Which is the cheaper/better buy?
1/4 gallon for $1.80 or 1/2 gallon for $2.10 or 1 gallon for $4.25 or 2 gallon for $5.98

The algebraic solutions are x < -5 and x > 3.

The graph is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x² + 2x > 15

x² + 2x - 15 > 0

x² + (5 - 3)x - 15 > 0

x² + 5x - 3x - 15 > 0

x(x + 5) - 3(x + 5) > 0

(x - 3)(x + 5) > 0

x + 5 > 0 and x - 3 > 0

x < -5 and x > 3

The graph is given below.

Thus,

x < -5 and x > 3 is the solution.

The graph is given below.

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To find the gradient field of the function f(x,y,z) = ln(2x^2) + 2ln(y^2) + 3ln(z^2), we need to find the partial derivatives of f with respect to x, y, and z. The gradient field of f is given by: F(x,y,z) = (2/x)i + (4/y)j + (6/z)k

∂f/∂x = 4x/2x^2 = 2/x

∂f/∂y = 4y/ y^2 = 4/y

∂f/∂z = 6z/ z^2 = 6/z

So the gradient vector of f is given by:

∇f(x,y,z) = (2/x)i + (4/y)j + (6/z)k

where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

Therefore, the gradient field of f is given by:

F(x,y,z) = (2/x)i + (4/y)j + (6/z)k

Note that the gradient field is a vector field, meaning that at each point in the domain of f, it assigns a vector that points in the direction of the maximum increase of f at that point

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Answer:

i think songs it might be correct but im not sure

The inequality that represents the number of songs and videos Patrick can buy using only his gift certificate is s + 2.50v ≤ 25

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.

Let's suppose the number of songs is 's' and number of videos is 'v'

Total cost for songs = $s

Total cost for videos = $2.50v

Patrick has a gift certificate for $25

Then the inequality that represents the number of songs and videos Patrick can buy using only his gift certificate is:

s + 2.50v ≤ 25

Thus, the inequality that represents the number of songs and videos Patrick can buy using only his gift certificate is s + 2.50v ≤ 25

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Its 6/9

2 x 3 = 6

3 x 3 = 9

therefore,

6/9

Answer:

the and is C 11-2 because its the right answer

Yes, it is better to use percentages to compare groups when making a graph. This is because percentages allow for a more accurate comparison of the data, as they take into account the relative size of each group. If we only use frequencies, we may get a skewed view of the data, as one group may be much larger than the other.

Here is the side by side bar graph showing the men's and women's responses to the question "Do you play sports?":

Gender Yes No

Male 9 7

Female 7 14

The graph indicates that a higher percentage of males play sports compared to females. However, it also shows that there are more females who do not play sports compared to males. This suggests that there may be a gender difference in the participation of sports among students.

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The points (x, y) on the curve C where the tangent line TL is vertical or horizontal are: (2, 0), (-2, 0), (0, 4), and (0, -4).

To find the points (x, y) on the curve C defined by the parametric equations x(t) = 2cos(t) and y(t) = 4sin(t) where the tangent line TL is vertical or horizontal, we need to find the values of t that correspond to these points.

For the tangent line to be vertical, the derivative dy/dx must be undefined. In other words, the slope of the tangent line must be infinite. So, we look for the values of t where dx/dt = 0.

We have x(t) = 2cos(t), so dx/dt = -2sin(t). Setting dx/dt = 0, we get -2sin(t) = 0. This equation is satisfied when sin(t) = 0, which occurs at t = 0, π, 2π, etc.

Substituting these values of t back into the parametric equations, we find the corresponding points (x, y): At t = 0: x(0) = 2cos(0) = 2, y(0) = 4sin(0) = 0. So, the point (2, 0) is on the curve.

At t = π: x(π) = 2cos(π) = -2, y(π) = 4sin(π) = 0. Thus, the point (-2, 0) is on the curve. Similarly, at t = 2π, we get the points (2, 0) and (-2, 0).

For the tangent line to be horizontal, the derivative dy/dx must be zero. In other words, the slope of the tangent line must be zero. So, we look for the values of t where dy/dt = 0.

We have y(t) = 4sin(t), so dy/dt = 4cos(t). Setting dy/dt = 0, we have 4cos(t) = 0. This equation is satisfied when cos(t) = 0, which occurs at t = π/2, 3π/2, etc.

Substituting these values of t back into the parametric equations, we find the corresponding points (x, y): At t = π/2: x(π/2) = 2cos(π/2) = 0, y(π/2) = 4sin(π/2) = 4. So, the point (0, 4) is on the curve.

At t = 3π/2: x(3π/2) = 2cos(3π/2) = 0, y(3π/2) = 4sin(3π/2) = -4. Thus, the point (0, -4) is on the curve. Similarly, at t = 5π/2, we get the points (0, 4) and (0, -4).

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question: when do you take the SAT test

Answer:

16 meters

Step-by-step explanation:

Factors of 64: 1, 2, 4, 8, 16, 32, 64

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The greatest common factor of 64 and 48 is 16.

Answer:

Step-by-step explanation:

To find the length of the longest scale that can measure 64 m and 48 m exactly, we need to find the greatest common factor (GCF) of 64 and 48. The GCF is the largest number that divides both numbers without leaving a remainder. One way to find the GCF is to list the factors of both numbers and find the largest one that they have in common. For example:

Factors of 64: 1, 2, 4, 8, 16, 32, 64

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The largest factor that both numbers have in common is 16. Therefore, the GCF of 64 and 48 is 16.

This means that the longest scale that can measure both lengths exactly is 16 m. We can check this by dividing both lengths by 16 and seeing that there is no remainder:

1664​=4

1648​=3

Answer:

the like terms are -13, 17,-8g, and 6g. the terms are all, coefficents are -8 ang 6. constants are 7h

Step-by-step explanation:

The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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Hinduism is one of the suggested timelines for the foundation of significant world religions. Islam Buddhism Christianity The right answer is C.

With more than two billion adherents, Christianity is the largest of the world's main religions. Christianity, which has been around for around 2,000 years, is founded on the life and teachings of Jesus. Faith and reason have always been seen as the basis of religious beliefs. There are reportedly 10,000 different religions in the globe, although almost all of them have localised, insignificant followings.

JUDAISM.

CHRISTIANITY.

ISLAM.

HINDUISM.

BUDDHISM.

SIKHISM.

ANIMISM.

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Answer:

318

Step-by-step explanation:

find area of the big triangle then split the remaining shape into a large rectangle and a smaller rectangle

Answer:

318 mi²

Step-by-step explanation:

Formulae

Area of a rectangle = width x length

Area of a triangle = 1/2 x base x height

Divide the figure into 1 triangle and 2 rectangles (see attachment).

Area of Triangle 1 = 1/2 x (10 + 6 + (11 - 8)) x 22

                             = 1/2 x 19 x 22

                             = 209 mi²

Area of Rectangle 2 = 5 x (11 + 6)

                                  = 85 mi²

Area of Rectangle 3 = 4 x 6

                                  = 24 mi²

Total area = 209 + 85 + 24 = 318 mi²

The answer is

\(y = - \frac{1}{5} x + \frac{24}{5} \)

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

y - 5x = 1

y = 5x + 1

Comparing with the above formula

The slope / m of the line is 5

Since the is perpendicular to y = 5x + 1 it's slope it's the negative inverse of y = 5x + 1

That's

Slope of the perpendicular line = - 1/5

Equation of the line using point (-1,5) is

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

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

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

We have the final answer as

\(y = - \frac{1}{5} x + \frac{24}{5} \)

Hope this helps you

Answer:

\(\huge\boxed{y=-\dfrac{1}{5}x+\dfrac{24}{5}\to x+5y=24}\)

Step-by-step explanation:

The slope-intercept form of an equation of a line:

\(y=mx+b\)

m - slope

b - y-intercept

Let

\(k:y=m_1x+b_1;\ l:y=m_2x+b_2\)

therefore

\(k||l\iff m_1=m_2\\k\perp l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\)

We have the equation of a line in the standard form. Convert it to the slope-intercept form:

\(y-5x=1\)      add 5x to both sides

\(y-5x+5x=1+5x\\\\y=5x+1\to m_1=5;\ b_1=1\)

Calculate the slope:

\(m_2=-\dfrac{1}{5}\)

Substitute the value of a slope and the coordinates of the given point (-1, 5) to the equation of a line:

\(y=m_2x+b\)

\(5=\left(-\dfrac{1}{5}\right)(-1)+b\)

\(5=\dfrac{1}{5}+b\)           subtract 1/5 from both sides

\(5-\dfrac{1}{5}=\dfrac{1}{5}-\dfrac{1}{5}+b\)

\(\dfrac{25}{5}-\dfrac{1}{5}=b\\\\\dfrac{24}{5}=b\to b=\dfrac{24}{5}\)

Final answer:

\(y=-\dfrac{1}{5}x+\dfrac{24}{5}\)

convert to the standard form (Ax + By = C):

\(y=-\dfrac{1}{5}x+\dfrac{24}{5}\)       multiply both sides by 5

\(5y=(5)\left(-\dfrac{1}{5}x\right)+(5)\left(\dfrac{24}{5}\right)\)

\(5y=-x+24\)        add x to both sides

\(x+5y=24\)

Answer:

it has a 16.25% chance to happen

The standard normal distribution  becomes smaller.

What is standard deviation?

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller.

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Answer:

C on edg

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Pat's Potato farm grew 490 pounds of potatoes. If Pat delivered 3/7 of the potatoes to the vegi stand, it means that the number of pounds of potatoes that pat delivered to the vergi store is

3/7 × 490 = 210 pounds

The owner of the vegi stand delivered 2/3 of the potatoes he bought to the grocery store. It means that the amount delivered to the grocery store is

2/3 × 210 = 140

If half of the delivered potatoes was packaged in bags of 5 pounds each, it means that the amount of potatoes packaged in the bags is 140/2 = 70 pounds.

The number of bags of 5 pounds that the grocery store packaged is

70/5 = 14 bags

The distance to the top of the building changing when they are 60 feet from the base of the building is 2.19 ft/s.

In the given question we have to find how fast is the distance to the top of the building changing when they are 60 feet from the base of the building.

A family is walking toward their home, which is in an apartment building 123 feet tall.

They are walking at a rate of 5 ft/sec.

So according to the given statement diagram is

In the diagram x represent base and s represent the distance.

Using the Pythagorean theorem to find the value of s.

So the equation should be

\(s^2=x^2+(123)^2\)........................(1)

From the question, x=60 feet

Now putting the value

\(s^2=(60)^2+(123)^2\)

\(s^2\) = 3600+15129

\(s^2\) = 18729

s = 136.85

Differentiate equation 1 with respect to t using the power rule then solve the expression for ds/dt

2s ds/dt=2x dx/dt+0

2s ds/dt= 2x dx/dt

Divide by 2s on both side, we get

ds/dt= x/s dx/dt.......................(2)

They are walking at a rate of 5 ft/sec.

So dx/dt=5

Putting the value in the equation 2

ds/dt=60/136.85 ×5

ds/dt=0.438×5

ds/dt=2.19 ft/s

The distance to the top of the building changing when they are 60 feet from the base of the building is 2.19 ft/s.

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Answer:

Step-by-step explanation:

357x

The expression for the surface area of cube are solved and:

a) S₁ = 6x² + 24x + 24

b) S₂ = 54a² + 36a + 6

c) S₃ = 24c⁴ + 72c² + 54

Given data:

The expressions for the side length of the cube is represented as a.

Now, Surface area S = 6a² ,

where a is the side of the cube

a)

a₁ = x + 2

So, S = 6a²

S₁ = 6 ( x + 2 )²

On simplifying the expression:

S₁ = 6x² + 24x + 24

b)

a₂ = 3a + 2

So, S = 6a²

S₂ = 6 ( 3a + 2 )²

On simplifying the expression:

S₂ = 54a² + 36a + 6

c)

a₃ = 2x² + 3

So, S = 6a²

S₃ = 6 ( 2x² + 3 )²

On simplifying the expression:

S₃ = 24c⁴ + 72c² + 54

Hence, the surface area are solved.

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The complete question is attached below:

for exercises 47-49, each expression represents the side length of a cube. Write an expression in standard form for the surface area of each cube.

Answer:  Answer:

Company C

Step-by-step explanation:

Company A sells 12 tigers for $33.24.

Cost per tiger = $33.34 / 12

= $2.78

Company B sells 16 tigers for $44.80. Company

Cost per tiger = $44.80 / 16

= $2.8

C charges $41.10 for 15 tigers.

Cost per tiger = $41.10 / 15

= $2.74

The company that has the best buy is company C that charges $2.74 per tiger

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The curve y = 8e^x has maximum curvature at the point (0, 8).there is no point where the second derivative equals zero,

To determine the point of maximum curvature on the curve y = 8e^x, we need to find the second derivative of the function and identify the point where it equals zero. The second derivative represents the rate of change of the slope, or the curvature, of the curve.

First, we find the first derivative of y = 8e^x with respect to x:

dy/dx = 8e^x

Then, we differentiate again to find the second derivative:

d²y/dx² = d(8e^x)/dx = 8e^x

Setting the second derivative equal to zero:

8e^x = 0

Exponential functions, such as e^x, are never equal to zero for any value of x. Therefore, there is no point where the second derivative equals zero, indicating that the curve y = 8e^x does not have any inflection points or points of maximum curvature.

However, we can determine the point where the curvature is the greatest by considering the graph of y = 8e^x. Since the exponential function e^x is always positive, the curve y = 8e^x is always concave up. This means that the curvature is positive throughout the curve, but there is no specific point of maximum curvature.    

In conclusion, the curve y = 8e^x does not have a point of maximum curvature but is always positively curved.  

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Step-by-step explanation:

2(6)(4)+(4)(4)

48+16

64 square Centimeters

Answer:the original number is 7

Step-by-step explanation:

Let the number be represented as X

so that when  multiplied by 4 gives 4x

which on addition to 12 gives

4x +12=40

4x=40-12

4x =28

x=28/4=7