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3 years ago

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HELP!! 30 POINTS AND WILL MARK BRAINLIEST One month, Henry's grandfather gives him a box of 523 baseball cards. Each month, star

ting the second month, Henry buys 24 baseball cards to add to this collection. What is the explicit rule for the number of baseball cards Henry has in his collection after n months? Enter your answer in the box.

2 answers:

Bezzdna [24]3 years ago

4 0

Answer:

nth term = 523 + 24(n - 1

Step-by-step explanation:

This is modelled by an arithmetic series where first term a1 = 523 and common difference d = 24.

nth term = a1 + d(n - 1).

Here it is 523 + 24(n - 1) (answer)

ASHA 777 [7]3 years ago

3 0

Answer:

The answer is:24n+499

Step-by-step explanation:

As we know Henry's grandfather gave him a box of 523 baseball cards in the first month.

from the second month Henry start to collect 24 baseball cards each month.

if the total process took n months, so Henry himself collected 24 baseball cards for 'n-1' months.

so total cards collected by Henry in (n-1) months is=24(n-1)

hence, Henry's total collection is=number of baseball cards his grandfather gave him+number of baseball cards collected by Henry himself

=523+24(n-1)

=523+24n-24

=24n+499

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Answer:

1, $\frac{m}{n}$ , $\frac{1-m}{n}$ .

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c) Pr( first m persons get a phone belonging to last m persons) = $\frac{1-m}{n}$

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3 years ago

Three co-workers are packing books in a storage bin. The bin is 4 feet high, 9 feet long, and 11 feet wide. If 6 books fill 1 cu

evablogger [386]

Alright, lets get started.

Height of the bin = 4 ft

Length of the bin = 9 ft

Width of the bin = 11 ft

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3 years ago

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Solve the equation for an ellipse for y. Assume that y > 0. y^2/a^2 + x^2/b^2 = 1

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Multiply each term by a^2b^2:-

b^2y^2 + a^2x^2 = a^2b^2
subtract a^2x^2 from both sides
b^2y^2 = a^2b^2 - a^2x^2
Now divide both sides by b^2

y^2 = a^2 - a^2x^2 / b^2 = a^2 (1 - x^2/b^2)

take positive square root ( because y > 0)

y = a sqrt(1 - x^2/b^2)

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3 years ago

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Punctele O, A, B, C sunt coliniare în această ordine, iar segmentele OA, AB și BC au lungimile exprimate în cm, prin numere natu

julia-pushkina [17]

Răspuns:

a) OC = 18cm

b) MN = 6cm

Explicație pas cu pas:

Găsiți diagrama la întrebarea atașată.

a) Din diagramă se poate observa că OC = OA + AB + AC

OC = 2n + 2n + 2 + 2n + 4

OC = 6n + 6

Următorul este să obțineți valoarea lui n:

OM = OA + AM

Să obținem segmentul AM;

Deoarece M este segmentul mijlociu al AC, atunci;

AM = AC / 2

AM = AB + BC / 2

AM = 2n + 2 + 2n + 4/2

AM = 4n + 6/2

AM = 2n + 3

Din moment ce OM = OA + AM

OM = 2n + 2n + 3

OM = 4n + 3

Dat fiind OM = 11

11 = 4n + 3

4n = 11-3

4n = 8

n = 2

Următorul pas este să calculați OC;

OC = 6n + 6

OC = 6 (2) + 6

OC = 18

Prin urmare, lungimea segmentului OC este de 18 cm

b) Această întrebare ne cere să găsim segmentul de linie MN.

Din diagramă, MN = AM - AN

Deoarece AM = 2n + 3 din întrebarea 1;

AM = 2 (2) +3

AM = 4 + 3

AM = 7

Acum, să obținem AN:

Din diagramă, AN = ON-OA și ON = OB / 2

AN = OB / 2 - OA

AN = (2n + 2n + 2) / 2 - 2n

AN = 4n + 2/2 - 2n

AN = 2n + 1 - 2n

AN = 2n-2n + 1

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3 years ago

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omeli [17]

Answer:

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Step-by-step explanation:

Given

<u>Pyramid A</u>

$s = 4$ -- base sides

$V = 36$ -- Volume

<u>Pyramid B</u>

$s = 6$ --- base sides

Required

Determine the volume of pyramid B <em>[Missing from the question]</em>

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

$V = \frac{1}{3} * B * h$

Where B represents the area of the base equilateral triangle, and it is calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

$B = \frac{1}{2} * s^2 * sin(60)$

$B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}$

$B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}$

$B = 4\sqrt 3$

The height is calculated from:

$V = \frac{1}{3} * B * h$

This gives:

$36 = \frac{1}{3} * 4\sqrt 3 * h$

Make h the subject

$h = \frac{3 * 36}{4\sqrt 3}$

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To calculate the volume of pyramid B, we make use of:

$V = \frac{1}{3} * B * h$

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$h = \frac{27}{\sqrt 3}$

The base area B, is then calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

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$s = 6$

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$B = \frac{1}{2} * 6^2 * sin(60)$

$B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}$

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Where

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$V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9 * 27$

$V = 81$

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3 years ago

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