Let f be a one-to-one function. If f(2)=7 and
f-1(-3)=5, determine the following ;
(a). f-1(7)
(b) f(5)

We calculate the arc length to be 6.86 inches by rounding to the closest hundredth.

The distance between two places in a curve's section is known as the arc length of a circle. Any portion of a circle's circumference is an arc. The angle formed by the two line segments joining a point to an arc's endpoints at any given position is known as the arc's angle.

An arc with a radius of 18 inches and a centre angle of 22° can be calculated using the formula below:

Arc length = (central angle / 360°) × (2πr)

where r denotes the circle's radius.

Substituting the given values, we get:

Arc length = (22° / 360°) × (2π × 18 inches)

Arc length = (0.0611) × (2π × 18 inches)

Arc length ≈ 6.86 inches

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After answering the presented question, we can conclude that As a equation result, the value of x is 34.

An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

We can see from the diagram that PQ is parallel to BC and that the line segments PQ and BC overlap at point O.

As a result, we have:

angle QPO stands for angle. 70° angle = ABC QOP stands for angle. ACB = 110°

angle AOB = angle - 180 ACB - ABC angle = 180 - 70 - 110 = 0

This indicates that points A, O, and B are collinear and that angle AOB is a straight angle, implying that angles AOP and POB are supplementary angles.

We may use this data to calculate the value of x:

AOP angle + POB angle = 180

(3x - 10) + (2x + 20) = 180

5x + 10 = 180

5x = 170

x = 34

As a result, the value of x is 34.

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A bisector in math is a line or a line segment that divides an angle or a line segment into two equal parts.

The bisector, also known as the perpendicular bisector, is a geometric concept in mathematics that is used to construct a line that is perpendicular to a given segment and passes through its midpoint. The bisector is an important tool in geometry and is used in a variety of applications, including constructing triangles, circles, and finding the circumcenter.

To construct the bisector of a segment, one must first locate the midpoint of the segment. This is done by dividing the length of the segment in half, using a straightedge to connect the two endpoints, and then drawing a perpendicular line through the midpoint. The resulting line is the bisector of the segment.

The bisector has several important properties. First, it is always perpendicular to the segment it bisects. This means that the angle between the bisector and the segment is always 90 degrees. Second, the bisector always passes through the midpoint of the segment. Finally, any point on the bisector is equidistant from the two endpoints of the segment. This means that the bisector can be used to construct other geometric objects that are equidistant from the endpoints of the segment, such as circles.

In summary, the bisector is a line that is perpendicular to a given segment and passes through its midpoint. It is an important tool in geometry and is used in a variety of applications, including constructing triangles, circles, and finding the circumcenter.

Note: This question is in Spanish. Here is the translation to English.

Bisector: the line by which a segment is divided into two parts perpendicularly.

Please explain this.

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The measure of the angle formed by the intersection of the River Line and the Northeast Line is equal to: C. 42°.

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of the given angles are supplementary angles:

60° + (8x - 18)° + (3x + 6)° = 180°

60° + 8x - 18° + 3x + 6° = 180°

11x = 180° - (18° - 6° - 60°)

11x = 180° - 48°

11x = 132°

x = 132/11

x = 12

For the intersection of the River Line and the Northeast Line, we have:

R = (3x + 6)°

R = 3(12) + 6

R = 36 + 6

R = 42°.

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Complete Question:

What is the measure of the angle formed by the intersection of the River Line and the Northeast Line?

40

41

42

43

This point does not always have a positive y-coordinate, it is still a useful point in creating a trend line.

A. It is easy to compute the slope using this point.

B. The​ y-coordinate of this point is the​ y-intercept.

A data point with an x-coordinate of 0 is a good point to use when creating a trend line for a data set because it is easy to compute the slope using this point. The y-coordinate of this point is also the y-intercept, which is the point at which the line crosses the y-axis. Additionally, the coordinates of this point are both 0, making it easy to locate on a graph. While this point does not always have a positive y-coordinate, it is still a useful point in creating a trend line.

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We can predict that in 120 tries, we would expect to get heads and an odd number around 30 times. However, it is important to note that this is just a prediction and the actual number of times this occurs may vary due to chance.

When flipping a dime, there are two possible outcomes: heads or tails. Similarly, when rolling a die, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. An odd number is any number that is not divisible by 2, so the odd numbers on a die are 1, 3, and 5.

The probability of flipping heads on a dime is 1/2, and the probability of rolling an odd number on a die is 3/6 or 1/2. To predict how many times you would flip heads and roll an odd number in 120 tries, we can use the multiplication rule of probability.

The multiplication rule of probability states that the probability of two independent events occurring together is the product of their individual probabilities. Since flipping a dime and rolling a die are independent events, we can multiply the probability of flipping heads and the probability of rolling an odd number to get the probability of both events occurring together.

So, the probability of flipping heads and rolling an odd number is:

P(heads and odd) = P(heads) x P(odd)

P(heads and odd) = (1/2) x (1/2)

P(heads and odd) = 1/4

We can estimate that in 120 trials, we should get heads about 30 times and an odd amount about the same. It is crucial to keep in mind that this is only a prediction and that there is a possibility that the actual frequency of occurrence will differ.

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Answer:

[tex]\huge\boxed{\sf 10(9n + 8m)}[/tex]

Step-by-step explanation:

= 90n + 80 m

Common factor = 10

So, the expression becomes:

[tex]\rule[225]{225}{2}[/tex]

Answer: C

Step-by-step explanation: If you factor 10 out of 90n and 80m then you get 9n and 8m for each. to make the equation you get: 10(9n+8n)

Answer:

1, 2, 3, 6

Step-by-step explanation:

The area of the equilateral triangle with side length 2cm is approximately 1.73 cm².

An equilateral triangle with side length 2cm can be divided into two right triangles with hypotenuse equal to 2cm and the other two sides of length 1cm each.

We can then use the Pythagorean theorem to find the length of the height of the equilateral triangle, which is also the height of the right triangles.

Let h be the height of the equilateral triangle, then:

h² = 2² - 1²

h² = 3

h = √3

The area of the equilateral triangle can be found using the formula:

Area = (base × height) / 2

Since the equilateral triangle has three equal sides, the base is also equal to 2cm. Therefore, we have:

Area = ( 2 × √3 ) / 2

Area = √3

Rounding to the nearest hundredth, we get:

Area = 1.73 cm²

Therefore, the area of the equilateral triangle is  1.73 cm².

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The expected number of applicants who need to be interviewed in order to find the first one with advanced training is 8.

We can calculate this by using the formula for the geometric series. The formula for the geometric series is given by S = a1(1-rn)/1-r, where a1 is the first term in the series, r is the common ratio, and n is the number of terms. In this problem, a1 = 1 (since the probability of finding the first applicant with advanced training is 1/8), and r = 1/8 (since the probability of finding the next applicant with advanced training is 1/8). Thus, plugging these values into the formula yields S = 1(1-(1/8)^n)/1-(1/8) = 8. Therefore, the expected number of applicants who need to be interviewed in order to find the first one with advanced training is 8.

S = a1(1-rn)/1-r

S =[tex]1(1-(1/8)^n)/1-(1/8)[/tex]

S = 8

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As per the given equation, the beanbag will reach the ground after 1.5 seconds.

To find the time it takes for the beanbag to reach the ground, we need to set h equal to zero, since the beanbag will be on the ground when its height is zero. So we have the equation:

0 = −(2t − 3) − 8t(2t − 3)

We can simplify this equation by factoring out the common factor of (2t − 3):

0 = (2t − 3)(−1 − 8t)

Now we can use the Zero Product Property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero. So we can set each factor equal to zero and solve for t:

2t − 3 = 0 or −1 − 8t = 0

Solving the first equation for t, we get:

2t = 3

t = 3/2

Solving the second equation for t, we get:

−1 − 8t = 0

8t = −1

t = −1/8

However, we need to discard the negative value of t, because time cannot be negative. So the time it takes for the beanbag to reach the ground is t = 3/2 seconds or 1.5 seconds

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Answer:

D

Step-by-step explanation:

To calculate the percentage decrease in price, we need to find the difference between the original price and the reduced price, divide that difference by the original price, and then multiply by 100 to express it as a percentage.

The original price of the iPhone was $320, and it was reduced to $224. Therefore, the difference between the two prices is:

$320 - $224 = $96

To find the percentage decrease, we divide this difference by the original price:

$96 ÷ $320 = 0.3

Finally, we multiply this result by 100 to express it as a percentage:

0.3 × 100 = 30%

Therefore, the answer is D. The price of the iPhone was reduced by 30%.

Answer:

Step-by-step explanation:

2534 i think

The total surface area of the solid cone, given the slant height and the radius, would be 374 m².

To find the surface area of a solid cone, we need to consider both the curved lateral surface and the circular base.

Lateral Surface Area = π x 7 m x 10 m = 70π m²

The base of a cone is a circle with radius r. The area of the base can be calculated using the formula:

Base Area = π x (7 m)² = 49π m²

Total Surface Area = Lateral Surface Area + Base Area = 70π m² + 49π m² = 374 m².

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Answer: not sure

Step-by-step explanation: it would help me if you had a pic of the worksheet to help you with the problem

Assuming that ∠1 and its adjacent angle form a straight line, we know that the sum of the angles on a straight line is 180°. Therefore, the measure of the adjacent angle is 180° - 39° = 141°.

we can also look at the other angles in the figure. From the diagram, we can see that ∠2 and ∠3 are acute angles, which means they are less than 90°. Additionally, we know that the sum of the angles in a triangle is 180°, so ∠2 + ∠3 + ∠4 = 180°.

Since ∠2 and ∠3 are acute, their sum must be less than 180°. Therefore, ∠4 must be an obtuse angle (greater than 90°) in order for the sum to be 180°. This makes sense, as an obtuse angle is required to form a triangle with two acute angles.

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Therefore , the solution of the given problem of unitary method comes out to be the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).

By applying what was acquired and bringing this variable tactic into practise, along with all supporting information from two people who used a particular tactic, the work can be finished. In other words, if the wanted expression result occurs, either the entity specified in the formula will also be discovered, or both crucial processes will actually ignore the colour. A refundable fee of Rupees ($1.01) may be necessary for forty pencils.

Here,

The water bottle is currently 3/5 full and contains 24 1/4 ounces of water.

By dividing the bottle's capacity by the percentage that indicates how filled it is, we can determine how much water is inside:

=> 24 1/4 × 3/5 = (97/4) × (3/5)

=> 291/20 = 14 11/20

Therefore, there are 14 11/20 ounces of water in the water container.

We want to fill three cups, each of which needs five ounces of water, so we will need:

=>  5 x 3 = 15 ounces

There isn't enough water in the bottle to fill three glasses with 5 ounces each because the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).

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If Leopold takes one part away from each of the fractions, they will not be equal anymore.

Two or more fractions are said to be equal or equivalent if we simplify them and obtain the same result for both. Let's analyze the fractions given:

5/5 = 1

3/3 = 1

Even when some fractions are equivalent if you modify them this will change the equivalence property, let's prove it with the fractions given:

4/5 = 0.8

2/3 = 0.66

Note: This question is incomplete; here is the missing section:

Leopold takes one part away from each. Will the fraction still be equal?

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Using hypothesis testing, the critical value of z for a 5 percent level of significance, left-tailed test is -1.645.

(a) For a 10 percent level of significance, two-tailed test, the critical value of z is:

z_critical = ± invNorm(1 - (0.10/2))

where invNorm is the inverse normal cumulative distribution function. Evaluating this expression gives:

z_critical = ± 1.645

Therefore, the critical value of z for a 10 percent level of significance, two-tailed test is ±1.645.

(b) For a 1 percent level of significance, right-tailed test, the critical value of z is:

z_critical = invNorm(1 - 0.01)

Evaluating this expression gives:

z_critical = 2.326

Therefore, the critical value of z for a 1 percent level of significance, the right-tailed test is 2.326.

(c) For a 5 percent level of significance, left-tailed test, the critical value of z is:

z_critical = invNorm(0.05)

Evaluating this expression gives:

z_critical = -1.645

Therefore, the critical value of z for a 5 percent level of significance, left-tailed test is -1.645.

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The total distance that Mishka covers on the trip is 265 miles.

Speed measures how fast an object is moving with respect to time. Speed is the ratio of total distance to total time.

Speed = distance / time

Distance = speed x time

Distance covered while driving on the highway = 75 x 3 = 225 miles

Distance covered while driving on the side road = 40 x 1 = 40 miles

Total distance covered = 225 miles + 40 miles = 265 miles

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Combination of red and yellow paint that follows the ratio of 3 parts yellow for every 2 parts red will make the shade of orange Lin needs.

Red  Yellow  

2   3

4   6

6   9

8   12

The formula for this specific shade of orange paint is 3 parts yellow for every 2 parts red. To calculate the amounts of red and yellow paint that can be used for different combinations we can use the following equation:

Yellow = 2 x Red/3

For the first combination of 2 parts red and 3 parts yellow, the equation can be written as:

Yellow = (2 x 2)/3

Simplified, that is 2/3, or 3 parts yellow.

For the second combination of 4 parts red and 6 parts yellow, the equation can be written as:

Yellow = (2 x 4)/3

Simplified, that is 4/3, or 6 parts yellow.

For the third combination of 6 parts red and 9 parts yellow, the equation can be written as:

Yellow = (2 x 6)/3

Simplified, that is 8/3, or 9 parts yellow.

For the fourth combination of 8 parts red and 12 parts yellow, the equation can be written as:

Yellow = (2 x 8)/3

Simplified, that is 16/3, or 12 parts yellow.

Therefore, any combination of red and yellow paint that follows the ratio of 3 parts yellow for every 2 parts red will make the shade of orange Lin needs.

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The rockets are at a height of 83.15 meters after 1.36 seconds. Rounded to the nearest hundred, this is 83 meters.

To find the moment when the rockets are at the same height, set f(x) = g(x) and solve for x:

-4.9x2 +50x = -4.9x2 +25x + 34

50x = 25x + 34

25x = 34

x = 1.36

Therefore, the rockets are at the same height after 1.36 seconds. To calculate the height, plug x = 1.36 into either function:

f(1.36) = -4.9(1.36)2 +50(1.36)

f(1.36) = -4.9(1.85) + 68

f(1.36) = 83.15 meters

Therefore, the rockets are at a height of 83.15 meters after 1.36 seconds. Rounded to the nearest hundred, this is 83 meters.

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The simplest form of the given radical expression as required to be determined is; -3³√2a.

As evident form the task content; the given expression whose simplified form is to be determined is;

3 ³√2a - 6 ³√2a

Since; 3³√2a is common to both terms of the expression; Hence, by factorisation; we have;

3³√2a (1 - 2)

= 3³√2a • -1

= -3³√2a

Ultimately, the simplified form of the radical expression is; -3³√2a.

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Check the picture below.

The resistance of the coil is given by R = N x ρL = 70 x ρ x 0.0897 = 617.9 x ρ ohms.

The length of the wire is equal to the circumference of the circular coil. The circumference C of a circle of radius r is C = 2πr, so for the circular coil of radius 1m, the length of the wire is 2π x 1m = 6.28m.

The number of loops around the coil (N) is 70. Therefore, the length of one loop is L = 6.28/70 = 0.0897 m.

The resistance of the coil (R) is equal to the resistance of the single loop multiplied by the number of loops (N). Therefore, R = N x R', where R' is the resistance of a single loop.

The resistance of a single loop is equal to the resistance of the wire per unit length multiplied by its length. Therefore, R' = ρL, where ρ is the resistivity of the wire and L is the length of one loop of the wire.

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Complete question:

What is the resistance of a circular coil of radius 1m that consists of 70 loops of wire?

Janella recognizes a gain of $36,000 and her basis in the distributed property is $54,000.

Janella's basis in her partnership interest is $120,000, which includes her share of partnership debt. When the partnership pays off its debts and liquidates, Janella receives a proportionate liquidating distribution consisting of $42,000 cash and inventory valued at $24,000 (adjusted basis to the partnership = $20,000).

To calculate Janella's recognized gain or loss, we need to compare her basis in the partnership interest to the fair market value of the distributed assets.

The fair market value of the distributed assets is $42,000 (cash) + $24,000 (inventory) = $66,000.

The amount of the loss is the excess of her basis over the fair market value of the distributed assets, which is $120,000 - $66,000 = $54,000.

To determine Janella's basis in the distributed property, we need to adjust her basis in the partnership interest by the amount of the liquidating distribution she received.

Janella received a total liquidating distribution of $42,000 cash + $24,000 inventory = $66,000. Her share of partnership debt was $150,000, and the partnership paid off all its debts, so she no longer has any debt basis.

Janella's distribution of $66,000 exceeds her adjusted basis of $30,000 by $36,000. She recognizes a gain of $36,000. Therefore, Janella's new basis in the distributed property is $120,000 - $66,000 (liquidating distribution) = $54,000.

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The experimental probability of not selecting a peppermint candy is 77.78%, so the correct option is the third one.

We want to find the experimental probability of selecting a candy that is not peppermint.

To get this, we need to get the difference between 1 and the probability of getting a peppermint candy, then we will get:

p = 1 - 2/9

p = 7/9

Now we want to express this as a percentage, so we need to multiply this by 100%

p = (7/9)*100%

p = 77.78%

We can see that the experimental probability is the one in the third option.

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The lifetime cost of the model is $765.

Kate is re-modelling her kitchen.

She is going shopping for a refrigerator.

The model price is $405, and the estimated energy cost per year is $36.

If the model has an estimated lifetime of 10 years,

Lifetime cost of the model:

The lifetime cost of the model is $765

Explanation: Given, The model price is $405

Estimated energy cost per year is $36.

The model has an estimated lifetime of 10 years.

Lifetime cost of the model can be calculated as follows:

Total lifetime cost = Initial cost + (Estimated energy cost per year × Estimated lifetime)

Initial cost = $405

Estimated energy cost per year = $36

Estimated lifetime = 10 years

Total lifetime cost = $405 + ($36 × 10)

Total lifetime cost = $405 + $360

Total lifetime cost = $765

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Answer:

1.)

[tex]R = 8/17\\S = 15/17[/tex]

2.)

[tex]R = 5/13[/tex]

[tex]S=12/13[/tex]

Step-by-step explanation: sin represents the ratio between a side opposite to an angle and the hypotenuse. It is important to learn these ratios as they allow for you to solve for side lengths in a triangle and angles. We were in this case finding the ratios. A lowercase letter represents a side length opposite to the angle. So to find R we would just need to divide r by t. In the first example, it would just be 16/34 which simplifies to 8/17. Do the same thing for s, and it would be for 30/34 which simplifies to 15/17. Repeat the same steps and you should get 5/13 for R and 12/13 for S.

5/6

The probability of rolling a sum greater than 12 or a sum that is an odd number after rolling two balanced and fair dice is 47/96.What is the probability of rolling a sum greater than 12 or a sum that is an odd number?The given information says that there are two balanced and fair dice. One is a six-sided die, and the other is an eight-sided die. We need to find the probability of rolling a sum greater than 12 or a sum that is an odd number after rolling the two dice.It's necessary to know the possible outcomes of the dice game when two dice are rolled. The 6-sided die has possible outcomes {1,2,3,4,5,6}, and the 8-sided die has possible outcomes {1,2,3,4,5,6,7,8}.The possible outcomes for each sum from 2 to 14 are shown below in the following table:The sum of the faces is odd if only one of the dice has an even number. In contrast, the sum of the faces is even if both dice have an even number. The red color represents the sum of the faces, which is an odd number, while the blue color represents the sum of the faces, which is an even number. Now we can easily calculate the total number of sums that are either greater than 12 or an odd number. It is important to note that the sum of 2 and 4 is even, and the sum of 13 and 14 is greater than 12. So the total number of sums that are either greater than 12 or an odd number is: 1 + 4 + 1 + 6 + 8 + 8 + 6 + 1 + 4 + 1 = 40It's also necessary to calculate the total number of possible outcomes when rolling two dice. The number of possible outcomes when rolling two dice is 6 x 8 = 48.We now have everything we need to find the probability of rolling a sum greater than 12 or a sum that is an odd number:Probability = Number of favorable outcomes / Total number of possible outcomes= 40/48 = 5/6Therefore, the probability of rolling a sum greater than 12 or a sum that is an odd number is 5/6.

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