Sydney pays a flat rate of $20 plus a
rate of 7 cents per minute in her phone
plan. Which function shows the cost, "C",
of Sydney's plans as a function of time
in minutes?

Step-by-step explanation:

the most common form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and since for b.

for slope a :

x changes by -6 (from 4 to -2)

y changes by +36 (from -31 to 5)

so, the slope is +36/-6 = -6

and the equation looks now like this

y = -6x + b

let's use the second point

5 = -6×-2 + b = 12 + b

-7 = b

the full equation is

y = -6x - 7

Answer:

Explain to the person the most common ones: Red- usually the color of anger, sexual excitement, physical strength or aggression. Orange- physical comfort, having enough food, warmth, and security, sometimes frustration. Yellow- friendliness, cheerfulness, optimism, confidence, sometimes fear

fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1 , ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05 are the required functional estimations of a given representations.

However, we can estimate the partial derivatives with respect to x (fv) and y (ft) at the point (40,20) using the definition of partial derivatives:

fv = ∂f/∂x ≈ (f(40+h,20) - f(40,20))/h

where h is a small increment in the x direction. Similarly,

ft = ∂f/∂y ≈ (f(40,20+k) - f(40,20))/k

where k is a small increment in the y direction.

To estimate fv(40,20) and ft(40,20), we need to choose small values of h and k and evaluate the function at the corresponding points. Let's say h = 0.1 and k = 0.05:

fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1

ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05

We can then use these estimates to approximate the value of f(40.1,20.05) using the first-order Taylor approximation:

f(40.1,20.05) ≈ f(40,20) + fv(40,20)0.1 + ft(40,20)0.05

Note that this is an approximation and may not be very accurate if the function is highly nonlinear or has discontinuities. However, it can give us a rough idea of the value of f(40,20) and how it changes with small variations in x and y.

To know more about   first-order Taylor click here:

brainly.com/question/14787721

#SPJ4

The surface area of the box as a function of x will be f(x) = x² + 20000/x² where x is the length of the square base's edge.

Here it is given that the box has a square base.

This implies that length = breadth

Now, the volume of a box = lbh = 5000 cu in

where l is the length of the box. b is the breadth of the box, and h is the height of the box.

or, x²h = 5000

or, h = 5000/x²

Let the surface area function be f(x) where x is the length of the edge of the square base.

Since the box is open, the surface area will be

lb + 2bh + 2lh

= x² + 10000/x² + 10000/x

= x² + 20000/x²

Hence the surface area as a function of x will be

f(x) = x² + 20000/x²

To learn more about function visit

https://brainly.com/question/14002287

#SPJ4

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

For more questions on expected value

https://brainly.com/question/14723169

#SPJ8

Given that sin(x) = -5/13 and the condition is to provide the answer without using sin, cos, or tan, I assume you are looking for the value of cos(x).

We can use the Pythagorean identity: sin²(x) + cos²(x) = 1

Substitute the given value of sin(x):
(-5/13)² + cos²(x) = 1

Solve for cos²(x):
cos²(x) = 1 - (-5/13)²

cos²(x) = 1 - (25/169)

Now find the common denominator (169) and subtract:
cos²(x) = (169/169) - (25/169)

cos²(x) = 144/169

Since we need the value of cos(x), we take the square root of both sides:
cos(x) = ±√(144/169)

cos(x) = ±12/13

Since the value of sin(x) is negative, we are in the third or fourth quadrant, where the cosine is also negative. Therefore, we choose the negative value for cos(x):

cos(x) = -12/13

Visit here to learn more about sin brainly.com/question/19213118

#SPJ11

Answer:

  f(x) = 0, -2, 4, 18

Step-by-step explanation:

It is convenient to let a graphing calculator or spreadsheet do the repetitive calculations for you. The filled-in table is attached.

__

Additional comment

When evaluating polynomial functions by hand, it is convenient to write them in "Horner form."

  f(x) = (x +5)x +4

  f(-4) = (-4 +5)(-4) +4 = -4 +4 = 0

  f(-2) = (-2 +5)(-2) +4 = -6 +4 = -2

  f(0) = 4 . . . . the constant term

  f(2) = (2 +5)2 +4 = 14 +4 = 18

Answer:

make y the subject first

Step-by-step explanation:

y=5/7(x) -27/7

parallel lines have equal gradient m1=m2

y-y1=m(x-x1)

y-(-3)=5/7(x-4))

y=5/7(x) -20/7 -3

final answer

y=5/7(x) -41/7

Answer:

3 and -3

Step-by-step explanation:

First, we need to split the equation into 2, based on the definition of absolute value.

Those 2 equations will be -2h = 6 and -2h = -6

Next, we divide by -2 on both sides of both equations.

-6 divided by -2 is 3, and 6 divided by -2 is -3.

Therefore, our two answers are -3 and 3.

The total arc length AB that the pendulum travels is approximately 13.96 inches.

To find the total arc length traveled by the pendulum, we can use the formula for the arc length of a pendulum given by:

Arc length (s) = θ × r

where θ is the angle in radians and r is the length of the pendulum.

However, in this case, we are given the angle in degrees, so we need to convert it to radians. The formula for converting degrees to radians is:

θ (in radians) = (π/180) × θ (in degrees)

Given that the angle is 80°, we can convert it to radians as follows:

θ (in radians) = (π/180) × 80° = (4π/9) radians

Now, we can calculate the arc length:

Arc length (s) = (4π/9) radians × 10 inches

The total arc length traveled by the pendulum is therefore:

Arc length (s) = (40π/9) inches

To approximate the answer, we can use the value of π as approximately 3.14:

Arc length (s) ≈ (40 × 3.14/9) inches

Arc length (s) ≈ 13.96 inches

Therefore, the total arc length AB that the pendulum travels is approximately 13.96 inches.

Please note that this calculation assumes that the pendulum swings in a perfect arc without any friction or external factors affecting its motion. In reality, there may be slight variations due to factors such as air resistance or imperfections in the pendulum's motion.

For more such question on pendulum visit:

https://brainly.com/question/26146375

#SPJ8

A 2x2 nondiagonal matrix that is diagonalizable but not invertible is the matrix A = [(0, 1), (0, 0)].

A diagonalizable matrix has linearly independent eigenvectors, while an invertible matrix has a nonzero determinant. The given matrix A = [(0, 1), (0, 0)] is not diagonal since it has off-diagonal elements.

To check if it's diagonalizable, we find the eigenvalues:
1. Calculate the characteristic equation: det(A - λI) = (0 - λ)(0 - λ) - (1)(0) = λ^2
2. Solve for λ: λ = 0 (double root)

Now, find the eigenvectors for λ = 0:
(A - λI)v = 0
[(0, 1), (0, 0)]v = 0

From the system of linear equations, we have one equation: v2 = 0. Choose v1 = 1, then the eigenvector is (1, 0). Since we have two linearly independent eigenvectors, the matrix A is diagonalizable.

To check if it's invertible, calculate the determinant:
det(A) = (0)(0) - (1)(0) = 0

Since the determinant is zero, the matrix A is not invertible. Therefore, A is a 2x2 nondiagonal matrix that is diagonalizable but not invertible.

To know more about eigenvectors click on below link:

https://brainly.com/question/30725137#

#SPJ11

The first option is correct. The series of transformations that would result in an image being similar but not congruent to its preimage is reflection over the x-axis, reflection over the y-axis, and translation up 3.

The state of being in agreement or concord is referred to as congruency. It is a notion that is employed in many fields of life, including mathematics, psychology, and philosophy. Congruency is the belief that in order for an idea, system, or process to be effective, all of its components must agree with each other.

Reflection along the x-axis: This transformation includes reflecting the shape along an imaginary line drawn across the coordinate plane's origin. This produces a mirror copy of the original shape, with the left side of the shape mirrored to the right side and the right side of the shape reflected to the left.

Reflection along the y-axis: This transformation includes reflecting the shape along an imaginary line drawn across the coordinate plane's origin. This produces a mirror copy of the original shape, with the top side of the shape reflecting to the bottom side and the bottom side of the shape reflecting to the top side.

Translation up 3: In this transformation, the shape is moved up by a given number of units. The form will be pushed forward three units without affecting its size or orientation as a result of this.

Reflection over the x-axis, reflection over the y-axis, reflection over the x-axis: This transformation requires reflecting the shape twice across an imaginary line drawn through the coordinate plane's origin. This produces a mirror copy of the original shape, with the left side of the shape mirrored to the right side and the right side of the shape reflected to the left.

Dilation by a scale factor of 3: This modification enlarges or contracts the shape by a certain scale factor. This causes the form to be three times larger or smaller than it was before, without affecting its orientation.

180° anticlockwise rotation: This transformation includes rotating the shape by a given amount. This will spin the form 180° anticlockwise without affecting its size or orientation.

To know more about congruency, visit

brainly.com/question/6108628

#SPJ1

Answer:

x = 49

Step-by-step explanation:

The sum of angles in a triangle add up to 180°.

∠CBA = ∠EBD (Vertically opposite angles are equal)

          = 52°

Since in the triangle DBE, you already know two of the angles, you can find ∠BDE which is equal to ∠CAB (x + 9)°.

∠BDE = 180° - 70° - 52°

          = 58°

∠BDE = ∠CAB

          = ∠(x + 9)°

          = 58°

x + 9 = 58

x = 58 - 9

x = 49

Answer:

A. (-10,18); 412 yards

Step-by-step explanation:

Answer:

It's A

Step-by-step explanation:

For the given continuous random variable x:

(a) p(x < 4) = -8/27.

(b) p(3 ≤ x < 4) = -5/27

The continuous random variable x that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 x)/27.

(a) To find p(x < 4), we need to integrate the density function from x = 2 to x = 4:

p(x < 4) = ∫24 2(1 x)/27 dx

= (2/27) ∫24 (1 - x) dx

= (2/27) [(x - x2/2)]24

= (2/27) [(4 - 42/2) - (2 - 22/2)]

= (2/27) [(4 - 8) - (2 - 2)]

= (2/27) [(-4) - 0]

= (2/27) (-4)

= -8/27

So, p(x < 4) = -8/27.

(b) To find p(3 ≤ x < 4), we need to integrate the density function from x = 3 to x = 4:

p(3 ≤ x < 4) = ∫34 2(1 x)/27 dx

= (2/27) ∫34 (1 - x) dx

= (2/27) [(x - x2/2)]34

= (2/27) [(4 - 42/2) - (3 - 32/2)]

= (2/27) [(4 - 8) - (3 - 4.5)]

= (2/27) [(-4) - (-1.5)]

= (2/27) (-2.5)

= -5/27

So, p(3 ≤ x < 4) = -5/27.

Know more about continuous here:

https://brainly.com/question/18102431

#SPJ11

The doubles fact for 7 8 is 7+7+1=15.

In simple words, Double Plus One Fact is a strategy for adding two consecutive numbers . To get final result then simply add a smaller number to itself or double it then and add 1.

The numbers that are added together are known as doubles. For example, 5+5=10, 3+3=6, so the doubles plus one fact are simply adding 1 to the resultant of the double fact.

For given, the doubles fact is 7+7=14, then add 1 to get 15.

As a result, 7+7+1=15 is the doubles fact for 7 8.

To learn more about doubles fact refer here

https://brainly.com/question/6244809

#SPJ4

Answer:

11 and 9

Step-by-step explanation:

X+Y=20

X*Y=99

Y=20-X

X*(20-X)=99

20X-X^2=99

20X-X^2–99=0

-(X - 11) (X - 9) = 0

Two solutions

X-11=0, X=11

X-9=0, X=9

Y=20-X, so if X is 9, Y is 11

Y=20-X, so if X is 11, Y is 9

The two numbers are 11 and 9

The value that is added on the left-hand side to make the equation equal is -1/100.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows: multiplication, division, addition, and subtraction.

Given [1/-2  - 3/4  of -8/15],

to add a number so the sum equals the product of -7/50 and 11/14

let the number be x

according to the question,

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

taking LHS

[1/-2  - 3/4  of -8/15] = -1/2 - (3(-8)/60)

[1/-2  - 3/4  of -8/15] = -1/2 + 24/60

[1/-2  - 3/4  of -8/15] = (-30 + 24)/60

[1/-2  - 3/4  of -8/15] =-6/60 = -1/10

RHS

-7/50*11/14 = -77/700 = -11/100

substitute the values

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

-1/10 + x = -11/100

x = -11/100 + 1/10

x = (-11 + 10)/100

x = -1/100

Hence -1/100 is added to make the equation equal.

Learn more about Mathematical operators;

https://brainly.com/question/8959976

#SPJ1

Answer:

80 mm

Step-by-step explanation:

Pythagorean theorm can be applied here to solve for the length of the last leg, \(a^{2}\) + \(b^{2}\) = \(c^{2}\), where (a) and (b) are the legs of the triangle and (c) is the hypotenuse. We can rearrange the pythagorean theorm for our purposes like the following:

b = √c^2 - √a^2

  = √(82)^2 - √(18)^2

  = √6724 - √324

  = √6400

  = 80 mm

Answer:

680, hope this helps!

Based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

To determine the amount of capital this year based on the given information, we can use the investment and depreciation rates.

Let's denote the amount of capital this year as K1.

According to the information provided:

People invest 55% of income, but we don't have any information about income. Therefore, we cannot determine the exact investment amount.

10% of capital depreciates. Based on this, the capital at the beginning of this year (K1) can be calculated as follows:

K1 = K - 0.1K

= 0.9K

Since we know that the capital last year was equal to 25, we substitute K = 25 into the equation above:

K1 = 0.9 * 25

= 22.5

Therefore, based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

Learn more about information from

https://brainly.com/question/27894163

#SPJ11

Our answer will be Silty Loam.

Silt loam is a type of soil that needs at least 70% silt and clay mixed, and at least 20% sand. This kind of soil, which belongs to the loam soil kinds, is actually ideal for virtually every plant's growth. The silt loam's exceptional productivity and suitability for virtually all plants are due to the precise proportions of silt, clay, and sand particles that make up its composition. Although it is not a particularly common soil in nature, it is nonetheless present on enough land all over the world.

So, therefore based on the given data it is clear that the soil sample contains the necessary percentages to be categorized as Silty Loam.

To learn more about Silty Loam, visit: https://brainly.com/question/1581089

#SPJ4

The correct option is B: V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy

This integral will give us the Volume of the solid generated when region R is revolved about the vertical line x = 1.

The volume of the solid generated when region R is revolved about the vertical line x = 1, we can use the method of cylindrical shells.

The formula for the volume of a solid generated by revolving a region R about a vertical line is given by:

V = 2π ∫[a,b] x * f(x) dx

In this case, since we are revolving the region R about the vertical line x = 1, the limits of integration will be from y = 2 (where the horizontal line y = 2 intersects the graph y = 2x - 2) to y = 0 (where the graph y = 2x - 2 intersects the x-axis).

Let's analyze the options provided:

A. π ∫[1,2] ((y + 2)/2 - 1)^2 dy

B. π ∫[0,2] ((y + 2)/2 - 1)^2 dy

C. π ∫[1,2] (2 - (2x - 2))^2 dy

D. π ∫[0,2] ((y + 2)/2)^2 - 1^2 dy

Option A: The limits of integration are incorrect. We need to integrate with respect to y, not x.

Option B: This appears to be the correct integral setup, integrating with respect to y and using the correct limits of integration.

Option C: This option incorrectly uses the expression (2 - (2x - 2))^2, which doesn't match the function y = 2x - 2.

Option D: The limits of integration are incorrect. We need to integrate from y = 2 to y = 0.

Therefore, the correct option is B:

V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy

This integral will give us the volume of the solid generated when region R is revolved about the vertical line x = 1.

For more questions on Volume .

https://brainly.com/question/27535498

#SPJ8

Answer:

a.is approximately normal because of the central limit theorem.

Step-by-step explanation:

The central limit theorem states that if we have a population with mean μ and standard deviation σ and we take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

For any distribution if the number of samples n ≥ 30, the sample distribution will be approximately normal.

Since in our question, the sample of observations is 50, n = 50.

Since 50 > 30, then our sample distribution will be approximately normal because of the central limit theorem.

So, a is the answer.

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

Read more about domain and range at

brainly.com/question/27910766

#SPJ1

Answer:

In order to be called a 'rational' number, a number must be the quotient that results when one non-zero integer is divided by another. An irrational number can be written as a decimal, but not as a fraction. Your number is (3 sqrt(2)) / sqrt(2) = 3, and is a rational number indeed.