The population of a town was 5655 in 2010. The population grows at a rate of 2.6% annually.
(a) Use the exponential growth model to write an equation
that estimates the population t years after 2010.
(b) Fill in the following table for each value of . Show your work. You may use a calculator to
calculate the final answer. Round your answers to the nearest whole number.

Answer:

-6

Step-by-step explanation:

f(x) = -2x - 7 and g(x) = -4x + 6

Find f(-5)

f(-5) = -2(-5) -7 = 10-7 = 3

The find g(3)

g(3) = -4(3) +6

     = -12 +6 =-6

g(f(-5)) = -6

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

Explanation:

Add up the values to get

1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54

Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.

So the mean is approximately 1.8876923

---------------------

Now make a spreadsheet as shown below

We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.

After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.

That sum is approximately 0.04403076924

Next, we divide that over n-1 = 13-1 = 12

0.04403076924 /12 = 0.00366923077

That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.

sqrt(0.00366923077) = 0.06057417576822

This rounds to 0.061 which is the final answer.

Answer:

0.05547

Step-by-step explanation:

Given :

_____Peter __ Alan __ Sui__total

Before 1838 __ 418 ___1475 _3731

After _ 1420 __ 329 ___1140_2889

Total _3258 __ 747 __ 2615 _6620

The expected frequency = (Row total * column total) / N

N = grand total = 6620

Using calculator :

Expected values are :

1836.19 __ 421.006 __ 1473.8

1421.81 ___325.994__ 1141.2

χ² = Σ(Observed - Expected)² / Expected

χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)

χ² = 0.05547

Answer:

The student's GPA is of 0.82.

Step-by-step explanation:

GPA:

To find the student's GPA, we find his weighed mean.

Grades:

7 hours worth 3(B)

6 hours worth 1(D)

20 hours worth 0(F). So

[tex]M = \frac{7*3 + 6*1 + 20*0}{7+6+20} = 0.82[/tex]

The student's GPA is of 0.82.

Answer:

The answer is Line Segment SR.

Answer:  Choice D

HG= 11 square root 3/3 and HI = 22 square root 3/3

In other words, [tex]\text{HG} = \frac{11\sqrt{3}}{3} \ \text{ and } \ \text{HI} = \frac{22\sqrt{3}}{3}\\\\[/tex]

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

Explanation:

Let's say that x is the short leg and y is the long leg

For any 30-60-90 triangle, we have this connection: [tex]y = x\sqrt{3}[/tex]

The long leg y is exactly sqrt(3) times longer compared to the short leg x.

Let's solve for x and then plug in y = 11

[tex]y = x\sqrt{3}\\\\x = \frac{y}{\sqrt{3}}\\\\x = \frac{y*\sqrt{3}}{\sqrt{3}*\sqrt{3}}\\\\x = \frac{y\sqrt{3}}{3}\\\\x = \frac{11\sqrt{3}}{3}\\\\[/tex]

Side HG, the shorter leg, has an exact length of [tex]\text{HG} = \frac{11\sqrt{3}}{3}\\\\[/tex]

------------------

Once we know the short leg, we double that expression to get the length of the hypotenuse. Like before, this only applies to 30-60-90 triangles.

[tex]\text{hypotenuse} = 2*(\text{short leg})\\\\\text{HI} = 2*\text{HG}\\\\\text{HI} = 2*\frac{11\sqrt{3}}{3}\\\\\text{HI} = \frac{22\sqrt{3}}{3}\\\\[/tex]

------------------

Since [tex]\text{HG} = \frac{11\sqrt{3}}{3}\\\\[/tex] and [tex]\text{HI} = \frac{22\sqrt{3}}{3}\\\\[/tex], this shows that choice D is the final answer.

Answer:

[tex]4x-1[/tex]

Step-by-step explanation:

Answer:

65% of 27.69 is 18.

Step-by-step explanation:

Formula = Number x 100

Percent = 18 x 100

65 = 27.69

Following shows the steps on how to derive this formula

Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.

18

65% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

65Y = 18 x 100

65Y = 1800

Y = 1800

100 = 27.69

Answer:

There is not enough evidence to support the claim that the bags are under filled.

Step-by-step explanation:

Given :

Population mean, μ = 433

Sample size, n = 26

xbar = 427

Variance, s² = 324 ; Standard deviation, s = √324 = 18

The hypothesis :

H0 : μ = 433

H0 : μ < 433

The test statistic :

(xbar - μ) ÷ (s/√(n))

(427 - 433) / (18 / √26)

-6 / 3.5300904

T = -1.70

The Pvalue :

df = 26-1 = 25 ; α = 0.05

Pvalue = 0.0508

Since Pvalue > α ; WE fail to reject the Null and conclude that there is not enough evidence to support the claim that the bags are underfilled

Answer:

40

Step-by-step explanation:

range is the difference between the highest and lowest number.

60 is the highest and 20 is the lowest

60-20=40

Answer:

False

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

The figure has total 15 faces, the correct option is A.

A hexagon is a polygon with six sides.

A hexagonal pyramid has 8 faces

From (2 hexagonal base + 6 lateral surfaces)

A hexagonal prism has 7 faces

From ( A hexagonal base + 6 lateral faces)

Total faces the figure has is 8 +7 = 15

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The given graph is a line and he line is the distance between two points.  The required equation of the line is y = 0.5x + 5

The given graph is a line and he line is the distance between two points. The equation of a line is represented as;

y = mx+ b

Given the coordinate points (-5, 4) and (1, 7)

Get the slope

Slope = 7-4/1-(-5)

Slope = 3/6

Slope = 0.5

The intercept is 5 (the point where the line cuts the y-axis)

Determine the required equation

y = 0.5x + 5

Hence the required equation of the line is y = 0.5x + 5

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Answer:

Logx(1/8) = -3/2

x = 4

Answered by GAUTHMATH

Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.

g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]

Option C

Hope this helps!

Answer:

30 and 270 respectively

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*4=1200 and (x-y)*5=1200. Solving it, we get x=270 and y=30

Answer:

I think its C:37

Step-by-step explanation:

And if im wrong sorry :/

Terms given

No of terms=8

We know

[tex]\boxed{\sf Mean=\dfrac{Sum\;of\:terms}{No\;of\:terms}}[/tex]

[tex]\\ \sf\longmapsto Mean=\dfrac{40+35+32+39+34+35+35+37}{8}[/tex]

[tex]\\ \sf\longmapsto Mean=\dfrac{270}{8}[/tex]

[tex]\\ \sf\longmapsto Mean=35[/tex]

Final Answer:

35

Step-by-step explanation:

-median is the middle number in the data set-

arrange the data set from least to greatest:

40, 30, 32, 39, 34, 35, 35, 37 ⇒ 30, 32, 34, 35, 35, 37, 39, 40

we start from the lowest number and the highest  number and work your way to the middle:

30, 32, 34, 35, 35, 37, 39, 40

notice that there is no middle number:

30, 32, 34, 35, ?, 35, 37, 39, 40

so what we do is add both 35's and then divide it by 2

35 + 35 = 70 ÷ 2 = 35

median: 35

The ratio of customers  from Zone 1 to  from Zone 3 is 1 : 2

This question appears to be incomplete.

Please find attached the graph required to answer this question

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

The graph is in the image is a bar graph

A bar graph is a pictorial representation of data. The rectangles measure the length of the data

Looking at the graph, the interval is 100

Looking at the rectangle that represents zone 1, it appears to be halfway between 400 and 500. It is concluded that the number of customers in zone 1 is 450

Looking at the rectangle that represents zone 3, it appears to lie on 900.

It can be concluded that there are 900 customers in zone 3

the ratio of zone 1 to 3

450 : 900

to convert to its simplest form, divide both side of the ratio by 450

1 : 2

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Answer:

The missing segment length is 20.

Step-by-step explanation:

2 is multiplied by 4 to get to 8, so 5 must be multiplied by 4 to get to 20.

Answer:

side AC is 5

Step-by-step explanation:

by using th pythagorean theorm you would square both sides add them together and the square root the sum to get you answer.

AB =3 BC=4

9+16=25

25 square root is 5

makeing AC=5

Answer:

[11.906 ; 12.894]

Step-by-step explanation:

Given :

Sample mean, xbar = 12.4

Sample standard deviation, s = 1.7

Sample size, n = 48

We use the T distribution since we are using the sample standard deviation;

α - level = 95% ; df = n - 1 = 48 - 1 = 47

Tcritical = T(1 - α/2), 47 = 2.012

Using the confidence interval for one sample mean

Xbar ± Tcritical * s/√n

12.4 ± (2.012 * 1.7/√48)

12.4 ± 0.4936922

C. I = [11.906 ; 12.894]

This value is approximate.

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

Explanation:

We have a normal distribution with these parameters

The goal is to find the area under the curve from x = 68 to x = 158, where x is the number of text messages sent per day. So effectively, we want to find P(68 < x < 158).

Let's convert the score x = 68 to its corresponding z score

z = (x-mu)/sigma

z = (68-128)/30

z = -60/30

z = -2

This tells us that the score x = 68 is exactly two standard deviations below the mean mu = 128.

Repeat for x = 158

z = (x-mu)/sigma

z = (158-128)/30

z = 30/30

z = 1

This value is exactly one standard deviation above the mean

-------------------------------------------

The problem of finding P(68 < x < 158) can be rephrased into P(-2 < z < 1)

We do this because we can then use the Empirical rule as shown in the diagram below.

We'll focus on the regions between z = -2 and z = 1. This consists of the blue 13.5% on the left, and the two pink 34% portions. So we will say 13.5% + 34% + 34% = 81.5%

Approximately 81.5% of the the population sends between 68 and 158 text messages per day. This value is approximate because the percentages listed in the Empirical rule below are approximate.

Answer:

C. 81.5%

Step-by-step explanation:

Answer:

Check the photo for the answer

Answer:-10

-3+-4+-3

-3-4=-7

-7+-3=-7-3

=-10

Answer:

Political stability is a variable of great importance in a country's evolution since, across time, it was identified as causing law level of economic growth, but also it was presented as a consequence of poor economic development.