Angie's car is valued at $22,000, and she owes $20,000 on it. What is her

current equity?

Answer:

i) 35

ii) 0.95

iii) employees’ annual earnings are strongly related to their tenure

iv) Employee earnings increase with tenure.

Step-by-step explanation:

i) The regression line for this data set has a slope close to m = 35

To find the slope of the regression line we need to find two points that lie on the line or that are very close to the line.

We have the following two points;

(1, 175) and (2.5, 225)

slope = (change in y) / (change in x)

         = (225-175)/(2.5-1) = 33.33

This is close to 35.

ii) The correlation coefficient is close to 0.95

The coefficient of correlation is a measure of the degree of association between two variables. Correlation coefficient gives information on the strength and direction of a linear association.

The scatter-plot reveals that the annual earnings and tenures of the employees of Stan & Earl Corp are strongly positively associated hence the correlation coefficient is close to 0.95.

iii) Based on this information, we can conclude that employees’ annual earnings are strongly related to their tenure.

The correlation coefficient was found to be close to 0.95. A value greater than 0.7 shows a strong degree of association between two variables. Therefore, employees’ annual earnings are strongly related to their tenure

iv) Employee earnings increase with tenure.

The slope of the regression line of the data set was found to be close to 35. A positive slope implies that the response variable increases with increase in the explanatory variable.

Nevertheless, the correlation coefficient was also found to be positive which suggests a positive association between employee earnings and tenure.

Answer:

The regression line for this data set has a slope close to m = (35) , and the correlation coefficient is close to (0.95) .

Based on this information, we can conclude that employees’ annual earnings are (strongly related) to their tenure. Employee earnings (increase with) tenure.

Step-by-step explanation:

Answer:

The Experimental Probability of the spinner stopping on Section A is 1/3.

Step-by-step explanation:

Number of time spinner landed on section A = 4

Number of time spinner landed on section B = 5

Number of time spinner landed on section C = 2

Number of time spinner landed on section D = 1

Total Number of spins = 12

[tex]Probability=\frac{Number\:of\;Favorable\:outcome}{Number\:of\:total\;outcome}=\frac{4}{12}=\frac{1}{3}[/tex]

Therefore, The Experimental Probability of the spinner stopping on Section A is 1/3.

Answer:

B

Step-by-step explanation:

If we imagine this is on a clock, then point P is at the 9-o'clock position.  When we rotate it 90 degrees clockwise, that's a quarter rotation, so P' will be at the 12-o'clock position.  So the coordinates of P' will be (0, 5).

Answer:

Answer: The slope is 2. The y-intercept is 4 which means point (0, 4).

Step-by-step explanation:

First, find the slope of the line that passes through those two points using the slope formula.

[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

where the points are [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex]

[tex] slope = m = \dfrac{18 - 4}{7 - 0} = \dfrac{14}{7} = 2 [/tex]

The slope is 2.

One of the given points is (0, 4). Since the y-intercept lies on the y-axis, the x-coordinate of the y-intercept is 0. Point (0, 4) is the actual y-intercept.

Answer: The slope is 2. The y-intercept is 4, or point (0, 4).

To find the slope, use the S=(y2 - y1)/(x2 - x1) formula

S=(18-4)/(7-0)

S=14/7

S=2

After finding the slope, us the intercept formula to find the intercept

m is the slope

y-y1=m(x-x1)

y-4=2(x-0)

y=2x+4

Answer:

jina by .1 cm

Step-by-step explanation:

3/5 = .6

caleb = 23.6

jina = 23.7

Jina's model of the Empire State Building was taller by 0.1 centimeter compared to Caleb's model.

The question is comparing the heights of two models of the Empire State Building. Jina's model is 23.7 centimeters tall. Caleb's model is 23 3/5 centimeters tall, which in decimal form is equivalent to 23.6 centimeters tall. Therefore, Jina's model is taller. The height difference between Jina's model and Caleb's model is 23.7 - 23.6 = 0.1 centimeter. So, Jina's model is 0.1 centimeter taller than Caleb's model.

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Answer:

What do I love to do?

What brings me joy?

What am I naturally good at?

Answer is all of the above - last choice

The answer is D

Let x = -2

f(-2) = 8 - 4(-2)

f(-2) = 8 + 8

f(-2) = 16

D is the answer.

If f(-2)=16 which could be the equation for f(x) f(x)=8-4x will yield f(-2)=16

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Given

Let x = -2

f(-2) = 8 - 4(-2)

f(-2) = 8 + 8

f(-2) = 16

therefore, f(x)=8-4x will yield f(-2)=16

To know more about functions refer to :

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Answer:

[tex](x-3)^2+(y+4)^2=9[/tex]

Step-by-step explanation:

The equation of a circle with center at (h,k) and radius r units is found using:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The given circle is centered at the (3,-4) and has radius 3 units,

The equation of this circle is obtained by substituting the given values.

This gives us:

[tex](x-3)^2+(y--4)^2=3^2[/tex]

We simplify to get:

[tex](x-3)^2+(y+4)^2=9[/tex]

Answer:

(x-3)2+(y-4)2=9

Step-by-step explanation:

Answer:

A) 3x

Step-by-step explanation:

The total of all the volumes is ...

(x -1) + (x) + (x +1) = (1+1+1)x +(-1+1) = 3x+0 = 3x . . . . . matches choice A

Answer:

20 centimeters

Step-by-step explanation:

27 / x = 12

x = 2.25 times

width would be 45 / 2.25 = 20 centimeters

the 23rd term would be 71. try using the website * m a t h w a y *and you can find answers like this.

hope i helped :)

Answer: Your answer is 71 and the other answerer is right m a t h w a y is really helpful with algebra and math questions.

Answer:

  Those line segments are parallel and all the same length.

Step-by-step explanation:

Translation modifies the coordinates of each point the same way, moving the point some distance in some direction. Hence the line segments connecting original to image points will all have the same length and direction.

_____

Comment on the question

The question is pretty open-ended. If it is multiple choice, perhaps there is a choice that more or less expresses the idea above. Otherwise, it is hard to tell what the question is driving at.

Answer:

20 students

Step-by-step explanation:

The percentage of students scoring a B or A = 38 + 25 = 63%

We need to evaluate 63% of the 32 students who did the test

(63/100)*32 = 20.16

Therefore, approximately 20 students earned a B or higher

Answer:

20

Step-by-step explanation:

The percentage of students gaining an A or B = 38 + 25 = 63%

Calculate 63% of the 32 students

63% = [tex]\frac{63}{100}[/tex] = 0.63, hence

0.63 × 32 ≈ 20

Answer:

ASA

Step-by-step explanation:

One pair of corresponding angles (in the bottom left/right) are already marked for us, and we're also given a pair of corresponding sides (the 8cm ones on the left and right). The two triangles have one more angle in common too - the one they're overlapping on the top corner. So, we have:

- Two pairs of congruent corresponding angles, and

- A pair of congruent corresponding sides between them,

which is enough information to call the triangles congruent by Angle-Side-Angle (ASA).

The problem describes a situation with 16 girls who are four more than twice the number of boys. By setting up and solving the simple algebra equation 2x + 4 = 16, we find there are 6 boys in the club.

This is a word problem which can be solved using simple algebra. Given that there are 16 girls in the club and the number of girls is four more than twice the number of boys, we can set up the equation:

2x + 4 = 16

Where x stands for the number of boys. Solving this equation, we subtract 4 from both sides to get: 2x = 12. Dividing both sides by 2, we find that there are x = 6 boys in the club.

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Answer:

i)

Find the attached

ii)

The mathematical model that best fits the data is;

y = 7.19 + 12.8 ln x

Step-by-step explanation:

i)

A scatter-plot can easily be constructed using applications such as Ms. Excel and Stat-Crunch.

In Ms. Excel we first enter the data in any two adjacent columns. Next, highlight the data, then click the insert ribbon and select the scatter-plot option.

Excel returns a scatter-plot chart as shown in the attachment below.

ii)

After obtaining the scatter-plot, we shall need to add a trend line in order to determine the mathematical model that best fits the data given.

Click anywhere inside the chart, then select the design tab under chart tools. Click on the Add Chart element in the upper left corner of the excel workbook and select more trend-line options. This feature will enable us to fit any trend-line to our data.

Select any trend line option ensuring you check the boxes; Display Equation on chart and Display R-squared value on chart.

Find the attached for the various trend-lines.

The mathematical model that best fits the data is;

y = 7.19 + 12.8 ln x

Since it has the largest R-squared value of 0.9905

[tex]\rm y = 7.19 + 12.8\ ln\ x[/tex], in this function, the scatter points follow this function. Then the correct option is C.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

Construct a scatterplot and identify the mathematical model that best fits the data.

Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models.

Use a calculator or computer to obtain the regression equation of the model that best fits the data.

You may need to fit several models and compare the values of R2.

A.  [tex]\rm y = 7.82x + 0.844[/tex], in this function, the scatter points do not follow this function.

B.  [tex]\rm y = 6.81 e^{0.316x}[/tex], in this function, the scatter points do not follow this function.

C.  [tex]\rm y = 7.19 + 12.8\ ln\ x[/tex], in this function, the scatter points follow this function. Because the best fits.

D.  [tex]\rm y = 4.40 + 5.00x[/tex], in this function, the scatter points do not follow this function.

The graph is shown.

More about the function link is given below.

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Answer:

Step-by-step explanation:

First of all the answer.

[tex]\lim_{n \to -\infty}2^x= 1/ \lim_{n \to \infty}1/2^x = 0[/tex]

[tex]\lim_{n \to -\infty} 1-2^x = 1[/tex]

This approaches 0/1 = 0

The graph is included to show that this is the answer I get.

Answer:

acceleration

Step-by-step explanation:

In a speed-time graph, the speed data is on the Y-axis and the time is represented on the X-axis.

A slope is the variation of Y-values over the variation of the X-values between to points.

So, the slope of a speed-time graph would be the variation of the speed over the variation of time.

Let's say your units are m/s for the speed and s for the time.

The slope units would then be calculated by dividing m/s by s... (m/s) / s....

That would give you m/s², which is an acceleration unit.

Answer:

the answer is C 0.75 to 1.0

Over the intervals 0.25 to 0.5, 0.5 to 0.75, and 0.75 to 1.0, the exponential and linear functions are approximately equal.

To determine over which interval the exponential and linear functions are approximately the same, we first need to define the functions. Let's denote the exponential function as [tex]\( f(x) = e^x \)[/tex] and the linear function as ( g(x) = mx + c ), where ( m ) is the slope and ( c ) is the y-intercept.

Given the intervals, we'll first need to calculate the values of the exponential function at the endpoints of each interval and then find the linear function that best approximates those values. We'll choose the linear function with the same value at the starting point of each interval and approximate the slope ( m ) based on the difference in the exponential function values at the endpoints of the interval.

Let's start with each interval:

1. Interval from 0.25 to 0.5:

  - Endpoint 1:[tex]\( f(0.25) = e^{0.25} \approx 1.284 \)[/tex]

  - Endpoint 2: [tex]\( f(0.5) = e^{0.5} \approx 1.649 \)[/tex]

  - Approximating a linear function starting at ( f(0.25) ):

  [tex]- \( m = \frac{f(0.5) - f(0.25)}{0.5 - 0.25} = \frac{1.649 - 1.284}{0.5 - 0.25} \approx 0.73 \)[/tex]

[tex]- \( c = f(0.25) \approx 1.284 \)[/tex]

    - So, the linear function is [tex]\( g(x) \approx 0.73x + 1.284 \)[/tex]

2. Interval from 0.5 to 0.75:

  - Endpoint 1:[tex]\( f(0.5) = e^{0.5} \approx 1.649 \)[/tex]

  - Endpoint 2: [tex]\( f(0.75) = e^{0.75} \approx 2.117 \)[/tex]

  - Approximating a linear function starting at ( f(0.5) ):

  [tex]- \( m = \frac{f(0.75) - f(0.5)}{0.75 - 0.5} = \frac{2.117 - 1.649}{0.75 - 0.5} \approx 0.934 \)[/tex]

 [tex]- \( c = f(0.5) \approx 1.649 \)[/tex]

    - So, the linear function is [tex]\( g(x) \approx 0.934x + 1.649 \)[/tex]

3. Interval from 0.75 to 1.0:

  - Endpoint 1: [tex]\( f(0.75) = e^{0.75} \approx 2.117 \)[/tex]

  - Endpoint 2: [tex]\( f(1.0) = e^{1.0} \approx 2.718 \)[/tex]

  - Approximating a linear function starting at ( f(0.75) ):

 [tex]- \( m = \frac{f(1.0) - f(0.75)}{1.0 - 0.75} = \frac{2.718 - 2.117}{1.0 - 0.75} \approx 1.202 \)[/tex]

 [tex]- \( c = f(0.75) \approx 2.117 \)[/tex]

    - So, the linear function is [tex]\( g(x) \approx 1.202x + 2.117 \)[/tex]

4. Interval from 1.25 to 1.5:

  - Endpoint 1:[tex]\( f(1.25) = e^{1.25} \approx 3.490 \)[/tex]

  - Endpoint 2: [tex]\( f(1.5) = e^{1.5} \approx 4.482 \)[/tex]

  - Approximating a linear function starting at ( f(1.25) ):

   [tex]- \( m = \frac{f(1.5) - f(1.25)}{1.5 - 1.25} = \frac{4.482 - 3.490}{1.5 - 1.25} \approx 3.946 \)[/tex]

    - [tex]\( c = f(1.25) \approx 3.490 \)[/tex]

    - So, the linear function is[tex]\( g(x) \approx 3.946x + 3.490 \)[/tex]

Now, we can compare each linear approximation to the exponential function within its respective interval:

1. For the interval from 0.25 to 0.5, the linear function [tex]( g(x) \approx 0.73x + 1.284 \)[/tex] is approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]

2. For the interval from 0.5 to 0.75, the linear function[tex]\( g(x) \approx 0.934x + 1.649 \)[/tex] is approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]

3. For the interval from 0.75 to 1.0, the linear function [tex]\( g(x) \approx 1.202x + 2.117 \)[/tex] is approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]

4. For the interval from 1.25 to 1.5, the linear function [tex]\( g(x) \approx 3.946x + 3.490 \)[/tex] is not approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]

So, the exponential and linear functions are approximately the same over the intervals from 0.25 to 0.5, 0.5 to 0.75, and 0.75 to 1.0.

Answer:

360,000

Step-by-step explanation:

The exclamation point is factorial:

9! = 9×8×7×6×5×4×3×2×1 = 362880

5! = 5×4×3×2×1 = 120

4! = 4×3×2×1 = 24

362880 - 120× 24 = 360000

To determine the number of small boxes and large boxes shipped, we can set up a system of equations and solve for the variables. In this case, we have two equations based on the total weight and the total number of boxes. By using the elimination method, we can find that 10 small boxes and 12 large boxes were shipped.

To solve this problem, we can set up a system of equations. Let's denote the number of small boxes as x and the number of large boxes as y. We can then write two equations based on the information given:

45x + 75y = 1350 (equation 1)   (since the total weight is 1350 pounds)

x + y = 22 (equation 2)   (since the total number of boxes is 22)

We can solve this system of equations by either substitution or elimination method. Let's use the elimination method. Multiply equation 2 by 45 to make the coefficients of x in both equations equal:

45x + 45y = 990 (equation 3)

Now, subtract equation 3 from equation 1:

45x + 75y - (45x + 45y) = 1350 - 990

30y = 360

y = 12

Substitute the value of y back into equation 2:

x + 12 = 22

x = 10

Therefore, the number of small boxes shipped is 10 and the number of large boxes shipped is 12.

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Pam shipped 10 small boxes and 12 large boxes of paper.

Let's denote:

- x : Number of small boxes of paper.

- y : Number of large boxes of paper.

1. Total number of boxes shipped:

x + y = 22

2. Total weight of the shipment:

[tex]\[ 45x + 75y = 1350 \][/tex]

Now, let's solve these equations step-by-step.

Solve for  x + y = 22

From equation (1):

[tex]\[ x + y = 22 \]\[ y = 22 - x \][/tex]

Substitute  y = 22 - x  into equation (2)

Substitute  y = 22 - x  into equation (2):

[tex]\[ 45x + 75(22 - x) = 1350 \][/tex]

Expand and simplify:

[tex]\[ 45x + 1650 - 75x = 1350 \]\[ -30x + 1650 = 1350 \][/tex]

Solve for x

Subtract 1650 from both sides:

[tex]\[ -30x = 1350 - 1650 \]\[ -30x = -300 \][/tex]

Divide both sides by -30:

[tex]\[ x = \frac{-300}{-30} \]\[ x = 10 \][/tex]

Find y

Now that we have ( x = 10 ), substitute back into ( y = 22 - x ):

[tex]\[ y = 22 - 10 \]\[ y = 12 \][/tex]

- Number of small boxes: 10

- Number of large boxes: 12

Check the total weight:

[tex]\[ 45 \times 10 + 75 \times 12 = 450 + 900 = 1350 \text{ pounds} \][/tex]

This matches the given total weight of 1350 pounds, confirming that our solution is correct.

Answer:

7,909 ft²

Step-by-step explanation:

If the diameter is 250 ft, that must mean the radius is 125 ft. For this problem, use the formula for area of a sector.

[tex]\frac{58}{360} \pi 125^{2}[/tex]

Answer:

≈ 7,909 ft^2

Step-by-step explanation:

Answer: C. 41

Step-by-step explanation:

The quadratic function is:

 [tex]f(x) = 6x^2-13[/tex]

Then, to find [tex]f(-3)[/tex] you need to substitute the input value [tex]x=-3[/tex] into the quadratic function, to obtain the corresponding output value.

Then, when [tex]x=-3[/tex] the  output value is:

[tex]f(x) = 6x^2-13[/tex]

[tex]f(-3) = 6(-3)^2-13[/tex]

[tex]f(-3) = 6(9)-13[/tex]

[tex]f(-3) = 41[/tex]

This matches with the option C.

Answer:

-4

Step-by-step explanation:

Please write f(x) as 6x^2 - 13; " ^ " indicates exponentiation.

With f(x) = 6x^2 - 13, we substitute -3 for x in both instances:

f(-3)       =(-3)^2 - 13 = 9 - 13  = -4

Answer:

  D. 4 jump ropes, 3 people, 15 friends

Step-by-step explanation:

In order to answer the question how many friends could play, you need to be able to determine the smaller of ...

You can find the first of these numbers using the values of answer A, but if the number of Franklin's friends is smaller than 12, then you need to know that in order to properly answer the question. Hence, we believe you need to know ...

Formula for degree to radian:

degree ×[tex]\frac{\pi }{180}[/tex]

so...

[tex]280* \frac{\pi }{180}[/tex]

Exact answer:

[tex]\frac{14\pi }{9}[/tex]

Rounded answer:

4.89

Hope this helped!

Answer:

23%

Step-by-step explanation:

156 / 678 * 100 = 23%

The correct answer is 23%

Final answer:

Joshua brought about 23% of his LEGOs to Emily's house, which is calculated by dividing 156 (the number of LEGOs he brought) by 678 (the total number he owns) and then multiplying by 100.

Explanation:

To find what percentage of LEGOs Joshua brought to Emily's house, you divide the number of LEGOs Joshua brought by the total number of LEGOs he owns and then multiply the result by 100.

The formula to find the percentage is:

(Number of items of interest ÷ Total number of items) × 100 = Percentage

So in this case, it would be:

(156 ÷ 678) × 100

First, you perform the division:

156 ÷ 678 = 0.23 (rounded to two decimal places)

Then multiply by 100 to find the percentage:

0.23 × 100 = 23%

Therefore, Joshua brought about 23% of his LEGOs to Emily's house.

Answer:

The minimun portion of inches that can be measured with the ruler is 1/16''.

Step-by-step explanation:

The precision , what is the minimun measurement that can be aprecciated by the ruler can be determined counting the number of disivion within 2 units.  To this ruler we can count 16 division bwtween one unit and asecutive one.

Answer:

Radius of the ball is approximately 6.5 cm to the nearest tenth

Explanation:

The ball has the shape of a sphere

Surface area of a sphere can be calculated using the following rule:

Surface area of sphere = 4πr² square units

In the given problem, we have:

Surface area of the ball = 531 cm²

Substitute with the area in the above equation and solve for the radius as follows:

[tex]531 = 4\pi r^2\\ r^2=\frac{531}{4\pi } = 42.255 \\ \\ r=\sqrt{42.255}=6.5004 cm[/tex] which is approximately 6.5 cm to the nearest tenth

Hope this helps :)

Answer:

im on the same question

Answer:

option c

Step-by-step explanation:

The object reaches -200 degrees C at 15 hrs, coldest temperature it ever achieved

Answer:

The correct option is C.

Step-by-step explanation:

It is given that the temperature of the material in degrees Celsius, y, can be modeled by the following graph, where x represents the time, in hours.

From the given graph it is clear that  

1. The y-intercept is 40, so the initial temperature is 40 degree Celsius.

2.The vertex of the upward parabola is at (15,-200), so material's temperature reaches a minimum -200 degrees Celsius at 15 hours.

3. The material return to its initial temperature after 30 hours because the temperature is 40 degree Celsius at x=30.

Therefore the correct option is C.