CyberCafe charges a computer station rental fee of $5 plus $0.20 for each quarter hour spent surfing. Which expression represents the total amount Carl will pay to use a computer station for three and a half hours?

Area of a sector AOM = ∅/360 × πr²

                                 = 32/360 × π × 6²

                                 = 16/5π or 10.05

Answer:

The larger canister has 8 times the volume and 4 times the volume of the smaller one.

Step-by-step explanation:

The smaller canister has a diameter of 9 cm (radius = 4.5 cm) and height of 12 cm.

The larger canister has double the diameter and height of the smaller one. The diameter of the larger canister is 18 cm (radius = 9 cm) and height of 24 cm.

The canisters are in the shape of a cylinder.

The volume of a cylinder is given as:

\(V = \pi r^2h\)

The surface area of a cylinder is given as:

A = 2πr(r + h)

SMALLER CANISTER

Volume = π * 4.5 * 4.5 * 12 = 763.41 cubic centimetres

Area = 2 * π * 4.5(4.5 + 12) = 2 * π * 4.5 * 16.5 = 466.53 square centimetres

LARGER CANISTER

Volume = π * 9 * 9 * 24 = 6107.26 cubic centimetres

Area = 2 * π * 9(9 + 24) = 2 * π * 9 * 33 = 1866.11 square centimetres

By reason of comparison, the larger canister has 8 times the volume and 4 times the volume of the smaller one despite having double the dimensions.

Answer:

Yeah, what they said above.

Step-by-step explanation:

Answer: x = -3

Step-by-step explanation: You isolate the variable by dividing each side by factors that don't contain the variable.

The value of x after solving the given equation gives x = -3.

Given equation is,

7.5x + 0.5 = 2/3 (6x - 15)

We have to find the value of x after solving the given equation.

For that, we have to operate together the like terms.

Using distributive property, the right hand side of the equation becomes,

2/3 (6x - 15) = (2/3 × 6x) - (2/3 × 15)

                    = 4x - 10

Substituting this to the right hand side,

7.5x + 0.5 = 4x - 10

Taking the like terms on one side,

7.5x - 4x = -10 - 0.5

3.5x = -10.5

Dividing both sides by 3.5, we get,

x = -3

Hence the value of x is -3.

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The sum of all the perfect squares between $15$ and $25$, inclusive, minus the sum of all the other integers between $15$ and $25$, inclusive, is \($-164$\).

To find the sum of all the perfect squares between $15$ and $25$, we need to list them out: $16$, $25$. The sum of these perfect squares is $16+25=41$.

To find the sum of all the other integers between $15$ and $25$, we can use the formula for the sum of an arithmetic series. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. In this case, the first term is $16$ and the last term is $25$, so there are $10$ terms. The average of the first and last term is \($\frac{16+25}{2}=20.5$\). Therefore, the sum of all the other integers between $15$ and $25$ is $20.5\times 10 = 205$.

Now we can subtract the sum of all the other integers from the sum of the perfect squares to get our final answer: $41-205 = -164$.

Therefore, the sum of all the perfect squares between $15$ and $25$, inclusive, minus the sum of all the other integers between $15$ and $25$, inclusive, is $-164$.

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Answer:

y is the variable in that expression.

Answer:

Set your calculator to degree mode.

sin(B) = 12/13, so B = sin^-1 (12/13) = 67.4°.

The source, format, assumptions and constraints, and other facts concerning certain data are collectively called 'metadata'.

Metadata provides information about data that helps users understand and use it effectively.

Some examples of metadata include,

The date and time the data was collected.

The file format of the data.

The units of measurement used.

And any assumptions or limitations that were made during the collection or analysis of the data.

By providing metadata along with the data, users can better understand the context and quality of the data.

This can help them make more accurate and informed decisions.

Metadata is classified into three types which are known as descriptive, administrative, and structural.

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The equilibrium price is the price at which the quantity demanded equals the quantity supplied.

Looking at the graph, we can see that the demand curve intersects the supply curve at a quantity of approximately 200 million boxes. To find the corresponding equilibrium price, we need to find the price level at this quantity.

From the graph, we can observe that the price axis ranges from $20 to $40. Since the graph is not accurately scaled, we can estimate the equilibrium price to be around $30 per box based on the midpoint of the price range.

Therefore, the equilibrium price in this market is approximately $30 per box.

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Answer:

B

Step-by-step explanation:

Answer:

No, it will not change

Step-by-step explanation:

Because the size of the tank is not a factor that can be used to find the rate of change. The rate of change will continue to be 30 gallons per minute.

The average rate of change of gallons per minute is 30 gallons per minute.

No, the average rate of change of gallons per minute will not change even if the size of the tank is doubled because the size of the tank is not used to find the average rate of change.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph,

Two coordinates to find the average rate of change in gallons per minute.

(1, 30) and (3, 90).

These coordinates represent a change in the amount of water in the given unit of time.

x-coordinates is the time.

y-coordinate is the amount of water.

Now,

The average rate of change of gallons per minute:

(1, 30) = (a, b) and (3, 90) = (c, d)

= d - b / c - a

= 90 - 30 / 3 - 1

= 60 / 2

= 30

Thus

The average rate of change of gallons per minute is 30 gallons per minute.

No, the average rate of change of gallons per minute will not change even if the size of the tank is doubled because the size of the tank is not used to find the average rate of change.

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Given:

The recursive formulae.

To find:

The correct explicit formulae for the given recursive formulae.

Solution:

If the recursive formula of a GP is \(f(n)=rf(n-1), f(1)=a, n\geq 2\), then the explicit formula of that GP is:

\(f(n)=ar^{n-1}\)

Where, a is the first term and r is the common ratio.

The first recursive formula is:

\(f(1)=5\)

\(f(n)=3f(n-1)\) for \(n\geq 2\).

It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:

\(f(n)=5(3)^{n-1}\)

Therefore, the required explicit formula for the first recursive formula is \(f(n)=5(3)^{n-1}\).

If the recursive formula of an AP is \(f(n)=f(n-1)+d, f(1)=a, n\geq 2\), then the explicit formula of that AP is:

\(f(n)=a+(n-1)d\)

Where, a is the first term and d is the common difference.

The second recursive formula is:

\(f(1)=5\)

\(f(n)=f(n-1)+5\) for \(n\geq 2\).

It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:

\(f(n)=5+(n-1)5\)

\(f(n)=5+5(n-1)\)

Therefore, the required explicit formula for the second recursive formula is \(f(n)=5+5(n-1)\).

The third recursive formula is:

\(f(1)=5\)

\(f(n)=f(n-1)+3\) for \(n\geq 2\).

It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:

\(f(n)=5+(n-1)3\)

\(f(n)=5+3(n-1)\)

Therefore, the required explicit formula for the third recursive formula is \(f(n)=5+3(n-1)\).

The nth term of the given quadratic sequence is 2n².

What is quadratic sequence?

The ordered sets of numbers known as quadratic sequences are based on the rule n^2 = 1, 4, 9, 16, 25,.... (the square numbers). Every quadratic sequence has a n^2 term.

Consider, the given quadratic sequence

2, 8, 18, 32, 50, ...

we have to find nth term of this quadratic sequence ; 2 , 8 , 18 , 32, 50, ...

To find the nth term, we have to find the relation between the given terms.

here we see,

1st term = 2 = 2 × 1 × 1 = 2 × 1²

2nd term = 8 = 2 × 2 × 2 = 2 × 2²

3rd term = 18 = 2 × 3 × 3 = 2 × 3²

4th term = 32 = 2 × 4 × 4 = 2 × 4²

similarly 5th term = 2 × 5² = 2 × 25 = 100

...........

so nth term = 2 × n² = 2n²

Hence, the nth term of the given quadratic sequence is 2n².

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Answer:

In order to write the equation of a circle, we need two things their centre as well as the radius. so….diameter always intersect each other at the centre of the circle, hence after solving the equation of diameter, we get the intersecting point(x, y)=(3,2). now, we have already given one point…and as per the question circle passing through that point itself. so by applying distance formula, we can obtain the value of radius. thus we get radius 2√2. now we have required things to get the equation of a circle. we know the standard equation of circle having centre =(x1,y1) and radius = r is (x-x1)²+(y-y1)²=r² hence we can find the equation of circle by putting the coordinate (x1,y1)=(3,2) and radius =2√2 in the above mentioned standard equation.

Step-by-step explanation:

:3

To find the volume of a solid obtained by rotating a region, you'll need to use the method of disks or washers, depending on the specific problem. The terms "long answer" are not relevant to the calculation.

1. Identify the region you want to rotate and the axis of rotation.
2. Set up an integral using the method of disks or washers, depending on the given problem.
  - Disks: Use the formula V = π * ∫[R(x)]^2 dx from x=a to x=b, where R(x) is the radius of the disk and a and b are the bounds of the region.
  - Washers: Use the formula V = π * ∫([R(x)]^2 - [r(x)]^2) dx from x=a to x=b, where R(x) is the outer radius and r(x) is the inner radius.

3. Evaluate the integral to find the volume of the solid.

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The required, we can conclude that the given series converges by the Alternating Series Test.

The given alternating series is \(\sum((-1)^{k+1})/((k+5)4^k)\) for k = 1 to ∞.

To determine whether this series converges or diverges, we can use the Alternating Series Test.

The Alternating Series Test states that if a series satisfies two conditions: (1) the terms alternate in sign, and (2) the absolute value of the terms decreases as k increases, then the series converges.

In this case, we can see that the terms alternate in sign since we have \((-1)^{k+1}\) in the numerator.

To check the second condition, let's consider the absolute value of the terms: \(|((-1)^{k+1})/((k+5)4^k)|\).

As k increases, the denominator \(((k+5)4^k)\) also increases. This means the absolute value of the terms is decreasing since the numerator remains constant \((-1)^{k+1}\).

However, to determine the convergence or divergence of the series, we need to evaluate the limit of the absolute value of the terms as k approaches infinity.

\(lim (k\rightarrow\infty) |((-1)^{k+1})/((k+5)4^k)| = 0.\)

Since the limit is zero, and the terms alternate in sign and decrease in absolute value as k increases, we can conclude that the given series converges by the Alternating Series Test.

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The correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A positive correlation means that as one variable (in this case, happiness) increases, the other variable (GPA) also tends to increase. The magnitude of the correlation coefficient, which ranges from -1 to 1, represents the strength of the relationship. A value of 0.90 indicates a very strong positive linear correlation, suggesting that there is a consistent and significant relationship between happiness and GPA.

This means that as the level of happiness increases among high school students, their GPA tends to be higher as well. The correlation coefficient of 0.90 suggests a high degree of predictability in the relationship between these two variables.

It is important to note that correlation does not imply causation. While a strong positive correlation indicates a relationship between happiness and GPA, it does not necessarily mean that one variable causes the other. Other factors or variables may also influence the relationship between happiness and GPA.

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Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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Sherry's commitment and love for reading allowed her to embark on a literary adventure that spanned two days. From the initial taste of 1/3 to the final bite of the remaining line 2/3, she had read the entire book, savoring every word and getting lost in the magic of storytelling.

Sherry's reading adventure began with her diving into a book, eager to explore its contents. She managed to devour a portion of the book, specifically 1/3 of it, before feeling the sweet embrace of sleep and deciding to call it a night.

The following day arrived, and Sherry's desire to unravel the remaining mysteries of the book was still burning bright within her. Determined to quench her thirst for knowledge, she dedicated herself to reading the rest of the book. With focused determination, she turned page after page, immersing herself in the story's captivating world.

As the hours ticked by, Sherry felt the satisfaction of progress. With each passing chapter, she could sense herself inching closer to the climax and resolution of the story. The characters became like old friends, and the plot twists kept her on the edge of her seat.

Finally, as the sun dipped below the horizon, Sherry turned the last page and completed the final chapter. She had done it. She had finished reading the entire book. The sense of accomplishment washed over her, accompanied by a bittersweet feeling that the journey had come to an end.

Reflecting on her reading experience, Sherry realized that she had initially read 1/3 of the book before retiring for the night. That meant there were still 2/3 of the book left for her to discover on the subsequent day. And indeed, she did just that. She dedicated her time and energy to devouring the remaining 2/3 of the book, leaving no page unturned.

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Answer:

3 kilometers

Step-by-step explanation:

divide the length value by 1000

Answer:

az-bz+3b^2-6ab+3a^2

Hope this helps

Answer:

In 75 minutes, both clocks will chime together.

Step-by-step explanation:

All you have to do is find the least common multiple of 15 and 25.

Multiples of 15:

15 x 1 = 15

15 x 2 = 30

15 x 3 = 45

15 x 4 = 60

15 x 5 = 75

Multiples of 25:

25 x 1 = 25

25 x 2 = 50

25 x 3 = 75

25 x 4 = 100

25 x 5 = 125

If you compare the two, you’ll find that 15 and 25 have a least common multiple of 75. So, in 75 minutes both clocks will chime at the same time

Answer:

perimeter: 4x+2 area: x^2+x

Step-by-step explanation:

for perimeter, you add x+x+x+x+1+1, which is 4x+2

for area, you multiply x*x+1, which would be x^2+x

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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In quadrant IV, \(\cos(A)\) is positive. So

\(\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258\)

Then by the definition of tangent,

\(\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}\)

Answer:

\(h(f(x)) =6x-2\)

Step-by-step explanation:

Given

\(f(x) = (3x-5)^3\\h(x) = 2\sqrt[3]{x}+8\)

Required

Write \(h(f(x))\) in terms of x

\(h(f(x)) = h((3x-5)^3)\)

To get \(h((3x-5)^3)\), we will replace x in h(x) with (3x-5)³ as shown:

\(h((3x-5)^3) = 2\sqrt[3]{(3x-5)^3} +8\\ h((3x-5)^3) = 2(3x-5) + 8\\ h((3x-5)^3) = 6x - 10 + 8\\ h((3x-5)^3) = 6x-2\\Hence \ h(f(x)) =6x-2\)

Hence the expression \(h(f(x))\) in terms of x is 6x - 2

Answer:

XYZ can be any number, so need the answer choices

Step-by-step explanation:

Answer:

13.60 cm

Step-by-step explanation:

Answer

x=5 y=2

Step-by-step explanation:

The volume of the solid is (7π/5) cubic units.

We have,

To find the volume of the solid obtained by rotating the region under the curve y = x³ about the line y = -1 over the interval [0,1], we can use the method of cylindrical shells.

Consider an infinitesimally thin vertical strip of width dx at a distance x from the y-axis.

The height of this strip is given by the difference between the curve

y = x³ and the line y = -1.

The height of the strip is (x³ - (-1)) = (x³ + 1).

The circumference of the cylindrical shell is given by 2πx, and the thickness of the shell is dx.

Hence, the volume of the shell is given by dV = 2πx (x³ + 1) dx.

To find the total volume, we integrate this expression over the interval [0,1]:

V = ∫ [0,1] 2πx (x³ + 1) dx.

To find the volume, we evaluate the integral:

V = ∫[0,1] 2πx (x³ + 1) dx

Let's integrate term by term:

V = 2π ∫[0,1] (\(x^4\) + x) dx

Integrating each term separately:

V = 2π [(1/5)\(x^5\) + (1/2)x²} evaluated from 0 to 1

Plugging in the limits:

V = 2π [(1/5)(\(1^5\)) + (1/2)(1²)] - [(1/5)(\(0^5\)) + (1/2)(0²)]

V = 2π [(1/5) + (1/2)] - [0 + 0]

V = 2π (7/10)

V = (14π/10)

Simplifying the fraction:

V = (7π/5)

Therefore,

The volume of the solid is (7π/5) cubic units.

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The equation Chad should program is \(y = -0.04x^2 + 20x.\)

The equation that Chad should program into his rocket launcher to win is:

\(y = -0.04x^2 + 8x\)

This is a quadratic equation in standard form, where the coefficient of x^2 is negative, indicating that the path of the rocket is a downward facing parabola. The coefficient of x^2 is -0.04, which means that the parabola is relatively flat, ensuring that the rocket will travel a horizontal distance of 20 feet when it reaches a height of 100 feet.

To sketch the rocket’s path, we can plot points on the graph of the equation. For example, when x = 0, y = 0, so the rocket starts at the origin. When x = 50, y = 200, so the rocket reaches its maximum height at x = 50 and y = 100. When x = 100, y = 0, so the rocket lands 20 feet away from the launch pad at ground level. We can connect these points to sketch the path of the rocket.

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