A mountain is 16, 694 feet above sea​ level, and a valley is 170 feet below sea level. What is the difference in elevation between the mountain and the​ valley?

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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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:

=>

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 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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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.

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

Answer:

Step-by-step explanation:

i believe the answer is 1270

Hypertension is known as the silent killer because often, early hypertension is asymptomatic. a systolic blood pressure of  140 mm Hg would make us concerned the patient was hypertensive.

Here, we know that Asymptomatic:

Any condition that a patient tests positive for but does not manifest any symptoms of is referred to in medicine as being asymptomatic. After a diagnosis, a medical illness may be deemed asymptomatic if no obvious symptoms emerge.

Absence of symptoms is referred to be asymptomatic. If your doctor says you are asymptomatic, this indicates you have a disease or condition but don't show any symptoms or outward indicators of being ill.

Instances of sickness that are symptom-free for all or part of the time are frequently referred to be asymptomatic. Pre-symptomatic, however, is a word sometimes used to describe patients that initially have no symptoms but later develop them.

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complete question:

Hypertension is known as the silent killer because often, early hypertension is asympotmatic. a systolic blood pressure of _____ would make us concerned the patient was hypertensive.

Answer:
79.95 yards.

Step-by-step explanation:

Each board is 16 feet long and there are 3 feet in 1 yard. So, each board is 16/3 = 5.33 yards long (rounded to two decimal places).

If Steven has 15 yards of these boards, the combined length of the boards in yards is 15 times the length of each board, which is 15 x 5.33 = 79.95 yards (rounded to two decimal places).

Therefore, the combined length of the boards in yards is approximately 79.95 yards.

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 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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Step-by-step explanation:

You didn't list any choices...see if either of these match

4x = -2x + 16

6x = 16

6x-16 = 0

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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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]

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).

The similarity ratio between the two octagons is 1:2 (Option b).

To begin, we need to know that similar figures have the same shape, but they may differ in size. For instance, we can have two octagons with different areas but the same shape. In this case, we are given that the two octagons are similar, and we are given the areas of the two octagons.

Let the similarity ratio between the two octagons be "x". For areas, we know that the ratio of the areas of two similar figures is the square of their similarity ratio. Therefore, we can set up the following equation:

x² = (Area of smaller octagon) / (Area of larger octagon)

Substituting the given areas, we get:

x² = 4 / 16    

x² = 0.25

Taking the square root of both sides, we get:

x = √0.25

x = 0.5

Therefore, the similarity ratio between the two octagons is 1:2 (Option b).

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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:

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:

<

Step-by-step explanation:

multiply 1/3 by 10 = 10/30

multiply 6/15 by 2 = 12/30

6/15 is greater

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 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:

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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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 Euler path of the given graph is CDBFADF.

A path in a finite graph known as an Euler path is one that traverses each edge precisely once while yet allowing for the revisiting of vertices.

A similar Euler trace that begins and finishes at the same vertex is known as an Euler circuit or cycle. When Leonhard Euler found a solution to the Seven Bridges of Konigsberg puzzle in 1736, it was first brought up for discussion.

A path known as an Euler path is one that utilises every edge in the graph once and only once. It doesn't have to return to the starting point because it is a path.

A circuit that utilises every edge in the diagram once is known as an Euler circuit. As it is a circle, it should start and terminate at the same vertex

The euler path of the given graph is CDBFADF.

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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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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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Step-by-step explanation:

The smallest number among the given options is (a) -1. This is because -1 is a negative number and is less than zero, while the other options are either positive or greater than zero. (b) -1/2 is greater than -1, (c) 0 is neither positive nor negative, and (d) 3 is greater than both -1 and -1/2. Therefore, the correct answer is (a) -1.

Answer:

A is correct

Step-by-step explanation:

its correct be cause negative is less than 0

its like being in dept

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)?