if so, find the following. (if an answer does not exist, enter dne.) f ^−1(2) = -2 incorrect: your answer is incorrect. f ^−1(7) =

Answer:

the second one

Step-by-step explanation:

Convert miles to yards and hours to minutes:

15 miles x 1760 = 26,400 total yards

2 hours x 60 = 120 total minutes

26400 yards / 120 minutes = 220 yards per minute.

Answer:

To prove:

Tan 15A - tan 10A - tan 5A = tan 15A * tan 10A * tan 5A

We will use the following trigonometric identities:

Tan (A + B) = (Tan A + Tan B) / (1 - Tan A * Tan B)

Tan (A - B) = (Tan A - Tan B) / (1 + Tan A * Tan B)

Now, let's start by expressing Tan 15A in terms of Tan 10A and Tan 5A:

Tan 15A = Tan (10A + 5A)

= (Tan 10A + Tan 5A) / (1 - Tan 10A * Tan 5A)

Next, we will use the identity Tan (A - B) to express Tan 10A and Tan 5A in terms of Tan 15A:

Tan 10A = Tan (15A - 5A)

= (Tan 15A - Tan 5A) / (1 + Tan 15A * Tan 5A)

Tan 5A = Tan (10A - 5A)

= (Tan 10A - Tan 5A) / (1 + Tan 10A * Tan 5A)

Substituting these values in the original expression, we get:

Tan 15A - Tan 10A - Tan 5A

= Tan 15A - (Tan 15A - Tan 5A) / (1 + Tan 15A * Tan 5A) - (Tan 10A - Tan 5A) / (1 + Tan 10A * Tan 5A)

= Tan 15A (1 + Tan 10A * Tan 5A) - (Tan 15A - Tan 5A) - (Tan 10A - Tan 5A) * Tan 15A * Tan 10A * Tan 5A / (1 + Tan 15A * Tan 5A) * (1 + Tan 10A * Tan 5A)

= Tan 15A * Tan 10A * Tan 5A

Therefore, we have proved that:

Tan 15A - tan 10A - tan 5A = tan 15A * tan 10A * tan 5A.

The number  300 can be written as 300/1 as a quotient of integers to show that it is rational.

A rational number is a number of the form p/q, where q not equal to 0 and p  and q must be co-primes.

To write a number in the form of quotient of integer, we write it as , where p/q.

Here,  300 can be written as  300/1 or 600/2 .

But we should also take care that p and q must be co-primes.

Co-primes are the pairs of numbers that have only one common factor which is 1.

So, 300 can be written as 300/1

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Answer:

please see photo attached for detailed analysis.

The linear relationship between time and distance can be considered proportional. The constant of proportionality in this case is 4.

In a proportional relationship, the ratio between the two quantities remains constant. Here, as time increases by 2 hours, the distance also increases by 8 miles. Let's calculate the ratio of distance to time for each pair of values:

For the first pair (2 hours, 8 miles):

Ratio = distance / time = 8 miles / 2 hours = 4 miles/hour

For the second pair (4 hours, 16 miles):

Ratio = distance / time = 16 miles / 4 hours = 4 miles/hour

For the third pair (6 hours, 24 miles):

Ratio = distance / time = 24 miles / 6 hours = 4 miles/hour

For the fourth pair (8 hours, 32 miles):

Ratio = distance / time = 32 miles / 8 hours = 4 miles/hour

As we can see, the ratio of distance to time remains constant at 4 miles per hour for all the pairs. This indicates a proportional relationship between time and distance.

Therefore, the linear relationship is also proportional, and the constant of proportionality is 4.

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Answer:

b and c

Step-by-step explanation:

All angles in a triangle add up to 180

The output of the function call doWork(30) is given as follows:

9.

The input of the function is given as follows:

n = 30.

Hence we apply the recursion as follows:

Now we apply the inverse procedure, as follows:

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Suppose that a square of length s is cut out from each corner of the cardboard. The length of the box will be x - 2s and the width of the box will be y - 2s. The height of the box will be s. The volume of the box will be given by V = s (x - 2s) (y - 2s) or V = 4s³ - 2(x + y) s² + xy s.

To find the maximum volume, we need to take the derivative of V with respect to s and set it equal to zero. We get:

dV/ds = 12s² - 4(x + y) s + xy = 0

Solving for s, we get:

s = [(x + y) ± √(x² + y² - 2xy)] / 6

Since s must be less than x/2 and less than y/2, we choose:

s = min {[(x + y) ± √(x² + y² - 2xy)] / 6, x/2, y/2}

Plugging this value of s into the formula for V, we get:

V = (xy/6) [(x + y) - √(x² + y² - 2xy)]

Therefore, the maximum volume of the box is given by:

Vmax = (1/6)xy(x + y - √(x² + y² - 2xy))

Thus, the maximum volume of a box that can be made by cutting out squares from the corners of an inch by inch rectangular sheet of cardboard and folding up the sides is given by (1/6) cubic inch, which is 0.166666 cubic inch. The justification is based on the given formula for the volume of the box.

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The area of the shaded region is  \(60 mm^2\)  .

The area of a double figure is a measurement of the area it encompasses. Inches or square metres are examples of squares, which are the most common unit of measurement.

The area of a figure is calculated by multiplying the length of one side by the height of the other. For illustration, the area of a rectangle is calculated by dividing its length by its breadth.

We must deduct the area of the triangle that isn't shaded from the area of the rectangle in order to determine the size of the shaded area.

Area  \(= length \times width = 12 mm \times 6 mm = 72 mm^2\)

The area of the triangle is

Area  \(= 1/2 \times base \times height\)

The rectangle's width, which is 6 mm, corresponds to the triangle's base. By deducting the longer side's length from the shorter side's length, we can determine the height, which is:

\(10 mm - 6 mm = 4 mm\)

Therefore, the area of the triangle is:

\(Area = 1/2 \times 6 mm \times 4 mm = 12 mm^2\)

We deduct the triangle's area from the rectangle's area to obtain the area of the darkened area.

Shaded area  \(= 72 mm^2 - 12 mm^2 = 60 mm^2\)

Therefore, The faded region's area is  \(60 mm^2\) .

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The length of segment PM would be 12 units

I won't proceed based on your circle's association with any specific segments; instead, I'll use the illustration below.

We can determine QM = 15, SM = 10, and RM = 18 from the image. We apply the formula for determining segment lengths when there are two chords in a circle to determine the length of segment PM.

Our equation QM = (SM)(RM) (PM)

We now enter the information and resolve: (10)(18) = (15)(x) (x)

(10)(18) = 180

(15)(x) = 15x

180 = 15x → 180 ÷ 15 = 12 & 15x ÷ 15 = x

x = 12

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we conclude that the correct option is the second one, the opposite of a positive number is a negative number (of equal absolute value).

For any real number X, we define the opposite of X as a number Y such that:

X + Y = 0

Solving for Y (by subtracting X in both sides)

X + Y - X = 0 - X

Y = -X

Then if X represents a positive number, the opposite of a positive number is Y = -X a negative number.

From that, we conclude that the correct option is the second one, the opposite of a positive number is a negative number (of equal absolute value).

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Answer:

D.

Step-by-step explanation:

The dark triangle is 6cm and the light is 10.5cm

Answer:

D 16.5

Step-by-step explanation:

6x2=12 divided by 2 equal 6. Answer to left triangle

7x3=21 divided by 2 equal 10.5 answer to right

Then add 10.5 +6= 16.5

Answer:

Step-by-step explanation:

1). Since, m∠1 + m∠2 = 180° [Supplementary angles]

   If m∠2 = 120°

   m∠1 + 120° = 180°

   m∠1 = 180° - 120°

   m∠1 = 60°

2). If a transversal intersects two parallel lines on the top and middle,

   ∠1 and ∠5 will be corresponding angles.

3). Since, m∠1 = m∠5 = 60° (Corresponding angles)

   Therefore, both the lines on top and middle will be parallel.

4). Since, m∠9 + m∠11 = 180° [Supplementary angles]

   If m∠11 = 120°

   m∠9 + 120° = 180°

   m∠9 = 60°

   Since, m∠1 = m∠9 = 60° [Corresponding angles]

   Therefore, both the lines on the top and bottom shelves will be parallel.

5). Since, m∠5 = m∠9 = 60° [Corresponding angles]

    Therefore, middle and bottom shelves will be parallel.

Answer:

43 hours

Step-by-step explanation:

\(\frac{y}{1} :\frac{408}{9.5}\)

y × 9.5 = 408 × 1

9.5y = 408

9.5y ÷ 9.5 = 408 ÷ 9.5

\(y=42\frac{18}{19}\)

43 hours

Answer:

Step-by-step explanation:

6+11=17/2*8=136/2

68.

The Solution to the given questions are:

A central angle is an angle whose vertex is at the centre of a circle and whose sides intersect the circle at two distinct points. The measure of a central angle is equal to the measure of the arc intercepted by the angle, where the arc is the portion of the circle between the two points of intersection.

An intercepted arc is a segment of a circle's circumference that is bounded by two points on the circle and contains all the points of the circle's circumference that lie between those two points. In other words, it is the portion of the circle that is "cut out" or intercepted by two points on the circle.

In this given question,

The circumscribed angle can be measured by dividing the central angle by 2.

Hence,

112°/2= 56°.

Therefore, the measurement of circumscribed angle is 56°.

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I believe the answer to be (-7)

Answer:

-7

Step-by-step explanation:

Step 1: Make an equation.

Step 2: Subtract 9 from both sides.

Step 3: Check if solution is correct.

Therefore, the integer that makes the addition sentence true is -7.

Answer:

14

Step-by-step explanation:

7(length) times 4(height) equals 28

28/2= 14

ANSWERS

• A = 36.8°

• B = 23.2°

• a = 7.6

EXPLANATION

We can find B using the law of sines,

We have b = 5, c = 11 and C = 120°. Using the last two ratios,

Rise both sides of the equation to -1 - i.e. flip both sides,

Multiply both sides by b,

And take the inverse of the sine,

Replace with the values and solve,

Then, knowing that the sum of the measures of all the interior angles of a triangle is 180°, we find A,

Solving for A,

Finally, let's find a using the law of sines with the first and last ratios,

Solving for a,

Hence, the missing elements are A = 36.8°, B = 23.2° and a = 7.6.

Answer:

\(l = 88 cm\)

Step-by-step explanation:

Volume of Cube = \(l*l*l\)

Volume of Cube = \((Length)^3\)

Where volume = 681472 cubic cm

=> \(l^3 = 681472\)

Taking square root on both sides

=> \(l = \sqrt{681472}\)

=> \(l = 88 cm\)

The width of the confidence interval increases as the sample size increases and decreases as the confidence interval decreases. The confidence interval decreases as the sample size increases and increases as the confidence level increases.

Sample size is defined as the number of observations used to determine

an estimate of a particular population. The size of the model is drawn by people. Sampling is the process of selecting a group of individuals from a population to estimate the characteristics of the entire population. Select the number of establishments in a population group for analysis.

The sample size increases with the square of the standard deviation and decreases with the square of the difference between the mean under the alternative hypothesis and the mean under the null hypothesis.

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The probability that the sample mean would differ from the population mean by greater than 0.5 millimeters is 1

From the question, the given parameters about the distribution are

The standard deviation is the square root of variance

So, we have

Standard deviation = 6

The z-score is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (0.5 - 127)/6

Evaluate

z = -21.08

The probability is then calculated as:

P(x > 0.5) = P(z > -21.08)

From the z table of probabilities, we have;

P(x < 0.5) = 1

Hence, the probability is 1.0

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The Greek mathematicians started using the symbol pi (π) for as long as 4000 years in mathematical world.

A Short History of Pi

Even if we counted the number of seconds in those 4000 years and round the value of pi (π) to so many places, we would still only be estimating the true value of pi. Pi has been known for over 4000 years. Below is a quick summary of the discovery of.

By multiplying the radius of a circle by three, the ancient Babylonians determined its area, yielding the number pi = three. About 1900–1680 BC Babylonian tablets show a value of 3.125 for, which is a more accurate estimate.

The Rhind Papyrus, which dates to around 1650 BC, sheds light on ancient Egyptian mathematics. The calculation used by the Egyptians to determine a circle's area yielded a result that was around 3.1605 for.

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Answer:

383 which is 400 m^2 to the nearest hundredth

Step-by-step explanation:

\(\pi {r}^{2} \)

use the equation for area of sector and multiply by 3/4

Answer:

383.03 m²

Step-by-step explanation:

area of circle = πr²

We use 3.14159 for π (pi).

The radius, r, is 12.75 m.

area = 3.14159 × (12.75 m)²

area = 3.14159 × 162.5625 m²

area = 510.70472 m²

The area of the full circle is 510.70 m²

The shaded area is 3/4 of the circle.

shaded area = 3/4 × 510.70 m²

shaded area = 0.75 × 510.70 m²

shaded area = 383.03 m²

(a) We have shown that there exists an element b ∈ B that is an upper bound for A.

(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.

(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.

Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).

Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.

(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.

Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.

This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.

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Answer:

3) x = 21.33

4) x = 33

5) x = 11

Step-by-step explanation:

3: (3x + 17) + (x + 40) + (2x - 5) = 180

6x + 52 = 180

6x = 128

x = 21.333...

4: 180 / 3 = 60

3x - 39 = 60

3x = 99

x = 33

5: 90 + (6x + 7) + (2x - 5) = 180

8x + 2 = 90

8x = 88

x = 11

To find Pedro's exam score, we can use the formula for calculating the z-score:

z = (x - μ) / σ,

where z is the z-score, x is the exam score, μ is the mean, and σ is the standard deviation.

Given that Pedro's z-score was 3, we can rearrange the formula to solve for x:

3 = (x - 68) / 10.

Multiplying both sides of the equation by 10, we get:

30 = x - 68.

Adding 68 to both sides, we find:

x = 30 + 68 = 98.

Therefore, Pedro's exam score was 98.

The z-score measures how many standard deviations an individual's score is above or below the mean. In this case, Pedro's z-score of 3 indicates that his exam score was 3 standard deviations above the mean of 68.

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Answer:

B.) (-5, 6)

Step-by-step explanation:

to solve algebraically, test the coordinate pairs in the equation \(y = -\frac{2}{5}x + 4\)

to solve graphically, enter the equation \(y = -\frac{2}{5}x + 4\) into a graphing calculator and graph the coordinate pairs as well to see which one is on the line.

(2, 3) is NOT a solution.

steps for solving algebraically:

first, identify the x and y values in your coordinate pair.

plug in 2 for x in \(y = -\frac{2}{5}x + 4\) (it doesn't matter if you plug in x or y first, i personally always start with the x-value but it really doesn't matter what order you do it in.)

now plug in 3 for y.

your equation is now 3 = -2/5(2) + 4. begin simplifying by multiplying -2/5 and 2.

now add -0.8 + 4 to simplify the rest of the right side of the equation.

3 and 3.2 are not equal, therefore (2, 3) is not a solution.

(-5, 6) IS a solution.

steps for solving algebraically:

first, identify the x and y values in your coordinate pair.

plug in -5 for x in \(y = -\frac{2}{5}x + 4\) (it doesn't matter if you plug in x or y first, i personally always start with the x-value but it really doesn't matter what order you do it in.)

now plug in 6 for y.

your equation is now 6 = -2/5(-5) + 4. begin simplifying by multiplying -2/5 and -5.

now add 2 + 4 to simplify the rest of the right side of the equation.

6 and 6 are equal, therefore (-5, 6) is a solution.

although we have identified (-5, 6) as a solution, i'm still going to check the rest of the points just to be sure! :)

(6, 2) is NOT a solution.

steps for solving algebraically:

first, identify the x and y values in your coordinate pair.

plug in 6 for x in \(y = -\frac{2}{5}x + 4\) (it doesn't matter if you plug in x or y first, i personally always start with the x-value but it really doesn't matter what order you do it in.)

now plug in 2 for y.

your equation is now 2 = -2/5(6) + 4. begin simplifying by multiplying -2/5 and 6.

now add -2.4 + 4 to simplify the rest of the right side of the equation.

2 and 1.6 are not equal, therefore (6, 2) is not a solution.

(-2/5, 4) is NOT a solution.

i see that they want to trick you with this one by using the values that are in other spots in the equation... that's crafty

steps for solving algebraically:

first, identify the x and y values in your coordinate pair.

plug in -2/5 for x in \(y = -\frac{2}{5}x + 4\) (it doesn't matter if you plug in x or y first, i personally always start with the x-value but it really doesn't matter what order you do it in.)

now plug in 4 for y.

your equation is now 4 = -2/5(-2/5) + 4. begin simplifying by multiplying -2/5 and -2/5.

now add 0.16 + 4 to simplify the rest of the right side of the equation.

4 and 4.16 are not equal, therefore (-2/5, 4) is not a solution.

as for finding the solution on a graph, enter the equation for the line as well as the coordinate pairs into a graphing calculator. here i used a handy little site called desmos in order to graph all of this. the first photo i attached contains what i entered into the calculator, and the second photo i attached shows the graph. as you can see, the only point that is actually on the line is (-5, 6), which is why (-5, 6) is a solution to \(y = -\frac{2}{5}x + 4\) , and the other coordinate pairs are not solutions to that equation because they are not on the line.

i hope this helps! have a lovely rest of your day <3

Answer:

its D you don't even need to do all the work bc the same numbers are right there in the equation