I need help please ‼️

i.  a sample size of 138 is needed to estimate the mean within +2 with 99% confidence. Sample size needed: 138

ii. Sample size needed: 342

iii. Sample size needed: 193

iv. Estimating process is legitimate due to the Central Limit Theorem.

What is normal distribution?

Normal distribution, also known as the Gaussian distribution or bell curve, is a continuous probability distribution that is symmetric and characterized by its mean and standard deviation.

i. To estimate the mean within +2 with 99% confidence, we can use the formula for the sample size needed for estimating the population mean:

[tex]n = (Z * \sigma / E)^2[/tex]

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (99% confidence corresponds to a Z-score of approximately 2.576)

σ = population standard deviation (given as √35 since [tex]o^2[/tex] = 35)

E = maximum error tolerance (+2 in this case)

Substituting the values into the formula:

[tex]n = (2.576 * \sqrt{35} / 2)^2 = 137.13[/tex] (approx)

Since the sample size needs to be a whole number, we round up to the nearest integer. Therefore, a sample size of 138 is needed to estimate the mean within +2 with 99% confidence.

ii. To estimate the true proportion within 22% with 99% confidence, we can use the formula for the sample size needed for estimating the population proportion:

[tex]n = (Z^2 * p * (1 - p)) / E^2[/tex]

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (99% confidence corresponds to a Z-score of approximately 2.576)

p = estimated proportion (0.5 is commonly used for unknown proportions)

E = maximum error tolerance (22% in this case, which is 0.22)

Substituting the values into the formula:

[tex]n = (2.576^2 * 0.5 * (1 - 0.5)) / 0.22^2 = 341.28[/tex]

Since the sample size needs to be a whole number, we round up to the nearest integer. Therefore, a sample size of 342 is needed to estimate the true proportion within 22% with 99% confidence.

iii. When the population variance [tex]o^2[/tex] is unknown, we can use the t-distribution instead of the Z-distribution for estimating the mean. The formula for the sample size needed for estimating the population mean with an unknown variance is:

[tex]n = (t * \sigma / E)^2[/tex]

Where:

n = sample size

t = t-score corresponding to the desired confidence level and degrees of freedom (in this case, for 95% confidence and a large sample size, t can be approximated as 1.96)

σ = estimated standard deviation (given as √50 since [tex]o^2[/tex] = 50)

E = maximum error tolerance (+1 in this case)

Substituting the values into the formula:

[tex]n = (1.96 * √50 / 1)^2 = 192.08[/tex]

Since the sample size needs to be a whole number, we round up to the nearest integer. Therefore, a sample size of 193 is needed to estimate the mean within +1 with 95% confidence using the 22.5% value.

iv. The estimating process is still legitimate in this case because the sample size is large and the Central Limit Theorem applies. The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the mean (or proportion) will be approximately normally distributed, regardless of the shape of the population distribution. This allows us to make inferences about the population mean or proportion using sample statistics. Additionally, the use of the t-distribution accounts for the uncertainty introduced by using the sample standard deviation instead of the population standard deviation.

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If the activities and assessments were designed to facilitate learning and encourage higher-order thinking skills, learners were exposed to opportunities for achieving mathematical proficiency (Kilpatrick, Swafford & Findell, 2001).

The teaching and learning process revolves around assessing the level of knowledge students have and guiding them to achieve specific goals.

The role of assessments in the classroom is to measure students' understanding of the taught content and to provide feedback to the teacher on areas where improvement is required.

Suppose the learning activity by Teacher Thato and all the three assessment of learning activities by the student teachers captures the entire learning experience of Teacher Thato's learners.

The extent to which Teacher Thato's learners were exposed to opportunities for achieving mathematical proficiency depends on the effectiveness of the teaching and learning process.

Mathematical proficiency is the knowledge and skills that learners gain through regular interactions with mathematical concepts.

Mathematical proficiency means understanding mathematics as well as being able to apply mathematical knowledge in real-world scenarios.

Therefore, if Teacher Thato's learning activities and assessment methods were designed to provide learners with opportunities to apply mathematical concepts to real-world problems, then they were exposed to opportunities for achieving mathematical proficiency (Kilpatrick, Swafford & Findell, 2001).

Similarly, if the activities and assessments required learners to engage in critical thinking, problem-solving, and other higher-order thinking skills, then it's possible that learners were exposed to opportunities for achieving mathematical proficiency (Kilpatrick, Swafford & Findell, 2001).

In summary, if the activities and assessments were designed to facilitate learning and encourage higher-order thinking skills, learners were exposed to opportunities for achieving mathematical proficiency (Kilpatrick, Swafford & Findell, 2001).

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Answer:

9

Step-by-step explanation:

let x be number of jeans

3/5 = x/15

x=(3/5)15

x=9

Answer:

9 jeans

Step-by-step explanation:

The 5 part of the ratio relates to 15 shirts , then

15 ÷ 5 = 3 ← value of 1 part of the ratio , then

3 parts = 3 × 3 = 9 ← number of jeans

Answer:

8

Step-by-step explanation:

The expected number of boats of the next 12 boats to dock is from Connecticut is 6.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Boats from all along the Atlantic coast dock at a busy marina.

Of the first 10 boats to dock at the marina one day, 5 were from Connecticut.

Probability that the boats which dock are from Connecticut = 5/10 = 1/2

When the next 12 boats also arrive,

Expected number of boats from Connecticut = 1/2 × 12 = 6

Out of 12, 6 boats are from Connecticut.

Hence the expected number of boats is 6.

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Answer:

[tex]\boxed {\boxed {\sf sin(\theta)=\frac {16}{20}}}[/tex]

Step-by-step explanation:

We are asked to find the sine for the angle indicated. Remember that sine is equal to the opposite over the hypotenuse.

Analyze the triangle given. We have the 2 legs (16 and 12), but we do not have the hypotenuse (the longest side). We must solve for it.

Since this is a right triangle, we can use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

Where a and b are the legs and c is the hypotenuse. We know 16 and 12 are the legs.

[tex](16)^2+(12)^2=c^2[/tex]

Solve the exponents.

[tex]256+144=c^2[/tex]

[tex]400=c^2[/tex]

Since we are solving for c, we must isolate the variable. It is being squared, so we take the inverse: a square root.

[tex]\sqrt{400}=\sqrt{c^2} \\20=c[/tex]

Now we know the hypotenuse is 20. The side opposite of the angle θ is 16.

[tex]sin (\theta)= \frac {opposite}{hypotenuse} \\sin (\theta)= \frac{16}{20}[/tex]

The sine of the angle is equal to 16/20. This can be reduced to 4/5 if necessary (by dividing the numerator and denominator by 4).

Answer:

b

Step-by-step explanation:

In this given problem, the random variable is the time it takes to wash dishes.

Because it is equally distributed between 5 minutes and 18 minutes, the time it takes to wash the dishes on a randomly chosen night is a continuous random variable in the given situation. A random variable is a numerical measure of the result of a probability experiment. It is a mathematical function that assigns numerical values to each possible outcome in the sample space of the experiment. A random variable can be discrete or continuous. In the given problem, the time it takes to wash the dishes on a randomly selected night is a continuous random variable since it is uniformly distributed between 5 minutes and 18 minutes.

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The possible values are not fixed but depend on the probability distribution or the experiment being performed.

In the context of the given problem, the random variable is the time it takes to wash the dishes on a randomly selected night.

A random variable is a variable that is subject to random variations over time.

In probability theory and statistics, it is a numerical quantity or a mathematical function assigned to every event in a sample space of a random phenomenon.

The variable may take on different values as a result of the random element.

To be precise, random variables are quantitative measures of the outcomes of a probability distribution.

Their possible values are not fixed but depend on the probability distribution or the experiment being performed.

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Answer:

- 14x - 9y = 6

Step-by-step explanation:

- 7x - y = 0 → (1)

7x + 8y = - 6 → (2)

Subtracting (2) from (1) term by term

- 7x - 7x - y - 8y = 0 - (- 6)

- 14x - 9y = 0 + 6

- 14x - 9y = 6

Answer:

B

Step-by-step explanation:

a is a cubic. A cubic is an equation that has 3 on its base x to become x^3 as it's highest power. That is not a quadratic. A cubic and a quadratic are not the same thing.

b is a quadratic The highest power is 2 on the base (x)  to become x^2. That is how a quadratic is defined.

c is a reciprocal. It has its highest power in the denominator, and that is not a quadratic. A quadratic is an equation whose highest power is 2 on its base (x) and whose highest power is in the numerator, not the denominator. This choice is rather tricky because the quadratic formula can be used on it if you change x = 1/z. Then the equation becomes f(x) = 4z^2 - 2z + 1. But as it is given and likely as you have been told, this is not a quadratic. This will factor into  (2z - 1)(2z - 1). If I were a student, I'd question this one. It would be interesting to see how your instructor would eliminate it.

d is just a linear function. Since x^2 is multiplied by 0, it disappears. What is left is f(x) = -9x + 7 which is a linear function.

Answer:

a

b

e

Step-by-step explanation:

remember length times width equals area

Answer:

Omar

Step-by-step explanation:

Given

See attachment for prism

Required

Whose expression is correct

The base of the attached prism is a triangle that has the following dimension.

[tex]Base =7cm[/tex]

[tex]Height = 24cm[/tex]

So, the area is:

[tex]Area = \frac{1}{2} * Base * Height[/tex]

[tex]Area = \frac{1}{2} * 7 * 24[/tex]

Comparing the expressions of Omar and Kari, we can conclude that Omar is correct

Answer:

She rented the table for 6 months

Answer:100 - 550= 440 than 75 x 12 is 900 so she will need 460 dollars left to completely rent the table.

Step-by-step explanation:

In market research, the willingness to pay (WTP) is the highest amount that a consumer will pay for a product or service. The product has high Accuracy (2.7) and Screen Size (9.6), and low Voice (14.9) and Price (34.5)

To calculate the WTP for product attributes from a table like the following and describe the product from the coding for the attribute levels, one can follow these steps:

Step 1: Determine the attributes of the product. The attributes are listed as Accuracy, Screen Size, Voice, and Price.  

Step 2: Use coding to describe the levels of each attribute.

The levels for Accuracy are 2.7 and 1.0; for Screen Size are 9.6 and 0.9; for Voice are 30.4 and 14.9; for Price are 40.6 and 34.5.  

Step 3: Use hypothesis testing to determine whether each attribute level is significant.

The t-statistic for each coefficient is greater than 2.0, indicating that each attribute is significant.  

Step 4: Calculate the WTP for each attribute by dividing the coefficient by the attribute level.

The WTP for Accuracy is $2.70, for Screen Size is $1.14, for Voice is $1.87, and for Price is $0.47.  

Step 5: Describe the product based on the coding for the attribute levels.

The product has high Accuracy (2.7) and Screen Size (9.6), and low Voice (14.9) and Price (34.5).

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Answer:

124

Step-by-step explanation:

To find the surface area, we add the area from all faces or the prism.

the first face, we can put 8 times 2.5, which is 20. There are two of these faces, so we have 40 in our area so far.

next the other face. 4  times 2.5 is 10, and there are two of these faces. 60 in out area.

now the top and bottom faces. 8 times 4 is 32. there are two of these faces, and 60 +64 = 124

Answer:

147/200

Step-by-step explanation:

The correct answer is D. The data are qualitative because they consist of counts or measurements.

Qualitative data refers to non-numerical information that is categorical or descriptive in nature. It describes qualities or characteristics of a subject.

In this case, the preferred hands of the experiment's participants would be categorical information, as it describes the quality or characteristic of which hand the participants prefer to use.

On the other hand, quantitative data refers to numerical information that can be measured or counted. It involves quantities or amounts.

Examples of quantitative data would include measurements such as height, weight, or number of participants.

Since the preferred hands in this scenario are categorical and not measured or counted, the data is qualitative. It focuses on the qualities or categories of left-handedness or right-handedness, rather than measuring or counting any specific quantities.

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Answer: $20.25

Step-by-step explanation:

If each cupcake is sold for $1, then all the cupcakes are sold together for $30. Now subtract 9.75 from 30 and you get 20.25.

Hope this helps :)

Late answer, but whatever.

Answer:

36. There are 36 students in the class.

Step-by-step explanation:

4/12 oatmeal

2/12 cinnamon

3/12 chocolate

9 peanut

The fractions added together = 9/12

This means the 9 students = 3/12 of the class

3 x 4 = 12

9 x 4 = 36

Mr. Blanco has the right to refuse treatment, even if it means he will die. The doctor should respect Mr. Blanco's decision and engage in open and honest communication with him to understand his concerns.

1. The ethical principles pertinent to this case include autonomy, beneficence, non-maleficence, and respect for patient's wishes. Autonomy refers to Mr. Blanco's right to make decisions about his own healthcare. Beneficence and non-maleficence require the healthcare professionals to act in Mr. Blanco's best interest and do no harm. Respect for patient's wishes entails honoring his decision and preferences.

2. Yes, Mr. Blanco should have the right to refuse treatment even if the consequence may be that he will die. It is his autonomy and right to make decisions about his own body and medical treatment. As long as he is mentally competent, he has the right to make choices about his healthcare, even if they go against medical advice.

3. It is important to consider the possibility that Mr. Blanco may be seriously depressed and not mentally competent to make the decision. In such cases, a thorough evaluation of his mental capacity and emotional state should be conducted by healthcare professionals to ensure that he is able to make an informed decision. If he is found to lack mental competence, appropriate steps should be taken to protect his best interests.

4. Given that Mr. Blanco had previously given his written consent for the surgery but verbally withdrew it later, the doctor should respect his current decision. A patient's consent can be withdrawn at any time, and healthcare professionals should prioritize the patient's current wishes. It is essential to engage in open and honest communication with Mr. Blanco to understand his concerns and explore alternative options if available.

5. The decision may be different if Mr. Blanco were refusing treatment for another condition such as terminal cancer or irreversible heart failure. In such cases, the prognosis and potential outcomes may be different, and the balance between preserving life and respecting autonomy may shift. Each case should be evaluated individually, considering the patient's medical condition, prognosis, quality of life, and their values and preferences. Open discussions with the patient, their family, and the healthcare team are crucial in reaching the most ethically appropriate decision.

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Answer:

900,000 6

∴ there are 900,000 6-digit numbers in all.

Answer:

minimum is 55

maximum is 71

Step-by-step explanation:

got this from another answer so i hope it helps you

Answer:

2/8 or 1/4

Step-by-step explanation:

The equivalent double integral in polar coordinates is: 1 = ∫∫(2 - r²cosθ) rdr dθ.

In polar coordinates, we can express the given double integral as 1 = ∫∫(2 - r²cosθ) rdr dθ. To convert from rectangular coordinates to polar coordinates, we substitute x = rcosθ and y = rsinθ. The element of area in polar coordinates is given by dA = rdr dθ.

By making these substitutions and adjusting the limits of integration accordingly, we obtain the equivalent double integral in polar coordinates.

The integral becomes 1 = ∫∫(2 - r²cosθ) rdr dθ. This form allows us to integrate with respect to r first and then with respect to θ, simplifying the evaluation process.

Polar coordinates provide an alternative way to express integrals, particularly when dealing with problems involving circular or radial symmetry.

They use the distance from a fixed point (the origin) and the angle measured from a reference direction (usually the positive x-axis) to represent points in the plane.

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Answer:

70 ft squared

Step-by-step explanation:

Separate into rectangle and triangle then add the found areas together for total area.

rectangle...

10×4=40

triangle...

[tex] \frac{bh}{2} = [/tex]

(12×5)/2=

60/2=30

add area for rectangle and triangle...

40+30=70

Answer:

1/8

Step-by-step explanation:

1 number out of eight possible choices.

Answer:

1/8

Step-by-step explanation:

the answer

Answer: 48 grams

Step-by-step explanation:

The half-life of an element refers to the amount of time that it takes for half of it to decay.

For instance, if the half life is 2 hours and the element weighs 12 g, the element will only weigh 6g after 2 hours.

The half-life of the above is 6 hours, in 3 hours therefore, it would only have lost of the half that it would have lost in 3 hours which means it would have lost only a quarter.

= 64 * ( 1 - 1/4)

= 48 grams

The correct answer is: 0, -3, and 3. At  0, -3, and 3 of x does fx) x4-18x2 have a critical point where the graph changes from decreasing to increasing.

To find the critical points where the graph of the function f(x) = x^4 - 18x^2 changes from decreasing to increasing, we need to find the values of x where the derivative of the function is equal to zero or does not exist.

Let's find the derivative of f(x) with respect to x:

f'(x) = 4x^3 - 36x

To find the critical points, we set the derivative equal to zero and solve for x:

4x^3 - 36x = 0

Factor out 4x:

4x(x^2 - 9) = 0

Now we have two factors:

1) 4x = 0, which gives x = 0

2) x^2 - 9 = 0, which gives x = ±3

So, the critical points where the graph changes from decreasing to increasing are x = 0, x = -3, and x = 3.

Therefore, the correct answer is: 0, -3, and 3.

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The maximum number of ways for all these players to play in the given scenario is 12.

To determine the maximum number of ways for the players to play, we can consider the possible match-ups between the players. Since a player always plays with the nearest rank player who is still in the competition, we can start with the highest-ranked player (#1) and pair them with the next nearest player in rank (#2). This creates one match. Then, the remaining players (#3, #4, and #5) can be paired in different ways: (3, 4), (4, 5), and (3, 5). This results in three more matches. Therefore, in total, we have four matches.

For each match, the winner moves on to the next round, while the loser is eliminated. Following this process, we can have a maximum of three rounds of matches, resulting in a total of 12 possible ways for all the players to play.

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Answer:

It's 16m

Step-by-step explanation:

Let's say the missing side is C, and since the triangle is right-angle triangle, you can use Pythagoras theorem. Which is

C squared is equal to A squared plus B squared

Like this: c^2 = a^2+b^2

Then

c^2= (10)^2 + (12)^2

c^2= 100 + 144

c^2= 244

c=

[tex] \sqrt{244} [/tex]

c = 15.6

Hope this helps :)