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4 years ago

|1-3x| + 6 = 29 Justify Each Step With An Algebraic Property Please show work =)

1 answer:

8 0

X= -23/3, 23/3 calculate absolute value move constant to the right subtract those two numbers divide both by 3 then you get the answer i put up there

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Which pairs of angles are supplementary?

vfiekz [6]

Supplementary angles = Angles that add up to 180°.

∠5 + ∠7 = 180° ← supplementary angles

∠1 = ∠5
Since ∠5 + ∠6 = 180°
⇒ ∠1 and ∠6 will also be 180° . ← supplementary angles

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Answer: ∠5 + ∠7 (Answer D) and ∠1 + ∠6 (Answer A)
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7 0

4 years ago

Read 2 more answers

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a

shepuryov [24]

Answer:

a) $P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

b) $P(X>77)=P(\frac{X-\mu}{\sigma}>\frac{77-\mu}{\sigma})=P(Z>\frac{77-75}{10})=P(z>0.2)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.2)=1-P(Z$

c) $z = \frac{70-75}{\frac{10}{\sqrt{16}}}= -2$

$z = \frac{80-75}{\frac{10}{\sqrt{16}}}= 2$

And we can find this probability with this difference:

$P(-2$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

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

$X \sim N(75,10)$

Where $\mu=75$ and $\sigma=10$

Part a

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

Part b

$P(X>77)=P(\frac{X-\mu}{\sigma}>\frac{77-\mu}{\sigma})=P(Z>\frac{77-75}{10})=P(z>0.2)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.2)=1-P(Z$

Part c

For this case we select a sample size of n =16. and we want this probability:

$P(70 < \bar X$

We know that the distribution for the sample mean $\bar X$ is given by:

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

And we can find the z scores for the limits like this:

$z = \frac{70-75}{\frac{10}{\sqrt{16}}}= -2$

$z = \frac{80-75}{\frac{10}{\sqrt{16}}}= 2$

And we can find this probability with this difference:

$P(-2$

6 0

4 years ago

Scientists studying dolphin echolocation simulate the projection of a bottlenose dolphin's clicking sounds using computer

lina2011 [118]

Step-by-step explanation:

The equation of a parabola with focus at (h, k) and the directrix y = p is given by the following formula:

(y - k)^2 = 4 * f * (x - h)

In this case, the focus is at the origin (0, 0) and the directrix is the line y = -1.3, so the equation representing the cross section of the reflector is:

y^2 = 4 * f * x

= 4 * (-1.3) * x

= -5.2x

The depth of the reflector is the distance from the vertex to the directrix. In this case, the vertex is at the origin, so the depth is simply the distance from the origin to the line y = -1.3. Since the directrix is a horizontal line, this distance is simply the absolute value of the y-coordinate of the line, which is 1.3 inches. Therefore, the depth of the reflector is approximately 1.3 inches.

4 0

2 years ago

Find the sides on this 30-60-90 triangle

Serga [27]

Answer:

A = 3, B = 5.2

Step-by-step explanation:

i think that is right, i hope this helps.

6 0

3 years ago

Add. 588 + 130 + (–642) A. –76 B. 76 C. 1360 D. –1360

Licemer1 [7]

588+130=718

718-642=76

B is the answer.

4 0

4 years ago

Read 2 more answers