Please I need help and the calculation of which contract is better.


The monthly contract I am considering costs $30 per month with 75 minutes of free calls and 100 free text messages. Additional calls cost 10¢ per minute and additional text messages 10¢ each. An alternative is ‘Pay as you go’ which has no monthly charge but all calls cost 30¢ per minute and texts cost 10¢ each. I typically make 100 minutes of calls and 60 text messages each month. Which would be the better contract for me and by how much?

The point e. x = 5, y = 0 satisfies the two linear constraints simultaneously. We have two linear constraints which are given as;

2x + 5y ≤ 10 (Equation 1)

10x + 6y ≤ 42 (Equation 2)

We need to find the point which satisfies both equations. Let us plug in the values one by one to check which one satisfies the two equations simultaneously.

a. x= 6, y = 2

In Equation 1:2x + 5y = 2(6) + 5(2) = 17

In Equation 2:10x + 6y = 10(6) + 6(2) = 66

Thus, this point does not satisfy equations 1 and 2 simultaneously.

b. x=6, y=4

In Equation 1:2x + 5y = 2(6) + 5(4) = 28

In Equation 2:10x + 6y = 10(6) + 6(4) = 72

Thus, this point does not satisfy equations 1 and 2 simultaneously.

c. x=2, y = 1

In Equation 1:2x + 5y = 2(2) + 5(1) = 9

In Equation 2:10x + 6y = 10(2) + 6(1) = 26

Thus, this point does not satisfy equations 1 and 2 simultaneously.

d. x=2, y = 6

In Equation 1:2x + 5y = 2(2) + 5(6) = 32

In Equation 2:10x + 6y = 10(2) + 6(6) = 52

Thus, this point does not satisfy equations 1 and 2 simultaneously.

e. x = 5, y = 0

In Equation 1:2x + 5y = 2(5) + 5(0) = 10

In Equation 2:10x + 6y = 10(5) + 6(0) = 50

Thus, this point satisfies both equations simultaneously.

To learn more about two linear constraints, refer:-

https://brainly.com/question/32636996

#SPJ11

Answer:

True

Step-by-step explanation:

I cant show you a picture but if you go to desmos you can put in the coordinates and see where they are.

Answer:

Since from the laws of exponents we have that x−n=1xn , it implies that we may write 18=8−1 . 18=123=2−3.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The domain and range of a function can be determined by analyzing its graph and also algebraically.

MAFS.912.F-IF.2.4 standard of Florida Mathematics State Standards is based on identifying the domain and range of a function. The domain is a set of input values that the function is defined for, while the range is a set of output values that the function produces. Here are the answers to the given question:35. State the domain and range for each function

.(a) f(x)

= 3x - 2

Domain: All real numbers Range:

All real numbers(b) g(x)

= x² - 5

Domain: All real numbers Range

: y ≥ -5(c) h(x)

= √(x + 4)

Domain: x ≥ -4

Range: y ≥ 0(d) k(x)

= 4

Domain: All real numbers Range: {4}.The domain and range of a function can be determined by analyzing its graph and also algebraically.

To know more about domain visit:

https://brainly.com/question/30133157

#SPJ11

Answer: \(y-10=\frac{8}{5}(x-10)\)

Step-by-step explanation:

\(5x+8y=-9\\\\8y=-5x-9\\\\y=-\frac{5}{8}x-\frac{9}{8}\)

Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the line we need to find is 8/5.

So, the equation is \(y-10=\frac{8}{5}(x-10)\).

By setting the numerator and denominator equal to each other, we eliminate any potential for additional solutions or asymptotes in the rational equation. Therefore, the equation y = x represents a rational equation with one solution.

To create a rational equation with one solution, we can start with a simple linear equation, such as y = x. We can then turn this equation into a rational equation by dividing both sides by x. This gives us the equation y/x = 1.

To ensure that the rational equation has one solution, we can set the numerator and denominator of the rational function equal to each other. This gives us the equation y = x. This equation represents a rational function where the graph is a straight line passing through the origin with a slope of 1.

Learn more about rational:

https://brainly.com/question/24398433

#SPJ11

The recurrence relation N(n) = N(n - 2) + N(n - 2) + N(n - 3) + N(n - 1) represents the number of ways to spend all the money when we have a certain amount of dollars and four options for spending it: milk, juice, coffee, and cookies.

Let's denote the number of ways of spending all the money as N(n), where n represents the amount of money we have. Our goal is to find the recurrence relation for N(n).

To start, let's consider the base cases. When n = 0, it means we have no money left. In this case, there is only one way to spend the money, and that is by not buying anything. Therefore, N(0) = 1.

Now, let's consider the cases when n > 0. We have four options for spending the money: milk, juice, coffee, and cookies. Let's analyze each option separately.

If we decide to buy milk, it costs $2. After buying milk, we are left with n - 2 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 2).

Therefore, the number of ways of spending all the money when buying milk is equal to N(n - 2).

If we decide to buy juice, it also costs $2. After buying juice, we are left with n - 2 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 2).

Therefore, the number of ways of spending all the money when buying juice is equal to N(n - 2).

If we decide to buy coffee, it costs $3. After buying coffee, we are left with n - 3 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 3). Therefore, the number of ways of spending all the money when buying coffee is equal to N(n - 3).

If we decide to buy cookies, it costs $1. After buying cookies, we are left with n - 1 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 1). Therefore, the number of ways of spending all the money when buying cookies is equal to N(n - 1).

Now, let's consider the total number of ways to spend all the money when considering all the options. Since each option is independent, we can add up the number of ways for each option. Therefore, the recurrence relation for N(n) can be expressed as:

N(n) = N(n - 2) + N(n - 2) + N(n - 3) + N(n - 1)

This recurrence relation allows us to compute the number of ways of spending all the money for any given amount of money. By using dynamic programming techniques, we can start with the base case N(0) = 1 and compute the values of N(n) iteratively until we reach the desired amount of money.

To know more about recurrence relation here

https://brainly.com/question/30895268

#SPJ4

Answer:

? = 120, ? = 145, respectively

Step-by-step explanation:

? + 60 = 180

? (+ 60 - 60) = 180 - 60

? = 120

35 + ? = 180

(35 - 35) + ? = 180 - 35

? = 145

Answer:

For 7 houses you will need 5.83 acres of land and the builder will have 4.16 acres of land unused 

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

64.50=5x+58.50

64.50=5(1)+58.50

64.50=63.50 CORRECT

It can't be 2 because it will be over 64.50

5(2)+58.50

10+58.50

68.50 WRONG

Avery can use up to 1.2 gigabytes of data while staying within her budget of $64.50 per month.

The equation to determine the number of gigabytes of data Avery can use while staying within her budget can be written as:

$58.50 + $5x = $64.50

Where:

$58.50 represents the flat cost per month

$5x represents the cost based on the number of gigabytes used (x gigabytes)

$64.50 is the total budget she wants to stay within

To solve for x, we can subtract $58.50 from both sides of the equation:

$5x = $6.00

Then, divide both sides by $5:

x = 1.2

So, Avery can use up to 1.2 gigabytes of data while staying within her budget of $64.50 per month.

To know more about equation:

https://brainly.com/question/29657983

#SPJ3

The statement "the number of people who shop at grocery stores each day will yield variability

This is the ability of a data to change. It determine the measure at which data points diverge that is far from each other.

For the number of people who shop at grocery stores each day." will yield variability since different set of people from different location to patronize the grocery shop.

The statement "the number of people who shop at grocery stores each day will yield variability

Learn more on variability here: https://brainly.com/question/6499629

#SPJ1

Given:

The figure of a triangle.

The perimeter of the triangle ABC is 31.

To find:

The value of x in the given triangle.

Solution:

Three sides of the triangle ABC are AB, BC, AC are their measures are \(3b-4,2b+1,b+10\) respectively.

The perimeter of the triangle ABC is 31.

\(AB+BC+AC=31\)

\((3b-4)+(2b+1)+(b+10)=31\)

\(6b+7=31\)

Subtract 7 from both sides.

\(6b=31-7\)

\(6b=24\)

\(b=\dfrac{24}{6}\)

\(b=4\)

Now, the measures of the sides are:

\(AB=3b-4\)

\(AB=3(4)-4\)

\(AB=12-4\)

\(AB=8\)

\(BC=2b+1\)

\(BC=2(4)+1\)

\(BC=8+1\)

\(BC=9\)

And,

\(AC=b+10\)

\(AC=4+10\)

\(AC=14\)

Using the law of cosines, we get

\(\cos A=\dfrac{b^2+c^2-a^2}{2bc}\)

\(\cos A=\dfrac{(AC)^2+(AB)^2-(BC)^2}{2(AC)(AB)}\)

\(\cos A=\dfrac{(14)^2+(8)^2-(9)^2}{2(14)(8)}\)

\(\cos A=\dfrac{179}{224}\)

Using calculator, we get

\(\cos A=0.7991\)

\(A=\cos ^{-1}(0.7991)\)

\(x=36.9558^\circ\)

\(x\approx 37.0^\circ\)

Therefore, the value of x is 37.0 degrees.

The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

learn more about first dark fringe click here:

https://brainly.com/question/27548790

#SPJ11

Answer:

The answer is 13, please let me know if I am wrong

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

\(f(5)=9\)

Step-by-step explanation:

\(f(5)=2(5+3)-7=2(8)-7=16-7=9\)

Answer:

its -13 trust me

Step-by-step explanation:

Answer:

t ≤ -13

Step-by-step explanation:

Pull out like factors :

-5t - 65  =   -5 • (t + 13)

Divide both sides by  -5

Remember to flip the inequality sign:

Solve Basic Inequality :

Subtract  13  from both sides

t ≤ -13

Answer: 17% increase

Step-by-step explanation:

Percentage increase/decrease = (final value - initial value) / initial value x 100
% change = (1,544,400 - 1,320,000) / 1,320,000 x 100
% change = 224,400 / 1,320,000 x 100
% change = 0.17 x 100
% change = 17% increase

Answer:

60,000

or

sixty thousand

The statistic T-test, is independent test on a random sampling of 20 fuses. As t(0.1,19) < t(calculated value), so the claim of the manufacturer of an electrical fuse is valid.

We have, the manufacturer of an electrical fuse claims that fuse's link will break with a 10% electrical overload within 12.31 minutes. So, μ = 12.31 min

Sample size, n = 20

mean time for link breakage, M = 10.50 minutes

Standard deviations, σ = 2.61 minutes

Since the sample follows a student T distribution, the value of t for the sample = X. So, T test formula is t = ( M - μ )/σ/√n

=> t = (12.31 - 10.59)/2.61/√20

= 0.659×√20

=> t = 2.95

Degree of freedom = n - 1 = 19

For one tailed test 0.1 , so using t distribution table, t(0.1,19) = 1.729. Also, we see 2.95 < 1.729. Since, t(0.1,19) < t(sample), so it is significant results and null hypothesis is true. Hence the manufacturers claim is valid.

For more information about t-test, visit :

https://brainly.com/question/14099859

#SPJ4

The volume of the rectangular box can be represented as 4w²h.

To find the volume of a rectangular box, you need to multiply the width, height, and length. Given that the base length (l) is four times the width (w), we can represent the length as l = 4w. Let's use the given variables w, h, and l to denote the width, height, and length, respectively.

Write the formula for the volume of a rectangular box.
Volume = width × height × length
Replace the length (l) with the expression in terms of width (w).
Volume = w × h × (4w)
Simplify the expression.
Volume = 4w²h
The volume of the rectangular box can be represented as 4w²h, where w is the width, h is the height, and l is the length, which is four times the width.

Know more about volume here,

https://brainly.com/question/28058531

#SPJ11

An equation in the form:

is the standard form for the equation of a circle with center (a,b) and radius r. Here we have:

Then, group the x and y terms separately and "move" the constant to the right side of the equation:

Complete the square:

Factor:

Express the right side as a square:

Therefore:

The center is: (3, - 2), the radius is 2

Answer:

Answer:

\(1.71*10^6\)

Step-by-step explanation:

Lets understand the term "E6"

"E" Always equals \(*10\)

"6" is the exponent applied to 10

Therefore, 1.71E6 in Scientific Notation is:

\(1.71*10^6\)

To calculate the chances of something happening when doing the same thing multiple times, given a 3% chance of it happening each time, you can use the concept of probability and multiply the individual probabilities together.

If there is a 3% chance of something happening in one trial, it means there is a 0.03 probability of it occurring. To find the probability of it happening in multiple trials, you multiply the individual probabilities together.

For example, if you want to know the chances of this event happening in two trials, you would multiply 0.03 by 0.03:

0.03 * 0.03 = 0.0009

So, there is a 0.09% chance (0.0009 probability) of this event occurring in two trials.

Similarly, if you want to know the chances of it happening in three trials, you would multiply 0.03 by itself three times:

0.03 * 0.03 * 0.03 = 0.000027

So, there is a 0.0027% chance (0.000027 probability) of this event occurring in three trials.

In general, if you want to calculate the chances of this event happening in 'n' trials, you would multiply 0.03 (or the decimal equivalent of the percentage) by itself 'n' times.

Keep in mind that this assumes the events are independent, meaning that the outcome of one trial does not affect the outcome of subsequent trials.

To learn more about probability here:

https://brainly.com/question/32117953

#SPJ4

The power series expansion of f(x) = ln(1 + x²) about a=0 can be found using geometric series, differentiation, and integration of power series. The expansion is given by:

ln(1 + x²) = x² - (1/2)x⁴ + (1/3)x⁶ - (1/4)x⁸ + ...

To find the power series expansion, we start by considering the geometric series expansion of ln(1 + x). Using the formula for the sum of an infinite geometric series, we have:

ln(1 + x) = x - (1/2)x² + (1/3)x³ - (1/4)x⁴ + ...

Now, we substitute x² for x in the above series to get the power series expansion for ln(1 + x²):

ln(1 + x²) = x² - (1/2)(x²)² + (1/3)(x²)³ - (1/4)(x²)⁴ + ...

Simplifying the terms, we have:

ln(1 + x²) = x² - (1/2)x² + (1/3)x⁶  - (1/4)x⁸ + ...

The interval of convergence for this power series expansion is -1 < x < 1, which means the expansion is valid for values of x within this interval. The radius of convergence is 1, which indicates that the series converges absolutely for values of x within the interval -1 < x < 1.

Learn more about Power series expansions

brainly.com/question/16774911

#SPJ11

Answer:

equation: 6x = -105

answer: x = -17.5

Step-by-step explanation:

the product of 6 and a number (6x) is the same (=) as -105 (-105)

6x = -105

/6        /6

x = -17.5

Answer:

hi

0.25 ounces

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

positive numbers are always bigger than negative numbers

Answer:

the method we follow is area of the triangle is 12bh b is base and h is the height of the triangle

Based on the equation, the total value of the bill is Q75.00.

Total contribution - Total bill = Shortage

125 * Number of people - X = 50

Total contribution - Total bill = Surplus

150 * Number of people - X = 75

We now have a system of two equations with two variables. Let's solve it to find the value of the total bill (X).

Equation 1: 125 * Number of people - X = 50

Equation 2: 150 * Number of people - X = 75

We can rearrange Equation 1 to solve for X:

X = 125 * Number of people - 50

Substituting this expression for X into Equation 2, we get:

150 * Number of people - (125 * Number of people - 50) = 75

Simplifying the equation:

150 * Number of people - 125 * Number of people + 50 = 75

25 * Number of people + 50 = 75

25 * Number of people = 25

Number of people = 1

Substituting the value of the number of people into Equation 1 to find X:

X = 125 * 1 - 50

X = 125 - 50

X = 75

Therefore, the total value of the bill is Q75.00.

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

A group of friends have dinner at a restaurant and decide to share the value of the bill in equal parts. If each one contributes Q125.00, Q50.00 is missing to pay the account, but if each one contributes Q150.00, then Q75.00 is left over. Which account value?