Here is a balanced hanger diagram in which a circle has a mass of 3 grams and a square has a mass of 2 grams.

The figure shows a flagpole and its shadow. The shadow has a length of 43 feet and the sun's rays make an angle of 30° with the

Nataliya [291]

Answer:

B, 25 ft

Step-by-step explanation:

This can be modeled as a triangle. Let x be the height of the flagpole. From the picture, we can see that tan30 = x/43. x = 43tan30 = 25 ft.

6 0

2 years ago

1. Identify the LCM for 6 and 18. O 36 O 6 O 18 O 108

Sphinxa [80]

Answer: 18

Step-by-step explanation: 6 x 3 = 18, 18 x 1 = 18

8 0

2 years ago

A single gram of a certain metallic substance has 0.52 grams of copper and 0.26 grams of zinc. The remaining portion of the subs

Vitek1552 [10]

First of all, if we have 1 gram of a substance that has 0.52 gram of copper and 0.26 gram of zinc, the remainder will be:

Since we know that the remaining portion of the material is nickel, we have 0.22 gram of metal.

Now, Ben estimates that 1 gram of the substance has 0.2 gram of nickel. To find how many grams of metal are in 35 grams of the material, we are going to multiply the grams of the substance by the gram of nickel:

We can conclude that according to Ben, 35 grams of the content has 7 grams of metal.

But we know that in 1 gram of the substance are not 0.2 gram of nickel but 0.22. So let's multiply the grams of the material by 0.22 to find the actual grams of nickel in it:

We can conclude that 35 grams of the substance have 7.7 grams of metal.

8 0

3 years ago

Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard

ziro4ka [17]

Answer:

a) $P(X$

b) $P(\bar X$

And using a calculator, excel ir the normal standard table we have that:

$P(Z$

c) Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

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".

Part a

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

$X \sim N(72,12.5)$

Where $\mu=72$ and $\sigma=12.5$

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:

$P(X$

Part b

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

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

The new z score is given by:

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

$P(\bar X$

And using a calculator, excel ir the normal standard table we have that:

$P(Z$

Part c

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

4 0

3 years ago

Please explain your answer too :D

NISA [10]

Answer:

43°

Step-by-step explanation:

The angle of a straight line is 180°, 62° and 75° of the angle is taken so what is remaining is the angle for BEC.

180-(62+75)

180-137

43°

7 0

2 years ago