Please help me with these exercises that uses area and surface area

The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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The probability P(Xˉ−2<114<Xˉ+2) is approximately 0.95. (Option 3)

We know that the population mean is 114 and the standard deviation is 6. We also know that the sample size is 36, which is large enough to apply the central limit theorem. Thus, the distribution of sample means follows a normal distribution with a mean of 114 and a standard deviation of 6/√36=1.

Now, we need to calculate the z-score for the lower and upper bound of the inequality.

z1=(114-2-114)/1=-2

z2=(114+2-114)/1=2

Using a standard normal distribution table, we can find that the area to the left of -2 is 0.0228 and the area to the left of 2 is 0.9772. Thus, the area between -2 and 2 is approximately 0.9772-0.0228=0.9544, which is approximately 0.95.

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Complete Question:

In 2022, NBA teams score 114 points per game on average with a standard deviation of 6 points per game. Suppose that we randomly sample 36 NBA scores from this season and consider the sample mean (

Xˉ ); the average points per game scored in this sample.

Calculate P( Xˉ 2<114< Xˉ +2)

Answer:

50.46

Step-by-step explanation:

The given expression is proved by integrating the Taylor series for z-1 about zo = 1.

Given that we need to prove that Log z = n=1Σ[infinity] ((-1)^n+1))/(z-1)^n whenever |z-1|<1.

We know that the Taylor series for z-1 about zo = 1 is given by;

f(x)= f(a) + (x-a)f'(a)/1! + (x-a)^2 f''(a)/2! + .....+ (x-a)^n f^n(a)/n!

Since zo = 1, f(z) = log(z).

Let's differentiate it to get its derivatives.

1st derivative: f'(z) = 1/z

2nd derivative: f''(z) = -1/z^2

3rd derivative: f'''(z) = 2!/z^3

4th derivative: f^(4)(z) = -3!/z^4...

We notice that the signs of the derivatives alternate between negative and positive (-1, 2!, -3!,...).

We can therefore group the series as follows:

f(z) = f(1) + (z-1)(-1/1.1) + (z-1)^2(2!/1.1.2) + (z-1)^3(-3!/1.1.2.3) +...

From the general form of the series above, we can rewrite it as follows:

f(z) = f(1) + (1-z) (1/1.1) - (1-z)^2 (1!/1.1.2) + (1-z)^3 (2!/1.1.2.3) -...

We notice that the signs are alternating (+, -, +, -...) and so we can write the series as:

f(z) = ∑((-1)^n+1/(n-1)! (z-1)^n)

= n=1Σ[infinity] ((-1)^n+1))/(z-1)^n whenever |z-1|<1.

Therefore, the given expression is proved by integrating the Taylor series for z-1 about zo = 1.

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Answer:

Median

Step-by-step explanation:

In FGH, K is the midpoint of GH.

Therefore, FK is the median segment.

Therefore , the solution of the given problem of standard deviation comes out to be Mary beat about 62.44% of the other triathletes in her division, finishing first.

Statistics uses variance as a gauge of variation. The photograph of that figure is used to compute the average deviation between what was collected and the mean. In contrast with numerous other valid measures of variability, it includes those data points on their own by comparing each value to the mean. Variations may be brought on by willful mistakes, irrational expectations, or shifting economic or business conditions.

Here,

a) Men, 30-34 years old group: N(4313, 5832) Women, 25-29 years old group: N(5261, 8072)

(b)

=> Z score = (4948 - 4313) / 583 = 1.09 for Leo.

Mary's Z score is

=>   (5513 - 5261) / 807 = 0.31.

(c) We must compare their Z scores in order to evaluate their rankings. Leo ended ahead of his group's mean, according to his Z score of 1.09, while Mary came in below it, according to her Z score of 0.31.

(d) . With the aid of a table or computer,

we determine that this region is roughly 0.8621 or 86.21%.

Leo outperformed about 86.21% of the triathletes in his division, finishing first.

(e) A table or calculator helps us determine that this region is roughly 62.44%.

Mary beat about 62.44% of the other triathletes in her division, finishing first.

(f) Our responses to sections (b) through (e) could change if the distributions of finishing times are not virtually normal.

Z ratings only have significance when the distribution is normal or roughly normal.

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The equations for the line with the given properties: General form:

2x - y + 15 = 0, Slope-intercept form: y = 2x + 15

To find the equation of a line parallel to the line y = 2x and containing the point (-5, 5), we need to determine the slope of the parallel line first.

Since the given line, y = 2x, is in slope-intercept form (y = mx + b) where the coefficient of x (m) represents the slope, we can see that the slope of the given line is 2.

Parallel lines have the same slope, so the slope of the line we are looking for is also 2.

Using the point-slope form of the equation of a line, which is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope, we can substitute the values into the equation:

y - 5 = 2(x - (-5))

Simplifying:

y - 5 = 2(x + 5)

Expanding the right side:

y - 5 = 2x + 10

Rearranging the equation to the slope-intercept form:

y = 2x + 10 + 5

Simplifying further:

y = 2x + 15

So, the equation of the line parallel to y = 2x and containing the point (-5, 5) is y = 2x + 15.

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The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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Answer:

I believe the balance would be 5,221.6 (Rounded to the Nearest Tenth)

Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.

the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²)  to calculate the separation between any two locations.

Given data:

Points on  y-axis and an x-axis are given,

M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).

Starting and ending point is F.

Points lies between the starting and ending are-

F ,G, H, I, J, K, L, M, F

Total length = sum of all length

d = √((x2 - x1)²+(y2 - y1)²)

FG =  √((8 - 8)²+(2 - 5)²)

FG =  √9

FG =  3

GH =  √((8 - 3)²+(2 - 2)²)

GH  =  √25

GH =  5

HI =  √((3 - 3)²+(2 + 5)²)

HI  =  √49

HI  =  7

IJ =  √((3 + 8)²+(-5 + 5)²)

IJ =  √121

IJ =  11

JK =  √((-8 + 8)²+(-2 - 5)²)

JK =  √9

JK =  3

KL =  √((-8 + 3)²+(-2 + 2)²)

KL =  √25

KL =  5

LM =  √((-3 + 3)²+(-2 - 5)²)

LM =  √49

LM =  7

MF =  √((8 + 3)²+(+5 - 5)²)

MF =  √121

MF =  11

Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11

Total length = 52 units

Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.

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Answer:

first number = 7

second number = 11

Step-by-step explanation:

A first number is 4 less than a second number

f = s - 4

Four times the first number is 6 more than twice the second

4f = 2s + 6

-----------------------------

Substitute for f = s - 4

4(s - 4) = 2s + 6

distribute

4s - 16 = 2s + 6

subtract 2s from both sides

2s - 16 = 6

add 16 to both sides

2s = 22

Divide both sides by 2

s = 11

Substitute for s = 11 in

f = s - 4

f = 11 - 4

f = 7

The maximum mortgage payment allowed for someone with an annual salary of $73.025 would be $2,190.75 per month.

The correct answer is an option  A.

In this question we need to find the maximum mortgage payment allowed for someone with an annual salary of $73,025 using the standard 28/36 guidelines.

We know that the standard 28/36 rule used to calculate the amount of debt an individual or household should assume.

This rule says that a household should spend a maximum of 28% of its gross monthly income on total housing expenses and no more than 36% on total debt service.

Let the maximum mortgage payment allowed be x dollars

So, x = ((73025 x 36) / 100) / 12

x = (2,628,900 / 100) / 12

x = $2,190.75

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A complete question is:

Using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $73,025?

a. $2,190. 75

b. $2,044. 70

c. $1,703. 92

d. $1,217. 8.

Answer:

a

Step-by-step explanation:

The number of different ways the marbles can be arranged in a line can be found using combinatorics. Considering the given quantities of red (2), yellow (4), and green (5) marbles, the total number of different arrangements is 11! / (2! * 4! * 5!), which simplifies to 27,720.

To find the number of different arrangements, we use the concept of permutations with repetition. We calculate the total number of arrangements for the 11 marbles, taking into account the repeated marbles of the same color.

Using the formula for permutations with repetition, the total number of arrangements is given by 11! / (2! * 4! * 5!). Here, 11! represents the total number of ways to arrange all 11 marbles, while 2!, 4!, and 5! account for the arrangements of the repeated red, yellow, and green marbles, respectively.

Simplifying the expression, we find that the marbles can be arranged in a line in 27,720 different ways.

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In Costello et al. (2003), the independent variable that was not manipulated by the research team was the gender of the participants.

The study examined the effects of different levels of alcohol consumption on cognitive performance and mood states in young adults. Participants were assigned to different alcohol consumption groups based on their self-reported drinking habits. However, the gender of the participants was not manipulated, and the study included both male and female participants. This means that any differences in the results based on gender cannot be attributed to the research team's manipulation of the independent variable, but rather to other factors that may have affected the results.

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The algorithm constructs a regular grammar without unit productions while preserving the language: g' = (V, Σ, S, P), where c(g) = c(g').

The algorithm for constructing a regular grammar without unit productions can be outlined as follows:

Input: A regular grammar g = (V, Σ, S, P) with unit productions

Output: A regular grammar g' = (V, Σ, S, P) without unit productions, where c(g) = c(g')

The algorithm iteratively expands unit productions by replacing them with equivalent productions until no unit productions remain in the grammar.

The resulting grammar g' will have the same language as the original grammar g (c(g) = c(g')), but without any unit productions.

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Given:

A polynomial has a root of −2.

To find:

The factor that will divide evenly into the polynomial.

Solution:

We know that, if c is a root of a polynomial P(x), then (x-c) is a factor of polynomial P(x).

we have,

-2 is a root of polynomial.

⇒ (x-(-2)) is a factor of polynomial.

⇒ (x+2) is a factor of polynomial.

⇒ (x+2) will divide the polynomial completely.

Therefore, the factor (x+2) will divide evenly into the polynomial.

The factors of a polynomial divide the polynomial evenly, without remainder

The factor of the polynomial is x + 2

The root of the polynomial is given as:

\(\mathbf{Root = -2}\)

Assume the polynomial is a function of x.

i.e. the variable of the polynomial is x

Then the root can be represented as:

\(\mathbf{x= -2}\)

Add 2 to both sides

\(\mathbf{x + 2= -2 +2}\)

So, we have:

\(\mathbf{x + 2= 0}\)

Hence, the factor of the polynomial is x + 2

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Answer:

I can’t post an image, but I’ll explain below

Step-by-step explanation:

Start at a point where the line crosses through a coordinate exactly, like (0,1), and find a second one. Draw a line from the first to the right until it’s over the second point, then go down to the second point. It should look like half of a rectangle. Just follow the lines of the graph :)

G for bag A could also be written as 1g

The equation could then be written as 1g - 0.40g, which if you subtract can be solved as 0.60g

The answer is 0.60g

Given that,

A food truck is selling 2 burritos for $5.

Solution,

We need to find the relationship between burritos and dollars.

2 burritos = $5

To find the value of 1 burrito. Divide 5 by 2 as follows :

\(1\ \text{burrito}=$\dfrac{5}{2}\\\\1\ \text{burrito}=$2.5\)

Hence, the relation between burritos and dollars is " \(1\ \text{burrito}=$2.5\)"

Answer:

The answer is 10

Step-by-step explanation:

To get this you will make the improper fraction into a fraction and then turn that into decimal form

\(4 \frac{1}{8} = 4\)

and

\(5 \frac{6}{10} = 6\)

That is how you find the estimated answer

Hope this Helped

Answer:

  (4, -8)

Step-by-step explanation:

The components of a vector are found by subtracting the tail from the head.

__

  Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)

⇒ The component form is (4, -8), or maybe 4i -8j.

_____

Additional comment

There are many ways that the components of vectors can be described. The particular format you are expected to use will likely be found in your curriculum materials.

(4,-8) is the answer

The volume of the piñata is

1152 cubic in

The volume is solved by breaking the composite shape into two prisms

The volume is solved individually and then added together

Volume of square prism

= area x thickness

= 12 x 12 x 6

= 864 square in

Volume of triangular prism

= area x thickness

= 1/2 x 8 x 12 x 6

= 288 square in

The volume of the piñata

= 864 square in + 288 square in

= 1152 cubic in

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Answer:

  9

Step-by-step explanation:

The 79-digit number of interest can be formulated as a sum of shorter numbers whose remainders can be computed.

The expanded form of the number can be written as ...

  a_44 = 01×10^78 +23×10^76 +45×10^74 +67×10^72 +89×10^70 +...

  +10×10^68 +11×10^66 +... +43×10^2 +44×10^0

Each number except the last is multiplied by a power of 10. Powers of 10 modulo 45 are ...

  10 mod 45 = 10

  100 mod 45 = 10

This lets us conclude that any positive power of 10 mod 45 is 10.

In short, all of the multiplication by powers of 10 can be collapsed to a single multiplication by 10. Hence, the mod 45 value of a_44 will be ...

  a_44 mod 45 = (((01 +23 +45 +67 +89) +10 +11 +12 +... +43)×10 +44) mod 45

  = (((01 +23 +45 +67 +89) mod 45 + sum(10 .. 43) mod 45)×10 +44) mod 45

  = (((225 mod 45) +(901 mod 45))×10 +44) mod 45

  = ((0 +1)×10 +44) mod 45

  a_44 mod 45 = 54 mod 45 = 9

__

Additional comment

The result can be confirmed by a suitable calculator.

__

The sum of the 34 numbers from 10 to 43 is the product of their average value (10+43)/2 = 26.5 and their number, 34. (26.5×34) = 901.

Answer: 9

Step-by-step explanation:

we can manually do this by dividing 1234567891011121314151617181920212223242526272829303132333435363738394041424344

on the calculator. I saw multiple hate comments on the answer above, and I wanted to test it manually - it still is 9.

The dimensions of the garden that will require the least amount of fencing are 450 m and 900 m and the perimeter of the area is 1800 m.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Let's suppose x and y are the sides of the rectangular garden and y is the parallel to the river.

Then according to the problem:

2x + y = P ..(1)

P is the perimeter of the rectangle.

xy = 405000  (area of the rectangle)

Plug the value of y in the equation (1) from the above equation.

P(x) = 2x + 405000/x

P'(x) = x—405000/x² = 0

x = 450 m

P''(x) > 0 hence at x = 450 the value of P(x) is minimum.

y = 405000/450

y = 900 m

P(min) = 1800 m

Thus, the dimensions of the garden that will require the least amount of fencing are 450 m and 900 m and the perimeter of the area is 1800 m.

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The limit of the given function if \(\lim_{x \to 0} f(x)=4\) is 64

Given the following limit of a function expressed as;

\(\lim_{x \to 0} f(x)=4\)

We are to determine the value of the function

\(\frac{1}{4} \lim_{x \to 0} [f(x)]^4\)

This can also be expressed as

\(\frac{1}{4} \lim_{x \to 0} [f(x)]^4\\ = \frac{1}{4}(4)^4 \\=1/4\times 256\\=64\)

Hence the limit of the given function if \(\lim_{x \to 0} f(x)=4\) is 64

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Answer:

quotient

Step-by-step explanation:

yup it just is

Answer:quotiant

Step-by-step explanation:

i wont ask for brainliest

The correct option is D that is the value of se represents the standard error of the estimate, which is a measure of the variability of the errors in predicting the response variable (weights) from the predictor variable (heights) using the regression equation.

Specifically, se represents the standard deviation of the residuals, which are the differences between the observed values of the response variable and the values predicted by the regression equation. A smaller value of se indicates that the regression equation provides a better fit to the data and that the predictions of the response variable are more accurate.

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According to the histogram, the expected mean exam score is approximately 6.5. This value is centered on the majority of scores, indicating that it is most likely the exam's average.

A histogram is a graph that shows data points arranged in user-defined ranges. By grouping a large number of data points into logical ranges or bins, the histogram, which looks like a bar graph, makes a data series easier to understand.

Histograms and bar charts both use columns to present a visual display, and the terms are frequently used interchangeably. However, technically speaking, a histogram depicts the frequency distribution of a data set's variables.

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