A "golden rectangle” is a rectangle where the ratio of the longer side to the shorter side is the "golden ratio.” These rectangles are said to be visually pleasing. An example of a "golden rectangle” has a length equal to x units and a width equal to x – 1 units. Its area is 1 square unit. What is the length of this golden rectangle?

Answer:

I don't see any symbols, so I'll simply compare the two measurements.

Step-by-step explanation:

2 yards and 4 inches

Each yard has 3 feet.  Each foot has 12 inches.  The total inches in 3 yards is therefore:

(2 yards)*(3 feet/yard)*(12 inches/Foot) = 72 inches  [Note how the units cancel to leave only inches]

This means we have a total of 72 + 4 inches = 76 inches total

19 Inches

Compared to 19 inches, 72 inches is almost 3.79 times longer.

Answer:

oh ok. So, first, you get the equation in the form y=ax2+bx+c. Next, you calculate -b / 2a. This is the x-coordinate of the vertex. Then finally, you plug in the value of -b / 2a into the equation into the x variable and solve for the y variable. This is the coordinate of the vertex.

Step-by-step explanation:

Hope this helps!

Answer:

26, 28, 29, 32, 36, 37, 38, 40

Step-by-step explanation:

The volume of a tennis ball is about 8.65 cubic inches

The volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches

From the question, we are to determine the volume of a tennis ball

From the given information,

The circumference of a tennis ball is 8 inches

That is,

C = 2πr (C is circumference)

8 = 2πr

∴ r = 8/2π

r = 4/π inches

This the radius of a tennis ball

Now, for the volume of a tennis ball

Using the formula for calculating the volume of a sphere

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

Then, the volume of a tennis is

[tex]V = \frac{4}{3}\pi \times (\frac{4}{\pi})^{3}[/tex]

[tex]V = \frac{4}{3}\pi \times \frac{64}{\pi^{3}}[/tex]

[tex]V = \frac{256}{3\pi^{2}}[/tex]

V = 8.64607 cubic inches

V ≅ 8.65 cubic inches

Hence, the volume of a tennis ball is about 8.65 cubic inches

b. To find the amount of space within the cylinder not taken up by the tennis balls

First, we will calculate the volume of the cylinder

Using the formula for calculating the volume of a cylinder

V = πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

r = 1.43 inches

h = 8 inches

Putting the parameters into the formula, we get

V = π × 1.43² × 8

V = 16.3592π

V = 51.39 cubic inches

This is the volume of the cylinder

Now, for the amount of space within the cylinder not taken up by the tennis balls

Since there are three tennis balls,

The amount of space not taken up will be

51.39 cubic inches - 3(8.65 cubic inches)

51.39 cubic inches - 25.95 cubic inches

= 25.44 cubic inches

Hence, the volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches

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The distance between the refreshment stands is 440 feet

From the question, we are to determine how far apart are the refreshment stands in feet

From the given information,

The parade route is 3/4 mile long

and

There are refreshment stands at the beginning and end of the route. And there will also be 8 refreshment stands along the route.

This means there will be 10 refreshment stands in all.

If there are 10 refreshment stands in all, then there will be 9 spaces between the refreshment stands.

∴ The distance between any two refreshment stands will be

3/4 mile ÷ 9 = 3/36 mile = 1/12 mile

Now, we will convert this to feet

NOTE: 1 mile = 5280 feet

∴ 1/12 mile = 1/12 × 5280 feet

= 440 feet

Hence, the distance between the refreshment stands is 440 feet.

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A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant. The correct option is B.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given the measure of arc, RS is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.

(3x-14)° + (3x-14)° + (2x+8)° = 180°

8x -20 = 180

8x = 200

x = 25

Hence, the correct option is B.

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Answer:

[tex] 56\: in^2[/tex]

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Every number is divided by 3

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the missing number in the sequence

[tex]\star~\mathrm{324,108,36,12,(~~)}[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Since every number here is divided by 3, we divide 12 by the common ratio, 3:

[tex]\mathrm{12\div3}[/tex]

[tex]\star~\star~\mathrm{4}\star~\star[/tex]

Hope it helps you out! :)

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

The series is a convergence series and the sum of the series is -8/3

The series is given as:

[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]

The above series has the following properties:

Start by calculating the absolute value of the common ratio

Absolute value = |-1/2|

This gives

Absolute value = 1/2

The above value is less than 1.

It means that the series converges.

This is calculated using:

[tex]S_{\infty} = \frac{a}{1 -r}[/tex]

So, we have:

[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]

Evaluate the sum

[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]

Evaluate the quotient

[tex]S_{\infty} = \frac{-8}{3}[/tex]

Hence, the sum of the series is -8/3

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Answer:

10

Step-by-step explanation:

Fish can't drown.

Answer:

A=5.4×4.4=23.76 in

because the are of the paralelogram is base ×high

Answer:

-1/2

Step-by-step explanation:

It mentions that the x-intercept is equal to twice the y-intercept.

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

Let :

⇒ x-intercept = (2a, 0)

⇒ y-intercept = (0, a)

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

Slope formula :

m = y₂ - y₁ / x₂ - x₁

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

Solving :

⇒ m = a - 0 / 0 - 2a

⇒ m = a / -2a

⇒ m = -1/2

Answer:

Answer is $2,637.38

Step-by-step explanation:

Correlation analysis is meant to determine the strength of a linear

relationship between variables.

The complete question is as below:-

Which of the following statements is true of the correlation analysis? The null hypothesis for the Pearson correlation coefficient states that there is always a strong association between two variables. The larger the correlation coefficient, the weaker the association between two variables. The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero. The Pearson correlation coefficient measures the degree of linear association that ranges from 1.0 to 10.0. The Pearson correlation coefficient measures the degree of linear association between three variables.

Correlation analysis is a test to determine the presence and or amount of relationship that exists between variables.

During a hypothesis test aimed at determining the existence of a correlation between variables, the null and alternative hypotheses are as follows;

The null hypothesis, H₀: There are no relationships between the variables

H₀: r = 0

The alternative hypothesis, Hₐ: The variables have an association

Hₐ: r ≠ 0

Therefore, the true statement of the correlation analysis is; The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.

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The solution to the equation 4 + √(5x + 66) = x + 10 is x = -10 and x = 3

From the question, we have the following parameters that can be used in our computation:

4 + √(5x + 66) = x + 10

Subtract 4 from both sides

So, we have

√(5x + 66) = x + 6

Take the square of both sides

5x + 66 = x² + 12x + 36

So, we have

x² + 7x - 30 = 0

When expanded, we have

x² + 10x - 3x - 30 = 0

So, we have

(x + 10)(x - 3) = 0

Solve for x

x = -10 and x = 3

Hence, the solution to the equation 4 + √(5x + 66) = x + 10 is x = -10 and x = 3

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In the triangle , Angle A is 51.1 degrees,  B is 54.5 degrees , C  is 74.4 degrees.

A triangle is defined as a polygon with three sides , three angles and three vertices.

Using the Law of Cosine to solve the Triangle and to determine the value of all the angles

c² = a²+ b² -2abCosC

a = 42 , b=44 , c = 52

52² = 42² + 44² -2 * 42 * 44 cos C

2704 = 1764 + 1936 -3696 cos C

cos C = 0.269

C =74.4 ° (degrees)

Similarly calculating for A and B will give

Angle A is 51.1 degrees

Angle B is 54.5 degrees

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Turn into coordinates pair

Slope

Equation

#1

A week is of 7 days

total fishes Sara has=2(7)=14

Total mel will have

#2

The each day Sara caught 2fishes

pattern for Sara 's total

d is days

#3

Mel also caught 2(2)=4 fishes a day

Mel caught all together is 2(Sara)

#4

They are in proportion to each other

#5

Sara would have 10(2)=20fishes

Mel would have.

Answer:

Q1)

The number of fish Sara caught increases by 2 each day.

The number of fish Sara caught increases by 4 each day.

[tex]\large \begin{array}{| c | c | c |}\cline{1-3} & \sf SARA& \sf MEL\\\sf Days & \sf fish\:caught & \sf fish\:caught \\& \sf altogether & \sf altogether\\\cline{1-3} 1 & 2 & 4 \\\cline{1-3} 2 & 4 & 8 \\\cline{1-3} 3 & 6 & 12 \\\cline{1-3} 4 & 8 & 16 \\\cline{1-3} 5 & 10 & 20 \\\cline{1-3} 6 & 12 & 24 \\\cline{1-3} 7 & 14 & 28 \\ \cline{1-3}\end{aligned}[/tex]

Q2)

Sara caught 2 fish each day.

The pattern that describes how many fish Sara caught altogether is:

2 times the number of days

Q3)

Mel caught 4 fish each day.

The pattern that describes how many fish Mel caught altogether is:

4 times the number of days

Q4)

The number of fish Mel caught altogether is twice the number of fish Sara caught altogether.

Q5)

The number of fish Sara and Mel would have caught by day 10:

Answer:

if im not mistaken the andswer is D

The statements that are true about the given points on the line are; Options B, C and D

A plane is defined by a line and a point outside of it. Meanwhile, a line is defined by two points. Thus, whenever we have 3 non-collinear points, we can define a plane.

Let us check each of the given options;

A) There are exactly two planes that contain points A, B, and F;

If these points are collinear, they can't make a plane and If they are not collinear, they define a plane.

Since we can't make two planes with them, then the statement is false.

B) There is exactly one plane that contains points E, F, and B;

Due to the same reasoning in part A, the statement is true assuming the points are not collinear.

C) The line that can be drawn through points C and G would lie in plane X;

The statement is true because both points C and G lie on plane X, and as such the line that connects them also should lie on the same plane.

D) The line that can be drawn through points E and F would lie in plane Y; Similar to above, this statement is true.

E) The only points that can lie on plane Y are points E and F.

This statement is false because infinite points can lie on a plane.

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The correct answer is option D which is the second coordinate of the vertex of the quadratic function that represents the maximum height of the baseball.

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The second coordinate of the vertex of the quadratic function represents the maximum height of the ball.

The height of a baseball hit from a bat is modeled by a quadratic function of time, h(t)

General form of h(t) will be -16x² + v(t) + h

Where v represents initial velocity and h represents the initial height

h(t) represents the height of the baseball

h(t) is negative so the height reaches the maximum

vertex (h,k) represents maximum height (k) when time t=h

So the second coordinate of the vertex of the quadratic function represents the maximum height of the ball.

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Answer: D

Step-by-step explanation

Answer: Exponential

After plotting the points as shown in the image, it is obvious they follow an exponential trend.

Answer:

Angle AED: 40
Angle BEC: 105

Explanation:
1) To find Angle AED, you have to do arc BC minus arc AD then divide by 2.
120 - 40 = 80.
80 / 2 = 40

2) To find Angle BEC, you have to do arc BA + CD then divide by 2. But that's only angle CED. You'll have to double the number because BEA is vertical; then minus 360.

62 + 88 = 150
150 / 2 = 75
75 times 2 = 150
360 - 150 = 210
210 / 2 = 105
- You'll divide 210 by 2 because of the vertical angles of AED and BEC.

Using it's formula, it is found that their monthly payments for the mortgage loan will be of $515.45.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

In this problem, we have that the parameters are given as follows:

P = 80000, r = 0.06, n = 25 x 12 = 300.

Hence:

r/12 = 0.06/12 = 0.005.

Then, the monthly payment will be of:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 80000\frac{0.005(1.005)^{300}}{(1.005)^{300} - 1} = 515.45[/tex]

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Answer:

x = 97.5 degrees

Step-by-step explanation:

First, we need to know what the total sum of interior angles. We use the formula (n-2) * 180, n being the number of sides.

Since this is a 6-sided polygon, the sum is (6-2) * 180, or 720 degrees.
We have the total sum of interior angles, so now we have all the information we need.
720 degrees = (2x-50) + (x+40) + 80 + (x+20) + 90(right angle symbol) + 150
720 = 4x + 330 (subtract 330 from both sides)

390 = 4x (divide by 4)
x = 97.5 degrees

No, to be parallel the two given angles would need to be the same(corresponding angles)

The two lines are not parallel.

The mean absolute deviation of highway fuel economy of various popular vehicles is 4.9

Find the mean of the data set

= (38 + 48 + 25 + 35 + 33 + 37 + 32 + 34 + 23 + 30) / 10

= 335 / 10

= 33.5

Mean deviation of each set;

38 - 33.5 = 4.5

48 - 33.5 =14.5

25 - 33.5 = -8.5

35 - 33.5 = 1.5

33 - 33 .5 = -0.5

37 - 33.5 = 3.5

32 - 33.5 = -1.5

34 - 33.5 = 0.5

23 - 33.5 = -10.5

30 - 33.5 = -3.5

Absolute deviation of each value

|4.5| = 4.5

|14.5| = 14.5

|8.5| = 8.5

|1.5| = 1.5

|-0.5| = 0.5

|3.5| = 3.5

|-1.5| = 1.5

|0.5| = 0.5

|-10.5| = 10.5

|-3.5| = 3.5

Total absolute deviation = 4.5 + 14.5 + 8.5 + 1.5 + 0.5 + 3.5 + 1.5 + 0.5 + 10.5 + 3.5

= 49

Mean absolute deviation = Total absolute deviation / mean

= 49/10

= 4.9

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[tex]\large{\underline{\underline{\pmb{\sf{\color {red}{Solve:}}}}}}[/tex]

[tex] \sf \red{1. \: (3x - x) (x + 2) = 0}[/tex]

[tex] \sf \red{2. \: (q + 2)^{2} - 40}[/tex]

[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]

2.soln:

(q + 2)² - 40

=> (q)² + 2.q.2 + (2)² - 40

=> q² + 4q + 4 - 40

=>q² + 4q - 36

Here, a = 1, b = 4 and c = - 36

By, using Quadratic formula

See the attachment

Answer:

I think m is 70 and n is 40 because I did a bunch of adding and subtracting

The slant height of the pyramid can be calculated using Pythagoras theorem. Therefore, the slant height is 6.7 mm

The slant height x, can be found using Pythagoras theorem,

Therefore,

c² = a² + b²

where

Therefore,

x² = 4.5² + 5²

x² = 20.25 + 25

x² = 45.25

x = √45.25

x = 6.72681202354

x = 6.7 mm

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The inequality described can be written as:

y < 3x + 2.

First, we know that we have a dashed line, and the region to the left of that line is shaded, then we will have:

y < line.

The linear equation is of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we know that the line passes through (-3, -7) and (0, 2), so the slope is:

[tex]a = \frac{2 - (-7)}{0 - (-3)} = 9/3 = 3[/tex]

And because the line passes through (0, 2), the y-intercept is 2, then the inequality is:

y < 3x + 2.

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