Suppose you are headed toward a plateau 70 m high. If the angle of elevation to the top of the plateau is 60 degrees, how far are you from the base of the plateau?

Answer:   C. (-1, 2)

Step-by-step-explanation:

The center is the midpoint of the endpoints

  →          [tex]\bigg(\dfrac{x_1+x_2}{2}[/tex]       ,      [tex]\dfrac{y_1+y_2}{2}\bigg)[/tex]

    →           [tex]\bigg(\dfrac{-7+5}{2}[/tex]         ,       [tex]\dfrac{3+1}{2}\bigg)[/tex]

    →               [tex]\bigg(\dfrac{-2}{2}[/tex]             ,          [tex]\dfrac{4}{2}\bigg)[/tex]

    →                (-1              ,            2)

The midpoint is (-1, 2)

The cylinder has base diameter of 6 centimeters and the height, [tex] h [/tex], of 8 centimeters.

Since the base diameter of the cylinder is 6 cm, therefore, it's radius, [tex] r [/tex], will be 3 cm.

Now, we know that the volume, [tex] V [/tex], of such a cylinder will be:

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

Plugging in the values given we get the volume to be:

[tex] V=\pi(3)^2\times 8=3.14\times9\times8=226.08 [/tex] [tex] cm^3 [/tex]

Since Rene needs to make 2000 [tex] cm^3 [/tex] of ice and one cylinder's volume is 226.08 [tex] cm^3 [/tex], Rene would need...

[tex] \frac{2000}{226.08}\approx8.846\approx\boldsymbol{9} [/tex] such identical cylindrical containers.

Final answer:

To make 2000 cm3 of ice, Rene would need a minimum of 9 identical containers, given the volume of one container is 226.08 cm3.

Explanation:

To determine the number of identical cylindrical containers needed to make 2000 cm3 of ice, we must first calculate the volume of one container. Given that the diameter of the base is 6 centimeters, the radius (r) is half of that, which is 3 centimeters. We're also given the height (h) of 8 centimeters. We can use the formula for the volume of a cylinder, V = πr2h.

Plugging in the values, we get:

V = 3.14 × (3 cm)2 × 8 cm

which simplifies to V = 3.14 × 9 cm2 × 8 cm = 226.08 cm3.

Now we can divide the total volume of ice Rene wants to make by the volume of one container:

2000 cm3 ÷ 226.08 cm3 = approx 8.85.

Since Rene cannot use a fraction of a container, she would need a minimum of 9 identical containers to make at least 2000 cm3 of ice.

Answer:

Option: A is the correct answer.

The equation of parabola is:

                              [tex]x^2=8y[/tex]

Step-by-step explanation:

Clearly we could observe that the parabola opens upward with vertex at (0,0) this means that the general equation of the parabola is:

          [tex]x^2=4ay[/tex]

The focus of parabola is: (0,a) and equation of directrix is: y= -a

From the image provided to us we get:

                 a=2

             and directrix is: y= -2

           Hence, the equation of  a parabola is:

                       [tex]x^2=8y[/tex]

Part A:

The most expensive item on the menu is roast beef wrap at $4.50

6% tax on it becomes: [tex]4.50+(0.06\times4.50)=4.77[/tex] dollars

15% tip on it becomes: [tex]4.77+(0.15\times4.77)=5.485[/tex] dollars

The least expensive item on the menu is coffee at $0.90

6% tax on it becomes: [tex]0.90+(0.06\times0.90)=0.954[/tex] dollars

15% tip on it becomes: [tex]0.954+(0.15\times0.954)=1.097[/tex] dollars

So, the difference between roast beef wrap and coffee cost is :

[tex]5.485-1.097=4.388[/tex] dollars nearest to $4.36

Option B is the answer.

Part B:

You and your friend ordered two roast beef wraps, one soup, one fries, and two coffees.

Total becomes:

[tex](2\times4.50)+(2.25)+(1.50)+(2\times0.90)[/tex]

= [tex]9+2.25+1.50+1.8=14.55[/tex] dollars

Sales tax of 5% and 15% tip means 20% more on $14.55

[tex]14.55+(0.20\times14.55)=17.46[/tex] dollars

Change you will receive = [tex]20-17.46=2.54[/tex]dollars

Option D is the answer.

Answer:

Simple Random answer

Step-by-step explanation:

It says that he divided town into eight regions and randomly chose 10. The sample she formed was the Simple Random Answer.

According to the information we can infer that the Lower Quartile is 23.5, the upper quartile is 32,5, and the interquartile range is 9.

Arrange the data in ascending order: 20, 22, 25, 28, 29, 30, 32, 33, 34.

Calculate the position of the lower quartile using the formula: (n + 1) / 4, where n is the number of data points.

Since 2.5 falls between the 2nd and 3rd data points, you need to find the average of these two values:

Upper Quartile (Q3):

Calculate the position of the upper quartile using the formula: 3 * (n + 1) / 4.

Since 7.5 falls between the 7th and 8th data points, find the average of these two values:

Interquartile Range (IQR):

Calculate the IQR by subtracting Q1 from Q3:

So, the lower quartile (Q1) is 23.5, the upper quartile (Q3) is 32.5, and the interquartile range (IQR) is 9.

Learn more about interquartile in: https://brainly.com/question/29173399
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The required dimensions of the rectangular field are 34 yards by 136 yards.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle  and L is the length of the rectangle

Let's represent the width of the field x. Since the field is four times as long as it is wide, the length of the field is 4x.

The perimeter of the field is the sum of all four sides of the field. This can be written as:

2(x) + 2(4x) = 340

Solving this equation for x, we find that the width of the field is x = 34 yards.

Since the length of the field is four times the width of the field, the length of the field is 4 × 34 = 136 yards.

Therefore, the width of the field is 34 yards, and the length of the field is 136 yards.

Learn more about the Perimeter of the rectangle here:

brainly.com/question/15287805

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Answer:

A

Step-by-step explanation:

n1=8. 7+1=8

n2=9. 7+2=9

n3=10. 7+3=10

n4=11. 7+4=11

n5=12. 7+5=12

Answer:

[tex]x=10.5[/tex]

Step-by-step explanation:

Use Thales' Theorem which says: If two lines, not necessarily parallel, are cut by a system of parallel lines, then the segments that result on one of the two lines are proportional to the corresponding segments obtained on the other.

Take a look at the picture I attached you, from it, It is true that:

[tex]\frac{AB}{A'B'} =\frac{BC}{B'C'}[/tex]

Hence:

[tex]\frac{12}{6} =\frac{21}{x}[/tex]

Solving for x:

[tex]x=\frac{21}{2} =10.5[/tex]

Final answer:

Switching the axes of two hyperbolas affects the equations of the asymptotes.

Explanation:

When the transverse axis and conjugate axis are switched in two hyperbolas, it affects the equations of the asymptotes. The equations of the asymptotes are determined by the ratio of the coefficients of x² and y² in the hyperbola equation. When the axes are switched, this ratio changes, resulting in different equations for the asymptotes.

For example, let's consider two hyperbolas with equations:

1) 8x² + 10xy - 3y² - 2x - 4y - 2 = 0

2) 8y² + 10xy - 3x² - 2x - 4y - 2 = 0

In the first hyperbola, the ratio of the coefficients of x² and y² is 8/(-3), which determines the equation of the asymptotes. In the second hyperbola, the ratio is (-3)/8, leading to different equations for the asymptotes.

The area of the slice of pie that was cut, rounded to the nearest hundredth is; D: 98.83 ft²

We are given the angle of the sector of the circle as θ = 37°.

We are given;

Diameter; d = 35 ft

Thus;

Radius; r = 35/2 = 17.5 ft

Now, the formula for area of a sector of a circle is;

A = (θ/360) * πr²

Thus;

A = (37/360) * π * 17.5²

Approximating to the nearest hundredth gives;

A = 98.883 ²

Read more about Area of a Sector at;https://brainly.com/question/22972014

Stella divided 12/8.

If we divide 12 by 8, we get exactly 1.5.

Let us check given options one by one .

A) Stella made an error : Stella didn't made an error because it's just division of two numbers.

B) The answer is exactly 1.5.  : On dividing 12 by 8, we get exactly 1.5, so this option is correct.

C) The calculator rounded the answer. : On dividing 12 by 8, we get exactly 1.5. So, no rounding is required.

D) The calculator truncated the answer. : On dividing 12 by 8, we get exactly 1.5. So, no truncation in the answer.

Therefore, correct option is B) The answer is exactly 1.5.

Answer:

upper quartile is 93

lower quartile is 80.5

Step-by-step explanation:

I got a 100 on quiz