Five students took a quiz. The lowest score was 4, the highest score was 6, the average (mean) was 5.2, and the mode was 6. A possible set of scores for the students is:

Answer:

1st option

Step-by-step explanation:

Consider the coordinates of F and F'

F (- 3, 4 ) and F' (- 1, 3 )

To go from - 3 → - 1 in the x- directions , means adding 2

To go from 4 → 3 in the y- direction means subtracting 1

Then translation rule is

(x, y ) → (x + 2, y - 1 )

Consequently, y = 1/4x - 8 is the equation of the line that goes through the points (4, -7) and (8, -6).

A mathematical assertion that two forms are equivalent is known as an equation. It frequently includes one maybe more numbers, constants, and mathematical processes like exponents, logarithms, division, multiplication, and addition. It may also include trigonometric functions. Equations can be used to solve issues in a variety of disciplines, including algebra, physics, engineering, economics, and far more. Equations serve to represent relations between quantities. Equations can be classified into a wide range of categories, including algebraic, differential, integral, and more. The most prevalent kind of equations are algebraic equations, which include quadratic expressions and rational expressions. Algebraic equations can have one or more factors and can be either linear or nonlinear.

given

The point-slope form of the equation of a line can be used to determine the equation of the line that goes through the points (4, -7) and (8, -6).

y - y1 = m(x - x1) (x - x1)

where (x1, y1) is one of the specified points on the line, m is the slope of the line, and First, using the two provided coordinates, we can determine the slope:

m = (y2 - y1) / (x2 - x1) = (-6 - (-7)) / (8 - 4)\s= 1/4

We can now select one of the points to use as a replacement for (x1, y1) in the point-slope form. The first number (4, -7) will be used:

y - (-7) = 1/4(x - 4) (x - 4)

When we simplify this solution, we obtain:

y + 7 = 1/4x - 1

When we take 7 away from both edges, we get:

y = 1/4x - 8

Consequently, y = 1/4x - 8 is the equation of the line that goes through the points (4, -7) and (8, -6).

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The MLE of σ² is a biased estimator of σ²

The maximum likelihood estimator (MLE) of σ² is a biased estimator, we need to demonstrate that its expected value is different from the true population variance, σ².

Let's start with the definition of the MLE of σ². In the context of simple linear regression, the MLE of σ² is given by:

MLE(σ²) = SSE/n

where SSE represents the sum of squared errors and n is the number of observations.

The expected value of the MLE, we need to take the average of all possible values of MLE(σ²) over different samples.

E(MLE(σ²)) = E(SSE/n)

Since the expectation operator is linear, we can rewrite this as:

E(MLE(σ²)) = 1/n × E(SSE)

Now, let's consider the expected value of the sum of squared errors, E(SSE). In simple linear regression, it can be shown that:

E(SSE) = (n - k)σ²

where k is the number of predictors (including the intercept) in the regression model.

Substituting this result back into the expression for E(MLE(σ^2)), we get:

E(MLE(σ²)) = 1/n × E(SSE)

= 1/n × (n - k)σ²

= (n - k)/n × σ²

Since (n - k) is less than n, we can see that E(MLE(σ²)) is biased and different from the true population variance, σ².

Therefore, we have shown that the MLE of σ² is a biased estimator of σ².

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The question is incomplete the complete question is :

Show that σ² = SSE/n, the maximum likelihood estimator of σ² is a biased estimator of σ²?

The calculated summation value with the message "Summation: " preceding it. The program assumes that the user will provide valid numerical inputs (integers) when prompted.

Here's a Python program that calculates the sum using a loop based on the user's input values for `i` and `k`. The program handles cases where `i` is larger than `k` and continuously asks for proper values until valid inputs are provided.

```python

while True:

   i = int(input("Enter value for i: "))

   k = int(input("Enter value for k: "))

   if i <= k:

       break

   else:

       print("Error: i cannot be greater than k.")

summation = 0

for x in range(i, k+1):

   summation += 2 * x

print("Summation:", summation)

```

In this program, we use a `while` loop to repeatedly prompt the user for values of `i` and `k`. We convert the inputs to integers using `int()` for numerical comparison. If the condition `i <= k` is satisfied, we break out of the loop; otherwise, an error message is displayed, and the loop continues.

Once we have valid values for `i` and `k`, we initialize the `summation` variable to 0 and use a `for` loop with `range(i, k+1)` to iterate through the values of `x` from `i` to `k` (inclusive). We accumulate the sum by adding `2 * x` to `summation` in each iteration.

Finally, we print the calculated summation value with the message "Summation: " preceding it.

Note: The program assumes that the user will provide valid numerical inputs (integers) when prompted.

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Therefore, to ensure with probability 0.9 that the class average would be within 5 of 60, the professor would need 118 students to take the final exam.

The Central Limit Theorem states that the distribution of the sum or average of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution.

Therefore, in this example we can use the Central Limit Theorem to approximate the mean of the test scores of the students taking the final exam. If the professor knows that the mean of the test scores is 60 and the standard deviation is 16, then the professor can calculate the sample size necessary to ensure that the class average is within 5 of 60 with a probability of 0.9.

Using the formula \(n = (zα/2 * σ/ε)2\), where zα/2 is the z-score associated with a confidence level of 0.9, σ is the standard deviation of the population, and ε is the margin of error desired, we can calculate the sample size necessary for this professor.

\(n = (1.645 * 16/5)2 = 118.03\)
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Answer:

It was not my intention to post that answer, as it does not solve the question, but hope it helps somehow.  

Step-by-step explanation:

\($\text{b)} \frac{\sin(a)}{\sin(a)-\cos(a)} - \frac{\cos(a)}{\cos(a)-\sin(a)} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $\)

You want to verify this identity.

\($\frac{\sin(a)(\cos(a)-\sin(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} - \frac{\cos(a)(\sin(a)-\cos(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $\)

The common denominator is

\((\sin(a)-\cos(a))(\cos(a)-\sin(a))= \boxed{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}\)

Solving the first and second numerator:

\(\sin(a)(\cos(a)-\sin(a))=\sin(a)\cos(a)-\sin^2(a)\)

\(\cos(a)(\sin(a)-\cos(a))= \cos(a)\sin(a)-\cos^2(a)\)

Now we have

\($\frac{ \sin(a)\cos(a)-\sin^2(a) -(\cos(a)\sin(a)-\cos^2(a))}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$\)

\($\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$\)

Once

\(-\sin^2(a) +\cos^2(a) = \cos(2a)\)

\(2\cos (a)\sin(a) = \sin(2a)\)

Also, consider the identity:

\(\boxed{\sin^2(a)+\cos^2(a)=1}\)

\($\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}=\boxed{\frac{ \cos(2a)}{\sin(2a)-1}}$\)

That last claim is true.

Answer:

37

Step-by-step explanation:

3 to the 3rd power is 3x3x3=27, (-5x-2)=10 because two negatives cancel each other out and make a positive, add 27 and 10 and that equals 37. Hope this helps :)

The value of P0.05 < 0.19658. We do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.

According to the question we will set up Hypothesis

Null,  H0: U=26

Alternate, H1: U<26

Test Statistic

Population Mean(U)=26

Sample X(Mean)=24.4

Standard Deviation(S.D)=9.2

Number (n)=25

we use Test Statistic (t) = x-U/(s.d/√(n))

to =24.4-26/(9.2/√(25))

to =-0.87

| to | =0.87

Critical Value

The Value of |t α| with n-1 = 24 d.f is 1.711

We got |to| =0.87  & | t α | =1.711

According to this, we have to make a decision

Hence Value of  |to | < | t α |

P-Value: Left Tail -Ha : ( P < -0.8696 ) = 0.19658

Hence Value of P0.05 < 0.19658

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The water level is rising at a rate of 5 / (4π) inches per second.

To determine the rate at which the water level is rising in the cylindrical container, we can use the formula for the volume of a cylinder:

V = πr^2h,

where V is the volume, r is the radius, and h is the height.

We are given that water flows into the container at a rate of 5 in^3/s. This means that the rate of change of volume with respect to time is dV/dt = 5 in^3/s.

We want to find the rate at which the water level is rising, which is the rate of change of height with respect to time (dh/dt).

We can express the volume V in terms of the height h:

V = πr^2h = π(2^2)h = 4πh.

Taking the derivative of both sides with respect to time, we have:

dV/dt = d(4πh)/dt = 4π(dh/dt).

Now we can solve for dh/dt:

dh/dt = (dV/dt) / (4π).

Substituting the given value for dV/dt:

dh/dt = 5 / (4π).

Therefore, the water level is rising at a rate of 5 / (4π) inches per second.

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Answer:

48.6 km/hr

Step-by-step explanation:

(135/10)×(18/5)

48.6 km/hr

Answer:

expected value =210*(1/38)-6*(37/38)=$-0.32 player would expected to lose =$315.79  a) x P(x) 0 0.0156 1 0.0938 2 0.2344 3…

Step-by-step explanation:

In the game of roulette, a player can place a $6 bet on the number 26 and have a 38 probability of winning. If the metal ball lands on 26, the player gets to keep the $6 paid to play the game and the player is awarded $210. Otherwise, the player is awarded nothing and the casino takes the player's $6. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose? The expected value is $ (Round to the nearest cent as needed.) The player would expect to lose about $ (Round to the nearest cent as needed.) \

By using the concept of Probability and binomial distribution we get that 0.1107 is the probability that exactly 4 seeds don`t grow into plants.

Probability defines the likelihood of the happening of an event. We use probability in our daily life, although we didn`t realize. There are many aspects where probability play a key role.

The probability the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible:

The probability of not growing the plant is =1−0.80=0.20

According to the formula of the binomial probability distribution

P(X)=\(\frac{n!}{X!} \frac{1}{(n-X)!}(p^x)(1-p)^(n-X)\)

So, we have to grow 11 seeds

Therefore, P(11)=\(\frac{11!}{4!7!} (0.20)^{4} (0.80)^{7}\)

P(11)=0.1107

Hence, the probability that exactly 4 seeds don`t grow is 0.1107

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Solution

Perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial.

To determine if the trinomials in the question is a perfect trinomial, we will factor each of the trinomials and then decide which is a perfect trinomial

The first trinomial above is a perfect trinomial

The second trinomial above is a perfect trinomial

The third trinomial above is not a perfect trinomial

The fourth trinomial above is a perfect trinomial

The summary of the solution is given below

Look I tried ok???? Sorry... =_=

True, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line.

As given in the question,

Given statement is: Parabola consist of set of all the points which are equidistant from fixed point and fixed line.

Therefore, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line is a true statement.

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Answer:

whats the exact question screen shot it but i think *{{76 you have to {{ it since its a ombre

Step-by-step explanation:

First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

If the computed probability of an event occurring is 0.01, the correct statement is b) "We would expect the event to occur about one percent of the time."

When the computed probability of an event occurring is 0.01, it indicates that there is a 1% chance of the event happening. This means that out of 100 trials or occurrences, we would expect the event to occur approximately once.

Option a) "The event is likely to occur" might be misleading since a probability of 0.01 is relatively low, indicating a low likelihood of the event happening.

Option c) "The event cannot occur" is incorrect because the probability is greater than zero, suggesting that the event is possible, although with a low likelihood.

Option d) "All of the above" is incorrect because only statement b) accurately reflects the situation, stating that we would expect the event to occur about one percent of the time

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Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64

The fact that they split the money evenly means that they split it in half which each person getting the same amount.

This means that the total amount they found was twice the amount that Jessica and her best friend got.

The total amount found is therefore:

= Jessica's share + Best friend's share

= 16.32 + 16.32

= $32.64

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Answer:

90 minutes

Step-by-step explanation:

it will take twice as long therefore 90 minutes

The reliability of two components in series is 0.996.

To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.

Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.

We can find this probability multiplying all the ten reliabilities:

P = 0.998^2 = 0.996004

Rounding to three decimal places, we have P = 0.996

The reliability of the engine is 0.996.

Hence,

The reliability of two components in series is 0.996.

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If Jenise wants to find out if the students at her school would support using money to buy new band uniforms, the survey that will result in a random sample is D. She picks 75 names at random, sends emails, and records those that return.

A random sample is a sample that gives each unit in the population an equal chance of participation or being selected.

A random sample involves selecting a subset of the population.  The result of the sample survey is generalized on the population to each some conclusions about the population parameters.

Thus, the correct option is D because it involves a random selection.

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Answer:

f(2) = 11

hope this helps

Step-by-step explanation:

3(2)+5

6+5

11

Answer:

11

Step-by-step explanation:

3(2)+5=11

Substitution -- :D

Answer:

(In order, top to bottom. )

Definition of a rectangle

opposite sides of a rectangle are congruent

reflexive property of congruence

SAS congruence postulate

Step-by-step explanation:

Parallelogram JKLM is a rectangle and by definition of a rectangle, ∠JML

and ∠KLM are right angles, ∠JML ≅ ∠KLM because, all right angles are

congruent, ≅ because opposite sides of a parallelogram are congruent, and ≅ by reflective property of congruence. By the SAS

congruence postulate, ΔJML ≅ ΔKLM.

congruent parts of congruent triangles are congruent, ≅

The given quadrilateral is a parallelogram, that have interior angles that are right angles, therefore, the figure has the properties of a rectangle, and

parallelograms including the length of opposite sides are equal, all right angles are congruent and equal to 90° and the length of a side is equal to itself by reflexive property, & ≅

The Side-Angle-Side SAS postulate states that if two sides and an included

angle of one triangle are congruent to the corresponding two of sides and

included angle of another triangle, the two triangles are congruent.

Answer:

50% of 30 is 15. 25% of 40 is 10. So, the product of 50% of 30 and 25% of 40 is 150.

Here's the calculation:

```

(50/100) * 30 * (25/100) * 40 = 150

```

Step-by-step explanation: