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3 years ago

HELP!!!

Mathematics

2 answers:

xz_007 [3.2K]3 years ago

6 0

Step-by-step explanation:

Given that the graph shows the normal distribution of the length of similar components produced by a company with a mean of 5 centimeters and a standard deviation of 0.02 centimeters.

A component is chosen at random, the probability that the length of this component is between 4.98 centimeters and 5.02

=P(|z|<1) (since 1 std dev on either side of the mean)

=2(0.3418)

=0.6826

=68.26%

The probability that the length of this component is between 5.02 centimeters and 5.04 centimeters is

=P(1<z<2) (since between 1 and 2 std dev from the mean)

=0.475-0.3418

=0.3332

=33.32%

Yanka [14]3 years ago

5 0

Answer:

1) 68.3%

2)33.3%

Step-by-step explanation:

Given:

mean, x= 5 cm

Standard deviation, sd= 0.02 cm

probability that the length of this component is between 4.98 centimeters and 5.02 centimeters=?

probability that the length of this component is between 5.02 centimeters and 5.04 centimeters is =?

As the graph shows the normal distribution

a component is chosen at random, the probability that the length of this component is between 4.98 centimeters and 5.02 centimeters is about:

1 sd on either side of the mean on normal distributed graph means

P(|z|<1)

=2(0.3418)

=0.683

=68.3%

the probability that the length of this component is between 5.02 centimeters and 5.04 centimeters is about:

=P(1<z<2) (since between 1 and 2 std dev from the mean)

between 1 and 2 sd on either side of the mean on normal distributed graph means

P(1<z<2)

=0.47-0.342

=0.333

=33.3%!

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I have a right triangle. The hypotenuse is 12. The base is 7 and the other side is 9.7. The sin(x) is 0.014. Cos(x) is 0.99 and

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Answer:

$\sin(x)=\frac{\sqrt{95}}{12}=0.8122$

$\cos(x)=\frac{7}{12} \approx .5833$

$\tan(x)=\frac{\sqrt{95}}{7} \approx 1.3924$

$x=\sin^{-1}(\frac{\sqrt{95}}{12}) \approx 54.3147$ degrees.

I don't know what you want to round to but I can tell you are rounding...

Step-by-step explanation:

Soh Cah Toa is the acronym we will use to help us solve this.

This says sine is opposite over hypotenuse.

It also says cosine is adjacent over hypotenuse.

And finally tangent is opposite over adjacent.

Note: Opposite and adjacent can change depending on how you are looking at the triangle, like which angle you are referring to.

Let's look at x:

The side that is opposite, not touching, the angle whose measurement is x, is the side that has measurement $\sqrt{95} \approx 9.7$ .

I see you already found this measurement. This is really good. I might use the exact value for now and round at the end.

The side that is the hypotenuse no matter the angle you are referencing is always going to be opposite the angle whose measurement is 90 degrees. It is also the longest side (since it is opposite the largest angle). This side has measurement 12.

The hypotenuse will be one of the sides touching your angle you are referencing. The other side that is touching your angle is the adjacent side. This side has measurement 7.

Anyways let's plug into the definitions we had above:

$\sin(x)=\frac{\sqrt{95}}{12}$ (O/H)