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krek1111 [17]
3 years ago
6

Define the proper and improper subsets?

Mathematics
2 answers:
natima [27]3 years ago
8 0
An improper subset is a subset containing every element of the original set. A proper subset contains some but not all of the elements of the original set.

Example: For example, consider a set {1,2,3,4,5,6}. Then {1,2,4} and {1} are the proper subset while {1,2,3,4,5} is an improper subset.
Lana71 [14]3 years ago
4 0

Answer: A proper subset is one that contains few elements of the original set whereas an improper subset, contains every element of the original set along with the null set.

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A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past
Vadim26 [7]

Answer:

We conclude that deluxe tire averages less than 50,000 miles before it needs to be replaced which means that the claim is not supported.

Step-by-step explanation:

We are given that a particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8000.

From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9800 miles.

<u><em>Let </em></u>\mu<u><em> = average miles for deluxe tires</em></u>

So, Null Hypothesis, H_0 : \mu \geq 50,000 miles   {means that deluxe tire averages at least 50,000 miles before it needs to be replaced}

Alternate Hypothesis, H_A : \mu < 50,000 miles    {means that deluxe tire averages less than 50,000 miles before it needs to be replaced}

The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about population standard deviation;

                                  T.S.  = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean lifespan = 46,500 miles

            \sigma = population standard deviation = 8000 miles

            n = sample of tires = 28

So, <u><em>test statistics</em></u>  =  \frac{46,500-50,000}{\frac{8000}{\sqrt{28} } }

                               =  -2.315

The value of the test statistics is -2.315.

Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is less than the critical value of z as -2.315 < -1.6449, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that deluxe tire averages less than 50,000 miles before it needs to be replaced which means that the claim is not supported.

4 0
3 years ago
Lisa ran around a rectangular field 150 m long and 50 m wide at an average speed of 100 m/min. How long did she take to complete
Anarel [89]

Answer:

20 minutes

Step-by-step explanation:

To make one round of the field, Lisa will have to cover the entire perimeter of the field.

The perimeter of a rectangle = 2(l+w) Where L = length and W = width.

The multiplication of 2 means two lengths and widths that each rectangle has. The perimeter of the field = 2(150 +50) = 400m

Lisa's average running speed = 100m/min

The time taken to cover one round of the field or one perimeter of the field = 400/100 = 4 minutes.

To cover 5 rounds or 5 perimeters Lisa will take 5x4 minutes = 20 minutes.

6 0
3 years ago
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Question 5 of 10
Darina [25.2K]

Answer:

x= 38

Step-by-step explanation:

add 34 to each side of the equation.

which will give you x= 38

done!

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Work out the surface area of this solid prism.<br> 29cm<br> 25cm<br> 20cm<br> 40cm<br> 36cm
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Is there a picture that goes with this?
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S_A_V [24]
(3a-5) - (a+3)
Subtract a from 3a while subtracting 3 from 5
Final Answer: 2a - 8
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