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Complete question :

The exponential model A=16.2e^0.01t describes the population, A, of a country in millions, t years after 2003. What was the population in 2003?

Answer:

16.2 million

Step-by-step explanation:

Given the equation :

A=16.2e^0.01^t

Where, t = number of years after 2003

The population in year 2003 ; can be obtained thus ;

t = 2003 - 2003 = 0

Put t = 0 in the equation :

A(0) =16.2e^0.01^0

A(0) = 16.2 * 1

A(0) = 16.2

Hence, population in 2003 is 16.2 million

i)It ended at  21:13

ii) 440*10/100

44 mins longer

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

110% = 440 minutes (Tuesday journey)

100% = 100/110 x 440

100% = 400 minutes (Monday journey)

Tuesday's journey took 40 minutes longer than Monday's journey.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

On Tuesday the train journey took 7 hours and 20 minutes and began at

13:53.

The time train journey ended.

= 13:53 + 7 hours + 20 minutes

= 13 hours + 53 minutes + 7 hours + 20 minutes

= 20 hours + 73 minutes

= 20 hours + 60 minutes + 13 minutes

= 20 hours + 1 hour + 13 minutes

= 21 hours + 13 minutes

This means,

= 21:13

The train ended the journey at 21:13

Tuesday's time of 7 hours and 20 minutes was 10% more than Monday's journey time.

This means,

Converting into minutes.

7 hours 20 minutes

= 60 x 7 + 20 minutes

= 420 minutes + 20 minutes

= 440 minutes

Monday's journey time.

110% = 440 minutes:

100% = 100/110 x 440

100% = 400 minutes

Thus,

Tuesday's journey took 40 minutes longer than Monday's journey.

Learn more about percentages here:

https://brainly.com/question/11403063

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Answer:

x = -47/3

Step-by-step explanation:

R = 3x + 9y

7 = 3x + 9(6)

7 = 3x + 54

-47 = 3x

x = - 47/3

Can't be reduced because 47 is prime

Answer:

x=  -47/3

Step-by-step explanation:

So the information we already have is

7 = 3x + 9 * 6

9 * 6 = 54

now it is

7 = 3x + 54

The equation can also be

3x + 54=7

First subtract 54 from both sides

3x + 54 - 54= 7 - 54

3x= -47

Then divide both sides by 3

3x/3= -47/3

x= -47/3

Answer:

x=-7

Step-by-step explanation:

8x - 2 = -11 + 7x + 2

First, separate the terms: move x to one side

subtract 7x from both sides

8x -7x - 2 = -11 + 7x -7x + 2

x - 2 = -11 + 2

Now get x by itself by adding 2 to both sides

x - 2 +2 = -11 + 2 +2

x = -11 + 4

simplify

x = -7

you're welcome

Simplify A:

2(x+3)-2

Use distributive property:

2x+6-2

Combine like terms:

2x+4

This is the same as B.

A and B are equivalent.

Answer:

Cost of five blouses = $145

Step-by-step explanation:

Let

x = cost of blouse

y = cost of skirt

15x + 2y = 505 (1)

5x + 2y = 215 (2)

Subtract (2) from (1) to eliminate y

15x - 5x = 505 - 215

10x = 290

x = 290/10

x = 29

Substitute x = 29 into (2)

5x + 2y = 215 (2)

5(29) + 2y = 215

145 + 2y = 215

2y = 215 - 145

2y = 70

y = 70/2

y = 35

x = cost of blouse = $29

y = cost of skirt = $35

How much do 5 such blouses cost?

cost of a blouse = $29

Cost of five blouses = $29 × 5

= $145

Cost of five blouses = $145

The age of Sita is five years more than Gautam's age. 5 years ago, the ratio of their ages was 3:2. Find their present ages.

The age of Sita = (x + 5) years.

And, the age of Gautam = x years.

Now,

5 years ago, the ratio of their ages was 3 : 2

[tex] \therefore [/tex] [tex] \bf \frac{3}{2} \: = \frac{x \: + \: 5}{x} [/tex]

Now by cross multiplying, we get,

3x = 2(x + 5)

3x = 2x + 10

3x - 2x = 10

Hence, the age of Sita = (x + 5) = (10 + 5) = 15 years.

And, the age of Gautam = x = 10 years.

Now,

The present age of Sita = 15 + 5 = 20 years. (Answer)

And, the present age of Gautam = 10 + 5 = 15 years. (Answer)

Answer:

-5, +3.4, -3.35, and- 9 1 3

Step-by-step explanation:

To find the opposite of any number we multiply it with -1 or divide it with -1

The opposite of 5 is given by  5 (-1)= -5

The opposite of -3.4 is given by  -3.4 (-1)= 3.4

The opposite of 3.35 is given by  3.35 (-1)= -3.35

The opposite of 913 is given by  913 (-1)= -913

This property is called the additive inverse. The additive inverse is that property which on addition of the numbers gives the answer = zero.

5-5= 0

-3.4+3.4= 0

3.35-3.35=0

913-913=0

Answer:

12

Step-by-step explanation:

Answer:

6 sessions

Step-by-step explanation:

s= session

silver gym: 30 +  45s

session 1: 75

session 2: 120

session 3: 165

session 4: 210

session 5: 255

session 6: 300

fit factor: 90+ 35s

session 1: 125

session 2 : 160

session 3: 195

session 4: 230

session 5: 265

session 6: 300

Answer:

X=5

Step-by-step explanation:

-3x+8=-7

-3x=-15

X=5

Answer:

56 meters or 56 m

Step-by-step explanation:

We first want to find the small square at the top it has 3 sides of the same length so it must be a square

5+5+5 is = to 15.

Then to find the bottom rectangle we so 7+7+11+11+5 and we get 14+22+5 and then 36+5 to end up getting 41

Then 41+15=56

Answer:The mean absolute deviation (MAD) of the number of pages in the 5 books Rori read =24

Step-by-step explanation:

To find the the mean absolute deviation (MAD,we start firt by

Getting  the mean of all values

Mean =120, 106, 94, 100, 180/5  =600/5=120

Next we subtract the mean value  from each value which is called distance

120 -120  = 0

106 -120 = -14

94 -120=  -26

100 -120=-20

180 -120=60

Thirldly, we find the mean of the distances  ignoring the negative signs

0+14+26+20+60 / 5 = 120/5=24

Answer:

X=-2

Step-by-step explanation:

equation a)

-y=42+18x

equation b)

y= (-43x+34)/20

Solution

42+18x= (-43x+34)/20

20(42+18x)=-43x+34

840+360x = -43x+34

360x+43x=34-840

403x= -806

x= -(806/403)

x= -(2)

x= -2

Answer:

12%

Step-by-step explanation:

For every value of x, the initial value is increased by 1+0.12 = 100% + 12%.

meaning we are adding 12% for every value of x

Answer:

x= -45

Step-by-step explanation:

Answer:

The area of it is 52 square feet

Answer:

13 pounds

Step-by-step explanation:

We know that the total weight of everything is 205 pounds, and the fridge itself is 192 pounds. So we need to calculate the weight of everything that is not a fridge, which would be:

205 - 192 = 13 pounds

That means that the box and the packaging is 13 pounds. Hope this helps!

Answer:

3.5 qt or 3 qt and 2c

Step-by-step explanation:

4 cups makes 1 quart

14/4 = 3.5

Answer:

3 In²

Step-by-step explanation:

Talking about surface area, the total area of an object is taken into consideration.

NB: Kindly check the attached picture for the diagram of the 3D object.

In this question, the surface area has to be determined and we will have to take into consideration all the area of the 3D object given in the question.

Surface Area = 6 × k².

Surface area = 6 × ( 1.8 × 1.8) cm².

Surface Area = 19.44 cm².

The next thing to do here is to convert the cm² to in². Therefore, 19.44 cm² ------>  x in².

19.44 × 0.155 in² = 3 in².

Answer:

x = .06418

Step-by-step explanation:

2 + (9.2)−8x = 2.32

(9.2)−8x = 2.32 − 2

log (9.2)−8x = log .32

−8x log 9.2 = log .32

−8x log 9.2

−8 log 9.2

=

log .32

−8 log 9.2

x = .06418

The qyaeriin has no attached diagram. A related diagram was found and used to provide the steps required to solve the problem.

Answer:

1 inch = 8.333 feets

Step-by-step explanation:

Initial dimension of rectangle :

100 feets by 10 feets

Fractional decrease in garden = 2/3

New Dimension of garden :

2/3(100 feets) by 2/3(10 feets)

66.667 feets by 6.6667 feets

Hence

From the picture attached :

8 inch = 66.667

1 inch = 8.333

The new scale of the drawing = 1 inch = 8.333 feets

PLEASE READ THIS EXPLANATION: It is an EXTREMELY foundational concept in algebra that must be understood. Ask questions in the comments if you do not understand anything because I love helping others learn! Do not be shy. :)

Alright, so let's just understand the problem. The interval [3,6] means that the smallest x-value is x=3 and the largest x-value is x=6, and they both INCLUDE x=3 and x=6 (It would exclude x=3 and x=6 if it was like interval (3,6) with parentheses). Since f(x) is an exponential function, the change per x is not consistent and its growth actually grows as it continues in the direction of infinity, so that is why the average rate of change is interesting and very much relies on what range there is. The average rate of change from x=3 to x=6 will be far smaller than the average rate of change farther down the road at x = 99999 and x = 100003.

So, how do we find the average rate of change? All you have to do is find the slope between two points. Simple as that.

So, how do we apply that here? Imagine a graph with two points, one point at x = 3 and one point at x = 6 and we do not know the y-value of either of these points. So, that's our first step!

We need to first find how much it grows at x=3 and x=6 separately to find the the y-value of these points. f(x) = 2^x for x = 3 means y = 8, and f(x) = 2^x for x = 6 means y = 64. We now have two points:

(3, 8) and (6, 64)

Now, all we have to do is find the slope between these lines. All we have to do is use the normal formula for finding slope:

(y₂ - y₁) / (x₂ - x₁) OR (y₁ - y₂) / (x₁ - x₂)

Most people use the first one, but they give you the exact same answer, so don't ever think it's impossible to use the second one. Let's just use the first formula anyway.

(3, 8) = (x₁, y₁)

(6, 64) = (x₂, y₂)

Now, let's use the formula (remember you can use either one because it won't affect your answer):

(y₂ - y₁) / (x₂ - x₁) = (64 - 8) / (6 - 3) = 56 / 3 = 18 and 2/3

So, the average rate of change is 18 and 2/3 or 18.666666667.

Answer:

14.4

Step-by-step explanation:

Answer:

if I'm right, you are trying to find the area of the parallelogram. if you are trying to find the area, then based on the information provided, you need to add the purple side (9.2 cm) with the grey side (2 cm) which gives you 11.2 cm. then you would multiply this answer by the blue line (7 cm) giving you 78.4 cm. finally, you divide this by 2 giving you 39.2 cm. I'm not sure if this was what you were looking for, but I hope this helps either way.

Step-by-step explanation:

(9.2 + 2) x 7/2

11.2 x 7/2

78.4/2 = 39.2

Volume of a cylinder = area of base x height:

50.24 x 3 = 150.72 ft^3

Answer:

150 ft³

Step-by-step explanation:

base = circle..................base area = area of the circle = πr².

to get the radius of the circle, we substitute from the formula.

let π be 3.142

3.142 × r² = 50.24.............................. 3.142r² = 50.24

divide both sides by 3.142 to get r² = 15.99....................find the square root of 15.99 to get r = 3.999.

VOLUME = πr²h

                = 3.142 × 3.999 ×3.999 × 3 = 150.72 ft³

This is another way of doing it.