HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Main Answer:The area of the first five squares in the sequence are: 1,4,9,16,25.This is a quadratic progression and the general term of the sequence is \(n^{2}\) ,where n is the term number.

The sum of the areas of the infinite squares generated by this sequence is infinte.

Supporting Question and Answer:

What is the formula for the sum of an infinite series of quadratic terms?

The formula for the sum of an infinite series of quadratic terms is ∑\(n^{2}\) =\(\frac{n(n+1)(2n+1)}{6}\) ,where ∑\(n^{2}\) represents the sum of the terms in the sequence,from n=1 to infinity.

Body of the Solution: The first five squares in the sequence are: \(1^{2} ,2^{2}, 3^{2}, 4^{2} ,5^{2}\)

And their corresponding areas are:

1,4,9,16,25

We can observe that this is a quadratic progression, since the difference between consecutive terms in the sequence increases by a constant amount of 2, indicating a quadratic relationship between the terms.

The general term of the sequence is \(n^{2}\) ,where n is the term number.

To calculate the sum of the areas of the infinte squares generated , we can use the formula for the sum of an infinite series of quadratic terms:

∑\(n^{2}\) =\(\frac{n(n+1)(2n+1)}{6}\) ,where ∑\(n^{2}\) represents the sum of the terms in the sequence,from n=1 to infinity.

Substituting n=∞ in the formula ,we get:

∑\(n^{2}\)= \(\lim_{n \to \infty} \frac{n(n+1)(2n+1)}{6}\)

Evaluting the limit,we get

∑\(n^{2}\)=∞

That is, the sum of the areas of the infinite squares generated by this sequence is infinte.

Final Answer: The area of the first five squares in the sequence are: 1,4,9,16,25.

This is a quadratic progression.

The general term of the sequence is \(n^{2}\) ,where n is the term number.

The sum of the areas of the infinite squares generated by this sequence is infinte.

To learn more about the formula for the sum of an infinite series of quadratic terms from the given link

https://brainly.com/question/11752555

#SPJ4

Let X be the number of people who experience mild side effects after taking the drug. X follows a binomial distribution with parameters n = 100 (the number of people taking the drug) and p = 0.75 (the probability of mild side effects).

To find the probability that more than 70 people will experience mild side effects, we need to calculate:

P(X > 70) = 1 - P(X ≤ 70)

Using the cumulative distribution function (CDF) of the binomial distribution, we can find:

P(X ≤ 70) = F(70) = ∑(i=0 to 70) [nCi * p^i * (1-p)^(n-i)]

where nCi is the binomial coefficient for choosing i items out of n.

We can use a software or calculator to calculate this sum, or use an approximation like the normal approximation to the binomial distribution.

Assuming normal approximation is appropriate, with mean μ = np = 75 and standard deviation σ = sqrt(np(1-p)) = 3.354, we can calculate the z-score:

z = (70.5 - μ) / σ = (70.5 - 75) / 3.354 = -1.33

Using a standard normal distribution table or a calculator with normal distribution functions, we can find the probability of z-score less than -1.33 is 0.0918, which is the probability of 70 or fewer people experiencing mild side effects.

Therefore, the probability of more than 70 people experiencing mild side effects is:

P(X > 70) = 1 - P(X ≤ 70) = 1 - 0.0918 = 0.9082

Using the binomial distribution, there is a probability of approximately 0.9082 that more than 70 people will experience mild side effects out of 100 people who take the drug.

Answer:

Therefore the total amount that Jackson's Bakery made in one week from sheet cakes is: = $2,238

Step-by-step explanation:

Step One:

To arrive at the total amount made from the sheet cakes, we have to assign the prices of each type of cake. They are:

Step Two:

If the new pastry sold 17 small, 11 medium and 20 large sheet cakes respectively, the total money made comes to the following:

= (36 x 17) + (11 x 46) + (56 x 20)

= 612 +  506 + 1120

Therefore the total amount that Jackson's Bakery made in one week from sheet cakes is:

= $2,238

Cheers!

Answer:

29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

29-28=1

1+28=29

29+11=40

40-11=29

Thank you for this challenge that was half the challenge of a challenge........

Better hope you stay up long enough to see the animatronics. :)

Answer: 37, 15, 12, 0, -6, -8, -23

Step-by-step explanation:

So, the higher the negative number, the lower the value is. Hope this helps!

Answer: 9 inches is NOT big

Step-by-step explanation:

Answer:

The median is 33.5

Step-by-step explanation:

In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.

The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.

The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.

To find the median of the given numbers, we first need to arrange them in ascending order:

12 17 28 31 36 54 55 71

Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.

To find the average, we add the two numbers and divide by 2:

(31 + 36) / 2 = 67 / 2 = 33.5

Therefore, the median of the given numbers is 33.5.

Learn more about median of numbers in https://brainly.com/question/26177250

#SPJ11

Answer:

1. 128=x

2.37=x

3. 55=x

4. 15=x

5. 76=x

Step-by-step explanation:

The expressions on the left and right sides are equivalent in part b) and not equivalent in part a) and c).

a) The expressions on the left and right sides are not equivalent.

The left side states that for all values of x, if there exists a value of y such that Q(x, y) is true, then P(x) must be true. The right side states that for all values of x, both the existence of a value of y such that Q(x, y) is true and P(x) must be true.

b) The expressions on the left and right sides are equivalent.

The left side states that it is not the case that there exists an x such that for all values of y, P(x, y) is true. The right side states that for all values of x, there exists a value of y such that either P(x, y) is true or Q(x, y) is true.

c) The expressions on the left and right sides are not equivalent.

The left side states that for all values of x, there exists a value of y such that P(x) implies Q(x, y). The right side states that for all values of x, P(x) implies that there exists a value of y such that Q(x, y) is true.

To learn more about Equivalences with Quantifiers

Visit; brainly.com/question/24067769

#SPJ4

The margin of error (E) is approximately 0.848 (rounded to three decimal places).

To find the margin of error (E) given the values of c, \(\(\sigma\)\), and n, we can use the formula:

\(\[ E = z \cdot \frac{\sigma}{\sqrt{n}} \]\)

where z is the critical value corresponding to the desired confidence level c, \(\(\sigma\)\) is the population standard deviation, and n is the sample size.

In this case, we are given c = 0.90, \(\(\sigma\) = 3.6, and n = 49.

To find the critical value z, we can refer to the table of common critical values for the desired confidence level c.

For a confidence level of 0.90, the corresponding critical value is approximately 1.645.

Substituting the values into the formula, we have:

\(\[ E = 1.645 \cdot \frac{3.6}{\sqrt{49}} \]\)

Simplifying the expression, we get:

\(\[ E \approx 1.645 \cdot \frac{3.6}{7} \]\)

\(\[ E \approx 0.848 \]\)

Therefore, the margin of error (E) is approximately 0.848 (rounded to three decimal places).

To know more about standard deviation refer here :

https://brainly.com/question/32318350

#SPJ11

Since a is a nilpotent matrix, it satisfies a^m = 0 for some m > 1. Therefore, the only eigenvalue of a is 0.

To prove that 0 is the only eigenvalue of a nilpotent matrix, let's assume that there exists a nonzero eigenvalue λ for a, such that a v = λ v for some nonzero vector v. We want to show that this assumption leads to a contradiction.

Since a is nilpotent, there exists an integer m > 1 such that a^m = 0. We can apply the power of a to both sides of the eigenvalue equation:

a^m v = (a a^(m-1)) v = a (a^(m-1) v) = a (λ^(m-1) v) = λ (a^(m-1) v) = λ (0) = 0.

We can simplify this equation by multiplying both sides by v:

a^m v = 0 implies a (a^(m-1) v) = 0 v.

Since v is nonzero, a^(m-1) v is also nonzero, which implies that a (a^(m-1) v) cannot be zero. However, we obtained a contradiction because we assumed a nonzero eigenvalue λ. Therefore, our assumption was incorrect, and the only eigenvalue of a nilpotent matrix is 0.

In conclusion, for a nilpotent matrix, the only eigenvalue is 0.

Learn more about matrix here: brainly.com/question/29132693

#SPJ11

2.7r + 5.3r = (2.7 + 5.3) * r = 8r

Answer: 8r.

Answer:

C

Step-by-step explanation:

trust me

One plane can be drawn so it contains all three points. Then the correct option is C.

Non-collinear points are multiple or more points that cannot all lie on a single straight line. The points are considered non-collinear if any one of them is not situated on the same line as the other ones.

Let n be the number of non-collinear points. Then the number of lines that can be made will be

Number of lines = ⁿC₂

And the number of planes that can be made will be

Number of planes = ⁿC₃

If there are 3 non-collinear points, then the number of lines will be

Number of lines = ³C₂

Number of lines = 3

Then the number of planes will be

Number of plane = ³C₃ = 1

One plane can be drawn so it contains all three points. Then the correct option is C.

More about the non-collinear points link is given below.

https://brainly.com/question/24250339

#SPJ2

The correct answer is B. Increase the sample size and modify the design of the survey to decrease the standard deviation.

The confidence level in statistics denotes the likelihood that the estimation of the position of such a statistical parameter (e.g., an arithmetic mean) in a survey study is also true for such population.

Some characteristics of confidence level are-

To know more about the confidence level, here

https://brainly.com/question/15712887

#SPJ4

The complete question is-

A researcher is conducting a survey for which she currently has 93% confidence level. What would be two actions that she could take that would be most likely to increase the confidence level in her survey result?

A. Increase the sample size and modify the design of the survey to increase the standard deviation.

B. Increase the sample size and modify the design of the survey to decrease the standard deviation.

C. Decrease the sample size and increase the randomness of the survey sample.

D. Modify the design of the survey to increase the standard deviation and decrease the randomness of the survey sample

The volume of the complex figure is determined as 66 ft³ .

The volume of the complex figure is calculated from the summation of volume of the triangle and the volume of the cuboid.

Volume of the cuboid is calculated as follows;

V = 6ft x 2 ft x 3 ft

V = 36 ft³

The area of the triangle is calculated as follows;

A = ¹/₂ x base x height

A = ¹/₂ x 10 ft x 2 ft

A = 10 ft²

The volume of the triangle is calculated as follows;

V = Aw

V = 10 ft² x 3 ft

V = 30 ft³

Total volume = 30 ft³ + 36 ft³ = 66 ft³

Learn more about volume of cuboid here: https://brainly.com/question/22694657

#SPJ1

The solution is Option B.

The base of the triangle is given by the equation B = 4 inches

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the base of the triangle be represented as B

The length of the rectangle L = 9 inches

The width of the rectangle W = 8 inches

Now , the area of the rectangle = length x width

So , the area of rectangle = 9 x 8 = 72 inches²

And , area of triangle = ( 1/4 ) area of rectangle

Area of triangle = 72/4 = 18 inches²

And , area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

18 = ( 1/2 ) x 9 x B

On simplifying the equation , we get

The base of the triangle B = ( 18 x 2 ) / 9

The base of the triangle B = 4 inches

Hence , the base of the triangle is 4 inches

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ1

The information given that A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.

Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle.

It should be noted that an equilateral triangle simply means the triangle tht had equal shape and angles. Here, since A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.

Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle. On such triangle, two out of the three sides are equal.

Learn more about triangles on:

brainly.com/question/1058720

#SPJ1

Answer:

\(x = 2\)

Step-by-step explanation:

\( - 5(4x - 2) = - 2(3 + 6x) \\ - 20x + 10 = - 6 - 12x \\ 20x - 12x = 10 + 6 \\ 8x = 16 \\ \\ x = \frac{16}{8} \\ \\ x = 2\)

Hey there!

Solve for x :

x = 2 ✅

Distributive property: A(B + C) = AB + AC

-5(4x - 2) = -2(3 + 6x)

>> Distribute the -5 to the 4x and to the -2 :

-5(4x) + (-5)(-2) = -2(3 + 6x)

-20x + 10 = -2(3 + 6x)

>> Distribute the -2 to the 3 and to the 6x :

-20x + 10 = -2(3) + (-2)(6x)

-20x + 10 = -6 - 12x

>> Substract 10 from both sides :

-20x + 10 - 10 = -6 - 12x - 10

-20x = -12x - 16

>> Add 12x to each side :

-20x + 12x = -12x - 16 + 12x

-8x = -16

>> Divide both sides by -8 :

-8x / -8 = -16 / -8

x = 2

▪️Let's verify :

-5(4(2) - 2) ⇔ -5(8 - 2) ⇔ -5(6) ⇔ -30

-2(3 + 6(2)) ⇔ -2(3 + 12) ⇔ -2(15) ⇔ -30

Therefore, your answer is x = 2

Similar questions :

↣https://brainly.com/question/17139226

↣https://brainly.com/question/14621119

Answer:

80%

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

50 times .8 aka 80 percent is 40

Answer:

Please check the format of the equation in the question.

Step-by-step explanation:

7x (5-98) ^4 = x +2

I will assume that the x in "7x" is the variable x, and not the multiplication sign.  The expression (5-98)^4 is a bit odd, so please check.  I'll assume it is correct.

7x (5-98) ^4 = x +2

7x (-93) ^4 = x +2

7x (74805201) = x +2

523636407x = x+2

523636406x = 2

x = 2/(523636406)

This seems to be an extraordinarily odd number, but that's the solution to

7x (5-98) ^4 = x +2

Answer:

The decimal is 2.8 The 8 is the repeating decimal I just couldn't add the line to the top. So it would be 2.88888...

Step-by-step explanation:

Answer:10

Step-by-step explanation:

Each chicken egg is 5

so day 2 and 5 combined is 15

and day 3 is 25

so subtract 25-15 its 10

Answer:

I think pretty sure its 2

Step-by-step explanation:

If you add the eggs from pen 2 and 5 you get 3 eggs in total. Then you gather all the eggs from pen 3 and minus the eggs you got from pen 2 and 5 which would be 5-3 which would then equal 2 eggs in total. I hope this helped :).

Answer:

43 is your answer......

Answer:

the third one

Step-by-step explanation:

Forming linear equations, the cost of a t-shirt and a notebook will be $1 and $6 respectively.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Another term for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There are three more constants in addition to the constant C: the variables x and y, the coefficients A and B, and the variables.

Now,

Given that

club A sold 2 t-shirts and 3 notebooks, and made $20.

Club B sold 2 t-shirts and 1 notebook, for a total of $8.

Let x and y be the cost of t-shirt and notebook respectively

then 2x+3y=20--->1

and 2x+y=8 --->2  will be the equations formed.

Now subtracting 2 from 1

we get 2x-2x+3y-y=20-8

2y=12

y=6

then  2x+6=8

x=1

Hence,

          the cost of a t-shirt and a notebook will be $1 and $6 respectively.

To know about linear equations visit the link

https://brainly.com/question/29739212

#SPJ1

The converted point in the form of spherical coordinate will be (10, -45°, 30°).

To convert the given rectangular coordinate point (-5√2,5√2, 10√3) to spherical coordinate system, let's follow the steps below:

Step 1: We need to calculate the magnitude (r) of the given rectangular coordinates.

We use the distance formula to find r.r = sqrt(x^2 + y^2 + z^2)Where x,y and z are the rectangular coordinates.

                                     r = sqrt((-5√2)^2 + (5√2)^2 + (10√3)^2)r = 10

Step 2: We need to find the angle θ (theta) from the positive x-axis to the projection of the point onto the xy-plane.

We use the formula below to find the θ.

                                 θ = arctan(y/x)θ = arctan(5√2/(-5√2))

                              θ = arctan(-1)θ = -45°

Step 3: We need to find the angle φ (phi) between the positive z-axis and the line segment connecting the origin to the point.

We use the formula below to find the φ.

                                   φ = arccos(z/r)φ = arccos(10√3/10)

                                   φ = arccos(√3)φ = 30°

Thus, the rectangular coordinates (-5√2,5√2, 10√3) is equivalent to the spherical coordinates (10, -45°, 30°).

Hence, the converted point in the form of spherical coordinate will be (10, -45°, 30°).

Learn more about spherical coordinate

brainly.com/question/31745830

#SPJ11

Answer:

96m

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

12/35

▹ Step-by-Step Explanation

\(\frac{4}{5} * \frac{3}{7} \\\\= \frac{12}{35}\)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

12/35

Step-by-step explanation:

4/5 * 3/7 = (4 * 3)/(5 * 7) = 12/35

3x^{2}+5 is the area of rectangle .

What is a rectangle, exactly?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral.

                 The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

The height of the first rectangle is 2 and the area is 6x^{2}. To get to 6x^{2} you have to multiply by 3x^2.

Similarly, to find the width of the other rectangle you multiply 5 by 2 to get to 10.

The answer is 3x^{2}+5

Learn more about rectangle

brainly.com/question/29123947

#SPJ1