Data plans from phone company A costs $50.00 for 10G. Company B charges $65.00 for 12 G. Which is the better rate? PLEASE Show your work!!!!

The minimum sample size need for the given condition is 14

What is Confidence Level in Statistics?

The proportion of likelihood, or certainty, that the confidence interval will include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.

Solution:

The minimum sample sixe required when,

Confidence Level = 99%

Variance = 50%

Generally going through the table

Minimum sample size is

X = 14

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Answer:

The possible dimensions are;

If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units

Step-by-step explanation:

Let;

Length of Rectangle A be a

Width of Rectangle A be b

Length of Rectangle B be c

Width of Rectangle B be d

Thus;

Area of Rectangle A = a × b

Area of Rectangle B = c × d

We are told that the area of Rectangle A is twice the area of Rectangle B:

Thus;

2cd = ab - - - - - eq. 1

perimeter of Rectangle A = 2a + 2b

perimeter of Rectangle B = 2c + 2d

We are told that the perimeter of Rectangle A is 20 units greater than the perimeter of Rectangle B. Thus, we now have;

20 + 2c + 2d = 2a + 2b - - - - eq. 2

We have 4 unknowns which are (a, b, c and d) but only 2 equations, so we need to reduce to 2 unknown variables and calculate the other ones. In this way, one of the infinite solutions is obtained.

Let's assume that c = 1 and d = 2, we obtain:

From eq 1, we have;

2 * 1 * 2 = a*b

ab = 4 or a = 4/b

From eq 2, we have;

20 + 2(1) + 2(2) = 2a + 2b

26 = 2a + 2b

Putting a = 4/b into this, we have;

26 = 2(4/b) + 2b

Multiply through by b to get;

26b = 8 + 2b²

So,we have;

2b² -26b + 8 = 0

Using quadratic formula for this,

b = 0.315 or 12.685

When, b = 12.685, a = 4/12.685 = 0.315

When, b = 0.315, a = 4/0.315 = 12.685

So, the possible dimensions are;

If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units

Answer:

18 ft^2

Step-by-step explanation:

1^2=1

1*6=6

6*3=18

Answer: 18 square feet.

Step-by-step explanation:

You can find the surface area of the ice cubes by taking the area of each square side and multiplying it by 6.

1 * 1 = 1, so each side is 1 square foot.

There are six sides on a cube, so each ice cube has a surface area of six feet squared.

There are three ice cubes there, so 3 * 6 = 18 square feet.

Three ice cubes have a surface area of 18 feet squared.

Half-life of the radioactive material is approximately 3.07 years, rounded to two decimal places.

We need to find the half-life (h) of the radioactive material using the given formula:

\(y = yo (0.5)^{t/h\)

Here are the provided values:
y = 21 grams
yo = 565 grams
t = 9 years

Let's plug these values into the formula:

\(21 = 565 * (0.5)^{9/h\)

Now, we will solve for h step by step.

1. Divide both sides by 565:

\(21/565 =\) \((0.5)^{9/h\)

2. Simplify the left side:

\(0.03717 ≈ (0.5)^{9/h\)

3. Take the logarithm of both sides (use base 0.5):

\(log_0.5(0.03717) = log_0.5((0.5)^{9/h\)

4. Use the logarithm property \(log_a(a^x) = x\)

log_0.5(0.03717) = 9/h

5. Solve for h:

h = 9 / log_0.5(0.03717)

6. Calculate the value:

h ≈ 3.07 years

The half-life of the radioactive material is approximately 3.07 years, rounded to two decimal places.

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On a number line, an absolute value equation that has the given solution set is |m - 4| = 2.

By critically observing the given question, we can infer and logically deduce that the solution sets for this absolute value equation is given by:

m = {2, 6}

Next, we would calculate the mean of the solution sets as follows:

m₁ = (2 + 6)/2

m₁ = 8/2

m₁ = 4.

Also, we would calculate the difference in the solution sets as follows:

m₂ = (6 - 2)/2

m₂ = 4/2

m₂ = 2.

Mathematically, the absolute value equation is given by:

|m - m₁| - m₂ = 0

|m - 4| - 2 = 0

|m - 4| = 2.

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Answer:

y=2/3x -7

Step-by-step explanation:

4x -6y=42

-4x     = -4x +42

     -6y= -4x + 42

      -6     -6     -6      divide both sides by -6

        y= 4/6x -7           simplify

        y= 2/3x -7

To simplify the expression (f(7+h) - f(7))/h, we need to substitute the given function f(x) = 1/(x+3) into it. Let's calculate step by step:

f(7+h) = 1/(7+h+3) = 1/(h+10)

f(7) = 1/(7+3) = 1/10

Now, we substitute these values into the expression:

(f(7+h) - f(7))/h = (1/(h+10) - 1/10)/h

To simplify this expression, we need to find a common denominator. The common denominator is 10(h+10), so let's adjust the fractions:

= (10/(10(h+10)) - (h+10)/(10(h+10)))/h

Combining the fractions:

= (10 - (h+10))/(10(h+10))/h

= (10 - h - 10)/(10(h+10))/h

Simplifying the numerator:

= (-h)/(10(h+10))/h

= -h/(10(h+10))/h

Now, we can simplify further by canceling out the h terms:

= -1/(10(h+10))

Comparing this with the desired form -1/(ah+b), we can see that:

a = 10

b = 10

Therefore, the quotient (f(7+h) - f(7))/h can be simplified to -1/(10h+10), with a = 10 and b = 10.

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Answer:

21.5

Step-by-step explanation:

Make sure they are in order.

A median is basically (or literally) the number in the middle of the data set.

In this case, it is 19 and 24. To get the middle number, you have to:

Add the two numbers and divide them by 2.

19 + 24 = 43

43/2 = 21.5

Finding the union of the sets A and C is the first step in solving P(A U C). Since set C only contains the number 6, the union of A and C has the elements 1, 2, 3, 4, and 6. A U C thus equals 1, 2, 3, 4, and 6.

The power set of A U C, which comprises all conceivable subsets of 1, 2, 3, 4, and 6, must then be located. If all conceivable subsets are listed, the power set of A U C, designated as P(A U C), will be discovered.

P(A U C) = { {}, {1}, {2}, {3}, {4}, {6}, {1,2}, {1,3}, {1,4}, {1,6}, {2,3}, {2,4}, {2,6}, {3,4}, {3,6}, {4,6}, {1,2,3}, {1,2,4}, {1,2,6}, {1,3,4}, {1,3,6}, {1,4,6}, {2,3,4}, {2,3,6}, {2,4,6}, {3,4,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,6}, {1,3,4,6}, {2,3,4,6}, {1,2,3,4,6}}.

There are 31 subsets in the power set P(A U C) that result from the union of sets A and C.

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Answer:

CA=6x-24 and BD = 2x+8

Find CE

CA=BD => 6x-24=2x+8 => x=8

CE=1/2(CA) or 1/2(BD) => 1/2(6x-24)=12

CE=12

CA=24

BD=24

Step-by-step explanation:

Answer:

6 yd

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The parameterization of the ellipse in a counterclockwise manner is x = 3cos(t) y = 2sin(t) where t varies from 0 to 2π.

One common way to parameterize an ellipse is to use trigonometric functions such as sine and cosine. We can write the equation of the ellipse as:

4x² + 9y² = 36

We can then use the following parameterization:

x = 3cos(t) y = 2sin(t)

where t is the parameter that varies between 0 and 2π, traversing the ellipse once in a counterclockwise manner.

To see why this parameterization works, let's substitute x and y into the equation of the ellipse:

4(3cos(t))² + 9(2sin(t))² = 36

Simplifying this equation gives:

36cos²(t) + 36sin²(t) = 36

Which is true for any value of t. This shows that our parameterization does indeed describe the ellipse 4x² + 9y² = 36.

Furthermore, we can see that when t=0, we get x=3 and y=0, which is the starting point (3,0). As t varies from 0 to 2π, x and y will trace out the ellipse exactly once in a counterclockwise manner.

Therefore, the parameterization of the ellipse 4x² + 9y² = 36 that begins at the point (3,0) and traverses once in a counterclockwise manner is:

x = 3cos(t) y = 2sin(t)

where t varies from 0 to 2π.

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The value of the expression,

F(x) + G(x) is -6x⁴ -2x³ + 8x² -x + 11.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

An expression,

F(x) = -6x⁴ + 2x² + 12

And G(x) = -2x³ + 6x² - x - 1

To solve F(x) + G(x):

F(x) + G(x)

= -6x⁴ + 2x² + 12 -2x³ + 6x² - x - 1

Simplifying,

=  -6x⁴ -2x³ + 8x² -x + 11

Therefore, the value is -6x⁴ -2x³ + 8x² -x + 11.

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The complete question:

F(x) = -6x⁴ + 2x² + 12

And G(x) = -2x³ + 6x² - x - 1

Find out, F(x) + G(x)?

Answer:

{ - 2, 10 }

Step-by-step explanation:

Given

x² - 8x = 20

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = 20 + 16, that is

(x - 4)² = 36 ( take the square root of both sides )

x - 4 = ± \(\sqrt{36}\) = ± 6 ( add 4 to both sides )

x = 4 ± 6

Thus

x = 4 - 6 = - 2

x = 4 + 6 = 10

Answer:

d is it

Step-by-step explanation:

The expression of tan θ in terms of x for the triangle is x/√(52 - x²)

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

The right triangle

The tangent of an angle is calculated as

tan angle = opposite/adjacent

Where we have

y² = 52 - x²

This gives

y = √(52 - x²)

In this case, we have

opposite = x

adjacent = y = √(52 - x²)

So, we have

tan θ = x/√(52 - x²)

Hence, the expression of tan θ in terms of x for the triangle is x/√(52 - x²)

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The percentage of this plane that's enclosed by the pentagons is closest to: D. 56.

Since the side of the small square is a, then the area of the tile is

given by:

Area of tiles = 9a²

Note: With an area of 9a², 4a² is covered by squares while 5a² by pentagons.

This ultimately implies that, 5/9 of the tiles are covered by pentagons and this can be expressed as a percentage as follows:

Percent = 5/9 × 100

Percent = 0.555 × 100

Percent = 55.5 ≈ 56%.

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Complete Question:

The plane is tiled by congruent squares of side length a and congruent pentagons of side lengths a and a²/a, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58

Answer:

294cm

Step-by-step explanation:

6 × a² (length of side)

6 × 0.7²

6 × 0.7 × 0.7 = 2.94m

Final answer = 294cm.

Answer:

Step-by-step explanation:

(2-4x)+(2-4x)+(-2x+8)=12-10x

9514 1404 393

Answer:

  8.6 cm

Step-by-step explanation:

We notice the hypotenuse is given, and the desired length is of the side opposite the given angle.

The mnemonic SOH CAH TOA reminds you of the relevant relationship:

  Sin = Opposite/Hypotenuse

  sin(35°) = x/(15 cm) . . . . . . fill in the given information

We can multiply by 15 cm to find the value of x.

  x = (15 cm)sin(35°)

  x ≈ 8.6

_____

For those inclined to copy this answer to a different question, we suggest ...

  y = (15 cm)cos(35°) ≈ 12.3 cm

Answer: 8.603646545 or rounded to the nearest tenth 8.6

Step-by-step explanation:

you are going to have to use (sin). so,

(15)sin(35)

8.603646545 or 8.6

this is correct.

Answer:

68, 68, 44

x = 68

x - 24 = 44

Step-by-step explanation:

If you have a shape with three interior angles, it is a triangle. The three angles in a triangle add up to 180. Use this idea to write and solve an equation.

x + (x - 24) + 68 = 180

Combine like terms.

2x + 44 = 180

Subtract 44.

2x = 136

Divide by 2.

x = 68

So we can find x - 24

68 - 24 is 44.

The three angles are 68 (given), 68 (because x = 68), and 44 (because x-24)

The angles are 68, 68, and 44

We will have the following:

We will determine the decrease after 9 minutes as follows:

Here each unit in the exponent represent each half life period.

So, after 9 minutes (3 sets of the half life) there wil be 12 grams of it.

The evaluated expression is x/√(1 - x²). This expression represents the tangent of the angle whose cosine is 2x/2.

To evaluate the expression tan(cos^-1(2x/2)), let's break it down step by step:

We start with the innermost operation, which is cos^-1(2x/2). Here, 2x/2 simplifies to just x, so we have cos^-1(x).

The expression cos^-1(x) represents the inverse cosine function. It takes a value between -1 and 1 as its input and returns an angle between 0 and π (or 0 and 180 degrees) as its output.

Taking the inverse cosine of x means finding the angle whose cosine is x. So, cos^-1(x) = θ, where cos(θ) = x.

Now, we substitute cos^-1(x) with θ in the original expression, which gives us tan(θ).

The tangent function (tan) relates the ratio of the opposite side to the adjacent side of a right triangle. In this case, since we have θ, which is an angle, we can think of it as the ratio of the sine to the cosine of θ, which is sin(θ)/cos(θ).

Combining steps 4 and 5, we have tan(θ) = sin(θ)/cos(θ) = x/√(1 - x²).

Therefore, the evaluated expression is x/√(1 - x²). This expression represents the tangent of the angle whose cosine is 2x/2.

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Answer:

2 1/4

Step-by-step explanation:

\(4\frac{1}{4} - 1\frac{3}{4}\)

\(3\frac{1 - 3}{4}\)

\(2\frac{4-3}{4}\) = 21/4

1. The total distance of the race is 44 miles. 2. There are 13 female senators and 71 female members of the House of Representatives in Congress. Jane will pay $387.50 per month.

1. We are given that Mark ran half the distance and swam a quarter of the distance before starting to bike the remaining 11 miles. Let's represent the total distance of the race as "D."

The distance Mark ran is half of D, so it is D/2.

The distance Mark swam is a quarter of D, so it is D/4.

After Mark's break, he started biking the remaining 11 miles.

Since the total distance of the race is the sum of the distances Mark ran, swam, and biked, we can set up the following equation:

D/2 + D/4 + 11 = D

To solve for D, we can simplify the equation and solve for D:

Multiply the equation by the common denominator, which is 4:

2D + D + 44 = 4D

3D + 44 = 4D

Subtract 3D from both sides:

44 = D

Therefore, the total distance of the race is 44 miles.

2. In the second problem, we are given that there are 84 female officials in Congress, and the number of female members of the House of Representatives is 58 more than the number of female senators. Let's represent the number of female senators as "S" and the number of female members of the House of Representatives as "H."

We are given that the total number of female officials is 84, so we can write the equation:

S + H = 84

We are also given that the number of female members of the House of Representatives is 58 more than the number of female senators:

H = S + 58

To solve for the values of S and H, we can substitute the second equation into the first equation:

S + (S + 58) = 84

2S + 58 = 84

Subtract 58 from both sides:

2S = 26

Divide both sides by 2:

S = 13

Substitute the value of S back into the equation for H:

H = 13 + 58

H = 71

Therefore, there are 13 female senators and 71 female members of the House of Representatives in Congress.

3. In the third problem, Jane and her two friends will rent an apartment for $775 a month, but Jane will pay double what each friend does because she will have her own bedroom. Let's represent the amount each friend pays as "F" and the amount Jane pays as "J."

We are given that Jane will pay double what each friend pays, so we can write the equation:

J = 2F

The total amount they will pay is $775, so we can write the equation:

F + F + J = 775

Substituting the value of J from the first equation into the second equation:

F + F + 2F = 775

4F = 775

Divide both sides by 4:

F = 193.75

Substitute the value of F back into the equation for J:

J = 2(193.75)

J = 387.50

Therefore, Jane will pay $387.50 per month.

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Answer:

33

Step-by-step explanation:

Most of the time a number only has the least common multiple of that number multiplied by 11.

Answer:

c

Step-by-step explanation:

The required answer is $1850

It is important for Judy and Jill's cupcake shop to generate a monthly revenue of at least $1850 in order to cover their monthly expenses. By making at least this amount, they can ensure that their revenue is sufficient to cover their costs and keep the business running.

Generating more revenue than their expenses would allow them to make a profit, while generating less revenue would result in a loss. Therefore, meeting or exceeding the $1850 monthly expenses is crucial for the financial stability of their cupcake shop.

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Answer:

56 students

Step-by-step explanation:

If 40% of students who picked Jaguars are freshmen, and the total who picked it is 140 means \(140\times0.4 = 56\)

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