It takes Gary 1 hour to milk all the cows, and it takes Dana 1.5 hours. How long will it take them to do the job together? Please explain all the steps and models/equations used. Thanks so much.

Answers

Answer 1

Answer: It takes Gary 1 hour to milk all the cows. 1 hour per job ==> 1 job per hour.

It takes Dana 1.5 hours. 1.5 hour per job ==> 1/1.5 job per hour.

Working together, they can do (1/1 + 1/1.5) job per hour.

To add these fractions, put them over a common denominator:

(1/1 + 1/1.5) = (1.5/1.5 + 1/1.5) = (2.5/1.5) = 5/3 job per hour.

5/3 job per hour ==> 3/5 hour per job.

3/5 hour = 36 minutes.

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if a scale map is 1 cm: 15 Km. find the actual distance corresponding to the scale map. 13) 2.5 cm 14) 0.2 cm 15) 15 cm 16) 4.6 cm

Answers

All you gotta do is multiply the cm by 15,
For 13) you'd do $2.5*15$
14) $0.2*15$
15) $15*15$
then for 16) $4.6*15$

Let

x-------> distance in the map in cm

y-------> actual distance in Km

we know that

$Scale\ Map=(x)/(y) \n \n Scale\ Map=(1)/(15)(cm)/(Km)$

$(x)/(y)=(1)/(15)$

$y=15x$ --------> equation $1$

Part 13) find the actual distance corresponding to the scale map $2.5\ cm$

In this problem we have

$x=2.5\ cm$

Substitute the value of x in the equation $1$ to find the actual distance

$y=15*2.5=37.5\ Km$

therefore

the answer part 13) is

the actual distance is $37.5\ Km$

Part 14) find the actual distance corresponding to the scale map $0.2\ cm$

In this problem we have

$x=0.2\ cm$

Substitute the value of x in the equation $1$ to find the actual distance

$y=15*0.2=3\ Km$

therefore

the answer part 14) is

the actual distance is $3\ Km$

Part 15) find the actual distance corresponding to the scale map $15\ cm$

In this problem we have

$x=15\ cm$

Substitute the value of x in the equation $1$ to find the actual distance

$y=15*15=225\ Km$

therefore

the answer part 15) is

the actual distance is $225\ Km$

Part 16) find the actual distance corresponding to the scale map $4.6\ cm$

In this problem we have

$x=4.6\ cm$

Substitute the value of x in the equation $1$ to find the actual distance

$y=15*4.6=69\ Km$

therefore

the answer part 16

the actual distance is $69\ Km$

Solve the problem. Round to the nearest cent.Mark knows that he will need to buy a new car in 5 years. The car will cost $15,000 by then. How much should he invest now at 8%, compounded quarterly, so that he will have enough to buy a new car?
a. $9452.54
c. $12,328.91
b. $11,025.45
d. $10,094.57

Answers

Answer:

He invest $10101.01.

Step-by-step explanation:

Given : Mark knows that he will need to buy a new car in 5 years. The car will cost $15,000 by then.

To find : How much should he invest now at 8%, compounded quarterly, so that he will have enough to buy a new car?

Solution :

Using compound interest formula,

$A=P(1+r)^t$

Where, A is the amount A=$15000

P is the principle P=?

r is the rate r=8%=0.08

t is the time t= 5 years

Substitute the value,

$A=P(1+r)^t$

$15000=P(1+(0.08)/(4))^(5*4)$

$15000=P(1+0.02)^(20)$

$15000=P(1.02)^(20)$

$15000=P* 1.485$

$P=(15000)/(1.485)$

$P=10101.01$

Therefore, He invest $10101.01.

Answer:

Step-by-step explanation:

x - initial investment

8% - annual rate

x·=15,000,

so x = 10094.54

ANSWER: $10,094.57

Which statement best describes a solution to the system of equations 3x+Y=17 X+2y=49 A. It has no solution B. It has infinite solutions C. It has a single solution x=15 y=17 D. It has a single solution x=-3 y=26

Answers

Answer:

It has a single solution x=-3 y=26

Step-by-step explanation:

The ratios of coefficients of x and y are different, so the pair of equations has one solution. It is easy to tell the first offered solution (15, 17) does not satisfy the first equation, so that choice is eliminated.

Fortunately, the second offered solution, (x, y) = (-3, 26), satisfies both equations.

The equations have a single solution: (x, y) = (-3, 26).

Answer: The equation has a single solution x = -3 , y = 26.

( -3, 26 )

Step-by-step explanation:

3x + y =17 ---------------------(1)

x + 2y = 49 -------------------(2)

Using substitution approach

From (2)

x = 49 - 2y --------------------(3)

Now put (3) in equation (1) and solve.

3(49 - 2y) + y = 17

Open the bracket and solve

3 x 48 - 3 x 2y + y = 17

147 - 6y + y = 17

Gather like terms

-5y = 17 - 147

-5y = -130

Multiple through by (-1)

5y = 130

Divide by 5

y = 130/5

y = 26.

Substitute for y now in equation (3) to get the value of x

3x + y = 17

3x + 26 = 17

3x = 17 - 26

3x = -9

Now , divide by 3

x = -3

The equation had a single solution of x = -3 , y = 26

Chech.

3 x -3 + 26

-9 + 26

= 17

How many ways can 11 pairs of shoes be arranged?

Answers

Answer:

5 pairs with 1 extra shoe

Step-by-step explanation:

The sum of three consecutive odd numbers is 183. What is the smallest of the three numbers ?

Answers

Answer:

Step-by-step explanation:

Average = 183/3 = 61

Two consecutive odd numbers differ by 2.

Hence, the numbers are 61-2, 61, 61 +2 or 59, 61, 63

The smallest is 59.

If a goat is reduced by 19% in a sale to £25.92, find the original price

Answers

Answer:

32 dollars

Step-by-step explanation:

Given that selling price of a goat after reduced by 19% is 25.92.

We have to find the original price of the goat.

Let original price = 100

Reduced % = 19

Selling price = 81

81 dollars is equivalent to selling price of 25.92 $

100 dollars is equivalent to selling price of 100(25.92)/81 = 32 $

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