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gulaghasi [49]
3 years ago
8

Louie is trying to find a rectangular canvas for his art project. Its height must measure 18 inches and form a 48° angle with th

e diagonal at the top of the canvas. What is the length of the diagonal of the canvas? Round your answer to the nearest inch.
Mathematics
1 answer:
KengaRu [80]3 years ago
8 0

Answer:

27 inches

Step-by-step explanation:

To find the length of the diagonal, we just need to use the cosine relation of the 48° angle.

The adjacent side to the angle is the height of the canvas, and the hypotenuse formed is the diagonal of the canvas. So, we have that:

cos(48) = height / diagonal

0.6691 = 18 / diagonal

diagonal = 18 / 0.6691 = 26.9 inches

Rounding to the nearest inch, the diagonal of the canvas measures 27 inches

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The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring t
gayaneshka [121]

Answer:

Answer for the question:

The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 69 and standard deviation 2.7.

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is given in the attachment.

Step-by-step explanation:

Download pdf
7 0
4 years ago
The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).
natita [175]

Answer:

68% of jazz CDs play between 45 and 59 minutes.

Step-by-step explanation:

<u>The correct question is:</u> The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

According to the 68-95-99.7 rule, what percentage of jazz CDs play between 45 and 59 minutes?

Let X = <u>playing time of jazz CDs</u>

SO, X ~ Normal(\mu=52, \sigma^{2} =7)

The z-score probability distribution for the normal distribution is given by;

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Now, according to the 68-95-99.7 rule, it is stated that;

  • 68% of the data values lie within one standard deviation points from the mean.
  • 95% of the data values lie within two standard deviation points from the mean.
  • 99.7% of the data values lie within three standard deviation points from the mean.

Here, we have to find the percentage of jazz CDs play between 45 and 59 minutes;

   For 45 minutes, z-score is =  \frac{45-52}{7}  = -1

   For 59 minutes, z-score is =  \frac{59-52}{7}  = 1

This means that our data values lie within 1 standard deviation points, so it is stated that 68% of jazz CDs play between 45 and 59 minutes.

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Answer:

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Step-by-step explanation:

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