A cell phone company charges a monthly fee plus $0.25$0.25 for each text message. The monthly fee is $30.00$30.00 and you owe $59.50$59.50. Write and solve an equation to find how many text messages xx you had.An equation is

The tangent line to the curve at (0, 2) is y = 2x + 2, and the normal line is y = -1/2x + 2.

To find the equations of the tangent line and normal line to the curve at the given point (0, 2) for the function y = [tex]x^{4} +2e^{x}[/tex], we first need to determine the derivative of the function at that point.

1. Differentiate the function y =[tex]x^{4} +2e^{x}[/tex] with respect to x:

dy/dx = [tex]4x^{3} +2e^{x}[/tex]

2. Evaluate the derivative at the given point (0, 2):

dy/dx |(0, 2) = [tex]4(0)^{3}[/tex] + 2[tex]e^{0}[/tex] = 2

3. The slope of the tangent line at the point (0, 2) is 2.

4. Use the point-slope form to find the equation of the tangent line:

y - 2 = 2(x - 0)

y = 2x + 2

5. The slope of the normal line is the negative reciprocal of 2, which is -1/2.

6. Use the point-slope form to find the equation of the normal line:

y - 2 = (-1/2)(x - 0)

Simplify:

y = -1/2x + 2.

Question- Find the equation of the tangent line and normal line to the curve at a given point y=[tex]x^{4} +2e^{x}[/tex], (0, 2).

The recipe requires 2.5 pounds of meat.

we have,

To convert ounces to pounds, we use the conversion factor that 16 ounces is equal to 1 pound.

This means that every pound is made up of 16 ounces.

Given that the recipe calls for 40 ounces of meat, we can divide this quantity by the conversion factor of 16 ounces per pound to find the equivalent in pounds.

Dividing 40 by 16 gives us 2.5. So, the recipe requires 2.5 pounds of meat.

This conversion is based on the relationship between ounces and pounds, where each pound consists of 16 ounces.

So,

When converting from ounces to pounds, we divide the number of ounces by 16 to find the equivalent number of pounds.

Therefore,

The recipe requires 2.5 pounds of meat.

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Answer:

C.) Point B is between points A and C.

Step-by-step explanation:

The simplest way to analyze this is as a line.

This line goes from A to C and somewhere in the middle, is B.

But they tell you that AB + BC = AC.

The distance from A to B plus the distance from B to C is the same as the distance from A to C.

Option A about planes is not the correct one because there's no mention of planes.

Option B about angles is not correct because they only talk about some points of a line. You don't know if there's some angle in between.

The same happed with options D and E.

To find the probability that no two people will occupy adjacent seats, consider that n people are seated in a random manner in a row containing 2n seats. Using counting rule for combinations the total number of ways to select n seats of 2n seats is N=(2n/n). 

Now consider an event M that all two people occupy adjacent seats. This can be done by occupying all odd seats so that the even seats are left empty. This arrangement leaves the last 2nth seat empty. Even if one occupies that seat the condition of the event will not break. So, we have (n + 1) seats available for the n people to seat so that no two people occupy adjacent seats. N(M) = (n+1). Thus, the probability that no two people will occupy adjacent seats in a row of 2n seats can be computed as shown :

The probability that no two people will occupy adjacent seats is [(2n-1)!!]/[(2n)!].

To find the probability that no two people will occupy adjacent seats, we need to count the total number of possible arrangements where no two people are seated next to each other, and divide it by the total number of possible arrangements.

Let's consider a scenario where we have 2 people and 4 seats. In this case, the possible arrangements where no two people are seated next to each other are:

So, there are 3 possible arrangements where no two people are seated next to each other out of the total 6 possible arrangements.

Generalizing this, for n people seated in a row containing 2n seats, there are (2n-1)!! possible arrangements where no two people are seated next to each other. The double exclamation mark denotes the double factorial.
Hence, the probability is [(2n-1)!!]/[(2n)!].

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Final answer:

By calculating slopes of the triangle's sides and identifying that two of them are negative reciprocals of each other, it's confirmed that the triangle with vertices (-4, 4), (1, 5), and (2, 0) is a right triangle.

Explanation:

To determine if the triangle with vertices (-4, 4), (1, 5), and (2, 0) is a right triangle, we calculate the slopes of all three sides. The slope of the line between points (-4, 4) and (1, 5) is calculated using the slope formula m = (y2 - y1) / (x2 - x1). Using the coordinates, the slope is (5 - 4) / (1 - (-4)) = 1 / 5. Similarly, the slope between points (1, 5) and (2, 0) is (0 - 5) / (2 - 1) = -5. Lastly, the slope of the line between (-4, 4) and (2, 0) is (0 - 4) / (2 - (-4)) = -4 / 6, which simplifies to -2 / 3. A right triangle has one 90-degree angle, and the slopes of perpendicular lines are negative reciprocals of each other. Therefore, if two of these slopes are negative reciprocals, the triangle is a right triangle. In this case, the slopes -5 and 1/5 are negative reciprocals, confirming that the triangle is a right triangle.

You would have to wait approximately 3691.86 years for 1/5 of the radium to disappear, considering its half-life of 1590 years.

The decay of a substance with a half-life can be modeled using the formula [tex]\(N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{\text{half}}}}\)[/tex], where:

- [tex]\(N(t)\)[/tex] is the remaining quantity after time \(t\),

- [tex]\(N_0\)[/tex] is the initial quantity,

- [tex]\(T_{\text{half}}\)[/tex] is the half-life.

In this case, [tex]\(N(t) = \frac{1}{5}N_0\)[/tex] and [tex]\(T_{\text{half}} = 1590\)[/tex] years.

Substituting these values into the formula and solving for \(t\):

[tex]\[ \frac{1}{5}N_0 = N_0 \left(\frac{1}{2}\right)^{\frac{t}{1590}} \][/tex]

Solving this equation yields[tex]\(t \approx 3691.86\)[/tex] years.

Therefore, you would have to wait approximately 3691.86 years for 1/5 of the radium to disappear, considering its half-life of 1590 years.

Answer:    

The correct option is C. f(x) = |x + 3| + 2

Step-by-step explanation:

The parent function in this case is : mod x = |x|

Let the parent function be f(x) = |x|

Now, The parent function is transformed 3 units to the left

⇒ f (x) = f(x + 3)

⇒ f(x) = |x + 3|

Also, The parent function is transformed up by 2 units

⇒ f(x) = f(x) + 2

⇒ f(x) = |x + 3| + 2

Therefore, The correct option is C. f(x) = |x + 3| + 2

To compute for combinations, we will use the method nCr = n! / r! * (n - r)!

Where: n signifies the number of items, and r signifies the number of items being selected at a time.

Solution

1.       11C5 = 11!/ 5! * (11-5)! = 462 ways

2.       6C5 = 6!/ 5! * (6-5)! = 6 ways

3.       6/462 = 1/77 or 0.1230 is the probability that the selected group will consist of all men.

The calculation involves using combinations to find the total number of ways to select 5 people from 11, and then to find the probability of selecting 5 men by dividing the number of ways to select 5 men from 6 by the total number of selections.

The student's question deals with the topic of combinatorics, specifically the selection of groups and calculation of probabilities using the hypergeometric distribution. To find how many ways 5 people can be selected from a group of 11 (6 men and 5 women), we use the combination formula [tex]C(n, k) = n! / (k!(n-k)!).[/tex]

For the first part of the question, selecting 5 people out of 11, the calculation is C(11, 5). To calculate the number of ways 5 men can be selected from 6 men, we use C(6,5).

Lastly, to find the probability that the selected group will consist of all men, we divide the number of ways to select 5 men by the total number of ways to select 5 people from the whole group:

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to find x divide 16 by the sin of 30

16 / sin(30) = 32

 if you need 2 decimal places it would be 32.00

Answer:

16  sin30 = 32

Step-by-step explanation:

using the equation for the transformation:

(x+1, 3y)

 add 1 to very X and multiply y by 3

 so (-2,0) becomes (-1,0)

(-2,3) becomes (-1,9)

(-5,1) becomes (-4,3)

new coordinates are (-1,0) (-1,9) (-4,3)

you don't have an image attached, so to see if they are congruent, the sides need to stay the same lengths and the angles need to stay the same, from the coordinates of the new triangle, I would say they are not congruent

Answer:

This can be written as x/3, in which x is the number of students.

Step-by-step explanation:

The term quotient means to find what happens when you divide the first by the second. Then we need to pick a variable for the unknown number of students.

Final answer:

The derivative of 3g(x) is 3g'(x), obtained by taking the derivative of the function and multiplying it by the constant.

Explanation:

Derivative of 3g(x):

Yes, the derivative of 3g(x) is indeed **3g'(x)**.

When you have a constant multiplied by a function, you can simply take the derivative of the function and multiply it by the constant to find the derivative of the entire expression. In this case, the derivative of 3g(x) would be 3 times the derivative of g(x), which is 3g'(x).

The value of b is [tex]\dfrac{38}{5}[/tex].

In this, the power of x is 1. And it consists of the variable and/or constant term only.

Given

f(x)=5x−5

The average of that is 14 for the [0, b]

To find

The value of b.

For the x = 0, the value of f(x) will be

f(0) = -5

For the x = b, the value of f(x) will be

f(b) = 5b - 5

The average of that is 14.

[tex]\begin{aligned} \rm Average &= \dfrac{f(0)+f(b)}{2} \\14 &= \dfrac{(-5)+(5b-5)}{2} \\28 &= 5b -5 -5\\28 +5 + 5 &= 5b\\5b &= 38\\b &= \frac{38}{5} \\\end{aligned}[/tex]

Thus, the value of b is [tex]\dfrac{38}{5}[/tex].

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Answer with explanation:

If you will count the faces of this three dimensional geometrical shape , there are 5 faces in which there are 2 triangles and 3 Quadrilaterals.

So,to draw the net of this solid , you need

⇒As there are 3 Quadrilaterals which is in the shape of parallelogram,

   You need three rectangles ,to draw the net of this object.

Option C: 3

To find the zeros of the function f(x) = 4x2 – x – 5, we first set the equation to zero, factor it to find (4x - 5)(x + 1) = ​0, and solve for x, finding the zeros to be 5/4 and -1.

The first step in factoring the quadratic function f(x) = 4x2 – x – 5 is to set the equation to zero.

The factored form of a quadratic equation is generally represented as (ax + b)(cx + d) = 0, where x is the zeros of the function. So, the equation we have is 4x² - x - 5 = 0.

Now, we need to look for two numbers that multiply to (a*c) = -20 (4*-5) and add up to -1 which are -5 and 4. Hence, the middle expression -x can be expressed as -5x + 4x, so the equation becomes:
4x² - 5x + 4x - 5 = 0.

Factoring, we get the following:
x(4x - 5) + 1(4x - 5) = 0.

Or we could write as:
(4x - 5)(x + 1) = ​0.

Now, to find zeros of the function, we set each factor equal to zero and solve for x:

4x - 5 = 0 implies, x = 5/4.

x + 1 = 0 implies, x = -1.

So, the zeros of the function are 5/4 and -1.

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