if fm= 11, Mg= 3, and PM = 2, what is the measure of PQ?

Step-by-step explanation:

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By using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.

Given

\(\sin \text{x}^\circ= \ ?\)

\(\tan \text{x}^\circ=\dfrac{\text{a}}{4}\)

\(\cos \text{x}^\circ=\dfrac{4}{\text{b}}\)

Formula to find \(\sin \text{x}^\circ\)

\(\sin \text{x}^\circ=\dfrac{\text{Opposite}}{\text{Hypotenuse}}\)

\(\rightarrow\sin \text{x}^\circ=\bold{\dfrac{a}{b}}\)

Therefore, by using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

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Answer:

0.00137

Step-by-step explanation:

Answer:

Find the GCD (or HCF) of numerator and denominator. GCD of 9 and 3 is 3.

9 ÷ 33 ÷ 3.

Reduced fraction: 31. Therefore, 9/3 simplified to lowest terms is 3/1

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator. GCD of 9 and 3 is 3.

9 ÷ 33 ÷ 3.

Reduced fraction: 31. Therefore, 9/3 simplified to lowest terms is 3//

Answer:

5/8 =0.625

Step-by-step explanation:

Hope this helps

True or False.

A is true, a line has two points which are the two ends.

Answer: Choice D

Any three points lie on a distinct line

=============================================================

Explanation:

Let's go through each statement to see which are true, and which are false.

Side note: The spelling of "colinear" is sometimes "collinear" with two "L"s, instead of one. I'm not 100% sure which spelling is more acceptable. I've found sources that have used both.

Answer :

a) It is given that

Everyday a machine makes 500000 staples and puts them into the boxes.

The machine need 170 staples to fill a box

One box contans = 170 staples.

Total number of staples = 500000

Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.

\( \: :\implies \) 500000 /170

\( :\implies \: \) 2941 (approx)

Therefore, 2941 boxes are required to fill with 500000 staples.

b) It is given that,

Each staple is made of 0.21 g of metal .

Total weight of metal = 1 kg = 1000 g

1 staple = 0.21 g

Number of staples = weight of metal/ Weight of 1 staple.

\( \: :\implies \) 1000/0.21

\( \: :\implies \) 4761 (approximately)

Therefore, 4761 staples can be made from 1 kg of the metal.

Answer:

24

Step-by-step explanation:

If you need an explaination you should immediatly remove yourself from the Gene pool, this is a 3rd grade question.

The result is: 30 divided by 1.25 equals 24.

To divide 30 by 1.25, follow these steps in words:

The division 30 ÷ 1.25 can be written as the fraction 30/1.25.

Remove the decimal by multiplying both the numerator and denominator by a power of 10 to convert the decimal into a whole number.

Since 1.25 has two decimal places, multiply both the numerator and denominator by 100 to remove the decimal:

30/1.25 = (30 * 100) / (1.25 * 100) = 3000 / 125

Find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD to simplify the fraction:

GCD of 3000 and 125 is 25.

3000 ÷ 25 = 120

125 ÷ 25 = 5

So, 3000/125 simplifies to 120/5.

Divide the numerator by the denominator to get the final result.

Now, simply divide the numerator (120) by the denominator (5):

120 ÷ 5 = 24

The result is 24.

So, 30 divided by 1.25 equals 24.

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312 mg is not greater than 312 dg

Answer:

B

Step-by-step explanation:

The \(y\)-intercept is \((0,27)\), eliminating all the options except for B.

Answer:

C (Hypotenuse) = 9.9

Step-by-step explanation:

Given the two sides of a triangle, where a = 7, and b = 7:

We can use the Pythagorean Theorem where it states: c² = a² + b².

Substitute the given values into the Pythagorean Theorem to find the length of the hypotenuse.

c² = a² + b²

c² = 7² + 7²

c² = 49 + 49

c² = 98

\(\LARGE\mathsf{\sqrt{c^2}\:=\:\sqrt{98}}\)

c = 9.89 or 9.9

Therefore, the length of the hypotenuse is 9.9, making the given triangle an isoceles triangle with two equal sides.

The first step in evaluating the expression 3x{9-(4+2)/2 is to simplify the innermost parentheses. By performing operations within parentheses first, we can simplify the expression and make it easier to evaluate.

To begin, we evaluate the expression within the parentheses (4+2), which equals 6. Thus, the original expression becomes 3x{9-6/2}.

The next step is to simplify the division operation. We divide 6 by 2, resulting in 3. Now the expression becomes 3x{9-3}.

The subsequent step is to simplify the subtraction operation. We subtract 3 from 9, giving us 6. The expression now becomes 3x6.

Finally, we multiply 3 by 6, yielding a final result of 18. Therefore, the evaluation of the expression 3x{9-(4+2)/2 is equal to 18.

By simplifying the parentheses, performing the division, and evaluating the subtraction, we systematically reduce the expression to its simplest form. Following the order of operations (also known as PEMDAS or BODMAS), which prioritizes parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right), ensures an accurate evaluation of the expression.

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Answer:=

2π/3

Step-by-step explanation:

plato

Answer:

equal

Step-by-step explanation:

1/4 = .25

1÷4=.25

Therefore the value of x is less than 4 when x is in the inequality 3x + 2 < 14 and greater than -3 when x is in the inequality 2 x-5> -11

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. For instance, let's say you have 225 and want to purchase a new bicycle that costs $250.

Expressions are carried out, or evaluated, in order to yield a value. In an evaluation process, values of expressions can be employed as components of surrounding expressions.

To solve for x in the inequality 3x + 2 < 14, we can begin by subtracting 2 from both sides to get 3x < 12. Then, dividing both sides by 3 gives x < 4.

To solve for x in the inequality 2 x-5> -11, we can begin by adding 5 to both sides to get 2x> -6, then divide both sides by 2 to get x > -3

So x can be any number greater than -3 and less than 4

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Answer:

can you just mark me brainlest

Step-by-step explanation:

Answer:

the answer would probably

Step-by-step explanation:

PAY ATTENTION IN CLASS AND YOU WOULD KNOWWW

Answer:

0.7727 = 77.27% probability that it is small or green

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

11 large + 11 small = 22 total marbles = 22 total outcomes

11 small marbles  + 6 green large marbles = 17 desired outcomes.

What is the probability that it is small or green?

\(p = \frac{17}{22} = 0.7727\)

0.7727 = 77.27% probability that it is small or green

It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

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Answer:

the slope which is given is to plot the points on a graph.

Answer:

.45<.5

Step-by-step explanation:

the last one is correct

Answer:

0.45 < 0.5

Step-by-step explanation:

4.05 is not less than 0.45

4.05 is not equal to 0.45

0.45 is less than 0.5

therefore only the final statement is true.

30 is the fast surface area of the balloon expanding when the radius of the balloon is 4 inches

Now, According to the question:

A spherical balloon is expanding at the rate of 60 pie cubic inches /sec.

The radius of the balloon is 4 inches.

Now, Solving the problem:

By using formula:

The formula for the volume of a sphere is V = 4/3 π r³,

where V = volume and r = radius.

Volume = \(\frac{4}{3}\pi r^3\)

We have that:

Differentiate the formula:

\(\frac{dV}{dt}=4\pi r^2.\frac{dr}{dt}= 60\)

=> \(\frac{dr}{dt}=\frac{60}{4\pi r^2}\)

We know that \(A=4\pi r^2,\) and so we also have

\(\frac{dA}{dt}=8\pi r.\frac{dr}{dt}\)

Plug in what we found for dr/dt and plug in r=4 to get:

\(\frac{dA}{dt}=8\pi r.\frac{60}{4\pi r^2}\)

\(\frac{dA}{dt}=\frac{120}{r}=\frac{120}{4}\)

\(\frac{dA}{dt}=30\)

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Answer:

\(\textsf{b)} \quad \cos^{-1}\left(\dfrac{12}{13}\right)\)

Step-by-step explanation:

\(\textsf{Let}\;\;x=\tan^{-1}\left(\dfrac{5}{12}\right)\)

Therefore:

\(\implies \tan x=\tan\left(\tan^{-1}\left(\dfrac{5}{12}\right)\right)\)

\(\implies \tan x=\dfrac{5}{12}\)

The tan trigonometric ratio is the ratio of the side opposite the angle to the side adjacent the angle of a right triangle.  Therefore, O = 5 and A = 12.  Calculate the hypotenuse (H) by using Pythagoras Theorem.

\(\implies a^2+b^2=c^2\)

\(\implies \sf O^2+A^2=H^2\)

\(\implies 5^2+12^2=\sf H^2\)

\(\implies \textsf{H}=\sqrt{5^2+12^2}\)

\(\implies \textsf{H}=13\)

Therefore, the values are:

\(\boxed{\begin{minipage}{8cm}\underline{Trigonometric ratios}\\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\\\$\sf\csc(\theta)=\dfrac{H}{O}\quad\sec(\theta)=\dfrac{H}{A}\quad\cot(\theta)=\dfrac{A}{O}$\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}\)

Substitute the values into the sin, cos, sec and cosec ratios then take their inverses.

\(\sin x = \dfrac{5}{13}\implies \sin^{-1}(\sin x) = \sin^{-1}\left(\dfrac{5}{13}\right)\implies \boxed{x= \sin^{-1}\left(\dfrac{5}{13}\right)}\)

\(\cos x = \dfrac{12}{13}\implies \cos^{-1}(\cos x) = \cos^{-1}\left(\dfrac{12}{13}\right)\implies \boxed{x= \cos^{-1}\left(\dfrac{12}{13}\right)}\)

\(\sec x = \dfrac{13}{12}\implies \sec^{-1}(\sec x) = \sec^{-1}\left(\dfrac{13}{12}\right)\implies \boxed{x= \sec^{-1}\left(\dfrac{13}{12}\right)}\)

\(\csc x = \dfrac{13}{5}\implies \csc^{-1}(\csc x) = \csc^{-1}\left(\dfrac{13}{5}\right)\implies \boxed{x= \csc^{-1}\left(\dfrac{13}{5}\right)}\)

Therefore, from the given answer options:

\(x=\tan^{-1}\left(\dfrac{5}{12}\right)=\cos^{-1}\left(\dfrac{12}{13}\right)\)                                  

Answer: 3/11, 6/19/, 1/3, 5,8

Hope this helps

Step-by-step explanation:

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

\(\frac{115\sqrt{14} }{2}\)

Step-by-step explanation:

∫∫ ( x + y + z ) ds

where :

x = u + v ,  y = u - v ,  z = 1 + 2u + v ,  

0 ≤ u ≤ 5,  

0 ≤ v ≤ 1

R ( u,v ) = < u+v , u-v , 1 + 2u +v >   next we have to differentiate

attached below is a detailed solution

The surface integral S(x + y + z) dS, where S is the parallelogram is \(115\sqrt{14} /2\) and this can be determined by integrating the given expression.

Given :

The surface integra S(x + y + z) dS, S is the parallelogram with parametric equations  x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 7, 0 ≤ v ≤ 3.

The following calculation can be used in order to determine the surface integral.

\(\rm R_u\times R_v = <3,1,-2>\)

\(\rm ||R_u\times R_v|| = \sqrt{14}\)

Now, evaluate the surface integral.

\(\rm I = \rm \int\int_s(x+y+z)dr\)

\(\rm I = \int^5_{u=0}\int^1_{v=0}(u+v+u-v+1+2u+v)||R_u\times R_v||dA\)

\(\rm I = \int^5_{u=0}\int^1_{v=0}(u+v+u-v+1+2u+v)\sqrt{14} \;du\;dv\)

\(\rm I = \sqrt{14} \int^5_0(v+4uv+\dfrac{v^2}{2})^1_0\;du\)

\(\rm I = \sqrt{14} (\frac{3}{2}u+4\frac{u^2}{2})^5_0\)

Simplify the above expression.

\(\rm I = \dfrac{115\sqrt{14} }{2}\)

The surface integral S(x + y + z) dS, where S is the parallelogram is \(115\sqrt{14} /2\)

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the function is:

We can graph the function to be sure:

1) In this case the ellipse open vertically because there is a contraction in the x axis.

2) The right vertex is in the coordinate (8,2)

3) the eft vertex is in the coordinate (2,2)

4) the right focus is in the coordinate (14.5,2)

5) the left focus is in the coordinate (-4.5,2)

6) and the eccentricity is the divition between the distance of the center to the vertex by the distance of the center to the focus so:

Answer:

Elon Musk 269.7 B
Jeff Bezos: 170.15 B
Bill Gates: 130.23 B

Step-by-step explanation:

If you had a trail of 1 billion 1 dollar bills, it would stretch out to 96,900 miles.

If you did that with 100 billion 1 dollar bills, that would be 9,690,000 miles.

That is more than 300 times the circumference of the Earth.