It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work in temperatures of 200-500 degrees. In a test of one type of mask, 24 of 55 were found to have their lenses pop out at 325 degrees. Construct and interpret a 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees.

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Answer 1

Answer:

Answer:

The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{(\pi(1-\pi))/(n)}$

In which

z is the zscore that has a pvalue of $1 - (\alpha)/(2)$ .

For this problem, we have that:

$n = 55, \pi = (24)/(55) = 0.4364$

93% confidence level

So $\alpha = 0.07$ , z is the value of Z that has a pvalue of $1 - (0.07)/(2) = 0.965$ , so $Z = 1.81$ .

The lower limit of this interval is:

$\pi - z\sqrt{(\pi(1-\pi))/(n)} = 0.4364 - 1.81\sqrt{(0.4364*0.5636)/(55)} = 0.3154$

The upper limit of this interval is:

$\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.4364 + 1.81\sqrt{(0.4364*0.5636)/(55)} = 0.5574$

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A differential equation is given along with the field or problem area in which it arises. Classify it as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear.

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The question is incomplete. Here is the complete question.

A differential equation is given along with the field of problem area which it arises. Classify it as an ordinary differential equation (ODE) or a partial different equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear.

$x(d^(2)y )/(dx^(2) ) + (dy)/(dx) + xy = 0$ (aerodynamics, stress analysis)

Answer and Step-by-step explanation: The differential equation described above is anOrdinaryDifferentialEquation, because it has a definite set of variables: x and y.

It is of SecondOrder, since the highest derivative is of order 2: $(d^(2)y )/(dx^(2) )$

The differential equation is written as derivative of a function y in terms of x, which means: IndependentVariable is X and DependentVariable is Y.

As it is an ODE, the equation is Nonlinear, because y'' or $(d^(2)y )/(dx^(2) )$ is multiplied by a variable.

Final answer:

This question pertains to classifying and understanding differential equations in mathematics, specifically identifying whether it is an ordinary differential equation, determining its order, and identifying independent and dependent variables.

Explanation:

In mathematics, a differential equation is a mathematical equation that relates a function with its derivatives. An Ordinary Differential Equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term order of a differential equation is defined as the highest power of the derivative in the equation.

As an example, if we have an equation like dy/dx = x*y, it would be an ODE since it involves only one independent variable, 'x', and the dependent variable is 'y'. The order is one since the highest order derivative is dy/dx, and the equation is nonlinear because it does not meet the criteria for a linear ODE, which stipulates that the dependent variable and its derivatives are to the first power and are not multiplied together.

Learn more about Differential Equations here:

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Answer:

Its exponential

The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 145 sec and a standard deviation of 25 sec. The fastest 10% are to be given advanced training. What task times qualify individuals for such training? (Round the answer to one decimal place.)

Answers

Answer:

A task time of 177.125s qualify individuals for such training.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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

$Z = (X - \mu)/(\sigma)$

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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that:

A distribution that can be approximated by a normal distribution with a mean value of 145 sec and a standard deviation of 25 sec, so $\mu = 145, \sigma = 25$ .

The fastest 10% are to be given advanced training. What task times qualify individuals for such training?

This is the value of X when Z has a pvalue of 0.90.

Z has a pvalue of 0.90 when it is between 1.28 and 1.29. So we want to find X when $Z = 1.285$ .

$Z = (X - \mu)/(\sigma)$

$1.285 = (X - 145)/(25)$

$X - 145 = 32.125$

$X = 177.125$

A task time of 177.125s qualify individuals for such training.

For a field trip 9 students rode in cars andthe rest filled eight buses. How many
students were in each bus if 265 students
were on the trip?

Answers

Answer:

32 students were on each bus.

Step-by-step explanation:

First deduct 9 students from the total number: 265 - 9 = 256

Then divide the students among the total number of buses, which is 8: 256/8 = 32

So there are 32 students on each bus.

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Answers

Answer:

rewrite as improper fraction

then rewrite as multiplication

next multiply and put a non simplified answer

finally put a simplified answer including the correct sign

Step-by-step explanation:

You got this!

Over the past several months, the water level of a lake has been decreasing by 3% each week. If the highest water level before the decrease started was 520 ft, what was the level at the end of 8 weeks?