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saw5 [17]
3 years ago
7

Select the postulate of equality or inequality that is illustrated.

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
4 0

Answer: comparison postulate.


Explanation.


The given inequality might be either 3 + 2 > 5 or 2 + 2 < 5. The reasoning and the result is the same for effects of this question.


The comparison postulate states that one and only one of the following statements is true: a = b, a > b, a < b.


This is, a is either equal, or greater than or less than b, but not equal and greater, or equal and less, or greater and less. One and only one of them is true.


So, since  3 + 2 = 5, the comparison postulate assures that the inequality cannot both be true. This is 3 + 2 is equal to 5, and not greater or less than 5.


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Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a margin of error of 1 mile
Llana [10]

Answer: 37

Step-by-step explanation:

Given : Significance level : \alpha:1-0.98=0.02

Critical value : z_{\alpha/2}=z_{0.01}=2.33

margin of error : E= 1 mile per gallon

Population standard deviation: \sigma=2.6 miles per gallon.

We know that when the population standard deviation is known then the formula to find the sample size is given by  :

n=(\dfrac{z_{\alpha/2}\times \sigma}{E})^2

n=(\dfrac{(2.33)\times 2.6}{1})^2=36.699364\approx37  [Round to the next whole number.]

Hence, the required number of automobiles should be used in the test = 37

7 0
4 years ago
If sin square theta = 0.75, then cos =
sergeinik [125]

Answer:

\cos\theta=\pm0.5

Step-by-step explanation:

Given:

\sin^2\theta=0.75

To find \cos\theta

Using trigonometric relations for sums and differences of squares of the ratios.

We know:

\sin^2\theta+\cos^2\theta =1

Plugging in  \sin^2\theta=0.75 in the above relation.

0.75+\cos^2\theta =1

Subtracting both sides by 0.75.

0.75+\cos^2\theta-0.75 =1-0.75

\cos^2\theta =0.25

Taking square root both sides.

\sqrt{\cos^2\theta} =\sqrt{0.25}

∴ \cos\theta=\pm0.5  (Answer)

6 0
3 years ago
A carpenter wants to expand a square room. The new room will have one side 4 feet longer and the adjacent side 6 feet longer tha
gogolik [260]

Answer:

  Dimensions of original room = 12 x 12 feet.

Explanation:

 Let the size of old square room be a x a.

 New dimension = ( a+4 ) x ( a + 6 )

   We have area of the new room will be 144 square feet greater than the area of the original room.

  So,     ( a+4 ) x ( a + 6 ) = a x a + 144

              a²+10a+24= a²+144

              10a = 120

                  a = 12 feet.

 Dimensions of original room = 12 x 12 feet.

 

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