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2 years ago

6 clients are throwing a party. Each cake serves 24 servings and has a party of 70 +3staff how many cakes are needed?

Mathematics

2 answers:

Airida [17]2 years ago

8 0

4 cakes are needed fjfnccnfn

tiny-mole [99]2 years ago

4 0

Answer:

3 cake were required to serve 73 staff members.

Step-by-step explanation:

Given : 6 clients are throwing a party. Each cake serves 24 servings and has a party of 70 +3 staff

To find : How many cakes are needed?

Solution :

Each cake serves 24 serving

i.e, 24 people served = 1 cake

1 people served = $\frac{1}{24}$ cake

party has 70+3 =73 staff members

73 people served = $\frac{73}{24}$ cake

73 people served = 3.04 cake

Approximately, 3 cake were required to serve 73 staff members.

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While standing on a highway overpass, Jennifer wonders what proportion of the vehicles that pass on the highway below are trucks

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2 years ago

During April of 2013, Gallup randomly surveyed 500 adults in the US, and 47% said that they were happy, and without a lot of str

Brilliant_brown [7]

Answer:

number of successes

$k = 235$

number of failure

$y = 265$

The criteria are met

The sample proportion is $\r p = 0.47$

$E =4.4 \%$

What this mean is that for N number of times the survey is carried out that the which sample proportion obtain will differ from the true population proportion will not more than 4.4%

$r = 0.514 = 51.4 \%$

$v = 0.426 = 42.6 \%$

This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%

Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

Yes our result would support the claim because

$\frac{1}{3 } \ of N < \frac{1}{2} (50\%) \ of \ N , \ Where\ N \ is \ the \ population\ size$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 500$

The sample proportion is $\r p = 0.47$

Generally the number of successes is mathematical represented as

$k = n * \r p$

substituting values

$k = 500 * 0.47$

$k = 235$

Generally the number of failure is mathematical represented as

$y = n * (1 -\r p )$

substituting values

$y = 500 * (1 - 0.47 )$

$y = 265$

for approximate normality for a confidence interval criteria to be satisfied

$np > 5 \ and \ n(1- p ) \ >5$

Given that the above is true for this survey then we can say that the criteria are met

Given that the confidence level is 95% then the level of confidence is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha =0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p}{n} }$

substituting values

$E = 1.96 * \sqrt{ \frac{0.47 (1- 0.47}{500} }$

$E = 0.044$

=> $E =4.4 \%$

What this mean is that for N number of times the survey is carried out that the proportion obtain will differ from the true population proportion of those that are happy by more than 4.4%

The 95% confidence interval is mathematically represented as

$\r p - E < p < \r p + E$

substituting values

$0.47 - 0.044 < p < 0.47 + 0.044$

$0.426 < p < 0.514$

The upper limit of the 95% confidence interval is $r = 0.514 = 51.4 \%$

The lower limit of the 95% confidence interval is $v = 0.426 = 42.6 \%$

This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%

Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

Yes our result would support the claim because

$\frac{1}{3 } < \frac{1}{2} (50\%)$

3 0

2 years ago

500 people are surveyed and asked to check the boxes that apply to them.

motikmotik

Answer:

1. A Venn diagram is attached. The amount of people that have health insurance and is confident about the economy is 287.

2. The amount of people that have health insurance and is not confident about the economy is 116.

3. The amount of people that have health insurance or is confident about the economy is 437.

Step-by-step explanation:

1) Using sets theory, we know:

U: 500 people surveyed

A: people who is confident in the economy

B: people that have health insurance

A' and B': people who is not confident in the economy and don't have health insurance.

A=321

B=403

A' and B' =63

In the attached picture we can see a Venn diagram that represents the situation. In order to obtain the intersection of both sets A∩B, we calculate:

(321 - x) + (403 - x) + x + 63 = 500

321 - x + 403 - x + x + 63 +x -500 = 500 +x - 500

321 + 403 + 63 -500 = x

x= 287

2) The amount of people that have health insurance and is not confident about the economy is given by the intersection of the complement of set A and set B:

A' ∩ B can be calculated as:

B - (A ∩ B)= 403 - 287= 116

3) The amount of people that have health insurance or is confident about the economy is given by:

(A∪B) = (A) + (B) - (A ∩ B)

(A∪B) = 321 + 403 - 287= 437

7 0

2 years ago