Joey borrows 2000 from his grandfather and pays the money back in monthly payments of 200.
1. Write a lineat function that represents the remaining money owed L(x) after x months.
2. Evaluate L(10) and interpret the meaning in the context of this problem.
A. L(x) - 200x + 2,400; L(10) = 4,400, This represents the amount Joey has paid his grandfather after 10 months.
B. L(x) = 200x + 2,400; L(10) - 4,400, This represents the amount Joey still owes his grandfather after 10 months.
C. L(x) = -200x + 2,400; L(10) = 400, This represents the amount Joey has paid his grandfather after 10 months.
D. L(x) = -200x + 2,400; L(10) = 400, This represents the amount Joey still owes his grandfather after 10 months.

Answer:

[tex]\boxed{13}[/tex] pages

Step-by-step explanation:

Divide the total number of pages by 5 to get how many sets of every 5 pages will contain 2/3 of a page of advertisements.

[tex]\frac{98}{5} = 19.6[/tex]

Multiply this value by [tex]\frac{2}{3}[/tex] to get the total number of pages.

[tex]19.6 * \frac{2}{3} \approxeq 13[/tex] pages

Answer:

A) 64 observations

B) analytic study

Step-by-step explanation:

Given:  

There are 3 number of factors i.e. armature length, spring load, and bobbin depth.

There are 4 levels i.e. low, fair, moderate, and high

There is a single i.e. 1 observation on flow made for each combination of levels.

A)

To find:

Number of observations.

There are 4 levels so these 4 levels are to be considered for each factor.

Number of observations = 4.4.4 = 64

For example if we represent low fair moderate and high as L,F,M,H

and factors armature length, spring load, and bobbin depth as a,s,b

Then one of the observations can be [tex]L_{a} F_{s} H_{b}[/tex]

So resulting data set has 64 observations.  

B)

This is analytic study.

The study basically "analyses" the amount of flow through a solenoid valve in an automobiles pollution control system. This study is conducted in order to obtain information from this existing process/experiment and this study focuses on improvement of the process, which created the results being analysed. So the goal is to improve amount of flow through a solenoid valve practice in the future. Also you can see that there is no sampling frame here so if the study was enumerative that it should focus on collecting data specific items in the frame so it shows that its not enumerative but it is analytic study.

Answer:

the answer is c...............

Answer:

I got 45, but I may be wrong.

Step-by-step explanation:

When a number is even, the number must end in an even number. Here, the even numbers are 4 and 6, so the numbers we are going to create are all going to end in 4 and 6.

To answer this question, we just have to find as many possible combinations following the guidelines provided.

334

344

354

364

374

434

444

454

464

474

534

544

554

564

574

634

644

654

664

674

336

346

356

366

376

436

446

456

466

476

536

546

556

566

576

636

646

656

666

676

736

746

756

766

776

Answer:

D

Step-by-step explanation:

this is the only one inside the overlapping inequalitlies

Answer:

the amount of space occupied by a three-dimensional solid object

Step-by-step explanation:

Volume is a measure of the space in a 3D solid object enclosed by the closed surfaces of the solid object.

By using the definition of volume, we can see that the correct option is the last one:

"The amount of space occupied by a three-dimensional solid object"

Volume is defined as a 3-dimensional metric derived from longitude, that measures a region in the space. So, each region that "takes space" has a volume.

With that in mind, the option that correctly describes volume is the last option:

"The amount of space occupied by a three-dimensional solid object"

If you want to learn more about volume, you can read:

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Answer:

(x – 4)^2 + (y + 7)^2 = 16

Step-by-step explanation:

The formula of a circle is:

(x – h)^2 + (y – k)^2 = r^2

(h, k) represents the coordinates of the center of the circle

r represents the radius of the circle

If you plug in the given information, you get:

(x – 4)^2 + (y – (-7))^2 = 4^2

which simplifies into:

(x – 4)^2 + (y + 7)^2 = 16

Answer:

[tex]z=(-\sqrt{3}+i)^6[/tex] = -64

Step-by-step explanation:

You have the following complex number:

[tex]z=(-\sqrt{3}+i)^6[/tex]       (1)

The Demoivres theorem stables the following:

[tex]z^n=r^n(cos(n\theta)+i sin(n\theta))[/tex]      (2)

In this case you have n=6

In order to use the theorem you first find r and θ, as follow:

[tex]r=\sqrt{3+1}=2\\\\\theta=tan^{-1}(\frac{1}{\sqrt{3}})=30\°[/tex]

Next, you replace these values into the equation (2) with n=6:

[tex]z^6=(2)^6[cos(6*30\°)+isin(6*30\°)]\\\\z^6=64[-1+i0]=-64[/tex]

Then, the solution is -64

Answer:

A) -64

Step-by-step explanation:

Edge 2021

Answer:

0.992774 ≅ .993

Step-by-step explanation:

a²+b²=c²

a=x

b=3

c=3.16

x²+3²=3.16²

x²+9=9.9856

x²=.9856

x=0.992774

x≅0.993

Answer:

Step-by-step explanation:

pt=700 is basically evaluate it form the bottom to the top and u must mark me as brainly

Answer:

(26+92)+17 = 26 + ( 92+17)

Step-by-step explanation:

The associative property of addition is

a + (b + c) = (a + b) + c

We want to move the parentheses

(26+92)+17 = 26 + ( 92+17)

Answer:

A) cooling constant =  0.0101365

B) [tex]\frac{df}{dt} = k ( 60 - F )[/tex]

c)  F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]

D)137.46 ⁰

Step-by-step explanation:

water temperature = 60⁰F

temperature of Bar after 20 seconds = 120⁰F

temperature of Bar after 60 seconds = 100⁰F

A) Determine the cooling constant K

The newton's law of cooling is given as

= [tex]\frac{df}{dt} = k(60 - F)[/tex]

= ∫ [tex]\frac{df}{dt}[/tex] = ∫ k(60 - F)

= ∫ [tex]\frac{df}{60 - F}[/tex] = ∫ kdt

= In (60 -F) = -kt - c

       60 - F = [tex]e^{-kt-c}[/tex]

      60 - F = [tex]C_{1} e^{-kt}[/tex]       ( note : [tex]e^{-c}[/tex] is a constant )

after 20 seconds

[tex]C_{1}e^{-k(20)}[/tex] = 60 - 120 = -60  

therefore [tex]C_{1} = \frac{-60}{e^{-20k} }[/tex] ------- equation 1

after 60 seconds

[tex]C_{1} e^{-k(60)}[/tex] = 60 - 100 = - 40  

therefore [tex]C_{1} = \frac{-40}{e^{-60k} }[/tex] -------- equation 2

solve equation 1 and equation 2 simultaneously

= [tex]\frac{-60}{e^{-20k} }[/tex] = [tex]\frac{-40}{e^{-60k} }[/tex]

= 6[tex]e^{20k}[/tex] = 4[tex]e^{60k}[/tex]

= [tex]\frac{6}{4} e^{40k}[/tex] = In(6/4) = 40k

cooling constant (k) = In(6/4) / 40 = 0.40546 / 40 = 0.0101365

B) what is the differential equation  satisfied

substituting the value of k into the newtons law of cooling)

60 - F = [tex]C_{1} e^{0.0101365(t)}[/tex]  

F(t) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

The differential equation that the temperature F(t) of the bar

[tex]\frac{df}{dt} = k ( 60 - F )[/tex]

C) The formula for F(t)

t = 20 , F = 120

F(t ) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

120 = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

[tex]C_{1} e^{0.0101365(20)}[/tex] = 60

[tex]C_{1} = 60 * 1.291[/tex] = 77.46

C1 = - 77.46⁰ as the temperature is decreasing

The formula for f(t)

= F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]

D) Temperature of the bar at the moment it is submerged

F(0) = 60 + 77.46[tex]e^{0.01013659(0)}[/tex]

F(0) = 60 + 77.46(1)

     = 137.46⁰

Answer:

The p-value is 2.1%.

Step-by-step explanation:

We are given that a study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed.

The sample average age was 24.2 with a standard deviation of 3.7.

Let [tex]\mu[/tex] = true average age a "child" moves permanently out of his parents' home in the United States.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 23      {means that the average age a "child" moves permanently out of his parents' home in the United States is at most 23}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 23      {means that the average age a "child" moves permanently out of his parents' home in the United States is greater than 23}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                            T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average age = 24.2

            s = sample standard deviation =3.7

            n = sample of U.S. Adults = 43

So, the test statistics =  [tex]\frac{24.2-23}{\frac{3.7}{\sqrt{43} } }[/tex]  ~  [tex]t_4_2[/tex]

                                    =  2.127

The value of t-test statistics is 2.127.

Now, the p-value of the test statistics is given by;

         P-value = P( [tex]t_4_2[/tex] > 2.127) = 0.021 or 2.1%

Answer:

x ≥ 4 AND  x + y ≤ 10

Step-by-step explanation:

If you need up to 10 volunteers, then you can take 10 or less. If we add y and x, we'll get the total amount of people, therefore making the inequality:

x + y ≤ 10.

Now, he needs no fewer than 4 females, so he can take 4 or greater. This means that x should be greater than or equal to 4.

x ≥ 4.

Nothing was mentioned about how many males he needed (y) so these two inequalities match the situation.

Hope this helped!

Answer:

x = 64

Step-by-step explanation:

A circle equal 360 degrees

180 + 90 + x + 26 = 360

Combine like terms

296+x = 360

Subtract 296 from each side

296+x-296 = 360-296

x = 64

Answer:

x=1

Step-by-step explanation:

1+1+2x+2x= 6

1+1=2

2x+2x=4x

2+4x=6

x=1

Answer: c(x) = $50*x + $24

Step-by-step explanation:

First, this situation can be modeled with a linear equation like:

c(x) = s*x + b

where c is the cost, s is the slope, x is the number of cubic yards of mulch bought, and b is the y-intercept ( a constant that no depends on the number x)

Then we know that:

The company charges $50 per cubic yard, so the slope is $50

A delivery charge of $24, this delivery charge does not depend on x, so this is the y-intercept.

Then our equation is:

c(x) = $50*x + $24

This is:

"The cost of buying x cubic yards of mulch"

Answer:

x=0

Step-by-step explanation:

If the slope is undefined, the line is vertical

vertical lines are of the form

x =

Since the point is (0,6)

x=0

Answer:

74w+10

Step-by-step explanation:

That's the answer

Answer:

The first part is of permutations.

We are selecting 3 elements from three different elements {1,2,3}

Points given:

We permit overlapped elements for the sequence. Here "overlapped elements" indicates that repetition is allowed.

So when repetition is allowed and order matters, we use permutations.

Formula to compute permutation is:

Lets say n is the three elements {1,2,3}

We have to select 3 elements so r = 3

Total number of selections using permutations = [tex]n^{r}[/tex] =  n × n × n

                                                                    = 3³ = 3 * 3 * 3

                                                                    = 27

This means if we have 3 different elements then we have have 3 choices each time for making a sequence.

Hence  If we make a sequence selecting three elements from three different elements  {1, 2, 3} and we permit overlapped elements for the sequence, then the total  number of sequences is 27.

Step-by-step explanation:

The second part indicates combinations.

This is because the statement of the question:  If we do not take into account the order.

When the order does not matter, we use combinations.

So when the order does not matter and repetition is allowed we use the following formula:

Total number of selections using combinations = (r + n - 1)! / r! (n - 1)!

                                                                                = (3 + 3 - 1) ! / 3! (3 - 1)!

                                                                                = (3 + 2) ! / 3! (2!)

                                                                                = 5! / 3! 2!

                                                                                = 5*4*3*2*1 / (3*2*1 ) (2*1)

                                                                                = 120 / 6 * 2

                                                                                = 120 / 12

                                                                                = 10

So these are the number of combinations of 3 elements taken 3 at a time with  repetition.

The total number that will be selected in the permutations is 27.

Based on the information given, the total number of permutations will be:

= n³

= 3 × 3 × 3

= 27

Also, the total number of selection using combination will be:

= (3 + 3 - 1)! / 3!(3 - 1)!

= 120 / (6 × 2)

= 120/12

= 10

Learn more about permutations on:

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Answer:

The slope is -4.

Step-by-step explanation:

The values -2 and -6 are 4 values apart.

The values -4 and -3 are 1 value apart.

Since the second coordinate is lower than the first one, the slope of this is negative.

4 / 1 = 1

Negating 1 gets us -1.

Hope this helped!

Answer:

[tex] \frac{y}{x} = \frac{ - 4}{1} = - 4[/tex]

Step-by-step explanation:

[tex]x = ( - 3) - ( - 4) = 1[/tex]

[tex]y = ( - 6) - ( - 2) = - 4[/tex]

Answer:

see explanation

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides

6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )

- 7a₁ + 30d = 156d ( subtract 30d from both sides )

- 7a₁ = 126d ( divide both sides by - 7 )

a₁ = - 18d

Now

a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required

Answer:

The graph of g is the graph of f shifted up by 3 units.

Step-by-step explanation:

Consider the graph of a function r with real numbers k and h.

Transformation Effect

r(x) + k shifts the graph up k units

r(x) - k shifts the graph down k units

r(x + h) shifts the graph to the left h units

r(x - h) shifts the graph to the right h units

It is given that g(x) = f(x) + 3. Therefore, the graph of g is the graph of f shifted up by 3 units.

Answer:

+40 to both sides of the = sign.

Step-by-step explanation:

x2-40=0

    +40=+40

x2=40

 /2=/2

x=20

Answer:

The dog will eat 3 lbs

Step-by-step explanation:

Take the amount eaten per day and multiply by the number of days

3/4 * 4 = 3

The dog will eat 3 lbs

Answer:

3 pounds

Step-by-step explanation:

Multiply the amount of dog food per day with the number of days.

[tex]\frac{3}{4} \times 4[/tex]

[tex]\frac{12}{4} =3[/tex]

In 4 days, Jamie's dog will eat 3 pounds of dog food.

Step-by-step explanation:

angle A = angle B( Corresponding angles)

so,

5x - 5 = 3x + 13

=> 5x - 3x = 13 + 5

=> 2x = 18

=> x = 9

angle B = 3x + 13 = (3×9) + 13 = 27 + 13 = 40

Answer:

x=9, ∠B=40

Step-by-step explanation:

In this case, ∠A≅∠B, as they are corresponding angles. Therefore, if you set up the equation to be 5x-5=3x+13,

2x=18, x=9

∠B=3(9)+13=27+13=40

Answer:

B

Step-by-step explanation:

It can't be A because of the fact that by multiplying 445 by "x" you'll get a higher, postitive number. Meaning that if adding that positive number, you'll get something higher than 18,259. Which isn't our goal. In addition, the key word is "depreciates" which is another word for subtracting. However, that only applies in some circumstances. It can't be D either since you're basically adding a negative number by another negative number. However, "18,259" has to be a positive in this problem. By that you can also eliminate C as well. Meaning that B would be the correct answer.

Answer:

1. k=0

2. yes, result is still a polynomial.

3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)

Step-by-step explanation:

1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)

for k=0 any polynomial f(x) will reduce f(k) to the constant term.

2. If we multiply a polynomial by a constant, is the result a polynomial?

Yes, If we multiply a polynomial by a constant, the result is always a polynomial.

3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?

Yes.  

If

deg(f+g) < deg(f) and

deg(f+g) < deg(g)

then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.

Answer:

2.01m; 0.41m + 2.10m + 3.52m = 6.03 6.03/3= 2.01

Step-by-step explanation:

0.41m + 2.10m + 3.52m = 6.03 6.03/3= 2.01

The average height of the three trees is 2.01 meters.

Given that,

The heights of the three trees are 0.41m, 2.10m and 3.52m.

To find the average height of the three trees,

Use the formula for calculating the mean

Add up their heights and then divide by the total number of trees.

So, we have:

Average height = (0.41 m + 2.10 m + 3.52 m) ÷ 3

We can simplify this expression:

Average height = 6.03 m ÷ 3

Average height = 2.01 m

Therefore, the average height of the three trees is 2.01 meters.

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Answer:

First answer.

Step-by-step explanation:

Multiply everything by 10, to get rid of the decimals.