Draw a rectangle that has a golden ratio of its sides. Label the rectangle’s sides. Show how it has a golden ratio of the sides.

To factor the expression 54a⁶b²+ 9ab², you can use the fact that a common factor of 54a⁶b² and 9ab² is ab².

Thus, you can rewrite the expression as:

ab²(54a⁶ + 9)

You can then factor the expression inside the parentheses using the fact that 3 is a common factor of both 54 and 9:

ab²(3 * 18a⁶ + 3 * 3)

This can be simplified as:

ab²(6a⁶ + 9)

This expression is completely factored and cannot be further simplified. Therefore, the completely factored form of the expression is:

ab²(6a⁶ + 9)

The compound interest is 61.342 years

What is compound interest ?

The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.

Formulas for Compound Interest

Formula for Monthly Compound Interest.

Compounded Quarterly Formula: Interest compounded monthly is calculated 12 times a year. Four times a year are used to calculate interest that is compounded quarterly.

Formulas for compound interest are available on a daily, annual, and other basis.

A = 1700

P = 500

r = 2%

n = 4

r = R/100

r = 2/100

r = 0.02 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.02/4)] )

t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.005)] )

t = 61.342 years

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Answer:

OD 4x³, x², 3x, 6

Step-by-step explanation:

The value of P = $7,000,r = 3.2%, n = 4, and money after 7 years will be $8749.6954.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

(A)

As per the given,

Principle amount P = $7,000

Rate of interest r = 3.2%

Number of times interest applied per time period n = 4 (Quarterly)

(B)

Time period T = 7 year

Total amount S(7) = 7,000(1 + 0.032/4)^(4 x 7)

S(7) = $8749.6954

Hence "The value of P = $7,000,r = 3.2%, n = 4, and money after 7 years will be $8749.6954".

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Answer:

12:52

Step-by-step explanation:

almost every card game has 52 cards, you have a 23% chance to draw a face card of any kind.

There are a king, queen, and jack for each of the four different suits: hearts, spades, clubs, and diamonds. The four suits have 13 cards each, for a total of 52 cards. Therefore, your chance of drawing a face card out of a deck of cards upon choosing the card at random is 12 out of 52, or about 23%.

Following values can be filled in the table:

(0,-3), (-1,0), (1,-8), (-2,1), (2,-15)

It can be solved using the concept of graph plotting and function.

What is graph?

When a set of points are connected together to form a strcture then the structure is known as graph. The set of ponts is known as ordered pair.

Consider the eqution.

[tex]y=-2(x+2)^2-3[/tex]

Substitute the simplest value x = 0 and find the value of y.

[tex]y=-2(0+2)^2-3\\=-11\\[/tex]

Now, substitute x = -1 and find the value of y.

[tex]y=-2(-1+2)^2-3\\=-5\\[/tex]

Now, substitute x = 1 and find the value of y.

[tex]y=-2(1+2)^2-3\\=-21\\[/tex]

Now, substitute x = -2 and find the value of y.

[tex]y=-2(-2+2)^2-3\\=-3\\[/tex]

Now, substitute x = 2 and find the value of y.

[tex]y=-2(2+2)^2-3\\=-35\\[/tex]

Hence, following values can be filled in the table:

(0,-11), (-1,-5), (1,-21), (-2,-3), (2,-35)

It can be solved using the concept of graph plotting.

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Step-by-step explanation:

[tex] {x}^{2} - 14x = 164[/tex]

[tex] {x}^{2} - 14x + 49 = 213[/tex]

[tex](x - 7) {}^{2} = 213[/tex]

[tex](x - 7) = \sqrt{213} [/tex]

[tex](x - 7) = - \sqrt{213} [/tex]

[tex]x = 7 + \sqrt{213} [/tex]

[tex]x = 7 - \sqrt{213} [/tex]

Answer:

8

Step-by-step explanation:

the answer is 8

Answer:

8

Step-by-step explanation:

total students=20

boys=2/5×20

=8

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin x= -3/√13

So, B = √13 - 9 = √4 =2

cos x= 2/ √13

So, sin 2x= 2 sin x cos x =2 (-3/√13 )(2/√13 ) = -12/√13

and, cos 2x= 1- 2 sin²x

                  = 1- 2( -3/ √13 )²

                  = -5/ √13

and, tan 2x = sin 2x/ cos 2x = 5/12

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Part a: the rate at which the shadow's tip moves away from the pole while the subject is 25 feet distant is 48/13 ft/sec.

Part b: the speed of the shadow from the speed of the man is 22/13 ft/sec.

A 5 feet 6 inch tall individual is going away from a 12 foot tall pole with a light on top at a 2 foot per second pace.

A) the speed at which the shadow's tip moves away from the pole while the subject is 25 feet distant;

Similar triangles allow us to say:

12/L = 55/(L - x)

Simpllifying,

12(l - x) = 5.5l

12l - 12x = 5.5l

6.5l = 12x

x = (6.5/12)l

Differentiate with respect to time;

dx/dt = (6.5/12)dl/dt or

dl/dt = (12/6.5)(dx/dt)

As, dx/dt = 2

dl/dt = (12/6.5)(2)

dl/dt = 24/6.5

dl/dt = 48/13 ft/sec

B: When a person is 25 feet from a pole, the point of the shadow travelling away from them at:

Subtract the speed of the shadow from the speed of the man.

Therefore,

48/13 - 2 = 22/13 ft/sec.

Thus, the speed of shadow from the speed of the man is 22/13 ft/sec.

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Answer:

Step-by-step explanation:

1:Pl 2:Th 3:Th 4:P 5:P 6:Pl 7:Pl 8:Th 9:Th 10:Th 11:Pl 12:P  

There you go, the numbers go down. So Iowa is 1 and so on, I don't know if they are all right but I did my best.

a) The step in which McKenna made her first mistake is given as follows: Step 4.

b) The correct simplified expression in standard form is given as follows: -15a - 15.

The expression in this problem is defined as follows:

3 − 5(3a + 6)

On the third step, the expression is given as follows:

3 + (−5)(3a + 6)

And on the fourth step, the expression is given as follows:

−2(3a + 6).

This is where the mistake happened, as the multiplication takes precedence over the subtraction.

Then to obtain the correct expression the first step is applying the distributive property, as follows:

3 − 5(3a + 6) = 3 - 15a - 18.

Then the like terms 3 and -18 are combined to obtain the correct simplified expression, as follows:

3 - 15a - 18 = -15a - 15.

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Answer:

15 1/3 miles in 23 minutes

(2/3)x in x minutes

Step-by-step explanation:

1 1/2=1.5

2 1/4=2.25

Convert to unit ratio

[tex]1.5/2.25=(2/3)/1[/tex]

2/3*23=46/3

Simplify

15 1/3 miles in 23 minutes

(2/3)x in x minutes

Answer:

No solution

Step-by-step explanation:

The square root of a negative number is not a real number

Answer: 192 cups

Step-by-step explanation: there's 16 cups in 1 gallon so you would do 2×16=32 to get 32 cups. Then you would do 10×16=160 to get 160 cups. Now add 32+160=192 cups.

The gradient of the line is 4/30 and it means that the amount for each unit of electricity used is 4/30

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

From the graph, we have the following ordered pairs

(0, 0) and (30, 4)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0) and (30, 4)

The gradient of the line is then calculated using the following slope equation

gradient = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (30, 4)

Substitute the known values in the above equation

So, we have the following equation

gradient  = (4 - 0)/(30 - 0)

Evaluate

gradient  = 4/30

Hence, the gradient of the line is 4/30

Generally, slope or gradient means rate

This means that the gradient of this line represent the rate

i.e. the amount for each unit is 4/30

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Answer: The bisector of [tex]\angle BAC[/tex]

Step-by-step explanation:

This is a standard construction.

Answer: C

Step-by-step explanation:

The mean of the data is x(bar) = 41.396

The Median of the data is  $40.76

The mode of all the values are appearing once and therefore there is no mode for the phone bill.

Now, According to the question:

Given the data:

$35.34, $42.09, $39.43, $38.87, $43.39, $49.26

Mean is the average of the data computed as x(bar) = Σ[tex]x_i[/tex] /n where [tex]x_i[/tex]

are the data points and n is the number of data points

x(bar) = 35.34 + 42.09 + 39.43 +38.87 +43.39 + 49.26 /  6

x(bar) = 248.38 /6

x(bar) = 41.396

The median is the data point that lies in the middle of the data set when the data is arranged in ascending or descending order.

Thus,

Ascending order:

$35.34, $38.87, $39.43, $42.09, $43.39, $49.26

The median lies between $39.43 and $42.09 and to get it, we find the average of the two numbers

Median = (39.43 + 42.09)/ 2

Median = $40.76

→ Mode is the value in a data set that is repeated most frequently. In the given data, all the values are appearing once and therefore there is no mode for the phone bill.

Hence, The mean of the data is x(bar) = 41.396

The Median of the data is  $40.76

The mode of all the values are appearing once and therefore there is no mode for the phone bill.

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A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

The value of x is 5.2.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

UH and FH are the two sides of the diagonal.

UH and FH are equal.

UH = FH

19 = 5x - 7

19 + 7 = 5x

5x = 26

x = 5.2

Thus,

The value of x is 5.2.

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Answer:

A) 2 14/25

Step-by-step explanation:

This is a question of order of operations, which PEMDAS helps describe.

P- parentheses

E - exponents

M, D - multiplication, division

A, S - addition, subtraction

In your problem, you'd start with P, what's in the parentheses.

16 ÷ (2 1/2)²

Then do the exponent, E. It might help to convert 2 1/2 to 5/2.

16 ÷ 25/4

Then divide, D. When dividing fractions, you can flip the numerator and denominator and multiply.

16 x 4/25

= 64/25

Then simplify. 25 goes into 64 two times, and there is 14 left over.

= 2 14/25

Answer:

A

Step-by-step explanation:

Evaluate the sum in the brackets first to give 2.5 and square that to give 6.25

Divide 16 by 6.25 to get A

You can make a chart in PowerPoint or Excel. If you have lots of data to chart, create your chart in Excel, and then copy it into your presentation. This is also the best way if your data changes regularly and you want your chart to always reflect the latest numbers. In that case, when you copy and paste the chart, keep it linked to the original Excel file.

To create a simple chart from scratch in PowerPoint, click Insert > Chart and pick the chart you want.

1. Click Insert > Chart.

2.Click the chart type and then double-click the chart you want.

3.In the worksheet that appears, replace the placeholder data with your own information.

4.When you insert a chart, small buttons appear next to its upper-right corner. Use the Chart Elements Chart Elements button button to show, hide, or format things like axis titles or data labels. Or use the Chart Styles Customize the Look of Your Chart button button to quickly change the color or style of the chart.

What is excel ?

Excel is a spreadsheet program from Microsoft and a component of its Office product group for business applications. Microsoft Excel enables users to format, organize and calculate data in a spreadsheet.

The main uses of Excel include: Data entry. Data management. Accounting.

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Answer:

A)  Pam had less water left over than apple juice.

Step-by-step explanation:

Given amounts of drinks left over:

To compare the amounts of drinks left over, convert the fractions into equivalent fractions that have the same denominator.

The denominators of the three fractions are 2, 5 and 10.

The lowest common multiple of the denominators is 10.

Therefore, rewrite the first two fractions so that their denominators are also 10.

[tex]\textsf{Soda}: \quad \dfrac{1}{2}=\dfrac{1 \cdot 5}{2 \cdot 5}=\dfrac{5}{10}[/tex]

[tex]\textsf{Water}: \quad \dfrac{1}{5}=\dfrac{1 \cdot 2}{5 \cdot 2}=\dfrac{2}{10}[/tex]

Therefore, as:

then:

Therefore, Pam had less water left over than apple juice.

Answer:

a) Pam had less water than apple juice.

★ Water < Soda < Apple juice

Step-by-step explanation:

Converting the fraction into decimals,

→ Soda left = 1/2 = 0.5 litres

→ Water left = 1/5 = 0.2 litres

→ Apple juice left = 8/10 = 0.8 litres

Let's order them in ascending order,

→ 0.2 < 0.5 < 0.8

→ 1/5 < 1/2 < 8/10

→ Water left < Soda left < Apple juice left

Now the applicable options is,

→ Pam had less water than apple juice.

Hence, option (a) is correct answer.

Determining whether each statement implies correlation or causation between two variables is as follows:

Correlation indicates that one independent variable causes another dependent variable to change.

Causation indicates that one dependent variable or event is the direct result of the occurrence of the other event or independent variable.

Causation shows cause and effect - unlike correlation which points out two events simultaneously occur or two variables change at the same time.

Thus, correlation is a test of association in relationship, while causation focuses on cause and effect.

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The solution of the system of equation are;

⇒ x = - 2

⇒ y = 0

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ 5x - 4y = - 10

⇒ - 4x + 5y = 8

Now,

Find the solution as;

The system of equation are,

⇒ 5x - 4y = - 10  ..(i)

⇒ - 4x + 5y = 8   ..(ii)

Multiply by 4 in equation (i) + Multiply by 5 in equation (ii);

⇒ 20x - 16y + (- 20x + 25y) = - 40 + 40

⇒ 9y = 0

⇒ y = 0

And,  - 4x + 5y = 8

⇒ - 4x + 0 = 8

⇒ x = - 2

Thus, The solution of the system of equation are;

⇒ x = - 2

⇒ y = 0

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The baby is 105.6  ounces or 6.96 pounds lighter than an average baby.

Weight is the measurement of Gravitational force on an object. It can be zero as in the space.

We are given in the question that A baby weighed only 14.4 ounces at birth the weight of an average baby is 7lb 8 ounces.

1 lb = 16 ounce

Therefore an average baby weight = 7 x 16 + 8 = 120 ounces

The baby weight is just 14.4 ounces

Hence, the baby is 120 - 14.4 = 105.6 ounces lighter than an average baby.

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The table that represents a proportional relationship is Table A.

A proportional relationship exists between two variables when their ratios are equal or equivalent.

With a proportional relationship, there is a constant rate of change between the comparable variables.

Proportions refer to ratios of equality between two or more variables.

Where there is a proportional relationship, we can determine the constant rate of change as the same quotient.

For instance, when the number of pages per book is divided by the reading time, a constant rate of change is established if the reading speed is the same for all three books.

Pages Lucas Read 208  156  234  

Time (hours)             8      6     9

Reading speed       26    26   26 (234/9)

Pages Britney Read 168  120  348  

Time (hours)               6     4       12

Reading speed        28    30    29 (348/12)

Thus, the constant rate of change or proportional relationship can be found in Table A and not in Table B.

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Pages Lucas Read 208  156  234  

Time (hours)             8      6     9

Pages Britney Read 168  120  348  

Time (hours)               6     4      12

Let no of level in one day is x. So, Zoe can play x= 12 level in a day.

The likelihood might be between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. In a sample space, each occurrence has a probability of one overall. the possibility that two or more events will follow one another. Since there are two or more of them, the events are either dependent or independent events. A dependent event—also referred to as a conditional event—is one in which the occurrence of the first event affects the occurrences that follow. The total number of outcomes will differ.

Probability = Possible outcomes/total outcomes

Factors of 12 can be written as:

1 * 12 = 12

2 * 6 = 12

3 * 4 = 12

For this question look for factors of 12-These would be

1 and 12 (1 x 12 = 12)

2 and 6 (2 x 6 = 12)

3 and 4 (3 x 4 = 12)

Hence Zoe could either play

1 level each day for 12 days

2 levels each day for 6 days

3 levels each day for 4 days

4 levels each day for 3 days

Or...

12 levels in one day

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By using the formula for slope, it can be calculated that

The slope of the given line is 10

What is slope of a line?

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan \theta[/tex]

If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], slope is calculated by the formula

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

Here, the line passes through (2, 3) and (3, 13)

Slope = [tex]\frac{13 - 3}{3-2}[/tex]

Slope = 10

So the slope of the given line is 10

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