I would like help on this can you please help

Answer:

it would be -2/3

since the equation layout is  formated like this:

F/G(-1)

you multiply -1 by everything.

The area of the triangle is 52.32 square units

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

The triangle (see attachment)

The base of the triangle is calculated as

base = 12 * tan(36)

The area of the triangle is then calculated as

Area = 1/2 * base * height

Where

height = 12

So, we have

Area = 1/2 * base * height

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

Area = 1/2 * 12 * tan(36) * 12

Evaluate

Area = 52.32

Hence, the area of the triangle is 52.32 square units

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Answer:

Now,

tan15°=

\( \frac{5100}{ae} \)

ae=

\( \frac{5100}{tan15} \)

.: ae = 19033.45

.: the aeroplane is 19033.45 m away from the control tower.

Answer:

The only fraction i can think of is 2/9

Step-by-step explanation:

\( {7x}^{4} + {12x}^{2} + 3x\)

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

The expression to make a true equation: (xyz)² - 1 = (____) x (xyz - 1) is (xyz + 1) using difference of two squares.

Considering two numbers a and b, the difference of their squares written as a² - b² is equal to the the product of the sum of the numbers and the difference of the numbers, that is (a + b)(a - b).

From the question, the expression: (xyz)² - 1 can be expressed as the difference of two square as follows:

(xyz)² - 1 = (xyz)² - 1

(xyz)² - 1 = (xyz - 1) × (xyz + 1)

Therefore, the expression (xyz + 1) will make the equation: (xyz)² - 1 = (____) x (xyz - 1) true using difference of two squares.

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Step-by-step explanation:

the answer is simply the volume of the whole model minus the volume of the core ball.

the volume of a sphere (ball, ...) is

4/3 × pi×r³

the radius is always half of the diameter.

radius of the whole model = 18/2 = 9 in.

radius of the core ball = 3/2 = 1.5 in.

so, we have as volume of the clay

4/3 × 3.14 × 9³ - 4/3 × 3.14 × 1.5³ =

= 4/3 × 3.14 × (9³ - 1.5³) = 4/3 × 3.14 × (729 - 3.375) =

= 4/3 × 3.14 × 725.625 = 3,037.95 in³

Answer:

bottom left. (arrow shaped)

Step-by-step explanation:

congruent shapes are the same size and shape

Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

Answer:

its 1.944

Step-by-step explanation:

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.

Answer:

Step-by-step explanation:

Kelly bought a total of 1500 pencil boxes.

Answer:

5000

Step-by-step explanation:

because 5280 minus 280 is 5000 and if u add 720 that is more than 720 so 5000 is correct

Answer:

100,000,000

Step-by-step explanation:

to evaluate means to calculate so

10^8 is really 1 with 8 zeros

Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

Answer:

72

Step-by-step explanation:

circumference = 20

arc = 4

4/20 =1/5

a circle = 360°

1/5 * 360 = 72

The difference between depths in January and July is 14 feets

The depth of a local river averages 16 ft., which is represented as |−16|.

In January,  The depth of a local river measured 4 ft. deep, or |−4|

in July, The depth of a local river  18 ft., or |−18|

The average depth of a local river  is measured as -16 because it is below the ground level and hence measured or plotted on -y axis

the difference between depths in January and July can be measured as

|−18| -  |−4|

This is absolute sign which means every number inside this sign should be treated as positive

18 - 4 = 14

Hence, the difference between depths in January and July is 14 feets

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Answer:

Step-by-step explanation:

Product means multiply.

-300

Step-by-step explanation:

3500 × 10/100

rs. 350 is the discount

and to find the amnt the customer should pay subtract 350 from 3500

which is,

3150 Rupees

The relationship between the length & the width of the closet and the length of the wall is an illustration of a linear equation.

Given that:

\(l = 2w\)

Divide both sides by 2

\(w = 0.5l\)

Equation of f(l)

The sum of the length and the width is represented as: f(l).

So, we have:

\(f(l) = l + w\)

Substitute \(w = 0.5l\)

\(f(l) = l + 0.5l\)

\(f(l) = 1.5l\)

See attachment for the graph of f(l)

The desired dimension

From the question, we understand that the total length is 12m.

This means that:

\(f(l) = 12\)

So, we have:

\(1.5l = 12\)

Divide both sides by 1.5

\(l = 8\)

Recall that:

\(w = 0.5l\)

\(w = 0.5 \times 8\)

\(w = 4\)

Hence, the desired length and width are 8m and 4m, respectively.

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Answer:

The total number of ways to choose 2 students from a class of 16 is given by the combination formula:

C(16,2) = 16! / (2! * (16-2)!) = (1615) / (21) = 120

This means there are 120 possible pairs of students that could be drawn.

The probability of you and your best friend being chosen is the number of ways that you and your friend can be selected divided by the total number of possible pairs. There is only 1 way to select you and your best friend out of the class of 16, so the probability is:

P(you and your best friend are chosen) = 1/120

Therefore, the probability that you and your best friend will be chosen is 1/120. Option (B) is the correct answer.

Answer:

The probability of choosing one specific student out of 16 is 1/16. After one student is chosen, there are 15 students left, so the probability of choosing the second specific student out of the remaining 15 is 1/15. The probability of both events happening is the product of the probabilities: (1/16) x (1/15) = 1/240. However, there are two ways that the students can be chosen (your friend first, then you or you first, then your friend), so we need to multiply the probability by 2: 2 x (1/240) = 1/120. Therefore, the probability of you and your best friend being chosen is 1/120. Answer: 1/120.

Answer:

The expected flight time is 2 hours 10 minutes

Step-by-step explanation:

Given

\(a = 2\ hours\)

\(b = 2\ hours\ 20\ mins\)

Required

The expected flight time

To do this, we simply calculate the mean using:

\(Mean = \frac{a + b}{2}\)

So, we have:

\(Mean = \frac{2\ hours + 2\ hours\ 20\ mins}{2}\)

\(Mean = \frac{4\ hours\ 20\ mins}{2}\)

\(Mean = 2\ hours\ 10\ mins\)

Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.

Answer:

\(\bar x =2.53\) -- Mean

\(Median= 2\)

\(Mode = 2\)

\(Range = 8\)

\(Q_1 = 1\)

\(Q_3 = 3\)

\(IQR = 2\)

Step-by-step explanation:

Given

n = 30

Data: 2 3 1 2 6 4 2 1 5 3 2 3 1 2 2 1 3 1 2 2 4 2 1 2 9 3 2 1 1 3

Solving (a): The mean

This is calculated as:

\(\bar x =\frac{\sum x}{n}\)

\(\bar x =\frac{2 +3 +1 +2 +6 +4 +2 +1 +5 +3 +2 +3+ 1+ 2 +2 +1 +3 +1 +2 +2 +4 +2 +1 +2 +9 +3 +2 +1 +1 +3}{30}\)

\(\bar x =\frac{76}{30}\)

\(\bar x =2.53\)

Solving (b): The median

First arrange the given data

Arranged: 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 5 6 9

\(Median =\frac{1}{2}(n+1)\)

\(Median =\frac{1}{2}(30+1)\)

\(Median =\frac{1}{2}(31)\)

\(Median = 15.5th\)

This implies that the median is the average of the 15th and 16th item

\(Median = \frac{2+2}{2}\)

\(Median = \frac{4}{2}\)

\(Median= 2\)

Solving (c): The mode

From the given data; 2 has the highest frequency of 11.

So,

\(Mode = 2\)

Solving (d): The Range

\(Range = Highest\ Data - Lowest\ Data\)

The highest is 9 and the lowest is 1,

So:

\(Range = 9 - 1\)

\(Range = 8\)

Solving (e): Lower (Q1) and Upper (Q3) quartile.

Q1 is calculated as:

\(Q_1 = \frac{1}{4}(n+1)th\)

\(Q_1 = \frac{1}{4}(30+1)th\)

\(Q_1 = \frac{1}{4}(31)th\)

\(Q_1 = 7.75th\)

\(Q_1 = 8th\ item\)

\(Q_1 = 1\) -- from the arranged data

Q3 is calculated as:

\(Q_3 = \frac{3}{4}(n+1)th\)

\(Q_3 = \frac{3}{4}(30+1)th\)

\(Q_3 = \frac{3}{4}(31)th\)

\(Q_3 = 23.25th\)

\(Q_3 = 23rd\ item\)

\(Q_3 = 3\) -- from the arranged data

Solving (f): The interquartile range (IQR)

\(IQR = Q_3 - Q_1\)

\(IQR = 3-1\)

\(IQR = 2\)

By contradiction we can prove that there is no positive integer 'n' for which √(n-1) + √(n+1) is rational.

Given: To show that there is no positive integer 'n' for which √(n-1) + √(n+1) rational.

Let us assume that √(n-1) + √(n+1) is a rational number.

So we can describe by some p / q such that

√(n-1) + √(n+1) = p / q , where p and q are some number and q ≠ 0.

Let us rationalize √(n-1) + √(n+1)

Multiplying √(n-1) - √(n+1) in both numerator and denominator in the LHS we get

{√(n-1) + √(n+1)} × {{√(n-1) - √(n+1)} / {√(n-1) - √(n+1)}} = p / q

=> {√(n-1) + √(n+1)}{√(n-1) - √(n+1)} / {√(n-1) - √(n+1)} = p / q

=> {(√(n-1))² - (√(n+1))²} / {√(n-1) - √(n+1)} = p / q

=> {n - 1 - (n + 1)] / {√(n-1) - √(n+1)} = p / q

=> {n - 1 - n - 1} / {√(n-1) - √(n+1)} = p / q

=> -2 / {√(n-1) - √(n+1)} = p / q

Multiplying {√(n-1) - √(n+1)} × q / p on both sides we get:

{-2 / {√(n-1) - √(n+1)}} × {√(n-1) - √(n+1)} × q / p = p / q × {√(n-1) - √(n+1)} × q / p

-2q / p = {√(n-1) - √(n+1)}

So {√(n-1) - √(n+1)} = -2q / p

Therefore, √(n-1) + √(n+1) = p / q                  [equation 1]

√(n-1) - √(n+1) = -2q / p                                 [equation 2]

Adding equation 1 and equation 2, we get:

{√(n-1) + √(n+1)} + {√(n-1) - √(n+1)} = p / q -2q / p

=> 2√(n-1) = (p² - 2q²) / pq

squaring both sides

{2√(n-1)}² = {(p² - 2q²) / pq}²

4(n - 1)  = (p² - 2q²)² / p²q²

Multiplying 1 / 4 on both sides

1 / 4 × 4(n - 1)  = (p² - 2q²)² / p²q² × 1 / 4

(n - 1) =  (p² - 2q²)² / 4p²q²

Adding 1 on both sides:

(n - 1) + 1 =  (p² - 2q²)² / 4p²q² + 1

n = (p² - 2q²)² / 4p²q² + 1

= ((p⁴ - 4p²q² + 4q⁴) + 4p²q²) / 4p²q²

= (p⁴ + 4q⁴) / 4p²q²

n = (p⁴ + 4q⁴) / 4p²q², which is rational  

Subtracting equation 1 and equation 2, we get:

{√(n-1) + √(n+1)} - {√(n-1) - √(n+1)} = p / q - (-2q / p)

=>√(n-1) + √(n+1) - √(n-1) + √(n+1) = p / q - (-2q / p)

=>2√(n+1) = (p² + 2q²) / pq

squaring both sides, we get:

{2√(n+1)}² = {(p² + 2q²) / pq}²

4(n + 1) = (p² + 2q²)² / p²q²

Multiplying 1 / 4 on both sides

1 / 4 × 4(n + 1)  = (p² + 2q²)² / p²q² × 1 / 4

(n + 1) =  (p² + 2q²)² / 4p²q²

Adding (-1) on both sides

(n + 1) - 1 =  (p² + 2q²)² / 4p²q² - 1

n = (p² + 2q²)² / 4p²q² - 1

= (p⁴ + 4p²q² + 4q⁴ - 4p²q²) / 4p²q²

= (p⁴ + 4q⁴) / 4p²q²

n =  (p⁴ + 4q⁴) / 4p²q², which is rational.

But n is rational when we assume √(n-1) + √(n+1) is rational.

So, if √(n-1) + √(n+1) is not rational, n is also not rational. This contradicts the fact that n is rational.

Therefore, our assumption √(n-1) + √(n+1) is rational is wrong and there exists no positive n for which √(n-1) + √(n+1) is rational.

Hence by contradiction we can prove that there is no positive integer 'n' for which √(n-1) + √(n+1) is rational.

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Answer:

18

Step-by-step explanation:

parallel lines cut by a transversal are proportional, thus we can set up a ratio to solve for the missing value

7/14 = 9/x

7x = 126

x = 18

The perimeter of the woods is 26 miles if each grid represents one mile in the figure.

It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.

The formula for finding the area of a rectangle is given by:

Area of rectangle = length × width

We know the perimeter of the rectangle = 2(length + width)

As we can see closely in the figure the perimeter of the wood is actually a perimeter of a rectangle if we shift vertical and horizontal lines to make it a complete rectangle.

Let's suppose each grid is expressing one mile.

So the length of the rectangle = 9 miles

The width of the rectangle = 4 miles

The perimeter of the woods  = 2(9+4) = 26 miles

Thus, the perimeter of the woods is 26 miles if each grid represents one mile in the figure.

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Answer:

3

Step-by-step explanation

3 x 2.50 = 7.50

7.50 x 0.06 = 0.45

7.50 + 0.45 = 7.95

So, she would be able to buy 3 sodas and it would cost $7.95