The capacity of a water tank is 1000 gallons. Don uses a bucket that can hold 2 gallons to fill the tank. It takes him 3 minutes to fill the bucket with water and pour it into the tank.

The equation of the line is expressed in slope-intercept form as:

y = -8.2x - 60.6

The equation of a line that passes through point (8, 5) and has a slope of -8.2 can be written in slope-intercept form as y = mx + b, where we have:

m as the slope

b as the y-intercept.

Find the y-intercept by substituting x = 8, y = 5, and m = -8.2 into y = mx + b:

5 = -8.2(8) + b

5 = 65.6 + b

5 - 65.6 = b

b = -60.6

Substitute m = -8.2 and b = -60.6 into y = mx + b:

y = -8.2x - 60.6

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The total cost of your eulerization is 111.

We can Eulerize a graph by ensuring  to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.

A good method to do this is by  adding  edges between pairs of vertices that have odd degree until all vertices have even degree.

We have to add all the edges to get the total cost

10+15+20+4+9+3+17+14+19

111

Hence, the total cost of your eulerization is 111.

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The rule that describes the transformation is (x, y) → (y, -x)

We are given that;

The points (-2,5),(2,5),(2,1).

Now,

To rotate a point 90° clockwise with the origin as the center of rotation, we can use the following rule:

(x, y) → (y, -x)

This means that the x-coordinate of the original point becomes the y-coordinate of the new point, and the y-coordinate of the original point becomes the opposite of the x-coordinate of the new point.

For example, applying this rule to the point (-2, 5), we get:

(-2, 5) → (5, 2)

Therefore, by the transformation the answer will be(x, y) → (y, -x)

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The probability that it weighs more than 51 pounds exactly 53 pounds.

Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.

We need to find the probability that it weighs more than 51 pounds,

P(X = 53) = 0

z = (51 - 50) / 0.5 = 2.00

P(X > 51) = P(z > 2.00) = 0.0228

z1 = (49 - 50) / 0.5 = -2.00

z2 = (51 - 50) / 0.5 = 2.00

P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544

Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.

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It takes the object 3(3/4) seconds to travel the full distance of the trip.

We have,

The object moves at a constant speed, so we can use the formula:

distance = speed x time

Let d be the full distance of the trip, and t be the time it takes the object to travel that distance.

We can write the proportion as:

(1/20) / (3/4) = d / t

Simplifying the left-hand side:

(1/20) x (4/3) = d / t

1/5 = d / t

Now, we can solve for t by multiplying both sides by 5:

t x (1/5) = d x (1/5)

t = d/5

Now,

The time it takes the object to travel the full distance of the trip is equal to the distance divided by 5.

So, the object takes 5 times as long to travel the full distance as it takes to travel 1/20 of the distance.

And,

The time it takes the object to travel the full distance is:

t = (5 x 3/4) seconds

t = 15/4 seconds

t = 3 3/4 seconds

Therefore,

It takes the object 3 3/4 seconds to travel the full distance of the trip.

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The complete question:

An object moves in a straight line at a constant speed. The object moves 1/20 of the way in 3/4 of a second. At that speed, how many seconds does it take the object to travel the full distance of the trip?

Answer:

16864

Step-by-step explanation:

16694 + 170 = 16864

If in a triangle ABC, right angle is at C, BA is hypotenuse, the length of side BC is 5√7 units.

In a right triangle, the hypotenuse is the longest side and is opposite the right angle. Therefore, in triangle ABC, side BA is the longest side, and it is also the hypotenuse.

Using the Pythagorean theorem, we can find the length of the third side BC. The theorem states that the square of the hypotenuse (BA²) is equal to the sum of the squares of the other two sides (BC² + CA²).

BA² = BC² + CA²

16² = BC² + 9²

256 = BC² + 81

BC² = 256 - 81

BC² = 175

BC = √175

BC = 5√7

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Answer:

136.95

Step-by-step explanation:

hope u understand

Answer:3.14

Step-by-step explanation:This is the only number that I know that corresponds with the Pie symbol.

In the given diagram, the total surface area of the composite figure is 361.28 square yards

From the question, we are to calculate the total surface area of the given composite shape

In the composite shape, we have a cone and a hemisphere

The total surface area of the composite figure = Surface area of the hemisphere + Curved surface area of the cone

Surface area of the hemisphere = 2πr²

Where r is the radius

Curved surface area of a cone = πrl

Where r is the radius

and l is the slant height

In the given diagram,

Using the Pythagorean theorem,

l² = 12² + 5²

l² = 144 + 25

l² = 169

l = √169

l = 13 yd

Radius of cone and hemisphere = 5 yd

Total surface area of the composite figure = 2πr² + πrl

Substituting the parameters

Total surface area of the composite figure = 2π(5)² + π(5)(13)

Total surface area of the composite figure = 50π + 65π

Total surface area of the composite figure = 115π

Total surface area of the composite figure = 361.28 yd²

Hence,

The total surface area is 361.28 square yards

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The value of the function f(1/2) for the f(x) = 2 / 5 x- 5 / 2 is equal to -2.3.

Function is equal to,

f(x) = 2 / 5 x- 5 / 2

To get the value of f ( 1 / 2 ) .

Substitute the value of x equals to ( 1 / 2 ) we get,

f(x) = (2 / 5 ) x- ( 5 / 2 )

This implies,

f ( 1 / 2 ) = ( 2 /5 ) × ( 1 / 2 ) - ( 5 / 2 )

⇒ f ( 1 / 2 ) = ( 1 / 5 ) - ( 5 / 2 )

Take the least common multiple of 5 and 2 we get,

least common multiple of 5 and 2 is 10.

⇒ f ( 1 / 2 ) = ( 2  - 25 ) / 10

⇒ f ( 1 / 2 ) = -23 /10

⇒ f ( 1 / 2 ) = -2.3

Therefore, the value of f(1/2) for the given function is equal to -2.3.

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The above question is incomplete, the complete question is:

Consider the function: ƒ(x) = 2/5 x- 5/2 find the value of f( 1/2)?

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Answer:

The correct operator for the exponential expression 3^5 ? 4^6 is > (greater than), because we can compare the values of the two exponents:

3^5 = 243

4^6 = 4096

Since 4096 is greater than 243, we can write:

3^5 < 4^6

or

4^6 > 3^5

Therefore, the correct operator for the exponential expression 3^5 ? 4^6 is > (greater than).

Answer: The area left for development in the field outside the playground is C)1024ft^2

Step-by-step explanation:

We know  that area of rectangle formula is,

Area =  square unit

The total area of the field is the area of the large rectangle, which is:

=>

The area of the playground is the area of the smaller rectangle, which is:

=>

Therefore, the area left for development outside the playground is:

=>

Answer:

1/15 or 0.0667

Step-by-step explanation:

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bardai

chatgpt

red marble on the first draw is 2/6, or 1/3

red marble on the second draw, given that the first marble was red, is 1/5

(1/3) * (1/5) = 1/15

The equation for the temperature at 11PM as required is; T(11) = T(5) - 18°F.

The solution as required in the task content is; T(11) = -4°F.

It follows from the task content that the temperature at 11PM is to be determined from the given information.

On this note, we have that; the equation which represents the situation is;

T(11) = T(5) - 18°F where, the temperature at 5pm T(5) = 14°F.

T (11) = 14°F - 18°F

T (11) = -4°F.

Ultimately, the temperature at 11PM is; -4°F.

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Answer:

<

Step-by-step explanation:

multiply 1/3 by 10 = 10/30

multiply 6/15 by 2 = 12/30

6/15 is greater

Answer:

4, 2

Step-by-step explanation:

the mode is the data sets that occur most frequently

let's firstly convert tyhe mixed fraction to an improper fraction.

[tex]\stackrel{mixed}{37\frac{5}{7}}\implies \cfrac{37\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{264}{7}} \\\\[-0.35em] ~\dotfill\\\\ \textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=\frac{264}{7} \end{cases}\implies \cfrac{264}{7}=2\pi r\implies \cfrac{264}{7}=2\cdot \cfrac{22}{7}\cdot r \\\\\\ \cfrac{264}{7}=\cfrac{44r}{7}\implies 264=44r\implies \cfrac{264}{44}=r\implies 6=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=6 \end{cases}\implies A=\pi (6)^2\implies A=\cfrac{22}{7}\cdot 6^2 \\\\\\ A=\cfrac{22}{7}\cdot 36\implies A=\cfrac{792}{7}\implies A=113\frac{1}{7}[/tex]

The quadratic equation in the given graph can be written as:

y = -3*(x + 2)^2 + 4

We can see a quadratic equation that opens downwards and we can see that the vertex is at (-2, 4), then if the leading coefficient is a, we can write this as:

y = a*(x + 2)^2 + 4

We can also see that the parabola passes through (0, -8) replacing these values we will get:

-8= a*(0 + 2)^2 + 4

-8 - 4 = a*4

-12/4 = a

-3 = a

Then the quadratic equation is

y = -3*(x + 2)^2 + 4

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The coordinates of the vertices for the image triangle after a translation 3 units up are A'(-3, 6), B'(0, 10), and C'(-3, 3). (option b)

Let's first visualize the given triangle ABC with vertices at A(-3, 3), B(0, 7), and C(-3, 0). We can plot these points on a coordinate plane and connect them to form the triangle. Now, let's consider the translation that moves the triangle 3 units up. This means that we need to add 3 to the y-coordinate of each vertex to get the coordinates of the image.

So, the coordinates of the vertices of the image triangle, let's call it A'B'C', will be:

A' = (-3, 3+3) = (-3, 6)

B' = (0, 7+3) = (0, 10)

C' = (-3, 0+3) = (-3, 3)

Now, we can plot these points and connect them to form the image triangle A'B'C'. We can see that the image triangle is simply the original triangle translated 3 units up.

Hence the correct option is (b).

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Answer:

Option B

Step-by-step explanation:

To factor 20w+30, we can first factor out the greatest common factor, which is 10:

20w+30 = 10(2w+3)

So the factored form of 20w+30 is 10(2w+3).

Answer:

10(2w+3)

Step-by-step explanation:

The smallest number of edges that would need be duplicated to eulerize the graph is 10.

Given that a graph has 20 vertices.

In order for a graph to be eulerized, it has to added an edge to each vertex having odd valence.

Here total number of vertices = 20

So, the smallest number of edges that would need be duplicated to eulerize the graph is half of the total number of vertices.

Number of edges = 20/2 = 10

Hence it is needed 10 edges to eulerize the graph.

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The polar coordinates of the point (-9, 4) are approximately (9.85, -24.04°).

To find the polar coordinates (r,θ) corresponding to the rectangular coordinates (-9, 4), we can use the following formulas:

r = sqrt(x^2 + y^2)

θ = arctan(y/x)

Substituting the values x = -9 and y = 4, we get:

r = sqrt((-9)^2 + 4^2)

= sqrt(81 + 16)

= sqrt(97) ≈ 9.85

θ = arctan(4/-9)

= -0.42 radians

≈ -24.04 degrees

Therefore, the polar coordinates of the point (-9, 4) are approximately (9.85, -24.04°).

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The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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The equation that describes the weight of the dog as a function of time is

y = 5x + 1.

We have,

To determine the equation that will describe the dog's weight, we can use the formula for linear interpolation:

y = mx + b

where y is the weight of the dog in kg, x is the number of months since birth, m is the rate of increase of the dog's weight every month in kg/month, and b is the initial weight of the dog in kg.

From the problem, we know that the initial weight of the dog is 1 kg and the monthly average weight gain is 5 kg.

Therefore, we can substitute these values into the formula:

y = 5x + 1

This equation describes the weight of the dog as a function of time.

To predict the dog's weight after five months, we can simply substitute

x = 5 into the equation:

y = 5(5) + 1 = 26 kg

Therefore, we can predict that the dog will weigh 26 kg after five months.

To represent this graphically, we can plot the equation y = 5x + 1 on a coordinate system with time (x-axis) and weight (y-axis).

We can then plot the predicted weight of the dog after five months

(x=5, y=26) as a point on the graph.

The resulting graph will be a straight line with a positive slope of 5, passing through the point (0,1) and the predicted point (5,26).

Thus,

The equation that describes the weight of the dog as a function of time is

y = 5x + 1.

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Answer:

We don't know the initial value of the principal but we do know that the accumulated value is double (twice) the principal. It takes 9.9 years for money to double if invested at 7% continuous investment

The factorized form of the equation is A = -16 ( t + 1 ) ( t - 5 )

Given data ,

Let the polynomial be represented as A

Now , the value of A is

A = -16t² + 64t + 80

On factorizing the equation , we get

A = -16 ( t² - 4t - 5 )

On further simplification , we get

A = -16 ( t² + t - 5t - 5 )

A = -16 ( t ( t + 1 ) - 5 ( t + 1 ) )

A = -16 ( t + 1 ) ( t - 5 )

Hence , the factorized form is A = -16 ( t + 1 ) ( t - 5 )

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