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4 years ago

Determine whether the sequence converges or diverges. If it converges, give the limit.

Mathematics

1 answer:

joja [24]4 years ago

7 0

Answer:

Converges; 51 3/7

Step-by-step explanation:

The common ratio is -10/60 = (5/3)/-10 = (-5/18)/(5/3) = -1/6.

Then the sum of the sequence is given by ...

S = a1/(1 -r) = 60/(1 -(-1/6))

S = 60/(7/6) = 360/7

S = 51 3/7

_____

If you erroneously evaluate the formula for the sum using +1/6 as the common ratio, then you will get S=60/(1-1/6) = 60·6/5 = 72.

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A highly selective boarding school will only admit students who place at least 1.5 z-scores above the mean on a standardized tes

Butoxors [25]

Answer:

An applicant must score a minimum of 128

Step-by-step explanation:

To solve this question, we make use of the z-score formula.

Z = (X - mean)/standard deviation

Firstly, let’s list out the parameters from the question. From the question, we can deduce that:

Z = 1.5

X = ?

Mean = 110

Standard deviation =12

1.5= (X-110)/12

18 = X - 110

X = 110 + 18

X = 128

3 0

3 years ago

Solve: (-5/6) × (9/20) + (-5/6) × 7/25 = ?

jonny [76]

$\bf \underline{★ How \:to\: do -} \\$

Here, we are given with four fractions to multiply two of them and to add two of them. If we add them directly by taking the LCM and adding them is not a similar way. We can clearly observe that in those four fractions, we have two fractions as common i.e, we have two fractions as same. If we have two fractions or numbers as same, we can solve the sum by an other concept called as distributive property. In this property, we multiply the common fraction with the sum of other two fractions. This concept can also be done with fractions as well as integers. So, let's solve!!

$\:$

$\bf \underline{➤ Solution-} \\$

${\tt \leadsto \dfrac{(-5)}{6} \times \dfrac{9}{20} + \dfrac{(-5)}{6} + \dfrac{7}{25}}$

Group the non-common fractions in bracket.

${\tt \leadsto \dfrac{(-5)}{6} \times \bigg( \dfrac{9}{20} + \dfrac{7}{25} \bigg)}$

First we should solve the numbers in bracket.

LCM of 20 and 25 is 100.

${\tt \leadsto \dfrac{(-5)}{6} \times \bigg( \dfrac{9 \times 5}{20 \times 5} + \dfrac{7 \times 4}{25 \times 4} \bigg)}$

Multiply the numerators and denominators in the bracket.

${\tt \leadsto \dfrac{(-5)}{6} \times \bigg( \dfrac{45}{100} + \dfrac{28}{100} \bigg)}$

Now, write both numerators in bracket with a common denominator.

${\tt \leadsto \dfrac{(-5)}{6} \times \bigg( \dfrac{45 + 28}{100} \bigg)}$

Now, add the numerators in bracket.

${\tt \leadsto \dfrac{(-5)}{6} \times \bigg( \dfrac{73}{100} \bigg)}$

Write the numerator and denominator in lowest form by cancellation method.

${\tt \leadsto \dfrac{\cancel{(-5)} \times 73}{6 \times \cancel{100}} = \dfrac{(-1) \times 73}{6 \times 20}}$

Now, multiply the numerators and denominators.

${\tt \leadsto \dfrac{(-73)}{120}}$

$\:$

${\red{\underline{\boxed{\bf So, \: the \: answer \: obtained \: is \: \: \dfrac{(-73)}{120}}}}}$

3 0

3 years ago

A landscaping company charges customers for lawn care based on the area of their yards. Mr. Jones was charged $52 for his yard,

Zanzabum

Answer:

$80

Step-by-step explanation:

Area of Mr Jones's yard = 40 * 65 square feet

= 2600 square feet

Mr. Jones was charged $52 for the yard.

Therefore cost per square feet = 52/2600 = $0.02 per square feet

Area of neighbor's yard = 50 * 80 = 4000 square feet

Hence the neighbor will be charged 0.02 * 4000 = $80

For the area corresponding to the yard of size 4000 square feet, he will have to pay $80 to the landscaping company.

6 0

3 years ago

Read 2 more answers

A (5x − 3)° B E (7x+15)° D (6y + 7)° C

marishachu [46]

Answer:

The value of x = 14 ...

The value of ∠AED = ( 7x + 15) = 7(14) + 15 = 113

The value of ∠AEB = 5x-3 = 5(14) -3 = 67

Step-by-step explanation:

=> ∠BEC = ∠AED { vertically opposite angles }

∠AED = (7x + 15)°

=> ∠AEB + ∠BEC = 180° { linear pair }

=> ( 5x-3) + ( 7x+15) = 180°

=> 5x -3 + 7x + 15 = 180°

=> 12x + 12 = 180°

=> 12( x +1 ) = 180°

=> x+1 = 180/12

=> x +1 = 15

=> x = 15-1

=> x = 14

6 0

2 years ago

1. A store manager marked up the price of a $12 clock by 20%. What is the new price of the clock?

Anon25 [30]

Answer:

1) new price of the clock is $14.4

2) Kyra scored 70% marks

3) 43.75% students are not eighth graders

Step-by-step explanation:

1. A store manager marked up the price of a $12 clock by 20%. What is the new price of the clock?

Price of Clock = $12

Mark up = 20%

We need to find new price of clock.

The price of clock can be found by finding 20% of 12 and then adding that amount in original price.

So, finding 20% of 12

$20\% of 12 \\=\frac{20}{100}\times 12\\=2.4$

So 20% of 12 is 2.4

Now finding new price:

New Price = Actual Price + Mark up

New Price = 12 + 2.4

New Price = 14.4

So, new price of the clock is $14.4

2. On a math quiz, Kyra answered 7 of 10 questions correctly. Express her quiz score as a percent.

Total questions = 10

Correct answers = 7

We need to express her quiz score as percent

It can be found using formula: $Percent Score = \frac{Obtained\:Marks}{Total\:Marks}\times 100\%\\$

Putting values and finding percentage

$Percentage = \frac{Obtained\:Marks}{Total\:Marks}\times 100\%\\\\Percentage = \frac{7}{10}\times 100\%\\Percentage = 70\%$

So, Kyra scored 70% marks

3. 96 students are enrolled in the Dance Program at Castillero. Of those students, 54 are eighth-graders. The remaining students are 6th or 7th graders. What percentage of the students are not eighth graders?

Total Students = 96

Number of eighth-graders students = 54

Remaining students = 96 - 54 = 42

So, 42 students are 6th or 7th graders

We need to find percentage of the students are not eighth graders.

$\frac{42}{96}\times 100\%\\=43.75\%$

So, 43.75% students are not eighth graders

4 0

3 years ago