Aurora has a cell phone plan that charges $65 for phone service plus $12 for each gigabyte of data used each month.If her bill for September is $113, how many gigabytes of data did she use in September?

Enter your answer as a number, like this: 42

What is the question here? If you are asking what he earns daily it would be $1016.67

I hope this helps I inserted images of each of inequality of you need more please ask me in the comments. (:

Equivalent fractions are those that equal the same number.

We can apply two methods to find equivalent fractions:

Amplification: we multiply the numerator and the denominator by the same number.

Simplification: we divide the numerator and the denominator by the same number that divides them exactly.

To find out if two fractions are equivalent, we can transform them into a decimal number by dividing the numerator by the denominator.

The fractions two thirds and six ninths are equivalent because they are equivalent to the same decimal number:

\(\begin{gathered} \sf \boxed{ \frac{2}{3}} = 2 \div 3 = 0.666 \\ \\ \sf \boxed{\frac{6}{9}}= 6 \div 9 = 0.666\end{gathered}\)

We can also amplify the first fraction or simplify the second fraction:

\(\begin{gathered} \frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9} \\ \\ \sf\boxed{ \sf\frac{6}{9}} = \sf \boxed{ \sf\frac{6 \div 3}{9 \div 3} }= \sf \boxed{\frac{2}{3}} \end{gathered}\)

Answer:

Step-by-step explanation:

Ok: There are two steps.

Answer: They are both equivalent

1. Find the common multiple of both 2/3 and 6/9

The common multiple is 9, so increase 3 to the multiple!

2/3,6/9=

6/9,6/9

6/9=6/9 So The Statement is True!

2. Method 2

6/9 is not simplified. To simplify, you need to divide by a common factor.

In this case the common factor is 3.

6/9/3=

2/3=2/3

The statement is TRUE

Height of the ladder on the wall in decreasing at the rate of ≈ 6m/s

Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilizing only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.

let ym be the height of wall at  which ladder touches

Also let the foot of ladder be xm away from the wall

then by the pythagoras theorem we have ,

\(x^{2} +y^{2} =\) 64 [ length of ladder = 8 m ]

⇒ y = \(\sqrt{64 - x^{2} }\)

then , the rate of change of height (y) with respect to time (t) is given by

\(\frac{dy}{dt}=\frac{-x}{\sqrt{64 - x^{2} }} . \frac{dx}{dt}\)

it is given that \(\frac{dx}{dt}\) = 5 m/s

∴ \(\frac{dy}{dt}=\) \(\frac{-5x}{\sqrt{64 - x^{2} }}\)

now when x = 6m , we have :

\(\frac{dy}{dt} = \frac{-5 * 6}{\sqrt{64 - 6^{2} }}\)

  = -30 / 5 .3

  = -5.660377358490566

therefore height of the ladder on the wall in decreasing at the rate of ≈ 6m/s

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Angle BEC is congruent to angle DEC. The student's error lies in assuming that BC + CD = 2BC means that AB = 2BC, which is incorrect. The student concluded that AB = 2BC by incorrectly analyzing the given diagram.

The error can be explained as follows: Since EB is the perpendicular bisector of AD, AB = BD is true.

Angle BEC is congruent to angle DEC, which makes BC = CD true.

If BC + CD is added, it equals BD, which is also equal to AB. Consequently, BC + CD = AB. Also, BC + CD can be written as BC + BC = 2BC.

However, this does not imply that AB = 2BC, as the student incorrectly concluded.

It is because BC and CD are two separate line segments, and just because they have the same length does not imply that they add up to double their length.

So, the student's error lies in assuming that BC + CD = 2BC means that AB = 2BC, which is incorrect.

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The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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If the variance of a probability distribution is computed to be 4.8 grams, the standard deviation would be approximately 2.2 grams.

The standard deviation is the square root of the variance. In this case, the given variance is 4.8 grams. To find the standard deviation, we take the square root of the variance.

Using the formula, we have standard deviation = √variance. Plugging in the value of the variance, we get standard deviation = √4.8 ≈ 2.2 grams.

Therefore, the standard deviation of the probability distribution is approximately 2.2 grams, which corresponds to option b.

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A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;

(x, y)                               →            (y, -x)

Ordered pair B' (-2, 1)   →          E (1, 2)

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To find the scale factor, we just have to divide

Answer:

1.75

Step-by-step explanation:

=======================================================

Work Shown:

x = length of PQ

3x-20 = length of QS, since its 20 less than 3 times PQ

The triangles are similar (we can prove this through the AA similarity theorem), so we can set up a proportion like shown below to solve for x.

PT/RS = PQ/QS

6/8 = x/(3x-20)

6(3x-20) = 8x ..... cross multiplying

18x-120 = 8x

18x-8x = 120

10x = 120

x = 120/10

x = 12

So PQ is 12 units long.

This then means QS = 3x-20 = 3*12-20 = 36-20 = 16

Answer:

Step-by-step explanation:

Answer:

800

Step-by-step explanation:

You do 2 to the 5 power, which equals 32. Then add 13 and 12 to get 25. Then multiply 32 and 25 to get 800

The population has increased by 4.44 million

The current population of the city is 6.34 million residents

In 1914 of the city was 1.9 million residents

Therefore the population increase can be calculated by subtracting the population of residents in 1914 from the population after the year 1914, this means subtracting 1.9 million from 6.34 million

= 6.34 - 1.9

= 4.44

Hence the population increase is 4.44 million

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Point B is tangent to the circle so the angle ABC would be 90 degrees.

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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Answer:

8-2\(x^{2}\)

Step-by-step explanation:

Answer:

\(8 - |7 - 9| {x}^{3} \\ 8 - | - 2| {x}^{3} \\ 8 - 2 {x}^{3} \\ thank \: you\)

Answer:

the value of x = 9  and y =11.

Given the system of equation:

12x + 4y =152                  .......[1]

32x + 12y = 420              ......[2]

Multiply equation [1] by 3 we get;

Using distributive property:  

            ......[3]

On solving equation [2] and [3] simultaneously we get;

x = 9

Substitute the value of x= 9 in [1] to solve for y;

108 + 4y = 152

Subtract 108 from both sides we have;

108 + 4y -108 = 152- 108

Simplify:

4y = 44

Divide both sides by 4 we get;

Simplify:

y= 11

therefore, the value of x = 9  and y =11.

The solution to the system of equations will be;

⇒ (2, 0)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The first equation is,

y = - 2x + 4

And, A line goes through (0, 4) and (2, 0).

Now,

For the second linear equation;

The coordinates are,

(-4, -3) (0, -1) , (2, 0) , (6, 2)

Hence, The equation of line passes through the points (-4, -3) and (0, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - (-3)) / (0 - (-4))

m = 2 / 4

m = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - (-3)= 1/2 (x - (-4))

⇒ y + 3 = 1/2 (x + 4)

⇒ y = 1/2x + 2 - 3

⇒ y = 1/2x - 1

Now, We find the value of system of equations;

y = - 2x + 4

y = 1/2x - 1

Solve both above equation, we get;

1/2x - 1 = - 2x + 4

1/2x + 2x = 4 + 1

5/2x = 5

x = 2

And, y = 1/2 (2) - 1 = 0

Thus, The solution to the system of equations will be;

⇒ (2, 0)

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Answer:

A

Step-by-step explanation:

The probability that a person with periodontal disease will have a heart attack is 45.9%.

To find the probability, we need to use Bayes' theorem, which relates the probability of having a heart attack given that the person has periodontal disease (P(A|B)) to the probability of having periodontal disease given that the person had a heart attack (P(B|A)), the probability of having a heart attack (P(A)), and the probability of having periodontal disease (P(B)):

P(A|B) = P(B|A) * P(A) / P(B)

Using the given information, we have:

P(B|A) = 0.77 (77% of heart attack patients have periodontal disease)

P(A) = 0.14 (14% probability of heart attack)

P(B) = 0.3 (30% of healthy people have periodontal disease)

Plugging these values into the formula, we get:

P(A|B) = 0.77 * 0.14 / 0.3 = 0.459 or 45.9%

Therefore, if someone has periodontal disease, the probability that they will have a heart attack is 45.9%.

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Answer:

I believe it is 28 beads.

Step-by-step explanation:

Answer: 6 Painters

Step-by-step explanation:

Total painters needed to paint 7-room house = 3 painters

Rooms painted by each painter = 3/7

Total painters needed to paint 14-room house = 3/7×14

= 42/7

= 6 painters

Therefore it will require 6 painters to paint 14-room house

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Answer:

Step-by-step explanation:

Answer:

\(\huge\boxed{\bf\:E) \: \: 31.4 \: \:feet}\)

Step-by-step explanation:

Since the tetherball is in the centre of the circle, any distance from it to the edge of the circle will be its radius. So, radius (r) = 5 ft.

Now, the formula for the cirumference of a circle = 2πr

Circumference of the circle

= 2πr

= 2 × 3.14 × 5                      [π = 3.14]

= 31.4 feet (option E)

\(\rule{150pt}{2pt}\)

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

\(\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}}\diamond\)

          What is the circumference of the circle? (Its radius is 5 ft)

\(\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond\)

The distance from the tetherball pole to the edge of the circle is the radius of the circle; we're given that it's 5 feet (ft).

We're asked to find the circumference of the circle, which can be found using the following formula:-

❖  \(\sf{C=2\pi r}\)

Where:-

Substitute 5 for r:-

\(\sf{C=2\pi (5)}\)

On simplification,

\(\sf{C=10\pi}\)

On further simplification,

\(\sf{C=31.4\:feet}\)

So we conclude that the right option is:-

\(\checkmark\dashrightarrow\bigstar\boxed{\boxed{\bold{Option\:E}}}\bigstar\dashleftarrow\checkmark\)

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

The required percentage yield for the reaction when theoretical yield and actual yield are given is calculated to be 85.5 %.  

The maximum mass that can be generated when a particular reaction occurs is referred to as theoretical yield.

Theoretical yield is given as mt = 9.23 g

The actual amount of product recovered is given as ma = 7.89 g

We must comprehend that in order to calculate the reaction's percent yield, we must divide the total amount of product recovered by the utmost amount that can be recovered. If we multiply by 100%, we can represent this fraction as a percentage.

Percentage yield = ma/mt × 100 = 7.89/9.23 × 100 = 85.5 %

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Answer:

x=-5 y=6

Step-by-step explanation:

y-3x=21

y-3x+3x=21+3x

y=3x+21

x-5y=-35

x-5(3x+21)=-35

x-15x-105=-35

-14x-105=-35

-14x-105+105=-35+105

-14x=70

x=-5

y-3(-5)=21

y+15=21

y+15-15=21-15

y= 6

Answer:

x=5

y=6

Step-by-step explanation:

That is the answer