Given a circle with center (– 3, 6) and radius 5, what is an equation of the circle?

The decimal form of 2.998 x [tex]10^8[/tex] m/s is 29,980,000 m/s.

The number 2.998 x [tex]10^8[/tex] m/s represents the scientific notation of a very large number. It is a shorthand way of writing a number that is expressed as the product of a decimal number between 1 and 10 and a power of 10. In this case, the decimal number is 2.998 and the power of 10 is 8.

To convert this number to decimal form, we need to multiply the decimal number by 10 raised to the power of the exponent. So, we have:

2.998 x [tex]10^8[/tex] = 2.998 * 10,000,000

Multiplying 2.998 by 10,000,000, we get:

2.998 * 10,000,000 = 29,980,000

Therefore, the decimal form of 2.998 x [tex]10^8[/tex] m/s is 29,980,000 m/s.

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The perimeter of a table that is 3m long and 2m wide is 10m.

The perimeter includes the total lengths (2 lengths and 2 breadths) of the four sides or the total distance around the rectangle.

For a rectangle, the perimeter can be determined using the following formula:

Perimeter = 2(l + w)

Length of the table = 3m

Width of the table  = 2m

The perimeter of the table = 2(3 + 2)

= 10m

Thus, for a table that has lengths of 3 meters and width of 2 meters, the perimeter is 10 meters.

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The answers are n(A ∪ Bc) = 10 and n(Ac ∩ Bc) = 6.

To solve this question we need knowledge of set theory, union and intersection.

(c) To find n(A ∪ Bc), we first need to find the complement of B, which is Bc = {5, 6, 7, 8, 9, d, e}. Now, we can find the union of A and Bc, which is A ∪ Bc = {1, 2, a, e, 5, 6, 7, 8, 9, d}. The number of elements in this set is n(A ∪ Bc) = 10.

(d) To find n(Ac ∩ Bc), we first need to find the complement of A, which is Ac = {3, 4, 5, 6, 7, 8, 9, b, c, d}. Now, we can find the intersection of Ac and Bc, which is Ac ∩ Bc = {5, 6, 7, 8, 9, d}. The number of elements in this set is n(Ac ∩ Bc) = 6.

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The average number of likes per writer and the average number of comments per writer can be used to determine which website has more user engagement per a single writer

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the average number of likes per writer be L

Let the average number of comments per writer be C

Now , the number of writers for website A = 5

The number of writers for website B = 11

The average number of likes per post for A = 3500 likes

So , the average number of likes per writer A = ( 3500 / 5 ) = 700 likes

And , the average number of likes per writer B = ( 3500 / 5 ) = 700 likes

The number of comments per writer A = ( 500 / 5 ) = 100 comments

The number of comments per writer B = ( 450 / 11 ) = 40.90 comments

Hence , the average number of likes per writer and the average number of comments per writer are solved

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The fourth term in the geometric sequence is -81.

What is a geometric sequence?

In mathematics, a geometric progression, also known as a geometric sequence, is a set of non-zero numbers where each term after the first is derived by multiplying the previous one by a fixed, non-zero amount called the common ratio.

We are given a sequence as 3, –9, 27, ...

We can observe that each term is being multiplied by -3.

So, the common ratio i.e. r = -3

Here x = 4 and a₁ = 3.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₄ = a₁ r⁽⁴⁻¹⁾

⇒a₄ = a₁ r³

⇒a₄ = 3 (-3)³

⇒a₄ = 3 * -27

⇒a₄ = -81

Hence, the fourth term in the geometric sequence is -81.

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Answer:

x=4, y=5

Step-by-step explanation:

[tex]x=2y-6\\ x-2y=-6\\\\y=3x-7\\y-3x=-7\\\\\\\\-3x+y=-7\\-3(2y-6)+y=-7\\-6y+18+y=-7\\-5y+18=-7\\-5y=-25\\y=5\\\\\\x=2y-6\\x=2(5)-6\\x=4[/tex]

The baker needs a total of 3 hours to decorate 4 1/2 cakes.

To decorate one cake, the baker needs 2/3 hour.

To find out how long it takes to decorate 4 1/2 cakes, we need to multiply the time for one cake by 4 1/2 i.e. 9/2

Time for 4 1/2 cakes = (2/3) x (9/2)

When the products are evaluated, we have

Time for 4 1/2 cakes = 3

So, the time taken is 3 hours

Therefore, the baker needs a total of 3 hours to decorate 4 1/2 cakes.

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Alice needs to use 10.584 pounds of sugar for her jam recipe. This can be calculated using the conversion factor.

To convert 4.8 kg to pounds, we need to use the conversion factor of 1 kg = 2.205 pounds. This means that for every 1 kg, there are 2.205 pounds. To find out how many pounds are in 4.8 kg, we simply multiply 4.8 by 2.205.

The equation for this conversion is:

4.8 kg × 2.205 pounds/kg = 10.584 pounds

So, 4.8 kg is equivalent to 10.584 pounds.

Therefore, the correct answer is 10.584 pounds.

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In response to the query, we can state that Rounding to the nearest parallel lines hundredth, the value of x is approximately 4.89 inches. Therefore, the answer is not provided in the options.

In geometry, parallel lines are non-intersecting coplanar infinite lines. Parallel planes are ones that never intersect in a certain three-dimensional space. The term "parallel" refers to curves that have a fixed minimum distance between them and neither points of contact nor junction. In geometry, two lines are said to be parallel if they are in the same plane, equally spaced apart, and never intersect. Both horizontal and vertical can be used. Railroad tracks, columns of notebooks, and pedestrian crossings are examples of commonplace things that have parallel lines.  

A = (a + b)h/2

where a and b=lengths of the parallel sides of the trapezoid,

h =height

a = 550 in

b = 10 in

h = x in

A = (a + b)h/2 = (550 + 10)x/2 = 280x

And we know that the area of the trapezoid is 1,370 square inches:

A = 1,370

280x = 1,370

x = 1,370/280

x ≈ 4.89

Rounding to the nearest hundredth, the value of x is approximately 4.89 inches. Therefore, the answer is not provided in the options.

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Answer:

On June 1, 2013, Anchorage, Alaska experiences 18 and 1/4 hours of daylight.

In a 24-hour day, there are 24 - 18 and 1/4 = 5 and 3/4 hours without daylight.

Therefore, the number of hours without daylight on June 1, 2013 in Anchorage, Alaska was 5 and 3/4 hours.

Answer:

24-18.4=5 and3/4

Step-by-step explanation:

The diameter of the opening of the cone is approximately 8.92 units.

We can use the formula for the volume of a cone:

V = (1/3) × π × r^2 × H

where V is the volume, H is the height, and r is the radius of the base.

In this case, we are given the volume V = 196 and the height H = 12. We want to find the diameter of the opening, which is 2r.

First, we can rearrange the formula for the volume to solve for r

r = sqrt((3V) / (πH))

Plugging in the values, we get

r = sqrt((3 × 196) / (π × 12)) ≈ 4.46

So the radius of the base of the cone is approximately 4.46 units.

Finally, we can find the diameter of the opening:

d = 2r ≈ 8.92 units

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The given question is incomplete, the complete question is:

The volume of the cone is 196 cubic units. If the height of the ice cream cone is H=12 what is the diameter of the opening of the cone?

The expression  9-36x can be factorized as 9(1-4x)

An expression's factors are things that are multiplied by other things. A number, variable, phrase, or any other lengthier expression may be used. For instance, 2, x, and y are the factors of 2xy.

To factor the expression 9-36x completely, we need to find the greatest common factor (GCF) of the two terms and then use the distributive property to factor it out.

The GCF of 9 and 36 is 9, so we can factor out 9 from both terms:

9-36x = 9(1-4x)

Now the expression is factored completely.

So the final answer is:

9-36x = 9(1-4x)

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The distance between weather station A and the storm is  [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles, which can be calculated using the Pythagorean theorem.

The Pythagorean Theorem is an equation in geometry which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse.

Weather station A is 34 miles away from the thunderstorm located at point c. To measure the distance between weather station A and the storm, we must calculate the hypotenuse of a right triangle. The right triangle is formed by the two points of the storm and weather station A, with the 34 miles between them forming the base of the triangle. The hypotenuse of the triangle is the distance between the two points, which can be calculated using the Pythagorean theorem. The equation for the Pythagorean theorem is a² + b²= c², where a and b are the sides of the triangle, and c is the hypotenuse.

Therefore, the distance between weather station A and the storm is  [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles.

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The equation which represents the relationship between the variables is; y = 5x + 2.

As evident in the task content;

To define the variables;

Let x = amount of time in years and

y = weight of the carp.

Since the carp grows 5 pounds each year and initially weighs 2 pounds.

By the slope-intercept form equation;

y = mx + c;

Where,

m = 5 pounds

c = 2 pounds

Therefore, the required relationship which represents the situation is; y = 5x + 2.

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The simplified value of the expression "273- 8198- 274+ 8200 is 1.

A Numerical Expression is a combination of numbers and mathematical operations such as addition, subtraction, multiplication, and division that can be evaluated to a single numerical value.

We have to evaluate the expression 273 - 8198 - 274 + 8200, step by step,

Step(i) : We start with the leftmost operation, which is the subtraction of 8198 from 273.

⇒ 273 - 8198 = -7925

Step(ii) : Next, we have to subtract 274 from the result of the step(i) ,

⇒ -7925 - 274 = -8199

Step(iii) : We add 8200 to the result of the step(ii),

⇒ -8199 + 8200 = 1

Therefore, the simplified value is 1.

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Answer:

D. The other solution to function g is 9 + √2i

Step-by-step explanation:

The roots of a quadratic equation of the form ax² + bx + c = 0

are

[tex]x = -\dfrac{b}{2a} + \dfrac{\sqrt{b^2-4ac}}{2a}\\and\\x = -\dfrac{b}{2a} - \dfrac{\sqrt{b^2-4ac}}{2a}\\[/tex]

If one of the roots is 9 - √2i then
[tex]-\dfrac{b}{2a} = 9[/tex]

and

[tex]\dfrac{\sqrt{b^2-4ac}}{2a} = 2i[/tex]

So if one root is 9 - √2i then the other root must be 9 -+ 2i

This is answer choice D

Answer:

the answer is -2

Step-by-step explanation:

A square is a base of a square​ pyramid.

A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called a vertex) is called a square pyramid. It is called a pentahedron, due to its five faces.

A square base and four triangles joined at the vertex make up a square pyramid. It has a square base and triangular side faces with a central vertex.

A square pyramid has three components.

Properties of a Square Pyramid:

Let's go through the attributes we looked at in the graphic above. The definition of a pyramid is the source of all these characteristics.

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Complete question:

what is a base of a square​ pyramid?

Therefore, the total tax owed by a Single filer with a taxable income of equation $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.

When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.

Assuming that the taxable income of $57,000 is for the tax year 2021 and the person is filing as Single, we can use the following marginal tax rates to compute the tax owed:

Tax Rate Taxable Income Range

10% $0 - $9,950

12% $9,951 - $40,525

22% $40,526 - $86,375

24% $86,376 - $164,925

32% $164,926 - $209,425

35% $209,426 - $523,600

37% $523,601 or more

To compute the tax owed, we need to apply each tax rate to the corresponding portion of the taxable income and add up the results. Here's how we can do that:

The first $9,950 of taxable income is taxed at 10%, so the tax on this portion is $9950 x 0.1 = $995.

The next $30,575 ($40,525 - $9,950) of taxable income is taxed at 12%, so the tax on this portion is $30,575 x 0.12 = $3,669.

The remaining $17,475 ($57,000 - $40,525) of taxable income is taxed at 22%, so the tax on this portion is $17,475 x 0.22 = $3,844.50.

Therefore, the total tax owed by a Single filer with a taxable income of $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.

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Answer:

Step-by-step explanation:

Firstline = 33%

Second line = 36%

Answer:

Firstline = 33%

Second line = 36%

Step-by-step explanation:

We have to, the polynomial [tex]y^{(2)}+49.[/tex] is not factorable.

The given polynomial is [tex]y^{(2)}+49.[/tex]

This polynomial is not factorable because there are no two numbers that can be multiplied together to give a product of 49 and a sum of 0.

In other words, there are no two numbers that can be multiplied together to give 49 and added together to give 0. This means that the polynomial is not factorable.

Therefore, the answer is "not factorable".

In conclusion, the polynomial [tex]y^{(2)}+49[/tex] is not factorable.

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To solve the equation x^(3) = -13, we need to take the cube root of both sides of the equation. The cube root of x^(3) is x, and the cube root of -13 is -2.3513 (rounded to 4 decimal places). Therefore, the solution to the equation is x = -2.3513.

Here are the steps to solve the equation:

1. Start with the equation x^(3) = -13
2. Take the cube root of both sides of the equation: (x^(3))^(1/3) = (-13)^(1/3)
3. Simplify the left side of the equation: x = (-13)^(1/3)
4. Calculate the cube root of -13: x = -2.3513 (rounded to 4 decimal places)

So the solution to the equation is x = -2.3513.

Note: The original question had some typos and irrelevant parts, so I ignored those and focused on the main equation to solve.

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The researcher's study aims to examine how exercise and diet affect weight loss. The researcher collected data from 12 volunteers with similar weights and health conditions and randomly assigned them to one of three programs: Program I with diet only, Program II with exercise only, and Program III with a combination of diet and exercise. After three months, the weight loss of each participant was recorded and summarized. The researcher wishes to carry out nonparametric tests at a significant level of 0.05 to examine the effectiveness of the three programs and to compare the effectiveness of Program III to Program I.

a) To examine the effectiveness of the three programs, we can use the Kruskal-Wallis test, a nonparametric test that compares the medians of three or more groups. The null hypothesis is that the medians of the three programs are equal, and the alternative hypothesis is that at least one of the medians is different. We can use the R function kruskal.test() to carry out the test:

```
> weight_loss <- c(2,0,1,1,1,2,1,3,2,1,4,4)
> program <- factor(c(rep("I",4), rep("II",3), rep("III",5)))
> kruskal.test(weight_loss ~ program)
```

The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of the three programs.

b) To compare the effectiveness of Program III to Program I, we can use the Wilcoxon rank-sum test, a nonparametric test that compares the medians of two groups. The null hypothesis is that the medians of Program III and Program I are equal, and the alternative hypothesis is that the medians are different. We can use the R function wilcox.test() to carry out the test:

```
> weight_loss_I <- c(2,0,1,1)
> weight_loss_III <- c(3,2,1,4,4)
> wilcox.test(weight_loss_I, weight_loss_III)
```

The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of Program III and Program I.

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Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.

an arrangement of elements that faithfully represent an angle. The first number on a graph indicates the distance along, while the second number indicates the distance up or down. The point (12,5), for instance, is situated 12 below and 5 above.

A sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.

Explanation:

First, we need to reflect the original triangle RST across the y=x line. This will result in a new triangle that is congruent to the original one but with its vertices in different positions. The new vertices will be R(-1, -3), S(-1, -1), and T(-5, -4).

Next, we need to rotate this new triangle 90 degrees clockwise about the origin. This will result in another new triangle that is congruent to the previous one but with its vertices in different positions. The new vertices will be R'(3, -3), S'(3, -1), and T'(-1, -4), which are the vertices of △R′S′T′.

Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.

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Answer: a = 20°

Step-by-step explanation:

     We know that a straight line is equal to 180 degrees and that the little box represents 90 degrees. We will write an equation to solve.

               a = 180° - 90° - 70°

               a = 20°

Answer:

20 degrees

Step-by-step explanation:

Straight Angle: 180 degrees

You know that there is a right angle which is 90 degrees. You can subtract 180 by 90 to get 90. Then you are given an angle measurement of 70 degrees. Subtract 70 from 90 to get 20.

20 is the measure of the missing angle

The correlation coefficient, denoted by r, tells us how closely data in a scatterplot fall along a straight line. The closer that the absolute value of r is to one, the better that the data are described by a linear equation. If r =1 or r = -1 then the data set is perfectly aligned. Data sets with values of r close to zero show little to no straight-line relationship.

Due to the lengthy calculations, it is best to calculate r with the use of a calculator or statistical software. However, it is always a worthwhile endeavor to know what your calculator is doing when it is calculating. What follows is a process for calculating the correlation coefficient mainly by hand, with a calculator used for the routine arithmetic steps.

Answer:

a) The height of the building is 382 feet.

b) The rock is 382 feet above the ground at its highest point.

c) It takes the rock 3.25 seconds to reach a height of 200 feet.

d) Tt takes the rock 4.76 seconds to hit the ground.

Step-by-step explanation:

The function that models the distance (in feet) between the rock and the ground t seconds after it is thrown is a quadratic function.

As the leading coefficient of the quadratic function is negative, it is a parabola that opens downwards.

The rock is thrown from the top of the building. Therefore, the height of the building is the value of d(t) when t = 0. This is the y-intercept of the graphed function.

Substitute t = 0 into the given function:

[tex]\begin{aligned}\implies d(0)&=-16(0)^2-4(0)+382\\&=0+0+382\\&=382\; \sf feet \end{aligned}[/tex]

Therefore, the height of the building is 382 feet.

The highest point of the rock is the height of the building, since the rock is thrown down from the top.

Therefore, the rock is 382 feet above the ground at its highest point.

This can be proven by finding the vertex of the graph of the function.

The vertex (maximum point) of the graphed function is (-0.125, 382.25).

As the x-value of the vertex is negative, and time can only be positive, the path of the rock is on a downwards trajectory when t ≥ 0. Therefore, the highest point is the point at which the rock is thrown.

To calculate how long it takes for the rock to reach a height of 200 feet, substitute d(t) = 200 into the given function and solve for t.

[tex]\begin{aligned}\implies -16t^2-4t+382&=200\\-16t^2-4t+182&=0\\-2(8t^2+2t-91)&=0\\8t^2+2t-91&=0\\8t^2+28t-26t-91&=0\\4t(2t+7)-13(2t+7)&=0\\(4t-13)(2t+7)&=0\\\\\implies 4t-13&=0 \implies t=\dfrac{13}{4}=3.25\; \sf s\\\implies 2t+7&=0 \implies t=-\dfrac{7}{2}=-3.5\; \sf s\end{aligned}[/tex]

As time is positive, t = 3.25 s only.

Therefore, it takes the rock 3.25 seconds to reach a height of 200 feet.

The rock will hit the ground when d(t) = 0.

Therefore, to calculate how long it takes for the rock to hit the ground, substitute d(t) = 0 into the given function:

[tex]\implies -16t^2-4t+382=0[/tex]

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Solve for t using the quadratic formula.

[tex]\implies t=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(-16)(382)}}{2(-16)}[/tex]

[tex]\implies t=\dfrac{4 \pm \sqrt{24464}}{-32}[/tex]

[tex]\implies t=-\dfrac{4 \pm \sqrt{16 \cdot 1529}}{32}[/tex]

[tex]\implies t=-\dfrac{4 \pm \sqrt{16} \sqrt{1529}}{32}[/tex]

[tex]\implies t=-\dfrac{4 \pm 4\sqrt{1529}}{32}[/tex]

[tex]\implies t=-\dfrac{1 \pm \sqrt{1529}}{8}[/tex]

[tex]\implies t=-5.01280...,4.76280...[/tex]

As time is positive, t = 4.76 s only.

Therefore, it takes the rock 4.76 seconds to hit the ground.

The structure has a 382-foot height. The rock's highest peak is 39 1/2 feet high, or 195.5 feet. The time it takes for the rock to touch the ground is roughly 6.289 seconds.

In arithmetic, we use angles and distance to determine an object's height. The distance between the items is measured horizontally, and the height of an object is determined by the angle of the top of the object with respect to the horizontal.

By setting t = 0, we can determine the rock's starting height:

d(0) = -16(0)^2 - 4(0) + 382

= 382

The highest point of the rock occurs at the vertex of the parabolic route, which is determined by the formula t = -b/2a

where a = -16 and b = -4.

t = -(-4) / 2(-16) = 1/8

d(1/8) = -16(1/8)^2 - 4(1/8) + 382

= 391/2

The equation d(t) = -16t^2 - 4t + 382 = 200 for t:

-16t^2 - 4t + 382 = 200

-16t^2 - 4t + 182 = 0

4t^2 + t - 45.5 = 0

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Answer:

59400

Step-by-step explanation:

59407

4 is the hundredth

0 is the number before 4 so it doesn't round up

so it's 59400

Answer:

59,400

Step-by-step explanation:

If it were 59,450 then it would be 59,500 but it is 59.407 witch would mean we are rounding down to 59,400

Answer:

Let's assume that the number of text messages sent in a day is x. Then the cost of Michelle's phone plan is:

Cost of Michelle's plan = 0.22x

And the cost of Jeff's phone plan is:

Cost of Jeff's plan = 0.12x + 1

We want to find the number of text messages for which the two plans have the same cost. So we can set the two expressions for the cost equal to each other and solve for x:

0.22x = 0.12x + 1

0.1x = 1

x = 10

Therefore, for 10 text messages per day, the cost of Michelle's plan and Jeff's plan will be the same.

We can also verify this by plugging x = 10 into the two expressions for the cost:

Cost of Michelle's plan = 0.22(10) = $2.20

Cost of Jeff's plan = 0.12(10) + 1 = $2.20

So the cost of the two plans is indeed the same for 10 text messages per day.

Answer:

Step-by-step explanation:

cost m = 0.22x

cost j = 0.12x+1

0.22x=0.12x+1

0.1=1

x=10

cost m = 0.22(10) = $2.20

cost J =0.12(10)+1=$2.20

So the answer is 10