Which expression is the answer

The vectors v = 6i - 3j and w = i + 2j are orthogonal.

To determine if the vectors v and w are orthogonal, we need to find their dot product. If the dot product is 0, the vectors are orthogonal.

Here are the steps to find the dot product of v = 6i - 3j and w = i + 2j,

1. Identify the components of the vectors: v = (6, -3) and w = (1, 2)

2. Multiply the corresponding components of the vectors:

\((6 \times 1) + (-3 \times 2) = 6 - 6 \)

3. Add the products: 6 - 6 = 0 Since the dot product is 0, the vectors v = 6i - 3j and w = i + 2j are orthogonal.

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Correct question is " Are these vectors orthogonal? v = 6i - 3j and w = i+2j"

The given statement that a trinomial is always a higher degree than a monomial is false because greater number of terms does not means higher degree.

A monomial is an algebraic expression with only one term. Or we can say that the representation of a single concept is a monomial.

An example of an unary expression is: 12

A trinomial is an algebraic expression containing three terms. An example of a ternary is: x + y + 7

A trinomial is always of higher degree than a monomial is false statement .

A counterexample can be used to explain why this is wrong. Suppose we have a monomial, 8⁵ and then a trinomial x² + 2x + 3 . This is just a random example. This monomial has a higher degree because 5 is greater than 2. So basically it doesn't matter what the monomial is, if the degree is higher it is just a term than the maximum degree of the trinomial. Just because this has three terms does not mean that the highest degree term is greater than his one term in the monomial.

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Answer: 1200 percent increase

Step-by-step explanation:

Increase = New Number - Original Number

divide the increase by the original number and times 100

3.25-0.25=3

3/0.25=12*100

1200 percent

The equation of the line is y = √2x - 2. And the coordinate of point A will be (√2, 0).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = 1 - 2 / x²

The x-intercept is given as,

y = 0

1 - 2 / x² = 0

x² = 2

x = √2

The equation of the line that passes through points A (√2, 0) and B (0, -2) will be given as,

(y + 2) = [(0 + 2) / (√2 - 0)](x - 0)

y = √2x - 2

The equation of the line is y = √2x - 2. And the coordinate of point A will be (√2, 0).

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Answer:

  you have to read at least 5 books per month (on average)

Step-by-step explanation:

The given inequality is incorrect. "At least 75" means "greater than or equal to 75", so the inequality should be ...

  15x ≥ 75

  x ≥ 5 . . . . . . divide by 15

You have to read at least 5 books per month.

The value of set of side lengths can be used to construct a triangle are,

⇒ 3, 5, 7

We have to given that;

To find the set of side lengths can be used to construct a triangle.

Now, We know that;

The sum of two side of a triangle is always greater than third side.

Hence, We can check all options as;

⇒ 3, 4, 9

Since, 3 + 4 = 7 < 9

Hence, It does not form a triangle.

⇒ 3, 5, 7

Since, 3 + 5 = 8 > 7

Hence, It form a triangle.

⇒ 3,5, 8

Since, 3 + 5 = 8 = 8

Hence, It does not form a triangle.

⇒ 2, 6, 8

Since, 2 + 6 = 8 = 8

Hence, It does not form a triangle.

Thus, The value of set of side lengths can be used to construct a triangle are,

⇒ 3, 5, 7

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There exists a number x (specifically, the cube root of a non-perfect cube rational number) such that x³ is irrational and x⁵ is rational.

To justify the statement "there is a number x such that x³ is irrational and x⁵ is rational," we can use the fact that the product of a rational number and an irrational number is always irrational.

Let's assume that x is a rational number. Then, since any rational number raised to an odd power will remain rational, x³ and x⁵ would both be rational numbers. This would contradict our statement that x³ is irrational.

Therefore, x must be an irrational number. Now, let's consider the product x³ × x² = x⁵. Since x³ is irrational and x² is rational (since any real number raised to the power of 2 is always non-negative and therefore rational), the product x⁵ must be irrational.

However, we are looking for a number x such that x³ is irrational AND x⁵ is rational. To satisfy this, we can take x to be the cube root of a rational number that is NOT a perfect cube (i.e. not the cube of any rational number). This way, x³ will be irrational since it is the cube root of a non-perfect cube rational number.

Then, x⁵ = (x³) × (x²) will be rational since x³ is irrational and x² is rational.

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Answer:

8

Step-by-step explanation:

Divide 30 by 3.75 to get 8.

Hope that this helps!

Answer:

Step-by-step explanation:

The Discussion to all points are shown below:

In order to gather information about a service, product, or process, a survey is described as the act of looking at a process or questioning a predetermined sample of people. Surveys used to gather data ask a specific set of people about their beliefs, actions, or knowledge.

Given:

a) No, there isn't a control group in this trial. This is evident from the fact that all of the gasoline tyres are being evaluated in all of the different automobile types; no specific group is under supervision.

b )In order to randomly assign Groups 1, 2, and 3 to each of the three feel kinds, the researcher should utilise a computer generator to run through the 90 generators.

c) Miles driven should be used as a criterion for blocking rather than vehicle type because the latter could have an impact on fuel economy.

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Answer:

1. 142°

2. 137°

3. 140°

Step-by-step explanation:

First we have to assume that each of the statements 1, 2 and 3 are independent of each other, otherwise the results will be inconsistent

Since m and n are parallel to each other and t is a straight line

1. ∠3 =∠7 = 142°

2. ∠1 + ∠2 = 180° ;  ∠2 = 180°-∠1 = 180° - 43° = 137°

3. ∠7 = ∠6 =140°

Answer:

you have to answer the question and then solve the question

The solution indicates that the car accelerates to 24 m/s, or 5 m/s, after 4 seconds.

The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case. Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating.

The rate at which an object's velocity varies with respect to time is known as acceleration in physics. Newton's Second Law states that an object's acceleration is the combined effect of all forces acting on it. The metre per second squared (m s2) unit of acceleration in the SI is used.

Acceleration  = \(\frac{(Final velocity) - (initial velocity)}{time}\)

Acceleration = (20 - 0) / 4

                      = 5m/s

According to the solving  the car's acceleration  = 5m/s.

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Sample size n= 601 (rounded up) needed for 90% confidence, 4% margin of error, assuming p=0.5.

To conclude the model size expected to measure a general population degree with a security cradle at 90% conviction, we can use the condition:

n = \((z^2 * p * q)/E^2\)

Where:

n is the model size

z is the z-score

p is the surveyed people degree

q is 1-p

E is the ideal wellbeing cradle

we can expect a protected estimate for p of 0.5, which grows the model size.

Expecting a security cushion of 4%, we have:

n = \((1.645^2 * 0.5 * 0.5)/0.04^2\)

n ≈ 600.25

We need a model size of something like 601 to get a space for compromise of 4% at 90% sureness, assembling to the accompanying whole number.

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Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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Answer:

Surface area of a cone = 461.58 In²

Step-by-step explanation:

Surface area of a cone = πrl + or

Surface area of a cone = πr(r+l)

Where r = radius

Radius= diameter/2

Radius=14/2

Radius= 7 inch

And l slant height= 14 inch

Surface area of a cone = πr(r+l)

Surface area of a cone = π*7(7+14)

Surface area of a cone = 7π(21)

Surface area of a cone = 147π

Surface area of a cone = 461.58 In²

The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

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Both M and S in sexagesimal notation = 3600D.

Here converting 'D' into minutes.

We know that a degree is made up of 60 minutes.

so multiply D with 60 we get

⇒ D x 60 = M

Now convert 'M' into seconds.

Again, there are 60 seconds in a minute,

so multiply M with 60 we get,

⇒ M x 60 = S

Simplify this equation by substituting D x 60 for M,

⇒D x 60 x 60 = S

Simplifying further, we get,

⇒ 3600D = S

Hence, 3600D is equal to both M and S in sexagesimal notation.

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Answer:

I mean, I think it varies by house and by location but a general range would be:

Min: 64 *F

Max: 74 *F

The probability of the ball landing on a red slot on the next spin is still 18/38 or approximately 0.4737 or 47.37%.

The probability of the ball landing on a red slot on a single spin of a standard roulette wheel is 18/38 or approximately 0.4737 or 47.37%. This is because there are 18 red slots out of a total of 38 slots on the wheel.

The outcome of the previous 210 spins has no effect on the probability of the ball landing on a red slot on the next spin. Each spin is an independent event, and the probability of the ball landing on a red slot remains the same for each spin.

Therefore, even though the ball has landed on a red slot for the past 210 spins, the probability of it landing on a red slot on the next spin is still 18/38 or approximately 0.4737 or 47.37%.

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The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ .

In the question it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ.

In the question, it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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The function values are 4, 6, 8, 10, 12, and 14. The appropriate domain for this function is {1, 2, 3, 4, 5, 6} since these are the only values that can be rolled on a six sided die.

The function f(x) = 2x + 2 assigns a certain number of points to a player based on the value rolled on a six sided die.

The domain of a function is the set of all possible values of the input variable that the function can accept. In this case, the input variable is the value rolled on the die, which can be any integer between 1 and 6, inclusive. Therefore, the domain of the function f(x) is {1, 2, 3, 4, 5, 6}.

To find the function values for a given input, substitute the input into the function and solve for the output.

Thus, the function values for the domain {1, 2, 3, 4, 5, 6} are:

f(1) = 2(1) + 2 = 2 + 2 = 4

f(2) = 2(2) + 2 = 4 + 2 = 6

f(3) = 2(3) + 2 = 6 + 2 = 8

f(4) = 2(4) + 2 = 8 + 2 = 10

f(5) = 2(5) + 2 = 10 + 2 = 12

f(6) = 2(6) + 2 = 12 + 2 = 14

Therefore, the function f(x) = 2x + 2 assigns the following number of points to a player based on the value rolled on a six sided die:

Value rolled on die Points awarded

1                                          4

2                                        6

3                                        8

4                                       10

5                                      12

6                                      14

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Answer:

(a+b)²-2ab

Step-by-step explanation:

First we need to factorize (a+b)²

(a+b)² = a² + 2ab + b²

(a+b)² = a²+b²+2ab

Subtract 2ab from both sides

(a+b)² - 2ab = a²+b²+2ab - 2ab

(a+b)²-2ab = a²+b²

Swap;

a²+b² = (a+b)²-2ab

Hence the expression of a² + b² is  (a+b)²-2ab

Answer:

200%

Step-by-step explanation:

The quadrilateral in the picture is a square since all four sides are equal.

The angles are all equal and all are right angles.

Clearly, the quadrilateral is a square.

Answer:

q= -3.25 and p= -6.25

Step-by-step explanation:

p=5q+10. p=q-3

p-5q=10. p-q=-3 subtract the two equations

-4q=13 q= -3.25 and p= -6.25

Answer:

x ≤ 12

Step-by-step explanation:

The problem can be represented by the equation:

25 - x = y and y ≥ 13

So, we find that 25 - 12 = 13, which means that any number greater than 12 would result in a difference lower than 13. This sets 12 as the maximum.

The normal distribution curve gives useful information regarding the distribution of students' grades, such as the average grade, the dispersion of grades, the likelihood of receiving a specific grade, and the presence of any outliers.

The normal distribution curve generated by the educator offers multiple insights into the distribution of academic achievement among her pupils. The analysis of the curve yields various informative data such as:

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Answer:

10√3

Step-by-step explanation:

Square the first number

100*3 is 300

100 is square root of 10