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1 year ago

(c) if the corresponding terms of two arithmetic sequences are added, is the resulting sequence arithmetic?

1 answer:

5 0

To determine whether the corresponding terms of 2 arithmetic sequence's added will give new arithmetic sequence or not, Let' take 2 Arithmetic sequences.

In one first term is a1 and common difference is d1, in the other first term is a2 and common difference is d2.

Now nth term for first sequence = a1+(n-1) d1

nth term for second sequence = a2+(n-1) d2

Now add the 2 terms: a1+(n-1)d1 +a2 +(n-1)d2

= a1+a2 + (n-1)(d1+d2)

This is again new arithmetic sequence with first term a1+a2 and common difference d1+d2.

Hence if we add corresponding terms of 2 arithmetic sequence, we will again get an arithmetic sequence.

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In a second grade class containing 13 girls and 10 boys, 2 students are selected at random to give out the math papers. what is

Natali5045456 [20]

The fact that the first chosen student was a girl is already decided, so there is no need to find the probability of that happening. There are a total of 13+10, or 23 students. A girl was already selected, so that leaves 22 students. The chance that a boy is chosen is 10/22, or 5/11.

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2 years ago

Which value represents |7.8|?

nika2105 [10]

Since absolute value is just taking the positive value of whatever you put in the function, it is 7.8 as well. Also, absolute value can be described as the distance from 0 on the number line. 7.8 is 7.8 "units" away from 0, thus meaning it is equal to 7.8.

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2 years ago

The most economical proportion for a right circular cone is to have its height three times long as its base diameter. What later

defon

9514 1404 393

Answer:

∛(2500π)√37 m² ≈ 120.911 m²

Step-by-step explanation:

If the height is 3 times the diameter, it is 6 times the radius. Then the volume is ...

V = 1/3πr²h

V = 1/3πr²(6r) = 2πr³

For a volume of 100 m³, the radius is ...

100 m³ = 2πr³

r = ∛(50/π) m

The lateral area of the cone is computed from the slant height. For this cone, the slant height is found using the Pythagorean theorem:

s² = r² +(6r)² = 37r²

s = r√37

Then the lateral area is ...

LA = πrs

LA = π(∛(50/π) m)(∛(50/π) m)√37

LA = ∛(2500π)√37 m² ≈ 120.911 m²

5 0

1 year ago

M and N are two events P(M) = 0.60, P(N) = 0.20, and P (M and N) = 0.1.

saul85 [17]

Answer:

Step-by-step explanation:

i just took the test :)

8 0

1 year ago

the distribution of scores on a recent test closely followed a normal distribution wotb a mean of 22 and a standard deviation of

soldi70 [24.7K]

Answer:

1) 22.66%

2) 20

Step-by-step explanation:

The scores of a test are normally distributed.

Mean of the test scores = u = 22

Standard Deviation = $\sigma$ = 4

Part 1) Proportion of students who scored atleast 25 points

Since, the test scores are normally distributed we can use z scores to find this proportion.

We need to find proportion of students with atleast 25 scores. In other words we can write, we have to find:

P(X ≥ 25)

We can convert this value to z score and use z table to find the required proportion.

The formula to calculate the z score is:

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

Using the values, we get:

$z=\frac{25-22}{4}=0.75$

So,

P(X ≥ 25) is equivalent to P(z ≥ 0.75)

Using the z table we can find the probability of z score being greater than or equal to 0.75, which comes out to be 0.2266

Since,

P(X ≥ 25) = P(z ≥ 0.75), we can conclude:

The proportion of students with atleast 25 points on the test is 0.2266 or 22.66%

Part 2) 31st percentile of the test scores

31st percentile means 31%(0.31) of the students have scores less than this value.

This question can also be done using z score. We can find the z score representing the 31st percentile for a normal distribution and then convert that z score to equivalent test score.

Using the z table, the z score for 31st percentile comes out to be:

z = -0.496

Now, we have the z scores, we can use this in the formula to calculate the value of x, the equivalent points on the test scores.

Using the values, we get:

$-0.496=\frac{x-22}{4}\\\\ x=4(-0.496) + 22\\\\ x=20.02\\\\ x \approx 20$

Thus, a test score of 20 represent the 31st percentile of the distribution.

3 0

2 years ago

​(c) if the corresponding terms of two arithmetic sequences are​ added, is the resulting sequence​ arithmetic?

(c) if the corresponding terms of two arithmetic sequences are added, is the resulting sequence arithmetic?