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mamaluj [8]
3 years ago
14

Write the contrapositive of the conditional statement. If it is January, then there are 31 days this month.

Mathematics
2 answers:
guajiro [1.7K]3 years ago
8 0

Answer:

If there are not 31 days this month, then it is not January.

Step-by-step explanation:

Contrapositive of the conditional statement means switching the hypothesis and conclusion of a conditional statement and negating both.

Given statement is :

If it is January, then there are 31 days this month.

Its contrapositive will be :

If there are not 31 days this month, then it is not January.

kifflom [539]3 years ago
5 0
If there aren't 31 days this month, then it isn't January. 

Hope this helps!
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a.  X~N(2,885, 651)

b.  0.086291

c.  0.00058

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a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting  the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

P(X

#substitute the given values in the formula to solve for P:

P(X

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058

Hence, the proportion of customers consuming over  5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

-We equate this to the formula to solve for the mean consumption:

0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09

Hence, the least amount of calories consumed to qualify for the award is 3213.10 calories.

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