What is the simplified form of the following expression

Answer:

A. 27 square units

Step-by-step explanation:

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To solve tan^5x - 9tanx = 0, we factor to get tanx(tan^4x - 9) = 0 leading to solutions where x = kπ and x = ±π/3 + kπ. The constant A in the solution Akiπ is determined to be ±π/3.

To find all solutions to the equation tan^5x - 9tanx = 0, we can factor it as follows:

tanx(tan^4x - 9) = 0

This leads to two possible sets of solutions: tanx = 0 and tan^4x = 9.

For tanx = 0, x would be any integer multiple of π, i.e., x = kπ where k is an integer.

For tan^4x = 9, taking the fourth root gives us tanx = ±9√3. Since tangent is periodic with π, the solution would be of the form x = tan⁻¹(±9√3) + kπ, but since tan⁻¹(±9√3) simplifies to ±π/3, the solution can be written as x = ±π/3 + kπ.

However, if we are given that the solution is in the form Akiπ, we must determine the constant A. From the provided solutions, A must be a solution to tanx = 0 or tan⁻¹(±9√3), giving us A = 0 or ±π/3. Yet, since we cannot have a zero multiple of π (because that would give us a null solution), we dismiss A = 0 and take A from the non-zero solutions, so A = ±π/3.

Step-by-step explanation: To convert pounds into ounces, we need to start with a conversion factor for pounds and ounces which is 16 ounces = 1 pound.

Next, since we are going from a larger unit "pounds" to a smaller unit "ounces" we will multiply the pounds by our conversion factor.

Finally, our product will be our answer.

Answer:

Ken is left with $2.79.

Step-by-step explanation:

We are given the following information in the question:

Ken allowance =  $20

Money spent on movies =

[tex]\displaystyle\frac{1}{5}\times 20 = \$4[/tex]

Money spent n snacks =

[tex]\displaystyle\frac{3}{8}\times 20 = \$7.5[/tex]

Money spent on games =

[tex]\displaystyle\frac{2}{7}\times 20 = \$5.71[/tex]

Total money spent =

[tex]4 + 7.5 + 5.71 = \$17.21[/tex]

Money left =

[tex]=\text{Allowance}-\text{ Total money spent}\\= 20 - 17.21\\=\$2.79[/tex]

Ken is left with $2.79.

Answer:

simple interest  = $9.75

Step-by-step explanation:

given data:

Principle = $1300

annual rate  = 9% [tex]= \frac{9}{`12} = 0.75 [/tex]

time = 6 year =

we knwo that simple interest is given as

Simple interest [tex]= \frac{P\times R\times T}{100}[/tex]

FOR ABOVE QUESTION

Time is 1 month

simple interest  [tex]= \frac{1300\times 0.75 \times 1}{100}[/tex]

simple interest  = $9.75

Answer:

  d.  0.2; 0.08, 0.016, 0.0032

Step-by-step explanation:

The common ratio is the ratio of adjacent terms:

  r = 2/10 = 0.4/2 = 0.2

__

Multiplying the last term by this ratio gives the next term:

  0.4×0.2 = 0.08

  0.08×0.2 = 0.016

  0.016×0.2 = 0.0032

The next 3 terms are 0.08, 0.016, 0.0032.

Answer:

Option D)

Common ration = [tex] \frac{1}{5}[/tex] = 0.2

The next three terms of the given series are: 0.08, 0.016, 0.0032

Step-by-step explanation:

We are given the following information in the question:

We are given a geometric sequence:

[tex]10, 2, 0.4, ...[/tex]

Geometric Series

We have to find the common ration of the given geometric series:

[tex]\text{Common ration} = \displaystyle\frac{\text{Second term}}{\text{First term} }=\frac{2}{10} = \frac{1}{5}[/tex]

The [tex]n^{th}[/tex] term of a geometric sequence is given by:

Formula:

[tex]a_n = a_1\timesr^{n-1},\\\text{where }a_1 \text{ is the first term of the geometric series and r is the common ratio}[/tex]

[tex]a_4 = a_1\times r^{4-1} = 10\times \bigg(\displaystyle\frac{1}{5}\bigg)^3 = 0.08\\\\a_5 = a_1\times r^{5-1} = 10\times \bigg(\displaystyle\frac{1}{5}\bigg)^4 = 0.016\\\\a_6 = a_1\times r^{6-1} = 10\times \bigg(\displaystyle\frac{1}{5}\bigg)^5 = 0.0032[/tex]

First let us calculate for the z score using the formula:

z = (x – u) / s

where u is the mean height of men = 69 in, x is the height of the door = 76, and s is the standard deviation = 2.8 in

z = (76 – 69) / 2.8

z = 2.5

From the standard probability table, at z = -2.5 the probability P is:

P = 0.9938 = 99.38%

To solve this expression, apply the rules of exponents and convert the fractions to decimal values. Simplify the expression and use a calculator to find the decimal values of the powers. Divide the values and express the final result in scientific notation.

To solve this expression, we can first look at the different components. 12^10 means 12 raised to the power of 10. 75^15 means 75 raised to the power of 15. 15^25 means 15 raised to the power of 25. And finally, 80^5 means 80 raised to the power of 5.

Now, we can substitute these values back into the original expression: (12^10 · 75^15)/(15^25 · 80^5).

By using the rules of exponents, we can simplify this expression. For example, when you multiply two powers with the same base, you add the exponents. When you divide two powers with the same base, you subtract the exponents. Applying these rules, we get:

12^10 · 75^15/15^25 · 80^5 = (12/15)^10 · (75/80)^15/15^25 · 80^5 = (4/5)^10 · (3/4)^15/15^25 · 80^5.

To further simplify, we can convert the fractions into decimal values: 4/5 is equal to 0.8 and 3/4 is equal to 0.75. Substituting these values, we get:

(0.8)^10 · (0.75)^15/15^25 · 80^5 = 0.8^10 · 0.75^15/15^25 · 80^5.

We can use a calculator to find the decimal values of 0.8^10 and 0.75^15. After calculating the values and substituting them back into the expression, we get:

0.4 × 10^2 · 1.99 × 10^4/3.12 × 10^4 · 2.32 × 10^6 = 0.4 × 1.99/3.12 × 2.32 × 10^2 × 10^4 × 10^6 = 0.796/7.244 × 10^2 × 10^4 × 10^6.

Simplifying further, we get:

0.796/7.244 × 10^(2+4+6) = 0.796/7.244 × 10^12.

Dividing 0.796 by 7.244, we get approximately 0.1099373. So, the simplified expression is approximately 0.1099373 × 10^12.

Answer:

4.0 *  10^-2

Step-by-step explanation:

Assuming that Standard Form is using Scientific Notation, then you would move the decimal until it is directly after the 4. Then, you would multiply that by 10 raised to the negative exponent of how many spaces that you had to move the decimal. In this case, you moved it two places to the right (+), SO THE EXPONENT IS NEGATIVE!

0.04 = 4.0 * 10^-2

Answer:  The required common ratio for the given geometric sequence is [tex]\dfrac{1}{5}.[/tex]

Step-by-step explanation:  We are given to find the common ratio for the following geometric sequence :

225,   45,   9,   .   .   .

We know that

in a geometric sequence, the ratio of any term with the preceding term is the common ratio of the sequence.

For the given geometric sequence, we have

a(1) = 225,  a(2) = 45,   a(3) = 9,  etc.

So, the common ratio (r) is given by

[tex]r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=~~.~~.~~.~~.[/tex]

We have

[tex]\dfrac{a(2)}{a(1)}=\dfrac{45}{225}=\dfrac{1}{5},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{9}{45}=\dfrac{1}{5},~etc.[/tex]

Therefore, we get

[tex]r=\dfrac{1}{5}.[/tex]

Thus, the required common ratio for the given geometric sequence is [tex]\dfrac{1}{5}.[/tex]

Miami's annual rainfall was 14.13 inches greater than Albany's. It is not possible to determine from the given information how much less rainfall Nashville had than Miami.

To find the difference in annual rainfall between Miami and Albany, we need to subtract the rainfall of Albany from Miami.

Miami rainfall = 61.05 inches

Albany rainfall = 46.92 inches

So, Miami's annual rainfall is greater by:

61.05 inches - 46.92 inches = 14.13 inches

Now regarding the second question about Nashville and Miami, we don't have the absolute rainfall measurement for Nashville, thus we can't answer specifically how much less rainfall Nashville had than Miami.

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The nominal GDP in base year 2014 was $40 billion. The nominal GDP in year 2015 with price index 120 was $57.6 billion. The real GDP in 2015 can be calculated as follows :

GDP (real) = GDP (nominal) / price index * 100

GDP (real) = 57.6 / 120 * 100

GDP (real) = $48 billion

The growth rate in real GDP from 2014 to 2015 is 1.2%.

Growth rate = 48 * (100/40) = 1.2%

Therefore the growth rate is 12%

The nation's real GDP increased from $40 billion in 2018 to $48 billion in 2019, resulting in an economic growth rate of 20% for that year.

To calculate the economic growth rate of a nation, we need to look at the increase in its real GDP. Real GDP is calculated by dividing the nominal GDP by the GDP deflator and then multiplying by 100. The GDP deflator is like a price index that reflects the level of prices of all new, domestically produced, final goods and services in an economy.

For the nation in question:

To find the economic growth rate, we subtract the previous year's real GDP from the current year's real GDP, divide by the previous year's real GDP, and then multiply by 100 to get a percentage:

Economic Growth Rate = [(2019 Real GDP - 2018 Real GDP) / 2018 Real GDP]
100

Economic Growth Rate = [($48 billion - $40 billion) / $40 billion]
100 = (8 / 40)
100 = 20%

The nation's economic growth rate during the year was 20%.

Answer: the sales tax is 1050

The probability that the candidate selects the route of three specific capitals out of 48 states is [tex]\( \frac{1}{17296} \)[/tex].

To calculate the probability of the candidate selecting the route of three specific capitals out of 48 states, we need to consider the total number of possible routes and the number of routes that include the specific capitals.

Calculate the total number of possible routes.

Since the candidate plans to visit 3 out of 48 states, the total number of possible routes is the number of ways to choose 3 states out of 48, which can be calculated using combinations:

[tex]\[ \text{Total number of routes} = \binom{48}{3} \][/tex]

Calculate the number of routes including the specific capitals.

Since the candidate plans to visit the capitals of three specific states, there is only one way to choose each of those specific states. So, the number of routes including the specific capitals is 1.

Calculate the probability.

[tex]\[ \text{Probability} = \frac{\text{Number of routes including specific capitals}}{\text{Total number of possible routes}} \][/tex]

[tex]\[ = \frac{1}{\binom{48}{3}} \][/tex]

Now, let's compute this.

[tex]\[ \binom{48}{3} = \frac{48!}{3!(48-3)!} = \frac{48 \times 47 \times 46}{3 \times 2 \times 1} = 17296 \][/tex]

So, the probability is:

[tex]\[ \text{Probability} = \frac{1}{17296} \][/tex]

Therefore, the probability that the candidate selects the route of three specific capitals out of 48 states is [tex]\( \frac{1}{17296} \)[/tex].

Answer:

C. 5

Step-by-step explanation:

I did the test

Answer: 8 inches.11 inches.32 centimeters. 44 centimetres.

Step-by-step explanation:

Answer:

(4, 4)

Step-by-step explanation:

There are a couple of ways to go at this:

1. The distance formula tells us for some point (x, y) on the parabola, the distance d satisfies ...

... d² = (x -2)² +(y -8)² . . . . . . . the y in this equation is a function of x

Differentiating with respect to x and setting dd/dx=0, we have ...

... 2d(dd/dx) = 0 = 2(x -2) +2(y -8)(dy/dx)

We can factor 2 from this to get

... 0 = x -2 +(y -8)(dy/dx)

Differentiating the parabola's equation, we find ...

... 2y(dy/dx) = 4

... dy/dx = 2/y

Substituting for x (=y²/4) and dy/dx into our derivative equation above, we get

... 0 = y²/4 -2 +(y -8)(2/y) = y²/4 -16/y

... 64 = y³ . . . . . . multiply by 4y, add 64

... 4 = y . . . . . . . . cube root

... y²/4 = 16/4 = x = 4

_____

2. The derivative above tells us the slope at point (x, y) on the parabola is ...

... dy/dx = 2/y

Then the slope of the normal line at that point is ...

... -1/(dy/dx) = -y/2

The normal line through the point (2, 8) will have equation (in point-slope form) ...

... y - 8 = (-y/2)(x -2)

Substituting for x using the equation of the parabola, we get

... y - 8 = (-y/2)(y²/4 -2)

Multiplying by 8 gives ...

... 8y -64 = -y³ +8y

... y³ = 64 . . . . subtract 8y, multiply by -1

... y = 4 . . . . . . cube root

... x = y²/4 = 4

The point on the parabola that is closest to the point (2, 8) is (4, 4).

Answer:

The highest ground temperature in Death Valley is [tex]201^{\circ}F [/tex].

Step-by-step explanation:

We are given that in death valley , Callifornia the highest ground temperature recorded was [tex]94^{\circ}C[/tex]

We are given formula

[tex] C=\frac{5}{9}(F-32)[/tex]

Where C represents the temperature in degrees Celsius  and F represents the temperature in degrees Fahrenheit.

We have to find the highest ground temperature in Death Valley in Fahrenheit to the nearest degree

Using formula [tex] F=\frac{9}{5}C+32[/tex]

Substituting the value of temperature in Celsius

Then we get

[tex]F=\frac{9}{5}\times 94+32[/tex]

[tex]F=\frac{846}{5}+32[/tex]

[tex]F=169.2+32[/tex]

[tex]F=201.2^{\circ}F[/tex]

[tex]F=201^{\circ}F[/tex]

Hence, the highest ground temperature in Death Valley is [tex]201^{\circ}F [/tex].