in a random sample of 29 people, the main commute time to work was 33.6 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a T distribution to construct and 99% confidence interval for the population mean. What is the margin of error of the mean? Interpret the results.

1. To prove that if x+y = x+z then y = z, we can use the vector space axioms to show that y+0 = z+0, which implies y = z.

To prove that if x+y = x+z then y = z, we can use the following vector space axioms:
- Closure under addition: For any vectors x, y, and z in V, x+y and x+z are also in V.
- Associativity of addition: For any vectors x, y, and z in V, (x+y)+z = x+(y+z) and (x+z)+y = x+(z+y).
- Identity element of addition: There exists a vector 0 in V such that for any vector x in V, x+0 = x.
- Inverse elements of addition: For any vector x in V, there exists a vector -x in V such that x+(-x) = 0.
- Commutativity of addition: For any vectors x and y in V, x+y = y+x.

Now, suppose that x+y = x+z. Adding the inverse of x to both sides, we get (x+y)+(-x) = (x+z)+(-x). By the associative and commutative properties of addition, we can simplify this to y+(x+(-x)) = z+(x+(-x)), which is equivalent to y+0 = z+0. Using the identity element of addition, we get y = z, as required.

2. The set of all polynomials p(z) in Ps satisfying p(0) = 0 is a subspace of Ps.

To determine if the set of all polynomials p(z) in Ps satisfying p(0) = 0 is a subspace of Ps, we need to check if it satisfies the three subspace axioms:
- Closure under addition: For any polynomials p(z) and q(z) in the set, p(z)+q(z) also satisfies p(0)+q(0) = 0, since p(0) = 0 and q(0) = 0. Therefore, the set is closed under addition.
- Closure under scalar multiplication: For any scalar c and polynomial p(z) in the set, cp(z) also satisfies cp(0) = 0, since p(0) = 0. Therefore, the set is closed under scalar multiplication.
- Contains the zero vector: The zero polynomial satisfies p(0) = 0, so it is in the set.

Therefore, the set of all polynomials p(z) in Ps satisfying p(0) = 0 is a subspace of Ps.

3. The set {0a0} is not a spanning set for R3.

The set {0a0} is not a spanning set for R3, since it only contains one vector and cannot generate all possible vectors in R3.

4. The set {0a0} is linearly dependent in R3.

The set {0a0} is linearly dependent in R3, since it only contains one vector and that vector can be expressed as a scalar multiple of itself (namely, 0 times the vector).

5. a) The span of {0a0} is the zero vector, so it has dimension 0.
b) To extend the span to a basis of R3, we need to find two linearly independent vectors that are not already in the span. One example would be {100} and {010}, since they are both linearly independent and not in the span. Therefore, a basis for R3 would be {0a0, 100, 010}.
c) No, 3b) is not a basis of R3, since it contains three vectors and the dimension of R3 is 3. Therefore, we need to remove one vector to make it a basis.
d) We can remove any vector that is a linear combination of the other two vectors in 3b), since it would not add any new information to the span. For example, we can remove {100}, since it can be expressed as a linear combination of {0a0} and {010}. Therefore, a basis for R3 would be {0a0, 010}.

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Systems that support management decisions that are unique and rapidly changing, using advanced analytical methods are called real-time decision support systems (RTDSS).

Real-time decision support systems (RTDSS) are designed to assist managers in making timely and informed decisions in rapidly changing and unique situations. These systems leverage advanced analytical methods and technologies to process and analyze large volumes of data in real-time, providing managers with up-to-date information and insights to support their decision-making process.

RTDSS employ techniques such as data mining, predictive modeling, machine learning, and artificial intelligence to extract valuable patterns, trends, and correlations from diverse data sources. They integrate data from multiple systems and sensors, including internal and external data, and apply sophisticated algorithms to analyze the data and generate actionable insights. This enables managers to assess the current state of affairs, anticipate future scenarios, and make informed decisions based on real-time information.

The key features of RTDSS include rapid data processing, real-time monitoring and reporting, interactive visualization, and proactive decision support. These systems allow managers to track performance indicators, detect anomalies or emerging patterns, simulate different scenarios, and evaluate the potential outcomes of different decisions.

By leveraging advanced analytical methods, RTDSS provide managers with a competitive edge by enabling them to respond swiftly and effectively to rapidly changing situations and make data-driven decisions.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer: 27/45 > 20/45

Step-by-step explanation:

You must make the denominator of each fraction equivalent while keeping the value of each individual fraction the same.

3/5 x (9/9) = 27/45

4/9 x (5/5) = 20/45

27/45 > 20/45

Answer: 27/45 > 20/45

Step-by-step explanation:

You must make the denominator of each fraction equivalent while keeping the value of each individual fraction the same.

3/5 x (9/9) = 27/45

4/9 x (5/5) = 20/45

27/45 > 20/45

Answer:

2ax(5x+7a) is your answer ☺️☺️☺️

i hope so it help you .........

(f∘g)(x) = 14x + 3.

Given function,f(x) = 2x + 3g(x) = 4x + 3x = 7x.

Simplification of f∘g(x).

To solve (f∘g)(x), we need to perform the following operations.

Substitute g(x) in f(x) as follows: f(g(x)) = 2(7x) + 3 = 14x + 3Thus, the simplification of (f∘g)(x) is 14x + 3. Therefore, (f∘g)(x) = 14x + 3.

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Answer:

Population: all men in the country

Sample: the 1,002 men selected

Step-by-step explanation:

The population describes the people/group of people involved.

The sample describes a portion taken out of the population.

Thus, in this case study, the population is all men in the country

The sample is the 1,002 men selected.

Answer:

Online Real Estate Investment Opportunities

Hiring a Property Management Company

Make Sure There's Enough Money Available

Calculate Your Expenses

You Should Earn roughly 10% After Costs and Income are Calculated

Step-by-step explanation:

hope it helps

mark me brainliest

The angle of depression from the top of the flag pole to point A is 36.2 degrees.

From trigonometric ratio: cos(θ) = Adjacent / Hypotenuse

Given that;

cos(θ) = Adjacent / Hypotenuse

Cos(θ) = 25ft/31ft

Cos(θ) = 0.80645

θ = cos⁻¹( 0.80645 )

θ = 36.2°

Therefore, the angle of depression from the top of the flag pole to point A is 36.2 degrees.

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Therefore, to make the game fair, you should earn a profit of $3 when you win.

To determine the profit you should earn when you win in order for the game to be fair, we need to consider the overall expected value.

In this gambling game, you win 25% of the time and lose 75% of the time. Let's assume that when you win, you earn a profit of P dollars. When you lose, you lose $1.

The expected value can be calculated as follows:

Expected Value = (Probability of Winning * Profit) + (Probability of Losing * Loss)

Since the game should be fair, the expected value should equal zero. Thus, we can set up the equation:

0 = (0.25 * P) + (0.75 * (-1))

Simplifying the equation:

0 = 0.25P - 0.75

0.75 = 0.25P

P = 0.75 / 0.25

P = 3

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Answer:

angle DGC

Step-by-step explanation:

you know that because if angle FGE is 90 then you knwo all the other 4 are  as well

the picture explains more

hope it helpes

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Given the number line, it appears that in every 1/2 of a number, there are 5 bars in it. And in every 5 bars, 4 bars were shaded.

Adding the number of shades, we get:

4 + 4 + 4 = 12

Adding the total number of bars, we get:

5 + 5 + 5 = 15

The total number of bars sums up to be 3/2 in the number line.

Putting this into an equation, we get:

Therefore, the answer is 4/5 of 3/2. It is letter B.

Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is  8000 + 120C <= 27500

An inequality is a relationship that allows us to contrast two or more mathematical expressions.

Knowing that;

Each carton weighs 120 kg.

The container's maximum weight when loaded is 27500 kg.

Weight of the container as it is currently loaded: 8000 kg

Now that we have merged, we have;

Solution

because 8000 grams have already been loaded kilograms

into the container

each crate weighs 120 kilograms.

so 8000 + 120C <= 27500

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Answer:

big bodie built

Step-by-step explanation:

i used to be dusty

Based on the calculations, the value of the given prefix expression is equal to 2205.

The preorder traversal of a tree (T) are typically used in discrete mathematics to determine the value of a prefix expression on a specific expression tree.

For the preorder traversal of this tree (T), we would start from the right most expression:

Prefix expression = * + 3 + 3 ↑ 3 + 3 3 3

Prefix expression = * + 3 + 3 ↑ 3 6 3

Prefix expression = * + 3 + 3  3⁶  3

Prefix expression = * + 3 3 729 3

Prefix expression = * + 3 732 3

Prefix expression = * 735 3   ⇒ 735 × 3

Value = 2205.

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Complete Question:

Given the following prefix expression:

* + 3 + 3 ↑ 3 + 3 3 3

What is the value of the prefix expression?

Answer:

\(33.8^{\circ}\)

Step-by-step explanation:

\(\sin x=\frac{10}{18} \implies x=\arcsin(10/18) \approx 33.8^{\circ}\)

Answer:

Slope is -2, y-intercept is 2

Step-by-step explanation:

The formula for slope is y2-y1/x2-x1, therefore:

-6-(-2)/4-2 = -4/2 = -2

As for the y-intercept, you can easily follow the pattern of the table. If y increases by 4 every time x increases by 2, you could count down (or because we're in the negatives, you'd technically count up):

-2+4 = 2

Answer:

Poor physical health can lead to an increased risk of developing mental health can negatively impact on Physical health leading to an increased risk of some conditions

Step-by-step explanation:

The association between mental and physical health are poor mental is a risk factor for chronic physical conditions . if this is not correct don't report me or blame me just trying to help ......

Asaad having median salary makes more money in comparison to Amahle who makes minimum salary.

From the attached box plot we have,

Box plot always shows,

First Minimum → Lower quartile → Median → Upper quartile → Maximum

The minimum salary for an actuary is equals to

Approximately 35 dollars

And the median salary for a CPA from the box plot is equals to,

Approximately 60 dollars

Here , by comparing the both the values we have,

Median salary for CPA (60 dollars ) is greater than minimum salary for actuary ( 35 dollars ).

The median salary for a CPA is typically higher than the minimum salary for an actuary.

Therefore, Asaad representing median salary makes more money than Amahle .

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The above question is incomplete, the complete question is:

Amahle makes the minimum salary for an actuary. Asaad makes the median salary for a CPA. Who makes more money?

Box plot is attached.

Answer:

4 pencils

Step-by-step explanation:

Note=  pencils costing 0. 90p

Given data

Balance= £10

pen= 3*1.45= £4.35

pencils=0.90p

change= £2.05

2.05= 10-4.35-90p

solve for p

2.05= 5.65-90p

collect like terms

5.65-2.05= 0.90p

3.6=90p

divide both sides by 90

p=3.6/0.90

p=4

Answer:

This is a fraction equal to6 miles ÷ 3 minutesWe want a unit rate where1 is in the denominator,so we divide top and bottom by 36 miles÷ 33 minutes÷ 3=2 miles1 minute=2 milesminute= 2 miles per minute

Step-by-step explanation:

the answer is 2 miles per minute

Answer:

Step-by-step explanation:

Answer:

Answer on a graph

Answer:

3+4=7

3/7*184=552/7=78.86

4/7*184=736/7=105.14

Answer:

2.02

2.15

0.13

Step-by-step explanation:

Fastest time = smallest value =  2.02 secs

Slowest time = largest value = 2.15 secs

Range = largest value - smallest value = 2.15 - 2.02 = 0.13 secs

Answer:

2.02

2.15

0.13

Step-by-step explanation:

The guy/gal/person above me is correct

Using binomial probability, the probability of having exactly 4 dice on 4, 5 or 6 is 5/32.

Using binomial probability, we can calculate the probability that out of the 5 dice thrown, the probability of having exactly 4 dice on 4, 5 or 6 can be calculated as;

\(P(X=k) = C(n, k) * p^k * (1-p)^(^n^-^k^)\)

In the given data;

n = 5

k = 4

p = 3/6 = 1/2

Using the binomial probability formula, we can calculate:

P(X=4) = C(5, 4) * (1/2)⁴ * (1 - 1/2)⁵⁻⁴

P(X=4) = 5 * (1/2)⁴ * (1/2)¹

P(X=4) = 5 * (1/16) * (1/2)

P(X=4) = 5/32

Therefore, the probability that exactly 4 dice land on a 4, 5, or 6 when rolling five fair dice is 5/32.

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Answer:

x = 3/9

= 1/3

Step-by-step explanation:

i did this assignment and got it right