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3 years ago

X/4 - y/3 =1 X and Y axis standard form

Mathematics

1 answer:

Semenov [28]3 years ago

5 0

Answer:

Step-by-step explanation:

x/4 - y/3 = 1..multiply everything by the LCD....which is 12

3x - 4y = 12 <== standard form

=====================================

if it makes it easier for u, x/4 is the same as (1/4)x and y/3 is the same as (1/3)y

so ur problem can be written as : (1/4)x - (1/3)y = 1....multiply by 12

12(1/4)x - 12(1/3)y = 12(1)

(12/4)x - (12/3)y = 12.....reduce

3x - 4y = 12

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Which expression represents the phrase, "half the sum of 10 and a number"? 12x+10

Nonamiya [84]

I think it is 12(10+x)

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3 years ago

What is a transformation that proportionally reduces or enlarges a figure.

Ratling [72]

Answer: Dilation is a transformation that proportionally reduces or enlarges a figure.

Step-by-step explanation:

A dilation a transformation that changes the size of the shape by using scale factor in particular ways .

It stretches or shrinks the actual figure. It produces similar figures.

Since the corresponding sides of similar figures are in proportion.

⇒ It proportionally reduces or enlarges a figure.

Hence, A dilation is a transformation that proportionally reduces or enlarges a figure.

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3 years ago

How does the volume of a sphere compare to that of the volume of a cylinder? What would you say the scale factor for Vol sphere:

borishaifa [10]

Answer:

The volume of a sphere is 2/3 times the volume of a similar cylinder

Scale factor : 2/3

Step-by-step explanation:

Let us consider a sphere of radius r. The volume of the sphere will be given as

$V_{s}=\frac{4}{3} \pi r^{3}$

Similarly, let us consider a cylinder with its height being twice the radius of the sphere. We will have its volume given as:

$V_{c}=\pi r^{2}h$

but h = 2r

Hence we have

$V_{c}= 2\pi r^{3}h$

We can divide the two volumes to get a constant that links them together

$\frac{V_{s}}{V_{c}}=\frac{\frac{4}{3} \pi r^{3}}{2\pi r^{3}h}$

this will give us 2/3

Hence the scale factor for Vol sphere: Vol cylinder is 2/3

3 0

3 years ago

MUST ANSWER ALL PARTS!!!!

dsp73

Hello there,

The outlier of the data set is 92. Lets first find everything with the outlier.
Mean: 60.08
Median: 57
Mode: 52
Range:46

Now let's take out the outlier of the set and see the difference.
Mean: 54.27
Median:56
Mode: 52
Range: 15

So as we can see without the outlier everything is closer together. The outlier shouldn't be included because that makes the entire set screwed up. The data is more accurate without the outlier.

Hope this helps!

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3 years ago

A ski lift is designed with a total load limit of 20,000 pounds. It claims a capacity of 100 persons. An expert in ski lifts thi

Yanka [14]

Answer:

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n values of a distribution, the mean is $\mu \times n$ and the standard deviation is $\sigma\sqrt{n}$

An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.

This means that $\mu = 200*100 = 20000, \sigma = 30\sqrt{100} = 300$

If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload

Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20000 - 20000}{300}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

1 - 0.5 = 0.5

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

5 0

3 years ago