One number is 5 times another. The sum of their reciprocals is 2/5. Determine the smaller number.

Answers

Answer 1
Answer: so x=5y
reciprocal of x=1/x then

sum of reciprocals means 1/x+1/y=2/5
subsitute x=5y for x in 1/x+1/y=2/5 and get
1/5y+1/y=2/5
multiply 1/y by 5/5 to make it 5/5y so you can add since the denomenators (bottom number) are the same

1/5y+5/5y=2/5
6/5y=2/5
multiply both sides by 5y
6=2y
divide both sides by 2
3=y
put this into x=5y so 
x=5(3)
x=15
y=3

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A school bus has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second grade travel in the bus. How many ways can the students be seated if all of the second-grade students occupy the first row?a. 25P20
b. 5P5 × 20P15
c. 5C5 × 25C14
d. 5P5 × 15P15
e. 5P5 × 25C15

Answers

Answer:

The correct option is b.

Step-by-step explanation:

It is given that the school bus has 25 seats, with 5 rows of 5 seats.

The number of students from the first grade is 15 and the number students from the second grade is 5.

The formula to arrange r items in n places is

^nP_r=(n!)/((n-r)!)

The number of seats in first row is 5 and the number students from the second grade is 5. So, the total number of arrangement is

^5P_5

The number of seats except first row is 20 and the number students from the first grade is 15. So, the total number of arrangement is

^(20)P_(15)

The total number of ways the students can be seated if all of the second-grade students occupy the first row is

^5P_5* ^(20)P_(15)

Therefore the correct option is b.

Answer:

b

Step-by-step explanation:

plato fam

A grocery store clerk is putting cans of soup on the shelves.She has 12 boxes,wich each contain 24 cans of soup.Altogether,how many cans of soup will the clerk put ont he shelves

Answers

it's 12x24=288 problem solved

What is this percent of change 40;72

Answers

Given:
Original or base : 40
New amount : 72

We need to find the difference of the new amount and the original amount

72 - 40 = 32

We then divide the difference by the original amount

32/40 = 0.80

We multiply the quotient by 100%

0.80 x 100% = 80%

The percentage of change is 80%

I Need help Please, Geometry1. If 2. Fill in the blanks for each conjunction, sin 20 = cos __ , sin 33 = cos __ , sin 45 = cos __
3. find the value of x,
3a. sin(x) = cos 31,
3b. sin 75 = cos(x),
3c. sin(x-4) = cos 50

Answers

Step-by-step explanation:

Answer:

\frac{7}{4}

4

7

Explanation:

______________________

We know the values of

i) cos0° = 1

ii) sin45° = \frac{1}{\sqrt{2}}

2

1

iii) sin30° = \frac{1}{2}

2

1

iv) sin90° = 0

v) cos45° = \frac{1}{\sqrt{2}}

2

1

vi ) cos60° = \frac{1}{2}

2

1

_____________________

Now,

The value of

(cos 0+sin 45+sin 30)(sin 90-cos 45+cos 60)

= \left(1+\frac{1}{\sqrt{2}}+\frac{1}{2}\right)\left(1-\frac{1}{\sqrt{2}}+\frac{1}{2}\right)(1+

2

1

+

2

1

)(1−

2

1

+

2

1

)

= \left(\frac{3}{2}+\frac{1}{\sqrt{2}}\right)\left(\frac{3}{2}-\frac{1}{\sqrt{2}}\right)(

2

3

+

2

1

)(

2

3

2

1

)

= \left(\frac{3}{2}\right)^{2}-\left(\frac{1}{\sqrt{2}}\right)^{2}(

2

3

)

2

−(

2

1

)

2

/* By algebraic identity

(a-b)(a+b) = a²-b² */

= \left( \frac{9}{4}-\frac{1}{2}\right)(

4

9

2

1

)

= \frac{9-2}{4}

4

9−2

= \frac{7}{4}

4

7

••••

Tom has taken out a loan for college. He started paying off the loan with a first payment of $200. Each month he pays, he wants to pay back 1.2 times as the amount he paid the month before. Explain to Tom how to represent his first 30 payments in sigma notation. Then explain how to find the sum of his first 30 payments, using complete sentences. Explain why this series is convergent or divergent.

Answers

Answer:

In this geometric series, a represents the first term, what he pays back monthly is the common ratio which is 1.2, and the first 30 payments are what is being used to find the total amount which is represented by n. Thus, a=$200, n=30 and r=1.2. The sum is found by sn=(a((r^n)-1))/(r-1), which will be 200((1.2^30)-1))/(1.2-1). The solution is = $ 236,376 and the series is divergent because of the common ratio being greater than 1.

Step-by-step explanation:

This is a geometric series. The first payment represents the first term, a. The number of times he wants to pay back for subsequent payments represent the common ration, r. The first 30 payments represents the number of terms to use in finding the sum, n.

Hence, a = $ 200, n = 30 and r = 1.2.

The sum of a geometric sequence is given as:

Sn = (a((r^n)-1))/(r-1)

     =(200((1.2^30)-1))/(1.2-1) 
  
     = $ 236, 376. 31

Explain why this series is convergent or divergent.

Since the common ratio, r, is greater than 1, the series is divergent

The employees of Neat Clothes work Monday through Friday. Every other Friday the company issues payroll checks totaling $32,000. The current pay period ends on Friday, July 3. Neat Clothes is now preparing quarterly financial statements for the three months ended June 30. What is the adjusting entry to record accrued salaries at the end of June

Answers

Answer:

Step-by-step explanation:

Rationale: Amount accrued: $32,000 x 7/10 = $22,400

Because we know:

  • The current pay period ends on Friday, July 3
  • Neat Clothes is now preparing quarterly financial statements for the three months ended June 30

From Friday, June 30 to July 3 is 10 days