Please help me!!!!!!!

Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes.

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Answer:

Theoretical probability is what is expected to happen, where as experimental probability is what happens when you test out that theory. There is a very unlikely chance that a concept in theory would be the same as a concept in action, therefore explaining why these answers are not alike.

Step-by-step explanation:

Hope this helps take off some stress from school, have a great day :))

The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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Given that a polynomial function \(f(x)\) has,

And we need to find \(f(x)\)

as we know that if a polynomial has zeroes as \(\alpha\) , \(\beta\) and \(\gamma\) , then the cubic polynomial is given by,

\(\longrightarrow f(x)=k (x-\alpha)(x-\beta)(x-\gamma)\\ \)

where ,

Now substitute the given zeroes, as ;

\(\longrightarrow f(x)=2[ (x-2)(x-\sqrt3)(x+\sqrt3)]\\ \)

\(\longrightarrow f(x)= 2[(x-2)\{ x^2-(\sqrt3)^2\}]\)

\(\\\longrightarrow f(x)= 2[ (x-2)(x^2-3)]\\ \)

\(\longrightarrow f(x)=2[ x(x^2-3)-2(x^2-3)]\\ \)

\(\longrightarrow f(x)= 2[ x^3-3x -2x^2+6]\\ \)

\(\longrightarrow \underline{\underline{ f(x)= 2x^3-4x^2-6x+12}}\)

and we are done!

Answer:

\(f(x)=2x^3-4x^2-6x+12\)

Step-by-step explanation:

Given characteristics of the polynomial:

As the polynomial has 3 roots, it is a cubic polynomial.

\(\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a cubic polynomial}\\\\$y=a(x-r_1)(x-r_2)(x-r_3)$\\\\where:\\ \phantom{ww}$\bullet$ $r_n$ are the roots. \\ \phantom{ww}$\bullet$ $a$ is the leading constant.\\\end{minipage}}\)

Substitute the given leading coefficient and roots into the formula:

\(f(x)=2(x-2)(x-\sqrt{3})(x+\sqrt{3})\)

Expand to standard form:

\(\implies f(x)=2(x-2)(x+\sqrt{3}x-\sqrt{3}x-3)\)

\(\implies f(x)=(2x-4)(x^2-3)\)

\(\implies f(x)=2x^3-6x-4x^2+12\)

\(\implies f(x)=2x^3-4x^2-6x+12\)

Answer:

He had a different number of points to the left of the vertical line than to the right of the vertical line.

Step-by-step explanation:

Divide-center method is the method which involves dividing the data on the graph into two equal parts and then fin the line of best fit. The center of each group is approximated and then a line is constructed between two centers which is estimated as line of best fit.

The age of the twins is 13 years old.

These are equations that consists of unknown variables and equations.

Let the age of Johnson twins be x

Let the age of their older sister be y

If the Johnson twins were born six years after their older sister, then;

x = y + 6

If this year, the product of the three siblings ages is exactly 3166 more than the sum of their ages, then;

xy = x+y+3166

Substitute the first equation into the second

x * x * (x+6) = x + x + (x+6) + 3166

x² * (x+6) = 3x + 3172

x³ + 6x² = 3x + 3172

x³ + 6x² - 3x - 3172 = 0

x = 13

Therefore the age of the twins is 13 years old.

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When the patient recovery time from a specific surgical procedure is normally distributed, with a mean of 5.2 days and a standard deviation of 2.3 days, the probability of spending more than 2 days in recovery will be 0.61.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. Information about the likelihood that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.

Here,

z=(X-μ)/σ

X=2

μ=5.2

σ=2.3

Z=(2-5.2)/2.3

Z=-1.39

-1.39+1

=0.39

1-0.39=0.61

The probability of spending more than 2 days in recovery will be 0.61 when the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days.

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Answer:

Sale price of a sweat shirt is $15.30 and a soccer ball is $21.08.

Step-by-step explanation:

A). Usual price of a sweat shirt is = $18

Sale price of the sweat-shirt is 85% of the usual price.

Therefore, Sale price = 85% of $18

=

= $15.30

B). Usual price of a soccer ball is = $24.80

Sale price of the soccer ball is 85% of its usual price.

Therefore, Sale price = 85% of $24.80

=

= $21.08

Therefore, sale price of a sweat shirt is $15.30 and a soccer ball is $21.08.

heres the real answer hope it helps :)

Answer:

a translation 5 units to the left

Step-by-step explanation:

                                                 Answer

                                       Part 1: B. 5 units left

                                     Part 2: C. 7 units down

                                             Hope it helps!

                                     Have an amazing day!!

                                                     ^ω^

-- FTS

The second solution, y2, to the given second-order differential equation is y2(t) = t³.

To find the second solution using the method of reduction of order, we assume that the second solution can be written as y2(t) = v(t) y1(t), where y1(t) is the known first solution (given as y1(t) = t²).

We substitute y2(t) = v(t) y1(t) into the differential equation:

t²v''(t) + 2tv'(t) - 4t²v'(t) - 4tv(t) + 6t²v(t) = 0.

Simplifying the equation, we get:

t²v''(t) - 2tv'(t) + 2tv'(t) - 4tv(t) + 6t²v(t) = 0,

t²v''(t) + (2t - 4t + 6t²)v(t) = 0,

t²v''(t) + (6t² - 2t - 4t)v(t) = 0,

t²v''(t) + (6t² - 6t)v(t) = 0.

Dividing the equation by t², we have:

v''(t) + (6 - 6/t)v(t) = 0.

Now, let u(t) = v'(t), then u'(t) = v''(t). Substituting these into the equation, we get:

u'(t) + (6 - 6/t)u(t) = 0.

This is a first-order linear ordinary differential equation. We can solve it by separation of variables:

du/u = (6 - 6/t)dt,

ln|u| = 6t - 6ln|t| + C1,

|u| = e^(6t-6ln|t|+C1),

|u| = e^(6t-6ln|t|) * e^C1.

Let C = ±e^C1, then |u| = C * e^(6t-6ln|t|).

Now, integrating u(t) = ±C * e^(6t-6ln|t|) dt, we get:

v(t) = ±C * ∫[e^(6t-6ln|t|)] dt.

Evaluating the integral, we find:

v(t) = ±C * t³.

Therefore, the second solution is y2(t) = t³, which forms a fundamental set with the given first solution y1(t) = t².

Using the method of reduction of order, we found the second solution y2(t) = t³ to the given second-order differential equation t²y''(t) - 4ty'(t) + 6y(t) = 0. The fundamental set {y1(t) = t², y2(t) = t³} satisfies the differential equation and allows us to express the general solution of the equation.

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Teniendo en cuenta la definición de sistema de ecuaciones y resolviendo por el método de sustitución, la opción correcta es la opción c: Las edades de Juan y Luis son 12 y 18 años respectivamente.

En primer lugar, debes saber que un sistema de ecuaciones es un conjunto de ecuaciones con las mismas incógnitas.

Un  sistema de ecuaciones lineales es un sistema de ecuaciones en el que cada ecuación es lineal.

Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema.

Es decir, en los sistemas de ecuaciones, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en ambas ecuaciones.

Para resolver se puede aplicar el método de sustitución.

El método mencionado consiste en despejar o aislar una de las incógnitas y sustituir su expresión en la otra ecuación. De este modo, obtienes una ecuación de primer grado con la otra incógnita.

En este caso, las incógnitas son:

Juan tiene \(\frac{2}{3}\) años de la edad de Luis. Esto es: J= \(\frac{2}{3}\)×L

Dentro de 6 años la edad de Juan será de \(\frac{3}{4}\) la edad de Luis. Esto es:

(J+6)=\(\frac{3}{4}\)×(L+6)

Entonces el sistema de ecuaciones a resolver es:

\(\left \{ {{J=\frac{2}{3}xL } \atop {J+6=\frac{3}{4}x(L+6) }} \right.\)

Resolviendo por el método de sustitución, ya que la variable J se encuentra aislada en la primer ecuación, se decide reemplazar la expresión en la segunda ecuación, obteniendo:

\(\frac{2}{3} xL+6=\frac{3}{4} x(L+6)\)

Resolviendo:

\(\frac{2}{3}\)×L+ 6= \(\frac{3}{4}\)×L+

\(\frac{2}{3}\)×L+6= \(\frac{3}{4}\)×L+ \(\frac{9}{2}\)

\(\frac{2}{3}\)×L- \(\frac{3}{4}\)×L= \(\frac{9}{2}\) -6

\(-\frac{1}{12}\)×L= -\(\frac{3}{2}\)

L=(-\(\frac{3}{2}\)) ÷ (\(-\frac{1}{12}\))

L= 18

Ahora sustituyendo este valor en la primer ecuación se obtiene:

J= \(\frac{2}{3}\)×L

J= \(\frac{2}{3}\)×18

J=12

Entonces, finalmente se obtiene que la opción correcta es la opción c: Las edades de Juan y Luis son 12 y 18 años respectivamente.

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The total area of the composite figure made up of triangle, rectangle and square is; 106 m²

The area of the Triangle is;

A_t = (1/2) * (6 + 4) * 9

A_t = 45 m²

Area of Square;

A_s = 5 * 5

A_s = 25 m²

Area of Rectangle is;

A_r = 6 *  6

A_r = 36 m²

Total Area = 45 m² + 25 m² + 36 m²

Total Area = 106 m²

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Answer:

59+b or b+59

Step-by-step explanation:

If b is Beth, then 59+b is Andy.

The number of books Andy has is b+59 or 59+b

Answer:

Step-by-step explanation:

because when we factorise we take the number or variable which is common to both

Answer:

x = 35, x = 27

Step-by-step explanation:

(9)

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

141° is an exterior angle, thus

x + 24 + 2x + 12 = 141 , that is

3x + 36 = 141 ( subtract 36 from both sides )

3x = 105 ( divide both sides by 3 )

x = 35

-----------------------------------------------------------

(11)

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180, that is

2x - 9 + 3x + 2x = 180

7x - 9 = 180 ( add 9 to both sides )

7x = 189 ( divide both sides by 7 )

x = 27

Answer:

Unfortunately I can't do the first one, but the second one is easy

Step-by-step explanation:

To find X in the Q) 11:

1. The triangle is an equilateral traingles meaning angles add up to 180°

2. Add the numbers - 2x - 9 + 3x + 2x = 7x -9

3. Add 9 to 180 (your adding because you changed the side of the number) - 189 = 7x

4. Divide 7 by 189

Your answer is x = 27

The value of y when x = 4 is 3.

In this given condition statement, if x is greater than 5, the value of y is 1. If x is less than 5, there is an additional condition.

If x is less than 3, the value of y is 2.

Otherwise, if x is not less than 3, the value of y is 3. Lastly, if x is equal to 5, the value of y is 4.

In the case of x = 4, x is less than 5 but not less than 3.

Therefore, the condition statement within the else condition is satisfied, resulting in the value of y being 3.

This means that when x is equal to 4, the value of y equals 3 as per the given conditions.

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The probability value of (m, n) is (1, 2^1005).

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

(1/2) ⋅ (2^1004 + (-1)^1005)

Thus, the probability is: P = (1/2^1004) ⋅ (1/2) ⋅ (2^1004 + (-1)^1005) = 1/2 + 1/2^1005. Hence, (m, n) = (1, 2^1005).

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Complete question:

If m/n is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with m and n being relatively prime positive integers. what is probability value of m and n?

The probability value of (m, n) is (1, 2^1005).This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

\((1/2) * (2^{1004} + (-1)^1005)\)

Thus, the probability is: P = \((1/2)^{1004}* (1/2) *(2^{1004} + (-1)^{1005}) = 1/2 + 1/2^{1005}.\)

Hence, (m, n) = (\(1, 2^{1005\)).

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Answer:

A. m-6/24

Step-by-step explanation:

This is the required expression because,

1. Quotient of 24 and 6 less than m.

2. It means the quotient of 24 and 6 subtracted from m.

3. Representing it mathematically, m-6/24.

The algebraic expression for the word phrase "the quotient of 9 and 8 less than m" is: \(m - \dfrac{9}{8}\\\\\)

An algebraic expression is a mathematical expression using at least one variable in it, in contrast to numerical expressions which only use constants in it.

The quotient of a and b is  \(\dfrac{a}{b}\) , not counting remainder.

The phrase "less than m" can be expressed as making subtraction from m.

Thus, the algebraic expression for the word phrase "the quotient of 9 and 8 less than m" is: \(m - \dfrac{9}{8}\\\\\)

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The correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.

What is the system of equations?

A system of equations is a set of two or more equations with the same variables. The goal of a system of equations is to find the values of the variables that simultaneously satisfy all the equations in the system.

The given equations are

3x + y = 12

x + 4y = 4

To graph the system of equations, we can start by finding the x-intercepts and y-intercepts of each line.

The x-intercept is the point where the line crosses the x-axis, which means that the y-value is 0. To find the x-intercept, we can set y = 0 and solve for x:

3x + y = 12

3x + 0 = 12

3x = 12

x = 4

So, the x-intercept of the first line is (4, 0).

Next, we can find the y-intercept, which is the point where the line crosses the y-axis, meaning that the x-value is 0. To find the y-intercept, we can set x = 0 and solve for y:

3x + y = 12

0 + y = 12

y = 12

So, the y-intercept of the first line is (0, 12).

We can repeat this process for the second line to find its x-intercept and y-intercept:

x + 4y = 4

x + 4 * 0 = 4

x = 4

So, the x-intercept of the second line is (4, 0).

Next, we can find the y-intercept by setting x = 0:

x + 4y = 4

0 + 4y = 4

4y = 4

y = 1

So, the y-intercept of the second line is (0, 1).

Now that we have found the x-intercepts and y-intercepts of each line, we can plot these points on a coordinate plane and draw lines through them to obtain the graph of the system of equations.

The graph shows a line with an x-intercept at (4, 0) and a y-intercept at (0, 12). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 1).

Therefore, the correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.

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Answer:

Determine whether a number is a solution to an equation.

Substitute the number for the variable in the equation. Simplify the expressions on both sides of the equation. Determine whether the resulting equation is true. If it is true, the number is a solution.

The graph of g is the graph of f translated 5 units right , the equation of g(x) = 2x-4.

The complete function is

Consider the function f(x) = 2x + 6 and the graph of the function g shown below.

The graph of g is the graph of f translated (1,4,5 or 6) units (left, right, up, or down) ?

and g(x) = ?

A Straight line function is given by y =- mx +c , where m is the slope and c is the intercept on y axis.

From the graph it can be seen that

for y = mx+c

at x =0 ,y= -4

at y=0, x=2

Slope = 4/2 = 2

y = 2x +c

-4 =c

y = 2x -4

From the equation it can be concluded that the graph of g is the graph of f translated 5 units right .

Therefore the equation of g(x) = 2x-4

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Answer:

answer is 1

Step-by-step explanation:

2-1=1

Answer:

9 hours

Step-by-step explanation:

just do 441/7 and then you get 63 miles per hour

and then you divide 567/63 and you get 9!

easy peasy hope I helped

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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Answer:

The 5 for $10 because its 2 dollars for a bag while the first is 3 dollars for a bag

Step-by-step explanation:

Answer:

I'm guessing the five for $10. If you were to by 5 for $3 it would be more than the five for $10. If there are 5 bags for $10 I'm assuming each bag is $2 which is lower than $3.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The number which makes \(5x=10\) true is 2.

\(5(2)=10\)

\(10=10\)

Therefore, 2 is the true value for this. But, lets check an equation like this.

\(\frac{5x}{3}=10\)

We can use algebraic methods to solve this, first multiply 3

\(5x=30\)

Divide by 5

\(x=6\)

Because  6 > 2, the number 2 does not make the two equations equivalent.

Answer:

i think is the third one

Step-by-step explanation:

One inequality could be x > 3. So when x = 4 this is true because 4 is greater than 3.

Answer:

-25x≥100

Step-by-step explanation: