a mini bottle of water contains 8 ounces of water you need 4 1/4 gallons of water how many mini water bottles do you need

the evaluated integral is:

∫acos(5r)(r-b) dr = (r - b)/5 (asin(5r) + C) + (1/25) (acos(5r) + D) - (1/5) C,

where C and D are constants of integration.

To evaluate the integral ∫acos(5r)(r-b) dr, we can use integration by parts. Integration by parts is based on the formula:

∫u dv = uv - ∫v du,

where u and v are functions of the variable of integration.

Let's assign u = (r - b) and dv = acos(5r) dr. Then, we can find du and v as follows:

du = d(r - b) = dr,

v = ∫acos(5r) dr.

To evaluate v, we can use a substitution. Let's assign t = 5r, which implies dr = (1/5) dt. Substituting these values, we have:

v = ∫acos(t) (1/5) dt = (1/5) ∫acos(t) dt.

The integral ∫acos(t) dt can be evaluated using the formula for the integral of the cosine function:

∫acos(t) dt = asin(t) + C,

where C is the constant of integration.

Now, substituting back for t = 5r, we have:

v = (1/5) (asin(5r) + C).

Applying the integration by parts formula, we have:

∫acos(5r)(r-b) dr = uv - ∫v du

                    = (r - b) (1/5) (asin(5r) + C) - ∫(1/5) (asin(5r) + C) dr

                    = (r - b)/5 (asin(5r) + C) - (1/5) ∫asin(5r) dr - (1/5) C.

The integral ∫asin(5r) dr can be evaluated in a similar manner as above, resulting in:

∫asin(5r) dr = -(1/5) (acos(5r) + D),

where D is the constant of integration.

Substituting this back into the previous expression, we have:

∫acos(5r)(r-b) dr = (r - b)/5 (asin(5r) + C) - (1/5) (-(1/5) (acos(5r) + D)) - (1/5) C

                    = (r - b)/5 (asin(5r) + C) + (1/25) (acos(5r) + D) - (1/5) C.

So, the evaluated integral is:

∫acos(5r)(r-b) dr = (r - b)/5 (asin(5r) + C) + (1/25) (acos(5r) + D) - (1/5) C,

where C and D are constants of integration.

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Answer:

Step-by-step explanation:

Part A

x-intercepts of the graph → x = 0, 6

Maximum value of the graph → f(x) = 120

Part B

Increasing in the interval → 0 ≤ x ≤ 3

Decreasing in the interval → 3 < x ≤ 6

As the price of goods increase in the interval [0, 3], profit increases.

But in the price interval of (3, 6] profit of the company decreases.

Part C

Average rate of change of a function 'f' in the interval of x = a and x = b is given by,

Average rate of change = \(\frac{f(b)-f(a)}{b-a}\)

Therefore, average rate of change of the function in the interval x = 1 and x = 3 will be,

Average rate of change = \(\frac{f(3)-f(1)}{3-1}\)

                                         = \(\frac{120-60}{3-1}\)

                                         = 30

The length of the rectangular countertop is 6x - 4.

To find the length of the rectangular countertop, we have to substitute the given values in the formula for the area of the rectangle, which is A = l × w
12x² + 10x - 12 = (2x + 3) × l
6x² + 5x - 6 = 3x × l + 3 × l
6x² + 5x - 6 = 3lx + 3l
6x² + 5x - 6 = 3l(x + 1)
3l = (6x² + 5x - 6) / (x + 1)
3l = (6x² + 9x - 4x - 6) / (x + 1)
3l = 3(2x² + 3x - 2) / (x + 1)
l = (2x² + 3x - 2) / (x + 1)
l = [(2x - 1) (x + 2)] / (x + 1)
Therefore, the length of the rectangular countertop is 6x - 4.

Summary:
The formula for the area of the rectangle is A = l × w. We substitute the given values in the formula to find the length of the rectangular countertop. After simplifying the expression, the length of the rectangular countertop is found to be 6x - 4.

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Answer: I think it is C

Step-by-step explanation: 32/4=8 so 1 cm = 8km

The Cartesian equation for the given curve is 25y = x².

To eliminate the parameter θ and find a Cartesian equation for the curve, we'll use the given parametric equations:
x = 5cos(θ) and y = sec²(θ)

First, let's solve for cos(θ) in the x equation:
cos(θ) = x/5

Now, recall that sec(θ) = 1/cos(θ), so sec²(θ) = 1/cos²(θ). Replace sec²(θ) with y in the second equation:
y = 1/cos²(θ)

Since we already have cos(θ) = x/5, we can replace cos²(θ) with (x/5)²:
y = 1/(x/5)²

Now, simplify the equation:
y = 1/(x²/25)

To eliminate the fraction, multiply both sides by 25:
25y = x²

This is the Cartesian equation for the given curve: 25y = x².

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Answer:

Step-by-step explanation:

which numbers are composite:49,35,32

which numbers are equal :2/3=4/6=6/9

your answer would be 4/6,6/9

explanation

(2/3)×2=4/6

therefore 4/6 is a multiple of 2/3

(2/3)×3=6/9

therefore 6/9 is a multiple

if we comprise 4/6 & 6/9 we get 2/3

Answer:

the answer is x and y have a weak, positive correlation.

Step-by-step explanation:

if a correlation is strong, it will either be close to 1 or -1 and the further in the decimal, the weaker the correlation becomes. the correlation is positive so that’s how I got the positive.

P.S. im sorry someone sent you a virus. dont download them.

Answer:

a virus

Step-by-step explanation:

Answer:

To find the equation of the line through the two given points, we can use the slope-intercept form of the equation of a line, which is $y = mx + b$, where $m$ is the slope of the line and $b$ is the $y$-intercept (the point where the line crosses the $y$-axis).

We can find the slope of the line by using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the two given points. In this case, the slope is

$$m = \frac{(-3) - 5}{3 - (-6)} = \frac{-8}{9} = -\frac{4}{3}.$$

To find the $y$-intercept, we can plug the coordinates of one of the points and the slope into the equation of a line, so we have $y = -\frac{4}{3} x + b$. If we plug in the coordinates of the first point, we get

$$5 = -\frac{4}{3} (-6) + b \Rightarrow b = -\frac{4}{3} (-6) + 5 = \frac{28}{3}.$$

Therefore, the equation of the line through the two given points is

$$y = -\frac{4}{3} x + \frac{28}{3} = -\frac{4}{3} x + \frac{28}{3}.$$

Answer:

Step-by-step explanation:

(-6,5)     (3,-3)

The equation of the line:    

 \(\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }\)

x₁=-6      x₂=3     y₁=5     y₂=-3

Hence,

\(\displaystyle\\\frac{x-(-6)}{3-(-6)} =\frac{y-5}{-3-5} \\\\\frac{x+6}{3+6}=\frac{y-5}{-8} \\\\\frac{x+6}{9} =\frac{y-5}{-8} \\\\\)

Multiply both parts of the equation by -72:

\(-8(x+6)=9(y-5)\\\\-8x-48=9y-45\\\\-8x-48+45=9y-45+45\\\\-8x-3=9y\\\\\)

Divide both parts of the equation by 9:

\(\displaystyle\\-\frac{8}{9} x-\frac{1}{3} =y\\\\Thus,\ y=-\frac{8}{9}x-\frac{1}{3}\)

Answer:

  D)  Hungary

Step-by-step explanation:

You are being asked to compare 4 pairs of numbers. The population will have decreased if the number in the 2005 column is less than the number in the 1985 column.

Whenever you compare numbers, you start with the most-significant digit. If the most-significant digit has a higher place value, the number is larger. If the digits have the same place value, the number with the larger digit is larger. If no determination can be made by these comparisons, then the digits to the immediate right are compared.

  27,... > 19,...  2 > 1 in the 10-millions place

  10,... > 9,...  1 has a greater place value

  29... > 24...  comparison shifts to the 10-thousands place: 9 > 4

  10,058,... < 10,649,... . . . . the population decreased (0 < 6)

The "population decreased" result is found on the last line of the table, identified by the Country name "Hungary."

Hungary's population decreased from 1985 to 2005.

Answer:

step 2

Step-by-step explanation:

from -8(a+6) to -80 - 48 is incorrect

when you multiply -8 x a it's -8a not -80

Therefore , the solution of the given problem of test statistic comes out to be it help us decide whether we successfully deny the null hypothesis or not.

The only approach that comes close to a Z-test uses the Z-statistic, which verifies the accuracy of the traditional null hypothesis. Think about extrapolating a score of 2.5 E s in the outcomes of a 2 X y exam with a 0.05 level of significance. 0.0124 is the p-value associated with this Z-value.

Here,

A two-sample t-test for the disparity in values between the two groups is the proper reasoning method in this situation.

(new fertilizer vs. another fertilizer).

When comparing the means of two populations, we use a two-sample t-test because we have two separate samples (plots treated by a fresh fertilizer or plots treated with another fertilizer).

The alternative hypothesis could be that there is a substantial difference between the means of both populations,

while the null hypothesis used for the test would be that there isn't a difference between an means of the two populations.

The t-test is used to compute a test statistic and a p-value,

which help us decide whether we successfully deny the null hypothesis or not.

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Answer:

The inequality represented by the graph is y >  \(\frac{1}{2}\) x + 2

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where

From the given figure

∵ The line passes through points (0, 2) and (2, 3)

∴ x1 = 0 and y1 = 2

∴ x2 = 2 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m = \(\frac{3-2}{2-0}\) = \(\frac{1}{2}\)

∴ m =  \(\frac{1}{2}\)

→ b is the value of y at x = 0

∵ At x = 0, y =2

∴ b = 2

→ Substitute the value of m and b in the form of the equation above

∵ y =  \(\frac{1}{2}\) x + 2

∴ The equation of the line is y =  \(\frac{1}{2}\) x + 2

∵ The line is dashed

∵ The shaded area is over the line

∴ The sign of inequality is >

→ Replace = in the equation by >

∴ y >  \(\frac{1}{2}\) x + 2

∴ The inequality represented by the graph is y >  \(\frac{1}{2}\) x + 2

Answer:

400 in.²

Step-by-step explanation:

Surface area of the triangular prism = bh + L(s1 + s2 + s3)

Where,

b = 8 in.

h = 15 in.

s1 = 17 in.

s2 = 15 in.

s3 = 8 in.

L = 7 in.

Plug in the values

S.A = 8*15 + 7(17 + 15 + 8)

S.A = 120 + 7(40)

S.A = 120 + 280

S.A = 400 in.²

Answer:

y = 45x + 15

Step-by-step explanation:

We have the next function

And we must find f(-2) and f(0.3)

To find f(-2) and f(0.3) we need to know that

We can see that we have a constant function because it has the next form

That means, for any value of x the function will always be equal to 4.

Using that, we obtain

ANSWER:

f(-2) = 4

f(0.3) = 4

Answer:

\( \frac{909}{10000} \)

Step-by-step explanation:

The function f ( x ) is translated to form h ( x ) by horizontal transformation of 3 units to left , upward translation of 2 units and a vertical compression of 2 units

Given data ,

The graph of the function h(x) = 1/2(x+3)² + 2 is obtained by translating the parent graph of the quadratic function f(x) = x²

where the translation factors are

The term (x+3) inside the parentheses indicates a horizontal translation to the left by 3 units.

The term (1/2) multiplies the entire function, which causes a vertical compression by a factor of 1/2.

The term +2 shifts the graph vertically upward by 2 units

Hence , the translation of the function is solved

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The computer loses \(50\)% of its value each year, according to the given graph.

Based on the graph, the computer's value changes exponentially over time. The given points \((0, 500) \ and \ (1, 250)\) indicate a decreasing exponential function.

To determine how the computer's value changes over time, we can calculate the percentage decrease in value per year. From the given points, we observe that the computer's value decreases by half within one year. This corresponds to a \(50\)% decrease in value.

Therefore, the computer loses \(50\)% of its value each year. This indicates a rapid decline in its worth over time. It is important to note that exponential decay functions tend to exhibit diminishing returns, meaning the value decreases more rapidly in the initial years and slows down over time.

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Answer:

Area_square = 4 cm2

Area_triangle = 4 cm2

Step-by-step explanation:

The first thing to do is calculate the area of both figures.

The area of the square is given by:

Area_square = side * side

The side of the square is 2 cm, so:

Area_square = 2 * 2 = 4 cm2

The area of the triangle is given by:

Area_triangle = base * height / 2

The base is 2 cm, and the height is 4 cm, so we have:

Area_triangle = 2 * 4 / 2 = 4 cm2

So we have that Area_square = Area_triangle = 4 cm2

To convert 72 feet per day to a different unit, we can use unit conversion factors:

1 day = 24 hours

1 hour = 60 minutes

1 foot = 12 inches

So, we can set up the following calculation:

72 feet/day × (1 day/24 hours) × (1 hour/60 minutes) × (12 inches/1 foot) = 0.1 inches/minute

Therefore, the converted rate is in units of inches per minute.

Answer: (4) inches/minute

Answer:

it's a and c

luk closely

To simplify an expression means to reduce it to its simplest form while retaining the same value as the original expression. In the given expression, we have 19 – 6(-k+4). To simplify, we need to distribute the negative sign outside the brackets and simplify the resulting expression. This gives us:

19 + 6k - 24

Combining like terms, we get:

6k - 5

Therefore, the equivalent expression is 6k - 5.

Simplifying expressions is an essential skill in algebra and mathematics in general. It allows us to make complex expressions easier to work with and helps us to identify patterns and relationships between different variables. Being able to simplify expressions is particularly important when solving equations and inequalities. By simplifying the expressions involved, we can isolate the variable we are trying to solve for and find its value. Therefore, it is crucial to master the skill of simplifying expressions in order to succeed in mathematics.

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The price of a used book in the bookstore after the percentage increase in its price is $7.50.

Percentage can be described as the fraction out of an amount that is usually expressed as a number out of hundred. Percentages are represented with this sign - %.

Price = 1.50 x ( 1 + 4)

1.5 x 5 = $7.50

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Answer:

j 6.00

Step-by-step explanation:

i took the test hope this helps good luck

The mass will reach a maximum height of 0.82 m above its equilibrium position before falling back down due to gravity.

We need to use the principles of Hooke's law and conservation of energy.

Hooke's law states that the force exerted by a spring is proportional to its displacement from equilibrium, and this relationship can be expressed mathematically as F = -kx, where F is the force, k is the spring constant, and x is the displacement.

Given that a mass of 3 kg stretches a spring 5/2, we can determine the spring constant using the formula k = (mg)/x, where m is the mass, g is the acceleration due to gravity, and x is the displacement.

Plugging in the values, we get:
k = (3 kg x 9.8 m/s^2)/(5/2 m) = 58.8 N/m

Now we can use the conservation of energy to find the maximum height that the mass will reach.

At the highest point, all of the potential energy is converted to kinetic energy, and vice versa at the lowest point.

Therefore, we can equate the initial potential energy to the final kinetic energy, using the formulas:
PE = mgh
KE = 1/2 mv^2

where PE is potential energy, KE is kinetic energy, m is the mass, h is the height, and v is the velocity.

Plugging in the values, we get:
PE = (3 kg x 9.8 m/s^2 x 1 m) = 29.4 J
KE = (1/2 x 3 kg x 4 m/s^2) = 6 J

Since energy is conserved, we can equate these two values and solve for h:
PE = KE
mgh = 1/2 mv^2
h = v^2/2g
h = (4 m/s)^2 / (2 x 9.8 m/s^2)
h = 0.82 m

Therefore, the mass will reach a maximum height of 0.82 m above its equilibrium position before falling back down due to gravity.

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The way Odysseus hides himself in the leaves to sleep is compared to the way a burning coal is buried deep in the embers to preserve a spark for the next day.

Odyssey, epic poem in 24 books traditionally attributed to the ancient Greek poet Homer. The poem is the story of Odysseus, king of Ithaca, who wanders for 10 years (although the action of the poem covers only the final six weeks) trying to get home after the Trojan War. On his return, he is recognized only by his faithful dog and a nurse. With the help of his son, Telemachus, Odysseus destroys the insistent suitors of his faithful wife, Penelope, and several of her maids who had fraternized with the suitors and reestablishes himself in his kingdom.

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Answer:

12 groups

Step-by-step explanation:

brainliest pls

Answer:

12 because 180÷9=12 so it will be the are 12 groups or however it says ...

Answer:

f=1

Step-by-step explanation:

You're welcome :)

Answer:

y = 2x

Step-by-step explanation:

We know

They earn $2 for each cup of lemonade they sell. So, the equation is

y = 2x

Answer:

1)E

2)C

3)G

4)A

5)B

6)F

7)D

Step-by-step explanation:

Answer:

1: E

2: C

3: G

4: A

5: B

6: F

7: D

Step-by-step explanation: