A right triangle has legs 2m and 3m in length. What is the
length of its hypotenuse?

Answer:

10

Step-by-step explanation:

\(\\ \rm\longmapsto Speed=\dfrac{Distance}{Time}\)

\(\\ \rm\longmapsto Speed=\dfrac{800}{10}\)

\(\\ \rm\longmapsto Speed=80km/h\)

\(\\ \rm\longmapsto Distance=Speed(Time)\)

\(\\ \rm\longmapsto Distance=80(14)\)

\(\\ \rm\longmapsto Distance=1120km\)

Answer:

Parallel!!

Step-by-step explanation:

They're facing the same direction and are beside each other so its parallel!!

Answer:

B. Parallel

Step-by-step explanation:

Parallel Lines NEVER Touch

Answer:

\(8x+46\)

Step-by-step explanation:

Insert the original values of C and D into the new expression:

\(2(x+8)+3(2x+10)\)

Simplify the expression. Use the distributive property:

\(2(x)+2(8)+3(2x)+3(10)\\\\2x+16+6x+30\)

Combine like terms:

\((2x+6x)+(16+30)\\\\8x+46=2C+3D\)

:Done

Answer \(=7085760\)

Step-by-step explanation:

Use order of operations and evaluate the exponent first

\(30*4*3^{10}\)

\(30*4(59049)\)

\(30*236192\)

\(=7085760\)

Answer: 1920

Step-by-step explanation:

4x4x4=64

64x30=1920

CosA is negative for the largest angle in an obtuse triangle. Using the law of cosines, a²>b²+c², a>b, and a>c are derived.

Step 1: As the obtuse triangle has the largest angle A (more than 90 degrees), the cosine function's value is negative.

Step 2: By applying the Law of Cosines in the triangle, a²>b²+c², which is derived from a²=b²+c²-2bccosA, and hence a>b and a>c can be derived.

Step 3: From the previously derived inequality a²>b²+c², we can conclude that a>b and a>c as a²-b²>c². The value of a² is greater than both b² and c² when a>b and a>c.

Therefore, the largest angle of an obtuse triangle is opposite the longest side.

Step 4: In triangle ABC, A=103°, a=25, and c=30.

a² = b² + c² - 2bccos(A),

a² = b² + 900 - 900 cos(103),

a² = b² + 900 + 900 cos(77),

a² > b² + 900, so a > b.

Similarly, a² > c² + 900, so a > c.

Therefore, triangle ABC satisfies a>b and a>c.

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The equation will be 5d + 1 = 16 and the distance from Pablo's house to school will be d = 3 miles.

It is given that distance from Pablo's house to mall is 1 more than 5 times the distance from his house to his school.  Also ,  the distance from Pablo's house to the mall is 16 miles.

We have to find out an equation and distance d from Pablo's house to his school.

What will be the expression for 2 times of a number x added with 2 ?

The expression will be 2x+2.

Let's assume the distance from Pablo's house to his school is d miles.

The distance from Pablo's house to the mall will be ;

= 5d + 1

This distance will be equal to 16 miles as given in the question.

∴ The equation will be ;

    5d + 1 = 16

Now to find the distance from Pablo's house to his school, we have to solve this equation. The distance will be

   5 × d = 15

    or

   d = 3 miles

Thus, the equation will be 5d + 1 =16 and the distance from Pablo's house to school will be d = 3 miles.

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The main answer is: (1) 22x.

Among the given options, the expression that represents the total cost of x number of t-shirts for the team is (3) 22x + 150.

This expression takes into account the cost of each individual t-shirt, which is represented by 22x, and adds the additional fixed cost of 150 that is independent of the number of t-shirts purchased.

This is consistent with the notion that there is a base cost per t-shirt (22x) along with an additional fixed cost (150) for the entire order. Therefore, option (3) 22x + 150 correctly represents the total cost of x number of t-shirts for the team.

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If beta = 0.7500, then the power of the experiment is 0.2500.


Beta (β) is the probability of making a type II error, which is failing to reject a false null hypothesis. In other words, beta represents the likelihood of concluding that there is no difference between two groups when in fact there is a difference.

Power (1-β) is the probability of correctly rejecting a false null hypothesis. In other words, power represents the likelihood of detecting a difference between two groups when in fact there is a difference.

So if beta = 0.7500, then the probability of failing to reject a false null hypothesis is 0.7500. Therefore, the probability of correctly rejecting a false null hypothesis (power) is 1 - 0.7500 = 0.2500.

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Answer:

27.1

Step-by-step explanation:

Rounded values without the decimal places A. $4,578, B. $5,878, C. $5,072 and D. $6,372.

To change the values from decimal places to the nearest dollars, we need to round each value to the nearest whole number.

A. $4,577.57 rounds to $4,578

B. $5,877.87 rounds to $5,878

C. $5,072.00 remains unchanged since it is already in whole numbers.

D. $6,372.00 remains unchanged since it is already in whole numbers.

Rounding to the nearest dollar involves looking at the digit to the right of the decimal point. If the digit is 5 or greater, we round up. If the digit is less than 5, we round down. In the case of C and D, the decimal part is already .00, indicating a whole number, so there is no need for rounding.

The final answers, rounded to the nearest dollars, are:

A. $4,578

B. $5,878

C. $5,072

D. $6,372

These rounded values represent the amounts in dollars without the decimal places.

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A,C and D

Step-by-step explanation:

Option A,C and D are not polynomials.

Step-by-step explanation:

Polynomial functions are given by

             p(x) = a₀ + a₁x¹+ a₂x²+ ...........+aₙxⁿ

             Where a₀, a₁, a₂, ..., an are constant coefficients and n is non negative integer.

Option A

        Here one exponent of x is -2, so this is not a polynomial function.

Option B

        Here all the exponents are non negative integer, so this is a polynomial.

Option C

        Here one exponent of x is 0.5, so this is not a polynomial function.

Option D

      p(x)= x⁻²+x+1

        Here one exponent of x is -2, so this is not a polynomial function.

Option E

        Here all the exponents are non negative integer, so this is a polynomial.

Option A,C and D are not polynomials.

Answer:

A

D

Step-by-step explanation:

I believe those are correct however im not that good at this soooooo.

Good luck

The required probability is 0.4408.

The operating characteristics of the loading gate problem are:

L = λ/ (μ - λ)

W = 1/ (μ - λ)

Lq = λ^2 / μ (μ - λ)

Wq = λ / μ (μ - λ)

ρ = λ / μ

P0 = 1 - λ / μ

Where, L represents the average number of cars either being loaded or waiting.

W represents the average time a car spends either being loaded or waiting.

Lq represents the average number of cars waiting.

Wq represents the average waiting time of a car.

ρ represents the utilization factor.

ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.

P0 represents the probability that the system is empty.

The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,

P (n > 6) = 1 - P (n ≤ 6)

Now, the probability of having less than or equal to six cars in the system at a given time,

P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]

Putting the values of λ and μ, we get,

P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]

P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592

Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408

Therefore, the required probability is 0.4408.

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The best conclusion based on a large F-test statistic and a small p-value in a test of analysis of variance is A.

There is sufficient evidence to support the claim that the samples are from populations having means that are not all the same.

In hypothesis testing using analysis of variance (ANOVA), the F-test statistic is used to compare the variances between groups to the variances within groups.

A large F-test statistic indicates that the variances between groups are significantly greater than the variances within groups. A small p-value indicates strong evidence against the null hypothesis, which assumes that the means of all populations are equal.

In this scenario, if the F-test statistic is large and the p-value is small, it implies that the observed difference between the group means is unlikely to have occurred by chance alone.

Therefore, we reject the null hypothesis of equal means and conclude that there is sufficient evidence to support the claim that the samples are from populations having means that are not all the same. This aligns with option A.

Option B states that there is not sufficient evidence to reject the claim that the samples are from populations having means that are all equal, which contradicts the information given.

Option C suggests that the means are all different, which goes beyond what the F-test and p-value can conclude. Option D states that the means are all equal, which is the null hypothesis that we reject in this case.

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Large=40 pounds

small=30 pounds

and this is the solution

Answer:

28 units

Step-by-step explanation:

Since the perimeter of both triangles is same,

the sum of all sides of first triangle = sum of all sides of second triangle

or, 6x + 3 + 2x + 4x = 5x + 5x + 3x + 2

or, 12x + 4 = 13x + 2

or, 4-2 = 13x - 12x

or, 2 = x

Now,

Putting the value of x in the perimeter of first triangle,

12x + 4= 12* 2+ 4

= 28 units

T(t) = 1 / 100√13 is the value in space curve.

Given, the space curve r(t) = (16sin(t))i + (16cos(t))j + 12tk.

We need to find T(t), N(t), and κ(t).

To find the T(t), we need to find the first derivative of the given space curve r(t).

Differentiate the given space curve r(t) partially with respect to t, we get, r'(t) = 16cos(t)i - 16sin(t)j + 12kT(t) is the unit tangent vector, which is given by:T(t) = r'(t) / ||r'(t)||

Therefore, T(t) = (16cos(t)i - 16sin(t)j + 12k) / √(16²sin²(t) + 16²cos²(t) + 12²)T(t)

           = (16cos(t)i - 16sin(t)j + 12k) / 20

            = 4/5cos(t)i - 4/5sin(t)j + 3/5k

To find the N(t), we need to find the second derivative of the given space curve r(t).

Differentiate the T(t) partially with respect to t, we get, T'(t) = -16sin(t)i - 16cos(t)jN(t) is the unit normal vector, which is given by: N(t) = T'(t) / ||T'(t)||

Therefore, N(t) = (-16sin(t)i - 16cos(t)j) / √(16²sin²(t) + 16²cos²(t))N(t)

                        = -sin(t)i - cos(t)j

To find the κ(t), we need to find the derivative of the T(t) and the N(t).

Differentiate the T(t) partially with respect to t, we get, T'(t) = -4/5sin(t)i - 4/5cos(t)j

Differentiate the N(t) partially with respect to t, we get, N'(t) = -cos(t)i + sin(t)jκ(t) is the curvature of the space curve, which is given by:

                        κ(t) = ||T'(t)|| / ||r'(t)||³

Therefore, κ(t) = 4/5 / 20³/2 = 1 / 100√13

Therefore, T(t) = 4/5cos(t)i - 4/5sin(t)j + 3/5kN(t) = -sin(t)i - cos(t)jκ(t) = 1 / 100√13

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The sinusiodal function created from 2 given points is y = 3 sin (πx + 90) + 3

From the case, we have:

Minimum point = (-3,0)

Maximum point = (-9,6)

The sinusoidal fuction would be in the form of:

y = A sin (Bx - C) + D

where:

A = amplitudo

B = 2π / Period

C = Phase shift

D = Midline

First, we need to find the amplitudo:

A = (Y max - Y min) / 2

A = (6 - 0) / 2

A = 3

Periode = (X max - X min) x 2

Periode = (-9 - (-3) x 2

Periode = -6

B = 2π / Periode

B = 2π / 6

B = 1/3 π

D = (Y max + Y min) / 2

D = (6 + 0) / 2

D = 3

We can use one point to find the value of C:

0 = 3 sin (π/3 (-3) - C) + 3

0 = 3 sin (π - C) + 3

-3 = 3 sin (π - C)

sin (π - C) = -1

(π - C) = 270

C = -1/2 π

C = - 90

Then the sinusiodal function would be:

y = 3 sin (πx + 90) + 3

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Answer:

4.2 units^3

Step-by-step explanation:

Volume of a cone 1/3(nr^2h)

n = 22/7

r = radius  

h = height

1/3 x (22/7) x (2^2) = 4.2

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

Answer:

5:6 lol

Step-by-step explanation:

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

125y

Step-by-step explanation:

5x5x5. Because cubed means to multiply the same number 3 times

Answer:

72 cm

Step-by-step explanation:

200+16=216

216/3=72 cm

A set of simultaneous equations is often known as a system of equations or an equation system. The solution of the system of equations is (1.791,11.374) and (-2.791, -2.374).

A set of simultaneous equations, often known as a system of equations or an equation system, is a finite collection of equations for which common solutions are sought.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

The solution of the two of the given function will be when the graph of the two the function will intersect with each other.

Using the graph the solutions are (1.791,11.374) and (-2.791, -2.374).

Hence, the solution of the system of equations is (1.791,11.374) and (-2.791, -2.374).

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Answer:

GCF, Greatest Common Factor

Step-by-step explanation:

Hope this helped

Answer:

c!!

Step-by-step explanation:

nswer

First image

Angle ABC covers around the inside and outside of the circle.

Second image

Angle x l

hird image

Angle DBE l

ngle of arc DE l

ngle of arc AC l

ourth angle

ll the angles at U lie inside the circle.

ngle 78° l

ngle 114° l

ope this Helps!!!

Answer:

A:$4.50 x ? =$36. $36 divided by$4.50=?

B)8 divide it

C)replace the ? With x and then solve it algebraically and it would still equal to the number 8

Step-by-step explanation:

Yes, there exist surjective linear maps from R2 (two-dimensional real space) to R3 (three-dimensional real space). An example of such a map is provided by extending the dimensions of the input vector.

A linear map is defined as surjective if it covers the entire target space.

In this case, we are considering linear maps from R2 to R3, which means we need to find a transformation that maps every vector in R2 to a unique vector in R3.

To construct a surjective linear map, we can extend the dimensions of the input vector in order to match the dimensions of the output vector.

One possible example is the map L: R2 → R3 defined by L(x, y) = (x, y, 0), where (x, y) is a vector in R2 and (x, y, 0) is the corresponding vector in R3.

This linear map takes a two-dimensional vector and adds a zero in the third component, effectively embedding R2 within R3 as a plane parallel to the xy-plane.

Since every point in R3 can be reached by extending a point in R2, this map covers the entire target space and is therefore surjective.

In conclusion, there exist surjective linear maps from R2 to R3, and an example is given by extending the dimensions of the input vector.

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The reciprocal of \(A^m\)  is \(1/A^m.\)

This means that\(A^{-m\) is equivalent to\(1/A^m.\)

The correct answer is\((a) 1/a^m.\)

To understand why, let's break down the expression \(A^{-m}.\)

In mathematics, a negative exponent indicates the reciprocal or inverse of the base raised to the positive exponent.

In this case, \(A^{-m\) can be rewritten as \(1/A^m.\)

The reciprocal of a number is obtained by flipping the fraction or raising it to the power of -1.

So,\(1/A^m\) means the reciprocal of\(A^m.\)

To further simplify, we can rewrite \(A^m\) as \((A^m)^1,\) using the property of raising a power to another power.

Now, by applying the power of a product rule, we have \(A^{(m \times 1)},\) which simplifies to\(A^m\).

Therefore, the reciprocal of \(A^m\) is \(1/A^m\).

This means that \(A^{-m }\) is equivalent to \(1/A^m.\)

The correct answer is (a) \(1/a^m.\)

In summary, the correct answer is (a)\(1/a^m\)for \(A^{-m}.\)  

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