Solve for x. Round to the nearest tenth.
24
X
18
30

The bus tickets and price are illustrations of a quadratic function, and the maximum revenue the bus company can earn is $5107.6

The variable representation used in this scenario are:

The price is given as:

Price = $156

The number of seats is given as:

Seats = 56

When the bus is at half capacity, we have:

Seats = 28

As the price decreases by $5, the rider gains 2 more.

So, the revenue equation is:

y = (156 - 5x)(28 + 2x)

Expand

y = 4368 - 140x + 312x - 10x²

Differentiate

y' = 0 - 140 + 312 - 20x

Evaluate the sum

y' = 172 - 20x

Equate to 0

172 - 20x =0

Add 20x to both sides

20x = 172

Divide both sides by 20

x = 8.6

Substitute x = 8.6 in y = (156 - 5x)(28 + 2x)

y = (156 - 5 * 8.6)(28 + 2 * 8.6)

Evaluate

y = 5107.6

Hence, the maximum revenue the bus company can earn is $5107.6

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In circle , arc length is  18.84 ft and sector area = 75.36 ft .

What is arc?

In mathematics, an arc is referred to as a section of a circle's or curve's perimeter. The term "open curve" can also be used to describe it. The circumference, also known as the perimeter, is the measurement around a circle that defines its edge.

Length of an arc = Angle/360 * pi * diameter

                      =  135/360 * 3.14 * 16

                      = 18.84 ft

sector area = Angle/360 * π * r²

                    = 135/360 * 3.14 * 8 * 8

                   = 75.36 ft

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Equilibrium potential increases by 2.303 times when Na is increased by factor 10.

Equilibrium potential increases by 4.606 times  Na is increased by factor 100.

Equilibrium potential decreases by 4.606 times Na is decreased by factor 100.

Given,

Sodium ion

Here,

Using nernst equation,

E = RT/nF \(ln\frac{Na_{ex} }{Na^+_{in} }\)

E = 58mV

When \({Na_{ex}\) increased by a factor of 10,

E' = RT/nF ln(10 Na)/Na

E/E' = 1/ln(10)

E/E' = 1/2.303

E' = 2.303E

Thus equilibrium potential increases by 2.303 times.

Now when Na is increased by a factor of 100

E' = 4.606E

Equilibrium potential increases by 4.606 times.

Now when Na is decreased by a factor of 100

E' = 4.606E

Equilibrium potential decreases by 4.606 times.

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Complete question is attached below.

Answer:

The probablilty would prob be 1/3 of a chance

The sum in expanded form is 6 Σ (1 / i + 1) as i ranges from 1 to 6, the sum in expanded form is 6 Σ (i^3) as i ranges from 4 to 6. the sum in expanded form is n Σ (f(xi) * Δxi) as i ranges from 1 to n.

The sum 6 Σ (1 / i + 1) as i ranges from 1 to 6 can be expanded as: (1/1 + 1) + (1/2 + 1) + (1/3 + 1) + (1/4 + 1) + (1/5 + 1) + (1/6 + 1), The sum 6 Σ (i^3) as i ranges from 4 to 6 can be expanded as: 4^3 + 5^3 + 6^3.

The sum n Σ (f(xi) * Δxi) as i ranges from 1 to n represents a Riemann sum, where f(xi) represents the value of a function at a particular point xi, and Δxi represents the width of the interval.

To expand this sum, you would need specific values for n, f(xi), and Δxi. For example, if n = 4, the expanded form would look like: f(x1) * Δx1 + f(x2) * Δx2 + f(x3) * Δx3 + f(x4) * Δx4

The expansion of the sum depends on the specific values and the nature of the function being evaluated.

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Answer: y = x + 7

Step-by-step explanation:

the slope is rise / run which is 1 /1 so our slope would be 1 aka x

next is the y intercept which is 7

so the equal would be y = x + 7

Answer:

no

Step-by-step explanation:

2 · (-10) -5 < -7

-20 - 5 < -7

-25 < -7

ok

-10 -5 ≥ -6

-15 ≥ -6

false

Answer:

not a solution

Step-by-step explanation:

to determine if (- 10, 5 ) is a solution to the system of inequalities.

substitute the coordinates of the point into the left side of both inequalities and compare the result to the right side.

Both inequalities must be true for the point to be a solution.

2x - y = 2(- 10) - 5 = - 20 - 5 = - 25 < - 7 ← true

x - y = - 10 - 5 = - 15 < - 6 ← false

since both inequalities are not true then (- 10, 5 ) is not a solution

Answer: $51.48

Step-by-step explanation:

If a $52 item is marked up by 10%, its new price will be:

$52 + 10% of $52 = $52 + $5.20 = $57.20

Then, if this new price is marked down by 10%, the final price will be:

$57.20 - 10% of $57.20 = $57.20 - $5.72 = $51.48

Therefore, the final price of the item after the markup and markdown is $51.48.

Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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The least appropriate measure of central tendency for a data set that contains outliers is the mean. This is because the mean is calculated by taking the sum of all the values in the data set and dividing it by the number of values. This means that the mean is heavily influenced by outliers, as they are included in the calculation.

The median, 2nd quartile, and 50th percentile are all more appropriate measures of central tendency for a data set that contains outliers, as they are not affected by the presence of outliers. The median is calculated by taking the middle value of the data set, the 2nd quartile is calculated by taking the median of the upper half of the data set, and the 50th percentile is calculated by taking the value at the 50th percentile of the data set.

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Answer: 99/130

Payment made by any method except credit card is 95+4=99 and altogether there is three payment method including a credit card which sums up to 130.

So the probability is 99/130.

Having a rectangular pasture for the animals to graze in is something a farmer wants in order to start growing cows, horses, goats, and sheep. She has decided to purchase 7500 ft of fencing. 1875 square feet is the maximum possible area that each of the four pens will enclose.

The maximum possible area of each pen is 1875 square feet. To calculate this, first calculate the total area of the large rectangle that the farmer is enclosing. To do this, multiply the total length of the fencing (7500 feet) by the width of the fence (1 foot). This gives us 7500 square feet as the area of the large rectangle.

Next, divide the area of the large rectangle by 4 to get the area of each pen. This gives us 1875 square feet as the maximum area of each pen.

Total Area of Large Rectangle = 7500 ft x 1 ft = 7500 sq ft

Area of Each Pen = 7500 sq ft / 4 = 1875 sq ft

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Answer:

C

Step-by-step explanation:

Money lost. Keyword "lost". Ages, people, and height can't be negative. ( I guess people can be negative mentally but not physically)

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

In each empty table square, fill in the value that is computed by replacing 'n' in the rule to the left with the value of 'n' above that square.

For example:

The upper left empty square will be filled with ...

  n -5 . . . . with n replaced by 1

  1 - 5 = -4 . . . . the value that goes in the upper left square.

__

Another example:

The lower right square will be filled with ...

  4n -3 . . . . with n replaced by 100

  4·100 -3 = 400 -3 = 397 . . . . the value that goes in the lower right square

_____

Additional comment

When there are numerous table values to fill, it can be convenient to let a spreadsheet do the calculations. Here, each formula was entered once, then filled to the right.

The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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Answer:

a.   max. 25c. min.13c

b.  2:00

Step-by-step explanation:

Answer:

That's incredible.  I have that exact problem on my website.

Here is my explanation.

My website says probability = 0.131944444444445

https://www.1728.org/occupncy8.htm

Step-by-step explanation:

the 90% confidence interval estimate for the true proportion of undergraduate college students (18-23 years) with broadband internet access is approximately 0.7723 to 0.9721.

To estimate the true proportion of undergraduate college students (18-23 years) with broadband internet access, we can use the sample proportion and construct a confidence interval.

Given:

Sample size (n) = 180

Number of undergraduates with access (x) = 157

First, we calculate the sample proportion (\(\hat{p}\)):

\(\hat{p}\) = x/n = 157/180 = 0.8722

Next, we can use the formula for constructing a confidence interval for a proportion:

Confidence interval = \(\hat{p}\) ± z * √((\(\hat{p}\) * (1 - \(\hat{p}\))) / n)

Where:

\(\hat{p}\) is the sample proportion,

z is the z-value corresponding to the desired confidence level,

and n is the sample size.

For a 90% confidence level, the corresponding z-value is approximately 1.645 (obtained from the standard normal distribution table).

Substituting the values into the formula:

Confidence interval = 0.8722 ± 1.645 * √((0.8722 * (1 - 0.8722)) / 180)

Calculating the values within the square root:

√((0.8722 * (1 - 0.8722)) / 180) ≈ √(0.110 * 0.128) ≈ 0.0607

Substituting this value back into the confidence interval formula:

Confidence interval = 0.8722 ± 1.645 * 0.0607

Calculating the upper and lower bounds of the confidence interval:

Upper bound = 0.8722 + 1.645 * 0.0607 ≈ 0.9721

Lower bound = 0.8722 - 1.645 * 0.0607 ≈ 0.7723

Therefore, the 90% confidence interval estimate for the true proportion of undergraduate college students (18-23 years) with broadband internet access is approximately 0.7723 to 0.9721.

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Answer:

Step-by-step explanation:

32000 ÷ 8 = 4000boxes

Answer:

4000

Step-by-step explanation:

32000÷8 because 32÷8 is 4 but instead of '32',they changed it to '32000' to trick you're brain

Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

\(C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}\)

      \(=142506\)

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

\(\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}\)

where;

\(\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}\)

\(\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}\)

\(\mathbf{^nC_r = 142506}\)

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Answer:

y = -31.26

Step-by-step explanation:

- 0.5y - 3.25 = 12.38

add 3.25 to both sides:

- 0.5y - 3.25 + 3.25 = 12.38 + 3.25

- 0.5y = 15.63

divide both sides by -0.5:

-0.5y/- 0.5 = 15.63/- 0.5

y = -31.26

Answer:

Step-by-step explanation:

Answer:

The parallel is just when slope of line equal to slope of the other and here the 17/3 is just the y intercept

Answer:

  C. 64 = 0.80 x n; 80

Step-by-step explanation:

In this context "of" means "times." The given relation can be translated to ...

  64 is 80% of what

  64 = 0.80 × what

If we let "n" represent the number that would answer "what", then this is ...

  64 = 0.80 × n

__

Dividing by the coefficient of n, we find the value of n to be ...

  64/0.80 = n = 80

If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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Answer:

No Solution

Step-by-step explanation:

It's false there's no solution

Answer:

D

Step-by-step explanation:

Got it right on edge

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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