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kompoz [17]
3 years ago
10

In the recursive formula an = an−1 + 5, the value of the previous term is represented by

Mathematics
1 answer:
den301095 [7]3 years ago
6 0

Step-by-step explanation:

In the recursive formula an = an−1 + 5

a_n = a_{n-1}+5

Suppose if a_5 is the nth term then previous term is a_4

To get the previous term we need to subtract 1 from the n

So a_n is the nth term

a_{n-1} is the previous term

Here 5 represents the common difference between two terms

So value of previous term is represented by

a_{n-1}

Answer : a_{n-1}

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Thomas brings over 1/2 of his marble collection. He divides these marbles equally among 3 friends. What fraction of Thomas's ent
aleksley [76]

Answer:

Each of the three friends will get one-sixth of the Thomas's enitre marble collection.

Step-by-step explanation:

Fraction of the total marble collection brought by Thomas = \frac{1}{2}

Now, Thomas divides these marbles equally among his three friends. So, each of the three friends will get one-third of the total marble collection brought by Thomas.

Fraction of total marble collection got by each friend = \frac{1}{3} \;of\;fraction\;of\;total\;marble\;collection\;brought\;by\;Thomas

= \frac{1}{3}\times\frac{1}{2}=\frac{1}{6}

∴ Each of the three friends of Thomas will get one-sixth of his entire collection of marbles.

7 0
3 years ago
Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.
Mice21 [21]

Answer:

<em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

Step-by-step explanation:

Making factors of 8y^{6}+ 144y^{5}+ 640y^{4}

Taking 8y^{4} common:

\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)

Using <em>factorization</em> method:

\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times  4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)

Now, Making factors of 2y^{4} + 40y^{3} + 200y^{2}

Taking 2y^{2} common:

\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)

Using <em>factorization</em> method:

\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10)        ............ (2)

The underlined parts show the Highest Common Factor(HCF).

i.e. <em>HCF</em> is 2y^{2} (y+ 10).

We know the relation between <em>LCM, HCF</em> of the two numbers <em>'p' , 'q'</em> and the <em>numbers</em> themselves as:

HCF \times LCM = p \times q

Using equations <em>(1)</em> and <em>(2)</em>: \Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)

Hence, <em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

5 0
2 years ago
Find the measure of the exterior Angle1 (I’m a bit confused on how exterior angles work)
sergejj [24]

Answer:

70

Step-by-step explanation:

I would do 40 + 30 = 70

180-70 = 110

110 is the last angle bc all angles add to 180 in a triangle

Then 180 - 110 = 70 for angle 1 because their supplementary

I don't know if you could just add the 2 inside angles but I would do it this way to be safe until I know for sure.

7 0
3 years ago
GIVING BRAINLIESTTTTT
andreev551 [17]

Answer:

D.Place the compass on a point on the original line.

Complete Question:

A.Create only one arc that intersects the original line.

B.Create two arcs that intersect the original line.

C.Place the compass on a point off the original line.

D.Place the compass on a point on the original line.

Step-by-step explanation:

* Lets revise the steps of constructing parallel lines and a perpendicular line through a point on the line

# Contracting parallel lines

- Given: Line AB and point P not on AB

1. Draw a slant line through point P and intersects AB at point C, this line is the transversal of the parallel lines

2. Place the pin of the compass at point C and draw an arc intersects AB at D and CP at E

3. Without changing the distance of the compass put the pin of the compass on point P and draw an arc intersects CP at point Q

4. Use the compass to measure the distance from D to E and place the pin of the compass at point Q and draw an arc intersects the arc from P to CP at point U

5. Join P and U by a line this line is parallel to AB

# Constructing a perpendicular line through a point on the line

- Given line AB and point P lies on it

1. Place your compass pin at P and draw an arc of any size below AB that crosses the line twice at points C and D

2. Stretch the compass to a larger distance

3. Place the compass pin on point C and draw a small arc above the line

4. Without changing the distance of the compass place the compass pin on point D and draw another arc intersects the arc from C at point E

5. Using a straightedge, join P and E where PE is perpendicular to AB

* Lets find the same steps in the constructions

∵ In first construction we put the pin of the compass at point C which  lies in the original line AB

∵ In second construction we put the pin of the compass at point P which lies in the original line AB

∴ The common step is:  "Place the compass on a point on the original line"

6 0
3 years ago
The management of a department store is interested in estimating the difference between the mean credit purchases of customers u
Mkey [24]

Answer:

Step-by-step explanation:

1) Point estimate is the difference between the sample means. Therefore,

A point estimate for the difference between the mean purchases of the users of the two credit cards is = 140 - 125 = $15

2) Margin of error = z√(σ²/n1 + σ2²/n2)

Where

z is the z score from the 95% confidence level. From the normal distribution table, z = 1.96

s1 and s2 are standard deviation for both customers respectively.

Standard deviation = √variance

σ1 = √100 = 10

σ2 = √641 = 25.32

Margin of error = 1.96√(10²/64 + 25.32²/49 = 7.5

At 95% confidence, the margin of error is 7.5

3) The confidence interval for the difference of two population means is expressed as point estimate ± margin of error

Confidence interval = 15 ± 7.5

The upper boundary for the confidence interval is

15 - 7.5 = 7.5

The lower boundary for the confidence interval is

15 + 7.5 = 22.5

A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is $7.5 to $22.5

4) Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)

z = (x1 - x2)/(√σ1²/n2 + σ2²/n2)

z = (140 - 125)/√10²/64 + 25.32²/49

z = 1.02

The test statistic for an alpha of .05 is 1.02

4 0
2 years ago
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