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VladimirAG [237]
2 years ago
9

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is

true. Show your work. Sn: 1^2 + 42 + 72 + . . . + (3n - 2)2 = (n(〖6n〗^2-3n-1))/2
Mathematics
1 answer:
cluponka [151]2 years ago
5 0
In the commutative ring of the integers, multiplication and addition are closed on the integers. There's your first two statements. S3 would be the additive identity element is 0.
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Solve value of x. solve for x
user100 [1]

Answer:

6

Step-by-step explanation:

8x+6x+6 = 90

14x = 84

x = 6

3 0
2 years ago
For a particular diamond mine, 81% of the diamonds fail to qualify as "gemstone grade". A random sample of 92 diamonds is analyz
Fed [463]

Answer:

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 92, p = 0.81

So

\mu = E(X) = np = 92*0.81 = 74.52

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{92*0.81*0.19} = 3.76

Find the probability that more than 79% of the sample diamonds fail to qualify as gemstone grade.

This is 1 subtracted by the pvalue of Z when X = 0.79*92 = 72.68. So

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

Z = \frac{72.68 - 74.52}{3.76}

Z = -0.49

Z = -0.49 has a pvalue of 0.3121

1 - 0.3121 = 0.6879

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

4 0
3 years ago
Find the slope of (-2,1),(2,-2)
Volgvan

Answer:

-3/4 is the slope.

Step-by-step explanation:

Use this formula to find slope.

y2-y1/x2-x1

PLUG IN

-2 -1/2- (-2) = -3/4

The slope is -3/4

3 0
3 years ago
Read 2 more answers
Which s.i. units are most accurate to use when measuring
liraira [26]
A. length = meter = m (base)
b. volume = cubic meter = m³ (derived)
c. mass = kilogram = kg (base)
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6 0
3 years ago
Ginny’s favorite cookie recipe requires 1 1/2 cups of sugar to make 24 cookies. How much sugar does Ginny need to make 36 of the
Delicious77 [7]

Ginny needs 2\frac{1}{4} cups of sugar to make 36 cookies.

Step-by-step explanation:

Given,

Sugar cups required for 24 cookies = 1\frac{1}{2}=\frac{3}{2}\ cups

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Let,

x be the number of cups needed for 36 cookies.

Ratio of sugar cups to cookies = x:36\\

Using proportion;

Ratio of sugar cups to cookies :: Ratio of sugar cups to cookies

\frac{3}{2}:24::x:36

Product of mean = Product of extreme

24*x=\frac{3}{2}*36\\24x=54

Dividing both sides by 24

\frac{24x}{24}=\frac{54}{24}\\x=\frac{9}{4}\\x=2\frac{1}{4}

Ginny needs 2\frac{1}{4} cups of sugar to make 36 cookies.

Keywords: fraction, proportion

Learn more about fractions at:

  • brainly.com/question/96882
  • brainly.com/question/96535

#LearnwithBrainly

7 0
3 years ago
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