1 2/3 ÷ 1/4
2 4/7 x 3/5
3 5/6 ÷ 1/2
4 8/9 x 5/6
5 3/4 ÷ 5/6
6 7/8 x 1/2
7 2/7 ÷ 5/6

The probability of randomly selecting a class section from the population with an average G.P.A. less than 2.50 is approximately 24.91%. The probability of randomly selecting a class section from the population with an average G.P.A. greater than 3.00 is approximately 6.84%.

To calculate the probabilities and the average GPA for the given questions, we can use the sample mean (2.66) and sample standard deviation (0.23) from the Average G.P.A. data, assuming they represent the population.

1. The probability of randomly selecting a class section from the population with an average G.P.A. less than 2.50 can be calculated using the z-score formula and the standard normal distribution.

The z-score is (2.50 - 2.66) / 0.23 = -0.6957. Using a standard normal distribution table or software, we find the probability to be approximately 24.91%.

2. The probability of randomly selecting a class section from the population with an average G.P.A. greater than 3.00 can be calculated using the z-score formula and the standard normal distribution.

The z-score is (3.00 - 2.66) / 0.23 = 1.4783. Using a standard normal distribution table or software, we find the probability to be approximately 6.84%.

3. The probability of randomly selecting a class section from the population with an average G.P.A. between 2.35 and 2.80 can be calculated by finding the area under the standard normal curve between the corresponding z-scores.

The z-scores for 2.35 and 2.80 are (-0.9130) and (0.6522) respectively. Using a standard normal distribution table or software, we find the probability to be approximately 46.20%.

4. To compute the average G.P.A. that represents the 90th percentile of all Introduction to Statistics class sections over the past five years, we need to find the corresponding z-score. Using a standard normal distribution table or software, we find the z-score to be approximately 1.2816.

We can then calculate the average G.P.A. using the formula: average G.P.A. = (z-score * standard deviation) + mean.

Substituting the values, we get (1.2816 * 0.23) + 2.66 = 2.9668. Therefore, the average G.P.A. that represents the 90th percentile is approximately 2.97.

Note: It is important to keep in mind that these calculations are based on the assumption that the sample accurately represents the population.

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Answer:

D. 20 in by 30 in by 10 in

Step-by-step explanation:

The rest of them would equal 600 in³ but answer choice D when multiplied together equaled 6,000 in³.

The correct phrase commonly used to word conditional probabilities is "given that." This phrase explicitly indicates the condition or event on which the probability calculation is based and emphasizes the dependence between events in the probability calculation.

Let's discuss each option in detail to understand why the correct phrase is "given that" when wording conditional probabilities.

"Dependent": The term "dependent" refers to the relationship between events, indicating that the occurrence of one event affects the probability of another event. While dependence is a characteristic of conditional probabilities, it is not the specific wording used to express the conditionality.

"Given that": This phrase explicitly states that the probability is being calculated based on a specific condition or event being true. It is commonly used to introduce the condition in conditional probabilities. For example, "What is the probability of event A given that event B has already occurred?" The phrase "given that" emphasizes that the probability of event A is being evaluated with the assumption that event B has already happened.

"Either/or": The phrase "either/or" generally refers to situations where only one of the two events can occur, but it does not convey the conditional nature of probabilities. It is often used to express mutually exclusive events, where the occurrence of one event excludes the possibility of the other. However, it does not provide the specific condition on which the probability calculation is based.

"Mutually exclusive": "Mutually exclusive" refers to events that cannot occur simultaneously. While mutually exclusive events are important in probability theory, they do not capture the conditionality aspect of conditional probabilities. The term implies that if one event happens, the other cannot occur, but it does not explicitly indicate the specific condition on which the probability calculation is based.

In summary, the correct phrase commonly used to word conditional probabilities is "given that." It effectively introduces the condition or event on which the probability calculation is based and highlights the dependency between events in the probability calculation.

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Answer:

10 minutes

Step-by-step explanation:

if 70 words = 1minute

862 words will be 862÷70=12.31 minutes

1,562 words will be 1562÷70=22.31 minutes

time needed to finish will be 22.31-12.31= 10 minutes

So the total time needed to finish will be 10 minutes

Answer:

The point after translation is: (-2, -2)

Step-by-step explanation:

Given point is:

(1, -7) => A(1,-7)

There are four cases for a point's translation:

Now we have to translate the given point 3 units to the left which means 3 will be subtracted from x coordinate.

Similarly, The point has to be translated 5 units up which means 5 will be added to the y-coordinate of point.

\(A(1,-7) ---> (1-3, -7+5) ---> A'(-2,-2)\)

Hence,

The point after translation is: (-2, -2)

The value of expression lim x→1 g(x) is 4.

In mathematics, a limit is a point at which a function becomes close to producing the desired result for the given input values. Limits are necessary for calculus and mathematical analysis and are also needed to establish integrals, derivatives, and continuity. It is used during the analysis process and continually thinks about how the function will act in a particular situation. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in the theory category.

Given expression,

\(4x\leq g(x)\leq2x^{4}-2x^{2} +4\)

For x → 1

4x = 4(1)

    = 4

\(2x^{4}-2x^{2} +4\) = 2(1)-2(1)+4

                     = 4

Hence, the value of lim x→1 g(x) is 4.

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If the events A and B are mutually exclusive, then they are always dependent events because the occurrence of one event precludes the occurrence of the other event.

Mutually exclusive events are events that cannot occur simultaneously. In other words, if event A occurs, then event B cannot occur and vice versa. Therefore, if A and B are mutually exclusive, the occurrence of one event provides information about the occurrence of the other event. This means that the probability of A occurring changes based on the knowledge that B did not occur, and vice versa. Therefore, A and B cannot be independent events.

In probability theory, independent events are events where the occurrence of one event does not affect the occurrence of the other event. Therefore, if two events are mutually exclusive, they cannot be independent.

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El volumen de material requerido para la construcción de la escultura es:

\(V_{tot}=122,26\: m^{3}\)

Esta escultura esta compuesta de dos volúmenes, un prisma de base hexagonal y una pirámide de base hexagonal. Calculemos el volumen de cada figura por separado, para luego sumarlos.

Prisma

La ecuacion del área de un hexágono está dada por:

\(A_{hex}=\frac{P*a}{2}\)

Donde:

Entonces el área será:

\(A_{hex}=\frac{24*3,4}{2}\)

\(A_{hex}=40,8\: m^{2}\)

Ahara, el volumen de un prisma de base hexagonal está dada por:

\(V_{prisma}=A_{hex}*h\)

h es la altura del prisma, en nuestro caso h = 2 m.

Entonces:

\(V_{prisma}=40,8*2\)

\(V_{prisma}=81,6\: m^{3}\)

Pirámide

El volumen de una pirámide de base hexagonal está dado por:

\(V_{piramide}=\frac{A_{hex}*H}{3}\)

Donde:

Nosotros tenemos la apotema del volumen 4,53 m, por lo tanto podremos calcular H usadon el teorema de pitagoras.

\(4,53^{2}=a^{2}+H^{2}\)

\(4,53^{2}=3,4^{2}+H^{2}\)

\(H=2,99\: m\)

Por lo tanto el volumen de la pirámide será:

\(V_{piramide}=\frac{40,8*2,99}{3}\)

\(V_{piramide}=40,66\: m^{3}\)

El volumen total del material necesario será:

\(V_{tot}=V_{prisma}+V_{piramide}\)

\(V_{tot}=81,6+40,7=122,26\: m^{3}\)

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Answer:

CD = 12.81

Step-by-step explanation:

2 x CS = CA

2x4 = 8 = CA

10 = AD

\(CD = \sqrt{(CA^{2} +AD^{2}) }\)

\(CD = \sqrt{(8^{2}+10^{2} ) }\)

\(CD = \sqrt{(64+100) } \\CD= \sqrt{164} \\CD=12.81\)

Answer:

{4, 5, 6}, {64, 65, 66}, {124, 125, 126}

Step-by-step explanation:

x = 1st number

x + 1 = 2nd number

x + 2 = 3rd number

{4, 5, 6}, {64, 65, 66}, {124, 125, 126}

The possible set of numbers are {4,5,6}, {64,65,66} and {124,125,126}

Consecutive numbers are the numbers which follow each other in order from small to greater number.

Let three consecutive numbers are, x ,x+1 and x+2.

According to given condition,

The first number is a multiple of 4,

The second number is a multiple of 5,

And The second number is a multiple of 6.

Start from 4 and then try to find out sequence,

The numbers can be 4, 5 and 6.

Further, the number can be 64,65 and66

And The numbers can be 124,125 and 126

So, three sets of numbers are {4,5,6}, {64,65,66} and {124,125,126}

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Answer:

k=-570

Step-by-step explanation:

P(x) = kx^3+23x^2+71x+30

If 2x-1 is a factor of p(x)

Then,

2x-1 =0

2x=1

x=1/2 and at this value, p(x) =0

Substitute x = 1/2 for x in p(x)

p(1/2) = k(1/2)^3 + 23(1/2)^2;+71(1/2)+30

k(1/8)+23/4 +71/2+30=0

k/8= -23/4 -71/2-30

k/8 = -285/4

k= -(285*8)/4

k=-570

Thus, the polynomial p(x) = -570x^3 +23x^2 +71x +30

Factorization of p(x)

(2x-1) (-285x^2 +131x-30).

the answere would be k=-570

oh and answere me :()

Answer:

25°

Step-by-step explanation:

25° because opposite angles are equal

the blue angle 25° is opposite the yellow angle x° making x=25°

Answer:

x = 25°

Step-by-step explanation:

We can see that the 25° and x° are vertical to each other and vertical angles are angles that are the same size and directly opposite each other thus they are equal!

a) Expected value = 50b.

b) Probability = 0.4c.

c) Probability that the game would take longer than 40 minutes is 0.2.

Let's discuss it further below.

In this question, we are given that the time required to play a certain game is uniformly distributed between 25 and 45 minutes. We are asked to find the expected value and variance of the time to complete the game, the probability of finishing within 33 minutes, and the probability that the game would take longer than 40 minutes.

a) To find the expected value and variance of the time to complete the game, we can use the following formulas:

Expected value = (minimum value + maximum value) / 2Variance = [(maximum value - minimum value)²] / 12

Using these formulas, we can calculate:

Expected value = (25 + 45) / 2 = 35Variance = [(45 - 25)²] / 12 = 50b.

b) To find the probability of finishing within 33 minutes, we can use the formula for a uniform distribution:

Probability = (x - minimum value) / (maximum value - minimum value)

Plugging in the values we know, we get:

Probability = (33 - 25) / (45 - 25) = 0.4c.

c) To find the probability that the game would take longer than 40 minutes, we can use the same formula as in part b, but with a different value for x:

Probability = (45 - 40) / (45 - 25) = 0.2

Therefore, the probability that the game would take longer than 40 minutes is 0.2.

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Answer:

(x+2.5166) (x-2.5166)

Step-by-step explanation:

consider,
a=3
b=0
c=16-35 = -19

as we know, for solving quadratic equation,
x= -b+/-(root(b^2-4ac))  / 2a = +/- 2.5166

Answer:

(3x - 5)(x + 7)

Step-by-step explanation:

I am assuming you mean:

3x^2 + 16x - 35

This =  

3x^2 + 21x - 5x - 35

= 3x(x + 7) - 5(x + 7)

= (3x - 5)(x + 7)

Answer:

6 months

Step-by-step explanation:

Here, the Laplace transform of f(t) being f(s), the Laplace transform is a technique used to convert a time-domain function, f(t), into a complex frequency-domain function, f(s). The response you're looking for would be the definition of the Laplace transform for positive s values and f(s) otherwise.

The Laplace transform is defined as:
F(s) = L{f(t)} = ∫(e^(-st) * f(t)) dt, from 0 to infinity,
where F(s) is the Laplace transform of f(t), s is a complex variable, and t is the time variable.
For all positive s values, the Laplace transform will exist if the integral converges. Otherwise, the Laplace transform does not exist, and you would use f(s) as given.
In summary, the Laplace transform of f(t) is F(s) for all positive s values when the integral converges, and f(s) otherwise.

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The age of the fossil is calculated as; 19188 years

We are given the parameters as;

Half life (T_¹/₂) = 5730 years

The ratio between a fossil to a living sample; N/N₀  = 10% = 0.1

t = ?

Let us find the disintegration constant from the formula;

T_¹/₂ = In 2/λ

where λ is radioactive decay constant.

λ = In 2/T_¹/₂

λ = 0.693/5730

λ = 0.00012

Now, the decay formula here is;

N/N₀ = e^(-λt)

Thus;

0.1 = e^(-0.00012t)

-0.00012t = In 0.1

-0.00012t = -2.302585

t = -2.302585/-0.00012

t = 19188 years

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The equation of the tangent line to the curve y = 6x sin(x) at the point (2, 3) is y = (12cos(2) + 6sin(2))(x - 2) + 12sin(2)

To find the equation of the tangent line to the curve y = 6x sin(x) at the point (2, 3), we need to find the slope of the tangent line and the coordinates of the point of tangency.

Let's start by finding the slope of the tangent line. The slope of the tangent line at a given point on a curve can be found using the derivative of the function.

This can be done by taking the derivative of y = 6x sin(x)  

To find the derivative, we can use the product rule and the chain rule. The derivative of 6x is 6, and the derivative of sin(x) is cos(x).

Applying the product rule, we get:

dy/dx = 6x × cos(x) + 6 × sin(x)

Now we can evaluate the derivative at x = 2 to find the slope of the tangent line at the point (2, 3):

dy/dx = 6(2) × cos(2) + 6 × sin(2)

= 12cos(2) + 6sin(2)

Next, we need to find the y-coordinate of the point of tangency,

which is y = 6(2) sin(2):

=> y = 12sin(2)

So the point of tangency is (2, 12sin(2)).

Now we have the slope of the tangent line (dy/dx) and a point on the line (2, 12sin(2)). We can use the point-slope form of a line to find the equation of the tangent line:

=> y - y₁ = m(x - x₁)

Plugging in the values, we have:

y - 12sin(2) = (12cos(2) + 6sin(2))(x - 2)

Expanding and rearranging the equation, we can find the final form of the equation of the tangent line:

y = (12cos(2) + 6sin(2))(x - 2) + 12sin(2)

Therefore,

The equation of the tangent line to the curve y = 6x sin(x) at the point (2, 3) is y = (12cos(2) + 6sin(2))(x - 2) + 12sin(2)

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Answer:

3/7

Step-by-step explanation:

This is because you need to count the tick marks to 1.

That should be 7.

Then you count to the red dot.

That should be 3.

3/7

Answer: 3/7

Step-by-step explanation:

There are 7 segments that separates 1 from 0, therefore our denominator of the fraction is 7.

The red dot is on the third tick, making our numerator 3.

Our answer is 3/7, or \(\frac{3}{7}\)

Answer:

 hi! i know its 3 weeks late and sorry about that a-hole that called you an idiot! You certainly are not, and believe the answer was/is 16 over 4 or 16/4

Step-by-step explanation:

Answer:

65% because 65 is more than half..And half is 50, 65 is more than 50

a) The area of a circle is given by the formula:

Where A is the area, π=3.14 and d is the diameter=8 ft.

By replacing values:

b) The circumference of a circle is given by:

Where C is the circumference, π=3.14 and d is the diameter=8 ft.

By replacing values:

Answer:

2(n+8)

sum is 30

Step-by-step explanation:

Answer:

2(n+8)

Step-by-step explanation: taking quiz right now

Answer:

None

Step-by-step explanation:

Square roots of negatives are imaginary numbers.

Solution:

Simplify the equation and solve.

The solution to the problem is 2281/2630.

Answer:

\(x\geq 0\\\)

Step-by-step explanation:

Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

The equilibrium level of income (Y), interest rate (i), consumption (C), investments (I), and budget surplus can be calculated using the given equations and information. When G increases by 100, the new values for investments and budget surplus can be determined. The crowding out effect resulting from the increase in G can also be evaluated. Additionally, if the increase in G is accompanied by an increase in M/P by 100, the equilibrium level of Y and r, as well as the crowding out effect, can be determined and explained.

To calculate the equilibrium level of income (Y), we set the total income (Y) equal to total expenditures (C + I + G), solve the equation, and find the value of Y that satisfies it. Similarly, the equilibrium interest rate (i) can be determined by equating the demand for money (L) with the money supply (M/P). Consumption (C), investments (I), and budget surplus can be calculated using the respective equations provided.

When G increases by 100, we can recalculate the new values for investments and budget surplus by substituting the updated value of G into the equation. The crowding out effect can be assessed by comparing the initial and new values of investments.

If the increase in G is accompanied by an increase in M/P by 100, the equilibrium level of Y and r can be calculated by simultaneously solving the equations for total income (Y) and the interest rate (i). The crowding out effect in this case refers to the reduction in investments resulting from the increase in government spending (G) and its impact on the interest rate (r), which influences private sector investment decisions.

Overall, by analyzing the given equations and their relationships, we can determine the equilibrium levels of various economic variables, evaluate the effects of changes in government spending, and understand the concept of crowding out.

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Answer:

(x + 10)^2 + (y - 5)^2 = r^2