As a part of their weather unit, Anoki’s science class took a hot air balloon ride. As they passed over a fenced field, the angle of depression of the closer side of the fence was 32°, and the angle of depression of the farther side of the fence was 27°. If the height of the balloon was 800 feet, estimate the width of the field. Round your answer to the nearest foot. 2016_01_25_17_23_501.png The width of the field is about feet

When the radius of a cylinder is increased by a factor of 5, the volume of the cylinder increases by a factor of 25.

The volume of a cylinder can be calculated using the formula V = πr2h, where V is the volume, r is the radius, and h is the height. In this case, the radius of the cylinder is increased by a factor of 5, but the height remains the same. Let's consider the original radius as r and the increased radius as 5r. The volume of the original cylinder is πr2h, and the volume of the new cylinder is π(5r)2h.

Simplifying the expression for the volume of the new cylinder, we get V' = 25πr2h. Comparing the volume of the new cylinder to the volume of the original cylinder, we can see that the volume has increased by a factor of 25. Therefore, statement B is correct: The volume of the cylinder increases by a factor of 25.

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The correct answer is B) The volume of the cylinder increases by a factor of [tex]25.[/tex]

Let's analyze the relationship between the volume of a cylinder and its dimensions.

The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:

[tex]\[ V = \pi r^2 h \][/tex]

where:

[tex]\( r \)[/tex] is the radius of the cylinder,

[tex]\( h \)[/tex] is the height of the cylinder.

Given that the height [tex]\( h \)[/tex] remains unchanged, if the radius [tex]\( r \)[/tex] is increased by a factor of [tex]5[/tex], the new radius [tex]\( r' \)[/tex] becomes[tex]\( 5r \).[/tex]

Now, let's compare the volumes before and after the increase in radius:

1. Original Volume [tex](\( V_{\text{original}} \))[/tex]

[tex]\[ V_{\text{original}} = \pi r^2 h \][/tex]

2. New Volume [tex](\( V_{\text{new}} \))[/tex]

After increasing the radius by a factor of [tex]5[/tex], the new radius [tex]\( r' = 5r \)[/tex].

[tex]\[ V_{\text{new}} = \pi (5r)^2 h = \pi (25r^2) h \][/tex]

Now, compare [tex]\( V_{\text{new}} \)[/tex] with [tex]\( V_{\text{original}} \)[/tex]

[tex]\[ \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{\pi (25r^2) h}{\pi r^2 h} = \frac{25r^2 h}{r^2 h} = 25 \][/tex]

Answer:

Option c. Population: 10 shipments of 1000 cartons of eggs

sample: every 50th carton in each shipment.

Step-by-step explanation:

First we find out population :

For ten shipments of 1000 cartons of eggs. In other words in each 10 shipments there are 1000 cartons of eggs.

Therefore, 1000 × 10 = 10,000  cartons of eggs.

Population : 10,000 cartons of eggs

Now it is given that she examines every 50th carton to see how many cartons contain cracked eggs.

Hence, Sample would be every 50th carton in each shipment.

In option a and b given cartons of eggs are 1,000,000, so they would be eliminated and in option d it is given that sample is only 50th carton of eggs

Therefore, option c would be correct.

The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.

Given :

The two legs are of equal length In any isosceles trapezoid that means:

7y - 4 = 8y - 18

Add 18 on both sides in the above equation.

7y - 4 + 18 = 8y - 18 + 18

7y + 14 = 8y

Now, subtract 7y on both sides in the above equation.

7y + 14 - 7y = 8y - 7y

Simplify the above expression in order to get the value of 'y'.

y = 14

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the law of cosines establishes:

  c² = a² + b² - 2 ab cos C 

in this problem

a=27

b=18

C=28°

c=m

m² = 27² + 18² - 2*(27)*(18)* cos(28°) 

m² = 729 + 324 - 972* cos(28°) 

m² = 1053 - 972* 0.8829

m² = 194.82-------------> m=13.96-----------> 14

the answer is m=14 units

Answer:

x = 14

x = negative 2

x = 2

x = negative 14

Step-by-step explanation:

Answer:

52 Days

Step-by-step explanation:

Answer:

The grasshopper needs to eat 10 blades of grass each day.

Step-by-step explanation:

The grasshopper in the food pyramid above must eat half its body weight in grass each day.

The average weight of the grasshopper is 2 grams.

The weight of one blade of grass is 0.1 grams.

Now,

The weight of grass eating by the grasshopper per day is 1 gram.

Let us assume that the grasshopper eats the "n" number of blades of the grass.

Therefore,

[tex]\begin{aligned}n \times 0.1\;\rm{gm}&=1\;\rm{gm}\\n&=\dfrac{1}{0.1}\\n&=10\end{aligned}[/tex]

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Writing [tex]5x-2y=-6[/tex] in slope-intercept form:

[tex]5x-2y=-6\\5x+6=2y\\\frac{5x+6}{2}=y\\y=\frac{5}{2}x +3[/tex]

The slope of the line is the number before "x", which is [tex]\frac{5}{2}[/tex].

The slope of the perpendicular to this line is the negative reciprocal of this.

So the slope of perpendicular is [tex]-\frac{2}{5}[/tex].

To find the equation of the perpendicular line, we need a point. It is given as [tex](5,-4)[/tex] where [tex]x_{1}=5[/tex] and [tex]y_{1}=-4[/tex].

Now we use the point-slope form of a line to figure out the equation:

[tex]y-y_{1}=m(x-x_{1})[/tex]

Plugging in the values of [tex]x_{1}[/tex] and [tex]y_{1}[/tex] and [tex]m=-\frac{2}{5}[/tex], gives us:

[tex]y-(-4)=-\frac{2}{5}(x-5)\\y+4=-\frac{2}{5}x+2\\y+\frac{2}{5}x=2-4\\y+\frac{2}{5}x=-2[/tex]

Multiplying everything by 5 [to get rid of the denominator] and re-arranging gives us:

[tex]y+\frac{2}{5}x=-2\\5y+2x=-10\\2x+5y=-10[/tex].

THIS IS THE SECOND OPTION.

ANSWER: [tex]2x+5y=-10[/tex]

Answer:

c

Step-by-step explanation:

Answer:

D. The manager should check both relative frequencies by row and by column to look for an association.

Step-by-step explanation:

the correct answer would be D

Final Answer:

The solutions to the equation [tex]\( y = x^2 + 7 \)[/tex] for x are: [tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]

Explanation:

To solve the equation [tex]\( y = x^2 + 7 \)[/tex] for x, you want to isolate x on one side of the equation. Here are the steps to do so:
1. **Subtract 7 from both sides**:  
  To isolate the [tex]\( x^2 \)[/tex] term, we first remove the constant term on the right side by subtracting 7 from both sides of the equation.
  [tex]\( y - 7 = x^2 + 7 - 7 \)[/tex]
  This simplifies to:
  [tex]\( y - 7 = x^2 \)[/tex]

2. **Take the square root of both sides**:  
  To solve for x, you need to get rid of the square on the x term. This is done by taking the square root of both sides. Remember that when you take the square root of both sides of an equation, you must consider both the positive and negative square roots.
  [tex]\( \sqrt{y - 7} = \pm\sqrt{x^2} \)[/tex]

  Simplifying the right side (since the square root and square operations are inverses of each other), we get:
  [tex]\( \sqrt{y - 7} = \pm x \)[/tex]

3. **Solve for x**:  
   We now have two solutions for x, a positive and a negative one, because squaring a positive or a negative number both give a positive result. Therefore, we write:

  [tex]\( x_1 = +\sqrt{y - 7} \\\\ \( x_2 = -\sqrt{y - 7} \)[/tex]

So, the solutions to the equation [tex]\( y = x^2 + 7 \)[/tex] for x are:

[tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]

Remember that you can only take the square root of a non-negative number in real numbers. So if y - 7 is negative, the solutions for x would be complex numbers.

Option C is correct,  the vertex of the parabola is (1, -4).

Any curve produced by the intersection of a plane and a right circular cone is called as Conic section.

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

The vertex is either the highest point or the lowest point on the parabola depending on whether the parabola opens upward or downward.

In this case, since the parabola opens upward, we can see that

the vertex is the lowest point on the parabola which is (1,-4).

Hence, Option C is correct,  the vertex of the parabola is (1, -4).

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Answer:

The correct answer is:

Michigan.

Michigan is the state that had a flat state income tax in 2009.

Step-by-step explanation:

A flat tax (short for flat-rate tax) is a tax system with a constant marginal rate, usually applied to individual or corporate income.

Flat tax benefits higher income brackets progressively due to decline in marginal value.

The state that had a flat state income tax in 2009 is:

Michigan.

Michigan is a flat-tax state that levies a state income tax of 4.25%

Answer:

$3.50 per hour

Step-by-step explanation:

Given : For working 13 hours you earned $45.50 and $94.50 for 27 hours

To Find :What is your rate of pay in dollars per hour?

Solution :

Pay for 13 hours =  $45.50

So, Pay for 1 hour =  [tex]\frac{45.50}{13}[/tex]

Pay for 1 hour =  [tex]3.50[/tex]

So, rate is $3.50 per hour

So, Option B is true

Hence rate of pay in dollars per hour is $3.50 per hour

Answer:

45% of 40 is 18% of 100

Step-by-step explanation:

45% of 40 is 18% of what number

First we find out what is 45% of number 40

45% times 40

[tex]\frac{45}{100} * 40= 18[/tex]

Now we find

18 = 18% of what number

Let the unknown number be x

18 = 18% * x

[tex]18= \frac{18}{100} * x[/tex]

18 = 0.18 * x

Divide by 0.18 on both sides

100= x

So 45% of 40 is 18% of 100

The complete statement is 45% of 40 is 18% of 100

From the question, we have the following parameters that can be used in our computation:

45% of 40 is 18% of what number

Represent the number with x

So, we have

45% of 40 is 18% of x

Express as an equation

45% of 40 = 18% of x

Next, we have

18 = 0.18x

Divide through by 0.18

x = 100

Hence, 45% of 40 is 18% of 100

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