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1 year ago

What is the measure of x?

Mathematics

1 answer:

marin [14]1 year ago

8 0

Answer:

$x = 75\degree$

Step-by-step explanation:

In $\triangle BDH,\: \angle x$ is the exterior angle.

$\implies x = 36\degree + 39\degree$ (By exterior angle theorem)

$\implies x = 75\degree$

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2 years ago

Y is directly proportional to x.

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2 years ago

Read 2 more answers

The lengths of lumber a machine cuts are normally distributed with a mean of 106 inches and a standard deviation of 0.3 inch. (

Vinvika [58]

Answer:

a) $P(X>106.11)=P(\frac{X-\mu}{\sigma}\frac{106.11-106}{0.3})=P(z>0.37)$

And we can find this probability with the complement rule:

$P(z>0.37)=1-P(z$

b) $z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}= 2.431$

And if we use the z score we got:

$P(z>2.431) =1-P(z$

Step-by-step explanation:

Let X the random variable that represent the lengths of a population, and for this case we know the distribution for X is given by:

$X \sim N(106,0.3)$

Where $\mu=106$ and $\sigma=0.3$

Part a

We are interested on this probability

$P(X>106.11)$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

And using this formula we got:

$P(X>106.11)=P(\frac{X-\mu}{\sigma}\frac{106.11-106}{0.3})=P(z>0.37)$

And we can find this probability with the complement rule:

$P(z>0.37)=1-P(z$

Part b

For this case we select a sample of n =44 and the new z score formula is given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score we got:

$z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}= 2.431$

And if we use the z score we got:

$P(z>2.431) =1-P(z$

6 0

2 years ago

The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 12 cm, the length of a radius of the circle i

nasty-shy [4]

Answer:

60cm^2

Step-by-step explanation:

We assume that is a circumscribing quadrilateral, rather than one that is circumscribed. It is also called a "tangential quadrilateral" and its area is ...

K = sr

where s is the semi-perimeter, the sum of opposite sides, and r is the radius of the incircle.

K = (12 cm) (5cm) = 60 cm²

_____

A quadrilateral can only be tangential if pairs of opposite sides add to the same length. Hence the given sum is the semiperimeter.

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2 years ago

A chemist has two alloys, one of which is 15% gold and 20% lead and the other which is 30% gold and 50% lead. How many grams of

vlabodo [156]

Answer: 490 grams of the first alloy should be used.

30 grams of the second alloy should be used.

Step-by-step explanation:

Let x represent the weight of the first alloy in grams that should be used.

Let y represent the weight of the second alloy in grams that should be used.

A chemist has two alloys, one of which is 15% gold and 20% lead. This means that the amount of gold and lead in the first alloy is

0.15x and 0.2x

The second alloy contains 30% gold and 50% lead. This means that the amount of gold and lead in the second alloy is

0.3y and 0.5y

If the alloy to be made contains 82.5 g of gold, it means that

0.15x + 0.3y = 82.5 - - - - - - - - - - - -1

The second alloy would also contain 113 g of lead. This means that

0.2x + 0.5y = 113 - - - - - - - - - - - - -2

Multiplying equation 1 by 0.2 and equation 2 by 0.15, it becomes

0.03x + 0.06y = 16.5

0.03x + 0.075y = 16.95

Subtracting, it becomes

- 0.015y = - 0.45

y = - 0.45/- 0.015

y = 30

Substituting y = 30 into equation 1, it becomes

0.15x + 0.3 × 30 = 82.5

0.15x + 9 = 82.5

0.15x = 82.5 - 9 = 73.5

x = 73.5/0.15

x = 490

6 0

2 years ago