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mixas84 [53]
3 years ago
13

How many different squares appear in this picture?

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
7 0

Answer:

27

Step-by-step explanation:

4 times 4 is 16

2 boxes in the middle

4 tiny boxes in each one in the middle

1 entire one on the outside

1+4+4+2+16= 27

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Show that 1n^ 3 + 2n + 3n ^2 is divisible by 2 and 3 for all positive integers n.
Dmitry_Shevchenko [17]

Prove:

Using mathemetical induction:

P(n) = n^{3}+2n+3n^{2}

for n=1

P(n)  = 1^{3}+2(1)+3(1)^{2} = 6

It is divisible by 2 and 3

Now, for n=k, n > 0

P(k) = k^{3}+2k+3k^{2}

Assuming P(k) is divisible by 2 and 3:

Now, for n=k+1:

P(k+1) = (k+1)^{3}+2(k+1)+3(k+1)^{2}

P(k+1) = k^{3}+3k^{2}+3k+1+2k+2+3k^{2}+6k+3

P(k+1) = P(k)+3(k^{2}+3k+2)

Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also

divisible by 2 and 3.

Hence, by mathematical induction, P(n) = n^{3}+2n+3n^{2} is divisible by 2 and 3 for all positive integer n.

3 0
3 years ago
How to solve y-b/x=m for y
Slav-nsk [51]
To solve for m we want to get m by itself on one side of the equals sign, with everything else on the other side. First we subtract b from both sides, to get it out of the right side of the equation:
y - b = mx + b - b
y - b = mx
Now we divide both sides by x, to get m completely by itself:
(y-b)/x = (mx)/x
(y-b)/x = m
So m is equal to (y-b)/x.
8 0
3 years ago
Read 2 more answers
BRAINLIEST AND MAX PTS<br><br> CONVERT y = 40x + 600 to point-slope form
IRISSAK [1]

Answer:

The answer to your question is y - 0 = 40(x - 15)

Step-by-step explanation:

                                  y = 40x + 600

Convert to                 y - y₁ = m(x - x₁)          

Process

1.- Factor 40 in the right side of the equation

                                 y = 40(x - 15)

2.- Give the form of the point slope form

                                 y - 0 = 40(x - 15)

where

y₁ = 0

m = 40

x₁ = 15

3 0
3 years ago
Read 2 more answers
To save money, you put $200 in your bank account each week. After saving for 4 weeks, you have $1,700 dollars in your account. W
Burka [1]

Answer: y - 1700 = 200(x-4)

5 0
3 years ago
Read 2 more answers
The average household income for a recent year was $30,000. five years earlier the average household income was $24,500. assume
ikadub [295]

Using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

According to the question,

The average household income for a recent year (x₁⁻) = $30,000

The average household income for a recent year (x₂⁻) = $24,500

sample sizes n₁ = n₂ = 34

standard deviation of both samples were $24,500. Thus, s₁ = s₂ = $5928.

Null hypothesis:  There is no evidence to believe that the average household income has increased.

H₀ : μ₁ ≤ μ₂

Alternative hypothesis:  There is evidence to believe that the average household income has increased.

H₁: μ₁ > μ₂  

To check hypothesis we have the formula

Standard error=  \sqrt{\frac{s_{1} ^{2} }{n_{1} } + \frac{s^{2} _{2} }{n_{2} }  }

= \sqrt{2067128.4706}

= 1437.7512

Thus, standard error is $1437.7512.

Formula for test statistic = [(x₁⁻ -  x₂⁻) - (μ₁ - μ₂)]/standard error

= [(30000 -  24500) - 0]/1437.7512

= 3.8254

The critical value of z at 5% level of significance is 1.6449.

Here, the calculated value is greater than the critical value so we reject H₀.

Hence using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

Learn more about hypothesis test here

brainly.com/question/15060525

#SPJ2

3 0
2 years ago
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