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2 years ago

The windscreen wiper of a car sweeps

Mathematics

1 answer:

AVprozaik [17]2 years ago

6 0

Answer:

A ≈ 530 cm²

Step-by-step explanation:

The swept area equals the total area covered by the blade minus the unswept area.

The area of a sector with radius r and angle θ is:

A = (θ / 360) πr²

So the swept area is:

A = (θ / 360) πR² − (θ / 360) πr²

A = (θ / 360) π (R² − r²)

A = (150 / 360) π (21² − 6²)

A ≈ 530 cm²

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In a recent year, Washington State public school students taking a mathematics assessment test had a mean score of 276.1 and a s

Oksi-84 [34.3K]

Answer:

a) $\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

b) From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

c) $P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

$P(Z\geq2.070)=1-P(Z$

Step-by-step explanation:

Let X the random variable the represent the scores for the test analyzed. We know that:

$\mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4$

And we select a sample size of 64.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Part a

For this case the mean and standard error for the sample mean would be given by:

$\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

Part b

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

Part c

For this case we want this probability:

$P(\bar X \geq 285)$

And we can use the z score defined as:

$z=\frac{\bar x -\mu}{\sigma_{\bar x}}$

And using this we got:

$P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

And using a calculator, excel or the normal standard table we have that:

$P(Z\geq2.070)=1-P(Z$

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3 years ago

The following formula can be used to find the distance that a person has run.

Mrrafil [7]

So distance = rate × time. You would do 3/4 × 5.5, which would get you 4.125.

8 0

3 years ago

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Last year, 400 signed up to take a virtual kickboxing class. This year, there was a 5% increase in registrations. How many peopl

ale4655 [162]

Answer:

420 people

Step-by-step explanation:

400*1.05=420

3 0

3 years ago

Find the shaded area of each figure, round your answer to one decimal place if necessary

Annette [7]

<h2>area of shaded portion = 49.5 yd²</h2><h2>____________________</h2>

<u>Step-by-step explanation:</u>

radius of circle = 5 yd ------ ( <em>g</em><em>i</em><em>v</em><em>e</em><em>n</em><em> </em><em>)</em>

height of triangle = 16 yd --- ( <em>g</em><em>i</em><em>v</em><em>e</em><em>n</em><em> </em><em>)</em>

base of triangle = 16 yd ----- ( <em>g</em><em>i</em><em>v</em><em>e</em><em>n</em><em> </em><em>)</em>

area of triangle = 1/2 × base × height

= 1/2 × 16 × 16

= 128 yd²

area of circle = π × radius²

= 3.14 × 5 × 5 --- ( π = 3.14 )

= 78.5 yd²

area of shaded portion = area of triangle - area of circle

area of shaded portion= 128 yd²-78.5 yd²

area of shaded portion = 49.5 yd²

<h2>--------------------------------------</h2><h2>PLEASE FOLLOW ME</h2>

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2 years ago

Vida correctly answered 18 of a 20 item test. Express her score in percent.

DerKrebs [107]

Her score in percent is 90%

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3 years ago

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