The populations P (in thousands) of a certain town in North Carolina, from 2006 through 2012 can be modeled by
P = 5.5ekt,
where t is the year, with
t = 6
corresponding to 2006. In 2008, the population was 7000.

Find the value of k, rounding to 4 decimal places

Then Use the model to predict the population in 2018 (nearest person)

Answer:

A

Step-by-step explanation:

4 x $0.85= $3.40  

$9-$3.40= $5.60

Answer:

A. $5.60

Step-by-step explanation:

4x0.85 =3.4 and 9 -3.4 = 5.6

Answer:

a. m<CBA = m<DBA because of the definition of an angle bisector (angle bisector cuts the angle in half) We are also told that segment BD and Segment BC are congruent.

We don't know if segment AC and AD are congruent so we can't say those angles (the other two) are congruent.

b. point A and B will stay fixed because they are colinear to segment AB (on the same line)

c. Those two are needed because If those are true we can prove that they are congruent by SAS (Side Angle Side)

d. the reflection an prove that the lines and angles are congruent.

Answer:

there are 46.80 milligrams in 6 ounces.

Step-by-step explanation:

Answer:

8.5

Step-by-step explanation:

-2(x-5)+3=-4

Step 1 distribute

−2+10+3=−4

Step 2 add the numbers

-2x+13=-4

Step 3 subtract 13 from both sides of the equation

−2-13+13=-4-13

Step 4 get ride of the two 13

-2x=-4-13

Step 5 subtract -4 subtract 13

-2x=-17

Step 6 divide -17 by -2

-2x/-17

Step 6 answer

8.5

I'm assuming

[tex]f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}[/tex]

(a) f(x) is a valid probability density function if its integral over the support is 1:

[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1[/tex]

Compute the integral:

[tex]\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16[/tex]

So we have

k / 6 = 1   →   k = 6

(b) By definition of conditional probability,

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)

It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).

We have

[tex]\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y<0\\3y^2-2y^3&\text{for }0\le y<1\\1&\text{for }y\ge1\end{cases}[/tex]

Then

P(Y ≤ 0.4) = F (0.4) = 0.352

P(Y ≤ 0.8) = F (0.8) = 0.896

and so

P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393

(c) The 0.95 quantile is the value φ such that

P(Y ≤ φ) = 0.95

In terms of the integral definition of the CDF, we have solve for φ such that

[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95[/tex]

We have

[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95[/tex]

which reduces to the cubic

3φ² - 2φ³ = 0.95

Use a calculator to solve this and find that φ ≈ 0.865.

Using probability concepts, it is found that

a) The value is k = 6.

b) P(Y ≤ .4|Y ≤ .8) = 0.554.

c) The 95th percentile is x = 0.86465.

The density function is:

[tex]f(y) = ky(1 - y)[/tex]

Item a:

The condition that makes it a probability density function is:

[tex]\int_0^1 f(y) dy = 1[/tex]

Thus:

[tex]\int_0^1 f(y) dy = \int_0^1 ky - ky^2 dy[/tex]

[tex]\int_0^1 f(y) dy = k(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0}^{y = 1}[/tex]

[tex]\int_0^1 f(y) dy = k(\frac{1}{2} - \frac{1}{3})[/tex]

Then

[tex]k(\frac{1}{2} - \frac{1}{3}) = 1[/tex]

[tex]k(\frac{3-2}{6}) = 1[/tex]

[tex]k = 6[/tex]

The value is k = 6.

Item b:

This probability is:

[tex]\int_0.4^0.8 f(y) dy = 6(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0.4}^{y = 0.8}[/tex]

Then

[tex]p = 6\left(\frac{0.8^2}{2} - \frac{0.8^3}{3} - \frac{0.4^2}{2} + \frac{0.4^3}{3}\right)[/tex]

[tex]p = 0.554[/tex]

Thus, P(Y ≤ .4|Y ≤ .8) = 0.554.

Item c:

This is x for which:

[tex]\int_0^x f(y) dy = 0.95[/tex]

Thus:

[tex]6(\frac{x^2}{2} - \frac{x^3}{3}) = 0.95[/tex]

[tex]-2x^3 + 3x^2 - 0.95 = 0[/tex]

Solving a cubic equation with the help of a calculator, and considering [tex]0 \leq x \leq 1[/tex], this is x = 0.86465.

A similar problem is given at https://brainly.com/question/22223588

Answer:

4

Step-by-step explanation:

Because she gets 3 per multiple choice question, so 3 times 18

she gets 5 per response question, so 5 times 6

Jill total score on the test is 3 • 18 + 5 • 6. The correct option is 4.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given;

Jill scored 3 points for each of the 18 multiple choice questions she answered correctly.

That means,

use the multiplication operation,

3 x 18

And 5 points for each of the 6 short response questions she answered correctly.

That means,

5 x 6

To find the total score:

Add the scores,

3 x 18 + 5 x 6

or, 3 • 18 + 5 • 6

Therefore, 3 • 18 + 5 • 6 is the required expression.

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[tex] - \sqrt{ \frac{5 - 2 \sqrt{5} }{10} } [/tex]

Answer:

a

Step-by-step explanation:

on edge

Answer:

30

Step-by-step explanation:

120/4

Answer:

30

Step-by-step explanation:

Just divide 120 with 4

Hope this helps!!!!!!

Answer:

1 /64

Decimal Form:

0.015625

Answer:

(m-(1/3))(m^2+(1/3)m+(1/9)

Step-by-step explanation:

Just use the difference of cubes

Answer:

8%

Step-by-step explanation:

Starting Principal: $  

3,000.00

Years:    

3

Annual Interest Rate:    

8

%

Results

Future Value, using...

 Simple Interest: $  

3,720.00

 Annually Compounded Interest: $  

3,779.14

Answer:

x=3.2

Step-by-step explanation:

4(6 – x) + 4 = 2 (3x + 1) – 6

24 - 4x + 4 = 6x + 2 - 6

28 - 4x = 6x -4

-4x - 6x = - 4 - 28

-10x = - 32

divide both sides

x = 16/5 or x = 3.2

hope this helps :)

Answer:

The discount is 20% off

hope this helps!

Answer:

Idrk

Step-by-step explanation:

6

because it is the only number that isn't being multiplied by a letter

Answer:

Perimeter: 16x + 16

Area: 40x + 15

Step-by-step explanation:

Remember, the perimeter is the sum of all the sides of a figure, it can be found by adding up all the sides. The area is the space within the figure, in the case of a quadrilateral can be found by multiplying the length by the width. Finally, in a rectangle, the opposite sides are congruent, parallel, and intersect in 90degree (right) angles.

Using this,

1. Find the perimeter

Since opposite sides are congruent, there will be two sides with a measure of ( 8x + 3 ), and two sides with the measure of 5. Hence the sum of all the sides would be

8x + 3 + 8x + 3 + 5 + 5

Add them together,

16x + 16.

The perimeter of the figure is 16x + 16

2. Find the area,

To find the area of a rectangle, multiply the length by the width.;

( 8x + 3 ) * 5

Distribute:

40x + 15

The area of the figure is 40x + 15

Answer:

24c

Step-by-step explanation:

First off, we know what in each case there are 24 bottles. So if we have c crates and want to know the water bottles inside them, we need to multiply 24 by c resulting in 24c or 24 x c.

Answer: 5.4  or  5 2/5 Hope this helps have a GREAT night

Step-by-step explanation:

Answer:

The student's GPA = 3.24

Step-by-step explanation:

To determine the student's GPA for the term,

First, we will determine the weighted grade points and then divide the result by the total credit.

The weighted grade point is the sum of the grade points in the courses.

Grade point for a course is calculated by multiplying the grade by the course credit.

For the Math course,

Grade point = 3.6 × 5 = 18.0

For the Music course,

Grade point = 2.5 × 2 = 5.0

For the Chemistry course,

Grade point = 3.0 × 5 = 15.0

For the Journalism course,

Grade point = 3.4 × 5 = 17.0

Hence,

The weighted grade point = 18.0 + 5.0 + 15.0 + 17.0

The weighted grade point = 55.0

Total credit = 5 + 2 + 5 + 5 = 17

∴ The student's GPA = 55.0 / 17 = 3.24

Hence, The student's GPA = 3.24

Answer:

5, -7

Step-by-step explanation:

Answer:

5 and -7

Step-by-step explanation:

Answer:

we conclude that the intervals in which the function P(t) is decreasing are:

Step-by-step explanation:

At x< 1, the function P(t) is decreasing

From the figure, it is clear that the function seems to be increasing

from (1, 3) and then 4 to onwards.

But it is clear that the function seems to be decreasing from the x < 1 and from the interval (3, 4).

Therefore, we conclude that the intervals in which the function P(t) is decreasing are:

Answer:

5.19

Step-by-step explanation:

first do 28.86 / 6 to find out how much each paid. then subtract that number (4.81) from 10

Answer - Every Person should get $5.19

Step-by-step explanation:

what i did is 6 x 10 = 60 then 60 - 28.86 = 31.14 / 6 = 5.19 Your welcome.

Answer:

Example 1: - If the item's label displays the weight as 3 lb 2 oz, type the shop name and item's brand, enter 3 in the pounds field, leave the 00 (decimal) value unchanged, enter 2 in the ounces field, leave the 00 (decimal) value unchanged, fill out the Price field and Calculate to get the price per ounce

Answer:

12 ounces

Step-by-step explanation:

3.60 = .3x

divide by .3 on both sides

12 = x

Answer:

D. A line of credit backed by collateral.

Step-by-step explanation:

Answer:

D. A line of credit backed by collateral.

Step-by-step explanation:

did the quiz

Answer:

157 divided by 2 is 78.5 round that to get 70

108 divided by 5 is 21.6 round that to get 22

The number of marbles Peter had when he arrived home was 43 marbles

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

The number of marbles Peter had on his way home = 171

The amount of marbles he lost on his way home = ( 3/4 ) th

Now , the amount of marbles Peter have left = 1 - amount of marbles he lost on his way home

The amount of marbles Peter have left = 1 - 3/4

                                                                = ( 1 / 4) th

So , The number of marbles Peter had left when he arrived home is =

Amount of marbles Peter have left x Number of marbles Peter had

The number of marbles Peter had left when he arrived home is = (1/4) x 171

= 171 / 4

= 42.75

≈ 43 marbles

Hence , the number of marbles Peter had left when he reached home is 43

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