All categories

2 years ago

6 use fermat’s theorem to find a number x between 0 and 28 with x85 congruent to 6 modulo 29. (

1 answer:

7 0

If

$x^{85}\equiv6\mod29$

then we have

$\dfrac{x^{85}}6\equiv1\mod29$

By Fermat's little theorem, if $a$ is not divisible by a prime $p$ , then

$a^{p-1}\equiv1\mod p$

This works for $x=6$ ; in this case, we would have

$\dfrac{6^{85}}6=6^{84}=\left(6^3\right)^{28}=\left(6^3\right)^{29-1}\equiv1\mod29$

You might be interested in

The mean yearly rainfall in Sydney, Australia, is about 134 mm and the standard deviation is about 66 mm ("Annual maximums of,"

svetlana [45]

Answer:

At least 202.44 mm in the top 15%.

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

$\mu = 134, \sigma = 66$

How many yearly mm of rainfall would there be in the top 15%?

At least X mm.

X is the 100-15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037.

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

$1.037 = \frac{X - 134}{66}$

$X - 134 = 66*1.037$

$X = 202.44$

At least 202.44 mm in the top 15%.

5 0

2 years ago

Suppose pieces of chocolate pie served at a restaurant average 350 calories with a standard deviation of 20 calories. Calories h

Over [174]

Answer:

Step-by-step explanation:

Suppose pieces of chocolate pie served at a restaurant average 350 calories with a standard deviation of 20 calories. Calories have a Normal distribution due to inexact cutting of the pies. Which graph represents the proportion of pieces of pie that have more than 375 calories.

Answer: The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and for a negative z score means the raw score is below the mean. The z score is given as:

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

Given that: μ = 350 calories, σ = 20 calories, x > 375

$z=\frac{x-\mu}{\sigma}\\\\z=\frac{375-350}{20}=1.25$

From the graph, The shaded area represents the proportion of pieces of pie that have more than 375 calories

From the normal distribution table, P(x > 375) = P(z > 1.25) = 1 - P(z < 1.25)

= 1 - 0.8944 = 0.1056 = 10.56%

3 0

2 years ago

Which of the following expressions are equivalent to 48a^3-75a? Select all that apply. Answer 1) 3(48a^3-75a). Answer 2) 3a(16a^

Ainat [17]

The answer is 4) 3a(4a+5)(4a-5)

8 0

2 years ago

Read 2 more answers

Jason bought a table for $98.00. The finance charge was $12 and she paid for it over 10 months. Use the formula, and calculate h

lutik1710 [3]

Answer:2.00

Step-by-step explanation:

approximate apr=(finance charge divided by#months)12 / amount financed

8 0

2 years ago

students at river view middle school are allowed to wear two different colors of uniform shirts. A survey of students at the sch

Vladimir79 [104]

Answer:

18 students are likely to be wearing red

Step-by-step explanation:

From the question, we know a student either wears red , or blue, with the probability of a student wearing red is 3 times more probable than wearing white.

So, let’s say out of the 24 students, x of them are wearing white. What this practically mean is that 3 * x = 3x of the students would be expected to be wearing red.

Now, adding the number of people wearing red and white together in terms of x, we have x + 3x = 4x

We equate this to 24; 4x = 24 and x = 24/4; x = 6

The number wearing red probably is 3 * x = 3 * 6 = 18 people

5 0

2 years ago