To model some data Gwyn ran an exponential regression and found the regression equation to be y = 6.72 x 0.996x

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

(h)^2 = (p)^2 + (b)^2

(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (√12)^2 + (√30)^2

→ x^2 = 12 + 30

→ x^2 = 42

→ x = √42

→ x = 6.480...

→ x = 6.5 cm. (approx)

(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√300)^2 = (x)^2 + (√200)^2

→ 300 = x^2 + 200

→ x^2 = 300 – 200

→ x^2 = 100

→ x = √100

→ x= 10 cm.

(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√66)^2 = (x)^2 + (√17)^2

→ 66 = x^2 + 17

→ x^2 = 66 – 17

→ x^2 = 49

→ x = √49

→ x = 7 cm.

(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (2√3)^2 + (5√12)^2

→ x^2 = 12 + 50

→ x^2 = 62

→ x = √62

→ x = 7.874...

→ x = 7.9 cm. (approx)

When the completing the square is applied, the rewritten function is (x + 2)^2 = 4

The equation is given as:

x^2 + 4x = 0

The above equation is a quadratic equation and the coefficient of x in the above equation is 4.

So, we have:

k = 4

Divide the variable k by 2

k/2 = 4/2

k/2 = 2

Square the above result

(k/2)^2 = 4

Next, we add 4 to both sides of x^2 + 4x = 0

x^2 + 4x + 4 = 4

Expand the equation by expressing 4x as 2x + 2x

This gives

x^2 + 2x + 2x + 4 = 4

Factorize the above equation

x(x + 2) + 2(x + 2) = 4

Factor out x + 2 from the above equation

(x + 2)(x + 2) = 4

Rewrite the equation as a perfect square of (x + 2)

(x + 2)^2 = 4

Hence, the rewritten function after completing the square is (x + 2)^2 = 4

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Considering the sum of the internal angles of the triangle, the angle of elevation from point L to point J is of 37º.

The sum of the internal angles of a triangle is of 180º.

In this problem, the angles are:

90º, 53º, x

Hence:

90 + 53 + x = 180

x = 180 - 143

x = 37º

The angle of elevation from point L to point J is of 37º.

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Answer:

53*

Step-by-step explanation:

took on edge

Answer: 0.1

Step-by-step explanation:

The smaller the absolute value of the correlation coefficient, the weaker the correlation.

The equation in function form is f(x)=-4x+80.

What is linear function?

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.

We can find the equation in function form as shown below:

We have given two points (5,60) and (10,40)

Slope of line

m = (40-60)/ (10-5)

m=-20/5

m=-4

Equation in slope intercept form

(y-y1) =m(x-x1)

(y-60) =-4(x-5)

y-60=-4x+20

y=-4x+20+60

y=-4x+80

y=f(x)

f(x)=-4x+80

Hence, the equation in function form is f(x)=-4x+80.

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The surface area of the composite figure is equal to 233.6 square centimeters.

The surface area is the area of all faces of a solid. Since the surface area of the figure is a combination of triangles and quadrilaterals, we must sum all the areas to determine the surface area of the figure. Now we proceed to determine this:

A = 4 · (1/2) · (3 cm) · (2 cm) + 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (2 cm) + 2 · (8 cm) · (3.6 cm)

A = 233.6 cm²

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a.

b.

A quadratic function is a function of the form y = ax² + bx + c

To write y = 5(x - 2)² + 7, we expand the bracket and simplify.

So, y = 5(x - 2)² + 7

y = 5(x² - 4x + 4) + 7

y = 5x² - 20x + 20 + 7

y = 5x² - 20x + 27

So,  the quadratic function y = 5(x - 2)² + 7 in standard form is y = 5x² - 20x + 27

The y intercept is gotten when x = 0.

So, y = 5x² - 20x + 27

y(0) = 5(0)² - 20(0) + 27

y(0) = 0 - 0 + 27

y(0) = 27

The y intercept is (0, 27)

Find the graph in the attachment

To write y = 3(x + 1)² + 12, we expand the bracket and simplify.

So, y = 3(x + 1)² + 12

y = 3(x² + 2x + 1) + 12

y = 3x² + 6x + 3 + 12

y = 3x² + 6x + 15

So, the quadratic function y = 3(x + 1)² + 12 in standard form is y = 3x² + 6x + 15

The y intercept is gotten when x = 0.

So, y = 3x² + 6x + 15

y(0) = 3(0)² - 6(0) + 15

y(0) = 0 - 0 + 15

y(0) = 15

The y-intercept is (0, 15)

Find the graph in the attachment

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[tex]\textbf{Heya !}[/tex]

basic math tips -»

"of" means multiply

[tex]\sf{\cfrac{1}{10}\cdot\cfrac{5}{1}}[/tex]

multiply the numerators and denominators times each other -»

[tex]\sf{\cfrac{5}{10}}[/tex]

reduce:-

[tex]\sf{\cfrac{1}{2}}[/tex]

`hope it was helpful to u ~

I think for the first part 505 m and 53.1 degrees (Like they wrote, you need to repeat it) and same goes for the drcond part. In the last part, I think you need to add the directions. HOPE IT HELPS

*TIP: you can delete the answer the second person gave you to be able to recive more answers :)

Answer: 13 feet

Step-by-step explanation:

Answer:

12.37 ft

Step-by-step explanation:

Hypotenuse(c): the ladder

Cathetus: the wall (a=12) and the floor (b=3)

Equation:

[tex]c^{2} =a^{2} +b^{2}[/tex]

[tex]c^{2} =(12)^{2}+ (3)^{2} =144+9[/tex]

[tex]c^{2} =153[/tex]

[tex]c=\sqrt{153}[/tex]

[tex]c=12.37[/tex]

The ladder is 12.37 feet long

Hope this helps

Answer:

-5y-4=-(x+3)2-1/(2)

Step-by-step explanation:

ANSWER: It's D

Have a great day!!!

The individuals in this data set that can be gotten is B) Compression bandage styles and this data set contains A) 3 variables, 1 of which is categorical.

A categorical variables serve as the variable type that posses two or more categories.

This categories could be nominal variable, however considering the data , we can see that the first two are quantitative data and the data are:

THE COMPLETE QUESTION IS:

Alek is taking an inventory of styles of compression bandages for work. Here is the data he has collected.

The individuals in this data set are:Choose 1 answer:

A) Blood Centers

B) Compression bandage styles

C) Nurses

This data set contains:Choose 1 Answer:

A) 3 variables, 1 of which is categorical

B) 3 variables, 3 of which are categorical

C) 6 variables, 1 of which categorical

D) 6 variables, 3 of which are categorical

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Answer:

========================

Parallel lines have equal slopes, so its equation is in the form of:

Since it passes through the points (4 , - 5), find the value of the y-intercept b by substituting x- and y- coordinates into this equation:

The equation of the parallel line is:

The relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y

The complete question is added as an attachment

From the attached figure, we have the following equation

x^4/y = 7

Multiply both sides of the equation by y

x^4 = 7y

The above represents a direct variation from x^4 to y.

Where 7 represents the variation constant

Hence, the relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y

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Interchange x and y

[tex]\\ \tt\leadsto x=\dfrac{1}{9}y-2[/tex]

[tex]\\ \tt\leadsto \dfrac{1}{9}y=x+2[/tex]

[tex]\\ \tt\leadsto y=9(x+2)[/tex]

[tex]\\ \tt\leadsto y=9x+18[/tex]

[tex]\\ \tt\leadsto f^{-1}(x)=9x+18[/tex]

Answer:

[tex]f^{-1}(x)=9x+18[/tex]

Step-by-step explanation:

[tex]f^{-1}(x)[/tex] is the notation for the inverse of a function.  

The inverse of a function is its reflection in the line y = x.

Given function:

[tex]f(x)=\dfrac{1}{9}x-2[/tex]

To find the inverse of the given function:

Replace f(x) with y to get an equation for y in terms of x:

[tex]\implies y=\dfrac{1}{9}x-2[/tex]

Rearrange the equation to make x the subject:

[tex]\implies y+2=\dfrac{1}{9}x[/tex]

[tex]\implies 9(y+2)=x[/tex]

[tex]\implies x=9y+18[/tex]

Replace x with [tex]f^{-1}(x)[/tex] and y with x:

[tex]\implies f^{-1}(x)=9x+18[/tex]

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Option D. The triangle inequality theorem is verified by by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side.

From the given picture we can see the length of the sides. These are 7, 4 and 15.

The length of the two sides cannot join due to the fact that they are less than 15.

4 + 7 < 15

11< 15

Hence the answer is D.

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by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side

The box-and-whisker plot for the data can be seen in the attachment.

The data given to us is:

50, 51, 54, 55, 57, 61, 62, 63, 65, 66, 67, 68, 71, 71, 76, 76, 77.

As the data is already ordered from least to greatest, we can apply the formulas.

The sample size, n = 17.

Start point = 50.

First quartile, Q1 = (n + 1)/4 th observation = (17 + 1)/4 th observation = 18/4 th observation = 4.5 th observation = average of the 4th and the 5th observation = (55 + 57)/2 = 112/2 = 56.

Median, Q2 = (n + 1)/2 th observation = (17 + 1)/2 th observation = 18/2 th observation = 9th observation = 65.

Third quartile, Q3 = 3(n + 1)/4 th observation = 3(17 + 1)/4 th observation = 3*18/4 th observation = 54/4 th observation = 13.5 th observation = average of the 13th and the 14th observation = (71 + 71)/2 = 142/2 = 71.

End point = 77.

Thus, the box-and-whisker plot should be designed as follows:

The start of the first whisker is from 50, representing the start point.

The start of the box is from 56, representing the first quartile.

The line inside the box is at 65, representing the median.

The end of the box is at 71, representing the third quartile.

The end of the whisker is at 77, representing the endpoint.

The box-and-whisker plot can be seen in the attachment.

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Step-by-step explanation:

Therefore,the answer is [tex] \cfrac{3}{y} - x[/tex].

Answer:

x = 0 , x = 5

Step-by-step explanation:

2x² - 10x = 0 ← factor out 2x from each term on the left side

2x(x - 5) = 0

equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

x - 5 = 0 ⇒ x = 5

Total amount paid over the next year including the initial down payment and finance charge = $856

The difference between paying in cash for the laptop and this financial arrangement = $106

Cost of laptop=$750

Down payment=$150

Finance charges = $25

Remaining amount =$600

Amount for 1 month including 13.5 % interest=600/12*13.5/100+600/12

                                                                       =$56.75

Total amount paid over the next year including the initial down payment and finance charge =  56.75*12+150+25 = $ 856

The difference between paying in cash for the laptop and this financial arrangement = $106

Benefits of financing laptop:

A costly laptop can be yours without having to pay in full.

Bank loans and conventional credit card services are not required.

Numerous retailers provide rewards, flexible payment plans, zero-interest rates, and other benefits.

Downsides of financing laptop:

It's dangerous to borrow money because late payments might result in fees and excessive interest rates.

A credit score may suffer if there is no interest charged.

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Answer:

c

Step-by-step explanation:

option a (x-4) translates the graph 4 units right, not down

option b (x)-4 translates the graph 4 units down, not left

option c (x)+4 translates the graph 4 units up, so it is correct

option d (x+4) translates the graph 4 units left, not right

if the number is outside of the parentheses, like (x)+4 or (x)-4, the graph undergoes a vertical translation, and it moves up/down, with + meaning up and - meaning down

if the number is inside of the parentheses, like (x+4) or (x-4), the graph undergoes a horizontal translation, and moves left/right, with - meaning right and + meaning left

It is true that the U.S. economic system would be seriously strained if we completely eliminated poverty level wages."

The poverty level wages stipulates the lowest or minimum possible wages that a person can be paid in a functional economy. The maintenance of the poverty level wages helps the economy to remain functional and afloat.

Thus, it is a true statement that; From a functionalist view point, the U.S. economic system would be seriously strained if we completely eliminated poverty level wages."

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The new values for the mean and the standard deviation are 38 and 5 respectively.

The mean of a population is given as [tex]\mu = \frac{\sum_{N}^{i}x_i}{N}[/tex] and its standard deviation is given as [tex]\sigma = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}}[/tex].

In the question, we are given that a population has a mean of μ = 35 and a standard deviation of σ = 5, and are asked for the new values for the mean and standard deviation when 3 points are added to every score in the population.

We let the new population formed be over the variable k.

Thus, [tex]k_i = x_i + 3[/tex], for all i from 1 to N.

Thus, the new mean can be calculated as:

[tex]\mu_k = \frac{\sum_{N}^{i}k_i}{N}\\\mu_k = \frac{\sum_{N}^{i}(x_i + 3)}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i + 3N}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i}{N} + 3\\\mu_k = \mu + 3\\\mu_k = 35 + 3 = 38 [Since, \mu = 35].[/tex]

Thus, the new mean is 38.

Thus, the new standard deviation can be calculated as:

[tex]\sigma_k = \sqrt{\frac{\sum_{N}^{i}(k_i-\mu_k)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i + 3-38)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-35)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}} [Since, \mu = 35]\\\sigma_k = \sigma = 5.[/tex]

Thus, the new standard deviation is 5.

Thus, the new values for the mean and the standard deviation are 38 and 5 respectively.

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The simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.

1) 4 2/7 - 2 1/3

First we convert the mixed fraction 4 2/7 and 2 1/3 into an improper fraction.

4 2/7 = (7×4 + 2 )/7 = 30/7

2 1/3 = (3×2 + 1 )/3 = 7/3

Hence,

30/7 - 7/3

( 30×3 - 7×7  )/21

( 90 - 49  )/21

41/21

2) 4.5 - 2 5/8

First we convert both 4.5 and 2 5/8 into an improper fraction.

4.5 = 4 5/10 = (4×10 + 5)/10 = 45/10 = 9/2

2 5/8 = (2×8 + 5 )/8 = 21/8

Hence,

9/2 - 21/8

(9×8 - 21×2  )/16

(72 - 42  )/16

30/16

15/8

3) 5 2/8 - 15%

First we convert both 5 2/8 and 15% into an improper and proper fraction respectively.

5 2/8 = (5×8 + 2)/8 = 42/8 = 21/4

15% = 15/100 = 3/20

Hence

21/4 - 3/20

(21×20 - 3×4  )/80

(420 - 12  )/80

408/80

51/10

Therefore, the simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.

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Answer:

  36 meters

Step-by-step explanation:

You are given an angle and the length of the side adjacent. You want to find the length of the side opposite, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

The height of Yuri's balcony is the sum of the heights of Kim's balcony and the height of Yuri's balcony above that. Each of those height is the side opposite a given angle in a right triangle. These can be found by solving the tangent relation for the opposite side:

  Tan = Opposite/Adjacent

  (Adjacent)(Tan) = Opposite

  height of Kim's balcony = (30 m)tan(40°)

  height above Kim's balcony = (30 m)tan(20°)

__

  height of Yuri's balcony = height of Kim's + height above Kim's

  height of Yuri's balcony = (30 m)tan(40°) +(30 m)tan(20°)

  height of Yuri's balcony = (30 m)(tan(40°) +tan(20°))

  height of Yuri's balcony ≈ (30 m)(0.8391 +0.3640) ≈ 36.092 m

The height of Yuri's balcony is about 36 meters.