A motorboat travels 74 kilometers in 2 hours going upstream. It travels 110 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Answer:

The equation in standard form of the line y=1/9x+5 is y-5=1/9(x-0)

The expression we get from the given functions r and s defined for all real numbers x.

r( s(-3))= -38

Given that,

All real numbers x are defined by the functions r and s.

r(x) =2x+1

s(x) =-2x²-2

We have to find the expression

r( s(-3))

Take the functions,

r(x) =2x+1

s(x) =-2x²-2

Now, Take

r( s(-3))

Substitute s function first

r(-2(-3)²-2)

r(-2(9)-2)

r(-18-2)

r(-20)

Now substitute r function

2(-20)+2

-40+2

-38

Therefore, The expression we get from the given functions r and s defined for all real numbers x.

r( s(-3))=-38

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The discount rate used in calculator wound be 4.56%.

Given that,

You anticipate getting a bonus of $10000 after five years on the job.

We have the result of your calculation for the parent value of this bonus is $8000. what percentage of a discount rate did you use.

We know that to find the present value of a future sum of money .

PV= FV/(1+r)ⁿ

Here,

PV is present value = $8000

FV is future value = $10000

r is discount rate we have to find

n is time = 5 years

Substitute in the formula,

$8000=$10000/(1+r)⁵

(1+r)⁵=$10000/$8000

(1+r)⁵=1.25

1+r=[tex]1.25^{1/5}[/tex]

1+r=1.0456

r=1.0456-1

r=0.0456

r=4.56%

Therefore, The discount rate used in calculator wound be 4.56%.

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The Mathematical Final Answer:

0

f(2) = -4

Step-by-step explanation:

f(2) = 3^2-13

f(2) = 9-13

f(2) = -4

Answer:

I hope that the picture below helps.

Step-by-step explanation:

It will take the word processor 165 minutes to check 22 pages

The given parameters in the question are:

Speed = 30 minuter per 4 pages

Number of pages = 22 pages

The number of hours to check the pages can be calculated using the following equation

Time = Speed * Number of pages

Substitute the known values in the above equation So, we have the following equation

Time = 30/4 * 22

There is no unit to convert

So, we have

Time = 30/4 * 22

Evaluate

Time = 165

Hence, the time is 165 minutes

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Answer:

(- 12, 10 )

Step-by-step explanation:

2x + 4y = 16 → (1)

- 2x - 3y = - 6 → (2)

add (1) and (2) term by term to eliminate x

0 + y = 10

y = 10

substitute y = 10 into (1) and solve for x

2x + 4(10) = 16

2x + 40 = 16 ( subtract 40 from both sides )

2x = - 24 ( divide both sides by 2 )

x = - 12

solution is (- 12, 10 )

Answer:

(- 12, 10 )

Step-by-step explanation:

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The liters of synthetic oil that are needed is 456 liters.

From the information, petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 6 liters of synthetic oil.

To make 836 liters of oil, the liters of synthetic oil will be:

= 6 / (6+5) × 836

= 6/11 × 836

= 456

Therefore, 456 liters are needed.

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The sales price of the yoga pants is $20.

It should be noted that from the information illustrated, the Yoga pants are on sale for 1/3 off the original price and a pair of yoga pants normally costs $60.

The sales price will be:

= Fraction given × Original price

= 1/3 × $60

= $20

The price is $20.

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Answer:

because u can't predict the days rain will fall so u can say it will fall in ratio 0:4

Answer:

Step-by-step explanation:

the answer is D i'm pretty sure

The equation of the line with coordinates (-7,3), (8,3) is y-3=0 as the slope of line is 0 because x-ordinate is same in both the points.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

The two point form of equation,

y-y1=m(x-x1)

m=(y2-y1)/(x2-x1)

m=(3-3)/(8--7)

m=0

y-3=0(x+7)

y-3=0

Because the x-ordinate is the same at both points, the equation for the line with coordinates (-7,3) and (8,3) is y-3=0.

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Answer: Possible Answers:

x2+x−12=0

x2−x−12=0

x2+3x−4=0

2x2+2x−6=0

x2−4x−3=0

Step-by-step explanation: youer welcome

The weight of one package beef is 8.26kg

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

For example, if 10 students are to share 100 oranges, if they are to share it equal, then each students will receive 100/10= 10 oranges

Similarly 132.16kg was placed into 16packages of equal weight.

Therefore the weight of each package beef will be 132.16/16= 8.26kg

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The equation of the line in slope-intercept form is y = 5x-22.

The slope-intercept form of a straight line is one of the most common forms used to represent the equation of a line.

The slope-intercept form of an equation is given as

Formula:

Where:

Substitute these values into equation 1

Hence, the equation in slope-intercept form is y = 5x-22.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

540x0.30=378

378x0.08=30.24

378+30.24=408.24

Answer: 29, 36, 38

Step-by-step explanation:

The sequence starts with 2 and proceeds to go to 9, which is a difference of 7.

After 9 it is 11, and the difference is 2.

After 11 it is 18 which is a difference of 7 again.

The pattern is difference of 7, difference of 2.

Since there was a difference of 7 between 20 and 27, the next difference will be 2, which is 29.

So, the pattern is +2, +7, +2 . . .

Therefore, your next three numbers will be 29, 36, 38

The equation in slope-intercept form is y = 85x - 43

The given parameters are

A linear equation is represented as

y = m(x - X) + Y

Where m is the slope

Substitute the known values in the above equation

So, we have the following equation

y = 85(x - 0) - 43

Evaluate

y = 85x - 43

Hence. the linear equation is y = 85x - 43

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Check the picture below.

Slope: -1/9

Y-Intercept: 2

The hourly rate that the business owner should pay the employees to obtain the desired net income of $40,000 is of:

$17.

The net income is calculated as the subtraction of the total income by the expenses.

In the context of this problem, the expenses are given as follows:

Hence the expression for the net income is given as follows:

110000 - [10800 + 2400 + 1800 + 1500 + 250 + 3(1040x)] = 40000

93250 - 3120x = 40000

3120x = 53250

x = 53250/3120

x = $17 an hour.

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Answer:

Step-by-step explanation:

so what is the difference from 1/4 to 5/8 ?   is the question

2/8=1/4

5/8-2/8 = 3/8

9 gallons of fuel fill 3/8 of the tank

since 3/8 is 9 gallons we can see that 1/8 will be 3 gallons or 9/3=3

then multiply 3 gallons by the 8 parts for the whole tank

3*8=24 gallons.

Than tank can hold 24 gallons

Answer:

a>11
[tex]a\leq 8[/tex]

Step-by-step explanation:

a+3>14
 -3.  -3

   a>11
a-5<=3

 +5. +5

  a<=8

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The radius of the tire is 1.17 yards.

According to the question,

We have the following information:

A tire could roll 200 yards in 27.28 revolutions.

We know that the tire is in the shape of a circle.

We also that the following formula is used to find the circumference of the circle:

2πr where r is the radius of the circle

Now, we have the following expression:

2πr*27.28 = 200

54.56πr = 200

r = 200/54.56π

r = 200/54.56*3.14

r = 200/171.32

r = 1.17 yards

(The unit of the radius will remain same as that of the distance given.)

Hence, the radius of the tire is 1.17 yards.

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The simplest form of fraction (1/4)/5 is 1/20.

A quotient is the simplest  or resultant value of division of two numbers. In two numbers, one number is dividend and another number is divisor,

quotient=dividend/divisor

The simplest form for fraction (1/4)/5,

(1/4)/5=1/(4×5)

         = 1/20

So, the simplest form of (1/4)/5 is 1/20.

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Answer:

10

Step-by-step explanation:

Round 492 to 500, then estimate 500/50