An architect is designing a home and needs to create a rectangular bedroom. The bedroom must be 425 ft2 and must be 8 ft longer than it is wide. What are the width and length of the bedroom?

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:

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

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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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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The area of the shaded region is equal to half the area of the circle.

What is the area of the circle?

The approximating parallelograms arbitrarily close and approximate the area of the circle by cutting it into ever-increasing slices.

The radius of the arc BC is |AB|=2rcosθ, and ∡AOB=π−2θ.

Dashed area= Area of sector BAC+ 2(Area of sector BOA−Area of triangleBOA)

= 1/2|AB|²(2θ)+2[1/2r²(π−2θ)−1/2r²sin(π−2θ)]

On the other hand, the area of the dashed surface is 1/2πr², then

1/2|AB|²(2θ)+2[1/2r²(π−2θ)−1/2r²sin(π−2θ)] = 1/2πr²

(2rcosθ)2(θ) + r²[π−2θ−sin(π−2θ)] = 1/2πr²

4θcos2θ+π−2θ−sin2θ = 1/2πr²

2θ(2cos2θ−1) = sin2θ−1/2π

2θcos2θ = (2sin2θ−π)/2

cos2θ = (2sin2θ−π)/4θ

Hence, the area of the shaded region is equal to half the area of the circle.

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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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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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Answer:

3/32

Step-by-step explanation:

When dividing fractions, we use keep change flip.

We keep the 1/4, change into multiplication, and flip 2 and 2/3.

First, we want to change 2 and 2/3 into improper fraction form, which is 8/3.

Our equation is now :

1/4 divided by 8/3

Now, we apply keep change flip.

1/4 * 3/8

Multiply numerator by numerator and denominator by denominator.

3/32

3/32 is your final answer. It cannot be simplified further.

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.

The speed of the car will be 25.41 m/h

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector quantity, whereas speed is a scalar quantity

According to the given information

d = [tex]\frac{s^{2} }{10}[/tex] + s

We are given that

distance is 90 feet

So, the expression becomes

90 = [tex]\frac{s^{2} }{10}[/tex] + s

[tex]s^{2}[/tex] + 10s - 900 = 0

which is quadratic in s

So applying the discriminant formula

[tex]$$[/tex]s [tex]=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex]

[tex]$$[/tex]and then we input the values:

s [tex]=\frac{-10 \pm \sqrt{(10)^2-4(1)(900)}}{2(1)}$$[/tex]

and solve:

s [tex]=\frac{-10 \pm \sqrt{3700}}{2}$$[/tex]

It will have two answers

s = -35.41 m/h

s = 25.41m/h

Speed cannot be negative

So

The speed of the car will be 25.41 m/h

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The solutions for the given questions are given below:

Earnings from employment, investments, or company operations. Sam, for instance, had a weekly income of $770 after receiving $30 in bank interest, $700 from his employment, and an additional $40 from buying and selling veggies.

Wages is the amount of money obtained through employment; income is the entire amount of money obtained, which includes earnings, benefits, pensions, and other types of payments.

1.a 500000 shares have been authorized.

1/(210000) = 210000 shares issued Number of shares issued [Common stock account balance / par value of each share]

1-c) The number of shares outstanding is 210000 - 3100, or 206900 shares.

2) The APC Account Balance is $4620000, which is calculated as 210000 * (23 - 1).

3) Net income divided by the number of outstanding shares equals 165520 divided by 206900, or 0.8 per share.

4) The dividend per common share was paid at 53794/206900, or 0.26 per share.

5) 3100 * 21 = $65,100 should be stated for Treasury Stock in the Stockholders' Equity part of the Balance Sheet.

6) Following the stock split, the par value of each share is equal to 1 / 2 ($0.50 per share).

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Answer:

8

Step-by-step explanation:

the answer is 8

Answer:

8

Step-by-step explanation:

total students=20

boys=2/5×20

=8

Answer:

Step-by-step explanation:

You want to write exponential functions through the given points.

The exponential function ...

  f(x) = a·b^x

will have the values ...

Using these relations we can write the function from the table values:

  f(x) = 10400·(2600/10400)^x

  f(x) = 10400·(1/4)^x

Then your table is ...

  [tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7}\vphantom{\dfrac{b}{g}}x&-1&0&1&3&4&6\\\cline{1-7}\vphantom{\dfrac{b}{g}}f(x)&41600&10400&2600&162.5&40.625&2.5390625\\\cline{1-7}\end{array}[/tex]

Using the given points in the exponential function form, we have ...

   4.32 = a·b^1

   59.71968 = a·b^4

Dividing the second equation by the first, we find ...

  59.71968/4.32 = b^3   ⇒   b = 2.4

Using this in the first equation, we get ...

  4.32 = a·2.4   ⇒   a = 1.8

The equation of the function is ...

  g(x) = 1.8·2.4^x

The exponential function ...

  y = a·b^x . . . . . . a > 0, b > 0

will be increasing when the growth factor (b) is greater than 1. When 'b' is less than 1, the function will be decreasing.

Sarah's belief is incorrect.

Answer:

[tex]\textsf{1.} \quad f(x)=10400(0.25)^x[/tex]

     (-1, 41600)  and  (3, 162.5)

[tex]\textsf{2.} \quad g(x)=1.8(2.4)^x[/tex]

3.   Sarah is incorrect.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

The y-intercept is when x = 0.  

Therefore, from inspection of the given table, the y-intercept is 10400:

[tex]\implies a=10400[/tex]

Substitute point (1, 2600) and a = 10400 into the exponential function and solve for b:

[tex]\implies 2600=10400b^1[/tex]

[tex]\implies 2600=10400b[/tex]

[tex]\implies b=\dfrac{2600}{10400}[/tex]

[tex]\implies b=0.25[/tex]

Therefore, the equation of the function is:

[tex]\boxed{f(x)=10400(0.25)^x}[/tex]

Find the value of x when f(x) = 41600:

[tex]\begin{aligned} f(x)&=41600\\\implies 10400(0.25)^x&=41600\\(0.25)^x &=\dfrac{41600}{10400}\\(0.25)^x &=4\\\ln (0.25)^x &=\ln 4\\x \ln (0.25)&=\ln 4\\x&=\dfrac{\ln 4}{\ln (0.25)}\\x&=-1\end{aligned}[/tex]

Find the value of f(x) when x = 3:

[tex]\begin{aligned}x=3 \implies f(3) & =10400(0.25)^3\\& =10400(0.015625)\\& = 162.5\end{aligned}[/tex]

Therefore, the completed table is:

[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} \vphantom{\dfrac12}x & -1 & 0 & 1 & 3 & 4 & 6\\\cline{1-7} \vphantom{\dfrac12}f(x) &41600 &10400 &2600 &162.5 &40.625 & 2.5390625\\\cline{1-7} \end{array}[/tex]

Given points:

Substitute the given points into the exponential formula g(x) = abˣ

[tex]\implies ab=4.32[/tex]

[tex]\implies ab^4=59.71968[/tex]

To find b, divide the equations:

[tex]\implies \dfrac{ab^4}{ab}=\dfrac{59.71968}{4.32}[/tex]

[tex]\implies b^3=13.824[/tex]

[tex]\implies b=\sqrt[3]{13.824}[/tex]

[tex]\implies b=2.4[/tex]

Substitute one of the points and the found value of b into the equation and solve for a:

[tex]\implies 2.4a=4.32[/tex]

[tex]\implies a=\dfrac{4.32}{2.4}[/tex]

[tex]\implies a=1.8[/tex]

Therefore, the equation of the function is:

[tex]\boxed{g(x)=1.8(2.4)^x}[/tex]

Sarah is incorrect.  For an exponential function in the form a · bˣ:

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)

Answer: 51.85

Step-by-step explanation: you use the formula given and plug is 25 for t because it is the number of years. So you get 200*e^(-0.054*25) = 51.85

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:

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%.

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.

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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The area of the shelf A is 30 square feet

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

Dimensions = 3 ft and 2 ft

The above parameters mean that

Length = 3 ft

Width = 2 ft

Number of shelves = 5

The area of the shelf A is then calculated as

Area = Number of shelves  * Length * Width

Substitute the known values in the above equation, so, we have the following representation

Area = 5 * 3 * 2

Evaluate the products

So, we have

Area = 5 * 6

Evaluate the products

So, we have

Area = 30

Hence, the area is 30 square feet

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The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

The name of the point located at (4, 3) is X.

Option D is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates of a point = (4, 3)

Point (4, 3) is located on the graph at point X.

(4, 3) means 4 is on the x-axis and 3 is on the y-axis.

The meeting point is point X.

Thus,

The name of the point located at (4, 3) is X.

Option D is the correct answer.

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Answer:

y=5/2x-4

Step-by-step explanation:

y=mx+b

5/2 is the slope

-4 is the y intercept

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

Step-by-step explanation:

This is a standard construction.

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

Answer:

OD 4x³, x², 3x, 6

Step-by-step explanation:

The inequality is [tex]|x|\geq4[/tex].

What are the inequalities of a graph?

We can see the areas that satisfy one or more inequalities by visualizing them as inequalities on a graph. These inequalities can be represented using straight-line graphs in GCSE maths because they are frequently linear. You might need to draw lines and designate a region that fulfills the system of inequalities to find solutions to the inequalities, or you might need to use the graphs that have already been provided.

Here, in the graph given, we see that the points on and from 4 / -4 are highlighted. Since the interval has 0 in between, we write the variable as [tex]|x-0|[/tex]. Now, the graph excludes points from -4 to 4.

Therefore, we conclude that the absolute value inequality for the given graph is [tex]|x|\geq4[/tex].

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Absolute value is 7 or greater.

What is inequality?

In mathematics, an inequality is a statement that compares two values or expressions using one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). For example:

2 < 3 (2 is less than 3)

5 > 3 (5 is greater than 3)

2 ≤ 3 (2 is less than or equal to 3)

5 ≥ 3 (5 is greater than or equal to 3)

Inequalities can be used to describe a range of values that a variable can take on. For example, the inequality x > 0 describes all values of x that are greater than 0.

Inequalities can be solved by finding the values of the variable that make the inequality true. For example, the solution to the inequality x > 0 is all values of x that are greater than 0, such as 1, 2, 3, etc.

Inequalities can also be combined using the logical operators "and" (represented by the symbol ∧) and "or" (represented by the symbol ∨). For example, the inequality x > 0 ∧ x < 10 describes all values of x that are greater than 0 and less than 10, such as 1, 2, 3, etc. The inequality x > 0 ∨ x < 10 describes all values of x that are either greater than 0 or less than 10, which includes all values of x.

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