Express all real numbers greater than 5 in interval notation.​

Answer: The given expression, 2430 + 15√2, cannot be simplified further as it is already in its simplest form. However, you can approximate its value using a calculator or by using a decimal approximation of the square root of 2.

Using a calculator, you can directly evaluate the expression to get:

2430 + 15√2 ≈ 2462.11

Alternatively, you can use a decimal approximation of the square root of 2, which is approximately 1.414:

2430 + 15√2 = 2430 + 15 * 1.414 ≈ 2430 + 21.21 = 2451.21

Therefore, 2430 + 15√2 is approximately equal to 2462.11 or 2451.21, depending on the method used for approximation.

Step-by-step explanation:

The output of the OR gate will be 1.

An important component for electronics and computing, the NOT gate or inverter is a basic digital logic gate. It is designed with one input and output that conduct logical negation.

Essentially, this means it turns the input signal to its opposite. When given an input binary value at "1," the method generates "0" as the output and vice versa.

Two input signals, P=0 and Q=1, are subjected to the following process. The message carried by Q is inverted via a NOT gate using its negation feature, returning Q' = 0 at its output.

The resultant value of Q' (evaluated as zero), is then processed using an OR logic operation along with input P into another gate. Outputs from an OR port may only produce "1" if any of the input signal(s) carry a 1. As one of the inputs from this specific procedure provides "0", the result will inevitably be "1".

Consequently, a final analysis reveals that regardless of what the initial value for P was, the result obtained formulating the two signals through a NOT and OR devices matches an outcome of "1".

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Answer:

3 and 4 ==> see work below

[tex]5. \quad\quad f^{-1}(x) = x^{1/7}[/tex]

[tex]6. \quad\quad f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]

Step-by-step explanation:

Definition of inverse functions

If f and g are inverse functions, then f(x) = y if and only if g(y) = x

Or, in other words
If f(g(x)) = (g(f(x)) = x
then f and g are inverse functions

Q3

We have f(x) = x + 4 and g(x) = x - 4

To find f(g(x)), substitute g(x) = x - 4 wherever there is an x term in f(x)

f(g(x)) = g(x) + 4

= x - 4 + 4 = x

g(f(x)) = f(x) - 4

= x + 4 - 4 =x

Hence f(x) and g(x) are inverse functions

Q4

[tex]f(x) = \dfrac{1}{4}x^3\\\\g(x) = (4x)^{1/3}[/tex]

[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\\\\end{aligned}[/tex]

[tex]\begin{aligned}(g(x))^3 &= \left((4x)^{1/3} \right)^3 \\& = (4x)^{\frac{1}{3} \cdot 3}\\& = 4x\end{aligned}[/tex]

Therefore

[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\&= \dfrac{1}{4} \cdot 4x\\&= x\\\end{aligned}[/tex]

[tex]\begin{aligned}g\left(f(x)\right) & = \left(4f(x)\right)^{1/3}\\&= \left(4 \cdot \dfrac{1}{4}x^3\right)^{1/3}\\& = \left(x^3\right)^{1/3}\\& =x& \end{aligned}[/tex]

So f(x) and g(x) are inverse functions

Q5

[tex]\text{Given $f(x) = x^7 $ we are asked to find inverse $f^{-1}(x)$}[/tex]

[tex]\rm{Let \: y = f(x) = x^7}\\[/tex]

Interchange x and y:
[tex]x = y^7[/tex]

Solve for y:
[tex]y = x^{1/7}[/tex]

The right hand side is the inverse function of f(x)

[tex]f^{-1}(x) = x^{1/7}[/tex]

Q6
[tex]\rm{Given \;f(x) = -\dfrac{2}{5}x^3 \:find\:the\:inverse,\;f^{-1}(x)}[/tex]

Using the same procedure as for Q5

[tex]y=-\dfrac{2}{5}x^3\\\\x=-\dfrac{2}{5}y^3\\\\\text{Solve for y}\\[/tex]

[tex]y^3=-\dfrac{5x}{2}[/tex]

[tex]y=-\left(\dfrac{5x}{2}\right)^{1/3}\\\\\\\text{Inverse of $f(x)$ is $f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]

The value of arc CD is 110⁰.

The value of arc AD is 120⁰.

The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

angle DEC = ¹/₂ (360 - 2x100) (sum of angle at a point)

angle DEC = ¹/₂ (360 - 200)

angle DEC = 80⁰

The value of arc CD is calculated as follows;

80 = ¹/₂ (CD + 50) (intersecting chord theorem)

2 x 80 = CD + 50

160 = CD + 50

CD = 110⁰

Arc AD = 360 - (50 + 80 + 110) (sum of angles in a circle)

arc AD = 120⁰

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The numeric value of the expression 3c + 4d when c = 56 and d = 10 is given as follows:

208.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The expression for this problem is given as follows:

3c + 4d.

Hence the numeric value of the expression is given as follows:

3 x 56 + 4 x 10 = 208.

The expression is:

3c + 4d.

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Answer

5

Solution

[5 (8^1/3 + 27^1/3)^3]^1/4

= [5 ((2^3)^1/3) + (3^3)^1/3)^3]^1/4

= [5((2+3)^3)1/4

= (5×5^3)^1/4

= (5^4)^1/4

= 5

For the given question the values,

Given value of the function when the condition for x is less than '0' is =

f(x) = x²   for x < 0

The value of the function when the condition x is equals to '0' is =

f(x) = 0     for x = 0

The value of the function when the condition x is greater than '0' is =

f(x) = 3x + 4    for x > 0

From the above information,

To find f(-1) we have to use the x value as x². So, f(-1) = (-1)² = 1

To find f(0) we have to use x value as 0. So, f(0) = 0

To find f(3) we have to use the x value as 3x + 4. So, f(3) = 3(3) + 4 = 13.

From the above analysis, we find the values of f(-1), f(0), and f(3).

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Answer:

2x³-5x² - 2x + 1

Step-by-step explanation:

We are given

f(x) = 2x³ - 5x²

g(x) = 2x - 1

and asked to find (f - g)(x)

(f - g)(x) is nothing but f(x) - g(x)

(f- g)(x) = f(x) - g(x) = 2x³-5x² - (2x - 1)

= 2x³-5x² - 2x + 1

The correct option regarding which bus has the least spread among the travel times is given as follows: Bus 14, with an IQR of 6.

The interquartile range is a better measure of spread compared to the range of a data-set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed by the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed by the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.'

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Hence Bus 14 is the more consistent bus, due to the lower IQR.

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The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

We have to given that;

The model shown below is a perfect cube with a volume of 27 cubic units.

Now, We can formulate;

⇒ V = 27 cubic units.

⇒ V = 3 × 9 cubic units.

⇒ V = 3 × 3² cubic units.

Thus, The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

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Answer:

366,699

Step-by-step explanation:

to solve this problem, we can use the following formula for exponential growth:

population = initial population x (1 + growth rate)^time

where the initial population is the current population, the growth rate is the rate of increase per year, and the time is the number of years.

Plugging in the given values, we get:

population = 300,000 x (1 + 0.02)^10

Simplifying, we get:

population = 300,000 x 1.02^10

Using a calculator, we get:

population ≈ 366,698.79

Rounding to the nearest whole number, we get:

population ≈ 366,699

The population in 10 years will be approximately 366,699

P(X=2) &= {14\choose 2}(0.08)^2(0.92)^{12} \

&= \frac{14!}{2!(14-2)!}(0.08)^2(0.92)^{12} \

[tex]\sf\implies\:&=\frac{14\times13}{2\times1}(0.08)^2(0.92)^{12}[/tex]

&= 91(0.08)^2(0.92)^{12} \

&\approx \boxed{0.2166

[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]

Answer:

Total amount of becomes after 16 year is $93649 .

By following trigonometry identities we get  b equals **7**

Trigonometric identities are equations involving trigonometric functions that hold for all possible values of the variables that occur and for which both sides of the equation are specified. These identities come in use if trigonometric function-based formulas need to be made simpler 1.

There are numerous distinctive trigonometric identities that involve a triangle's side length and angle 2. Only the right-angle triangle 2 is covered by the trigonometric identities. The three main trigonometric functions are sine, cosine, and tangent, while the other three are cotangent, secant, and cosecant.

Some of the most popular trigonometric identities are listed below:

sin²(x) + cos²(x) = 1

- tan(x) = sin(x)/cos(x)

- cot(x) = cos(x)/sin(x)

- sec(x) = 1/cos(x)

- csc(x) = 1/sin(x)

- sin(2x) = 2sin(x)cos(x)

- cos(2x) = cos²(x) - sin²(x)

- tan(2x) = (2tan(x))/(1 - tan²(x))

The use of these identities

.One angle in a right triangle is x°, where sin x°=4/5 . With this knowledge, we can use the inverse sine function (arcsin) to calculate the value of x, which gives us x = arcsin(4/5) = 0.9272952180016122 radians .

In addition, we are informed that NL = 22.5 and NM = 3b. We can get the value of LM, which is equal to√(NL2 + NM2), using the Pythagorean theorem. 2. When the given values are substituted, we obtain LM = √((22.5)2 + (3b)2) = sqrt(506.25 + 9b2).

LM is equivalent to b times cos(x°) since it is the polar opposite of the right angle. Consequently, we can write:

b cos(x°) = √(506.25 + 9b²)

Substituting x = arcsin(4/5), we get:

b cos(arcsin(4/5)) = √(506.25 + 9b²)

Simplifying this equation using trigonometric identities, we get:

b * (√1 - sin²(arcsin(4/5)) = sqrt(506.25 + 9b²)

b × (√(1 - (4/5)²)) = sqrt(506.25 + 9b²)

b× (√(1 - 16/25)) = sqrt(506.25 + 9b²)

b× (√(9/25)) = sqrt(506.25 + 9b²)

3b/5 = √(506.25 + 9b²)

Squaring both sides of the equation, we get:

9b²/25 = 506.25 + 9b²

Solving for b, we get:

b = 7

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The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40

Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;

f( - 4 ) = 15

g( - 2 ) = 5

Substitute the given parameters into the expression to have:

3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5

= 45 - 5

= 40

Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40

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The quotient of functions f(x) and g(x) is given as follows:

(f/g)(x) = (x + 4)/(x - 3).

The quotient function of f(x) and g(x) is given by the division of function f(x) by function g(x), as follows:

(f/g)(x) = f(x)/g(x)

The functions for this problem are given as follows:

The functions can be factored as follows:

The term (x + 3) is common to both numerator and denominator, hence it is simplified and the quotient function is given as follows:

(f/g)(x) = (x + 4)/(x - 3).

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Answer: y=16x - 86

Step-by-step explanation:

Answer:

1:8

Step-by-step explanation:

The original volume of the box can be calculated by multiplying the length, height, and width:

V = l x h x w = 40 x 8 x 20 = 6,400 cubic inches

If each of the dimensions is reduced by half, the new dimensions become:

Length = 20 inches

Height = 4 inches

Width = 10 inches

The volume of the new box can be calculated as follows:

V_new = l x h x w = 20 x 4 x 10 = 800 cubic inches

The ratio of the volume of the new box to the volume of the original box is:

V_new / V = 800 / 6,400 = 1/8

Therefore, the ratio of the volume of the new box to the volume of the original box is 1:8.

Answer:

I think it's 1 : 8

Step-by-step explanation:

if you don't understand, you can ask me

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Answer:

shape

Step-by-step explanation:

In a case wehereby you have $12,000 to invest and want to keep your money invested for 8 years the investment option that will earn you the most money is c.4.175% compounded annually

When an investment is compounded annually, it means that the interest earned on the investment is added to the principal amount once a year, and the interest is then calculated on the new total amount for the next year.

For example, if you invest $12,000 at an annual interest rate of 8%, compounded annually, at the end of the first year you will earn the interest of ( $12,000 x 8%) = $960

Then new total amount after one year will be $12,000 + $960 = $12 960 ,

This process will continue for each year of the investment and the  formula to calculate the future value (FV) of an investment compounded annually is: FV = P(1 + r)^n

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complete quesation:

You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.

a.

3.99% compounded monthly

b.

4% compounded quarterly

c.

4.175% compounded annually

d.

4.2% simple interest

Answer: Therefore, the population will exceed 100,000 in the year 2005 + 10.73 ≈ 2016.

Step-by-step explanation:   a) The population of the town in 2005 is given by the formula, where t = 0 since 2005 is the starting year:

P = 50,000(1.15)^0 = 50,000

Therefore, the population of the town in 2005 was 50,000.

b) We need to find the value of t when the population P exceeds 100,000:

100,000 = 50,000(1.15)^t

Divide both sides by 50,000:

2 = 1.15^t

Take the natural logarithm of both sides:

ln 2 = ln (1.15^t)

Apply the power rule of logarithms:

ln 2 = t ln 1.15

Divide both sides by ln 1.15:

t = ln 2 / ln 1.15

Using a calculator, we get:

t ≈ 10.73

A graph that correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r is: C. graph C.

In Mathematics and Geometry, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the length of an arc formed by a circle can be calculated by using the following equation (formula):

Arc length = 2πr × θ/360

In this context, we can reasonably infer and logically deduce that the arc length is directly proportional to the radian measure of the central angle.

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Answer: The answer is false

Answer:

False

Step-by-step explanation:

If you were asking true or false it is false

Answer:

Step-by-step explanation:

The remaining ribbon will be 14 feet.

Olga decorates blankets with ribbon she has 12 yards of ribbon

and, she uses 22 feet of the ribbon to decorates blankets

Now, we have to find the she decorates the blankets how many feet of ribbon will remain?

Firstly, Convert the yard into feet

We know that:

There are 3 feet in 1 yard

So, 36 feet in 12 yards

Now, The remaining ribbon will be the original amount less the amount used.

=> 36 - 12 = 14 feet

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Answer:

b

4 x 3.2 = 12.8

17.8 - 5 =12.8

so,

4 x 3.2 = 17.8-5

12.8=12.8

Answer:

-166/, -0.82,

Step-by-step explanation:

The above fraction, decimal are all evaluated answer for (11/16−(3/4)2)×1

Usually, a mixed number is the simplest way to express an improper fraction – but sometimes, the fraction ... Don't express the answer as a decimal. Instead ... So, add the whole number back in to get a final result of 6 1/2. ... Write out the factors for the numerator of your fraction, then write out the factors for the denominator.

Answer:

364 cents or $3.64

Step-by-step explanation:

We can first convert $4 into cents. There are a 100 cents in $1, so there are 400 cents in $4. Now we can subtract.

400 - 36 = 364

Difference is 364 cents or $3.64