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3 years ago

What is the difference between bounded above and bounded below?

1 answer:

8 0

The set EE is said to be bounded above if and only if there is an M∈RM∈R such that a≤Ma≤Mfor all a∈Ea∈E, in which case MM is called an upper bound of EE.A number ss is called a supremum of the set EE if and only if ss is an upper bbound of EE and s≤Ms≤M for all upper bounds MM of EE (In this case we shall say that EE has a finite supremum ss and write s=supEs=supE.

Let E⊂RE⊂R be nonempty.

the set EE is said to be bounded below if and only if there is an m∈Rm∈R such that a≥ma≥m for all a∈Ea∈E, in which case mm is called a lower bound of the set EE.A number tt is called an infimum of the set EE if and only if tt is a lower bound of EE and t≥mt≥m for all lower bounds mm of EE. In this case we shall say that EE has an infimum tt and write t=infE

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A laboratory experiment requires 2400 milligrams of sugar. How many kilograms of sugar does the experiment require?

telo118 [61]

Answer:

0.0024

Step-by-step explanation:

1 killogram=1000000

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3 years ago

Multiply: (49)(58)

IrinaVladis [17]

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3 years ago

A recent study found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports

hichkok12 [17]

Answer:

The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population

$t = 3.054$

The p-value is $p-value = P(Z > 3.054) = 0.0011291$

The conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The test statistics is

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 51$

The first sample mean is $\mu_1 = 36$

The second sample size is $n_2 = 41$

The second sample size is $\mu_2 = 25$

The first standard deviation is $\sigma _1 = 21.4 \ g$

The second standard deviation is $\sigma _2 = 12.8 \ g$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu_1 = \mu_ 2$

The alternative hypothesis is $H_a : \mu_1 > \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }$

=> $t = \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51} + \frac{ 12.8^2}{41} } }$

=> $t = 3.054$

The p-value is mathematically represented as

$p-value = P(Z > 3.054)$

Generally from the z table

$P(Z > 3.054) = 0.0011291$

=> $p-value = P(Z > 3.054) = 0.0011291$

From the values obtained we see that $p-value < \alpha$ so the null hypothesis is rejected

Thus the conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

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3 years ago

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Sergeu [11.5K]

Answer: the last option

Step-by-step explanation:

the top right is I, the top left is II, the bottom left is III, and the bottom right is IV

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3 years ago

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The Jaxon High School prom committee has 100 thumb drives to sell in a fundraiser. The function f(x) = 8x – 200 models their inc

Alina [70]

Answer:

25 = x

Step-by-step explanation:

Based on the equation we see that the thumb drives cost $200 which is why that is being subtracted. To calculate the break-even number of sales we need to make a total of 200 to cover the costs. We calculate this by matching the equation to 0 and solving for x...

0 = 8x - 200 ... add 200 on both sides

200 = 8x ... divide both sides by 8

25 = x

Finally, we can see that the committee will break even after selling 25 thumb drives which would make them $200 to cover all of their costs.

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2 years ago