Find the suma1 = -26/5 , d = -5/3 , n = 10

n(n+1)(n+5) can be a multiple of 3.

Utilizing the mathematical induction formula for any n > N, we are going to demonstrate it.

P(n) = n(n+1) n(n+5) = 3d, where d N

P(1)=1(2)(6)=12, that is cleavable by three, for n=1.

Suppose P(k) is true.

Where m N k three +6k a pair of +5k=3m k, P(k)=k(k+1)(k+5)=3m.

3\s =−6k \s2\s −5k+3m

We will currently demonstrate that P(k+1) is true.

P(k+1)=K+1, K+2, K+6, K 3 +9 K 2, K twenty K + twelve

When we plug the worth of k three into the equation on top of, we tend to get 3m6k a pair of 5k)+9k a pair of +20k+12 =3.

m+3k \s2\s +15k+12\s=3

(m+k \s2\s +5k+4)

in which r=m+k a pair of + 5k + four

P(k+1) is often true since P(k) is often true.

Therefore, in step with the induction principle, P(n) is cleavable by three for all n N.

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The amount of bond amortization for each six month period is [tex]\$225[/tex].

In the given question,

Towson Corporation issued [tex]\$150,000[/tex] of [tex]7\%[/tex] ten year bonds at [tex]103[/tex] on the semi-annual interest date.

Towson uses the straight line method to amortize any bond premium or discount.

We have to find the amount of bond amortization for each six month period.

Cash issued [tex]=\$150,000[/tex]

Rate [tex]=7\%[/tex] ten year bond at [tex]103[/tex] n the semi-annual interest date.

So the cash proceed on issue of bond = Cash issued [tex]\times103[/tex] [tex]/100[/tex]

Cash proceed on issue of bond [tex]=\$150,000\times\frac{103}{100}[/tex]

Firstly simplifying ratio

After simplification of ratio

Cash proceed on issue of bond [tex]=\$150,000\times1.03[/tex]

Now simplifying after multiplication

Cash proceed on issue of bond [tex]=\$154,500[/tex]

Hence, the cash proceed on issue of bond is [tex]\$154,500[/tex].

Now we find the premium that issued in the bond.

Premium on issue of bond [tex]=\$154,500-\$150,000[/tex]

Simplifying

Premium on issue of bond [tex]=\$4,500[/tex]

Hence, the premium on issue of bond is [tex]\$4,500[/tex]

Now finding the amount of bond amortization for each six month period.

Bond Amortization = (Premium on issue of bond/10 years) * 1/2

Bond Amortization [tex]=(\frac{\$4500}{10})\times\frac{1}{2}[/tex]

Simplifying the ratio

Bond Amortization [tex]=\$450\times0.5[/tex]

Bond Amortization [tex]=\$225[/tex]

Hence, the amount of bond amortization for each six month period is [tex]\$225[/tex].

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Answer:

Two numbers are called relatively prime if their greatest common divisor is $1$. Grogg's favorite number is the product of the integers from $1$ to $10$

Answer: The answer is 803. :) lol

Step-by-step explanation:

You gotta keep trying numbers. But the numbers cant be even because if it's even, it can be divided by 2! Try the odd numbers starting at 800. If the number is not divisible by any of the numbers from 1-10 then it's the correct number. Got it on my second try. LOL! I'm from AOPS like you. :) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

21 is -2 away, 22 is- 1 away 28 is 5 away, and 29 is 6 away

Step-by-step explanation:

Answer:

-2

-2

-2

-1

-1

-1

-1

-1

5

6

Solving for x,

Given:

Total number of cookies is, N = 36.

Number of friends is, n(f) = 8.

The objective is to find the number of cookies (c) will each of them get while sharing.

Consider the required number of cookies to each person as (c).

The value of c can be calculated as,

Hence, each of them will get 4 and a half cookies.

1) Probability of drawing a spade is 14

2) Probability of drawing a seven is 1/13

3) Probability that a heart or spade is drawn = 1/2

4) Probability that blackjack is drawn = 1/26

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

1) There are 13 spades in total.

hence, the likelihood of drawing a spade is 13/52, or 14.

2) The sum of the seven is four. (4 suits are in the room)

Probability = 4/52 = 1/13

(3) A heart or spade is drawn.

Total hearts and spades: 13 + 13 = 26

Probability = 26/52 = 1/2

4) A blackjack is drawn, with a total of two blackjacks.

Probability = 2/52 = 1/26.

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Answer:

C. The y-intercept is (0, 150). Diego has $150 before buying any

Step-by-step explanation:

Brainlylist?

Step-by-step explanation:

Answer: The answer would be A.

Step-by-step explanation:

Answer: 2 porters joined the group

Step-by-step explanation:

First, you are told that "13 porters are carrying a total weight of 195kg". You can use this information to create an equation to find the average weight carried by each porter.

[tex]\frac{195 kg}{13}=15kg[/tex]

^195kg (total weight) divided by 13 (the number of porters) is equal to 15kg (the average weight carried by each of the 13 porters).

You are then told that "extra porters join the group, so they carry an average weight of 13 kg of baggage". because some porters joined the group, you'll have to add p (p = number of porters) to the original equation and change the average weight from 15kg to 13kg.

[tex]\frac{195kg}{13 +p} = 13kg[/tex]

^195kg (total weight) divided by 13+p (total number of porters after some joined group) is equal to 13kg (new average weight)

You can then use your new equation to solve for "p" and find the number of porters added.

p = 2

Answer: just multiply 5  by 2

Step-by-step explanation:

Solve the inequality:

2x - 6 ≥ 6(x - 2) + 8

Operating the parentheses:

2x - 6 ≥ 6x - 12 + 8

Subtracting 6x:

2x - 6x - 6 ≥ - 12 + 8

Adding 6:

2x - 6x ≥ - 12 + 8 + 6

Simplifying:

- 4x ≥ 2

Dividing by -4 and changing the symbol:

x ≤ 2/(-4)

x ≤ -0.5

The solution in the number line starts at -0.5 and goes to the left with an arrow:

Answer:

$15

Explanation:

To find the price of each candle, we need to divide $75 by 5, so the price of each candle is:

$75 ÷ 5 = $15

So, the answer is $15

The value of 6 to the negative 3rd power times 6 to the 2nd power times 6 to the 5th power times 6 is 6^5.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Based on the information given, the numbers will be expressed as:

6^-3 × 6^2 × 6^5 × 6

= 6^5

It's important to note that they've the same base. Therefore, the powers will be added thus:

= -3 + 2 + 5 + 1

= 5

This gives 6^5. This illustrates the concept of exponents.

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This video from khan academy should clear up your confusion on scale factors.

https://www.khanacademy.org/math/7th-engage-ny/engage-7th-module-1/7th-module-1-topic-d/v/identifying-scale-factors

When x = 0, y = 2, then the constant term of the polynomial must be 2. This discards the last 2 options.

When x = 1, y = 11. Substituting x = 1 into the first two options, we get:

Then, y = 9x² + 2 is correct.

The area  that Xiao Mei covers in square tiles is 56 sq. units.

Given,

In the question:

Xiao Mei covers a table with 8 rows of square unit tiles.

and,  There are 7 tiles in each row.

To find the area that Xiao Mei covers in square tiles.

Now, According to the question:

Tables covers = 8 rows of sq. unit

In each row = 7 tiles

All you would have to do is multiply 8 times 7

it means, 8 x 7 = 56

Hence, The area  that Xiao Mei covers in square tiles is 56 sq. units.

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ANSWER:

The volumen of the cone is 667.07 cubic meters

The volume has the following formula

replacing:

The magnitude of the force with which the space station attracts Earth.

17714.8532 N

This is further explained below.

An influence that has the potential to alter the motion of an item is referred to as a force.

An object having mass may experience a change in its velocity, often known as acceleration, when subjected to a force.

Generally, the equation for the magnitude of the force  is

F = G.M.m/r2

Where

G=gravitational constant

M and m mass

r=radius

F=force of attraction

Therefore

6.67*10^{-11} * 5.98*10^{24} * 2070/((6370+457)2*10^6)

= 17714.8532 N

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29%

Probability is the likelihood or chance that ab event will occur. Mathematically;

Probability = Expected/Total

From the given table, the total number of male student is the total outcome as shown:

Total outcome = 4 +6+ 2 + 2

Total outcome = 14

If a male freshmen is selected at random, the expected outcome will be 4.

Determine the probability

Hence the probability that the male student is freshman is approximately 29%

Let x represent the total number of students that attended the dance. This means that

number of students that prefer tacos + number of students that prefer hot wings = x

Percentage is expressed in terms of 100. If 63% of the students preferred hot wings, then the number of students that preferred hotwings is

63/100 * x = 0.63x

If 296 students preferred tacos, it means that

293 + 0.63x = x

x - 0.63x = 296

0.37x = 296

x = 296/0.37

x = 800

Thus, a total of 800 students attended the dance

The value of x is equal to 10 and the exterior angle to angle d is equal to 141 degrees.

To solve this problem, we have to recall that the sum of angles in a triangle is equal to 180 degrees.

Applying that formula here;

[tex]m < d + m < e + m < f = 180^0\\(2x + 19) + (3x + 24) + 87 = 180\\x = 10[/tex]

But the exterior angle to angle D can be found assuming the angle lies on a straight line, then the sum of angle D and it's exterior angle would be equal to 180 degrees.

Let y = exterior angle

[tex]m < d + y = 180\\2x + 19 + y = 180\\x = 10\\2(10) + 19 + y = 180\\20 + 19 + y = 180\\39 + y = 180\\y = 141^0[/tex]

The value of the exterior angle to d is equal to 141 degrees.

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Answer: its C

Step-by-step explanation: i got it right

Since the chart has the name "Registered Country Voters", it only includes the registered voters, that is the approximately 300,000 people. Since 16% are independet, we can take 16% of 300,000 to get the registered independets. that is, multiply 0.16 (16%) by 300,000:

So, the answer is 48,000.

Answer:

x=55

Step-by-step explanation:

2x+6+x+9=180

3x=165

x=55

:]

Answer:

A: 2,0 B: 1,-5 C: 4,-3

Step-by-step explanation:

w

The given expression is,

Opening the brackets and multiplying each term inside the bracket with 5, we get,

The simplified expression is 15k = 35 and the value of k is 2.33.

More surprising was a recent report of severe erosion brought on by rain in a well-kept, drip-irrigated subtropical fruit orchard in Limpopo

It is widely known and has been extensively researched for many years how soil erosion occurs in rangelands and locations where crops are watered by rain. However, it appears that knowledge of and research on the severe soil erosion that occurs in irrigated regions is lacking. When center pivot irrigation was used on highly crusting, extremely unstable soils, such as those from the Eastern Cape and the Lowveld of Mpumalanga, major gully (donga) erosion ensued, according to information the author has previously and more recently received. After the irrigation was put in place, they grew quite fast. More surprising was a recent report of severe erosion brought on by rain in a well-kept, drip-irrigated subtropical fruit orchard in Limpopo.

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Given that Z follows the standard normal distribution, and that the left-tailed probability for a z-score c is:

Then, we can see that the value of c, round to two decimal places, is:

Given:

The given set of data is

To find: The mean for the given set of data?

Explanation:

We can calculate the mean of a given set of data by using the formula

Here,

We can calculate the sum of terms as

The sum of terms = 6+9+2+4+3+6+5

The sum of terms =35.

and

The number of terms = 7.

Now, by substituting the value in the above formula

Therefore,

Hence, the mean = 5.

Answer: The mean for a given set of data is 5.