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2 years ago

7

Ernie spends 6 hours reading each weekend. Ernie has 3 sisters. Each sister reads the same amount Ernie does each weekend. How m

any hours do Ernie and his sisters read in all?

1 answer:

lora16 [44]2 years ago

6 0

Ernie spend 6hrs. × his 3 sisters
so, 6×3=18
18hours in total.

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Suppose a1=12−12,a2=23−13,a3=34−14,a4=45−15,a5=56−16. a) Find an explicit formula for an: . b) Determine whether the sequence is

lorasvet [3.4K]

I'm going to assume you meant to write fractions (because if $a_n$ are all non-negative integers, the series would clearly diverge), so that

$a_1=\dfrac12-\dfrac12$

$a_2=\dfrac23-\dfrac13$

$a_3=\dfrac34-\dfrac14$

and so on.

a. If the pattern continues as above, we would have the general term

$a_n=\dfrac n{n+1}-\dfrac1{n+1}=\dfrac{n-1}{n+1}$

b. Note that we can write $a_n$ as

$a_n=\dfrac{n-1}{n+1}=\dfrac{n+1-2}{n+1}=1-\dfrac2{n+1}$

The series diverges by comparison to the divergent series

$\displaystyle\sum_{n=1}^\infty\frac1n$

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2 years ago

The sum of 6 consecutive even numbers is <br> 270.<br> What is the second number in this sequence?

KonstantinChe [14]

Lets find all the numbers..

x (1st number)
x + 2 ( 2nd number)
x + 4 (3rd number)
x + 6 (4th number)
x + 8 (5th number)
x + 10 (6th number)

Now add all those expressions and set them equal to 270 because that is the total.

x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 = 270
6x + 30 = 270
6x = 240
x = 40

Now we will substitute 40 for x in the expression of the second number.

x + 2
40 + 2
42

So the second number is 42

Hope this helps :)

4 0

2 years ago

If 20a-16=12(3-a), then a=?<br><br>a)5/8<br>b)13/8<br>c)21/16<br>d)5/2

lorasvet [3.4K]

ANSWER: B. 13/8

STEP BY STEP THING:

20a−16=12(3−a)

20a−16=−12a+36

32a−16=36

32a=52

32a/32 = 52/32

a = 13/8

5 0

2 years ago

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A deck of playing cards has four suits, with thirteen cards in each suit consisting of the numbers 2 through 10, a jack, a queen

Rudik [331]

A. True. There are 52 cards total and you only pick 5. Order doesn't matter.

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B. False. Order doesn't matter so you use a combination (instead of a permutation) as choice A shows.

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C. False. The answer is roughly 0.000858 as shown by the calculation below

(13/52)*(12/51)*(13/50)*(12/49)*(11/48) = 0.000858

-------------------------------------------

D. False. See calculation below

(13/52)*(12/51)*(11/50)*(10/49)*(9/48) = 0.000495

-------------------------------------------

E. True. See calculation below

(13/52)*(12/51)*(11/50)*(10/49)*(9/48) = 0.000495
this value rounds to roughly 0.0005

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2 years ago

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Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side Line segment

prisoha [69]

Answer:

<h2>A 16mm</h2>

Step-by-step explanation:

An equilateral triangle is a triangle that has all of its sides equal.

Perimeter of an equilaterial triangle = 3s where;

s is one side of the triangle.

Given the perimeter of ABC = 96mm

Substituting into the formula above to get s;

96 = 3s

s = 96/3

s = 32mm

Hence the length of one side of the triangle is 32mm

If a perpendicular bisector is drawn from angle A to side Line segment B C at point M, then MC will be half of BC and ΔAMC will be a right angled triangle.

Since all the sides of the triangle are equal, hence BC = 32mm. Since MC is the half of BC, then MC = 1/2 of 32mm

MC = 1/2 * 32mm

MC = 16mm

<em>Hence the length of Line segment MC is 16mm</em>

<em></em>

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2 years ago

Read 2 more answers