The clubhouse has a water tank from which hikers fill their water jugs before walking the trail. The tank is a 5-gallon cylindrical container with a height of 2 feet and a radius of 4 inches. Alex fills his 1-gallon jug from the clubhouse tank before going on a hike. If the 5-gallon tank was full, what was the height of the water in the tank after Alex filled the 1-gallon jug?

Answer:

Using the concept of linear equations, we made two equations. Solving those two equations, we find that the cost of couch is $678 and that of coffee is $339.

Step-by-step explanation:

Concept: Let the cost of couch be $x and that of coffee be $y. The total cost is $1017, so,

x + y = 1017

Also, the cost of couch is two times that of coffee. So,

x = 2y

Substitute the value of x in first equation

2y + y = 1017

3y = 1017

y = 339

And, x + y = 1017

x + 339 = 1017

x = 678

Using the two equations, we find that y = $339 and x = $678.

So, the cost of couch is $678 and that of coffee is $339.

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The limit of csc(3x)/cot(x) as x approaches 0 is 1, after applying trigonometric identities and the properties of limits.

The student is asking for the limit of the function csc(3x)/cot(x) as x approaches 0. This is a limit problem in calculus, which is a part of mathematical analysis that deals with the behavior of functions near certain points. To find the limit as x approaches 0 for the function csc(3x)/cot(x), we need to apply trigonometric identities and the properties of limits. The function csc(3x) can be rewritten as 1/sin(3x) and cot(x) as cos(x)/sin(x). So the original limit becomes:

lim(x → 0) [csc(3x)/cot(x)] = lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))].

Using the trigonometric limit lim(x → 0) (sin(x)/x) = 1 and lim(x → 0) (cos(x)) = 1, we can simplify the expression by substituting 3x for x in the limit sin(x)/x. We get:

lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))] = lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x).

As x approaches 0, cos(x) approaches 1 and 3x/x approaches 3, hence:

lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x) = lim(x → 0) (sin(x)/x) × lim(x → 0) 1/cos(x) × lim(x → 0) (3x/3sin(3x)) = 1 × 1 × (3/3) = 1.

The final limit of csc(3x)/cot(x) as x approaches 0 is 1.

Applying the product property of square roots to the expression 9 * √(56) * √(x^7) * √(y^12), we simplify to 18y^6 * √(14x) * |x^3|.

Apply the product property of square roots:

9 * √(56) * √(x^7) * √(y^12)

Evaluate the square root:

9 * 2 * √(2 * 7) * √(x^7) * √(y^12)

Multiply the numbers:

9 * 2 * √(14) * √(x^7) * √(y^12)

Simplify the square root of an exponential expression:

9 * 2 * √(14) * |x^3| * √(x) * √(y^12)

Simplify the square root of an exponential expression:

9 * 2 * √(14) * √(x) * |x^3| * y^6

Apply the product property of square roots to the product of square roots is equal to the square root of the product:

9 * 2 * y^6 * |x^3| * √(14x)

Multiply the numbers:

18 * y^6 * √(14x) * |x^3|

Answer:

Option 2. 0.69p

Step-by-step explanation:

A market sells bananas for = $0.69 per pound

The cost, in dollars of p pounds of bananas = 0.69 × p

So the expression represents the cost, in dollars of p pounds of bananas

= 0.69p

Option 2. 0.69p is the right answer.

for an isosceles right triangle the legs would be 2 times the square root of the hypotenuse

 so for this:

the legs would be 2sqrt(10)

Answer

third option

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The scale copy of a shape is the resulting shape when the original shape is dilated. Possible scaled rectangles of rectangle A are:

A. 6cm by 1.5cm because

D. 18cm by 4.5cm because

E. 80cm by 20cm because

Given that

[tex]Length = 12cm[/tex]

[tex]Width = 3cm[/tex]

Divide the length and the width of the rectangle

[tex]k = Length \div Width[/tex]

[tex]k = 12cm \div 3cm[/tex]

[tex]k = 4[/tex]

This means that a scaled copy of rectangle A must have a value of 4 when the dimensions are divided.

Possible rectangles are:

A. 6cm by 1.5cm because [tex]6cm \div 1.5cm = 4[/tex]

D. 18cm by 4.5cm because [tex]18cm \div 4.5cm = 4[/tex]

E. 80cm by 20cm because [tex]80cm \div 20cm = 4[/tex]

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Answer:

The tax would be $ 1,263.75

Step-by-step explanation:

Given,

Total earning in one year = $ 8,425,

Income tax percentage per year on earning = 15%

Hence, the amount of tax at the end of one year

= 15% of the total earnings

= 15% of 8425

[tex]=\frac{15\times 8425}{100}[/tex]

[tex]=\frac{126375}{100}[/tex]

= $ 1,263.75

Answer:

The shortest side is 4 feet.

Step-by-step explanation:

The perimeter is the border of a geometric figure and corresponds to the sum of the length of all its sides.

So the perimeter in the case of a triangle is the sum of its three sides:

L₁ + L₂ + L₃ =Perimeter

In this case, the perimeter is known and it is necessary to calculate the value of the shortest side. In that case it will be called L₁. So, you know:

Replacing:

L₁ + 2*L₁ + L₁ + 13= 29

Solving:

(1+2+1)*L₁ + 13= 29

4*L₁ + 13=29

4*L₁ = 29-13

4*L₁ =16

L₁= 16÷4

L₁=4

The shortest side is 4 feet.

A perpendicular bisector is a special type of bisector because it intersects a segment at a 90 degree angle, and it passes through the segments midpoint.

Therefore based from this, we can create two true statements:

XB = BZ

and

∠ABZ = ∠ABX

Therefore the answer is:

C

Answer:

The answer is C. <ABZ = <BAX hop this hope this help

Reflecting a function across the y-axis will not change its domain or range; for an even function, such as one described by y(x) = -y(-x), the function is inherently symmetric about the y-axis, and thus both the domain and range remain unchanged.

When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.

The domain of a function is the set of all possible x-values, and the range is the set of all possible y-values. For a function reflected across the y-axis, the x-values are negated, but since the domain typically includes both positive and negative values for x, the overall set of possible x-values (the domain) does not change. Moreover, the y-values stay the same since they are not affected by the reflection across the y-axis, and thus the range remains the same as well.

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Reflecting a function across the y-axis will not change its domain or range; for an even function, such as one described by y(x) = -y(-x), the function is inherently symmetric about the y-axis, and thus both the domain and range remain unchanged.

The correct option is  A. Both the domain and range change.

When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.

The domain of a function is the set of all possible x-values, and the range is the set of all possible y-values. For a function reflected across the y-axis, the x-values are negated, but since the domain typically includes both positive and negative values for x, the overall set of possible x-values (the domain) does not change. Moreover, the y-values stay the same since they are not affected by the reflection across the y-axis, and thus the range remains the same as well.

The correct option is  A. Both the domain and range change.

Final answer:

There are 32 sample points in this experiment.

Explanation:

In this experiment, the manufacturer selects 5 CDs from the production line to inspect. To determine the number of sample points in this experiment, we need to consider the possible outcomes for each CD. For each CD, it can either be defective or non-defective, meaning there are 2 possible outcomes. Since there are 5 CDs being inspected, we multiply the number of outcomes for each CD by itself 5 times  to find the total number of sample points. Therefore, there are 32 sample points in this experiment.

Therefore, the total number of sample points in this experiment is 32, calculated by multiplying the number of outcomes for each CD (2) by itself 5 times . This accounts for all possible combinations of defective and non-defective CDs in the sample of 5.

Answer: C is the answer

Step-by-step explanation:

To find the probability that no two people will occupy adjacent seats, consider that n people are seated in a random manner in a row containing 2n seats. Using counting rule for combinations the total number of ways to select n seats of 2n seats is N=(2n/n). 

Now consider an event M that all two people occupy adjacent seats. This can be done by occupying all odd seats so that the even seats are left empty. This arrangement leaves the last 2nth seat empty. Even if one occupies that seat the condition of the event will not break. So, we have (n + 1) seats available for the n people to seat so that no two people occupy adjacent seats. N(M) = (n+1). Thus, the probability that no two people will occupy adjacent seats in a row of 2n seats can be computed as shown :

The probability that no two people will occupy adjacent seats is [(2n-1)!!]/[(2n)!].

To find the probability that no two people will occupy adjacent seats, we need to count the total number of possible arrangements where no two people are seated next to each other, and divide it by the total number of possible arrangements.

Let's consider a scenario where we have 2 people and 4 seats. In this case, the possible arrangements where no two people are seated next to each other are:

So, there are 3 possible arrangements where no two people are seated next to each other out of the total 6 possible arrangements.

Generalizing this, for n people seated in a row containing 2n seats, there are (2n-1)!! possible arrangements where no two people are seated next to each other. The double exclamation mark denotes the double factorial.
Hence, the probability is [(2n-1)!!]/[(2n)!].

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Answer:

AAS Congruence Theorem

Step-by-step explanation:

i dont know bro

Answer: AAS Congruence Theorem

Step-by-step explanation:

In the given picture , we have given two triangles ΔFGJ and ΔHJG with one common edge i.e. GJ

Now, in the given triangles ΔFGJ and ΔHJG we have

∠F=∠H   [given]

and ∠FGJ=∠HJG  [given]

Also, GJ=GJ            [Reflexive property]

Therefore, by AAS Congruence Theorem,

ΔFGJ ≅ ΔHJG