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3 years ago

In the diagram, line x|| line y. Find the angle measures below.

Mathematics

1 answer:

Yanka [14]3 years ago

5 0

Answer:

<1 = 95

<2 =85

Step-by-step explanation:

<1 = 95

They are alternate exterior angles and alternate exterior angles are equal when the lines are parallel

<1 + <2 = 180 since they form a straight line

95+ <2 =190

Subtract 95 from each side

95-95+<2 =180-95

<2 =85

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Consider a binomial experiment with 15 trials and probability 0.35 of success on a single trial.

DedPeter [7]

Answer:

$P(X = 10 ) = 0.0096$

$P(X = 10 ) = 0.0085$

Option A is correct

Step-by-step explanation:

From the question we are told that

The sample size is n = 15

The probability of success is $p = 0.35$

The number of success we are considering is r = 10

Now the probability of failure is mathematically evaluated as

$q = 1- p$

substituting value

$q = 1- 0.35$

$q = 0.65$

Now using the binomial distribution to find the probability of exactly 10 successes we have that

$P(X = r ) = [\left n } \atop {r}} \right. ] * p^r * q^{n- r}$

substituting values

$P(X = 10 ) = [\left 15 } \atop {10}} \right. ] * p^{10}* q^{15- 10}$

Where $[\left 15 } \atop {10}} \right. ]$ mean 15 combination 10 which is evaluated with a calculator to obtain

$[\left 15 } \atop {10}} \right. ] = 3003$

$P(X = 10 ) = 3003 * 0.35 ^{10}* 0.65^{15- 10}$

$P(X = 10 ) = 0.0096$

Now using the normal distribution to approximate the probability of exactly 10 successes, we have that

$P(X = r ) = P( r < X < r )$

Applying continuity correction

$P(X = r ) = P( r -0.5 < X < r +0.5)$

substituting values

$P(X = 10) = P( 10-0.5 < X < 10+0.5)$

$P(X = 10 ) = P( 9.5 < X < 10.5)$

Standardizing

$P(X = r ) = P( \frac{9.5 - \mu }{\sigma } < \frac{X - \mu }{\sigma } < \frac{10.5 - \mu}{\sigma } )$

The where $\mu$ is the mean which is mathematically represented as

$\mu = n * p$

substituting values

$\mu = 15 * 0.35$

$\mu = 5.25$

The standard deviation is evaluated as

$\sigma = \sqrt{n * p * q }$

substituting values

$\sigma = \sqrt{15 * 0.35 * 0.65 }$

$\sigma = 1.8473$

Thus

$P(X = 10 ) = P( \frac{9.5 - 5.25 }{1.8473 } < \frac{X - 5.25 }{1.8473 } < \frac{10.5 - 5.25}{1.8473 } )$

$P(X = 10 ) = P( 2.30 < Z < 2.842 )$

$P(X = 10 ) = P(Z < 2.842 ) - P(Z < 2.30 )$

From the normal distribution table we obtain the $P(Z < 2.841)$ as

$P(Z < 2.841) = 0.99775$

And the $P(Z < 2.30)$

$P(Z < 2.30) = 0.98928$

There value can also be obtained from a probability of z calculator at (Calculator dot net website)

$P(X = 10) = 0.99775 - 0.98928$

$P(X = 10 ) = 0.0085$

Looking at the calculated values for question a and b we see that the values are fairly different.

8 0

4 years ago

A box is to be constructed with a rectangular base and a height of h cm. the length, l, of the box is 10 cm, and the width, w, i

vivado [14]

There are several information's already given in the question. based on those information's, the answer can be easily determined.
Height of the box = h cm
Length of the box = 10 cm
Width of the box = 2h
Then
Volume of the box = Length * height * width
= 10 * h * 2h cubic cm
= 20h^2 cm^3
I hope that the above procedure is clear enough for you to understand and it has actually come to your desired help.

5 0

3 years ago

In ΔEFG, the measure of ∠G=90°, EF = 38 feet, and FG = 30 feet. Find the measure of ∠F to the nearest degree.

Mamont248 [21]

Answer:

∠F = 42° to the nearest degree

Step-by-step explanation:

In this question, we are asked to calculate the value of the angle.

Kindly note that since one of the angles we are dealing with in the triangle is 90°, this means that the triangle is a right-angled triangle

Please check attachment for the diagrammatic representation of the triangle

From the diagram, we can identify that the EF is the hypotenuse and the length FG is the adjacent. Thus , the appropriate trigonometric identity to use is the cosine

mathematically;

Cosine of an angle = length of adjacent/length of hypotenuse

$Cos F = \frac{30}{38}\\Cos F = 0.7895\\F = Cos^{-1} 0.7895\\$