In​ 2012, the population of a city was 6.51 million. The exponential growth rate was 2.75​% per year. ​a) Find the exponential growth function. ​b) Estimate the population of the city in 2018. ​c) When will the population of the city be 10 ​million? ​d) Find the doubling time.

Using the speed formula, we know that Liam finished in 1 hour as opposed to Sam's 1/ 19 hours, earning him the victory.

Speed is calculated as follows: speed = distance * time.

Knowing the units for distance and time is necessary to calculate the units for speed.

The units will be in meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).

So, the speed formula is:

Speed = Distance/Time

Taking time for the subject:

Time = distance/Speed

Now, Sam:
Time spent ascending the hill = 1/1 = 1 hour

Time spent descending the hill = 1/9 hours

Sam spent 1 1/the9 total minutes climbing and descending the hill.

Now, Lian:

Time spent ascending the hill = 1/2 hours

Time spent descending the hill = 1/2 hour

Total time spent ascending and descending the hill = 1/2 + 1/2 = 1 hour

Sam, therefore, took 1/9 hour longer than Liam.

Therefore, using the speed formula, we know that Liam finished in 1 hour as opposed to Sam's 1/ 19 hours, earning him victory.

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Coffee A is 12.241 pounds, Coffee B is 18.269 pounds and Coffee C is 24.482 pounds.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let a pounds of coffee A needed

Let b pounds of coffee B needed

Let c pounds of coffee C needed

c= 2a.................(1)

a+ b+c= 55..........(2)

and, 14.99 a+ 13.99 b + 10.39 c /55 = 12.61

1499a + 1399 b + 1039 c = 69,355...............(3)

Subtract (2) from (3), we get

  1499 a+ 1399 b + 1039 c= 69355

-  1039 a - 1039 b - 1039 c = 57145

_____________________________

  460 a + 360 b = 12210

 46a+ 36 b = 1221

b= 1221/ 36 - 46 a/ 36

b= 407 / 12 - 23 a / 18

Put b in Equation (2)

a + 407 / 12 - 23 a / 18 + 2a= 55

-5a / 18 + 2a + 407/ 12 = 55

31a/ 18 = 253/ 12

a= 4554 / 372

a = 2277/ 186

a= 759/ 62

a= 12.241

and, c=2a = 24.482

b= 33.91 - 15.641

b= 18.269

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The surface area of the composite figure is calculated as: 640 square inches.

The surface area of a rectangular prism = 2(w*l + h*l + h*w), where:

The composite figure can be decomposed into two rectangular prisms, 1 and 2.

Rectangular prism 1:

l = 10 in.

w = 0.5 ft. = 6 in.

h = 4 + 7 = 11 in.

Surface area = 2*(6*10 + 11*10 + 11*6) = 472 in.²

Rectangular prism 2:

l = 10 in.

w = 0.5 ft. = 6 in.

h = 4 in.

Surface area = 2·(6·10+4·10+4·6) = 248 in.²

The area of the surface where both meet = (l)(w) = (10)(4) = 40 in.²

Therefore:

Surface area of the composite figure = 472 + 248 - 2(40) = 640 in.².

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The circumference of the circle will be 56.52 m.

And, The area of a circle will be 254.34 m².

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The radius of circle = 9 m

Now,

Since, The area of circle = πr²

Hence, The area of circle = 3.14 × 9²

                                        = 3.14 × 81

                                        = 254.34 m²

And, The circumference of the circle = 2πr

                                                         = 2 × 3.14 × 9

                                                         = 56.52 m

Thus, The circumference of the circle will be 56.52 m.

And, The area of a circle will be 254.34 m².

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This raffle's expected value per ticket is $ 0.25.

Given that 5,000 tickets are sold at $1 apiece for a charity raffle, and tickets are to be picked at random, the following monetary prizes will be awarded.

To estimate the expected value of this raffle if you buy 1 ticket, apply the following calculation: 1 prize of $ 500, 3 prizes of $ 200, 5 prizes of $ 10, and 20 prizes of $ 5.

⇒ (500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X

⇒ (500 + 600 + 50 + 100) / 5000 = X

⇒ 1250/5000 = X

Apply the division operation, and we get

⇒ 0.25 = X

Therefore, this raffle's expected value per ticket is $ 0.25.

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When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.

From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.

It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.

Therefore, the number of flags is 40.

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Eddie and Brad together shovel the snow in 1 hour 26 minutes.

Two or more expressions with an Equal sign is called as Equation.

Given that it takes Eddie 2 hours to shovel the snow from a driveway and sidewalk.

Brad can shovel the snow from the same driveway and sidewalk in 5 hours.

We now find how long would it take them working together to shovel the snow.

Eddie does 1/2 in 1 hour or x/2 in x hours

Brad does 1/5 in 1 hour or x/5 in x hours

the sum is 1 full job

(x/2)+(x/5)=1

multiply both sides by 10

7x=10

x=(10/7) hours or 600/7 minutes =86 minutes

As we know 1 hour has 60 minutes.

We can write 86 minutes as 1 hour and 26 minutes.

Hence, 1 hour 26 minutes is the time taken by Eddie and Brad to shovel the snow.

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Answer:

No real solutions.

Step-by-step explanation:

No real solutions.

The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N - 1

Population variance is a measure of dispersion that determines how far each data point is from the population mean.

On the population, the population variance is calculated. When the number of observations grows, a few data points are chosen to represent the entire population.

The variance calculated on these specific data points is referred to as the sample variance. The population variance can be estimated using the sample variance.

When the population variance is unknown , we estimate the population variance by using sample variance

The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N-1

Formula of sample variance  = [tex]s^2 = \frac{\sum f_i(x_i - \bar{x})}{N-1}[/tex]

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Answer: 2. 37.8%

3. 30% decrease

Step-by-step explanation:

Increase = New Number - Original Number

Then:  divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

36.99-22.99=14

100(14/36.99)

37.8%

First: work out the difference (decrease) between the two numbers you are comparing.

Decrease = Original Number - New Number

Then: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100

2.50-1.75=0.75

100(0.75/2.5)

30%

Answer:

  (11, 3)

Step-by-step explanation:

You want the point 1/6 of the way from A(14, -1) to B(-4, 23).

The point P that divides AB into the fractional parts k and (1 -k) is ...

  P = (1-k)A +kB

For k = 1/6, the dividing point is ...

  P = (5/6)(14, -1) +(1/6)(-4, 23) = (5·14 -4, 5(-1) +23)/6 = (66, 18)/6

  P = (11, 3)

The point 1/6 of the way from A to B is (11, 3).

Answer:

log(2)√xy

________

y

there good luck

Answer:

Step-by-step explanation:

[tex]\tt 30-19+29+30-29-10[/tex]

[tex]\tt 11+29+30-29-10[/tex]

[tex]\tt 40+30-29-10[/tex]

[tex]\tt 70-29-10[/tex]

[tex]\tt 41-10[/tex]

[tex]\tt 31[/tex]

__________________

Hope this helps you!

Have a nice day!

If in a recent poll, 280 people were asked if they liked dogs, and 42% said they did. the margin of error of this poll, at the 90% confidence level is 0.05.

Sample proportion =42%(phat)

Sample size =280

Standard error = √(0.42×( 1- 0.42)/280)

Standard error = √(0.42×(.58)/280)

Standard error =0.029

Hence,

Margin of error = z-critical for 90% confidence level× Standard error

Zα/2 = 1.645 for 90% confidence

Margin of error =  1.645 × 0.029

Margin of error  = 0.047

Margin of error =0.05 (Approximately)

Therefore the margin of error is 0.05.

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Assuming that the tips are approximately normally distributed, an interval to estimate the true average tip (as a percent of the bill) with 90% confidence is (10.47, 11.73).

Assuming that the tips are approximately normally distributed, we would determine both the lower limit and upper limit for the confidence interval where 90% of the sample means occur as follows;

Lower limit = μ - σ/√x

Lower limit = 11.1 - 2.8/√20

Lower limit = 11.1 - 0.63

Lower limit = 10.47

For the upper limit, we have:

Upper limit = μ - σ/√x

Upper limit = 11.1 + 2.8/√20

Upper limit = 11.1 + 0.63

Upper limit = 11.73

For 90% of the sample means to occur, the confidence interval is as follows;

Confidence interval = (10.47, 11.73)

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The number of catnip toys that Jose can buy will be 3 catnip toys. All the steps are described below.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The table is given below.

       Product                 Cost

Bag of Dog Food          $35

Bag of Cat Food            $18

Chew Toy                      $12

Catnip Toy                      $9

In the event that, your numbers are unique, you should simply supplant the qualities you have with the methodology here, and you ought to find an exact solution.

Presently, Emma has $100 to spend at the store. Along these lines, we really want to ascertain the amount she spends on shopping:

$35 + 2 x $12 = $59

In this way, she burned through $59 in the store, so she has left:

$100 - $59 = $41

She has $41 left to spend on something different. How about we check whether she has sufficient means to purchase multiple times catnip toys as bite toys:

Chew toys: 3 x 12 = $36

Catnip toy: 3 x 9 = $27

Furthermore, Emma has $41 left, so she can either purchase multiple times bite toys or multiple times catnip toys, however not the two of them at that point, on the grounds that the all-out would be 63% dollars, and she will be missing $22.

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The inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) quadratic function is

The problem seeks the inequality that will be less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).

Therefore the quadratic function should have zeros at -7 and 1

Substituting the point (2, 27/2) to the quadratic function to check the one that gives the points shows that

3/2 x² + 9 x - 21/2 at x = 2

3/2 * 2² + 9 * 2 - 21/2

= 27/2

Solving for the zeros in the quadratic function 3/2 x² + 9 x - 21/2

shows that the zero are at

x = -7 and

Therefore the inequality that meets the condition is y < 3/2 x² + 9 x - 21/2

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The correct option is All real values of a.

What is the real number?

The positive and negative integers, as well as the fractions created from them (also known as rational numbers), as well as the irrational numbers, are all real numbers.

We have,

3x² + 2xy = 4    ...................(1)

x + y = a             ...................(2)

By converting the second equation equals to y:

y = a - x             .....................(3)

By substituting the (3)rd equation into (1), we get

3x² + 2xy = 4

3x² + 2x(a - x) = 4

3x² + 2ax - 2x² = 4

x² + 2ax = 4

x² + 2ax - 4 = 0

Discriminant  = 4a² + 16 >=  0

2 distinct solutions & is ok for all a.

hence, the correct option is All real values of a.

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The required length of the longest side will be 28/5 cm in the triangle.

The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.

We have been given that the three sides of a triangle are in the ratio of 3:5:7

Let's assume the sides are 3x, 5x, 7x

Since the perimeter of the triangle is 12 cm.

So, 3x+5x+7x = 12

Apply the addition operation,

15x = 12

x = 12/15

Reduce the above fraction to the simplest form

x = 4/5

So, longest side = 7x = 28/5 cm

Thus, the required length of the longest side will be 28/5 cm in the triangle.

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Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.

The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/[tex]s^{2}[/tex]

They will strike the ground simultaneously if the table and the ground are both flat.

It is customary to divide an object's motion into a vertical component and a horizontal component. While they are on the table, neither of the balls is moving vertically. Both balls begin to accelerate downward as soon as they leave the table due to the effects of gravity. Given that both balls experience the same acceleration from gravity, they will fall at the same rate and with the same downward velocity.

Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.

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Answer:

55

Step-by-step explanation:

Because you would minus 180-125 to get angle 1 and they said that angle 2 is parallel so they would be the same anwser so the answer is 55.

The absolute value function that is represented in the graph is f(x) = |x + 1.5| So the correct option is D.

The general absolute value function is:f(x) = |x|This absolute value function has a vertex at the point (0, 0). We know that the graphed function has a vertex at the point (-1.5, 0).

So basically we had a horizontal translation of -1.5 units or 1.5 units to the left. That is written as: g(x) = f(x + 1.5)

Replacing the absolute value function we get:g(x) = |x + 1.5|

Then the correct option is D.

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[tex]\frac{\sin \theta}{300}=\frac{\sin 2\theta}{400} \\ \\ \frac{\sin \theta}{300}=\frac{2\sin \theta \cos \theta}{400} \\ \\ \frac{1}{300}=\frac{\cos \theta}{200} \\ \\ \cos \theta=\frac{2}{3} \\ \\ \theta=\arccos(2/3) \\ \\ \theta \approx \boxed{48^{\circ}}[/tex]

Answer:

5 weeks

Step-by-step explanation:

20 inches  /  ( 4 inches/week ) = 5 weeks

By using the concept of vector, it can be calculated that

Direction of the sum is 10.87° below the horizontal.

What is vector?

Anything that has both magnitude and direction and follow the vector addition law is called vector.

A = 2.71 m

[tex]A_x = 2.71 cos 60 = 1.355 \ m\\A_y = -2.71 sin 60 = -2.35 \ m[/tex]

B = 3.14 m

[tex]B_x = 3.14 cos 30 = 2.71 \ m\\B_y = 3.14 sin 30 = 1.57 \ m[/tex]

Sum of A and B = (1.355  +2.71) i + (-2.35 + 1.57) j

                           = 4.065i - 0.78j

Let the angle be [tex]\theta[/tex]

[tex]tan\theta = \frac{0.78}{4.065}\\tan\theta = 0.192\\\theta = tan^{-1}(0.192)\\\theta = 10.87^{\circ}[/tex]

Direction of the sum is 10.87° below the horizontal.

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Answer:

24 inches

Step-by-step explanation:

To find the longest possible length of the shorter pieces that Terri can saw, you need to find the greatest common factor (GCF) of the three original lengths: 30 inches, 48 inches, and 72 inches.

The GCF of 30, 48, and 72 can be found by finding the prime factorization of each number and taking the lowest exponent for each prime factor.

30 = 2 * 3 * 5

48 = 2^4 * 3

72 = 2^3 * 3^2

The GCF is 2^3 * 3 * 5, or 24 inches. Therefore, the longest possible length of the shorter pieces that Terri can saw is 24 inches.

Hello,

I hope you and your family are doing well!

To find the GCF is to use the Euclidean algorithm, which involves repeatedly dividing the larger of the two numbers by the smaller one until the remainder is 0. This can be a quicker method for finding the GCF of larger numbers.

For example:

72 / 30 = 2 with a remainder of 12

30 / 12 = 2 with a remainder of 6

12 / 6 = 2 with a remainder of 0

The last non-zero remainder is 6, so the GCF is 6.

Regardless of the method used, the GCF of 30, 48, and 72 is 6, so the longest possible length of the shorter pieces that Terri can saw is 6 inches.

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Answer:

(a) Equation of parallel line is y = x + 4

(b) Equation of perpendicular line is y = - x + 8

Step-by-step explanation:

Given line is

x - y = 4

Rewrite this as

x - 4 = y

or

y = x - 4

This is the equation of a line in slope intercept form which is generally

y = mx + b

where m is the slope and b the y-intercept

Here m = 1, b = -4

(a) A parallel line will have the same slope but a different y-intercept
So for starters we can write the equation of the parallel line as
y = x + b

Since this passes through (2,6) sub 2 for x and 6 for y to get

6 = 2 + b

==> b = 4

Equation of the line is
y = x + 4

(b) A perpendicular line will have as slope -1/m where m is the slope of the original line

Here m = 1, so -1/m = -1/1 = -1

Equation will be of the form
y = -x + b

Since this also passes through (2,6)
6 = -2 + b

==> b = 6 + 2 = 8

Equation of perpendicular line is
y = -x + 8