A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $1.90 and then an additional 6 cents per minute of use. In
Plan B, there is no monthly fee, but the customer pays 7 cents per minute of use.

For what amounts of monthly phone use will Plan A Cost than Plan B?
Use m for the numbers of minutes of phone use in a month, and solve your inequality for m.

When h is very small, then the slope would be equal to 6

We have

m = y2 - y1 / x2 - x1

where 2.97² - 3² / 2.97 - 3

we would have

-0.1791 / -0.03

m = 5.97

We have to do the same for   x = 3.001

3.001² - 3² / 3.001 - 3

m = 6.001

finally we have to solve for x = 3 + h

m = \(\frac{(3 + h)^2-(3)^2}{3+h-3}\)

m = \(\frac{9+h^2+6h-9}{h}\)

m = \((\frac{h}{h})*(\frac{h+6}{1} )\)

m = h + 6

if h is close to 0 then m = 6

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Answer:

m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Step-by-step explanation:

2m³ - 5m² - 7m = 0 ← factor out common factor m from each term

m(2m² - 5m - 7) = 0

factorise the quadratic 2m² - 5m - 7

consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × - 7 = - 14 and sum = - 5

the factors are + 2 and - 7

use these factors to split the m- term

2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )

2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term

(m + 1)(2m - 7)

then

2m³ - 5m² - 7m = 0

m(m + 1)(2m - 7) = 0 ← in factored form

equate each factor to zero and solve for m

m = 0

m + 1 = 0 ( subtract 1 from both sides )

m = - 1

2m - 7 = 0 ( add 7 to both sides )

2m = 7 ( divide both sides by 2 )

m = \(\frac{7}{2}\)

solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Answer:

(6,2)

Step-by-step explanation:

1) convert both equations  to slope intercept form:

y=-x+8

and

y=x-4

now graph both equations separately by intercepts:

x int:  0=-x+8

-8=-x

8=x

y int:  y=0+8

y=8

so the two coordinate points for first equation are (0,8) and (8,0)

lets move on two second equation: y=x-4

x int:  0=x-4

4=x

y int y=0-4

y=-4

so the 2 coordinate points are (4,0) and (0,4)

lets graph these two equations and see where they intersect:

(see graph below), the intersection is at (6,2) so (6,2) is our answer

hope this helps

f(x) = 6-5x

y = 6-5x .... replace f(x) with y

x = 6-5y .... swap x and y; solve for y

x+5y = 6

5y = 6-x

y = (6-x)/5

\(f^{-1}(x) = \frac{6-x}{5}\) ... replace y with the inverse function notation

Answer:

100°

Step-by-step explanation:

tThe sum of all arc measures that make up that circle is 360 degrees.

QS + RQ + RS = 360

QS = 360 - 120 - 140 = 100

An arc angle is the degree measurement of that angle inside the circle, opposite the arc

m∠R = arc QS = 100°

Answer:

∠ R = 50°

Step-by-step explanation:

the inscribed angle R is half the measure of its intercepted arc QS

the sum of the arcs on a circle is 360° , that is

RQ + QS + SR = 360°

120° + QS + 140° = 360°

QS + 260° = 360° ( subtract 260° from both sides )

QS = 100°

Then

∠ R = \(\frac{1}{2}\) × 100° = 50°

To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

Applying this property to the given expression:

-2(n-7) = -2 * n + (-2) * (-7)

Simplifying further:

-2(n-7) = -2n + 14

Therefore, the rewritten expression is -2n + 14.

The exponential function giving the number of bacteria after x hours is given as follows:

\(y = 250(2)^x\)

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 250, b = 2.

Hence the function is given as follows:

\(y = 250(2)^x\)

The problem asks for the exponential function giving the number of bacteria after x hours is given as follows:

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The fraction equivalent of the given fractions with the same denominator is written as \(\frac{56}{100} \ and \ \frac{55}{100}\)

The given parameters include:

\(\frac{14}{25} \ and \ \frac{11}{20}\)

To rewrite the given fractions to have the same denominator, we must find the LCM of the denominators;

The prime factorization of 25 = 5²

The prime factorization of 20 = 5 x 2²

The LCM of the two numbers = 5² x 2²  = 25 x 4 = 100

The fractions can rewritten as follows;

\(\frac{14}{25} \ = \frac{14}{25} \times \frac{4}{4} = \frac{14 \times 4}{25 \times 4} = \frac{56}{100} \\\\\frac{11}{20} \ = \frac{11}{20} \times \frac{5}{5} = \frac{11 \times 5}{20 \times 5} = \frac{55}{100}\)

Thus, the fraction equivalent of the given fractions with the same denominator is written as \(\frac{56}{100} \ and \ \frac{55}{100}\)

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Solving the inequality the range of x becomes 9.523 ≤ x ≤ 22.222.

The given inequality which needs to be solved is 200 ≤ 15.75x + 50 ≤ 400.

If 50 is subtracted from each part or side of the inequality we get,

200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 -50 which will be equal to,

150 ≤ 15.75x ≤ 350, now to solve this inequality divide the given inequality with the coefficient of x which is 15.75 to get the range of x.

Hence the inequality becomes 150÷15.75 ≤ 15.75x÷15.75 ≤ 350÷15.75. solving this equation the value of x becomes 9.523 ≤ x ≤ 22.222.

So the range of inequality that represents Kalis earning potential ranges from (9.523,22.222) for the given question.

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Given:

The number of bacteria in a refrigerated food product is given by:

where (T) is the temperature of the food.

When the food is removed from the refrigerator, the temperature is given by:

where (t) is the time in hours.

We will find the composite function N(T(t))

So, we will substitute the function (T) into the function (N):

Expand the function then simplify it:

So, the composite function will be:

Now, we will find the number of bacteria after 4.1 hours.

So, substitute t = 4.1 into the composite function

So, the answer will be:

The number of bacteria after 4.1 hours = 28161 bacteria

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

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Answer:

Step-by-step explanation:

The correct answer is Option D. The ratio for cos A is 15/17.

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse in a right-angled triangle.

It is frequently denoted as cos.

Consider a right-angled triangle with sides a, b, and c.

The cosine of angle A, denoted as cos(A), can be calculated as follows:

cos(A) = a/cIn the given case, the ratio for cos A is given as 15/17, which implies that:

cos(A) = 15/17

Therefore, in the right-angled triangle, the adjacent side is 15 units and the hypotenuse is 17 units.

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Answer:

X    |   y

---------------

-2   |   3

-1   |   0

0   |  -3

1   |  -6

We have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

To prove that the Newton-Raphson method for solving the equation \(x^k e^x = 0\), where k is a constant, is given by the formula

\(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,\)

we can start by considering the iterative process of the Newton-Raphson method.

Given an initial guess \(x_n\), we want to find a better approximation \(x_{n+1}\)that is closer to the root of the equation \(x^k e^x = 0.\)

The Newton-Raphson method involves the following steps:

Calculate the function value \(f(x_n) = x_n^k e^x_n\) and its derivative \(f'(x_n) = k x_n^(k-1) e^x_n.\)

Find the next approximation x_{n+1} by using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Let's apply these steps to our equation \(x^k e^x = 0\):

Calculate the function value and its derivative:

\(f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n\)

Find the next approximation x_{n+1} using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Substituting the function value and its derivative:

\(x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)\)

Simplifying the expression by combining like terms:

\(x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n\)

Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

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Answer:

Step-by-step explanation:

For women, the initial number is 6, constant rate of change is w, number of years is x.

Find the rate of change and work out the required formula:

Formula:

Similarly for men, we get:

Formula:

Answer:

Women = 44.5

Men = 63.5

Step-by-step explanation:

Answer 1 maybe

Step-by-step explanati

Answer:

b. -3

Step-by-step explanation:

30 - 3 = 27

27 - 3 = 24

24 - 3 = 21....

The distance around a figure is the perimeter, although around a circle is the perimeter is actually called the circumference.

Answer:

Step-by-step explanation:

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

Answer:

Word problem 3        

Step-by-step explanation:

Word Problem one is a subtraction problem since Felicia is giving away two marbles to Lucas. Word Problem two is a division problem since Felicia is evenly dividing the number of marbles she has into two bags. Word Problem three is a multiplication problem because Ryan has two times as many marbles that Felicia does. Word Problem four is an addition problem because she found two more marbles while she already has eight marbles. Keywords for subtraction word problems are: fewer than, decrease, take away, less than, minus, difference, change, lost reduced, and subtract. Keywords for division word problems are: As much, cut up, groups, equally, sharing, half, how many in each, parts, per percent, quotient, ratio, and separated. Keywords for multiplication word problems are: double, every, factor, increased, multiplied product, times, and tripled.

Answer:

------------------------

Find the slope of AB:

Use point-slope form and point A(2, 4) to determine the line:

Multiply both sides by 9 to clear fraction:

Open parenthesis and convert the equation into ax + by + c = 0:

The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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The slope of the curve  y⁴ = y² - x² is 1 and repeat the process for the second point.

Find the slopes of the curve y⁴ = y² - x² at the given points, we need to differentiate the equation implicitly with respect to x.
Differentiating both sides of the equation with respect to x, we get:
4y³ * (dy/dx) = 2y * (dy/dx) - 2x
Next, we can solve for (dy/dx) by isolating it on one side of the equation:
4y³ * (dy/dx) - 2y * (dy/dx) = -2x
(2y - 4y³) * (dy/dx) = -2x
(dy/dx) = -2x / (2y - 4y³)
Now, substitute the x and y values for each point into the equation to find the slopes at those points.
For example, if one point is (1, 1), we substitute x = 1 and y = 1 into the equation:
(dy/dx) = -2(1) / (2(1) - 4(1)³)
(dy/dx) = -2 / (2 - 4)
(dy/dx) = -2 / -2
(dy/dx) = 1
Repeat the process for the second point, and you will have the slopes of the curve at both points.

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This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.

Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.

If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.

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Answer:

The weight that does not round to 2.46 pounds is C 2.454 pounds.

Step-by-step explanation:

Based on the given information, the weights of the four similar packs of tomatoes are as follows:

Malcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:

From the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.

The required amount of liters used in 15% and 55% of acid solution are 10 and 70 liters respectively.

Percentage is defined as the value out of hundred.

Let x = liters of 15% acid

and y = liters of 55% acid

Then total liters of acid,

x + y = 80   ---------------------------------(1)

and question says 15% and 55% of each liters is 50% of 80 liters.

15x + 55y = 80(50)

⇒ 15x + 55y = 4000  ---------------------(2)

On solving above two equation, we get

X = 10 and Y = 70

Thus, 10 liters of 15% acid and 70 liters of 55% acid solution is used

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Answer:

D. 6i

Step-by-step explanation:

The range, in centimetres (cm), of the following lengths is 20.5 cm

What is the range?

The difference between the lowest and highest numbers is referred to as the range. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

Given, 15 cm, 0.5 cm, 10.3 cm, 16.7 cm, 21 cm, 8.6 cm

So, the highest value of length = 21 cm

the lowest value of length = 0.5 cm

Then, range = the highest value - the lowest value

                    = 21 - 0.5 = 20.5 cm

Hence, the range, in centimetres (cm), of the following lengths is 20.5 cm

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