Hannah owns a lemonade stand. She records her transaction throughout the day to keep
track of the balance in her cash register.
The customer isn't satisfied with 3 of the cups of lemonade. Hannah gave him a refund
of $2 for each cup. Which Expression represents the change to Hannah's balance?
Choose any correct answer.
-3x2
0-2 x (-3)
2x3
-2x3

The inverse of a function can be found by swapping the numbers in each ordered pair of the function.

When you have a function with ordered pairs, the inverse of that function can be found by reversing the order of the numbers within each pair. In other words, if you have a function f(x) with ordered pairs (a, b), the inverse function, f^ (-1) (x), will have ordered pairs (b, a). This process essentially switches the input and output values of the original function.

To find the inverse of a function, simply swap the numbers in each ordered pair, resulting in the ordered pairs for the inverse function.

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We have the inequality:

Now, in order to solve, we will do as follows:

n will take all the values from -9 to 7, any number smaller than -9 will make it false and any number greater than 7 will make it false.

Now, in order to graph the solution, we will have:

An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer: 81.2

Step-by-step explanation:

Answer: The slope is 6

The attachment shows the graph of this equation.

Step-by-step explanation: It will help to put this equation in order.

We can get standard form by subtracting 2y from both sides

12x=-10+2y becomes  12x - 2y = -10

For slope-intercept form, y = mx + b,  m is the slope, b is the y-intercept

we need to isolate y on the left.  Subtract 12x from both sides.

12x - 2y = -10 becomes  -2y = -12x - 10

Then divide both sides by -2 to end up with

y = 6x + 5

The slope is m, the coefficient of the x,

That is 6 in this equation.

The inverse of f(x) = log₁₀(x) is 10ˣ.

A logarithm is an exponent to which a base must be raised to generate a given number. Expressed mathematically, x is the logarithm of n to the base a if ax = n, in which case one writes x = logₐn.

A logarithm is defined using an exponent.

aˣ = b ⇔ logₐb = x

Here, "log" stands for logarithm. The arrow's right part is read as "Logarithm of b to the base a is equal to x".

We have the function,

f(x) = log₁₀(x)

Let y = f(x)

⇒y = log₁₀(x)

⇒\(10^{y}\) = x

∴\(f^{-1}\)(x) = 10ˣ

--The given question is incomplete; the complete question is

"What is the inverse of  f(x) = log₁₀(x)?"--

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x= 2

2(2) + 5 = 9

Hope this helps!

The areas under the curve y = 1/x between x = 1 and x = 2, x = 2 and x = 3, and x = 1 and x = 3. Concludes that ln(2) < 1 < ln(3) based on the comparison of these areas.

We can use the fact that the natural logarithm function is strictly increasing to compare the values of ln(2), 1, and ln(3).

Consider the area under the curve y = 1/x between x = 1 and x = 2, x = 2 and x = 3, and x = 1 and x = 3. We can approximate these areas using rectangles with a width of 1 and a height equal to the value of the function at the left endpoint of the interval.

For the area under the curve between x = 1 and x = 2, we have:

Area ≈ base × height = 1 × 1/2 = 1/2

For the area under the curve between x = 2 and x = 3, we have:

Area ≈ base × height = 1 × 1/3 ≈ 1/3

For the area under the curve between x = 1 and x = 3, we have:

Using the properties of the natural logarithm, we can see that:

Therefore, we have:

ln(2) < 1 < ln(3)

as desired.

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Answer:

- 43

Step-by-step explanation:

f ( x ) = - 2x² + 2x - 3

To find : f ( 5 )

f ( 5 ) = f ( x )

Here,

x = 5

f ( 5 ) = - 2x² + 2x - 3

        = - 2 ( 5 )² + 2 ( 5 ) - 3

        = - 2 ( 25 ) + 10 - 3

        = - 50 + 7

f ( 5 ) = - 43

Answer:

-43

Step-by-step explanation:

oon edge

mark me brain

Answer:

Yes, by AA

Step-by-step explanation:

A triangle adds up to 180 degrees.

This means:

angle E = 180-53-60

angle E= 67 degrees

Angle E=Angle H

Angle C= Angle F

2 angles equaling to each other when comparing triangles means they are similar by AA.

Answer:

C. Yes by AA

Step-by-step explanation:

The triangles have the smae anlges, one is just smaller, but they are the same size.

Answer: y + 5 = 2 ( x + 1 ) = 2 x − y + 2 = 5

Answer:

 Slope = 4.000/2.000 = 2.000

 x-intercept = 3/2 = 1.50000

 y-intercept = -3/1 = -3.00000

Step-by-step explanation:

I hope this helped!

Answer:

Whole numbers would be a set inside the integer set, where the integer set that is not in the whole number set would be all negative integers.

Step-by-step explanation:

whole numbers are defined to be positive numbers including zero.

Answer:

256

Step-by-step explanation:

4^4^4 = 4^(4^4) = 4^256

so written in base 4, there will be 256 zeroes after a 1.

This translates to approximately 154 digits in decimal.

Just like 2^2^2 =  2^4

there will be four zeroes after a 1.

2^2^2=2^(2^2) = 2^4 = 16 = 10000 (16 in base 2).

After 3 hours Dylan and Sam will be exactly 15 miles apart .

In the question ,

it is given that ,

the speed at which Dylan is jogging in east = 4 miles per hour .

the speed at which Sam is jogging in south = 3 miles per hour .

the distance covered by Dylan is = 4t

the distance covered by Sam is = 3t

we have to find the time when they are 15 miles apart .

Since Dylan walks in east and Sam walks in South  , it forms a right triangle , so , it will satisfy the Pythagoras Theorem ,

(3t)² + (4t)² = 15²

9t² + 16t² = 225

225 = 25t²

t² = 225/25 = 9

t = 3

Therefore , the time taken will be 3 hours .

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Answer:

  A: the proposed route is 3.09 miles, so exceeds the city's limit

Step-by-step explanation:

The length of the route in grid squares can be found using the Pythagorean theorem on the two parts of the route. Let 'a' represent the length of the route to the park from the start, and 'b' represent the route length from the park to the finish. Then we have (in grid squares) ...

  a^2 = (12-6)^2 +3^2 = 45

  a = √45 = 3√5

and

  b^2 = (6 -2)^2 +4^2 = 32

  b = √32 = 4√2

Then the total length, in grid squares, is ...

  3√5 + 4√2 = 6.7082 +5.6569 = 12.3651

If each grid square is 1/4 mile, then 12.3651 grid squares is about ...

  (12.3651 squares) · (1/4 mile/square) = 3.0913 miles

The proposed route is too long by 0.09 miles.

Answer:

11.0 hours

Step-by-step explanation:

The times, recorded for a particular order are shown below:

Move time                     2.7 hours

Wait time                       26.4 hours

Queue time                   6.4 hours

Process time                  1.8 hours

Inspection time              0.1 hours

Throughput time is also known as cycle time/ manufacturing throughput time, it is the time needed to produce an item. It is the time taken for the item/product to be converted from a raw material into a product ready for use. The throughput time is the sum of the move time, queue time, process time and inspection time.

Throughput time = move time + queue time + process time + inspection time.

Throughput time = 2.7 hrs + 6.4 hrs + 1.8 hrs + 0.1 hrs = 11 hrs

The equation of the line that passes through the points (6.4, 2.6) and (5.2, 9) is y = 5.333x - 30.178

To find the equation of the line that passes through the points (6.4,2.6) and (5.2,9), we need to determine the slope (M) of the line and the y-intercept (b).

The slope of a line can be found using the formula

M = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

Using the points (6.4, 2.6) and (5.2, 9), we have:

M = (9 - 2.6) / (5.2 - 6.4)

M = (-6.4) / (-1.2)

M = 5.333

Now, we can use the point-slope form of the equation of a line, which is

y - y₁ = M(x - x₁)

where (x₁, y₁) is any point on the line and M is the slope we just calculated.

We can choose either point (6.4, 2.6) or (5.2, 9) as (x₁, y₁). Let's use (6.4, 2.6)

y - 2.6 = 5.333(x - 6.4)

Simplifying, we get:

y = 5.333x - 30.178

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Answer:

Step-by-step explanation:

4 - 0.4 = 3.6

3.6 - 0.4 = 3.2

2.8 - 0.4 = 2.4

2.4 - 0.4 = 2

2 - 0.4 = 1.6

so the next numbers in the pattern are: 2.4, 2 and 1.6

Answer:

If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal.

Step-by-step explanation:

Answer:

2x/2x+3

Step-by-step explanation:

2x(3x+2) over 6x 2squared + 13 x 6 = 2x (3x+2) over (3x+2) (2x+3)

a) The range of the number of cans found is: 8

b) The range of the number of bottles found is: 5

The range of a dataset is basically  the simplest measurement of the difference between values in a data set. To find the range, we will simply subtract the lowest value from the greatest value while ignoring the others.

a) The range of the number of cans found is simply the difference between the highest number of cans found and the lowest number of cans found.

Thus:

Range of number of cans = 10 - 2

Range of number of cans = 8

b) The range of the number of bottles found is simply the difference between the highest number of bottles found and the lowest number of bottles found.

Thus:

Range of number of bottles = 6 - 1

Range of number of bottles = 5

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Answer:

A

Step-by-step explanation:

So 11/25 if you multiply all of it by 4, then you get 44/100. If you convert it to a decimal you get 0.44.

9514 1404 393

Answer:

  49°

Step-by-step explanation:

The sum of angles in a triangle is 180°.

  ∠A +∠B +∠C = 180

  (x +32) +(x +41) +(3x +22) = 180 . . . . angles assumed to be in degrees

  5x +95 = 180

  5x = 85

  x = 17

  x +32 = 49 . . . . measure of ∠A

The simplified form of trigonometric expression, cosec θ / sin θ + cos θ cot θ is 1.

Given,

The trigonometric expression = cosec θ / sin θ + cos θ cot θ

We have  to simplify this expression.

For that we can use trigonometric identities.

cosec θ = 1 / sin θ

cot θ = cos θ / sin θ

We can substitute the above given identities in the expression.

Then we get,

cosec θ / sin θ + cos θ cot θ = (1 / sin θ) / (sin θ + cos θ x (cos θ/sin θ))

= (1 / sin θ) / ((sin²θ + cos²θ) / sin θ)

Cancel sin θ from both numerator and denominator.

= 1 / sin² θ + cos² θ

We know that sin² θ + cos² θ = 1

So, we get,

1 / sin² θ + cos² θ = 1 / 1 = 1

Therefore, the simplified form of  cosec θ / sin θ + cos θ cot θ is 1.

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Answer:

120 square centimeters

Step-by-step explanation:

Therefore, David had 5 wrong answers.

To find out how many wrong answers David had, we need to calculate the number of correct answers first. Since each correct answer is awarded 10 points, and David scored a total of 75 points, we can divide 75 by 10 to find the number of correct answers.

75 ÷ 10 = 7.5

Since we can't have half a correct answer, we can conclude that David had 7 correct answers.

Now, to find the number of wrong answers, we subtract the number of correct answers from the total number of questions. In this case, there were 12 questions in total.

12 - 7 = 5

Therefore, David had 5 wrong answers.

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The final expression for the given problem is (f(3+h) - f(3))/h = -h - 3.

To solve this problem, we first need to determine the value of f(3+h) and f(3):

Given \(F(x) = 4 + 3x - x^2\), we can find f(3+h) by substituting 3+h for x:

\(f(3+h) = 4 + 3(3+h) - (3+h)^2\\f(3+h) = 4 + 9 + 3h - (9 + 6h + h^2)\\f(3+h) = -h^2 - 3h + 4\)

Next, we can find f(3) by substituting 3 for x:

\(f(3) = 4 + 3(3) - (3)^2\\f(3) = 4 + 9 - 9\\f(3) = 4\)

Now we can substitute these values into the expression (f(3+h) - f(3))/h:

\((f(3+h) - f(3))/h = ((-h^2 - 3h + 4) - 4)/h\\(f(3+h) - f(3))/h = (-h^2 - 3h)/h\\(f(3+h) - f(3))/h = -h - 3\)

Therefore, the final expression for the given problem is:

(f(3+h) - f(3))/h = -h - 3

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Yes, we can conclude that there is a positive correlation between the success of college students (measured by cumulative grade point average) and the income of their respective families.

For testing whether there is a significant correlation between two variables, we need to calculate the correlation coefficient r.

Given that the sample size (n) is 20, and the correlation coefficient (r) is 0.40. The test statistic value, t can be calculated using the formula:

(\(t = (r * \sqrt{n - 2} /\sqrt{1 - r^2} )\))

Therefore, substituting the values,

(\(t = (0.40 *\sqrt{20 - 2} / \sqrt{1 - 0.4^2} )\))

= 2.53

Using the t-table with 18 degrees of freedom (df = n - 2 = 20 - 2 = 18) at a significance level of 0.01, we find that the critical value of t is 2.878.

Since the calculated value of t is less than the critical value of t, we fail to reject the null hypothesis.

Therefore, we can conclude that there is a positive correlation between the success of college students (measured by cumulative grade point average) and the income of their respective families.

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The ferryman should transport the goat first, then return alone to bring the wolf, leaving the goat on the right bank. Finally, he should transport the cabbage and leave it with the wolf.

In order to solve this puzzle, the ferryman must make a series of careful moves to ensure the safety of the wolf, goat, and cabbage. The first step is to transport the goat to the right bank, leaving it there. The ferryman then returns to the left bank alone.

He takes the wolf across the river, but before leaving it on the right bank, he brings the goat back to the left bank. Now, the goat and cabbage are on the same side, while the wolf remains on the right bank.

The ferryman transports the cabbage to the right bank, leaving it there, and then returns alone to the left bank. Finally, he takes the goat across the river one last time, completing the puzzle. This sequence of moves ensures that the wolf and goat are never left alone together, nor are the goat and cabbage.

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Answer:

a) Mean shoe size = 7.8

b) 8.8, 9.8 and 10.8

c) see attached

d) Shoe size

Step-by-step explanation:

\(\sf Mean \ \mu= 7.8\)

\(\sf Standard \ deviation \ \sigma= 1\)

Therefore,

\(\sf 1 \sigma=\mu+1 \sigma=7.8+1=8.8\\\sf 2 \sigma=\mu+2 \sigma=7.8+2 \cdot 1=9.8\\\sf 3 \sigma=\mu+3 \sigma=7.8+3 \cdot 1=10.8\)