The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid.

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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The largest 3 digit number that is divisible by 9 and 7 is 945.

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.

If a number is divisible by 7 and 9 it shows that 7 and 9 are factors of the number. Since the number is a three digit number, the product of 7and 9 which is 63 will also be a factor.

the highest three digit multiple of 63 is 945.

This means that 945 can be divided by 7 and 9. i.e 945/7 = 135 and 945/9 = 105

Therefore the largest three digit number that can be divisible by both 9 and 7 is 945

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Answer: 20 + x = y.

Step-by-step explanation:

When you deposit, you are adding onto something. Because there is no real value for x, the expression would be 20 + x = y. Also, it would be = y because it says clearly the total amount would be equal to y. and also since why has no value in this context, it would still be y.

The 2x2x2 cube has 6 fully white faces.

A cube is a solid shape with six square faces. Each square face has the same side length and thus all the faces have the same size. A cube has 12 edges and 8 vertices. Each vertex refers to a corner where three edges of a cube meet.

from given conditions, a 2x2x2 cube is made of 8 small cubes of which 4 are blue and 4 are white. the surface of the cube is formed from 6 2x2 squares.

and have to arranged in such a a way that the surface has as many fully white faces (faces white no black color anywhere) as possible.

So, A 2x2x2 cube has a total of 6 faces, and since the goal is to have as many fully white faces as possible, there must be at least 1 fully white face on each of the 6 sides. hence, the 2x2x2 cube has 6 fully white faces.

Therefore, the 2x2x2 cube has 6 fully white faces.

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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 length of the side KL for the given similar triangles rounded to the nearest tenth is 10.6 units.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects.

When two triangles are comparable, their respective sides and angles are equally spaced out and congruent. This is the property of similar triangles.

Given that the triangle GHI is similar to triangle JKL.

According to the property of similar triangles:

[tex]\frac{GH}{HI} = \frac{JK}{KL} \\\\\frac{45}{34} = \frac{14}{y} \\\\y= \frac{(14)(34)}{45} \\\\y= 10.577[/tex]

Rounding the value to the nearest tenth 10.57 is 10.6.

Hence, the value of side KL is 10.6 units.

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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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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:

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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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 monster has 4 heads and 12 tails.

What is the ratio of the number?

A ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six .

We know that the ratio of the number of eyes to the number of heads is 5:1. If a monster has 20 eyes, we can set up the equation:

20 eyes = x heads

Where x is the number of heads.

We also know that the ratio of the number of heads to the number of tails is 2:6. We can set up the equation:

x heads = 2y tails

Where y is the number of tails.

We know the number of eyes is 20, therefore x = 20/5 = 4 heads

We also know the number of heads is 4, therefore y = 4*6/2 = 12 tails

Hence, the monster has 4 heads and 12 tails.

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On solving the provided question, we can say that the relationship between the domain and range of f(x) = [tex]y = 9x + 1 = 10 + (x-1)(9)[/tex]

Domain of a function is the set of possible values that it can accept. X-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. Set the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.

[tex]f(x) = y = 9x + 1 = 10 + (x-1)(9)\\f(1) = 9+1 = 10\\f(2) = 9(2)+1 = 19\\f(3) = 9(3)+1 = 28\\f(4) = 9(4)+1 = 37[/tex]

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Thursday and Friday show a negative balance, then the answer is option c: II and II.

Overdrafts are charged when your balance is negative because it means the bank made a loan (an unexpected one) to you.

An overdraft occurs when a bank account holder withdraws more money than they have in their account. Banks typically allow account holders to spend more money than they have in their accounts, but they charge a fee or interest for doing so.

Overdraft protection is a service offered by many banks that automatically covers a certain amount of overdrafts, usually up to a certain limit, by transferring funds from a savings account or a line of credit. Banks will also charge a fee for this service.

Initial balance: $274

Day                Debit ($)     Credit ($)          Balance($)

Monday          194.62        35.45              274.00 - 194.62 + 35.45 = 114.83

Tuesday             ---             11.20              114.83 - 0 + 11.2 = 126.03

Wednesday      145.86        24.75             126.03 - 145.86 + 24.75 = 4.92

Thursday           53.35          33.80             4.92 - 53.35 + 33.8 = - 14.63

Friday                31.60          45.77            -14.63 - 31.60 + 45.77 = -0.46

Saturday           12.90          61.63            -0.46 - 12.90 + 61.63 =48.27

Thursday and Friday show a negative balance, then the answer is option c: II and II.

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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!

Answer: A (yes) B (yes) C (yes)

Step-by-step explanation:

One half times by 28 is 14

seven times 8 is 56

15 plus 14 is 29

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: 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 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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Answer:

y = 0.5x + 4

Step-by-step explanation:

1. Move terms to one side of the equation

0.5y - 2= 0.25x +0

     +2               +2  

__________________

0.5y = 0.25x + 2

2. Divide the coefficient of y (0.5) to both sides of the equation

[tex]\frac{0.5y}{0.5} = \frac{0.25x}{0.5} + \frac{2}{0.5}[/tex]

3. Solve and simifpy

[tex]y = 0.5x +4[/tex]

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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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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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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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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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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Answer:

[tex]6 {x}^{2} + 10x[/tex]

Answer: A good equation would be 1.20/12 and then 0.80/12.

Step-by-step explanation: after getting the answers from both equations you can determine how much to spend on each tea to evenly spend your money on both

Answer:

B

Step-by-step explanation:

There are a total of 16 fingerboards. 4 of these are white. The probability that he will select a white fingerboard is 1/4. B represent 1/4.

The the probability of finding a white finger board is 0.25.

Probability is the measure of how likely are the chance for any event to happen.

Given is that David has a Collection of nine gray fingerboards 4 white fingerboards and 3 yellow fingerboards.

We can write the probability of finding a white finger board as -

P{white} = 4/16

P{white} = 1/4

P{white} = 0.25

Therefore, the the probability of finding a white finger board is 0.25.

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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.

The graph of the function h(x) = 7sin(x) is given by the image presented at the end of the answer.

The sine function is given as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

From this problem, the amplitude is given as follows:

A = 7.

Hence:

As there is no phase shift, the minimum and maximum values have the x-coordinate given as follows:

As the function has no phase shift, the period is given as follows:

2π.

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