3x² + 15x-5) •/. (x + 5)
Divide using synthetic division

Answer:

Geometric Sequence

Finding the sum

The sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Solution:

Geometric Series Sum Formula: S = a₁/1 - r

Given: a₁ = 3/4

          a₂ = -9/16

          a₃ = 27/64

          a₄ = -81/256

1. Find the common ratio.

      a_n = a₁r ⁿ ⁻ ¹

       a₂  = a₁r ⁿ ⁻ ¹

  -9/16 = 3/4 r ² ⁻ ¹

  -9/16 = 3/4 r

2. Divide both sides of the equation by 3/4 to find r.

   -9/16/3/4 = 3/4 r/3/4

 (-9/16)(4/3) = r

       -36/48 = r

           -3/4 = r

3. Using r = -3/4, find the sum of the infinite geometric series 3/4 -9/16 +27/64 -81/256+ ...

   S = a₁/1 – r

   S = 3/4/1 – (-3/4)

   S = 3/4/1 + ¾

   S = 3/4/4/4  + 3/4

   S = 3/4/7/4

   S = (3/4)(4/7)

   S = 12/28

   S = 3/7

4. Therefore, the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Definition:

     A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant while the sum of an infinite number of terms in a geometric sequence is called sum to infinity.

Code: 10.3.1.1

For more information regarding geometric sequence, go to the following links:

brainly.ph/question/154960

brainly.ph/question/1461781

brainly.ph/question/1634458

Step-by-step explanation:

The sample size should be 1843 at 99% confidence level with margin of error of 3%.

What is Inferential statistics?

By studying the samples that were drawn from the population data, inferential statistics aids in the development of a solid knowledge of the data. By utilising numerous analytical techniques, it aids in the creation of population-level generalisations.

Given, Margin of error (m) = 0.03

           z (at 99% confidence level)=2.576

We know that, Sample size(n) = (z/m)^2 p (1-p)

In order to find the sample size, we must know the value of proportion.

here, the value of proportion is missing so, in the absence of proportion, we will consider it as 0.5.

Now, we've p = 0.5

∴ Sample size = (z/m)^2 p (1-p)

                        = (2.576/0.03)^2 × 0.5 × (1-0.5)

                        = 1843 (approx).

Learn more about Inferential statistics from the link given below :

https://brainly.com/question/11215148

#SPJ4

Answer:

53

Step-by-step explanation:

PEMDAS

Parenthesis

multiply the numbers

Divide

Add

Subtract

Answer: 25 units

Step-by-step explanation:

distance with negatives is still an addition but you have to turn the negative into a positive to get the answer.

Elouise and Marcus are 20 km apart. There is a lake due west of Elouise that is also 10√3 km due north of Marcus, so 22.36 km distance the bearing of Marcus from Elouise.

According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two legs. Pythagoras theory triangles are another name for these triangles.

At first assume a triangle, In the triangle, assume Elouise at the point A and Marcus at the point B, and the lake at the C point.

Given that,

Elouise and Marcus are 20 km apart (AB)

There is a lake due west of Elouise that is also 10√3 km due north of Marcus (BC)

Now, according to a Pythagoras theorem,

(AC)² + (AB)² = (BC)²

or, (AC)² = (BC)²- (AB)²

or, (AC)² = (10√3)² - (20)²

or, AC = [tex]\sqrt{500}[/tex]

or, AC = 22.36 km

So, distance bearing of Marcus from Elouise is 22.36 km.

To know more about distance refer to:

https://brainly.com/question/13963928

#SPJ1

Answer:D is incorrect

Step-by-step explanation:

D is the only one that is incorrect because D is 9x-81

Answer:

  (d)  9(x -9)

Step-by-step explanation:

You want the expression that is not equivalent to the other three.

The simplified versions of the expressions are ...

The expression not equivalent to the other three is 9(x -9).

<95141404393>

An equation to represent the value of the car after 1 year is P(t) = 80,000(1 - 0.25)¹.

An equation to represent the value of the car after t years is P(t) = 80,000(1 - 0.25)^t.

Generally speaking, a physical asset that loses its value at specific period of time represent an exponential decay. Therefore, a mathematical model for any physical asset (car) that decreases by r percent per unit of time is an exponential equation of this form:

P(t) = I(1 - r)^t

Where:

Note: 1/4 is equal to 0.25.

For a car that loses 1/4 of its value annually, after 1 year its value is given by;

P(t) = 80,000(1 - 1/4)^1

P(t) = 80,000(1 - 0.25)¹

For a car that loses 1/4 of its value annually, after t year its value is given by;

P(t) = 80,000(1 - 0.25)^t

Read more on exponential functions here: brainly.com/question/28246301

#SPJ1

1. The students that the academy have per teacher is 18.

2. The students per tutor will be 10.

3. The tutors that the academy need if it has 60 students is 6 tutors.

Given that the arts academy requires there to be 4 teachers for every 72 students and 3 for every 30 students.

The students that the academy have per teacher will be:

= Number if students / Teacher

= 72/4

= 18 students per teacher.

The students per tutor will be:

= 30/3

= 10 students per tutor

The number of tutors for 60 students will be:

= 60 / 10

= 6 tutors.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

By using the formula for sample size, it can be calculated that the sample size is 62

What is sample?

At first it is important to know about population.

Population is the group of items from where samples are taken for study and research and for statistical purpose

A subset of population is called sample.

Here, margin of error E = 2

Value of z for 95 % confidence interval = 1.96

Standard deviation = 8

Sample size  = [tex](\frac{1.96 \times 8}{2})^2[/tex] [tex]\sim[/tex] 62

To learn more about sample, refer to the link-

https://brainly.com/question/17831271

#SPJ4

Answer: A = 2(x+3y)+2z=2z+4x+2y

B=2(x+3y)=4x+2y

c=x+3y=2x+y

d=2y=x

Step-by-step explanation:

Answer:

2y=x:D

x+3y=2x+y:C

2(x+3y)=4x+2y:B

2(x+3y)+2z=2z+4x+2y

Step-by-step explanation:

D is the only possibility for 2y=x because it has 3 total. Similarly for C. B only has two different types, so it must be 2(x+3y)=4x+2y.

The slope for the first table will be;

⇒ m = - 4/3

The slope for the second table will be;

⇒ m = 1 / 4

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

There are two table is shown in figure.

Now,

For first table;

Two points are,

⇒ (x, y) = (3, -6)  (0, - 2)

Since, The slope of the line passing through the points  (x₁ , y₁) and

(x₂, y₂) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, Slope for first table;

⇒ m = (- 2 - (-6)) / (0 - 3)

⇒ m = (- 2 + 6) / (-3)

⇒ m = - 4/3

And, For second table;

Two points are,

⇒ (x, y) = (0, -3)  (4, - 2)

Since, The slope of the line passing through the points  (x₁ , y₁) and (x₂, y₂) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, Slope for second table;

⇒ m = (- 2 - (-3)) / (4 - 0)

⇒ m = (- 2 + 3) / (4)

⇒ m = 1 / 4

Thus, The slope for the first table will be;

⇒ m = - 4/3

The slope for the second table will be;

⇒ m = 1 / 4

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ1

If 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.

In the given question, if 17% of men are bald, then we have to find the probability that at most 140 in a random sample of 900 men are bald.

As given that; 17% of men are bald.

So,p=0.17

Let X=Number of men that are bald

Sample size, n=900

Here X follows binomial distribution with parameters n= 900 and p =0.17

Since np≥5 and n(1-p)≥5, We can use normal approximation to the binomial with continuity correction.

So,Binomial can be approximated to normal with;

mean, μ=np

μ = 900*0.17

μ = 153

Standard deviation, σ = √np(1-p)

σ = √900*0.17*(1-0.17)

σ = √153*0.83

σ = √126.99

σ = 11.269

So, X→Normal (μ = 153, σ = 11.269)

Then, X= (X-μ)/σ

X=(X-153)/11.269

We need to find the probability that at most 140 in a random sample of 900 men are bald i.e. we need to find P(X≤140)

P(X≤140) =P(X<140+0.5)  [using continuity correction factor]

P(X≤140) =P(X<140.5)

P(X≤140) =P(z<(X-153)/11.269)

P(X≤140) =P(z<(140.5-153)/11.269)

P(X≤140) =P(Z<-1.11)  [z score rounded to 2 decimal places]

P(X≤140)  =0.1335

Hence, if 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.

To learn more about probability link is here

brainly.com/question/29657446

#SPJ4

Answer: C

Step-by-step explanation: This is because there is no y - intercept. But since there is still a slope an x but be next to the 3/4. Which represents the rate of change.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The number of local guests who visited the zoo is 600.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total number of visitors = 750

The percentage that visited the zoo.

= 100% - 20%

= 80%

Now,

The number of local guests who visited the zoo.

= 80% of 750

= 80/100 x 750

= 600

Thus,

The number of local guests who visited the zoo is 600.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ1

Answer: 5.76 x 10 to the 5th

Answer:

y=4x+4

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

B is y intercept

To find slope we use y2-y1/x2-x1

16-(-4)/3-(-2)

20/5

4 is the slope

We can fill this in

y=4x+b

To find b we fill in any coordinates

-4=4(-2)+b

-4=-8+b

+8. +8

4=b

Now we can fill it in

y=4x+4

Hopes this helps please mark brainliest

Answer:

15%

Step-by-step explanation:

Since the problem is to find how much 69 is as a percent if 60 is 100%, we can use a rule of three, simple, direct proportion to do it:

60 = 100%

68 = x

x = 69x100/60

x = 115

That means 69 is 115% of 60, which means that the error is of:

115 - 100 = 15%

Hope this helps, have a great day! :D

We have (123) different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .

According to our question-

Let n be the maximum number of subsets of five elements that can be selected from the first 14 natural numbers,

with at least two of the five numbers being consecutive.

I have made a block of two consecutive numbers (like (1,2),(2,3),(13,14) etc.).

Now we can choose this block in 13 ways. Now we have to choose 3 numbers from the rest 12 numbers.

Hence,  multiplication principle we come to know that there are  13×(123).

learn more about probability click here:

brainly.com/question/24756209

#SPJ4

Answer:

red im pretty sure

Answer:

6√3 centimeters

Step-by-step explanation:

This is an isosceles triangle because two of the sides are the same. We can divide this into two triangles to make two right triangles, and use the Pythagorean theorem. The base (a) will be divided by 2.

Pythagorean theorem: a^2 + b^2 = c^2

a and b are the legs of the triangle. c is the hypotenuse.

Let's replace the variables with the given information we know.

The hypotenuse is 6. One of the legs is 3. the other leg is a/2.

3^2 + b^2 = 6^2

9 + b^2 = 36

b^2 = 27

b = √27 = 3√3

Since this was for half of the base, we will multiply it by 2.

3√3 x 2 = 6√3

That is our answer.

I hope this helps.

n=(K+1)^3 the remainder when the positive integer n is divided by the positive integer k, where k > 1

What is Remainder?

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.

For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.

As a result, 10 3 3 R 1, where 1 is the remainder and 3 is the quotient.

As we are aware:
Dividend: Divisor x Quotient + Remainder
Therefore,
Dividend - Remainder (Divisor x Quotient)
The formula for the remainder is as follows.

[tex]n=(k+1)^3\\\\=k^3+3k^2+3k+1\\\\=k(k^2+3k+3)+1=(k+1)^3\\\\=k^3+3k^2+3k+1=k(k2+3k+3)+1 \\\\[/tex]

[tex]k(k^2+3k+3)[/tex] is clearly divisible by k, because 1 divided by k gives 1 as the result (since k > 1).

The remainder will be n= (K+1)^3

Learn more about Remainder from the link below

https://brainly.com/question/23148931

#SPJ4

An inverse-square central force field is  [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].

From Newton's second law of motion,

mass × acceleration = Force acting on the mass

Resolving the force F along x and y directions and applying Newton's second law of motion,

Using,

[tex]r = \sqrt{x^2+y^2}[/tex]

​

Therefore,

[tex]m\frac{d^2x}{dt^2} =-|F|cos \theta[/tex]

[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]

Where [tex]r = \sqrt{x^2+y^2}[/tex]

​ and cos⁡θ = [tex]\frac{x}{\sqrt{x^2+y^2} }[/tex]

Similarly using,

[tex]r = \sqrt{x^2+y^2}[/tex]

we get,

 [tex]m\frac{d^2y}{dt^2} = -|F|sin\theta[/tex]

[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]

Where [tex]r = \sqrt{x^2+y^2}[/tex]

​ and sinθ = [tex]\frac{y}{\sqrt{x^2+y^2} }[/tex]

Therefore we showed that holds

[tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex]

Hence the answer is an inverse-square central force field is  [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].

To learn more about coordinates click here https://brainly.com/question/17206319

#SPJ4

Solving the equation 8x − 4 = 2(2x + 4) the required integer to make the equation true is 3

The integer required to be found is solved as follows

The given equation is  8x − 4 = 2(2x + 4)

solving for x

8x − 4 = 2(2x + 4)

8x - 4 = 4x + 8

collecting like terms

8x - 4x = 8 + 4

4x = 12

dividing through by 4

x = 3

Learn more about equations at:
https://brainly.com/question/22688504

#SPJ1

if x is an integer it does not show the median of the 5 numbers to be greater than the average of the 5 numbers

The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.

Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: When the numbers are arranged (1, 4, 7), the number 4 lies in the center, making it the median of 4, 1 and 7.

(1) x must be higher than one or three. It will be the median if it is 8 or fewer.

Consequently, if x = 7, then the list is 1, 3, 7, 8, 12, and median is 7, while the average is 31/5, which equals 6.2, and the answer is YES.

The list is 1, 3, 8, 8, 12, and the median is 8 if x = 8. Average = 32/5 = 6.4; if x = REALLY BIG, the list is 1, 3, 8, 12, and x; and the median is 8; the answer is YES. The answer to the question is NO since the average is REALLY BIG.

insufficient

(2) According to the aforementioned findings, x must be at least 9.

Depending on the amount of x, the list is either 1, 3, 8, x, 12, or 1, 3, 8, x.

The median and mean expressions are the same, regardless of whether order is appropriate:

Mean (average): 8 median = (1 + 3 + 8 + 12 + x)/5 = (24 + x)/5 mean (average):

The mean is at least (24 + 9)/5 = 33/5 = 6.6 since x is at least 9.

This is not convincing because the mean might be either millions or 6.6 (if x = 9) (if x is huge).

insufficient

To find more about median click the following link :-

https://brainly.com/question/26151333

#SPJ4

Answer: your question is not very clear

Step-by-step explanation:

Answer:

Step-by-step explanation:

The word "Sum" = addition.

"A number" = the unknown, aka 'x'.

"Is equal to" is =.

Go piece by piece. I will set your equation exactly as it is worded as you read it. Follow along:

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

Imagine there is a "1" infront of the parenthesis around the -2. A positive * a negative always = negative. So.

Answer:

y={7,10,19,22}

Step-by-step explanation:

3(2)+1 = 6+1 = 7

3(3)+1 = 9+1 = 10

3(6) + 1 = 18+1 = 19

3(7) + 1 = 21+1 = 22

Answer:

(Not accurate because I'm estimating amounts) y = ((x-2)/2)^2 + 4

Step-by-step explanation:

Scales horizontally by 2, Shifts up 4, right 2

An equation with variables on both sides that equal 19 is x - 2 = 17.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign

Based on the information, the equation will be:

x - 2 = 17

Collect like terms

x = 17 + 2

x = 19

Learn more about equations on:

brainly.com/question/2972832

#SPJ1