What association would you expect if graphing number of hours worked and money earned? Negative Linear Nonlinear none of these​

Answer:

Step-by-step explanation:

To calculate the number of students Ms. Sheldon has this year, we need to first find 150% of the number of students she had last year.

150% of 30 students can be found by multiplying 30 by 1.5 (since 150% is the same as 1.5 times the original amount):

30 x 1.5 = 45

Therefore, Ms. Sheldon has 45 students in her class this year.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{300}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{600}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{600}-\underset{x_1}{300}}} \implies \cfrac{ 4 }{ 300 } \implies \cfrac{ 1 }{ 75 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ \cfrac{ 1 }{ 75 }}(x-\stackrel{x_1}{300}) \\\\\\ y-4 = \cfrac{ 1 }{ 75 }x-4\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 75 }x \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{180}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{450}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{450}-\underset{x_1}{180}}} \implies \cfrac{ 3 }{ 270 } \implies \cfrac{ 1 }{ 90 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{ 1 }{ 90 }}(x-\stackrel{x_1}{180}) \\\\\\ y-2=\cfrac{ 1 }{ 90 }x-2\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 90 }x \end{array}}[/tex]

Answer:

Step-by-step explanation:

To solve the equation |x-14|=14, we consider two cases:

Case 1: (x-14) is positive or zero, i.e., x-14 ≥ 0, which implies x ≥ 14. In this case, we have:

|x-14| = x-14 = 14

Solving for x, we get:

x = 14 + 14 = 28

Therefore, x = 28 is a solution in this case.

Case 2: (x-14) is negative, i.e., x-14 < 0, which implies x < 14. In this case, we have:

|x-14| = -(x-14) = 14

Solving for x, we get:

-x + 14 = 14

-x = 0

x = 0

Therefore, x = 0 is a solution in this case.

Hence, the solutions to the equation |x-14|=14 are x = 0 and x = 28. We can show these solutions on a number line as follows:

<--------[0]--------(14)--------[28]-------->

Answer:

[tex]\log_4(5x+4) = 9[/tex]

Step-by-step explanation:

When we take the log of both sides of the equation:

[tex]4^9 = (5x+4)[/tex]

we get:

[tex]\log_4(4^9) = \log_4(5x+4)[/tex]

[tex]\boxed{9 = \log_4(5x+4)}[/tex]

We can recognize this as option D.

_____

Note:

The logarithmic function outputs the exponent to which the base must be raised by to get the value in the function.

[tex]\log_\text{base}(\text{value})[/tex]

In this problem, 4 has to be raised to the exponent 9 to get [tex]4^9[/tex].

The point (3, 5) does not lie on the circle with center (-2, -1) and radius 6.

To determine whether the point (3, 5) lies on the circle with center (-2, -1) and radius 6.

Calculate the distance between the point and the center of the circle.

If the distance is equal to the radius, then the point lies on the circle. Otherwise, it does not.

The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

Substituting the coordinates of the given point and the center of the circle, we get:

d = √((3 - (-2))² + (5 - (-1))²)

d = √(5² + 6²)

d = √(61)

The distance between the point (3, 5) and the center (-2, -1) is √(61).

Since sqrt(61) is not equal to the radius of the circle, which is 6, the point (3, 5) does not lie on the circle with center (-2, -1) and radius 6.

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By answering the presented question, we may conclude that This circle's radius is the same as the radius of the circle whose equation is [tex]x^{2} + y^{2} = 9[/tex]. (False)

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator

A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases.

An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

The above equation may be rewritten as follows:

(x-1)² + y² = 10

When this equation is compared to the usual form of the circle equation:

(x-a)² + (y-b)² = r²

We can observe that the circle's centre is (1,0) and its radius is sqrt (10).

As a result, the following assertions are true:

The circle's radius is three units. (False) The circle's centre is on the x-axis. (False) The circle's centre is on the y-axis. (This is correct.) The usual form of the equation is  (x-1)² + y² = 3. (False)

This circle's radius is the same as the radius of the circle whose equation is [tex]x^{2} + y^{2} = 9.[/tex] (False)

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Answer:

j = [tex]\frac{-11}{6}[/tex]

Step-by-step explanation:

5(4/5 + 2) = 3 - 6j

First, simplify the left side of the equation:

5(4/5 + 2) = 5(1.8) = 9

Now we have:

9 = 3 - 6j

Subtract 3 from both sides:

6 = -6j

Divide both sides by -6:

j = -1

Therefore, the solution is j = -1.

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The tower is about 40 meters tall.

Distance between the foci = 2 * 34 = 68 meters

Distance from each focus to the vertex = 102 - 34 = 68 meters

(x^2 / 68^2) - (y^2 / 68^2) = 1

x = 68 meters

(68² / 68²) - (y²/ 68²) = 1

Solving for y, we get:

y² = 0, which implies y = 0

Since the origin is 40 meters above the ground, and the top of the tower is at y = 0, the height of the tower is:

Height = 40 meters

The tower is about 40 meters tall.

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Answer:

Step-by-step explanation:

first we find the area of ​​the horizontal rectangle, (the one above), then we find the area of ​​the square, from the area of ​​the square we subtract the area of ​​the rectangle and we have the area of ​​the vertical rectangle (the one below, with the inverse formula we find the side and add the side of the rectangle above, and we will have that x = 20 ( see the figure)

The diagonal of the rectangular box will be 9.7 inches.

Given that:

Length, L = 3 inches

Width, W = 2 inches

Height, H = 9 inches

The diagonal of the rectangular prism is given as,

d² = L² + W² + H²

The diagonal of the rectangular box will be calculated as,

d² = 3² + 2² + 9²

d² = 9 + 4 + 81

d² = 94

d = √94

d = 9.7 inches

The diagonal of the rectangular box will be 9.7 inches.

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So, the probability that Kyle chooses boots and the red shirt is 0.0625 or 6.25%.

Probability is a measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is used in many fields, including mathematics, statistics, economics, and science, to analyze and predict the behavior of complex systems.

Here,

There are 4 choices for the shirt, 2 choices for the pants, and 2 choices for the shoes. The total number of possible outcomes is 4 x 2 x 2 = 16.

There is only one way for Kyle to choose boots and the red shirt. Therefore, the probability that he chooses boots and the red shirt is:

P(boots and red shirt) = 1/16

= 0.0625

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The minimal transportation cost is 9900 with 7 buses and 15 vans.

Bus Van Available

No of students 40 8 400

Chaperons 3 1 36

cost 1200 100

Let x be the no of buses and y the vans

The objective is to minimize total cost Z = 1200x + 100y

Then 40x+8y >=400 or 5x+y>=50

3x+y<=36  

Hence feasible solutions are

(10,0) (12,0) and (7,15)

Z for (10,0) = 12000

Z for (12,0) = 14400

Z for (7,15) = 9900

Hence, the minimal transportation cost is 9900 with 7 buses and 15 vans.

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Based on the information provided, the area and perimeter for the sector is 28.01cm²  and 15 cm.  

A sector of a circle is created by the central angle formed with two radii, and it includes the area inside the circle from that center point to the circle itself. Acute central angles will always produce minor arcs and small sectors

Area of a sector = ∅/360 * 2*π*r²1.75

rad = 100.2676

area = 100.2676/360 * 2*22/7 *4 * 470588.3904/2520

Area = 28.01cm²

Perimeter = Length of area + 2RPerimeter = (100.2676/360 * 2*22/7 *4) + 2*417647.0976/2520 + 8

Perimeter = 7.00+ 8

Perimeter = 15 cm

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Answer:

Plot the points on the graphing calculator, then generate the exponential regression equation. That equation is

[tex]f(x) = 852.650 ({1.082}^{x} )[/tex]

[tex]f(9) = 1733[/tex]

Answer: 1/6

Step-by-step explanation: To solve the system of equations:

3y = 5x + 6 (equation 1)

3y - 5x = 8 (equation 2)

We can use substitution method or elimination method.

Substitution method:

From equation 1, we have:

3y = 5x + 6

y = (5/3)x + 2 (divide both sides by 3)

Substitute y in equation 2 with (5/3)x + 2:

3y - 5x = 8

3((5/3)x + 2) - 5x = 8

5x + 6 - 5x = 8

6 = 8

The equation 6=8 is not true, which means there is no solution that satisfies both equations.

Elimination method:

Multiply equation 1 by 5:

15y = 25x + 30 (equation 1 multiplied by 5)

Subtract equation 2 from equation 1:

15y - (3y - 5x) = 25x + 30 - 8

12y + 5x = 22

Simplify:

12y = -5x + 22

y = (-5/12)x + 11/6

Now substitute y in equation 1 with (-5/12)x + 11/6:

3((-5/12)x + 11/6) = 5x + 6

(-5/4)x + 11 = 5x + 6

11 - 6 = 5x + (5/4)x

5/4 x = 5

x = 4

Now substitute x = 4 in y = (-5/12)x + 11/6:

y = (-5/12)(4) + 11/6

y = -5/3 + 11/6

y = 1/6

Therefore, the solution to the system of equations is x = 4 and y = 1/6.

The sequence (7, 49, a3, ...) can be arithmetic, geometric, or neither, depending on the values of its terms.

If a3 = 56, then we can check if the sequence is arithmetic or geometric by looking at the common difference or common ratio between terms:

Common difference: d = 49 - 7 = 42, and a3 - 49 = 56 - 49 = 7. Since d is not equal to 7, the sequence is not arithmetic.

Common ratio: r = 49/7 = 7, and a3/49 = 56/49 = 1.14. Since r is not equal to 1.14, the sequence is not geometric either. Therefore, option A is not correct.

If a3 = 343, we can check again for the common difference or common ratio:

Common difference: d = 49 - 7 = 42, and a3 - 49 = 343 - 49 = 294. Since d is not equal to 294, the sequence is not arithmetic.

Common ratio: r = 49/7 = 7, and a3/49 = 343/49 = 7. Since r is equal to 7, the sequence is geometric. Therefore, option B is correct.

Option C mentions the Fibonacci sequence, which is a specific sequence where each term is the sum of the two previous terms (starting with 0 and 1 or 1 and 1). This sequence does not appear to be a Fibonacci sequence, as there is no clear pattern of adding the two previous terms to get the next term.

Option D is not correct, as we have already shown that the sequence can be either arithmetic or geometric depending on the value of a3.

Therefore, the correct answer is option B: the sequence is arithmetic if a1 = 343 and geometric if a1 = 56.

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The tangents of the acute angles in the right triangle gives:

tan(G) = 2

tan(H) = 1/2

It should be noted that tangent is the ratio of opposite over adjacent. Thus:

tan(angle) = opposite/adjacent

So for reference angle G, we say,

tan(G) = JH/GJ = 2/1 = 2

We'll treat tan(H) in a similar fashion, but the opposite and adjacent sides swap roles. That means we'll apply the reciprocal to the result above to get 1/2 for tan(H)

So we have this interesting property where

tan(G)*tan(H) = 2*(1/2) = 1

In general,

tan(A)*tan(B) = 1 if and only if A + B = 90 degrees

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Answer:

Picture G)

Step-by-step explanation:

Because the line always passes through the origin (0,0)

This is due to the fact that the anticipated value is determined by multiplying the likelihood of each potential occurrence by its value, then adding the results.

Probability is a metric for determining the possibility of an event happening in mathematics and statistics. It is a number between 0 and 1, where 0 denotes that the action is impossible and 1 denotes that it is guaranteed to occur. Usually, the likelihood of a particular occurrence is calculated through dividing the number of possible outcomes by the number of alternative ways the event could happen. As an illustration, the likelihood of rolling a six on a regular die is 1/6 since there is just one method for scoring a six and a total of six options. Many practical applications of probability can be found in the fields of insurance, banking, and gaming. Also, it aids in risk management and assessment throughout scientific research and decision-making processes.

given

The assertion "I discovered that there should be 2.5 more boys in a household of five than was anticipated. A family of 2.5 boys cannot exist, thus I must have made a mistake "contradicts itself.

A family cannot have 2.5 males just because the number of boys in a household of five is supposed to be 2.5. Instead, it suggests that a family with five children may typically anticipate to have 2.5 boys.

This is due to the fact that the anticipated value is determined by multiplying the likelihood of each potential occurrence by its value, then adding the results.

It is indeed impossible to have 2.5 males in a family of five.

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The tangent point of the line, given the center of the circle can be found to be  ( 5.39, -10.07).

We have the equation of the tangent line as 4x + 5y = -29 and the center of the circle as (-2, 4).

Equation of the line containing the radius as:

y - 4 = (5/4)(x - (-2))

y - 4 = (5/4)(x + 2)

Solving the system of equations:

y = (-4/5)x - 29/5

y - 4 = (5/4)(x + 2)

Eliminate y by substituting the first equation into the second:

(-4/5)x - 29/5 - 4 = (5/4)(x + 2)

Now, solve for x:

(-4/5)x - 29/5 - 20/5 = (5/4)x + 10/4

(-4/5)x - (5/4)x = 10/4 + 49/5

(-16/20)x - (25/20)x = 25/4 + 196/20

(-41/20)x = 221/20

x = 221/41

Now, find the y-coordinate by plugging the value of x into one of the equations. Let's use the first equation:

y = (-4/5)(221/41) - 29/5

y = (-884/205) - 1181/205

y = -2065/205

The tangent point is (221/41, -2,065/205) or ( 5.39, -10.07).

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The smallest positive integer whose cube ends in 888 would be = 192.

A positive integer is defined as the type of number that lies on the right hand side of the number line and are also called natural numbers or counting numbers.

The cube of a positive integer means the multiplication of the number by itself for three times. That is n³.

Therefore, the positive integer = 192 when multiplied 3 times will yield 7077888 which ends in 888.

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Let's represent the price of a pound of strawberries as "s" and the price of a pound of grapes as "g".

From the given information, we can create two equations:

Equation 1: 28s + 37g = 183.5

Equation 2: 14s + 16g = 85.5

We can use the method of elimination to solve for s and g. First, we'll multiply Equation 2 by 2 to make the coefficients of s in both equations equal:

28s + 32g = 171

Now we'll subtract Equation 1 from this equation to eliminate g:

28s + 32g - (28s + 37g) = 171 - 183.5

Simplifying:

-5g = -12.5

g = 2.5

Now that we know the price of a pound of grapes is $2.5, we can substitute that value back into either Equation 1 or Equation 2 to solve for s. Let's use Equation 1:

28s + 37(2.5) = 183.5

Simplifying:

28s + 92.5 = 183.5

28s = 91

s = 3.25

Therefore, the price of each pound of strawberries is $3.25 and the price of each pound of grapes is $2.50.

What are supplementary angles?

Supplementary angles are angles that sum up to give 180°

What are vertically opposite angles?

Vertically opposite angles are angles that are vertically opposite each other which equals the same.

So, since angle 2 is vertical to a 123° angle, angle 2 is also 123° because they are vertically opposite angles.

So, since supplementary angles are angles that sum up to give 180°, angle 1 = 180° - angle 2 which is 123°.

Angle 1 = 180° - 123° = 57°

Therefore angle 1 = 57°

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The linear function that models the situation is given as follows:

y = 2.5x + 5.

Meaning that:

Hence the cost for a 50 mile ride is given as follows:

$130.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The graph touches the y-axis at y = 5, hence the intercept b, representing the base fee, is given as follows:

b = 5.

When the distance increased by 2 miles, the fee increases by $5, hence the slope m, representing the cost per mile, is given as follows:

m = 5/2

m = 2.5.

Hence the equation is:

y = 2.5x + 5.

The cost for a 50 mile ride is given as follows:

y = 2.5(50) + 5

y = 130.

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18 centimeters is the lengths of the sides of the rectangle.

What is a rectangle in mathematics?

Four 90-degree vertices and four parallel, equal-length sides define the quadrilateral that a rectangle serves as an example of. It is therefore sometimes referred to as an equilateral quadrilateral.Due to its equal and parallel opposing sides, the term "parallelogram" can also be used to describe a rectangle.

                               A rectangle is a closed, two-dimensional shape with four sides, four angles, and four right angles (90°). Equal and parallel sides make up a rectangle's opposites. Rectangles are two-dimensional shapes, and as such, have length and width that are two separate dimensions.

Let x represent the distance from the center of the rectangle to the longer side. Then the distance to the shorter side is x+4. The short side of the rectangle will have length 2x, and the long side will have length 2(x+4) = 2x+8.

The perimeter is twice the sum of the side lengths, so is ...

 56 = 2(2x +(2x+8)) = 8x +16

 40 = 8x . . . . . . . subtract 16

 40/8 = x = 5 . . . divide by the coefficient of x

The side lengths are 2x=10 and 2x+8 = 18 centimeters.

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The MAD (mean absolute deviation) is 5. This means that on average, each quiz score deviates from the mean by about 5 points.

The mean is the average of a set of numbers, which is found by adding up all the numbers in the set and then dividing the sum by the total number of values in the set. It is a measure of central tendency that gives an idea of the typical or average value in a set of data.

Step 1: To find the mean, we add up all the quiz scores and divide by the total number of quizzes:

Mean = (85 + 86 + 84 + 88 + 99 + 96) / 6 = 92

So the mean is 92 (rounded to the nearest whole number).

Step 2: To find the distance of each quiz score from the mean, we subtract the mean from each quiz score:

|85 - 92| = 7

|86 - 92| = 6

|84 - 92| = 8

|88 - 92| = 4

|99 - 92| = 7

|96 - 92| = 4

Step 3: To find the average of the distances, we add up all the distances and divide by the total number of quizzes:

(7 + 6 + 8 + 4 + 7 + 4) / 6 = 5.3

So the MAD (mean absolute deviation) is 5 (rounded to the nearest whole number). This means that on average, each quiz score deviates from the mean by about 5 points.

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The interest rate required for Alejandro to end up with $11,000 is approximately 5.48%

From the question, we are to determine what interest rate would be required in order for Alejandro to end up with $11,000

Since the interest was compounded continuously, we will use the formula

A = Pe^(rt)

Where A is the amount

P is the principal

r is the interest rate

and t is the time.

From the given information,

P = $4,100

r = ?

t = 18

Putting the parameters into the formula

A = Pe^(rt)

11000 = 4100 × e^(r × 18)

11000 = 4100 × e^(18r)

11000 / 4100 = e^(18r)

2.682927 = e^(18r)

Take the natural log of both sides

ln(2.682927) = ln e^(18r)

0.986908 = 18r

r = 0.986908 / 18

r = 0.054828

r = 5.4828%

r ≈ 5.48%

Hence, the rate is 5.48%

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