4+3/4

17/2 - 7/4

34 - 7/4

27/4

Therefore, using mathematical operations, we know that 27/4 pounds of Ham are still left with M.D.

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The number of chickens that can be fed with 140 kg of corn is 2800.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 8 is an equation.

We have,

250 kg corn  = 5000 chicken

Multiply 140/250 on both sides.

140 kg of corn = 140/250 x 5000 chicken

140 kg of corn = 2800 chicken

Thus,

2800 chickens can be fed with 140 kg of corn.

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Answer:

x = -1

Step-by-step explanation:

First of all, we must find the value of what's inside the parentheses.

14 ÷ -2/3 =

14/1 x -3/2 = -42/2 = -21

That means the equation is now:

-21 = 6x - 15

+15        +15

-6 = 6x

-1 = x

Therefore, the solution to given problem is the density of metal block comes out to be 2717.4 kg/[tex]m^{3}[/tex]

The substance's density is defined as its mass per unit of volume. Although the Latin letter D can also be utilized, the most popular density symbol is. In mathematics, density is calculated as mass divided by volume:

Here,

Given : mass =5kg

volume = 1.84 x [tex]10^{-3}[/tex]

thus, density = mass/volume

we apply density formula , we get

density = 5/ 1.84 x [tex]10^{-3}[/tex]

density =2717.4 kg/[tex]m^{3}[/tex]

Therefore the density of metal block comes out to be 2717.4 kg/[tex]m^{3}[/tex]

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The measure of the angle ∠SRW will be 95°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

2 converging lines are shown. A line with focuses TRW converges a line with focuses SRV at point R. The angle ∠TRV is 95 degrees.

The angle ∠TRV and the angle ∠SRW are opposite angles. Then we have

∠TRV = ∠SRW

∠SRW = 95°

The measure of the angle ∠SRW will be 95°.

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Answer:

Step-by-step explanation:

y - 3 = x - 3

y = x

Answer:

£212.5

Step-by-step explanation:

15% of 250 = 37.5

250 - 37.5 = 212.5

Billy suffers from a stutter, so he expresses himself in a manner in which he can be successful.

Doctor Spivey grants McMurphy's request for a pass to take a fishing trip with nine other patients, accompanied by two of his aunts.

Why is McMurphy tired after the fishing trip?

McMurphy adds Rub-a-Dub George, a neat-freak Swedish fisherman and sailor, to the group. Nurse Ratched says they can't go because there isn't enough capacity in one car for all the patients when Candy Starr arrives without her buddy to pick up the patients for their outing.

McMurphy has his own weakness, his self-centeredness. At first he is willing to sacrifice the patients for his own well-being

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answer:

b=-3

step-by-step explanation:

the equation's format is y=mx+b so b is -3. you can also figure this out if you plug y in as 0. hope that helps!

Answer:

it is very easy for even a third grader 2x4=8

By factor theorem (v+5) is not a factor of the given polynomial f(v).

What does factor theorem mean?

When thoroughly factoring the polynomials, mathematicians apply the factor theorem. The polynomial's zeros and factors are connected by this theorem.

                   The factor theorem states that if a is any real number and f(x) is a polynomial of degree n 1 then (x-a) is a factor of f(x) if f(a)=0.

The factor theorem states that

f(x) has a factor (x-k) if and only if f(k) = 0

We are given the following information.

F(v) = v 4 + 16v 3 + 8v 2 - 725

        We have to check whether (v+5) is a factor of given polynomial.

( v + 5 ) = ( v - ( - 5 )

 f( -5 ) = [tex]( -5 )^{4} + 16( -5)^{3} + 8( -5)^{2} - 725[/tex]

          = - 1900

 f(-5) ≠ 0

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to get the slope of any straight line, we simply need two points off of it, let's use the ones in the picture below.

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{24}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{24}-\stackrel{y1}{12}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{ 12 }{ 2 } \implies \text{\LARGE 6}[/tex]

Answer: 251.20

Step-by-step explanation: