in order to solve for x which trig function would be used cosine sine or tangent​

Answer:

They are collinear

Step-by-step explanation:

They are all on the same line.

The points P,Q,R & S are collinear.

It is given that line PQ and line RS are different names for the same line.

We have to tell that what is true about points P,Q,R and S.

What do you mean by collinear ?

Three or more points are said to be collinear if they all lie on the same straight line.

As per the above definition ;

P, Q, R and S are the four points at the same line.

So, we can say that these four points are collinear i.e., they lie on the same straight line.

Thus , points P,Q,R and S are collinear.

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Answer:

Step-by-step explanation:

16.50 × m = 99

m = 6

A 24-hour clock will read:

To determine the time on a 24-hour clock after a certain number of hours, we can use modular arithmetic.

(a) 100 hours after the clock reads 2:00:

To find the time, we add 100 hours to 2:00 and take the result modulo 24 (to account for the 24-hour cycle):

Time = (2 + 100) mod 24 = 102 mod 24 = 6

(b) 45 hours after the clock reads 12:00:

Similarly, we add 45 hours to 12:00 and take the result modulo 24:

Time = (12 + 45) mod 24 = 57 mod 24 = 9

(c) 168 hours after the clock reads 19:00:

Again, we add 168 hours to 19:00 and take the result modulo 24:

Time = (19 + 168) mod 24 = 187 mod 24 = 19

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The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Statement "Zeros at x = 2 ± √3" and statement "the zeros are the hot dog prices that give $0.0 profit (no profit)" are correct choice would be (B) and (D).

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The given options are:

A. Zeros at x=2 and x = 6

B. Zeros at x = 2 ± √3

C. The zeros are the hot dog prices at which they sell 0 hot dogs

D. The zeros are the hot dog prices that give $0.0 profit (no profit).

We have a function:

y = -2(x - 2)² + 6

To find the zeros of the function plug y = 0

-2(x - 2)² + 6 = 0

(x - 2)² = 3

x - 2 =  ±√3

x = ±√3 +2 or

x = 2 ± √3

At x= 2 ± √3 value of y = $0

Thus, statement "Zeros at x = 2 ± √3" and statement "the zeros are the hot dog prices that give $0.0 profit (no profit)" are correct choice would be (B) and (D).

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Answer:

commutative and zero product properties

Answer:

See below

Step-by-step explanation:

Center:   (-3, 4)

radius = r = \(\sqrt{25}\) = 5

diameter = 2r = 10

Answer:

Center= (3,-4)   Radius=5   Diameter=10

Step-by-step explanation:

The numbers (3,-4) are the coordinates in the center of a circle. The radius is squared to get the end number so to get the radius, you have to find its square root- \(\sqrt{25\) =5. The diameter is 2 times bigger than the radius so 5 times 2= 10.

Answer:

25

Step-by-step explanation:

9+25=34

Presumably you're talking about a geometrical interpretation of the identity,

(a + b + c)² = a ² + b ² + c ² + 2 (ab + ac + bc)

See the attached sketch for a visual "proof" of it.

Answer:

C

Step-by-step explanation:

The equation for the red graph is,

⇒ 2y = f (x)

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

The black graph is the graph of,

⇒ y = f (x)

Now,

The red graph is spread out the function of blk graph.

Hence, We get;

The equation for the red graph is,

⇒ y = f (x) / 2

⇒ 2y = f (x)

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Answer:

A

Step-by-step explanation:

two numbers that times to make -12 but add to make +4

+6×-2=-12

+6+-2=4

The decimal number of bits required to store a + b or a - b is 17 bits.

The number of bits required to store the result of the operations equal.

For the given 4-digit hex numbers a and b, convert them to binary to determine the number of bits required. Each hexadecimal digit corresponds to 4 binary bits.

Therefore, the number of bits required to store a is 4 ×4 = 16 bits, and the number of bits required to store b is also 16 bits.

To calculate the number of bits required to store a + b or a - b, to consider the maximum value that can result from these operations. The maximum value will occur when both a and b have their highest possible values.

For a 4-digit hex number, the highest value is "FFFF" in hexadecimal or 65535 in decimal. When performing addition or subtraction, the maximum result will be 2 ×65535 = 131070, which represented by 17 bits.

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A damper element always dissipates energy because it converts the kinetic energy of a moving object into heat energy, which is described mathematically by the equations F = -c*v and E = 0.5*c*v^2.

A damper element, also known as a viscous damper or a shock absorber, is a mechanical component that is used to dissipate energy in a system. The damper element does this by converting the kinetic energy of a moving object into heat energy. This process can be described mathematically using the following equation:

F = -c*v

Where F is the force applied by the damper element, c is the damping coefficient, and v is the velocity of the object. This equation shows that the force applied by the damper element is always in the opposite direction of the velocity of the object, meaning that the damper element always works to slow down the object and dissipate its energy.

The amount of energy dissipated by the damper element can also be calculated using the following equation:

E = 0.5*c*v^2

Where E is the energy dissipated by the damper element, c is the damping coefficient, and v is the velocity of the object. This equation shows that the amount of energy dissipated by the damper element is proportional to the square of the velocity of the object, meaning that the damper element is more effective at dissipating energy when the object is moving at higher speeds.

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Answer:

$2399.99

Step-by-step explanation:

the price of the tv is discounted by 25%

that is the same as saying the tv is 75% of its original price

so we take $1799.99/75 to see what one percent of the price is

$1799.99/75=23.9998

then we take 23.9998*100 to see what the original price was

23.9998*100=2399.986667 and then we round to the nearest hundredth

so 2399.99

Answer:  -7.5

Step-by-step explanation:  Simplify. turn the 1/2 into a decimal and it will make it much easier

Answer:

24=1,2,3,4,6,8,12,24

18=1,2,3,6,9,18

I hope this helps!

Please mark brainliest!

Step-by-step explanation:

D.

subtracting the smallest value of the lower half of the data set from the biggest value of the lowest half of the data set

The lower quartile of a set of data is calculated by subtracting the smallest value of the lower half of the data set from the biggest value of the lowest half of the data set.

"A quartile is a statistical term that describes a division of observations into four defined intervals based on the values of the data and how they compare to the entire set of observations.

Just like the median divides the data into half so that 50% of the measurement lies below the median and 50% lies above it, the quartile breaks down the data into quarters so that 25% of the measurements are less than the lower quartile, 50% are less than the median, and 75% are less than the upper quartile."

From the definition it is clear that,

lower quartile of a set of data is calculated by :

subtracting the smallest value of the lower half of the data set from the biggest value of the lowest half of the data set.

Hence, D is the correct option.

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We have shown that 2ⁿ > (n choose 1/2) for every natural number n with n ≥ 6. This can be answered by the concept of

mathematical induction.

To prove that 2ⁿ > (n choose 1/2) for every natural number n with n ≥ 6, we can use mathematical induction.

Base case: When n = 6, we have 2⁶ = 64 and (6 choose 3) = 20. We can verify that 64 > 20, so the base case holds.

Inductive step: Assume that \(2^{k}\) > (k choose 1/2) for some natural number k ≥ 6. We want to show that\(2^{k+1}\) > ((k+1) choose 1/2).

Using the formula for binomial coefficients, we have:

\(\begin{equation*}\binom{k+1}{\frac{1}{2}} = \frac{(k+1)!}{\left(k+\frac{1}{2}\right)! \left(\frac{1}{2}\right)!}\end{equation*}\)
Simplifying, we get:

\(\binom{k+1}{\frac{1}{2}} = \frac{(k+1)!}{\left(k+\frac{1}{2}\right)!}\)

Now, we can use the assumption that 2^k > (k choose 1/2) to write:

\(2^{k+1} = 2 \times 2^k > 2 \times \binom{k}{\frac{1}{2}}\)

To show that\(2 \times \binom{k}{\frac{1}{2}} > \binom{k+1}{\frac{1}{2}}\), we can simplify and manipulate the expressions as follows:

\(2 \times \binom{k}{\frac{1}{2}} = 2 \times \frac{k!}{\left(k-\frac{1}{2}\right)! \left(\frac{1}{2}\right)!}\)

\(2 \times \frac{(k+1) \times (k-\frac{1}{2})!}{(k+\frac{1}{2}-1)! \times \frac{1}{2}!}\)

\((2k+1) \times \binom{k+1}{\frac{1}{2}} \div (k+1)\)

\(\frac{2k+1}{k+1} \times \binom{k+1}{\frac{1}{2}}\)
Now, we want to show that \(\frac{2k+1}{k+1} > 1\) We can do this by noting that:

\(\frac{2k+1}{k+1}-1=\frac{k}{k+1} > 0\)

Therefore,\(\frac{2k+1}{k+1} > 1\), and we have:

\(2 \times \binom{k}{\frac{1}{2}} > \binom{k+1}{\frac{1}{2}}\)
So, by mathematical induction, we have shown that 2ⁿ > (n choose 1/2) for every natural number n with n ≥ 6.

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The relation ‘equal to’ is an equivalence relation on A.

a) To give an example of an onto function f: A → B, we need to ensure that every element in set B is mapped to from set A. Since set B has three elements (5, 6, 7) and set A has four elements (1, 2, 3, 4), it is impossible to have an onto function from A to B.

This is because there are more elements in A than in B, so at least one element in B will not have a corresponding element in A.

b) A function g: A → B is a one-to-one function if each element of set A is paired with a distinct element in set B. Let us create a table to get the one-to-one function g.

Table of one-to-one function gA1234B5677The function g: A → B can be defined by g(1) = 5, g(2) = 6, g(3) = 7 and g(4) = 7.

Hence, this is a one-to-one function.

c) An equivalence relation is a relation that is reflexive, symmetric, and transitive.

We can define an equivalence relation on set A using the relation ‘equal to’. Every element of set A is equal to itself, i.e., ∀ a ∈ A, a = a.

Hence, this is a reflexive relation on A. Also, if a and b are two elements of A such that a = b, then b = a.

Hence, this is a symmetric relation on A. Also, if a, b, and c are three elements of A such that a = b and b = c, then a = c. Hence, this is a transitive relation on A.

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In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.

Find the lengths of the three sides of the triangle using the distance formula.

Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.

If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.

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Zoe spent "$5.25" on apples. A further solution is below.

As we know,

Now,

→ \(M = 3.50 P\)

here,

then,

By substituting the value, we get

→ \(M = 3.50\times 1.5\)

→      \(= 5.25\) ($)

Thus the above answer is correct.

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\(3\leqslant |x+2|\leqslant 6\implies \begin{cases} 3\leqslant |x+2|\\\\ |x+2|\leqslant 6 \end{cases}\implies \begin{cases} 3 \leqslant \pm (x+2)\\\\ \pm(x+2)\leqslant 6 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(3\leqslant +(x+2)\implies \boxed{3\leqslant x+2}\implies 1\leqslant x \\\\[-0.35em] ~\dotfill\\\\ 3\leqslant -(x+2)\implies \boxed{-3\geqslant x+2}\implies -5\geqslant x \\\\[-0.35em] ~\dotfill\\\\ +(x+2)\leqslant 6\implies \boxed{x+2\leqslant 6}\implies x\leqslant 4 \\\\[-0.35em] ~\dotfill\\\\ -(x+2)\leqslant 6\implies \boxed{x+2\geqslant -6}\implies x\geqslant -8\)

Answer:

To the first picture: it's 9

To the second: its sin3/5

Step-by-step explanation:

This would take some time to explain so I'll keep it brief

Pic 1) process of elimination through cos

Pic 2) You divide the opposite by the hypotenuse to get the degree of angle x

The final value theorem cannot be used for the given system output Y(s) = 1 / (s³ + 4s²) because the system is unstable. The correct option is A.

The final value theorem is used to find the steady-state value of a system's output y(t) as t approaches infinity, given the Laplace transform of the output Y(s). The final value theorem states that the steady-state value of y(t) is equal to the limit of s * Y(s) as s approaches 0.

For the final value theorem to be applicable, the system must be stable, meaning that all the poles of the system's transfer function must have negative real parts. In an unstable system, at least one of the poles has a positive real part.

In this case, the system has the transfer function Y(s) = 1 / (s³ + 4s²), which has poles at s = 0 and s = -2. The pole at s = 0 has a zero real part, indicating that the system is unstable.

Therefore, the correct answer is A. The final value theorem cannot be used because the system is unstable.

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Complete question:

The output of a system is Y(s)= 1/ s³+4s². The final value theorem cannot be used:
A. because the system is unstable
B. because there are poles
C. because there are two
D. because there are zeros system is at the imaginary axis poles at the origin at the imaginary axis unstable

To find the acceptance set A for a significance level of α = 0.09 and rejection set R of the form { |K - E(K)| > c}, we first need to calculate the expected value and variance of K.

(A) Since the coin is fair, E(K) = 50 and Var(K) = 25/2. Using the Central Limit Theorem, we can approximate K as a normal distribution with a mean of 50 and a standard deviation of 2.5. We can then find the value of c such that P(|K - 50| > c) = 0.09/2 = 0.045. Solving for c, we get c = 3.325. Therefore, the acceptance set A is {45 < K < 55}.

(b) For a significance level of α = 0.018 and rejection set R of the form {K > λ}, we again use the Central Limit Theorem to approximate K as a normal distribution with a mean of 50 and a standard deviation of 2.5. We can then find the value of λ such that P(K > λ) = 0.018. Using a normal distribution table or calculator, we find λ to be approximately 60.5. Therefore, the acceptance set A is {K ≤ 60}.

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Answer:

7.93

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the distance between two points with polar coordinates (r1, 1) and (r2, 2), we need to convert the polar coordinates to Cartesian coordinates.

The formula to convert polar coordinates to Cartesian coordinates is x = r cos(theta) and y = r sin(theta), where r is the distance from the origin and theta is the angle from the positive x-axis.

Using this formula, we can convert the first point (r1, 1) to Cartesian coordinates (x1, y1) as x1 = r1 cos(1) and y1 = r1 sin(1). Similarly, we can convert the second point (r2, 2) to Cartesian coordinates (x2, y2) as x2 = r2 cos(2) and y2 = r2 sin(2).

Once we have the Cartesian coordinates of the two points, we can use the distance formula to find the distance between them. The distance formula is d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Substituting the Cartesian coordinates, we get the formula for the distance between the points with polar coordinates (r1, 1) and (r2, 2) as:

d = sqrt((r2 cos(2) - r1 cos(1))^2 + (r2 sin(2) - r1 sin(1))^2)

In conclusion, to find the distance between two points with polar coordinates (r1, 1) and (r2, 2), we need to convert the polar coordinates to Cartesian coordinates and then use the distance formula. The resulting formula involves trigonometric functions and the difference between the angles of the two points.

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The correct answers are:

Positive, because as the quantity of water within the pond increases, the quantity of habitat will increase. There is a strong terrible courting indicating that with a boom within the age of male adults, there may be an associated lower in the amount of hair on the top. Plot 1: r = 0.96, Plot 2: r = -0.87

In reading the relationship between the amount of water (X) in a fishpond and the quantity of habitat (Y), we'd anticipate the correlation between X and Y to be tremendous. This is because as the amount of water inside the pond will increase, it gives more sources and areas for the habitat to thrive, ensuing in an increase in the extent of habitat.

Regarding the correlational examination on person men with the variables of age (X) and amount of hair on the pinnacle (Y), a correlation coefficient of r = -0.80 indicates a robust poor courting.

This means that as the age of male adults will increase, there's a related decrease in the quantity of hair on the top. The poor correlation indicates that older males generally tend to have less hair on their heads as compared to younger men.

For the two plots furnished, the quality matches for the correlation coefficients are:

Plot 1: r = 0.96

Plot 2: r = -0.87

These correlation coefficients imply a strong effective courting in Plot 1 and a robust terrible courting in Plot 2, respectively.

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The correct question is:

"Suppose you are in studying the relationship between the amount of water (X) in a fish pond and the volume of habitat (Y). You would expect the correlation between X and Y to be because O, because we cannot determine without data. Positive, because as the amount of water in the pond increases the volume of habitat increases Positive, because as the amount of water in the pond increases the volume of habitat decreases. Positive, because as the amount of water in the pond increases the volume of habitat decreases. Negative, because as the amount of water in the pond increases the volume of habitat decreases. Suppose you conducted a correlational study on adult males with the variables of age (x) and amount of hair on the head (Y). Your study revealed a correlation coefficient r = -0.81. What will be your interpretation for this result? There is a strong positive relationship indicating with an increase in age of male adults there is an associated decrease in amount of hair on the head. There is a weak positive relationship indicating with an increase in age of male adults there is an associated increase in amount of hair on the head. There is a weak negative relationship indicating with an increase in age of male adults there is an associated decrease in amount of hair on the head. The relationship between age of male adults and the amount of hair on the head is curvilinear There is a strong negative relationship indicating with an increase in age of male adults there is an associated decrease in amount of hair on the head. Based on the two plots provided below, match the correlation coefficients that best describe the two plots. Plot 1 Plot 2 3 10 11 2 2 9 Plot 1 = -0.002, Plot 2 = -0.80 Plot 1 = 0.96, Plot 2 = -0.87 Plot 1 = 0.96. Plot 2 - 0.40"