Answer the screenshot

Answer: 1/11

Step-by-step explanation:

16 is close to 20

217 is close to 220

20/220=2/22=1/11

In mathematics, the symbol ∆ (delta) is often used to indicate a change or difference in a quantity.

When used in the context of Calculus, ∆x (delta x) is a notation that represents the change in the independent variable x, often used in the study of limits, derivatives and integrals. It is defined as the difference between two nearby values of x, for example x2 - x1.

Also, In physics and engineering, the notation ∆x is used to refer to the change in position or displacement of an object. It is defined as the final position minus the initial position of an object.

In general, ∆x is used to represent a small change or difference in a variable, usually used in the context of calculus and physics.

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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:

-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!

The algebraic expression that shows the amount Ms. Jackson wants to rent a van for a week is T=320+0.50m

In order to calculate the total amount that Ms. Jackson will need to pay for renting we need to multiply the number of miles that she will drive by the price per mile driven.

Once we have that product we can simply add the weekly fee (w) to it which will give us the total (T) amount that Ms. Jackson will have to pay for her trip. This can all be combined into the following formula.

T = w + 0.50m

As per the mentioned table, a van containing ret for a week is 320, which is equal to the W value, then substitute the value in the equation we get:

T=320+0.50m

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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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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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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 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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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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Answer is c. 2.5, 4, 5

Step-by-step explanation:

To find the dimensions of the new triangle,

we need to apply the scale factor of 0.5 to the original triangle's dimensions.

This means we need to multiply each dimension by 0.5.

Original Dimensions: 5, 8, 10

New Dimensions:

5 x 0.5 = 2.5,

8 x 0.5 = 4

10 x 0.5 = 5

Therefore, the dimensions of the new triangle are 2.5, 4, 5.

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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

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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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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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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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.

8 percentage of the buttons were large. The solution has been obtained using arithmetic operations.

What are arithmetic operations?

There are four fundamental operations that all real numbers in mathematics must comprehend:

1. Adding the numbers together to get their total (with a "+").

2. Using the "-" sign to subtract two numbers yields the difference between the values.

3. Multiplication('×') is used to create the numbers' product.

4. The division('÷') procedure, which determines the numbers' quotient.

We are given that Victoria bought a bag of mixed buttons and she got 12 large buttons and 138 small buttons.

So, the total number of buttons = 138 + 12 = 150

Out of 150, she got 12 large buttons.

So, percentage of large buttons = 12*100/150 = 8%

Hence, 8 percentage of the buttons were large.

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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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Answer:

There are 6 workers in the team.

Step-by-step explanation:

Let's call the number of workers "n".

We know that the team of workers could have completed the job in 24 hours if they had worked together. We also know that the resulting work time would have been reduced by 6 hours if all but 5 workers had worked together from the start.

So, if n workers worked together from the start, the work time would be 24 - 6 = 18 hours.

We also know that the workers joined one by one, starting with 1 worker and ending with n workers working together.

The total work time can be calculated using the arithmetic series formula:

work time = n/2 * (1 + n)

So, if we set the work time to 18 hours:

18 = n/2 * (1 + n)

We can solve this equation for n:

18 = n/2 * (n+1)

36 = n^2 + n

n^2 + n - 36 = 0

We can solve this quadratic equation by factoring it.

(n-6)(n+6) = 0

So the solutions are n = 6 and n = -6.

But the number of workers can not be negative, so the answer is n=6.

A randomly selected subject has a 0.40 probability of completing more tasks than expected in 5 minutes while listening to relaxing music.

The Probability distribution is:

    X                     1                    2                3              4          

   P(x)             0.20          0.40      0.30             0.10

If listening to soothing music, the expected number of puzzles in 5 minutes can be calculated as follows:

            E(x) = ∑x p(x)

       ⇒ E(x) = 1 ×(0.20) + 2× 0.40 + 3 × 0.30 + 4× 0.1

       ⇒ E(x) = 0.20 + 0.8 + 0.9 + 0.4

       ⇒ E(x) = 2.3

Thus, a randomly selected subject could solve 5 puzzles while listening to soothing music. The probability of solving more tasks than expected in a minute is calculated as:

    P( X > 2.3) = P(X = 3) + P(X = 4)

                      = 0.30 + 0.10

                      = 0.40

Explanation for other  option:

(a) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music does not equal 0.1.

(c) 5 randomly selected participants. The probability of completing more tasks than expected in a minute of listening to relaxation music does not equal 0.8.

(d) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music is not equal to 1.

(e) The likelihood of randomly selected participants completing more tasks than expected in 5 minutes while listening to relaxing music cannot be determined.

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About 96.17% of the students who took the test earned a 70 points or higher

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The z score of a normal distribution is given by:

z = (raw score - mean)/standard deviation

The average test score from the last year's class was 85 points with a standard deviation of 9. Hence:

Mean = 85, standard deviation = 9

For a score of 70 points or higher:

z = (70 - 85) / 9 = -1.67

P(z > -1.67) = 1 - P(z < -1.67) = 1 - 0.0383 = 0.9617 = 96.17%

96.17% of the students earned a 70 points or higher

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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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x² - 10 = 36

x² = 46

x = +- sqrt(46)

If to the nearest whole number, then 2. If to the nearest tenth, then 1.5.

0.579 + .94 is 1.519.

When rounding to the nearest whole number, if the first number after the decimal point is 5 or higher, round up. If 4 or lower, then round down.

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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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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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

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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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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