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3 years ago

Paul uses the equation y=8x+40 to model the situation.

Mathematics

1 answer:

Leona [35]3 years ago

4 0

Answer:

The point 40 refers to the y-intercept of the linear model

Step-by-step explanation:

Looking at the equation, we can conclude that it is the equation of a straight line or a linear equation.

What this means is that it follows the general form of the equation of a straight line which is

y = mx + c

where m is the slope and c refers to the y-intercept

when we say the y-intercept, we mean the point at which the straight line plot crosses the y-axis at which x = 0

Extrapolating this, we mean the term 40 in the model refers to the y-intercept of the given linear equation

it is at the point 40 that the straight line crosses the or touches the y-axis.

Also at this point, the value of x = 0

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3 years ago

A bowl of buttons contains 10 MAGA [MAKE AMERICA GREAT AGAIN] buttons, 5 GND [GREEN NEW DEAL] buttons and 10 NAW [NEVER A WALL]

kondaur [170]

Answer:

a) Probability of picking Two MAGA buttons without replacement = 0.15

b) Probability of picking a MAGA and GND button in that order = 0.0833

Probability of picking a MAGA and GND button in with the order unimportant = 0.167

Step-by-step explanation:

10 MAGA [MAKE AMERICA GREAT AGAIN] buttons, 5 GND [GREEN NEW DEAL] buttons and 10 NAW [NEVER A WALL] buttons.

Total number of buttons = 10 + 5 + 10 = 25

Let probability of picking a MAGA button be P(M) = 10/25 = 0.4

Probability of picking a GND button be P(G) = 5/25 = 0.2

Probability of picking a NAW button be P(N) = 10/25 = 0.4

a) Probability of picking Two MAGA buttons without replacement = (10/25) × (9/24) = 3/20 = 0.15

b) Probability of picking a MAGA and GND button in that order = (10/25) × (5/24) = 1/12 = 0.0833

Probability of picking a MAGA and GND button in with the order unimportant = [(10/25) × (5/24)] + [(5/25) × (10/24)] = 1/6 = 0.167

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4 years ago

5.82-1.76 rounded to the nearest whole number

umka2103 [35]

Answer:

4.06 = 4

Step-by-step explanation:

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3 years ago

Resolve the expression <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%28x-2%29%7D%7B%28x%5E%7B2%7D%20%2B1%29%28x-1%29%5E%7B2%7D%20

Llana [10]

The partial fraction expansion will look like

(x - 2)/((x ² + 1) (x - 1)²) = (ax + b)/(x ² + 1) + c/(x - 1) + d/(x - 1)²

Get everything in terms of a common denominator, and compare the numerators on both sides:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

Expand the right side:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

x - 2 = (a + c) x ³ + (-2a + b - c + d) x ² + (a - 2b + c) x + b - c + d

Match up the coefficients and solve the resulting system of equations:

a + c = 0

-2a + b - c + d = 0

a - 2b + c = 1

b - c + d = -2

==> a = -1, b = -1/2, c = 1, d = -1/2

So the expansion into partial fractions is

(x - 2)/((x ² + 1) (x - 1)²) = (-x - 1/2)/(x ² + 1) + 1/(x - 1) - 1/(2 (x - 1)²)

… = -(2x + 1)/(2 (x ² + 1)) + 1/(x - 1) - 1/(2 (x - 1)²)

5 0

3 years ago