STORMS During a storm, a tree breaks 6 feet above the ground and falls to form a right triangle. If the top of the tree rests 20 feet from the base of the tree, approximately how tall was the tree before the storm?

The fraction of the area of the triangle that would be shaded in stage 7 is equal to 2,187/16,384.

No, there isn't a stage when the fraction of area shaded would be equal to 0.

In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Next, we would determine the area of the triangle that would be shaded in stage 2 is as follows;

Fraction of the area = 3/4 × 3/4 = 9/16.

The area of the triangle that would be shaded in stage 3 is as follows;

Fraction of the area = 3/4 × 3/4 × 3/4 = 27/64.

The area of the triangle that would be shaded in stage 4 is as follows;

Fraction of the area = 3/4 × 3/4 × 3/4 × 3/4 = 81/256.

Therefore, the area of the triangle that would be shaded in stage 7 is as follows;

Fraction of the area = 3/4 × 3/4 × 3/4 × 3/4 × 3/4 × 3/4 × 3/4 = 2,187/16,384.

In this context, we can reasonably infer and logically deduce that there isn't a stage when the fraction of area shaded in this triangle would be equal to zero (0) because there is a linear relationship between the shaded and unshaded area.

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The inequality - 15 > t has the same meaning as t > -15

An inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

The given inequality is - 15 >t

We can rewrite this as  t > -15

The above two inequalities have the same meaning.

Reading from right to left, the first inequality says, "b is greater than or equal to negative 18."

Reading from left to right, the second inequality says, "b is greater than or equal to negative 18."

Therefore the two inequalities have the same meaning.

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Step-by-step explanation:

Domain: The domain of the function is all real numbers.

Range: The range of the function is all real numbers less than or equal to 8. To see this, note that the leading coefficient of the polynomial is negative (-x^3), so the function approaches negative infinity as x approaches positive or negative infinity. The largest y-value the function can attain is 8, which occurs at x = 2.

Relative maxima and minima: To find the relative maxima and minima, we find the critical points of the function, which are the values of x that satisfy f'(x) = 0 or f'(x) does not exist. The first derivative of the function f(x) is given by:

f'(x) = -3x^2 + 16x - 15

Solving f'(x) = 0, we get:

-3x^2 + 16x - 15 = 0

x = 1, 5

We also need to determine the concavity of the function near each critical point to determine whether each is a relative maximum or minimum. To do this, we find the second derivative of the function and evaluate its sign at each critical point. The second derivative of f(x) is given by:

f''(x) = -6x + 16

Since f''(x) is always negative, the function is concave down and therefore has a relative maximum at x = 1 and a relative minimum at x = 5.

End behavior: The leading term of the function is -x^3, which means the function approaches negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity. The end behavior of the function is therefore negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.

Increasing and decreasing intervals: To find the increasing and decreasing intervals of the function, we find the critical points and the sign of f'(x) in the intervals between the critical points.

f'(x) = -3x^2 + 16x - 15

Since f'(x) is negative for x < 1 and positive for x > 1, the function is decreasing for x < 1 and increasing for x > 1. Similarly, since f'(x) is positive for x < 5 and negative for x > 5, the function is increasing for x < 5 and decreasing for x > 5. So, the increasing intervals are (negative infinity, 1) and (1, 5) and the decreasing intervals are (5, positive infinity).

An expression for the volume of a rectangular prism with length 7.5 ft, width w ft, and height 4.2 ft is 31.5w ft³.

Therefore the answer is 31.5 ft³.

The volume of a rectangular prism can be found by multiplying its length, width, and height. So, for a rectangular prism with length 7.5 ft, width w ft, and height 4.2 ft, the volume can be expressed as:

V = 7.5 * w * 4.2

V = 31.5 w ft³

So, the expression for the volume of this rectangular prism is 7.5 * w * 4.2, that is 31.5 w cubic feet.

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his gives us a coefficient of determination. Of around then see what you get 0.7 and we're going to round to 100.710. Is our explained, variance,

we are looking at the pounds of waste here and the number of people in the home, so we're asked to find the proportion of variance that can be explained. So was this. The variance explained basically refers to the coefficient of determination, r square,

pounds of waste= 0.27 ,1.41, 2.19, 2.83, 2.19, 1.81, 0.85, 3.05

           in home = 2       ,  3    ,  3,       6  ,   4  ,  2,    1,      5.

so we are basically asked to find r squared our r squared equation is

[tex]r^2=\frac{\sum(x_i-x')^2}{N}[/tex]

the mean is 1.8 ,

which is 1.8 multiplied by y minus its mean, which is around 3.3.

we calculate this giving us a sum of products that is = 9.35

We take this sum of x minus a mean 1.8 square, giving us a sum of square of x around 6.3 2 point now. Finally, for a sum with squares of y we're going to do the same

x'-xi=9.35.

his gives us a coefficient of determination. Of around then see what you get 0.7 and we're going to round to 100.710. Is our explained, variance,

The complete question is -

what is the proportioan of variance explained pounds of waste

pounds of waste= 0.27 ,1.41, 2.19, 2.83, 2.19, 1.81, 0.85, 3.05

           in home = 2       ,  3    ,  3,       6  ,   4  ,  2,    1,      5.

a) 0.710 b) 0.842 c)  0.549 d) 1.480

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Answer:

I think BC

Step-by-step explanation:

In the diagram, AC is a diameter of circle O. If the slope of BC is -1/2, then the slope of AB is 2.

What is the diameter of the circle?

The diameter of a circle is the length of the line starting from one point on a circle to another point and passing through the center of the circle. It is equal to twice the radius of the circle.

We have that,

ABC is a right triangle

so,

AB is perpendicular to BC

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1.

so,

m1 * m2 = -1

in this problem

mAB * mBC =-1

solve for mAB

mAB = -1 / mBC

mAB = -1 / -1/2

mAB = 2

therefore, In the diagram, AC is a diameter of circle O. If the slope of BC is -1/2, then the slope of AB is 2.

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Complete Question:

In the diagram, AC is the diameter of circle O. If the slope of BC is -1/2, what is the slope of AB?

Answer:

600

Step-by-step explanation:

She had -350 then ended with 250

First you get -350 to 0... that's by adding 350.

Then getting from 0 to 250, you add 250

Now we add 350 and 250 to get a total of 600

Answer:

a) 83.75% or 84% rounded to the nearest percent.

b) 84%

Step-by-step explanation:

[tex]\frac{64+85+92+94}{4}[/tex] = 83.75  changed to a percent and rounded to the nearest percent would be 84%

.15(.88) + .10(.76) + .75(.84) = .838 changed to a percent and rounded to the nearest percent would be 84%

Answer:

66 inches

Step-by-step explanation:

77→ 14

X→12

In the proportion

a/b=c/d

the product of the means equals the product of the extremes. That is,

ad=bc.

So,

77 * 12 = X * 14

x = (77 X 12) / 14 = 66

Answer:

5.196103885259%

Step-by-step explanation:

Negative values detected. All input values threated as percentages (e.g. an input of 0.1 is threated as 0.1%, -10 is threated as -10%).

The surface area of the cube of side length 0.125 inches is given as follows:

S = 0.09375 in².

The surface area for a cube of side length a is given by the equation presented as follows:

S = 6a².

The side length in this problem has the value given as follows:

a = 1/8 = 0.125 in.

Hence the surface area of the cube is calculated as follows:

S = 6(0.125)²

S = 0.09375 in².

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Answer:

933500

Step-by-step explanation:

You move the decimal over 5 spaces to the right

The number of subs in the order is 8 or 9

Let's call the number of subs in the order "x".

Since the cost of 3 subs is $20, the cost per sub is $20 / 3 = $6.67.

And since the cost of 4 subs is $26, the cost per sub is $26 / 4 = $6.50.

So the cost per sub is between $6.50 and $6.67.

If the total cost is $56, then the cost per sub must be $56 / x.

So:

x = 56/6.5 or x = 56/6.67

Evalutate

x = 8.6 or x = 8.4

Approximate

x = 9 or 8

Hence, the subs is 8 to 9

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The linear program has an optimal solution of 28.5 at (A, B) = (2, 5) when the right-hand side for constraint 1 is 10. If the right-hand side is increased to 11, the optimal solution remains 28.5 at the same point.

The dual value for constraint 1 stays the same as long as the right-hand side stays within the range 8.4 to 11. The value of the optimal solution will increase by 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is within the range 23 to 27.

a) To find the new optimal solution, we need to graph the feasible region and find the new corner points. After the change, the first constraint becomes 1A + 1B ≤ 11. The other two constraints remain the same. The corner points can be found by substituting the bounds of each variable into the constraints and solving for the other variable. The feasible region can then be graphed, and the maximum of the objective function can be found at one of the corner points.

The new corner points are (0,0), (0,9), (6,0), and (2,5). The feasible region can be graphed as a triangle with these corner points. The maximum of the objective function 3A + 2B occurs at the point (2,5), where the value of the objective function is 28.5.

b) The value of the objective function at the optimal solution is 28.5, at (A, B) = (2, 5).

c) The right-hand side range information for constraint 1 tells us that if the right-hand side is increased from 10 to 11, the dual value will remain the same (since the allowable increase is 2.6 and the right-hand side only increases by 1). The range for constraint 1 is 8.4 to 11. As long as the right-hand side stays within this range, the dual value of 2.6 is applicable.

d) The dual value for constraint 2 is 0.5. Using this dual value and the right-hand side range information, we can conclude that the value of the optimal solution will increase by 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is within the range 23 to 27.

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Complete question:

Consider the following linear program.

Max 3A + 2B s.t.

1A + 1B ≤ 10

3A + 1B ≤ 27

1A + 2B ≤ 18

A, B ≥ 0

The value of the optimal solution is 28.5. Suppose that the right-hand side for constraint 1 is increased from 10 to 11.

(a) Use the graphical solution procedure to find the new optimal solution.

What is the value of the objective function at the optimal solution?

(blank) at (A, B) =

Use the solution to part (a) to determine the dual value for constraint 1.

(c) The computer solution for the linear program provides the following right-hand side range information

. Constraint RHS Value Allowable Increase Allowable Decrease

1 10.00000 2.60000 1.00000

2 27.00000 3.00000 13.00000

3 18.00000 Infinite 6.50000

What does the right-hand side range information for constraint 1 tell you about the dual value for constraint 1?

The range for constraint 1 is (blank) to (blank) . As long as the right-hand side stays (within/outside) this range, the dual value of (blank) is applicable.

(d) The dual value for constraint 2 is 0.5. Using this dual value and the right-hand side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2?

The value of the optimal solution will increase by (blank) for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is (within/outside) the range (blank) to (blank).

The decimal number that lies between 0.7 and 0.8, has three digits to the right of the decimal point, and whose sum of the digits is 24 is 7.98.

A decimal number is a number that has a fractional part represented by a decimal point. The digits to the right of the decimal point represent values that are smaller than 1.

In this problem, we are given that the decimal number has three digits to the right of the decimal point and that its sum of the digits is 24. Let's call the decimal number x. We can write an equation to represent the sum of the digits:

x = a + b/10 + c/100

Where a, b, and c are the digits of x.

We know that 0.7 < x < 0.8 and that the sum of the digits of x is 24, so we can write two more equations:

0.7 < a + b/10 + c/100 < 0.8

a + b + c = 24

By solving these three equations, we can find the decimal number x.

We know that a must be 7 because 0.7 < x < 0.8, so a = 7. We also know that b + c = 24 - 7 = 17. Now we need to find two digits b and c such that b + c = 17 and b/10 + c/100 is between 0 and 0.1.

The largest value of b that still satisfies this condition is 9. This means that

=> c = 17 - 9 = 8.

Therefore, the decimal number

=> x = 7 + 9/10 + 8/100 = 7.98.

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Answer:

Step 2

Step-by-step explanation:

https://brainly.com/question/12924127

/\ Explantion hope it help...

The area of rectangle from the given vertices is 90 squared units

The area of a rectangle is the product of its length and width. If a rectangle has length "l" and width "w", its area can be calculated as:

A = l * w

where A is the area and l and w are the length and width of the rectangle, respectively.

The area of a rectangle can be calculated as the product of its length and width. Given the vertices, the length of the rectangle is 14 - 4 = 10 units, and its width is 2 - (-7) = 9 units. Hence, the area of the rectangle is 10 * 9 = 90 square units.

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Answer:

see below

Step-by-step explanation:

area of the garden is 4​(6.5x+2.5​).

combined area of the garden and the walkway is 4.5​(8x+4​).

so area of the walkway = 4.5​(8x+4​) -4​(6.5x+2.5​)

=36x+18 -26x-10

=10x+8

The correct Option for this question is option C i.e. x= 4tan34°. The other options which are given in the question are incorrect.

The Right angled triangle along with the base angle of 34°. The base is equal to 4.

θ= 34°

To find the value of x which is equal to the perpendicular of the right-angled triangle

According to the trigonometric ratio

tanθ = Perpendicular ÷ base

According to the above formula

tan 34 = x ÷ 4

Now, we have to multiply each side by 4.

x= 4× tan34° which means x= 4tan34°

tan 34° = 0.6745

x= 4× 0.6745

X=2.70

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The mean rainfall for the highland storms is 15.27 and the mean rainfall for the lowland storms is 12.05mm

The mean is also sometimes called the average

To find the mean, we can add up every number in the data set and divide that sum by the total number of data points within the set.

The sum of the data of Highlands storms:

= 2*2 + 3*4 + 2*6 + 3*8 + 4*10 + 3*12 + 4*14 + 5*16 + 5*18 + 4*20 + 2*22 + 24 + 2*26 + 2*28 + 30 + 32 = 672

the total number of data is 44

Mean = 672/44 = 15.27 mm

The sum of the data of Lowland storms:

= 3*2 + 5*4 + 3*6 + 3*8 + 5*10 + 7*12 + 6*14 + 4*16 +2*18 + 20 + 2*22 + 24 + 2*28 = 530

the total number of data is 44

Mean = 530/44 = 12.05 mm

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Full question:

The dot plots show rainfall totals for several spring storms in highland areas and lowland areas.

What is the mean rainfall for the highland storms?

a) 12.5 mm

b) 14 mm

c) 15.27 mm

d) 24 mm

What is the mean rainfall for the lowland storms?

a) 10.5 mm

b) 12.05 mm

c) 16.05 mm

d) 30 mm

Answer: 15.27 and 12.05

Step-by-step explanation:

The number can be broken apart from the factor 42 using the place value as 40 + 2 here 4 is in the tens place and 4 is in the one's place.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The number is 42.

As we know,

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

So, We get;

⇒ 42 = 40 + 2

⇒ 42 = 4 × 10 + 2 × 1

Thus, The number can be broken apart from the factor 42 using the place value as 40 + 2 here 4 is in the tens place and 4 is in the one's place.

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0

The graph is under 0. therefore it can be anything under

Answer: 0

Step-by-step explanation: The graph is shaded below the x-axis, so it includes all values of y that are under (or equal to) 0.

Answer:

see below

Step-by-step explanation:

We are here given that weight of an object having mass of 5kg is 450N .

As we know that,

Weight = mass * acceleration due to gravity (g)

So that ,

450N = g * 5kg

g = 450/5 m/s²

g = 90m/s²

Again in second case,

147N = g' * 50kg

g' = 147/50 m/s²

g' = 29.4 m/s²

since here g ≠ g'

Therefore,

mass and weight are not promotional in this case. This may be due to the fact that the acceleration due to gravitational force of each celestial object is different and weights may have been measured on different planets.

And the constant of proportionality is g ( acceleration due to the gravitational force) .

And we are done!

1/4 of the flour was used for the muffins and 5/6 of the remaining flour was used for the cake.

Let's call the total amount of flour in the bag "x".

The amount used for the muffins is 1/4 of the total bag, or x/4.

The amount used for the cupcakes is twice as much as for the muffins, or 2 * x/4 = x/2.

The amount used for the muffins was 3 times as much as for the cupcakes, so 3 * x/2 = 3x/2 grams of flour were used for muffins.

The amount used for the cake was 256.5 grams more than the muffins, so x/4 + 256.5 = 3x/2.

Solving for x, we find that x = 2048 grams.

So, 1/4 of the flour was used for the muffins, or 2048 * 1/4 = 512 grams.

And 5/6 of the remaining flour was used for the cake, or (2048 - 512) * 5/6 = 1024 grams.

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Answer:LxW

Step-by-step explanation:

Length x width