La edad de Alejandro equivale a las dos quintas partes de la edad de Andrea. Si la suma de
sus edades es 56, ¿qué edad tiene cada uno?

Jeff's golf score was 1 stroke under par.

Let's first find out what was Mike's golf score.

We know that Mike's score was 2 strokes more than Sam's score, so if Sam's score was 2 over par, then Mike's score must have been:

2 + 2 = 4 over par

We also know that Jeff's score was 5 strokes less than Mike's score. Therefore, Jeff's score relative to par would be:

4 + (-5) = -1 over par

So Jeff's golf score was 1 stroke under par.

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

Step-by-step explanation:

y=10

Leo is approximately 13.928 km away from the starting point.

Given that Leo walked 7 km south and then 12 km east, we need to determine the distance from the starting point,

To determine the distance from the starting point, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the distance Leo walked south forms one side of a right triangle, and the distance he walked east forms the other side. The distance from the starting point will be the length of the hypotenuse.

Using the Pythagorean theorem, we can calculate the distance from the starting point as follows:

Distance² = (7 km)² + (12 km)²

Distance² = 49 km² + 144 km²

Distance² = 193 km²

Taking the square root of both sides gives us:

Distance = √(193)

Distance ≈ 13.928 km

Therefore, Leo is approximately 13.928 km away from the starting point.

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Complete question =

Leo walk 7km south then 12km east. How far is he from the starting point?

Answer:

A =576 pi in ^2

Step-by-step explanation:

Circumference  is given by

C = 2 * pi *r

48 pi = 2 * pi *r

divide by 2 pi

48 pi /2 pi = 2 * pi * r / 2 pi

24 = r

We can find the area by

A = pi r^2

A = pi (24)^2

A =576 pi in ^2

Answer:

576π in^2

Step-by-step explanation:

Circumference of circle (C) = 2πr = 48π in

2πr = 48 π

r = 48π/2π = 24 in

Area of circle (A) = πr^2

r (radius of circle) = 24 in

A = π(24 in)^2 = 576π in^2

Answer:

8.9 is larger

Step-by-step explanation:

7/8 is 0.875 in decimal form

8/9 is 0.88 or 0.89 if you round up.

7/8 < 8/9

Hope this helps! Please have a great day :)

When 100 simulation trials are run each with a sample size of 50 and a point estimate of 0.18, observing a minimum sample proportion of 0.28 and maximum sample proportion of 0.40, the margin of error of the population proportion using an estimate of the standard deviation is ±0.04.

Therefore the answer is ±0.04

Margin of error of the population proportion using an estimate of the standard deviation is calculated by the formula

ME = 2 × (max - min)/ 6

We know that the sample proportion, p is 0.18.Also we know minimum sample proportion observed is 0.28 and maximum sample proportion observed is 0.40. Therefore margin of error is

ME = 2 × (0.40 - 0.28)/ 6

ME = (0.12)/ 3

ME= 0.04

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The standard parameterization for the tangent line :

x = 12t + 18 , y = 3t + 13 , z = 54t + 54

parametric equation, a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

as given,

r(t) = (2t^2) i + (3t + 4) j + (2t^3) k, t = t₀ = 3

so, \(x = 2t^{2}, y = 3t + 4 , z = 2t^{3}\)

\(\frac{dx}{dt} = 4t, y=3, z=6t^{2}\)

r'(t) = <4t, 3, \(6t^{2}\)>

and at t =3,

r'(t=3) = <12, 3, 54>

we have to find the tangent line to the curve at t=3,

x = 18, y = 13, z = 54

for t=3, (x, y, z) = (18, 13, 54)

finally,

x = 12t + 18

y = 3t + 13

z = 54t + 54

Thus, the standard parameterization for the tangent line :

x = 12t + 18 , y = 3t + 13 , z = 54t + 54

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The standard parameterization for the line tangent to the curve is

x=12t+18 , y=3t+9 , z=54t+54  

In parameterization the variables are independent variables , whereas continuous functions are dependent variables , that is it is dependent on another functions. The given curve is r(t)=(2t^2)i+(3t+4)j+(2t^3)k and given t=t0=3

Given , r(t)=(2t^2)i+(3t+4)j+(2t^3)k

r'(t)=(4t)i+3j+(6t^2)k

and also given t=t0=3

r(t=t0=3) => (18 , 9 , 54)

r'(t=t0=3) => (12 , 3 , 54)

The standard parameterization for the tangent line can be given by using r(t) and r'(t) . so by that we came to know the required standard parameterization.

x=12t+18

y=3t+9

z=54t+54

Therefore, the about mentioned x, y, z are the standard parameterization for the tangent line of given curve.

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1)

\(\sf {x}^{2} - 4 \\ \sf \: Use \: the \: sum \: product \: method\)

\(\sf {x}^{2} - 4 \\ = \sf{x}^{2} + 2x - 2x - 4\)

\(\sf \: Now \: take \: the \: common \: factor \: out \\ \sf{x}^{2} + 2x - 2x - 4 \\\sf = x(x + 2) - 2(x + 2)\)

\(\sf \: Factorize \: it \\ \sf \: x(x + 2) - 2(x + 2) \\ = \sf(x - 2)(x + 2)\)

Answer ⟶ \(\boxed{\bf{(x-2)(x+2)}}\)

_________________________

2)

\(\sf {x}^{3} - 27\)

\(\sf {x}^{3} \: and \: 27 \: ( {3}^{3} ) \: are \: perfect \: real \: cubes.\)

\(\sf \: So \: use \: the \: algebraic \: identity \: \\ \sf {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )\)

\(\sf \: a = \sqrt[3]{x^{3}} = x \\ \sf \: b = \sqrt[3]{27} = 3\)

\( \sf \: {x}^{3} - {3}^{3} \\ \sf= (x - 3)( {x}^{2} + 3x + {3}^{2} ) \\ = \sf \: (x - 3)( {x}^{2} + 3x + 9)\)

Answer ⟶ \(\boxed{\bf{(x-3)(x^{2}+3x+9)}}\)

Answer:

4y2 - 12y

Step-by-step explanation:

2+4y-16y+32(Combine like-terms)

2−12y+32(Combine like-terms)

Answer:

The answer is \(4y^{2} -12y\)

Step-by-step explanation:

To simplify the polynomial, start by combining like terms. Add \(y^{2}\) and \(3y^{2}\) to get \(4y^{2}\). Then, subtract \(16y\) from \(4y\) to get \(-12y\). Finally, the simplified answer is \(4y^{2} -12y\).

Answer:

0.267

Step-by-step explanation:

4/15 as a decimal is 0.26 repeating so rounded to the nearest thousandth would be 0.267

Answer:

B.  Graph of a one-to-one function.

Step-by-step explanation:

A one-to-one function will have a unique value, y, for each different value of x.  The graph displayed will have values very, very close to each other as x approaches ±4, but they won't be the same even at higher values of x.

The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)

f(x) = x^2 -2x +3 and f(x) = -2x + 12

which means

x^2 -2x +3  = -2x + 12

x^2 -2x +3  + 2x - 12 = 0

x^2 -9 = 0

by factorizing we have

(x-3)(x+3) = 0

x = 3 or -3

when x = 3

f(x) = -2x + 12

f(3) = -2(3) + 12 which is 6

when x = -3

f(-3) = -2(-3) + 12 which is 18

ordered pairs are (3, 6) and (-3, 18)

In conclusion, (3, 6) and (-3, 18) are the ordered pairs

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y = mx + b

y = y coordinate

m = slope

x = x coordinate

b = y intercept

Answer:

it's A & B

Step-by-step explanation:

got it right

Answer:

m<CPD = \(129.75^{o}\)

Step-by-step explanation:

From the given diagram,

m<APD ≅ m<BPC (vertically opposite angles)

m<APB ≅ m<CPD (vertically opposite angles)

But,

m<APD = (x + 1)

m<APB = (3x - 18)

In the given circle,

m<APD + m<BPC + m<APB + m<CPD = 360

(x + 1) + (x + 1) + (3x - 18) + (3x - 18) = 360

2(x + 1) + 2(3x - 18) = 360

2x + 2 + 6x - 36 = 360

8x - 34 = 360

8x = 360 + 34

8x = 394

x = 49.25

Thus,

m<CPD = (3x - 18)

            = (3(49.255) - 18)

            = 147.75 - 18

            = \(129.75^{o}\)

m<CPD = \(129.75^{o}\)

The percentage off of the coupon is 25%

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

Normal price = $24

Amount saved = $6

The above parameters mean that

Percentage of the coupon = Amount saved/Normal price

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

Percentage of the coupon = 6/24

Evaluate

Percentage of the coupon = 25%

Hence, the percentage is 25%

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Answer:

2h 30min

Step-by-step explanation:

130km ÷ 52km/h = 2.5h

                            = 2h 30min

Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{The\ slope\ of\ a\ line\ passing\ through\ the\ points\ (x_1,y_1)\ and\ (y_2,y_1)\ is\ given\ by:}\\\mathrm{Slope(m)=\frac{y_2-y_1}{x_2-x_1}}\\\\\mathrm{According\ to\ the\ question,}\\\mathrm{(x_1,y_1)=(0,-2)}\\\mathrm{(x_2,y_2)=(-2,-8)}\)

\(\mathrm{Therefore\ the\ slope=\frac{-8-(-2)}{-2-0}=\frac{-8+2}{-2}=3}\)

Answer:

2.5 60÷24=2.5 so there is ur answer hope it helps

Answer:

2nd graph

Step-by-step explanation:

Plz mark brainliest

Answer:

Its the second option

Step-by-step explanation:

i just did it

Main Answer: A normalized binary number typically consists of three parts:

Supporting Question and Answer:

What is a sign bit in a normalized binary number?

The sign bit is the leftmost bit of a normalized binary number and indicates whether the number is positive or negative .A value of 0 indicates a positive number, while a value of 1 indicates a negative number.

Body of the Solution: A normalized binary number typically consists of  the following three parts:

Final Answer: A normalized binary number typically consists of three parts:

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(a). The speed of the shock wave can be determined by setting [u]s = 0.

(b). The initial value problem u(0,x)={a,b,​x<0,x>0 has been solved.

(a) To determine the Rankine-Hugoniot condition for the speed of a shock, we consider the conservation of mass across the shock wave.

The given equation is:

ut + u^2ux = 0

The Rankine-Hugoniot condition for the conservation of mass is: [u]s = 0

where [u]s represents the jump in fluid velocity across the shock wave.

In this case, the equation is already in conservative form, so we can directly apply the Rankine-Hugoniot condition. Therefore, the speed of the shock wave can be determined by setting [u]s = 0.

(b) Now let's solve the initial value problem u(0, x) = {a, b} for two cases:

(i) |a| > |b|:

In this case, we have a shock wave. The solution will consist of a shock wave moving to the right with velocity s.

(ii) |a| < |b|:

In this case, we have a rarefaction wave. To determine the shape of the rarefaction wave, we can use Exercise 2.3.15, which involves solving the characteristic equations for the given PDE.

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There are five choices for the first digit, five choices for the second digit, and so on. The total number of 5-digit numbers with repetition is given by the formula: 5 * 5 * 5 * 5 * 5 = 3125. The total number of 5-digit numbers that can be formed using the digits 2, 3, 4, 5, and 6 with repetition is 3125.

The number of ways of choosing r items from n is given by the formula:nCr = n! / r! * (n-r)!

In order to calculate the number of 5-digit numbers that can be formed using the digits 2, 3, 4, 5, and 6 without repetition, we have to use the permutation formula: P(n,r) = n! / (n-r)!

Without Repetition: There are five choices for the first digit and after a digit has been chosen, there are only four remaining digits to choose from.

Therefore, we have five choices for the first digit and four choices for the second digit and so on.

So, the number of 5-digit numbers that can be formed using the digits 2, 3, 4, 5, and 6 without repetition can be calculated as follows: Total number of 5-digit numbers without repetition = 5 * 4 * 3 * 2 * 1= 120.

Therefore, the total number of 5-digit numbers that can be formed using the digits 2, 3, 4, 5, and 6 without repetition is 120.

With Repetition: In the case of repetition, we have five choices for each digit.

Thus, there are five choices for the first digit, five choices for the second digit, and so on.

Therefore, the total number of 5-digit numbers with repetition is given by the formula:5 * 5 * 5 * 5 * 5 = 3125.

Therefore, the total number of 5-digit numbers that can be formed using the digits 2, 3, 4, 5, and 6 with repetition is 3125.

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Answer:

-12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

3 - 7x + 2x

x = 3

Step 2: Evaluate

Answer:

if x is 3 then

3-7(3)+2(3)

-18+6

-12 done

The hypothesis test statement below is a Type I Error Failing to reject the claim that community college students pay at least $1,250 per year on textbooks when the actual amount that community college students pay for textbooks is actually less than $1,250 per year. Option C is the correct answer.

A Type I Error occurs when the null hypothesis is wrongly rejected, leading to the conclusion that there is a significant effect or difference when, in reality, there is no such effect or difference.

In this case, option c represents a Type I Error because it falsely fails to reject the claim of paying at least $1,250 per year on textbooks when the actual amount is less than $1,250.

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Answer:

x=-2.5(ERROR)

Step-by-step explanation:

An isosceles triangle is a triangle with two sides of equal length, called legs. The third side of the triangle is called the base. The vertex angle is the angle between the legs 1.

Since triangle ABC is an isosceles triangle with vertex angle B, we know that AB = AC.

Therefore, we can set up an equation:

20x - 2 = 25x

Solving for x:

20x - 25x = 2

-5x = 2

x = -2/5

Since x cannot be negative, there must be an error in the problem statement.

I hope this helps!

The slope of the tangent line, m, is the derivative of the function evaluated at x = 1.

Differentiation of the function y = ex + 8 + 9:

To differentiate the given function, we take the derivative of the terms separately. The derivative of e raised to x is e raised to x itself because e raised to x is its own derivative.

The derivative of 8 is 0 because a constant term has a derivative of 0.The derivative of 9 is also 0 because a constant term has a derivative of 0.

Therefore, the derivative of the given function y = ex + 8 + 9 is:y' = ex

Equation of the tangent line to the curve y = x4 + 7x2 − x at the point (1, 7):

To find the equation of the tangent line to the given curve at the point (1, 7), we find the derivative of the function first and then plug in the values of x and y.

The derivative of the given function is:

y' = 4x3 + 14x - 1

At x = 1, y = 1⁴ + 7(1²) - 1

               = 7

The slope of the tangent line, m, is the derivative of the function evaluated at x = 1.

So, m = 4(1)³ + 14(1) - 1

         = 17

The equation of the tangent line at the point (1, 7) is:

y - 7 = 17(x - 1)y

       = 17x - 10

Equation of the tangent line to the curve y = 7x − 6x​ at the point (1, 1):

To find the equation of the tangent line to the given curve at the point (1, 1), we find the derivative of the function first and then plug in the values of x and y.

The derivative of the given function is:

y' = 7 - 6x⁻²At x = 1,

y = 7(1) - 6(1⁻¹)

  = 1

The slope of the tangent line, m, is the derivative of the function evaluated at x = 1. So,

m = 7 - 6(1⁻²) = 1

The equation of the tangent line at the point (1, 1) is:

y - 1 = 1(x - 1)

y = x

Illustration of the curve and tangent lines:

The following graph shows the curve and tangent lines of the given functions.

The green line is the tangent line to the curve y = x⁴ + 7x² − x at the point (1, 7).

The blue line is the tangent line to the curve y = 7x − 6/x at the point (1, 1).

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The followings A, C, D, and F subsets of P₂ are subspace of P₂.

The subsets of P₂ that are subspace of P₂ are A, C, D, and F.

A.{p(t) | p'(t)+1p(t)+6=0} is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

B.{p(t) | p('t)='p(t) for all t} is not a subspace of P₂ because the derivative of p(0) does not equal p(4).

C. {p(t) | p(4)=7} is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

\({p(t) | \int_{-1}^{7}p(t)dt=0\) is constant } is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

E. {p(t) | '(8) = p(0)} is not a subspace of P₂ because the derivative of p(8) does not equal 0.

F. {p(t) | p(3)=0} for all t} is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

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Given:

△BCD≅△GEF , BC=10 , CD=3x+8 , EF=4x+6.

To find:

The measure of CD .

Solution:

We have,

\(\Delta BCD\cong \Delta GEF\)

Now,

\(CD=EF\)             (By CPCT)

\(3x+8=4x+6\)

Isolate variable terms.

\(8-6=4x-3x\)

\(2=x\)

So, put x=2 in\(CD=3x+8\).

\(CD=3(2)+8\)

\(CD=6+8\)

\(CD=14\)

Therefore, the measure of CD  is 14 units.