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IRISSAK [1]
3 years ago
8

Find the missing side or angle.

Mathematics
1 answer:
Nina [5.8K]3 years ago
8 0

Answer:

a=4.1

Step-by-step explanation:

The Law of Cosines is given as:

a^2=c^2+b^2-2cb\cos A.

Plugging in given values, we get:

a^2=4^2+2^2-2\cdot 4 \cdot 2\cos 78^{\circ},\\a^2=16+4-16\cos 78^{\circ},\\a^2\approx \sqrt{16.673},\\a\approx \fbox{$4.1$}.

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What does the PErron-Frobenius Theorem say, and why is it useful?
Alex787 [66]

Answer:

Perron–Frobenius theorem for irreducible matrices. Let A be an irreducible non-negative n × n matrix with period h and spectral radius ρ(A) = r. Then the following statements hold. The number r is a positive real number and it is an eigenvalue of the matrix A, called the Perron–Frobenius eigenvalue.

5 0
3 years ago
Can someone give me the answers and step by step instructions please??
professor190 [17]

Answer:

-1,4,-7,10,...  neither

192,24,3,\frac{3}{8},...  geometric progression

-25,-18,-11,-4,...  arithmetic progression

Step-by-step explanation:

Given:

sequences: -1,4,-7,10,...

192,24,3,\frac{3}{8},...

-25,-18,-11,-4,...

To find: which of the given sequence forms arithmetic progression, geometric progression or neither of them

Solution:

A sequence forms an arithmetic progression if difference between terms remain same.

A sequence forms a geometric progression if ratio of the consecutive terms is same.

For -1,4,-7,10,...:

4-(-1)=5\\-7-4=-11\\10-(-7)=17\\So,\,\,4-(-1)\neq -7-4\neq 10-(-7)

Hence,the given sequence does not form an arithmetic progression.

\frac{4}{-1}=-4\\\frac{-7}{4}=\frac{-7}{4}\\\frac{10}{-7}=\frac{-10}{7}\\So,\,\,\frac{4}{-1}\neq \frac{-7}{4}\neq \frac{10}{-7}

Hence,the given sequence does not form a geometric progression.

So, -1,4,-7,10,... is neither an arithmetic progression nor a geometric progression.

For  192,24,3,\frac{3}{8},... :

\frac{24}{192}=\frac{1}{8}\\\frac{3}{24}=\frac{1}{8}\\\frac{\frac{3}{8}}{3}=\frac{1}{8}\\So,\,\,\frac{24}{192}=\frac{3}{24}=\frac{\frac{3}{8}}{3}

As ratio of the consecutive terms is same, the sequence forms a geometric progression.

For -25,-18,-11,-4,... :

-18-(-25)=-18+25=7\\-11-(-18)=-11+18=7\\-4-(-11)=-4+11=7\\So,\,\,-18-(-25)=-11-(-18)=-4-(-11)

As the difference between the consecutive terms is the same, the sequence forms an arithmetic progression.

3 0
3 years ago
The cost of a pizza at the pizza palace depends on the size of the pizza and the number of toppings. For a large pizza, the cost
NeX [460]

Answer:

The 2 represents that each toppings costs $2.

5 0
3 years ago
Which of the following is true?
Oksana_A [137]

B is true

Step-by-step explanation:

because no number with them to lines can be a negative

4 0
3 years ago
Read 2 more answers
Based on historical data, your manager believes that 26% of the company's orders come from first-time customers. A random sample
scoundrel [369]

Answer:

\hat p \sim N( p, \sqrt{\frac{p (1-p)}{n}})

And we can use the z score formula given by:

z = \frac{\hat p -\mu_p}{\sigma_p}

And if we find the parameters we got:

\mu_p = 0.26

\sigma_p = \sqrt{\frac{0.26(1-0.26)}{158}} = 0.0349

And we can find the z score for the value of 0.4 and we got:

z = \frac{0.4-0.26}{0.0349}= 4.0119

And we can find this probability:

P(z>4.0119) = 1-P(z

And if we use the normal standard table or excel we got:

P(z>4.0119) = 1-P(z

Step-by-step explanation:

For this case we have the following info given:

p = 0.26 represent the proportion of the company's orders come from first-time customers

n=158 represent the sample size

And we want to find the following probability:

p(\hat p >0.4)

And we can use the normal approximation since we have the following two conditions:

1) np = 158*0.26 = 41.08>10

2) n(1-p) = 158*(1-0.26) = 116.92>10

And for this case the distribution for the sample proportion is given by:

\hat p \sim N( p, \sqrt{\frac{p (1-p)}{n}})

And we can use the z score formula given by:

z = \frac{\hat p -\mu_p}{\sigma_p}

And if we find the parameters we got:

\mu_p = 0.26

\sigma_p = \sqrt{\frac{0.26(1-0.26)}{158}} = 0.0349

And we can find the z score for the value of 0.4 and we got:

z = \frac{0.4-0.26}{0.0349}= 4.0119

And we can find this probability:

P(z>4.0119) = 1-P(z

And if we use the normal standard table or excel we got:

P(z>4.0119) = 1-P(z

8 0
2 years ago
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