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1 year ago

Mary works at a local Burger King restaurant. Her regular hourly wage is $14.70. If she works overtime, she

Mathematics

1 answer:

lidiya [134]1 year ago

8 0

Answer:

I’m pretty sure it’s 588

Step-by-step explanation:

14.70 * 40 = 588

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Ray is six years younger than Tom. John is three times as old as Ray. Let Tom be x years old. The three of them

gtnhenbr [62]

Answer:

Ray = 19 yrs old
Tom = 25 yrs old
John = 57 yrs old

Explanation:

Let x be the years of Tom

R = x - 6
J = 3R = 3(x - 6)
T = x

R + J + T = 101
x - 6 + 3(x - 6) + x = 101
2x - 6 + 3x - 18 = 101
5x - 24 = 101
5x = 125
x = 125/5 = 25

R = 25 - 6 = 19
J = 3(25 - 6) = 57
T = 25

6 0

2 years ago

If [infinity] cn8n n = 0 is convergent, can we conclude that each of the following series is convergent? (a) [infinity] cn(−3)n

pashok25 [27]

Answer:

a) we know that this is convergent.

b) we know that this might not converge.

Step-by-step explanation:

Given the $\sum^\infty_{n=0}C_n8^n$ is convergent

Therefore,

(a) $\sum^\infty_{n=0}C_n(-3)^n$ The power series $\sum C_nx^n$ has radius of convergence at least as big as 8. So we definitely know it converges for all x satisfying -8<x≤8. In particular for x = -3

∴ $\sum^\infty_{n=0}C_n(-3)^n$ is convergent.

(b) $\sum^\infty_{n=0}C_n(-8)^n$ -8 could be right on the edge of the interval of convergence, and so might not converge

8 0

3 years ago

The common ratio of a geometric series is 1/4 and the sum of the first 4 terms is 170.

Illusion [34]

Answer: the first term of the series is 128

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

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

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

r = 1/4 = 0.25

n = 4

S4 = 170

Therefore, the expression for the sum of the 4 terms, S4 is

170 = a(1 - 0.25^4)/(1 - 0.25)

170 = a(1 - 0.00390625)/(1 - 0.25)

170 = a(0.99609375)/(0.75)

170 = 1.328125a

a = 170/1.328125

a = 128

5 0

2 years ago

A plumber charges a one time

sashaice [31]

Answer: Probably Fee.

Step-by-step explanation:

8 0

3 years ago

The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 273 meters, find the dimensions

AleksandrR [38]

The length of the rectangle = 16 meters

The width of the rectangle = 10.5 meters

Step-by-step explanation:

Given that,

The Area of the rectangle is 273.

Step 1 :

Let, the width of the rectangle be 'x'

The length of the rectangle is 2x - 5

Step 2 :

Area of the rectangle = length $\times$ width

273 = (2x - 5) x

273 = 2x^2 - 5x

Step 3 :

The equation formed is 2x^2 - 5x -273 = 0

a= coefficient of x^2 = 2

b= coefficient of x = -5

c = constant = -273

Find the roots of the equation, to find the width.

Step 4 :

Find the roots using factorizing method,

ac = 2 $\times$ -273 = -546 and b= -5

Factorizing -546 as -26 $\times$ 21

The product of -26 $\times$ 21 = -546

The sum of -26 + 21 = -5

Step 5 :

The roots of the equation 2x^2 - 5x -273 = 0 are x= -26/2 and x= 21/2

The values of x are x= -13 and x= 10.5

Since the width cannot be a negative value, neglect x= -13

Step 6 :

Therefore,

The width of the rectangle = 10.5 meters

The length of the rectangle = 2x-5

= 2(10.5) - 5

= 21 - 5

length = 16 meters

5 0

3 years ago