The nth harmonic number is defined non-recursively as: 1 1/2 1/3 1/4 ... 1/n. Come up with a recursive definition and use it to guide you to write a method definition for a double-valued method named harmonic that accepts an int parameters n and recursively calculates and returns the nth harmonic number.

Answer: Cluster sampling.

Step-by-step explanation:

In the given situation Greyhound Lines randomly selects 90 buses during a certain week and surveys all passengers on the buses.

Here, week= Cluster

Buses = Elements

Therefore , the type of sampling is​ used = Cluster sampling.

Answer:  The proof is done below.

Step-by-step explanation:  We are given to prove that the following statement is true :

"For every natural number n, [tex]n^5+4n[/tex] is a multiple of 5."

We will prove the above statement by MATHEMATICAL INDUCTION.

Let n = 1. Then, we get

[tex]n^5+4n=1^5+4\times5=5,[/tex] a multiple of 5.

Let n = 2. Then, we get

[tex]n^5+4n=2^5+4\times2=40,[/tex] a multiple of 5.

Let the statement be true for n = m, where m is a natural number.

So,

[tex]m^5+4m=5k,[/tex] for any natural number k.

Then,

[tex](m+1)^5+4(m+1)\\\\=m^5+5m^4+10m^3+10m^2+5m+1+4m+4\\\\=(m^5+4m)+5m^4+10m^3+10m^2+5m+5\\\\=5k+5(m^4+2m^3+2m^2+m+1)\\\\=5(k+m^4+2m^3+2m^2+m+1),[/tex] which is a multiple of 5.

Therefore, if the statement is true for n = m, then it is true for n = m+1.

That is, the statement is true for all natural numbers n.

Hence proved.

Answer:

Depreciation

Step-by-step explanation:

Depreciation can be defined as the measure of the degree to which the economic value of a capital asset of an organization wear and tears over an existing period of time.

For example:

If a Tractor is bought for $15,000 and it has a useful lifespan of ten years, then every year, the value of the tractor will decline by $1,500. After five years, it will be worth $7,500. That is the tractor has depreciated by $7,500.

Answer:

[tex]sin(6\theta)sin(2\theta)[/tex]

Step-by-step explanation:

We are given that an expression

[tex]\frac{1}{2}cos(4\theta)-\frac{1}{2}cos(8\theta)[/tex]

The expression can be written as

[tex]\frac{1}{2}(cos(4\theta)-cos(8\theta))[/tex]

[tex]\frac{1}{2}(-2 sin (\frac{4\theta+8\theta}{2})sin(\frac{4\theta-8\theta}{2}))[/tex]

Using identity: [tex] cos A-cos B=-2 sin(\frac{A+B}{2})sin(\frac{A-B}{2})[/tex]

[tex]-sin(6\theta)sin(-2\theta)[/tex]

We know that

[tex] Sin(-x)=-Sin x[/tex]

By using this property

We get

[tex]sin(6\theta)sin(2\theta)[/tex]

To find the midpoint, add the two x values together and divide by 2, and then do the same with the Y values.

-3 + 3 = 0

0 / 2 = 0, the X value is 0

-1 + 3 = 2

2/2 = 1, the Y value is 1

The midpoint would be (0,1)

Answer:

The answer to your question is (0, 1)

Step-by-step explanation:

Data

B (3, -1)

C (-3, 3)

Formula

[tex]Xm = \frac{x1 + x2}{2}[/tex]

[tex]Ym = \frac{y1 + y2}{2}[/tex]

Substitution and simplification

[tex]Xm = \frac{3 - 3}{2}[/tex]

[tex]Xm = \frac{0}{2}[/tex]

      Xm = 0

[tex]Ym = \frac{-1 + 3}{2}[/tex]

[tex]Ym = \frac{2}{2}[/tex]

      Ym = 1

Result

           (0, 1)

Answer:

The answer is 18,019 days.

Step-by-step explanation:

Answer:

Required equation : [tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]

Together they can paint the same room in 2.25 hours or 2 hours 15 minutes.

Step-by-step explanation:

It is given that Dale Horton can paint a certain room in 3 hours.

One hour woks of Dale Horton = 1/3

Kathy Garcia can paint the same room in 9 hours.

One hour woks of Kathy Garcia = 1/9

Let together they can paint the same room in t hours.

One hour woks of both = 1/t

[tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]

[tex]\frac{1}{t}=\frac{3+1}{9}[/tex]

[tex]\frac{1}{t}=\frac{4}{9}[/tex]

After reciprocal we get

[tex]\frac{t}{1}=\frac{9}{4}[/tex]

[tex]t=2.25[/tex]

1 hour = 60 minutes.

0.25 hour = 15 minutes.

Therefore, together they can paint the same room in 2.25 hours or 2 hours 15 minutes.

Answer:the truck load of fruit weigh 440 pounces

Step-by-step explanation:

Let the total weight of the truck load of fruit weigh x pounds.

The truck carries apples, grapes, and blackberries in the ratio of 4:3:4

The total ratio is the sum of the proportions of apples, grapes, and blackberries. It becomes 4+3+4 = 11

if the apples weigh 160 pounds, it means that

4/11 × x = 160

4x/11 = 160

4x = 160×11 = 1760

x = 1760/4

x = 440

The exponential equation representing the situation is A = A₀ * (0.5)^(t/h). The half-life of this substance is approximately 67 minutes.

To represent the radioactive decay of the substance, we can use the exponential decay model:

A = A₀ * (0.5)^(t/h)

where A is the amount of the substance at time t, A₀ is the initial amount, h is the half-life, and t is the time elapsed.

In this case, we have:

250 = 32 * (0.5)^(250/h)

To find the half-life, we can rearrange the equation:

(0.5)^(250/h) = 250/32

Take the logarithm of both sides:

(250/h) * ln(0.5) = ln(250/32)

Solve for h:

h = (250 * ln(0.5)) / ln(250/32)

Using a calculator, we find that h is approximately 67 minutes.

https://brainly.com/question/12900684

#SPJ12

The radioactive decay of a substance is an exponential process represented by the equation [tex]N = N0 * e^(^-^k^t^)[/tex]. In this case, the half-life of the substance, or the time it takes for half the substance to decay, is approximately 66 minutes.

The subject matter at hand is related to the decay of a radioactive substance and its half-life. It's important to understand that the decay of radioactive material is an exponential process.

This can be represented with an equation of the form [tex]N = N0 * e^(^-^k^t^)[/tex], where N is the remaining amount of the substance, N0 is the initial amount, k is the decay constant, and t is time. In this given scenario, the scientist starts with 250 grams of the substance, and after 250 minutes, only 32 grams are left. Hence, we have [tex]32 = 250 * e^(^-^k^ *^ 2^5^0^)[/tex].

To find the half-life, we use the equation T = ln(2) / k, where T is the half-life. By solving these equations, we get the half-life to be approximately 66 minutes. Here the term 'half-life' is defined as the time it takes for half of the substance to decay; hence when the substance has gone through one half-life, only 50% of it would remain.

https://brainly.com/question/24710827

#SPJ11

Answer:

a) a continuous variable

b) a discrete variable

c) a continuous variable

d) a discrete variable

Step-by-step explanation:

Well first we need to define what are the continuous and discrete variables. Discrete variables are those whose values are obtained by counting, but continuous variables those whose values are obtained by measurement.

a) The weight of a dog can be measured. Therefore, it is a continuous variable.

b) The result of a roll of dice can be counted. Therefore, it is a discrete variable.

c) The weight of a bunch of bananas can be measured. Therefore, it is a continuous variable.

d) The number of people in line at a box office to purchase theater tickets can be counted. Therefore, it is a discrete variable.

The weight of a dog and a bunch of bananas are continuous variables, while the result of a dice roll and the number of people in line are discrete variables.

a. The weight of a dog is a continuous variable. It can take on any value within a certain range, such as 12.5 pounds, 20.2 pounds, or 35.7 pounds.

b. The result of a roll of dice is a discrete variable. It can only take on particular values, such as 1, 2, 3, 4, 5, or 6.

c. The weight of a bunch of bananas is a continuous variable. Like the weight of a dog, it can take on any value within a certain range.

d. The number of people in line at a box office to purchase theater tickets is a discrete variable. It can only take on whole number values, like 0, 1, 2, 3, and so on.

https://brainly.com/question/31373369

#SPJ3

Answer:

8y-11z=5

Step-by-step explanation:

2x + y − 4z = 4, -----------A

2x + 4y + z = 15,-----------B

6x − 5y − z = 7------------C

Solving A to find the value of x

2x= 4-y+4z

x=4-y+4z/2------------------D

Putting D in C

6(4-y+4z/2) -5y -z=7

3(4-y+4z) -5y-z=7

12-3y+12z-5y-z=7

12-8y + 11z=7

-8y +11z= 7-12

-8y +11z= -5

8y-11z=5--------------E

Answer:

1 ) B. {-5 , -4 , 2}

2 ) A. {-1 , 1 , 3}

Step-by-step explanation:

1. The range of a relation is an ordered pair of real numbers to which all the real numbers in the domain relate to.

Given the Relation R: { ( 3, -5 ) , ( 1 , 2 ) , (  -1 ,  -4 ) , ( -1 , 2 ) }

Here The Range is the ordered pair of number towards the right in each relation.

Range = { -5 , 2 , -4 }

2. The domain of a relation is an ordered pair of real numbers which are related to any one of the element in the range of the relation.

Given the Relation R: { ( 3 , -2 ) , ( 1 , 2 ) , ( -1 , -4 ) , ( -1 , 2 ) }

Here the domain is the ordered pair of numbers towards the left in each relation.

Domain = { -1 , 1 , 3 }

Answer:

Question 1

since triangles are similar

angle B = angle D

8x + 16 = 120

x = 13

Question 2

Ttiangles are similar

therefore, sides are in ratio

AB ÷ XY = BC ÷ YZ = AC ÷ XZ

substituting all values we get

BC = 22

BC = 22AC = 16

Answer:

[tex]y=7+1.73x-0.0016x^{2}[/tex]

Parbolic path.

Step-by-step explanation:

This is bidimensional motion, so the equation that relates the vertical and horizontal position is:

[tex]y=y_{0}+(tg(\theta))x-\frac{g}{2(v_{0}cos(\theta))^{2}}x^{2}[/tex]

Here, v₀, θ y g are constants, then we can rewrite (1) as:

[tex]y=a+bx-cx^{2}[/tex]

where:

Therefore the rectangular equation will be:

[tex]y=7+1.73x-0.0016x^{2}[/tex]

This type of path is a parabolic motion.

I hope it helps you!

Answer:

B. 27

Step-by-step explanation:

Given: g(x) = 3x² - 3x - 9

g(4) = 3(4)² - 3(4) - 9

g(4) = 48 - 12 - 9 = 48 - 21 = 27

Answer:

Option B). 27 is correct

ie., The value of [tex]g(4)=27[/tex] for the given function.

Step-by-step explanation:

Given function g is defined by [tex]g(x)=3x^{2}-3x-9[/tex]

Now to find the value of g(4):

That is put x=4 in the given function we get

[tex]g(x)=3x^{2}-3x-9[/tex]

[tex]g(4)=(3\times 4^{2})-(3\times 4)-9[/tex]

[tex]=(3\times 16)-12-9[/tex]

[tex]=48-21[/tex]

[tex]=27[/tex]

Therefore [tex]g(4)=27[/tex]

Option B). 27 is correct

ie., The value of [tex]g(4)=27[/tex] for the given function.

Answer:

  after 3.92 seconds

Step-by-step explanation:

Fill in the given value of h to find the formula for the height of the ball. Then set the value of that height to zero and solve for t.

  [tex]h_2(t)=-16t^2+246\\\\0=-16t^2+246\\\\0 = t^2-15.375 \quad\text{divide by -16}\\\\\sqrt{15.375}=t \quad\text{add 15.375, take the square root}\\\\t\approx 3.92[/tex]

Ball 2 reaches the ground after 3.92 seconds.

Answer:

This statement is true

Step-by-step explanation:

Remember that subset F of a metric (or topological) space X is said to be closed if X-F is open according to the metric (topology) of F.

Let F⊆X. For the "if" part, suppose that [tex]F=F_1\cap F_2\cap \cdots \cap F_n[/tex] where [tex]F_k[/tex] is a closed set for all k. Then by De Morgan's law, [tex]X-F=(X-F_1)\cup(X-F_2)\cup \cdots\cup(X-F_n)[/tex].

Now, since Fk is closed for all k, then X-Fk is open. In every metric (topological) space, the union of an arbitrary family of open sets open sets is open, thus X-F is open, that is, F is closed.

For the "only if" implication, suppose that F is closed. We always have that F=F∩F (y∈F if and only if y∈F and y∈F if and only if y∈F∩F). then F is a finite intersection of closed sets (F and F).

Answer: lung

Step-by-step explanation:

Attachedfile/picture shows the structure.

Respiration is a process of degradation of complex organic compound with the production of carbon dioxide, water and energy.

Respiration involves two phases, which are;

(1). External Respiration or Breathing: this is a process in which

animals take oxygen in and release carbon dioxide.

(2). Internal Respiration or Cellular Respiration: this process involve the release of energy from food substance with the release of carbondioxide and and water.

Single celled animals or unicellular animals such as amoeba exchange gases through cell surface. The STRUCTURE X IS THE PLASMA MEMBRANE. There is absorption of of Oxygen from the surrounding air or water,hence, giving out carbondioxide through plasma membrane by Diffusion.

PS: Lung is used in respiration process in Human

Answer:

number 1

Step-by-step explanation:

if you'd look at Number One X is negative and if you look at the two number problems the x that is negative is negative for and then the one that is positive is the Y which is 3

Question is not proper, Proper question is given below;

For a birthday party, Mr. Perkins orders 8 chocolate chip cookies and 16 sugar cookies. Each cookie is the same price. He also picks up a cupcake for himself, which costs $2.75. The total bill is $44.03. What is the cost of a cookie?

Answer:

The Cost of the cookie will be $1.72.

Step-by-step explanation:

Given:

Mr Perkins orders 8 chocolate chip cookies and 16 sugar cookies.

Since cost of both the cookies are same then Let us assume the cost of cookies be 'x'.

Total cost of the cookies = [tex](8 + 16)x = 24x[/tex]

Cost of Cup cakes = $2.75.

Total bill he pays = $44.03

We need to find the cost of each cookies.

Now we know that Total bill he pays is equal to sum of Cost of cookies and Cost of Cup cakes he bought.

Framing in equation form we get;

[tex]44.03 = 24x + 2.75[/tex]

Now Subtracting both side by 2.75 using Subtraction property we get;

[tex]2.75+24x-2.75 = 44.03 - 2.75\\\\24x = 41.28[/tex]

Now Dividing both side by 24 using Division property we get;

[tex]\frac{24x}{24} = \frac{41.28}{24}\\\\x=1.72[/tex]

Hence The Cost of the cookie will be $1.72.

Answer:

The population of Shanghai is 5 times larger than population of Monterrey.

Step-by-step explanation:

Given:

The population of Monterrey, Mexico is [tex]4\times10^6[/tex] people

The population of Shanghai, China is [tex]2\times10^7[/tex] people.

To find how many times the population of Shanghai is lager than Monterrey.

Solution:

In order to find how many times the population of Shanghai is lager than Monterrey we will find the ratio of populations of Shanghai and  Monterrey.

Thus we divide the population of Shanghai by the population of Monterrey to find how many time the population of Shanghai is larger.

Thus, we have:

[tex]\frac{2\times10^7}{4\times10^6}[/tex]

Simplifying by using properties of exponents.

⇒ [tex]\frac{2\times10^{(7-6)}}{4}[/tex]  [As [tex]\frac{a^x} ]{a^y}=a^{(x-y)}[/tex]

⇒ [tex]\frac{2\times10^{(1)}}{4}[/tex]

⇒ [tex]\frac{20}{4}[/tex]

⇒ [tex]5[/tex]

Thus, we can say that the population of Shanghai is 5 times larger than population of Monterrey.

Shanghai's population is 5 times larger than Monterrey's.

To find out how many times larger the population of Shanghai is compared to Monterrey, we need to divide the population of Shanghai by the population of Monterrey.

Population of Shanghai: 2x[tex]10^7[/tex] people

Population of Monterrey: 4x[tex]10^6[/tex] people

Now, divide the population of Shanghai by the population of Monterrey:

[tex]2x10^7[/tex] / 4x[tex]10^6[/tex] = (2 / 4) x 10(7-6)

This simplifies to:

0.5 x 101 = 5

Therefore, the population of Shanghai is 5 times larger than the population of Monterrey.

Answer:

Step-by-step explanation:

In order to qualify for the NBA playoffs, the New York Knicks must win at least 3/7 of their remaining games. Number of games remaining to be played is 15.

3/7 × 15 = 6.43

Since it is above 6 and closest to 7,

It means that they must win at least 7 games in order to qualify for the playoffs.

So they were correct by thinking that if they won 7 games from 15, they will be eligible to compete in the playoffs.

Answer:

With replacement

 21C2 = 210 outcomes

without replacement

20C2 = 190 outcomes

Step-by-step explanation:

For determining the number of possible outcomes you need count the number of possible combinations, because a combination is a selection of a number of items from a set of items where the order of selection does not matter.

The number of possible combinations is calculated thus

nCr = [tex]\frac{n!}{(n-r)!r!}[/tex]

           Where n: number of items of the set

                        r: number of selected items

a) If the group of states are selected with replacement then

   (n+r-1)Cr  

   n = 20 states

   r = 2 states

  then n +r -1 = 20 +2 -1 = 21

  21C2 = [tex]\frac{21!}{(21-2)!2!} = 210[/tex]

b) If the group of states are selected without replacement then

 nCr

 n = 20

 r = 2

20C2 = [tex]\frac{20!}{(20-2)!2!} = 190[/tex]

When two states are chosen with replacement from 20, there are 400 possible outcomes. Without replacement, there are 380 possible outcomes.

The question asks for the number of possible outcomes if two states are selected at random from a group of 20 states, with and without replacement. Replacement means a state can be chosen more than once, while without replacement means a state can only be chosen once.

When selecting with replacement, a state can be chosen, replaced, and then chosen again. Therefore, for each of the two selections, there are 20 possible states that can be chosen. This leads to a total of 20 * 20 = 400 possible outcomes.

In the scenario where states are chosen without replacement, the number of possible outcomes changes for the second selection because a state cannot be chosen twice. In this case, there are 20 options for the first state and 19 options for the second (since one state has been selected and is not replaced). Thus, the total number of possible outcomes is 20 * 19 = 380.

https://brainly.com/question/3806758

#SPJ11

Answer: Devaughn's age is 48 and Sydney's age is 24

Step-by-step explanation:

72 divided by 3 gives you 24.

24+24 is 48 which is Devaughn's age.48-72 gives you 24 which is Sydney's age

Sydney is 24 and Devaughn is 48

Answer:

[tex]P(pitcher)=\frac{20}{53}=0.377[/tex]

Step-by-step explanation:

Data given

Infielders: Outfielders = 7:4

Pitchers:Outfielders= 5:3

We can find a ratio in common for the 3 cases and in order to do this we can put the ratio with the same denominator of outfielders and we can do this:

Infielders:Outfielders x3 = 7:4 *3 = 21:12

Pitchers:Outfielders x4= 5:3 *4 = 15:12

And we have a one combined ratio:

Infielders:Outfielders:Pitchers = 21:12:20

And we have a basis or a total of 21+12+20 =53

And then we can find the probability that we select a pitcher like this:

[tex]P(pitcher)=\frac{20}{53}=0.377[/tex]

The probability of selecting a pitcher from the baseball team is approximately 0.3774 or 37.74%, found by establishing the combined ratio of all players and then calculating the ratio of pitchers to the total number of players.

To determine the probability of selecting a pitcher from the county-wide baseball team, we first need to establish the ratio of all players in their respective categories based on the given ratios. The ratio of infielders to outfielders is 7:4, and the ratio of pitchers to outfielders is 5:3. We should find a common multiple for the number of outfielders in both ratios so that we can combine them into a single ratio that includes infielders, outfielders, and pitchers.

Let's assume there are 12 outfielders which is a common multiple of both 4 and 3 (the numbers of outfielders in each provided ratio). This would give us 7*3 infielders and 5*4 pitchers when we scale the ratios accordingly.

Therefore:

Infielders = 7 * 3 = 21

Outfielders = 12 (our common multiple)

Pitchers = 5 * 4 = 20

The total number of players on the team would be 21 + 12 + 20 = 53.

The probability of selecting a pitcher would therefore be the number of pitchers divided by the total number of players:

P(Pitcher) = Number of Pitchers / Total Number of Players = 20 / 53.

The probability of selecting a pitcher is approximately 0.3774 (or 37.74%).

Answer:

The percent charge of Kanna's DS is 50%

Step-by-step explanation:

we know that

A Nintendo DS takes 4 hours to charge fully (100%)

4 hours is the same that 240 minutes

using proportion

Find out what percentage represent 108 minutes

[tex]\frac{100}{240}\ \frac{\%}{min} =\frac{x}{108}\ \frac{\%}{min}\\\\x=100(108)/240\\\\x=45\%[/tex]

Remember that

Kanna Kamui charge her DS from 5%

so

[tex]5\%+45\%=50\%[/tex]

therefore

The percent charge of Kanna's DS is 50%

To figure out the charge percentage of Kanna's DS, we need to know the time it takes for a full charge and the time Kanna's DS was charged. The calculation (108 minutes charged / 240 minutes for a full charge) x 100 gives approximately 45%.

The question is asking about the percentage charge of Kanna's DS after being charged for a specific period. First, we need to know how long it takes for a DS to become fully charged, which is 4 hours (equivalent to 240 minutes). Now, Kanna let her DS charge for 108 minutes, and the proportion of time spent charging to the total time needed to fully charge the DS represents the percentage of charge.

So, to calculate this, we would divide the time spent charging (108 minutes) by the total time needed for a full charge (240 minutes) and multiply by 100 to get the percentage.

Therefore, the calculation would be: (108/240) x 100 = 45% (rounding to the nearest whole number).

https://brainly.com/question/32197511

#SPJ12

Answer:

There are two possible values: MN=5 or MN=19

Step-by-step explanation:

The points L and N are collinear, so we can visualize them on a right line as in Figure 1.  

First suppose that M is between L and N as in Figure 2. Then we can compute the distance between L and N as LN=LM+MN. Substracting LM from both sides, we obtain that MN=LN-LM=12-7=5.

For the other possibility, suppose that M is not between L and N as in Figure 3. Because LM<LN, it's impossible that M is located further to the right than N. Then M isn't at the right of L. Therefore, M is at the left of L, so L is between M and N, so the distance between M and N is given by MN=ML+LN=LM+LN=7+12=19.

When points L, M, and N are collinear and LM=7 and LN=12, the possible values of MN are 5 or 19 depending on the arrangement of the points. If the order is L, M, N then MN = 5 while if the order is L, N, M then MN = 19.

In mathematics, collinear points are points that lie on the same line. In your question, three points L, M, and N are collinear. Given that LM = 7 and LN = 12, we want to find the possible length of segment MN.

There are two possibilities based on the relative placement of these points:

https://brainly.com/question/5191807

#SPJ11

The probabilities are (a) the probability that both balls are white is 0.058 and (b) the probability that both balls are the same color is 1.904.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

A bowl contains 6 red balls, 4 blue balls, 3 white balls and 1 green ball. You pick two balls without replacement.

Total number of balls : 6+4+3 +1 = 13

(a)

Out of 13 balls,

3 are white, so probability of getting first white ball is,

P(first white) = 3/13

After that 12 balls remaining out of which 3 are white so

P(second white| first white) = 3/12

So required probability is

P(both white) = P(Second white| first white)P(first white) = (3/13) x (3/12) = 0.0576 = 0.058

(b)

Since there is only one green ball, so both balls cannot be same. Therefore,

P(both of same color) = P(both blue)+P(both red)+P(both white) = 0.923+ 0.923+ 0.058= 1.904

The probability that both balls of same color is

P(both of same colors) = 1.904

Therefore, the probabilities are (a) 0.058 and (b) 1.904

To learn more about the probability;

brainly.com/question/11234923

#SPJ5

Annie paid 12800 pounds at end of 10 years

Solution:

Given that Annie borrows 8000 pounds at simple interest rate of 6 %

She also agrees to pay the loan back over a 10 year period

To find: total money paid back at the end of 10 years

The total amount paid is given as:

Total amount = simple interest + principal amount borrowed

The simple interest is given as:

[tex]S.I = \frac{pnr}{100}[/tex]

Where, "p" is the principal sum

"n" is the number of years

"r" is the rate of interest

Here, p = 8000 ; r = 6 % ; n = 10 years

[tex]S.I = \frac{8000 \times 10 \times 6}{100}\\\\S.I = 4800[/tex]

Therefore total amount paid at end of 10 years is:

Total amount = 4800 + 8000 = 12800

Thus Annie paid 12800 pounds at end of 10 years

Final answer:

Annie will pay a total of 12800 pounds at the end of 10 years for her loan of 8000 pounds with an annual simple interest rate of 6%.

Explanation:

To calculate the total amount of money Annie will have paid back at the end of 10 years on her loan of 8000 pounds with an annual simple interest rate of 6%, we first need to find the total interest she will pay over the period. Simple interest can be calculated using the formula: Interest = Principal × Rate × Time. In this case, the Principal (P) is 8000 pounds, the Rate (r) is 6% or 0.06 as a decimal, and the Time (t) is 10 years.

Interest = P × r × t = 8000 × 0.06 × 10 = 4800 pounds

The total amount of interest Annie will pay over 10 years is 4800 pounds. To find the total repayment amount, we add this interest to the original loan amount.

Total repayment = Principal + Interest = 8000 pounds + 4800 pounds = 12800 pounds

At the end of 10 years, Annie will have paid back a total of 12800 pounds.

Answer:

( 9x - 18 ) square inches

Step-by-step explanation:

Data provided in the question:

Side of the square piece of gift wrapping paper = x inches

Now,

According to the question:

He cut 6 inches off the right side of the paper and discarded the rectangular scrap

Therefore,

Dimension of the scrap formed will be 6x square inches

The dimensions of the paper left

Top width will be ( x - 6 ) and the right width will be x

Next he cut 3 inches off the top of the paper and again discarded the rectangular scrap

Therefore,

Dimension of the scrap will be

( x - 6 ) long wide and 3 inches wide

Hence,

The area of the scraps will be

⇒ 6x + 3(x - 6)

⇒ 6x + 3x - 18

⇒ ( 9x - 18 ) square inches