Raymond wants to know the costs of buying different numbers of songs for his mp3 player. The cost of each song is the same.

Answer:

4 1/24

Step-by-step explanation:

1 2/3 +2 3/8 = 5/3 +2 3/8 = 5/3 + 19/8 = 97/ 24 =4 1/24

Answer:

x= -1/5

hope this helps you

Answer:

x = - \(\frac{1}{5}\), x = 5

Step-by-step explanation:

Given

\(\frac{x+1}{x-1}\) - \(\frac{x-1}{x+1}\) = \(\frac{5}{6}\)

Multiply through by 6(x - 1)(x + 1) [ the LCM of the denominators ]

6(x + 1)² - 6(x - 1)² = 5(x - 1)(x + 1) ← expand factors and simplify

6(x² + 2x + 1) - 6(x² - 2x + 1) = 5(x² - 1)

6x² + 12x + 6 - 6x² + 12x - 6 = 5x² - 5

24x = 5x² - 5 ( subtract 24x from both sides )

0 = 5x² - 24x - 5 ← in standard form

0 = (x - 5)(5x + 1) ← in factored form

Equate each factor to zero and solve for x

5x + 1 = 0 ⇒ 5x = - 1 ⇒ x = - \(\frac{1}{5}\)

x - 5 = 0 ⇒ x = 5

Answer:

227.50

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

Diagram with vectors a, b, -3a, a+6, and a-6, including their lengths.

5. The surface in \(\(\mathbb{R}^3\)\) is described by \(\(z = x^2 + y^2 + 1\)\).

6. The cosine of the angle between the vectors (1, 2, 3) and (0, 1, 4) is \(\(\frac{14}{\sqrt{14}\sqrt{17}}\).\)

The angle between the vectors (1, 2, 3) and (0, 1, 4) is approximately 34.94 degrees.

7. The area of the parallelogram spanned by (1, 2, 3) and (0, 1, 4) is 9, and the volume of the parallelepiped spanned by those vectors and (3, 2, 6) is 22.

5. To describe and sketch the surface in \(\(\mathbb{R}^3\) given by \(z = x^2 + y^2 + 1\),\) we can observe that this equation represents a paraboloid in the z-axis.

The surface opens upwards, and its height (z-coordinate) increases as the distance from the origin (x and y coordinates) increases. We can plot this surface using a 3D graphing tool or by plotting points manually.

6. To find the cosine of the angle between the vectors \(\((1, 2, 3)\) and \((0, 1, 4)\),\) we can use the dot product formula:

\(\[ \cos(\theta) = \frac{\mathbf{a} \cdot \mathbf{b}}{\|\mathbf{a}\| \|\mathbf{b}\|} \]\)

where \(\(\mathbf{a}\) and \(\mathbf{b}\) are the given vectors, \(\cdot\) denotes the dot product, and \(\|\mathbf{a}\|\) and \(\|\mathbf{b}\|\)\) are the magnitudes (lengths) of the vectors.

Calculating the dot product and magnitudes:

\(\[\mathbf{a} \cdot \mathbf{b} = (1 \cdot 0) + (2 \cdot 1) + (3 \cdot 4) = 0 + 2 + 12 = 14\]\[\|\mathbf{a}\| = \sqrt{1^2 + 2^2 + 3^2} = \sqrt{14}\]\[\|\mathbf{b}\| = \sqrt{0^2 + 1^2 + 4^2} = \sqrt{17}\]\)

Plugging these values into the cosine formula:

\(\[\cos(\theta) = \frac{14}{\sqrt{14} \sqrt{17}}\]\)

7. To find the area of the parallelogram spanned by the vectors\(\((1, 2, 3)\) and \((0, 1, 4)\)\), we can use the cross product. The magnitude of the cross product of two vectors gives the area of the parallelogram spanned by those vectors. Let's calculate the cross product:

\(\[\mathbf{a} \times \mathbf{b} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 2 & 3 \\ 0 & 1 & 4 \end{vmatrix} = (-8, 4, -1)\]\)

The magnitude of the cross product is:

\(\[\|\mathbf{a} \times \mathbf{b}\| = \sqrt{(-8)^2 + 4^2 + (-1)^2} = \sqrt{81} = 9\]\)

Therefore, the area of the parallelogram spanned by the vectors\(\((1, 2, 3)\) and \((0, 1, 4)\) is 9.\)

To find the volume of the parallelepiped spanned by these two vectors and (3, 2, 6), we can take the dot product of the cross product of the two given vectors with the third vector. Let's calculate:

\(\[\mathbf{a} \times \mathbf{b} \cdot \mathbf{c} = (-8, 4, -1) \cdot (3, 2, 6) = (-8 \cdot 3) + (4 \cdot 2) + (-1 \cdot 6) = -24 + 8 - 6 = -22\]\)

The absolute value of this dot product gives the volume of the parallelepiped:

\(\[\left|\mathbf{a} \times \mathbf{b} \cdot \mathbf{c}\right| = |-22| = 22\]\)

Therefore, the volume of the parallelepiped spanned by the vectors\(\((1, 2, 3)\), \((0, 1, 4)\), and \((3, 2, 6)\) is 22.\)

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Answer:

56

Step-by-step explanation:

48 ounces would feed 6 people and if 16 oz is for two people than 8 oz is for one person. So, 48 plus 8 is 56.

Answer:

reeg

Step-by-step explanation:

Answer:

Step-by-step explanation:

I’m sorry that i can’t fully help and that i answered it wrong twice i also got stuck. I hope someone else helps you and that you get an a

18 3/4 as an improper fraction is 75/4.

75/4 can be re-written as 1875/100 (multiply both sides by 25)

3/50 can be re-written as 6/100 (multiply both sides by 2)

Dividing in math is the process of finding the quotient of two numbers.

The formula for dividing two numbers is a/b = c, where a and b are the two numbers being divided and c is the quotient.

Division is a mathematical operation that is used to split a whole number into parts. It is the opposite of multiplication, which combines numbers together. The formula for division is A / B = C, where A is the dividend (the number being divided), B is the divisor (the number dividing the dividend), and C is the quotient (the result of the division). To calculate, you divide the dividend by the divisor and the quotient is the resultTo calculate the quotient, you must divide a by b. For example, if we wanted to divide 8 by 4, we would divide 8 by 4 to get 2. The calculation would look like this: 8/4 = 2. As a result, 8 divided by 4 is equal to 2.

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Answer:

\( {3x}^{3} + {2x}^{2} - 27x - 18\)

Step-by-step explanation:

1) Use difference of squares: a² - b² = (a + b) (a - b).

\(( {x}^{2} - {3}^{2} )(3x + 2)\)

2) Simplify 3² to 9.

\(( {x}^{2} - 9)(3x + 2)\)

3) Use The FOIL method: (a + b) (c + d) = ac + ad + bc + bd.

\( {3x}^{3} + {2x}^{2} - 27x - 18\)

Therefor, the answer is 3x³ + 2x² + -26x -18.

1. The average time it takes a customer from when they arrive at the truck until they receive their taco is 141.67 seconds.

2. The average utilization of the truck 141.67 seconds.

3. On average, there is 1 person waiting in line.

4. In order to achieve a delay probability of under 10%, a minimum of 1 server is required.

1 The arrival rate is 1 customer every 2 minutes, which is equivalent to 0.5 customers per minute. The service rate is 1 customer per 50 seconds, which is equivalent to 1.2 customers per minute (since there are 60 seconds in a minute).

2 Average Number of Customers = (0.5 / 1.2) + 1 = 1.4167.

Average Waiting Time = 1.4167 * (50 + 50)

= 141.67 seconds.

3 The average utilization of the truck is given by the formula: Utilization = Arrival Rate / Service Rate.

Utilization = 0.5 / 1.2

= 0.4167 (or 41.67%).

The average number of people waiting in line can be calculated using the formula: Average Number of Customers - Average Utilization.

Average Number of Customers - Average Utilization = 1.4167 - 0.4167

= 1.

4 Given that the desired delay probability is 10% (or 0.1), we can rearrange the formula to solve for the utilization:

Utilization = Delay Probability / (1 + Delay Probability).

=

Utilization = 0.1 / (1 + 0.1) = 0.0909 (or 9.09%).

The utilization we calculated represents the maximum utilization to achieve a delay probability of 10%. In conclusion, to achieve a delay probability of under 10%, a minimum of 1 server is required.

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Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Given:

Number of green peas = 475

Number of yellow peas = 193

Let's find the 94% confidence interval to estimate the percentage of yellow peas.

Where:

Total number of peas = 475 + 193 = 668

For the sample proportion, we have:

For a 94% confidence interval, the significance level will be:

1 - 0.94 = 0.06

For the critical value, using the z-table, we have:

Now, to find the 94% confidence interval, apply the formula::

Where:

To find the margin of error E, we have:

Thus, we have:

Hence the confidence interval will be:

Lower limit = 0.2559 ==> 25.59%

Upper limit = 0.3219 ==> 32.19 %

The confidence interval does not contain 0.25, hence we can say that the true results contradicts the expectations.

ANSWER:

The confidence interval does not contain the expectation of 25%, hence, the true results contradicts the expectation.

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

an = 3+3(n-1)

Step-by-step explanation:

We are adding 3 each time

6-3 = 3  9-6 = 3

The common difference is 3

The explicit formula for an arithmetic sequence is

an = a1+d(n-1)

The first term is a1 = 3

d =3

an = 3+3(n-1)

Answer:

58 0.58

Step-by-step explanation:

I just know the answer I don't know any thing else

The following parts can  be answered by the concept from Standard deviation.

a. We need a sample size of at least 121 for each group.

b. We need a sample size of at least 78 for each group.

c.  We need a sample size of at least 97.48 for each group.

To find the sample size needed to estimate (P1-P2) for each of the given situations, we can use the following formula:

n = (Zα/2)² × (p1 × q1 + p2 × q2) / (P1 - P2)²

where:
- Zα/2 is the critical value of the standard normal distribution at the desired confidence level
- p1 and p2 are the estimated proportions in the two populations
- q1 and q2 are the complements of p1 and p2, respectively (i.e., q1 = 1 - p1 and q2 = 1 - p2)
- (P1 - P2) is the desired margin of error

a. For a margin of error equal to 0.11 with 99% confidence, assuming p1 ~ 0.6 and p2 ~ 0.4, we have:

Zα/2 = 2.576 (from standard normal distribution table)
p1 = 0.6, q1 = 0.4
p2 = 0.4, q2 = 0.6
(P1 - P2) = 0.11

Plugging in the values, we get:

n = (2.576)² × (0.6 × 0.4 + 0.4 × 0.6) / (0.11)²
n ≈ 120.34

Therefore, we need a sample size of at least 121 for each group.

b. For a 90% confidence interval of width 0.88, assuming no prior information is available to obtain approximate values of p1 and p2, we have:

Zα/2 = 1.645 (from standard normal distribution table)
(P1 - P2) = 0.88
Since we have no information about p1 and p2, we can assume them to be 0.5 each (which maximizes the sample size and ensures a conservative estimate).

Plugging in the values, we get:

n = (1.645)² × (0.5 × 0.5 + 0.5 × 0.5) / (0.88)²
n ≈ 77.58

Therefore, we need a sample size of at least 78 for each group.

c. For a margin of error equal to 0.08 with 90% confidence, assuming p1 = 0.19 and p2 = 0.3, we have:

Zα/2 = 1.645 (from standard normal distribution table)
q1 = 0.81
q2 = 0.7
(P1 - P2) = 0.08

Plugging in the values, we get:

n = (1.645)² × (0.19 × 0.81 + 0.3 × 0.7) / (0.08)²
n ≈ 97.48

Therefore, we need a sample size of at least 98 for group 1. For group 2, we can use the same sample size as group 1, or we can adjust it based on the expected difference between p1 and p2 (which is not given in this case).

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The following parts can  be answered by the concept from Standard deviation.

a. We need a sample size of at least 121 for each group.

b. We need a sample size of at least 78 for each group.

c.  We need a sample size of at least 97.48 for each group.

To find the sample size needed to estimate (P1-P2) for each of the given situations, we can use the following formula:

n = (Zα/2)² × (p1 × q1 + p2 × q2) / (P1 - P2)²

where:
- Zα/2 is the critical value of the standard normal distribution at the desired confidence level
- p1 and p2 are the estimated proportions in the two populations
- q1 and q2 are the complements of p1 and p2, respectively (i.e., q1 = 1 - p1 and q2 = 1 - p2)
- (P1 - P2) is the desired margin of error

a. For a margin of error equal to 0.11 with 99% confidence, assuming p1 ~ 0.6 and p2 ~ 0.4, we have:

Zα/2 = 2.576 (from standard normal distribution table)
p1 = 0.6, q1 = 0.4
p2 = 0.4, q2 = 0.6
(P1 - P2) = 0.11

Plugging in the values, we get:

n = (2.576)² × (0.6 × 0.4 + 0.4 × 0.6) / (0.11)²
n ≈ 120.34

Therefore, we need a sample size of at least 121 for each group.

b. For a 90% confidence interval of width 0.88, assuming no prior information is available to obtain approximate values of p1 and p2, we have:

Zα/2 = 1.645 (from standard normal distribution table)
(P1 - P2) = 0.88
Since we have no information about p1 and p2, we can assume them to be 0.5 each (which maximizes the sample size and ensures a conservative estimate).

Plugging in the values, we get:

n = (1.645)² × (0.5 × 0.5 + 0.5 × 0.5) / (0.88)²
n ≈ 77.58

Therefore, we need a sample size of at least 78 for each group.

c. For a margin of error equal to 0.08 with 90% confidence, assuming p1 = 0.19 and p2 = 0.3, we have:

Zα/2 = 1.645 (from standard normal distribution table)
q1 = 0.81
q2 = 0.7
(P1 - P2) = 0.08

Plugging in the values, we get:

n = (1.645)² × (0.19 × 0.81 + 0.3 × 0.7) / (0.08)²
n ≈ 97.48

Therefore, we need a sample size of at least 98 for group 1. For group 2, we can use the same sample size as group 1, or we can adjust it based on the expected difference between p1 and p2 (which is not given in this case).

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Answer:

4:7

Step-by-step explanation:

i don't think that you can simplify it any further so you just change the / to a :

Answer:

yes

Step-by-step explanation:

Given the graph of any function, an x-intercept is simply the point, or points where the graph crosses the x-axis. There might be just one such point, no such point, or many, meaning a function can have several x-intercepts.

Answer:

\(f^{-1} (x)=-\frac{x}{5} +2\)

Step-by-step explanation:

hope this helps

Answer:-3

Step-by-step explanation: -3 because when you do it I really don't know how to explain it srry

Answer:

h = 14.49 feet.

Step-by-step explanation:

From the attached figure,

Base = 14 ft

Height = h

Angle = 46°

We need to find the height of the main sail. To find it we can use trigonometry.

The relation between height, base and angle is given by :

\(\tan\theta=\dfrac{\text{Height}}{\text{Base}}\\\\\tan(46)=\dfrac{h}{14}\\\\h=\tan(46)\times 14\\\\h=14.49\ ft\)

So, the height of the main sail is 14.49 feet.

Answer: Reflection across = -2; clockwise rotation

Step-by-step explanation: To get this answer, you first must work out the other answers. If you reclect across the x-axis and rotate 90 degrees clockwise, you'll find the shape to be in almost the exact same place it was before.

The third choice is illogical, because if you reflect over the y-axis, the shape is nowhere near where you need it to be, and rotating it 90 degrees counterclockwise is gonna bring it back to where you started.

The fourth option is the same as the third yet this time the clockwise rotation will bring you down to the negative y's, which is the opposite of where you need to be.

Therefore, that is why the first option is the better one to choose. Reflecting the shape over x = -2 is going to give you the correct orientation you needed for the 90 degree rotation.

I hope this helps!

Answer:

reflection over -2 clockwise rotation

Step-by-step explanation:

Answer:

18/42 or

36/84

Step-by-step explanation:

Answer: 3 to 7

Step-by-step explanation: Trust me i got 100.

Answer: He pays x*0.642

Step-by-step explanation:

Suppose that we have an object with an initial price P.

If we have a discount of X%, then the new price will be:

NP = P*(1 - X%/100%)

And if we have an increase of X%, the new price is:

NP = P*(1 + X%/100%)

In this case, we have an initial item that costs x dollars, first we have a coupon for 40% off, then we have a discount of 40%.

Then the new price is:

NP = x*(1 - 40%/100%) = x*(1 - 0.4) = x*0.6

Now we add a tax of the 7%, then the final price will be:

FP = (x*0.6)*(1 + 7%/100%) = (x*0.6)*(1 + 0.07) = x*(0.6*1.07) = x*0.642

This is the total amount he pays at the register.

1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

y = a (x - h)² + k, where (h, k) is the vertex.

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

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Answer:

the last one: -7 1/4-(-3 1/3)

Answer:

I think it is 3 1/3-(-7 1/4)

Step-by-step explanation:

Algabra equation

+ + = +

+ - = -

- - = +

- + = -

I hope you got it...

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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The expression is equivalent to 45m^-6p^2v^12/15m^-2p^8v^-4 is Option b 3v^16/m^4p^6 .

Given :

expression is equivalent to for all values of m , p , and v where the expression is defined

= ( 45m^-6 ) * p^2 * v^12 / 15m^-2 * p^8 * v^-4

= ( 45 / 15 ) ( m^-6 / m^-2 ) ( p^2 / p^8 ) ( v^12 / v^-4 )

= 3 ( m^-6 - ( -2 ) ( p^2 - 8 ) ( v^12 - ( - 4 )

= 3 ( m^-6 + 2 ) ( p^-6 ) ( v^12 + 4 )

= 3 ( m^-4 ) ( p^-6 ) ( v^16)

= 3 * v^16 / m^4 * p^6

= 3v^16 / m^4p^6

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