if one base of a trapezoid is 34 inches long and the midsegment is 27 inches, how long is the other base?

Therefore , the solution of the given problem of function comes out to be  the one -to-one function is an inverse function.

Math is the science of numbers, their variations, math and nearby tissues, shapes, and their actual and potential places. The relation between a group of inputs, each of which has a related output, is referred to as a "function." A function is an association between inputs and outputs where each input results in a single, unique output. Each function is assigned a scope, or realm, and a city or municipality. Functions are typically denoted by the letter f. (x). Input does contain an x. Procedures fall into four main categories: on functions, each processes, a few more features, within operations, as well as on functions.

Here,

Given : May -to-one function

One -to-many function

One-to-one function and

Many-to-many.

Thus, To find which is a inverse function .

So , by observing the following properties of function the one -to-one function is an inverse function.

Therefore , the solution of the given problem of function comes out to be  the one -to-one function is an inverse function.

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The inequality that represents the numbers of large, and small, boxes that can be loaded in the trailer is 2x + y ≤ 60

A relationship between two expressions or values that are not equal to each other is called inequality.

Given that, One large box and two small boxes weigh a total of 100 pounds. One large box and four small boxes weigh a total of 150 pounds.

Let the weights of large and small boxes be x and y respectively.

x + 2y = 100

x = 100-2y...(i)

x + 4y = 150

x = 150-4y...(ii)

Solving eq(i) and eq(ii)

100 - 2y = 150 - 4y

2y = 50

y = 25

Put y = 25 in eq(i)

x = 100-50

x = 50

Therefore, weights of large and small boxes are 50 and 25 pounds respectively.

Now,

Since, weight limit of a trailer is 1500 pounds

Establishing the inequality,

50x + 25y ≤ 1500

or,

2x + y ≤ 60

Hence, the inequality that represents the numbers of large, and small, boxes that can be loaded in the trailer is 2x + y ≤ 60

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Answer:

8309.09

Step-by-step explanation:

Base = Total

So we know that 4570 is 55% of the total

55% = 55/100 = 0.55

It is the same as:

4570 = 0.55 * total

Total = 4570/0.55 = about 8309.09

Hope this helps :)

Let me know if this is correct or not

Have a great day!

Therefore , the solution of the given problem of triangle comes out to be height = 2 meters = 4 squares.

Triangles are polygons due to their 3 sides and three vertices. It is an essential geometric form. Triangle ABC is a triangle whose corners are at coordinates A, B, and C. The discovery of a single plane and triangle in geometric shapes occurs when four elements are not collinear. Due to its upper right corner and three corners, triangles are classified as polygons. The corners of a triangle are the three spots at which it intersects. You may get 180 degrees by multiplying the triple triangle angles.

Here,

Drawn using the Required Elevation's Construction Method

The scale is presented as 2 squares per meter.

The front elevation plane has a total of 16 squares, which is the quantity of cubes in the plane.

Front elevation: There are 4 squares in the front elevation's width.

Closest to the observer, there are 4 + 1 squares within the front portion.

The slant surface has 3 by 4 squares as the number of squares.

The front aspect of the supplied diagram is depicted in the drawing that is attached.

A side elevation;

Following the same format as before, we have the side elevation as follows;

The side elevation's lower side is 2 meters wide, or 4 squares.

The side elevation is 2 meters high, or 4 squares.

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Answer:

y=13(7)^x

Step-by-step explanation:

x = 0, y = 13, so we know that a = 13.

13b^2 = 637  ==> x=2 and y=637

b^2 = 49  ==> divide both sides by 13

b = 7  ==> take the square root on both sides

y = 13 * 7^x  ==> plug in 7 for b in y = 13b^x

Answer: y=13(7)^x

Giovanna's error is that she should have added the fractions instead of adding the whole numbers and the fraction. The correct calculation is 14 7/8 inches.

2 5/8 + 2 5/8 + 2 5/8 + 2 5/8 + 2 5/8 + 2 5/8 + 2 5/8

= (2 + 2 + 2 + 2 + 2 + 2 + 2) + (5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8)

= 14 + (5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8)

= 14 + (7/8)

= 14 7/8

Giovanna made an error when calculating the height of a stack of 7 books that are each 2 5/8 inches thick. The correct calculation was 14 7/8 inches, however, she calculated 14 + 5/8 inches. This is incorrect because it is necessary to add the fractions together in order to get the correct answer. To calculate the height of the stack of books, we need to add each book's thickness together. Since each book is 2 5/8 inches thick, we start by adding the whole numbers: 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14. Then, we add the fractions: 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 = 7/8. Adding these together gives us 14 + 7/8 = 14 7/8. Thus, the correct answer is 14 7/8 inches.

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The shaded region is made up of the area of a rectangle minus the areas of the semicircles. The semicircles have a diameter of 2 inches, so the radius of each semicircle is 1 inch.

The area of each semicircle can be found using the formula pir^2, where r is the radius. So the area of each semicircle is pi1^2 = pi square inches.

The area of the rectangle is found by multiplying the length by the width: 1 foot * 12 inches/feet = 12 square inches.

The shaded region is the area of the rectangle minus the area of the semicircles. So the area of the shaded region is 12 square inches - 2* pi square inches = 12 - 2* pi square inches.

It's important to note that the length of the shaded region is given in feet (1-foot) but the area of the semicircles and the rectangle is given in square inches.

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Mark completed the job by himself in time 5 hours, so they must have worked together for 25 hours.

They worked together for 25 hours.

Mark can do the job in time 20 hours and Phil can do the job in 30 hours.

If they both work together, it will take them less than 20 hours, but more than 30 hours.

We know that Mark finishes the job by himself in 5 hours.

Therefore, they must have worked together for 25 hours.

Mark and Phil worked together for 25 hours.

Mark and Phil worked together to overhaul an engine. It took them less than 20 hours and more than 30 hours. Mark completed the job by himself in 5 hours, so they must have worked together for 25 hours.

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If you have two options, A and B, exclusive means only one option is required (A or B) while inclusive means both options are available (A and B).

To calculate the answer to this question, we need to consider what the words “exclusive” and “inclusive” mean. Exclusive means that one option is required and the other is not, while inclusive means that both options are available. In the case of the question a, the answer is exclusive because you must take either chemistry or physics to graduate. In the case of question b, the answer is inclusive because you can have either a complimentary coffee or tea.

To illustrate the difference between exclusive and inclusive with a formula, we can use the following:

Exclusive: A + B = A

Inclusive: A + B = A + B

This formula demonstrates that if you have two options, A and B, exclusive means only one option is required (A or B) while inclusive means both options are available (A and B).

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Deana whose running rate is greater than Pavel's but less than Alberto ran 33 miles per week

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

The number of miles Pavel ran is,

= 672/21.

= 32 per week.

The number of miles Alberto ran is,

= 420/12.

= 35 miles per week.

Now, The rate per week must be an integer and it should be 33 or 34.

So, The number that divides 462 completely is 33.

Therefore, The number of miles Deana ran is 33 miles per week.

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The experimental probability that the next student Judith talks to will pick red is 1/2.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

Given that,

Yellow = 2

Red = 5

Blue = 3

Finding the experimental probability

Total number of trials = 2+5+3 = 10

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Probability = red/ Total number of trials = 5/10 = 1/2

Thus, the experimental probability that the next student Judith talks to will pick red is 1/2.

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Answer:

1/2

Step-by-step explanation:

A graph is called a regular graph if the degree of each vertex is equal.

N complete vertices make up an (N-1) regular graph.

Proof: Each vertex in a complete network with N vertices is connected to each of the (N-1) remaining vertices. Therefore, each vertex's degree is (N-1). The graph is hence (N-1) Regular.

If the degree of each vertex is equal, a graph is said to be a regular graph. If the degree of each vertex is K, a graph is said to be K regular.

A regular graph in graph theory is one in which every vertex has the same number of neighbors or the same degree of valency. The stronger requirement that each vertex's indegree and outdegree be equal must also be met by a regular directed graph.

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Answer:

-7.9n+9.8

Step-by-step explanation:

add em

Answer:

9.8 - 7.9n

Step-by-step explanation:

To simplify, we need to have the least amount of terms possible. To do this here, we need to group like terms. We will start by rearranging our equation to group our like terms, like this:

3.8 + 6 - 4.9n - 3n

Then, we will combine our liker terms, giving us:

9.8 - 7.9n

That is the most simplified we can get. So our simplified equation is

9.8 - 7.9n.

Hope this Helped!

Answer:

i) To find the maximum height of the projectile, we need to find the highest point that it reaches before falling back to the ground. In this case, the maximum height is the vertex of the parabola. To find the vertex, we can use the formula:

x=-b/2a

(12,845)

Substituting this value back into the original height equation, we find the maximum height:

h = -5(12)^2 + 120(12) + 125 = -300 + 1440 + 125 =845

So the maximum height of the projectile is 845 meters.

ii) To find when the projectile reaches its maximum height, we need to find the x-coordinate of the vertex of the parabola. As we found above, the x-coordinate of the vertex is 12 seconds. So the projectile reaches its maximum height at 12 seconds.

Answer:

(6, - 4 )

Step-by-step explanation:

[tex]\frac{x}{4}[/tex] - [tex]\frac{3}{8}[/tex] y = 3

multiply through by 8 ( the LCM of 4 and 8 ) to clear the fractions

2x - 3y = 24 → (1)

[tex]\frac{5}{3}[/tex] x - [tex]\frac{y}{2}[/tex] = 12

multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions

10x - 3y = 72 → (2)

multiplying (1) by - 1 and adding to (2) will eliminate y

- 2x + 3y = - 24 → (3)

add (2) and (3) term by term to eliminate y

8x + 0 = 48

8x = 48 ( divide both sides by 8 )

x = 6

substitute x = 6 into either of the 2 equations and solve for y

substituting into (1)

2(6) - 3y = 24

12 - 3y = 24 ( subtract 12 from both sides )

- 3y = 12 ( divide both sides by - 3 )

y = - 4

solution is (6, - 4 )

The component form of the unit vector obtained by rotating the vector counterclockwise about the origin is v = ⟨ |v|cos(θ), |v|sin(θ) ⟩.

the term vector in math is defined as a quantity which has both magnitude and direction and it defines the movement of the object from one point to another.

Here we have given the unit vector and we need to find the component form from it.

As we all know that the vector is a quantity that has magnitude and direction.

Here we also know that it can be written in component form where the components are the horizontal and vertical coordinates of the endpoint of the vector measured from the origin.

And the vector with magnitude of |v| and direction of θ which has an angle measured from the horizontal axis in the counter clockwise direction then it has the following components form that can be written as

=> v = ⟨ |v|cos(θ), |v|sin(θ) ⟩.

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Therefore, the answer to the above median problem is a) z-score = 1.50, b) age 34 has SD=1.5, and C. option B is correct.

The median value is the number that exactly lies in the middle of a dataset that has been arranged. The gap between the minimum and maximum 50% of the data is a maximum likelihood measure or average. Depending on whether you have an odd or possibly even amount of data points, different formulas are used to calculate the median and mode.

Here,

The average age is 36, it is stated.

2.5 standard deviations

a) The z-score is (34 - 28.3)/3.8 = 1.50.

b) Analysis

A 34-year-old is 1.50 standard deviations well above average in age.

c) The right answer is B.

Consequently, the provided issue of median's solution yields

Option B is right since age 34 has an SD of 1.5 and a C, and z-score is 1.50.

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Answer:

mt =84

mns = 78

Step-by-step explanation:

since mn=124 , ns=80 , ts=72

then mt= 360-(124+80+72)=84

if we draw a line from m to s

then angle msn=124÷2=62 (inscribed angle)

and angle smn=80÷2=40 ( // // )

then angle mns=180-(62+40)=78

Answer: 3.65, 3.7, 323

Step-by-step explanation:

The numbers from least to greatest are as follows:

3.65, 3.7, 323

Hope this helps

The solution set of the inequality " x/4 < (5x-2)/3 - (7x-3)/ 5 is C: (4, infinity).

x/4 < (5x-2)/3 - (7x-3)/ 5

taking the LCM of the right-hand side of the given inequality which is 15.

Now multiply 15 by both sides of the inequality

15 . x/4 < [ 15 . (5x-2)/3 ] - [ 15. (7x-3)/ 5 ]

15. x/4 <  [ 5 . (5x -2) ] - [ 3 . (7x -3) ]

15. x /4 < ( 25x - 10 )  -  ( 21x - 9 )

15. x/4 < 25x - 10  -  21x + 9

15. x/4 < 4x -  1

Now multiply boh sides with 4

4 (15 .  x/4) < 4. (4x - 1)

15 . x < 16x - 4

15x <  16x - 4

4 < - 15x  + 16x

4 < x

x  > 4

Hence, all real numbers x that are greater than 4 are the solution of the given inequality.

Therefore, the solution set of the given inequality is  (4, infinity).

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The average number of stamps collected per day was 24.

1st day: 8 stamps

2nd day: 8 + 8 = 16 stamps

3rd day: 16 + 16 = 32 stamps

4th day: 32 + 32 = 64 stamps

5th day: 64 + 64 = 128 stamps

Total number of stamps collected

= 8 + 16 + 32 + 64 + 128

= 248 stamps

Average number of stamps collected per day

= 248 / 5

= 24 stamps

Margaret started a stamp collection and collected 8 stamps on the first day. On the second day she collected 8 more stamps, for a total of 16. On the third day she collected 16 more stamps, for a total of 32. On the fourth day she collected 32 more stamps, for a total of 64. On the fifth day she collected 64 more stamps, for a total of 128. In total, she collected 248 stamps over the five days. The average number of stamps collected per day was 24.

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So Isabelle will have to multiply all the quantities in her recipe by a factor of 3.33 (or 333%) to increase the yield to 50 cups.

The percentage that Isabelle needs to multiply her original quantities by to increase the yield from 15 cups to 50 cups is known as the "scaling factor".

To find the scaling factor, you can divide the desired yield by the original yield and multiply by 100 to express it as a percentage:

Scaling factor = (50 cups / 15 cups) x 100% = 3.33 x 100% = 333%

So Isabelle will have to multiply all the quantities in her recipe by a factor of 3.33 (or 333%) to increase the yield to 50 cups.

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On solving the provided question, we can say that by unitary method we got that the 3, 3/4 yards of fabric that she bought did she actually use

[tex]3\frac{3}{4} - 9/10 = > 31/10[/tex]

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

she buys  = 3, 3/4 yards of fabric

she uses = 9/10 of this piece of fabric

the 3, 3/4 yards of fabric that she bought did she actually use

[tex]3\frac{3}{4} - 9/10\\15/4 - 9/10\\150 - 36/40\\124/40\\62/20\\31/10[/tex]

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Multiplying fractions can be a tricky task, but with the right steps, it can be easily accomplished.

To multiply two fractions together, first find the least common multiple (LCM) of the two fractions.

Once you have the LCM, divide it by each of the two fractions and multiply the resulting numbers together. This will give you the final answer to your multiplied fractions.

Let's look at an example. Suppose you wanted to multiply 3/4 and 5/8 together. First, you would need to find the LCM of 3/4 and 5/8. The LCM in this case would be 24.

Now divide 24 by 3/4 and 5/8 to get 32/24 and 30/24 respectively. Multiplying 32/24 and 30/24 together would give you 960/576 as the answer.

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Answer:

Step-by-step explanation:

To calculate the rate :

Interest = P x R x T

                    100

Here, P = 5000, T = 3, I = 1500

Therefore,

1500 = 5000 x R x 3

                  100

1500 = 150 R

1500 = R

 15

10 = R

Thus, the rate is 10%

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The probability that the sample contains two white balls and two red ones is 0.264. There are multiple draws without replacement.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

An urn contains 6 white balls and 15 red balls. A sample of four balls is selected at random from the urn. Find the probability that the sample contains two white balls and two red ones!

It means that there will be multiple draws without replacement.

The total balls are 6 + 15 = 21 balls.

The probability of drawing two white balls and two red ones is

= P(1st is white ∩ 2nd is white ∩ 3rd is red ∩ 4th is red)

= P(1st is white)*P(2nd is white)*P(3rd is red)*P(4th is red)

= (6/21)*(5/20)*(15/19)*(14/18)

= 0.044

There are 6 possible orders (WWRR, WRWR, WRRW, RWWR, RWRW, RRWW). So, the probability in any order would be

= 0.044 × 6

= 0.264

Hence, the probability of drawing two white balls and two red ones in any order is 0.264.

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Triangle proportionality theorem and the segment addition postulate, indicates that A_F : AT = A_F : 4×A_F, therefore;

A_F : AT = 1 : 4

The triangle proportionality theorem states that a segment drawn in a triangle, such that it is parallel to one side of the triangle and intersects the other two sides at two distinct points, then the proportion in which the segment divides the other two sides are the same.

The specified details of the triangle ΔABC are;

The location of the point D = AB, the location of the point B = AC

The point of intersection of the angle bisector of angle ∠A and DE = F

The point of intersection of the angle bisector of angle ∠A and BC = Point T

AD = 1, DB = 3, AE = 2, EC = 4

Drawing a line CU parallel to DE from point C to intersect AB at U, according to the triangle proportionality theorem, we get;

AE : EC = 2 : 4 = AD : DU = A_F : FV

AD : DU = 1 : 2

A_F : FV = 1 : 2

Therefore; FV = 2 × A_F

FV : VT = DU : BU = 2 : 1

FV = 2 × VT

2 × VT = 2 × A_F by substitution property, therefore;

FV = 2 × A_F

AT = A_F + FV + VT (segment addition postulate)

Therefore; AT = A_F + 2 × A_F + A_F = 4×A_F

A_F : AT = A_F : 4 × A_F = 1 : 4

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x² - 10 = 36

x² = 46

x = +- sqrt(46)

A. Huixian's mother has 1608  shares of company A. The share price of company B on day 12 is $1.16.

B. To calculate the number of shares of company A that Huixian's mother has, we can use the equation: Shares x Price = $7400. Since we know that the share price of company A on day 7 is $4.60, we can calculate the number of shares of company A by dividing $7400 by $4.60, which is 1608 shares.

To calculate the share price of company B on day 12, we can use the equation: Shares x Price = $5800. Since we know that the number of shares of company B on day 12 is 5000, we can calculate the share price of company B by dividing $5800 by 5000, which is $1.16.

Therefore, the number of shares of company A that Huixian's mother has is 2000 and the share price of company B on day 12 is $0.50.

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