help needed with this one

The population of the country will be 1051 million in 2014

The exponential model that describes the population of a country' in millions, t years after 2003 is given as:

A = 999.8 e0.002t

Rewrite the function properly as:

A = 999.8 * e^(0.002t)

When the population of the country is 1051 million, it means that:

A = 1051

Substitute the known values in the above equation

So, we have:

1051 =  999.8 * e^(0.002t)

Divide both sides by 999.8

1.0512 = e^(0.002t)

Take the natural logarithm of both sides of the equation

ln(1.0512) = ln(e^(0.002t)

Rewrite the equation as:

ln(e^(0.002t) = log(1.0512)

This gives

0.002t = log(1.0512)

Evaluate the logarithmic expression

0.002t = 0.0216

Divide both sides of the equation by 0.002

t = 0.0216/0.002

Evaluate the quotient

t = 10.8

Approximate 10.8 as 11

t = 11

11 years from 2003 is 2014

Hence, the population of the country will be 1051 million in 2014

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Answer:

x - 4

Step-by-step explanation:

monomial is one term

-11x is only one term

x-4 isn't

3 is one term

22xy is only one term

only x-4 isn't a monomial

Answer:

Step-by-step explanation: I did the test and the answer should be A

hope this helps :)

The value of length HL is 8.

A secant is a line that intersects a circle in exactly two points

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.

Therefore,

(EF + FL)FL = HL(GH + HL)

(10 + 14)10 = (HL + 30 - HL)HL

240 = 30(HL)

divide both sides by 30

Hence,

240 / 30 = 30HL / 30

8 = HL

Therefore,

HL = 8

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10 meters away is the bus from the bus stop after 10 seconds.

A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.

A bus moves away from bus stop in a straight line. After 1 second it was 10 meters away, after 2 seconds it was 20 meters and after 3 seconds it was 30 meters away.

In this way bus forms an arithmetic sequence

10, 20, 30, 40........up to 10 terms.

nth term of an arithmetic sequence is represented by

[tex]T_{n}[/tex] = a+ (n - 1)d

Here a = 10 and d = common difference = 10

Therefore 10th term = 10 + (10-1)10

                                  = 10 + 90

                                  = 100

Therefore after 10 seconds bus will be 10 meters away from the bus stop.

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If [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.

Given that [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 of commodities x and y.

Marginal utility is the additional utility that a consumer gets from consuming additional units of commodity. For maximising the utility of the consumer,the ratio of marginal utilities must be equal to the ratio of the products.

There can be two situations in our case:

Because [tex]MU_{x}/P_{x}[/tex]<[tex]MU_{y} /P_{y}[/tex]

So to equalise the ratio we need to reduce [tex]MU_{y} /P_{y}[/tex]. To reduce the utility of y the consumer needs to increase the consumption of y because as the consumption of commodity y increase it decreases the utility of commodity y.

Hence if [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.

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Answer: It is an equilateral square

Step-by-step explanation: it has 4 tick marks

The function y = 2sin has a phase shift of pi/2 to the right (2x - pi).

To find the function which has a phase shift to the right:

The function has a phase shift of pi/2 to the right.

By definition, you have the phase shift is:

When you substitute the values from the function [tex]y=2sin(2x-\pi )[/tex], where  [tex]c=-\pi[/tex]  and [tex]b=2[/tex], you obtain:

Therefore, the function y = 2sin has a phase shift of pi/2 to the right (2x-pi).

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The complete question is given below:
Which function has a phase shift of pi/2 to the right?

The multiplication shows that the answers will be:

1. 3744

2. 8244

3. 3630

4. 2616

5. 20772

6. 7820

7. 3916

8. 3521

9. 21285

10. 54162

11. 4548

12. 2091

13. 17128

14. 55692

15. $895

16. 4300 miles

1. 416 × 9 = 3744

2. 1374 × 6 = 8244

3. 726 × 5 = 3630

4. 872 × 3 = 2616

5. 2308 × 9 = 20772

6. 1564 × 5 = 7820

7. 4 × 979 = 3916

8. 503 × 7 = 3521

9. 5 × 4257 = 21285

10. 6018 × 9 = 54162

11. 758 × 6 = 4548

12. 3 × 697 = 2091

13. 2141 × 8 = 17128

14. 7 × 7956 = 55692

15. From the information given, the cost of each ticket is $179. Also, there are 5 people that are flying.

Therefore, the total cost will be:

= $179 × 5

= $895

16. Also, for the second question, since the distance between the two cities is 2150 miles. The exact distance will be:

= 2150 × 2

= 4300 miles.

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The probability is 1/3.

Probability is sincerely how likely something is to show up. whenever we're unsure about the final results of an event, we will communicate about the probabilities of positive consequences—how probably they're. The evaluation of events governed by way of possibility is called information.

Probability is the branch of mathematics concerning numerical descriptions of ways likely an occasion is to arise, or how in all likelihood it's far that a proposition is actual. The opportunity of an event is more than a few among 0 and 1, wherein, kind of talking, zero suggests impossibility of the occasion and 1 shows the truth.

Chance = the wide variety of approaches to achieving achievement. the whole range of viable consequences. as an example, the opportunity of flipping a coin and its being heads are ½ because there may be 1 manner of getting a head and the overall wide variety of feasible results is two (a head or tail). We write P(heads) = ½.

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Answer:

=========================

The distance traveled by two planes in an hour is:

Let the rate of one plane be x, then the other plane's rate is x - 66.

The sum of two rates is the distance traveled in one hour:

So the rate of one plane is 926 km/h and of the other plane is:

The total cost that company ABC uses to produce x graphing calculators in a month is given by y = 1.5x + 150

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard form of a linear function is:

y = mx + b

Where m is the rate of change and b is the initial value of y.

Let y represent the total cost of producing x calculators in a month, hence:

y = 1.5x + 150

The total cost that company ABC uses to produce x graphing calculators in a month is given by y = 1.5x + 150

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The mean of the sample from number of patients treated at Dr. Frank's dentist office each day for ten days is 8.2

Given data:

13, 9, 7, 8, 2, 4, 22, 12, 5, 0.

Mean of the sample = Total number of patients treated / number of days

= (13 + 9 + 7 + 8 + 2 + 4 + 22 + 12 + 5 + 0) / 10

= 82/10

= 8.2

Therefore, the mean of the sample is 8.2

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Answer:

=> Equilateral Triangle

Step-by-step explanation:

Equilateral Triangle is having 2-d shape with all equal sides and the sum of angles of any triangle is 180° .

Answer:

Connect the arcs to make a perpendicular bisector

Answer:

$0.32

Step-by-step explanation:

8 ounces is 1/16 of a gallon so

5.12*(1/16) = 0.32

Answer:

32 cents (0.32 dollars)

Step-by-step explanation:

One gallon contains 128 ounces

Calculate the cost of each ounce:

[tex]\frac{5.12}{128} =0.04[/tex]

costs 4 cents an ounce

Calculate the cost of 8 ounces:

[tex](8)(4)=32[/tex]

Hope this helps

The source of the force in the gas sample is; The force is composed of the sum of the collisions only between the gas molecules and the container

We are given that;

Pressure = Force /Area

Now, for any gas sample, force is defined as basically the force exerted by the gas molecules when they strike the surface and bounce back inside the container where they are located.

Now, from the definition above we can conclude that the source of the force in the gas sample will be The force is composed of the sum of the collisions only between the gas molecules and the container

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Using proportions, it is found that the difference between the two salary options each year is of $5,545.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

For the first option, $115 per week plus 9.5% commission on the associate’s total sales, the yearly salary is:

115 x 52 + 0.095 x 125000 = $17,855.

For the second option, $450 per week with no commission, the yearly salary is:

450 x 52 = $23,400.

Hence the difference is given as follows:

23400 - 17855 = $5,545.

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[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&96\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&160\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+96t+160[/tex]

Check the picture below.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+96}x\stackrel{\stackrel{c}{\downarrow }}{+160} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 96}{2(-16)}~~~~ ,~~~~ 160-\cfrac{ (96)^2}{4(-16)}\right) \implies \left( - \cfrac{ 96 }{ -32 }~~,~~160 - \cfrac{ 9216 }{ -64 } \right)[/tex]

[tex](3~~,~~160 + 144)\implies \underset{~\hfill feet}{\stackrel{seconds~\hfill }{(\stackrel{\downarrow }{3}~~,~~\underset{\uparrow }{304})}}[/tex]

Answer:  1.3125 gallons

Step-by-step explanation: The machine pumps 2.1 gallons of water every 1.6 minutes. 1.6 minutes is 1.6x more than 1 minute. So, we have to divide 1.6 by 1.6. Next, we have to divide 2.1 by 1.6. We can make this a bit easier by multiplying both of them by 10 to get 21/16 which is 1.3125.

Answer:

1.3125 gallons

Step-by-step explanation:

Using the given information, we can set up a proportion;

[tex]\frac{2.1gallons}{1.6minutes} = \frac{xgallons}{1minute}[/tex]

Now, we can cross multiply to solve for x.

2.1 = 1.6x
x = 1.3125 gallons

Answer:

Step-by-step explanation:

3. A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible). This will help me to see weather or not it is positive or negative.3

Step-by-step explanation:

x = the number of goals of the top scorer.

y = the number of goals of the second top scorer.

z = the number of goals of the third top scorer.

x + y + z = 98

x = y + 8

y = z + 15

using the third in the second equation we get

x = z + 15 + 8 = z + 23

and now using this and the third equation in the first equation gives us

z + 23 + z + 15 + z = 98

3z + 38 = 98

3z = 60

z = 20

y = z + 15 = 20 + 15 = 35

x = y + 8 = 35 + 8 = 43

the player with the most goals scored 43 goals.

Considering it's histogram, the shape of the distribution is given by:

D. Bimodal.

An histogram of a data-set is a graph that shows the number of times each element of x was observed.

In this problem, elements 1 and 10 were each observed 5 times, meaning that there are two modes in the data-set, hence the data-set is bimodal and option D is correct.

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The expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].

What is an expression?

To find which expression correctly sets up the quadratic formula to solve the equation:

Theory of quadratic equation - A quadratic equation is defined as any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

An example of a quadratic equation in x is [tex]-4x^{2} +4=9x[/tex].

How to solve any quadratic equation using the Sridharacharya formula?

Let us represent a general quadratic equation in x, [tex]ax^{2} +bx+c=0[/tex] where a, b and c are coefficients of the terms.

According to the Sridharacharya formula, the value of x or the roots of the quadratic equation is -

[tex]x=\frac{-b+-\sqrt{(b)^{2}-4(a)(c) } }{2a}[/tex]

The given equation is [tex]x^{2} -4x+3=0[/tex]

Comparing with the general equation of quadratic equation, we get a = 1, b = -4 , c = 3.

Putting the values of coefficients in the Sridharacharya formula,

[tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex]  which is (A).

Therefore, the expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].

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The complete question is shown below:

Consider this quadratic equation. x^2+3=4x. Which expression correctly sets up the quadratic formula to solve the equation?

since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.

[tex]\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}[/tex]

The required length of the side BM is 29.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

In the given question,

Point M is the midpoint of line AB.

AM = 4x + 13,

and BM = 3x + 17

To find the length of MB, use midpoint property.

Since, Point M is the midpoint of AB,

Therefore, AM = MB

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

The length of MB = 3x + 17 = 3 × 4 + 17 = 12 + 17 = 29.

The length of MB, where M is midpoint of AB, is 29.

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The simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1

The equation can be simplified as follows:

7y + 8 = 9 + 3y + 2y

We have to combine like terms

Hence,

7y + 8  = 9 + 3y + 2y

7y + 8 = 9 + 5y

subtract 5y from both sides

7y - 5y + 8 = 9 + 5y - 5y

2y + 8 = 9

Let's subtract 8 from both sides

2y + 8 - 8 = 9 - 8

2y = 1

Therefore, the simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1

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Answer:

8

Step-by-step explanation:

You are correct The distance from -6 to 2 is 8.

The given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.

According to the given question.

We have a sequence,

[tex]a_{n} = 2^{\frac{1}{n} }[/tex]

Since, we know that

The sequence of real numbers [tex]S_{n}[/tex], where n goes from 1 to infinity has a limit L, the the sequence is convergent to L. If the sequence doesn't have limit then it is divergent.

The nth root function is strictly increasing for positive real values.

Therefore,

[tex]1^{\frac{1}{n} } \leq 2^{\frac{1}{n} } \leq n^{\frac{1}{n} }[/tex]           [tex]\forall \ n\geq 2[/tex]

Also,

[tex]\lim_{n \to \infty} n^{\frac{1}{n} } = 1[/tex]

[tex]\implies \lim_{n \to \infty} 1^{\frac{1}{n} } =1[/tex]   ( by squeeze theorem)

Thereofore,

[tex]\lim_{n \to \infty}2^{\frac{1}{n} } =1[/tex]

So, the given sequecence has a limit i.e. 1. Which means [tex]2^{\frac{1}{n} }[/tex] is a convergent sequence.

Hence, the given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.

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