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3 years ago

Solve the following real-life problems.

Mathematics

1 answer:

Anika [276]3 years ago

4 0

Answer:

a) The two numbers are x = 11 and y = 41

b) Leon gets $33, Kokyangwuti gets $16.5, Jill gets $38 and Isaac gets $6.5

c) Elizabet started with $106

Step-by-step explanation:

These problems can be solved by systems of equations

I am going to say that the first number is x and the second number is y

The problem states that the sum of two numbers is 52. So x + y = 52.

The problem also states that one number is three less than quadruple the other number. So y = 4x - 3

We have the following system

1) x + y = 52

2) y = 4x - 3

Replacing 2) in 1)

x + 4x -3 = 52

5x = 55

x = 11

------

y = 4x - 3 = 4(11)-3 = 44-3 = 41

The two numbers are x = 11 and y = 41

I am going to say that x is how much money Leon gets, y is how much Kokyangwuti, z is how much Jill gets and w is how much Isaac gets.

Martha divides $94 amongst her four friends. So x + y + z + w = 94

Leon gets twice as much money as Kokyangwuti. So x = 2y.

Jill gets five more dollars than Leon, so z = 5 + x

Isaac gets ten less dollars than Kokyangwuti, so w = y-10

We have the following system:

1) x + y + z + w = 94

2) x = 2y

3) z = 5 + x

4) w = y - 10

I am going to replace 2) in 3), so we have z = 5 + 2y

Now i am going to replace 2), 3) and 4) in 1), so:

2y + y + 5 + 2y + y - 10 = 94

6y -5 = 94

6y = 99

y = $16.5

From 2): x = 2y = 2*16.5 = $33

From 3) z = 5 + x = 5 + 33 = $38

From 4): w = y - 10 = $16.5-10 = $6.5

So, Leon gets $33, Kokyangwuti gets $16.5, Jill gets $38 and Isaac gets $6.5

Elizabeth spent:

2 shirts for $22.99 each = $45.98

a drink for $2.02 = $2.02

2 books for $16 each = $32

In all, she spent 45.98 + 2.02 + 32 = $80

She has $26 left.

She started with $26 + $80 = $106.

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Misha Larkins [42]

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3 years ago

American adults are watching significantly less television than they did in previous decades. In 2016, Nielson reported that Ame

goldenfox [79]

Answer:

1. 0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.

2. 0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the normal distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\lambda$ is the mean in the given interval, which is the same as the variance.

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The Poisson distribution can be approximated to the normal with $\mu = \lambda, \sigma = \sqrt{\lambda}$

In 2016, Nielson reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day.

This means that $\lambda = 320n$ , in which n is the number of days.

1. Find the probability that an average American adult watches more than 309 minutes of television per day.

One day, so $\mu = 320, \sigma = \sqrt{320} = 17.89$

This probability is 1 subtracted by the pvalue of Z when X = 309. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{309 - 320}{17.89}$

$Z = 0.61$

$Z = 0.61$ has a pvalue of 0.729

1 - 0.729 = 0.271

0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.

2. Find the probability that an average American adult watches more than 2,250 minutes of television per week.

$\mu = 320*7 = 2240, \sigma = \sqrt{2240} = 47.33$

This is 1 subtracted by the pvalue of Z when X = 2250. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2250 - 2240}{47.33}$

$Z = 0.21$

$Z = 0.21$ has a pvalue of 0.583

1 - 0.583 = 0.417

0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.

6 0

4 years ago

The diagram shows an awning on the front of a building. The top of the awning makes a 40° angle with the building. The base of t

slamgirl [31]

Answer:

Height of the awning = 9.52 feet

Step-by-step explanation:

For better understanding of the solution, see the attached diagram of the problem :

According to the figure, AB is the height of the awning

Now, the base of awning will be perpendicular to the building

⇒ m∠ABC = 90°

In ΔABC, By using angle sum property of a triangle

m∠ABC + m∠ACB + m∠BAC = 180°

⇒ m∠ACB = 50°

$Now,\tan 50=\frac{Perpendicular}{Base}\\\\tan 50=\frac{AB}{8}\\\\\implies AB=8\times \tan 50\\\\\bf\implies AB=9.52 \textbf{ feet}$

Hence, Height of the awning = 9.52 feet

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3 years ago

What is the slope of the line in the graph

nikitadnepr [17]

Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

a 2015 Gallup poll of 1,627 adults found that only 22% felt fully engaged with their mortgage provider ?

Gala2k [10]

Answer:

1. The population of interest on this case is people who felt fully engaged with their mortgage provider

2. On this case the sample size is 1627 the number of people sample selected.

3. $ME=1.96\sqrt{\frac{0.22 (1-0.22)}{1627}}=0.0201$

4. The 95% confidence interval would be given (0.1999;0.2401).

5. We are confident 95% that the true proportion of proportion is between 0.1999 and 0.2401.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

1. What is the population?

The population of interest on this case is people who felt fully engaged with their mortgage provider

2. What is the sample size?

On this case the sample size is 1627 the number of people sample selected.

3. What is the 95% margin of error?

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If we replace we got:

$ME=1.96\sqrt{\frac{0.22 (1-0.22)}{1627}}=0.0201$

4. What is the 95% confidence interval?

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.22 - 1.96 \sqrt{\frac{0.22(1-0.22)}{1627}}=0.1999$

$0.22 + 1.96 \sqrt{\frac{0.22(1-0.22)}{1627}}=0.2401$

And the 95% confidence interval would be given (0.1999;0.2401).

5. Express your answer to 4 in a meaningful sentence.

We can conclude this:

We are confident 95% that the true proportion of proportion is between 0.1999 and 0.2401.

7 0

3 years ago