Oil flows back and forth between a small and large tank. When oil is moving into the large tank, the flow rate is positive. When oil is moving into the small tank, the flow rate is negative.

The large tank begins with 600 gallons of oil. The flow rate is recorded as –4 gallons per minute. After a period of 32 minutes, how much oil has been moved and to which tank?


into the
tank.
After the 32 minutes, how much oil is in the large tank?
gallons

Answer: $5

Step-by-step explanation:

For every $3 raised by basketball players, football players would raise $2.50.

If basketball players raised $6 therefore, we can use direct proportion to find out what football players raised:

3      :        2.50

6      :           x

Cross multiply:

3x = 15

x = 15 / 3

x = 5

Football players raised $5.

Answer:

536 cm is equal to 53.6 dm

Step-by-step explanation:

Answer:

=

Step-by-step explanation:

Answer:

x = number of cards that cost $2.50 each = 5

y = number of cards that cost $3.25 each = 1

Step-by-step explanation:

The equations are:

x + y = 6 (1)

2.5x + 3.25y = 15.75 (2)

From (1)

x = 6 - y

Substitute x = 6 - y into (2)

2.5x + 3.25y = 15.75 (2)

2.5(6 - y) + 3.25y = 15.75

15 - 2.5y + 3.25y = 15.75

- 2.5y + 3.25y = 15.75 - 15

0.75y = 0.75

y = 0.75/075

y = 1

Substitute y = 1 into (1)

x + y = 6

x + 1 = 6

x = 6 - 1

x = 5

Therefore,

x = number of cards that cost $2.50 each = 5

y = number of cards that cost $3.25 each = 1

Answer:

P=30

W=12

T=16

Step-by-step explanation:

The maximum clearance of the underpass ahead is 12 feet and 6 inches.

Based on the information provided, the sign indicates that there is an underpass ahead with a clearance of 12 feet and 6 inches. The sign further mentions that the train in question is also 12 feet and 6 inches long, and it highlights the presence of a narrow median, which is only 6-12 inches wide.

In this context, the sign serves as a warning to drivers approaching the underpass. The clearance measurement of 12 feet and 6 inches informs drivers of the maximum height of vehicles that can safely pass through the underpass without any risk of collision. Since the train length matches the clearance, it implies that vehicles longer than the underpass clearance may not be able to pass through safely if the train is present.

The mention of a narrow median emphasizes the limited space available between the opposing lanes of traffic. With a width of only 6-12 inches, the median may not provide sufficient room for larger vehicles to maneuver, particularly when encountering oncoming traffic or passing through the underpass while the train is present.

Overall, the sign conveys important information regarding the underpass clearance, the train length, and the narrow median, all of which should be considered by drivers to ensure safe passage through the upcoming area.

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The sign indicates the clearance height of an underpass, warns of a narrow median, and mentions the length of a train.

The sign in question is indicating that there is an underpass ahead with a clearance of 12 feet and 6 inches. This means that any vehicle taller than that would not be able to pass through without hitting the underpass ceiling. Additionally, the sign mentions that the train itself is also 12 feet and 6 inches long, so it is important for drivers to be cautious and aware of the height restrictions. The narrow median mentioned refers to the strip of land or barrier between lanes, which in this case is only 6-12 inches wide.

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Dilution without achieving the immobilization of contaminants is not an acceptable treatment option because it does not effectively address the problem of contamination.

When contaminants are diluted without being immobilized, they are simply dispersed in a larger volume of water or another medium. While this may reduce the concentration of contaminants in a given sample, it does not remove or neutralize them. As a result, the contaminants can still pose a risk to the environment, human health, or other organisms. Dilution without immobilization is essentially a temporary solution that does not provide a long-term remedy for the contamination issue.

In contrast, immobilization of contaminants involves capturing or binding them in a way that prevents their migration or release into the environment. This can be achieved through various methods such as solidification/stabilization, chemical reactions, or physical encapsulation. Immobilization effectively isolates the contaminants, reducing their mobility and potential for harm. It provides a more sustainable and permanent solution by minimizing the risk of contaminant release and spread.

Contaminant immobilization is an essential component of effective remediation strategies. It helps prevent the spread and recontamination of affected areas, safeguarding the environment and human health. Immobilization techniques can vary depending on the nature of the contaminants and the specific site conditions, and they often require careful consideration and expertise to ensure their effectiveness. By immobilizing contaminants, we can mitigate their negative impacts and work towards restoring contaminated sites to a safe and healthy state.

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The angle ∅ to the nearest tenth is 51.8 degrees.

The trigonometric ratio can be solved as follows:

tan ∅  = 14 / 11

We are asked to solve for the angle ∅.

Therefore,

tan ∅  = 14 / 11

∅ = tan⁻¹ 14 / 11

Hence,

∅ = tan⁻¹ 1.27272727273

∅ = 51.8421769502

Therefore,

∅ = 51.8 degrees

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Step-by-step explanation:

Notice the vertex and focus have the same y coordinate so this means we will have sideways parabola.

Equation of a sideways parabola is

\((y - k) {}^{2} = 4p(x - h)\)

Since the vertex is (0,0), we can get rid of h and k.

\( {y}^{2} = 4px\)

Next Section: Value of P:

The value of P is the displacement between the focus and vertex.

So we do

\(p = x _{focus} - x _{vertex}\)

\( p = - 6 - 0\)

\(p = - 6\)

\( {y}^{2} = 4( - 6)x\)

\( {y}^{2} = - 24x\)

or

\( - \frac{ {y}^{2} }{24} = x\)

Answer:

1, 4, 9, 16,25, 36, 49, 64, 81, 100, 121, 144

Step-by-step explanation: hope it helps

Answer:

1, 4, 9, 16, 25, 36

Step-by-step explanation:

Hi! So when you're looking at questions like these, you're normally going to want to find a pattern. So lets look at this problem. When you jump from the number 1 to the number 4, you increase by 3. When you jump from the number 4 to the number 9, you increase by 5. When you jump from the number 9 to the number 16, you increase by 7.

Based on this information, you can conclude that the pattern is that it is increasing by odd numbers, and the odd number is increasing by 2 each time.

Now that we know the information, we can start finding the next terms. Since the jump from 9 to 16 was 7, we know that the next number is going to be 9 away from 16, which is 25.

Now that we have that term, we can find the next. We know that the jump from 16 to 25 is 9, so we know that the next term will be 11 away from 25, which is 36.

You could keep doing this forever.

Hope this helps!!

To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

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To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

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Answer:

74 km/hr

Step-by-step explanation:

185 km  / 2.5 hr = 74 km/hr

Answer:

The most correct option for the recursive expression of the geometric sequence is;

4. t₁ = 7 and tₙ = 2·tₙ₋₁, for n > 2

Step-by-step explanation:

The general form for the nth term of a geometric sequence, aₙ is given as follows;

aₙ = a₁·r⁽ⁿ⁻¹⁾

Where;

a₁ = The first term

r = The common ratio

n = The number of terms

The given geometric sequence is 7, 14, 28, 56, 112

The common ratio, r = 14/7 = 25/14 = 56/58 = 112/56 = 2

r = 2

Let, 't₁', represent the first term of the geometric sequence

Therefore, the nth term of the geometric sequence is presented as follows;

tₙ = t₁·r⁽ⁿ⁻¹⁾ = t₁·2⁽ⁿ⁻¹⁾

tₙ =  t₁·2⁽ⁿ⁻¹⁾ = 2·t₁2⁽ⁿ⁻²⁾ = 2·tₙ₋₁

∴ tₙ = 2·tₙ₋₁, for n ≥ 2

Therefore, we have;

t₁ = 7 and tₙ = 2·tₙ₋₁, for n ≥ 2.

Answer:

SSS

Step-by-step explanation:

the corresponding sides of the triangles are proportional to each other

Answer:

He would be making 544.8$ each week

Step-by-step explanation:

These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

Gregory most likely took an intelligence test, specifically the Wechsler Adult Intelligence Scale (WAIS). The WAIS is designed to measure an individual's cognitive abilities and is commonly used in psychological assessments. It consists of a full scale or total score, which is a combination of the verbal score and the performance score. The verbal score measures an individual's language and communication skills, while the performance score measures an individual's ability to solve problems and complete tasks. These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

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By satisfying this inequality, the submarine will have a volume that is small enough to navigate through obstacles yet large enough to accommodate the required objects.

To satisfy the requirements mentioned, we can set up the following inequality:

80 ≤ Volume < 100

This inequality states that the volume of the submarine needs to be at least 80 m³ but smaller than 100 m³.

Here's a breakdown of the inequality:

- The lower bound: The volume needs to be greater than or equal to 80 m³ to ensure that it meets the minimum requirement of holding a certain number of objects.

- The upper bound: The volume needs to be smaller than 100 m³ to ensure that the submarine can navigate between rocks and seaweed.

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Answer:

answer is image

Step-by-step explanation:

I think it is eight.

The principle of cross-cutting relationships is a valuable tool in relative dating, which helps determine the sequence of events in geological formations. It states that any geological feature that cuts across another is younger than the feature it cuts through.

However, in the case of the Upheaval Dome investigations, using the principle of cross-cutting to determine the relative ages of sedimentary rock layers would be inappropriate.

Upheaval Dome is a unique geological feature in Canyonlands National Park, Utah, characterized by a large impact crater. The crater was formed by a meteorite impact, which disrupted the original sequence of sedimentary rock layers. The impact event caused intense deformation, fracturing, and uplift, resulting in the formation of the dome.

As a result, the principle of cross-cutting relationships cannot be reliably applied in this context because the impact event altered the original layering and created a complex mixture of rocks The fractures and deformations caused by the impact would make it challenging to establish a clear sequence of events based on cross-cutting relationships.

Therefore, alternative methods, such as radiometric dating or stratigraphic analysis, would be more appropriate for determining the relative ages of the sedimentary rock layers in the Upheaval Dome investigations.

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Answer:

4.2

Step-by-step explanation:

Four and one-sixth is equal to 4.2. One-sixth is the same as 1/6, which is equal to 0.16666666666666666. When you add this fraction to 4, you get 4.166666666666667, which can be rounded to 4.2. Four and sixteen hundredths is equal to 4.16, which is close to 4.2 but not exactly the same. Six twenty-fifths is equal to 0.24, which is also not equal to 4.2. 416% is equal to 4.16, which is also not equal to 4.2.

Answer:

36°

Step-by-step explanation:

2x+3x=5x

5x=180°

x=180°:5=36°

Answer: A

Step-by-step explanation:

Answer:

y2=3

Step-by-step explanation:

4y2+7=19

Subtract 7 from both sides.

4y  2 =19−7

Subtract 7 from 19 to get 12.

4y2=12

Divide both sides by 4.

y2= 12/4

Divide 12 by 4 to get 3.

y2=3

​  

Answer:

4y2 + 7 = 19

Step-by-step explanation:

4y2 =19-7

4y2=12

4yx2=12

8y=12

dbs by 8

y=1.5 or 2

solution of the linear equation is x = (2a - 16)/ 3 and y = - (a+16)/ 9

An algebraic expression that shows a relationship between two variables   that have only first order term. One of the main criteria for linear equation is that we get a straight line when plot this equation in a coordinate system.

.

we are given, two linear equations x - a -3y = 0

and a - 2x -3y - 16 =0

from the first equation, x = a + 3y

we put the value of x in the second equation, a - 2(a +3y) - 3y -16= 0

                                                                     a - 2a - 6y - 3y -16 = 0

                                                          - a - 9y -16 =0

                                                   - (a + 16) = 9y

                                              y = - (a+16) / 9

now we put the value of y in the equation, x = a + 3y

                                    get, x = a+ 3 [ - (a+16)] / 9

                                      x = a + [ - (a+16)] / 3

                                          x = (3a - a -16) / 3

                              x = (2a - 16)/ 3

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Answer:

It's D

Step-by-step explanation:

AB = BC = CD = DA ≈ 5.099.Since all four sides of the rectangle have the same length, we can conclude that rectangle ABCD may indeed be a square.

To determine whether rectangle ABCD may be a square, we can use the distance formula to calculate the lengths of its sides. If all four sides have the same length, then the rectangle is a square.

Let's calculate the distances between the points:

Side AB:

Using the distance formula, we have:

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

AB = √[(2 - 1)² + (-1 - 4)²]

AB = √[1 + 25]

AB = √26 ≈ 5.099

Side BC:

Using the distance formula, we have:

BC = √[(x₂ - x₁)² + (y₂ - y₁)²]

BC = √[(7 - 2)² + (0 - (-1))²]

BC = √[25 + 1]

BC = √26 ≈ 5.099

Side CD:

Using the distance formula, we have:

CD = √[(x₂ - x₁)² + (y₂ - y₁)²]

CD = √[(6 - 7)² + (5 - 0)²]

CD = √[1 + 25]

CD = √26 ≈ 5.099

Side DA:

Using the distance formula, we have:

DA = √[(x₂ - x₁)² + (y₂ - y₁)²]

DA = √[(1 - 6)² + (4 - 5)²]

DA = √[25 + 1]

DA = √26 ≈ 5.099

Comparing the lengths of all four sides, we see that AB = BC = CD = DA ≈ 5.099.

Since all four sides of the rectangle have the same length, we can conclude that rectangle ABCD may indeed be a square.

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The area of the rectangle is (343/48)sqrt(3), or approximately 6.177 square inches.

To solve this problem, we first need to draw a diagram. Let ABC be the triangle, with altitude AD of length 7 inches. Let EF be the rectangle inscribed in the triangle, with one side on AB. Let G be the point where EF meets AD. Let AG have length x, and GD have length y.

Since EF is a rectangle, its opposite sides are parallel. Therefore, EF is parallel to BC. Furthermore, EF and BC have the same length, since EF is inscribed in the triangle. Let the length of EF (and BC) be z.

Since AG and GD are the two parts of AD that EF intersects, we have x+y=7.

Since EF is half the length of BC, we have z=0.5(AB).

The area of the rectangle is zy. Using similar triangles, we can see that (x/z) = (y/(7-z)). Solving this equation for y, we get y=(7z)/(2z+x). Substituting this expression for y into the expression for the area of the rectangle, we get:

Area of rectangle = zy =

\((7z^2)/(2z+x)\)

To find the value of z, we use the fact that z=0.5(AB). Using the Pythagorean theorem in triangle ABC, we have:

\(AB^2 = AD^2 + BD^2 = 7^2 + (2z)^2 \)

\(= 49 + 4z^2\)

Using the fact that z=0.5(AB), we can solve for z:

\(z^2 = (AB^2)/16\)

\(

= [(49 + 4z^2)/16]\)

Multiplying both sides by 16 and rearranging, we get:

\(12z^2 = 49\)

\(z^2 = 49/12\)

\(z = (7/2) \sqrt{} (3)/2\)

Now we can substitute this value of z into the expression for the area of the rectangle:

Area of rectangle =

\([(7/2) \sqrt{} (3)/2][(49/3+4(49/48))]\)

\( = (343/48) \sqrt{} (3)\)

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