Based on the data in the video ( 100 pages for $5.25,200 pages for $7.75,300 pages for $10.25,400 pages for $12.75 ), a) How well will a line model the data? b) Find an equation for price in terms of the number of pages, n Price

Answers

Answer 1

Answer:

Answer: Price (P) = 0.025n + $2.75

Step-by-step explanation:

a) Based on the data provided, a line model will reasonably fit the data. The given data points form a consistent pattern, where the number of pages increases linearly with the price.

b) To find an equation for price in terms of the number of pages, we can use the slope-intercept form of a linear equation: y = mx + b.

Let's use the data points to determine the slope (m) and y-intercept (b) of the equation.

Using the points (100, $5.25) and (400, $12.75):

Slope (m) = (12.75 - 5.25) / (400 - 100) = 7.5 / 300 = 0.025

Now, let's substitute one of the data points into the equation to solve for the y-intercept (b). Let's use the point (100, $5.25):

$5.25 = 0.025(100) + b

$5.25 = 2.5 + b

b = $5.25 - $2.5 = $2.75

Answer 2

Answer:

Final answer:

The relationship between the number of pages and the price is linear, so a line will model the data well. The equation of the price per page can be found using the point-slope form of a line equation, which in this case leads to the equation: Price = $0.025*Pages + $5.00.

Explanation:

To determine how well a line will model the given data, it is essential first to examine the relationship between the number of pages and the price. Here, we observe a consistent increase of $2.50 for every 100 extra pages. This suggests a linear relationship, meaning a line should model the data well.

To find the equation for the price in terms of the pages, we can use the point-slope form of a line equation, y - y1 = m(x - x1). Here, (x1, y1) is a point on the line, and m is the slope of the line. The slope (m) can be found by determining the difference in price (y values) divided by the difference in pages (x values). The slope will be ($7.75 - $5.25)/(200 - 100) =$2.50/100 pages = $0.025/page.

Choosing the first data point (100, $5.25) as our point on the line, the price equation (Price = m * Pages + b) becomes Price = $0.025 * Pages + $5.00. Thus, based on the data, a line model is well-suited to represent the relation between the number of pages and the price.

Learn more about Linear Relationships and Line Models here:

brainly.com/question/31635535

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Solve.
1.5 - 0.25(a + 4)= 3 + 3(0.05 - 0.5a)

Answers

the answer should be 2.12

Ok HI again but the answer should be -0.68 the steps are below! Simplifying 5 + -0.25(a + 4) = 3 + 3(0.05 + -0.5a) Reorder the terms: 5 + -0.25(4 + a) = 3 + 3(0.05 + -0.5a) 5 + (4 * -0.25 + a * -0.25) = 3 + 3(0.05 + -0.5a) 5 + (-1 + -0.25a) = 3 + 3(0.05 + -0.5a) Combine like terms: 5 + -1 = 4 4 + -0.25a = 3 + 3(0.05 + -0.5a) 4 + -0.25a = 3 + (0.05 * 3 + -0.5a * 3) 4 + -0.25a = 3 + (0.15 + -1.5a) Combine like terms: 3 + 0.15 = 3.15 4 + -0.25a = 3.15 + -1.5a Solving 4 + -0.25a = 3.15 + -1.5a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5a' to each side of the equation. 4 + -0.25a + 1.5a = 3.15 + -1.5a + 1.5a Combine like terms: -0.25a + 1.5a = 1.25a 4 + 1.25a = 3.15 + -1.5a + 1.5a Combine like terms: -1.5a + 1.5a = 0.0 4 + 1.25a = 3.15 + 0.0 4 + 1.25a = 3.15 Add '-4' to each side of the equation. 4 + -4 + 1.25a = 3.15 + -4 Combine like terms: 4 + -4 = 0 0 + 1.25a = 3.15 + -4 1.25a = 3.15 + -4 Combine like terms: 3.15 + -4 = -0.85 1.25a = -0.85 Divide each side by '1.25'. a = -0.68 Simplifying a = -0.68

Find the 4th term of (x+2)^10

Answers

(x + 2)¹⁰

Would take the terms in reducing powers of x, and increasing powers of 2.

1st term = ¹⁰C₀ x¹⁰(2)⁰ = x¹⁰

Second term = ¹⁰C₁ x¹⁰⁻¹(2)¹ = ¹⁰C₁ x⁹(2)¹

Third term =    ¹⁰C₂ x¹⁰⁻²(2)² = ¹⁰C₂ x⁸(2)²

Fourth term = ¹⁰C₃ x¹⁰⁻³(2)³ = ¹⁰C₃ x⁷(2)³

So we shall now simplify the fourth term which is = ¹⁰C₃ x⁷(2)³

ⁿCr = n! /( r!(n -r)! )

¹⁰C₃ = 10! /( 3!(10 -3)! ) = 10! / (3!*7!) = (10 *9 * 8* 7!) / (3!*7!)

= 10*9*8 / 3! = (10*9*8) / (3*2*1) = 120

4th term = ¹⁰C₃ x⁷(2)³ = 120 *x⁷*(2)³ = 120*2³*x⁷

   = 120*8x⁷

   = 960x⁷

So the fourth term in reducing powers of x = 960x⁷

I hope this helped.

Select the correct way to write 0.28 as a fraction.

Answers

7/25 is equal to 0.28

Find the volume of each figure. Round your answer to the nearest hundredth, if necessary.

Answers

Formula for volume of cone:

V = $\pi r^(2) (h)/(3)$

r = 6 km

h = 12 km

V = $\pi 6^(2) (12)/(3)$

V = $\pi 36*4$

V = $\pi 144$

V = 452.389 km^3 <----------------------Using the calculators pi button

V = 452.16 km^3 <-------------------------Using 3.14 for pi

Hope this helped!

~Just a girl in love with Shawn Mendes

What is the measure of angle 1?

Answers

140 is the answer to the question

Hello there!

The answer is, the measure of angle 1 is 140 degrees.

Consider the following system of equations: y = −2x + 3
y = x − 5

Which description best describes the solution to the system of equations?

Lines y = −2x + 3 and y = 3x – 5 intersect the x-axis.

Line y = −2x + 3 intersects line y = x − 5.

Lines y = −2x + 3 and y = 3x − 5 intersect the y-axis.

Line y = −2x + 3 intersects the origin.