The scatterplot of the data below models what type of correlation?

Answer:x=11.42

Step-by-step explanation:

[tex]\frac{35}{20} =\frac{20}{x}[/tex]

[tex]35x=400[/tex]

[tex]X=11.42[/tex]

Answer:

a) To find the probability that a randomly chosen student completes the activity in less than 30.1 seconds, we need to standardize the value using the formula z = (x - mu) / sigma, where x is the time taken, mu is the mean, sigma is the standard deviation, and z is the standard normal variable.

z = (30.1 - 34.7) / 7.6 = -0.6053

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than -0.6053 is 0.2739.

Therefore, the probability that a randomly chosen student completes the activity in less than 30.1 seconds is 0.2739.

b) To find the probability that a randomly chosen student completes the activity in more than 38.1 seconds, we need to standardize the value using the same formula.

z = (38.1 - 34.7) / 7.6 = 0.4474

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than 0.4474 is 0.3274.

Therefore, the probability that a randomly chosen student completes the activity in more than 38.1 seconds is 0.3274.

c) To find the proportion of students taking between 30.9 and 38.5 seconds, we need to standardize both values and then find the area between them in the standard normal distribution.

z1 = (30.9 - 34.7) / 7.6 = -0.5

z2 = (38.5 - 34.7) / 7.6 = 0.5

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being between -0.5 and 0.5 is 0.3830.

Therefore, the proportion of students taking between 30.9 and 38.5 seconds to complete the activity is 0.3830.

d) To find the time taken by 90% of all students to finish the activity, we need to find the z-value corresponding to the 90th percentile of the standard normal distribution using a standard normal distribution table or calculator.

The z-value corresponding to the 90th percentile is approximately 1.28.

Now, we can use the formula z = (x - mu) / sigma to find the corresponding time value.

1.28 = (x - 34.7) / 7.6

x - 34.7 = 1.28 * 7.6

x - 34.7 = 9.728

x = 44.428

Therefore, 90% of all students finish the activity in less than 44.428 seconds.

Rolling a number higher than 3 has a 2/6 or 1/3 chance of happening. Another way to say this is to round a decimal to the closest millionth, which is  [tex]0.333333[/tex]  .

A standard die has 6 sides, labelled with the numbers 1 through 6. When the die is rolled, each side has an equal probability of landing face up.

Since we want to find the probability of rolling a number greater than 3, we need to determine the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.

When you roll a standard die, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. Since we want to find the probability of rolling a number greater than 3, we need to count how many of these outcomes satisfy that condition.

Therefore, the probability of rolling a number greater than 3 is 2/6 or 1/3. Alternatively, we could express this as a decimal rounded to the nearest millionth, which would be  [tex]0.333333[/tex] .

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Answer: I think its C

Answer:

Step-by-step explanation:

C is false. [tex]\angle BEC = \angle AED=126[/tex]   (vertically opposite).

The rest are correct.

Answer:

liv

Step-by-step explanation:

If Yin makes the maximum salary contribution to her 401(k), she will have made a total of $7,950.

Divide the part by the entire and multiply the result by 100 to obtain the percentage. A number can be expressed as a fraction of 100 by using the percentage, in other words.

If, for instance, there were 50 students in the class and 35 of them passed the test, and you want to know what percentage of those students passed the test, you may determine it by using the formula below.

% = (Number of students who passed / Total number of students) x 100 % = (35 / 50) x 100 % = 0.7 x 100 %

Percentage = 0.7 x 100

Percentage = 70%

If Yin may contribute up to 15% of her annual earnings to her 401(k) and her beginning salary is $50,000, her maximum annual contribution would be:

Maximum donation is = 15% of $50,000.

Maximum donation is 0.15 times $50,000.

Maximum annual contribution =  $7,500

Given that Yin's company will match up to 6% of her contributions, the maximum amount they might contribute annually is:

6% of $50,000 is the employer's contribution.

Employer contribution equals 0.6 times $50,000.

Annual employer contribution equals $3,000.

Hence, Yin's company will pay an additional $3,000 year if she contributes the maximum of $7,500 to her 401(k). Yin will contribute a total of $10,500 per year to her 401(k) ($7,500 + $3,000). (k).

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The expression that completes the equation the result of 30/100 + 9/10 is 1.2.

The typical form for linear equations with two variables is Ax+By=C. For instance, the linear equation 2x+3y=5 is in standard form. When attempting to solve problems containing two linear equations, this form is also quite helpful.

We must multiply the values of 30 and 100, then add the resulting product to the resulting product of the values of 9 and 10 in order to complete the equation 30 100 + 9 10.

The result of multiplying 30 by 100 is:

30 x 100 = 3000

The result of adding 9 and 10 is:

9 x 10 = 90

Thus, we must combine these two items to finish the equation:

3000 + 90 = 3090

30100 + 910 = 3090, which is the expression that completes the equation.

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the complete question is:

complete the equation

[tex]\frac{30}{100}+\frac{9}{10}[/tex]

Answer:

The answer is 39/100

Step-by-step explanation: Nothing more.

Answer: no they wouldn't be similar

Step-by-step explanation: if x=60 if triangle 1 then the third angle would be (180-(58+60)) =180-118=62
if we decide to calculate the third angle in triangle 2 we will have 180-(50+58) = 180-108=72

therefore not all angles in 1 are similar to angles in 2 so the triangles aren't similar

Answer: D

Step-by-step explanation: so if we look at the picture, youll notice 2 things right off the bat, firstly, the top shape goes over the y axis, so that wont work, secondly, the shapes are on the same side of the x axis (the positive side) so that wouldnt work, the last thing we now have to look at is making the shapes even, essentially if you were to flip one shape over a certain distance, the mirrored shape needs to be the same distance you flipped the first shape. In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.

side note: reflecting over the x axis or y axis, means the line of reflection is equal to 0 on either the y axis or x axis

To try to make this less confusing, another way to find the reflection is by evenly counting the shapes to the middle, how-ever many squares/spaces it takes for both shapes to reach the center of the two in this case, is how many spaces they are reflected.

The image undergoes a reflection at y=-3, Option D is correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

Reflections are congruence transformations that generate a mirror image of an object, without changing its size or shape.

In the given figure the above image is original and it is flipped to form the image which is below the x axis.

In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.

Hence, the image undergoes a reflection over y axis which is at y=-3.

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A finite sequence is a sequence with a finite number of elements, that is, a sequence that has a definite beginning and end.

In mathematics, a sequence is a set of numbers, arranged in a particular order. Each number in the sequence is called a term or element of the sequence, and is identified by its position or index in the sequence. For example, the sequence of natural numbers 1, 2, 3, 4, 5, ... can be represented as {a_n}, where a_1 = 1, a_2 = 2, a_3 = 3, and so on.

A sequence can be either finite or infinite. A finite sequence has a fixed number of terms, while an infinite sequence continues indefinitely. A sequence can also be arithmetic, geometric, or neither.

An arithmetic sequence is a sequence in which each term is obtained by adding a constant value, called the common difference, to the previous term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3.

In mathematics, a sequence is an ordered list of elements, typically numbers or other mathematical objects, that are written in a particular order. A finite sequence is a sequence with a finite number of elements, that is, a sequence that has a definite beginning and end.

For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of five elements. The first element is 1, the second element is 2, and so on, until the last element, which is 5. The sequence {1, 1/2, 1/4, 1/8, 1/16} is another example of a finite sequence, this time of decreasing terms.

Finite sequences are used in many areas of mathematics, including algebra, calculus, and number theory. They are often studied in their own right, and their properties and patterns can be used to solve problems and prove theorems.

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Answer: x = -2, [tex]\frac{2 }{3}[/tex]

Step-by-step explanation:

     Given:

0 = –3x² – 4x + 4

    The quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

    Substitute known values:

* a = -3, b = -4, c = 4

[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(-3)(4)} }{2(-3)}[/tex]

    Simplify with multiplication:

[tex]\displaystyle x=\frac{4\pm\sqrt{16+48} }{-6}[/tex]

    Simplify:

[tex]\displaystyle x=\frac{4\pm\sqrt{64} }{-6}[/tex]

[tex]\displaystyle x=\frac{4+8 }{-6}[/tex],    [tex]\displaystyle x=\frac{4-8 }{-6}[/tex]

[tex]\displaystyle x=\frac{12 }{-6}[/tex],    [tex]\displaystyle x=\frac{-4 }{-6}[/tex]

c) Horizon A would be less deep since there would be less topsoil due to erosion.

the soil profile in a mountainous region would typically be different from the one shown in the illustration, because the soil formation process is affected by different factors such as climate, vegetation, topography, and parent material.

In a mountainous region, the soil profile is likely to be thinner and shallower than in flat areas, due to the steep slopes and higher erosion rates. The topsoil horizon (A) may also be thinner or absent in some areas due to erosion or limited plant growth, which can make it difficult for organic matter to accumulate. In addition, the subsoil horizon (B) may be more prominent and closer to the surface due to the leaching of minerals from the upper layers, which can result in a more rocky and mineral-rich soil.

Therefore, the correct answer would be:

c) Horizon A would be less deep since there would be less topsoil due to erosion.

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Answer:

7

Step-by-step explanation:

if you add 7 4's you get 28.

4+4=8+4=12+4=16+4=20+4=24+4=28

now if you count all the single 4's then you will get 7

The answer is (B) 45 feet

Step-by-step explanation:

We can use proportions to solve this problem.

Let x be the length of the shadow cast by the telephone pole. Then we have:

(42 / 31.5) = (60 / x)

We can cross-multiply to get:

42x = 31.5 * 60

Simplifying this equation, we get:

x = (31.5 * 60) / 42

x = 45 feet

Therefore, the length of the shadow that the telephone pole casts is 45 feet.

Answer:

4.

a-9=15

or. a=15+9

or. a=24

5.

n-9=13

or. n=13+9

or. n=22

6.

b-8=9

or. b=9+8

or. b=17

7

x-5=16

or. X=16+5

or X=21

8

n-6=17

or. n= 17+6

or. n=23

Step-by-step explanation:

minus sign changes into plus sign when changing sides

AB/BC = DE/EF

35/15 = DE/60

DE = 35*60 / 15

DE = 140

answer

A 140

The set of numbers 36 and 96 has a greatest common factor of 12.

The greatest common factor (GCF) of a set of numbers is the largest number that can evenly divide all the numbers in the set. To find the GCF, we can list all the factors of each number and find the largest one they have in common.

For set A, the factors of 3 are 1 and 3, and the factors of 4 are 1, 2, and 4. There is no common factor greater than 1.

For set B, the factors of 6 are 1, 2, 3, and 6, and the factors of 18 are 1, 2, 3, 6, 9, and 18. The largest factor they have in common is 6.

For set C, the factors of 32 are 1, 2, 4, 8, 16, and 32, and the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The largest factor they have in common is 16.

For set D, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36, and the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. The largest factor they have in common is 12.

Therefore, set D, consisting of the numbers 36 and 96, has a greatest common factor of 12.

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In response to the stated question, we may state that Apply a 1.5 scale expressions factor dilation with the Centre of dilatation at point A.

An expression in mathematics is a collection of numbers, variables, and mathematical (such as addition, reduction, multiplication, division, exponentiation, etc.) that express a quantity or value. Expressions might be as basic as "3 + 4" or as complicated as "(3x2 - 2) / (x + 1)". They may also contain functions like "sin(x)" or "log(y)". Expressions can also be evaluated by substituting values for the variables and performing the mathematical operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

We must use one or more transformations to construct the second polygon from the first. Below are three sets of procedures for making the second polygon from the first using one, two, or three transformations:

One modification:

Begin with a pre-image polygon.

Apply a 1.5 scale factor dilation with the centre of dilatation at point A.

There are two transformations:

Three transformations are possible:

Begin with a pre-image polygon.

Put a reflection over the line that connects points A and B.

Apply a 45-degree anticlockwise rotation with the centre of rotation at point A.

Apply a 1.5 scale factor dilation with the centre of dilatation at point A.

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Therefore, the value of x is 9.

A triangle is a closed two-dimensional geometric shape that is formed by connecting three non-collinear points with three-line segments. The three line segments that connect the three points are called sides of the triangle, and the points themselves are called vertices. The angle formed between any two adjacent sides of a triangle is called an interior angle of the triangle. The sum of the interior angles of a triangle is always 180 degrees.

There are many different types of triangles, including equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles. An equilateral triangle is a triangle in which all three sides are equal, an isosceles triangle is a triangle in which two of the sides are equal, and a scalene triangle is a triangle in which none of the sides are equal. An acute triangle is a triangle in which all three interior angles are less than 90 degrees, an obtuse triangle is a triangle in which one of the interior angles is greater than 90 degrees, and a right triangle is a triangle in which one of the interior angles is exactly 90 degrees.

Given by the question.

According to Thel's theorems

[tex]\frac{5}{3} =\frac{15}{x}[/tex]

5x=45

x=9

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After answering the presented question, we can conclude that The vector expression of equal magnitude and opposite direction to  [tex]\vec{PQ}[/tex] is the same arrow but pointing in the opposite direction: QP vector

An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression.

Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form.

They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To find the vector that starts at [tex]P[/tex]  [tex](3,3)[/tex] and ends at  [tex]Q(-2,2)[/tex] , we can subtract the coordinates of the starting point from the coordinates of the ending point:

[tex]$\vec{PQ} = \begin{pmatrix} -2 \ 2 \end{pmatrix} - \begin{pmatrix} 3 \ 3 \end{pmatrix} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$[/tex]

So the vector that starts at P(3,3) and ends at  [tex]Q(-2,2) is $\vec{PQ} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$.[/tex]

To find the vector of equal magnitude and opposite sense to  , we can simply multiply   [tex]$\vec{PQ}$[/tex] by  [tex]-1:[/tex]

[tex]$-\vec{PQ} = -1 \begin{pmatrix} -5 \ -1 \end{pmatrix} = \begin{pmatrix} 5 \ 1 \end{pmatrix}$[/tex]

So the vector of equal magnitude and opposite sense to [tex]$\vec{PQ}$[/tex]   is [tex]$\begin{pmatrix} 5 \ 1 \end{pmatrix}$.[/tex]

Geometrically, we can represent the vectors graphic[tex]$\vec{PQ}$[/tex]ally by drawing them as directed line segments on a coordinate plane. The vector that starts at [tex]P(3,3)[/tex] and ends at [tex]Q(-2,2)[/tex] is represented by the line segment connecting [tex]P[/tex] to  [tex]Q[/tex].

Therefore, The vector of equal magnitude and opposite sense to  [tex]$\vec{PQ}$[/tex][tex]$\vec{PQ}$[/tex] is represented by the line segment starting at  [tex]Q[/tex] and ending at the point R, which is  [tex]5[/tex] units to the right and [tex]1[/tex] unit up from  [tex]Q[/tex].

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Answer: A.   -2√7

Step-by-step explanation:

3√7 - 5√7

= -2√7

Answer:

Experimental Procedure:

Materials:

Piece of wood

Electronic balance

Bunsen burner

Heat-resistant mat

Stopwatch or timer

Safety goggles

Lab coat

Safety Precautions:

Wear safety goggles and a lab coat to protect your eyes and clothing from any sparks or flames.

Place the heat-resistant mat under the Bunsen burner to prevent any accidental fires.

Use the Bunsen burner only under adult supervision.

Be cautious when handling hot objects, and allow them to cool before touching.

Procedure:

Measure the initial mass of the piece of wood using an electronic balance, and record it in a table.

Light the Bunsen burner, and place the piece of wood over the flame using tongs. Ensure that the wood is fully engulfed in the flame.

Use a stopwatch or timer to time how long the wood burns for (in this case, 15 minutes).

After 15 minutes, turn off the Bunsen burner and remove the piece of wood from the flame using tongs.

Allow the wood to cool, and then measure its final mass using the electronic balance, and record it in the table.

Calculate the difference between the initial and final mass of the wood, and record it in the table.

Repeat steps 1-6 three times to obtain three sets of data.

Calculate the average mass of the burned wood and compare it to the initial mass of the unburned wood to determine if the student's prediction was correct.

Conclusion:

If the average mass of the burned wood is less than the initial mass of the unburned wood, the student's prediction was correct, and he can conclude that the wood underwent a chemical change when it was burned. If the average mass is greater than or equal to the initial mass, the prediction was incorrect, and the student may need to revise his hypothesis or experimental design.

Answer:

  C.  396

Step-by-step explanation:

You want the LCM of 4, 18, and 44.

You can find the least common multiple by considering the unique factors to their highest powers.

  4 = 2^2

  18 = 2·3^2

  44 = 2^2·11

The unique factors are 2, 3, 11, and their highest powers are 2, 2, and 1, respectively. The LCM is ...

  2² × 3² × 11 = 396

__

Check

  396 = 4·99 = 18·22 = 44·9 . . . . . 99, 22, and 9 have no common factors

For the system of equations 2y = 2x and y = x, there are infinite number of solutions.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The system of equations given by 2y = 2x and y = x can be solved by substituting y = x into the first equation -

2y = 2x

Substituting y = x, we get -

2x = 2x

Now, on simplifying, we get -

x = x

The equation x = x is true for all values of x.

Therefore, there are infinitely many solutions to this system of equations.

In geometric terms, the two equations represent two lines in the coordinate plane that intersect at every point on the line y = x.

Therefore, the number of solutions is infinite.

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Answer:

  1759 square meters

Step-by-step explanation:

You want the surface area of a cuboid with a half-cylinder top.

The lateral area of the figure is the product of the length of the mailbox (0.45 m) and the perimeter of the end. The perimeter of the end is the sum of the lengths of the straight sides and half the circumference of a circle with diameter 0.3 m.

  P = 0.3 + 2·0.4 + π/2(0.3) = 1.571 . . . . . meters

  LA = Ph = (1.571 m)(0.45 m) = 0.70695 m²

The end area is twice the area of the rectangular portion of the end, plus the area of a circle 0.3 m in diameter.

 EA = (0.3 m)(0.4 m) + 3.14(0.3/2 m)² = 0.31065 m²

The total area of 1 mailbox is ...

  LA +EA = 0.70695 m² +0.31065 m² = 1.0176 m²

Then the area of 1728 mailboxes is ...

  1728 × 1.0176 m² ≈ 1758.4 m² ≈ 1759 m²

About 1759 square meters of aluminum will be needed for the 1728 mailboxes.

__

Additional comment

This presumes there is no waste in cutting the semicircular shape from the supplied aluminum.

Answer: 2.45 m/s.  

acceleration due to gravity 9.8 m/s

Answer: top two goes together, middle left goes to bottom right, bottom left goes to middle right

Step-by-step explanation:

Substitute x for an easy number like 2 and solve.

x - 2/3 - 1/2x = 1/2x - 2/3

x - 1/2 - 3/4x = 1/4x- 1/2

1/3x - 3/4 - 2/3x = -1/3x - 3/4

Answer:

To calculate the payback period (PBP) for this project, we need to determine how long it will take for the initial cash outlay of $40,000 to be recovered from the after-tax cash flows.

Year 1 cash flow = $10,000

Year 2 cash flow = $12,000

Year 3 cash flow = $15,000

Year 4 cash flow = $10,000

Year 5 cash flow = $7,000

Total cash inflows for year 1 and year 2 = $10,000 + $12,000 = $22,000

Total cash inflows for year 3 = $15,000

Total cash inflows for year 4 = $10,000

Total cash inflows for year 5 = $7,000

Cumulative cash inflows for year 1 and year 2 = $22,000

Cumulative cash inflows for year 3 = $37,000

Cumulative cash inflows for year 4 = $47,000

Cumulative cash inflows for year 5 = $54,000

It can be seen that the cumulative cash inflows reach the initial cash outlay of $40,000 after year 2, and therefore the payback period for this project is 2 years. Since the payback period is less than the maximum PBP of 3.5 years set by management, this project can be considered acceptable.

So, Hodgman Honest should recommend that Basket Wonders should accept this project as it has a payback period of only 2 years, which is less than the maximum PBP of 3.5 years set by management.

Answer:

"Undefined slope"

Step-by-step explanation:

The line is vertical on the graph.

Every point on the line has the same x-coordinate.

If the line crosses the x-axis where x=-7, then the

x-coordinate of every point on the line is -7, and the

equation of the line is

                                     x = -7 .

Hence, the system with nonlinear equations may contain one of these kinds of answers, depending on the particular equations and their graph.

Unable to form a straight line is a non-linear equation. With a fluctuating slope value, it resembles a graphed curve.

In general, there can be zero, one, many, or an infinite number of solutions to a system of nonlinear equations. It depends on the particular equations and how those interact with one another.

The problem has zero solutions if there are no values of the parameters that satisfy both equations, which occurs when the equations are inconsistant.

A single solution exists for the system if the equations cross at that point.

The system has multiple solutions if the equations cross more than once.

The system has an infinite number of solutions if the equations all describe the same curve.

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