Which is equivalent to (negative 2 m 5 n) squared, and what type of special product is it?

Let [tex]a[/tex] be the first term in the series and [tex]r[/tex] the common ratio. Then the infinite series converges to

[tex]a + ar + ar^2 + ar^3 + ar^4 + ar^5 + \cdots = \dfrac a{1-r}[/tex]

Removing the first three terms from the left side effectively multiplies the right side by 27, so

[tex]ar^3 + ar^4 + ar^5 + \cdots = \dfrac{27a}{1-r}[/tex]

By elimination,

[tex]a + ar + ar^2 = -\dfrac{26a}{1-r}[/tex]

Solve for [tex]r[/tex]. We can eliminate [tex]a[/tex] so that

[tex]1 + r + r^2 = -\dfrac{26}{1-r} \\\\ \implies 1-r^3 = -26 \\\\ \implies r^3 - 27 = 0 \\\\ \implies r^3 = 27 \implies \boxed{r=3}[/tex]

There are 6720 ways by 8 distinguishable books be placed in 5 shelves.

According to statement

The number of books (n) is 8

The number of shelves (r) is 5

Now, we find the ways by which the 8 books be placed in 5 distinguishable shelves

From Permutation formula

P(n,r) = n! / (n-r)!

Substitute the values then

P(n,r) = 8! / (8-5)!

P(n,r) = (8*7*6*5*4*3*2*1) / (3*2*1)

P(n,r) = 8*7*6*5*4

P(n,r) = 6720

So, there are 6720 ways by 8 distinguishable books be placed in 5 shelves.

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The simplified expression of (-2)⋅n⋅(8)⋅n⋅(-n) is 16n^3

The expression is given as:

(-2)⋅n⋅(8)⋅n⋅(-n)

Express as products

(-2) * n * (8) * n * (-n)

Multiply -2 and 8

-16 * n * n * (-n)

Multiply the three n's

-16 * -n^3

Evaluate the product

16n^3

Hence, the simplified expression of (-2)⋅n⋅(8)⋅n⋅(-n) is 16n^3

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Answer:

=Rs.10

Step-by-step explanation:

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A piece of cloth costs Rs. 200. If the piece was 5m longer and each meter of cloth costs Rs. 2 less the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per meter?

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Solution

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Let the length of the piece be x metres. Then, rate per metre =Rs.

x

200

New length =(x+5) metres

Since the cost remains same

New rate per metre =Rs.

x+5

200

It is given that

x

200

−

x+5

200

=2

⇒

x(x+5)

200(x+5)−200x

=2⇒

x(x+5)

1000

=2

⇒x

2

+5x=500⇒x

2

+5x−500=0$

⇒x

2

+25x−20x−500=0

⇒(x+25)(x−20)=0⇒x+25=0

orx−20=0⇒x=20orx=−25

But x cannot be negative. So, x=20

Rate per metre Rs.

x

200

=Rs

20

200

=Rs.10

The fill up for the missing steps are:

Note that we are given:

Based on the definition of perpendicular lines, ΔFHG ~ ΔKJG  are known to be right angles.

So: Δ FHG ≅  ΔKJG due to the fact that all the right angles are congruent.

ΔFHG  and  ΔKGJ are vertical angles and as such, the angle are congruent to angle  ΔKGJ

Based on AA similarity theorem, ΔFHG ~ ΔKJG

Due to the above, the fill up for the missing steps are:

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40 gallons of liquid b weighs the same as 30 gallons of liquid a.

A substance's density is defined as its mass per unit volume (more specifically, the volumetric mass density; also known as specific mass). Although the Latin letter D may also be used, the sign most frequently used for density is (the lower case Greek letter rho). Density is mathematically defined as mass divided by volume.

where m is the mass, V is the volume and D is the density, which is sometimes roughly characterized as weight per unit volume, while this is incorrect scientifically; this quantity is more precisely known as specific weight.

For liquid a,

8= mass/30

For liquid b,

6=mass/volume

For the two masses to be equal,

240=6*volume

volume=240/6

volume=40

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Answer:

Looks like an obtuse scalene triangle

Step-by-step explanation:

The angle of the top vertex looks to be obtuse. It if was acute isosceles it would have 2 equal sides. If it was a right triangle it would have a right angle (which it doesn't). It was obtuse isosceles it would have equal sides. So it should be A: Obtuse Scalene Triangle

Answer:

work hours: independent

salary: dependent

Step-by-step explanation:

The independent variable is what is you're "typically" in control of, or it has a constant increase. For example time, you're not really "in control" of time, but it has a constant change. One example where you are in control, is how much money you deposit into your account, you can slightly control it (you obviously can't deposit more than you have), but it's still somewhat in your control.

The dependent variable is what changes as a result of the independent variable changing. So for example in the previous example, where the money deposited was the independent variable, the dependent variable would be the total amount of money in your account

In this case the number of hours during the week is the independent variable and the salary depends on how many hours you work in the week so that is the dependent variable

The actual payment Eric made to the bank at 175.00 for 36 months is 6,300

Actual payment to bank = Monthly payment × Number of months

= 175.00 × 36

= 6,300

Therefore, the actual payment made to the bank is 6,300.

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The entrance fee at museum C is modeled by a proportional relationship with the number of visitors.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Researching the problem on the internet, the prices for three museums are given, but only one of them has a constant rate of which, which is Museum C, as:

k = 4/3 = 16/12 = 24/18 = 1.33.

Hence the relation for the entrance fee is:

y = 1.33x.

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The pair of the reciprocal function will be (7, 5) and (11, 9). Then the correct option is A.

Coordinate geometry is the study of geometry using the points in space.

If a linear function contains the pairs (5, 7) and (9, 11).

If the pairs should have the reciprocal function to this one. Then the coordinate gets swapped.

The pair of the reciprocal function will be (7, 5) and (11, 9).

Then the correct option is A.

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The probability is P(X >= 2).

200 random people, n = 200

Let us consider the Binomial expression

i.e.,

P(X = r) = nCr*p^r*q^(n-r)

Here we have to assume that the 3 initials are equally likely events.

i.e.,

p = 1/3

q = 1 - 1/3

= 2/3

Required probability = P(X >= 2)

= 1 - [P(X = 0) + P(X = 1)]

= 1 - [200C0*(1/3)^0*(2/3)^200 + 200C1*(1/3)^1*(2/3)^199]

= 1 - [1*1*(2/3)^200 + 200*(1/3)*(2/3)^199]

= 1 - [(2/3)^200 + 200*(1/3)*(2/3)^199]

= 1 - (2/3)^200 - 200*(1/3)*(2/3)^199

Probability is truly how possibly something is to happen. every time we're unsure about the final results of an event, we will talk about the possibilities of certain consequences and how probably they are. The evaluation of events ruled by means of possibility is called records.

3 styles of probability

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SOLUTION :-

Since, the pair of angles are supplementary

a + b = 180°

50° + b = 180°

b = 180° - 50°

→ b = 130°

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Answer:

130°

Step-by-step explanation:

supplementary angles are two angles that add up to 180°

(they form a straight line)

So, because we know that ∠b and 50° are supplementary, they must add up to 180:

b + 50 = 180

   - 50     -50             (subtract 50 from both sides to isolate b)

  b    =   130

So, ∠b [angle b] = 130°

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Answer:

It's 50 degrees and it is acute

Step-by-step explanation:

hope it helps

sorry if I'm wrong

The number of combinations of pins that can generated without using 19 in beginning are 3645 pins.

Given ten numbers from 0 to 9 and we are require to generate pins such that 19 will not come in beginning.

Total numbers=10

Combinations are the arrangement of numbers, variables, alphabets, etc. to form another numbers or word. In this problem we have to use combinations because there will be many combinations made from 10 numbers to form a 4 digit pin.

[tex]C=n!/r!(n-r)![/tex]

Combination: When 19 is not in beginning, we have to use 2 numbers in the beginning other than 19 so we can use all 9 numbers on thousandths place other than 1 and all the 9 numbers on hundredth place other than 9 and rest 2 places can be filled with any number from all 10 numbers so the combinations will be [tex]9 C_{1}*9C_{1}* 10C_{2}[/tex]=9*9*45=3645 pins.

Hence we can make 3645 pins of ATM from 10 numbers not starting with 19.

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Answer:

F. 23

Step-by-step explanation:

15/2 = 7.5

7.5 dozen eggs per 100 customers

15 + 7.5 = 22.5 which can be rounded to 23

= 23

When the first cars hit the roads they were as much (or more) a novelty, as they were the first step in mechanized transportation for the masses. Going for a “Sunday Drive” was an actual activity, not just an analogy for someone taking their sweet time. Vehicles were lighter and slower, and there wasn’t a constant sense of urgency to get from “Point A” to “Point B”.

Fast forward a little over a century and our vehicles have transformed into an average of a 2-ton living room/office/daycare that can cover 95 feet every second traveling down the road.

A lot of talks are occurring about distracted driving, but have you ever thought “I can take my eyes off the road for 2 seconds, it's no big deal”? To change a radio station, to answer a phone call, to look for an item you’ve dropped.  Nearly every single one of us has at some point, even those who use a hands-free device.  

The more times you take your eyes off the road for just those two seconds, the increases your likelihood of an incident

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[tex]P \: \div \: 7 \: = \: 14[/tex]

[tex] \frac{1}{7} P \: = \: 14[/tex]

[tex] \boxed{ \bold{P \: = \: 98}}[/tex]

Answer:

Here you go!

sorry for my writing -_-

Any confusion, you may ask me.

83 boxes are required to carry 800 books.

According to the question:

One Box can hold weight = 30 pounds

We know that ,  1 pound= 0.45 kg

hence, 30 pounds = 30 x 0.45 = 13.5kg  

hence,  one box can carry 13.5 kg of weight.

Now,

Weight of 1 book = 1.4 kg

So, Total Weight of 800 books= 1.4 x 800 kg

And , No. of boxes required to carry 800 books = (1.4 x 800)/13.5 = 82.96

                                                                             or approximately 83 boxes

Hence, 83 boxes are required to carry 800 books.

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Answer: 90 degrees

Step-by-step explanation:

An angle inscribed in a semicircle measures 90 degrees.

The probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.

Given the true proportion is 0.07, sample size 289.

We have to calculate the probability that the sample proportion will differ from the population proportion by more than 0.03.

Probability is the likeliness or chance of happening an event among all the events possible. The probability lies between 0 and 1.

Probability=number of items/ total items.

True proportion=0.07

n=289

sample population mean=0.07

Sample proportion standard error=[tex]\sqrt{pq/n}[/tex]

=[tex]\sqrt{0.07*0.93)/289}[/tex]

=[tex]\sqrt{0.0651/289}[/tex]

=[tex]\sqrt{0.00022}[/tex]

=0.015

Probability that the sample proportion will differ from the population proportion by more than 0.03=P(I P-p I>0.03)

=P( I Z I>0.03*0.015)

=P ( I z I >0.0045)

=0.99968.

Hence the probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.

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The value of y is increasing for x values in Graph C, the correct option is C.

A Linear Graph is the graphical representation of a Straight line equation.

From the graph attached with the answer, The x-y values for all the graphs are observed to determine the graph in which the y value goes up as the x value increases.

For the x value increasing, the value of y is decreasing in Graph A, B, and D.

The y value is rising only for Graph C.

Therefore, the correct option is C.

The complete question is attached with the answer.

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The division of 1987 by 12 when solved gives a quotient of; 165.5

We want to divide 1,987 by 12. This can be expressed as;

1987 ÷ 12

Now, it must be noted that when dividing, we have the divisor and the dividend. Where the number that is being divided is the dividend which is the numerator, while the number by which we divide is the divisor which is the denominator. Thus, in this question, we have;

Dividend = 1987

Divisor = 12

Thus;

1987/12 = 165.5

Thus, we can conclude that when we divide 1987 by 12, we get 165.5

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The amount of money that Davis has in this scenario is; $50

Let the amount of money he has be $X.

Now, if he buys 10 notebooks, he will have $10 left. Thus;

X - 10n = 10  -----(1)

If he buys 15 notebooks, he will be $10 short. Thus;

X - 15n = -10   ------(2)

Subtract eq 1 from eq 2 to get;

-5n = -20

n = -20/-5

n = 4

Thus;

X - 10(4) = 10

X = 10 + 40

n = $50

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The constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute a value for x and evaluate each expression, the values will not be equal.

Expression 1: [tex]-0.5(3x+5)[/tex]

Using the distributive property to expand the first expression, we get

[tex]-0.5(3x+5) = -1.5x-2.5\\[/tex]

Expression 2: [tex]-1.5x + 2.5[/tex]

Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent.

Also, if you substitute a value for x and evaluate each expression, the values will not be equal.

Q. Are the expressions –0.5(3x + 5) and –1.5x + 2.5 equivalent? Explain why or why not.

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Answer:Using the distributive property to expand the first expression, you would get -1.5x - 2.5. Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute in a value for x and evaluate each expression, the values will not be equal.

Step-by-step explanation: sample explanation

Answer:

(9,21)

Step-by-step explanation:

If you plug in all the pairs, the only one that is true is (9,21).

y=x+12

21=9+12

The above equation is true, and that is why (9,21) is the answer.

Hope this helped! :)

The congruence theorem that proves that △LON ≅ △LMN is: A. SSS congruence theorem

According to the SSS congruence theorem, if all three corresponding sides of two triangles are congruent, then both triangles are congruent.

In the image given, we have:

This means all three corresponding sides are congruent, therefore, the congruence theorem that proves both triangles are congruent is:

A. SSS.

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Answer: Option 1 or A. SSS

Step-by-step explanation: The congruence theorem that can be used to prove △LON ≅ △LMN is SSS.

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If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.

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Answer:

7/20

Step-by-step explanation:

15/25 * 14/24 = 210/600 = 21/60 = 7/20

Answer: 47

Step-by-step explanation:

The value of latoken in 2027 is $4731.

Given that in 2025 digital wallet users at $19900 and in 2027 latoken international clients will be $1000 and the number of monthly paying clients will grow from 30,000 at a 10% monthly rate till 2027 and 0 afterward.

The time esteem of cash states that a sum of cash is esteemed more presently than it'll be within the future. This is often due to the fact that cash can as it was extended by means of speculation. Speculation that's put off could be a missed opportunity. The time esteem of cash equation takes into consideration the amount of cash, its future esteem, the sum it can create, and the time period. The number of compounding periods is additionally a key variable for investment funds accounts.

By 2025=19900

By 2027 =1000 for client

Monthly pay =30000 each month

Rate=10%

At the end  the value is computed below:

AED=30000(1+0.1)¹²

AED=30000(1.1)¹²

AED=30000×3.138

AED=94140

To find the value computation is done below:

19900x=1000×v×AED

x=(94140×1000×140)/19900

x=4.731×1000

x=4731

Hence, the value of latoken in 2027 when digital wallet user at $19,900 by 2025 and latoken international client will be $1000 in 2027 is $4731.

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