Flight 101, headed straight north, climbed to 30,000 feet and started its cruising speed of 360 mph 10 miles south of the point directly above our location. Flight 222, headed straight west, already cruising at 30,000 feet at 300 mph, was 5 miles east of the point above us at that time. Clearly, the paths of the planes intersect directly above us. Do they collide? Parametrize the linear paths and give the times when they are at the intersection point. By how many seconds do they miss each other?

Answer:

Step-by-step explanation:

The Pythagorean theorem says:

[tex]a^2+b^2=c^2[/tex]

where a and b are the two legs of the triangle and c is the hypotenuse.  Here, let's say a = 6 and b = [tex]\sqrt{13}[/tex]. We then get the following equation:

[tex]c^2= (6)^2+(\sqrt{13})^2=49[/tex]

So c = 7. Technically, c can also equal -7 since (-7)^2 = 49 as well but that does not apply here because a side length cannot be <0. So 7 is the answer.

WAY to much to read,thanks for the points and have a good day

9514 1404 393

Answer:

  1487.31 yd³

Step-by-step explanation:

The volume of the composite figure is the sum of the volumes of a hemisphere of radius 7 yd, and a cylinder of the same radius and height 5 yd.

The volume of a sphere is 4/3πr³. The volume of a hemisphere is half that.

The volume of a cylinder is πr²h.

The total volume of this figure is ...

  V = (2/3)πr³ + πr²h

  V = πr²(2/3r +h)

  V = (3.14)(7 yd)²(2/3·7 yd +5 yd) = 3.14·49·29/3 yd³ ≈ 1487.31 yd³

The volume of the figure is about 1487.31 yd³.

Answer:

4187.31 yd³ is thr volume of a fugure

Answer:

63

Step-by-step explanation:

angle abc =half of arc DE + half of arc AC

Answer:

33.75 or rounded to the nearest tenth: 33.8

We can use the formula: is/of = %/100.

% = 60

of = 160

[tex]\frac{x}{160}=\frac{60}{100}[/tex]

100x = 9600

x = 96

96 students participated in the fundraiser.

Answer:

308915776 six-letter passwords are possible with repetitions

Step-by-step explanation:

Since repetition is allowed, this means there are 26 possible choices for the first letter of the password, 26 possible choices for the second letter of the password, and so on until the sixth letter.

This can be represented as 26^6=308915776

With repetition 26⁶ passwords can be formed using the letters A to Z taken six at a time.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, The six letter passwords are formed using the letters A through Z

with repetition is Nⁿ, Where N is the total number of letters and n is is the number of letters taken at a time.

Therefore it would be,

= 26⁶ passwords.

learn more about permutation and combination here :

https://brainly.com/question/28720645

#SPJ2

Answer:

none of the above is a pythagorean triple

Answer:

27

Step-by-step explanation:

Answer:

No equations given but the answer is c=1x+7.96

Step-by-step explanation:

I'm not sure what is meant by "partitioning the x-axis" - partition is a term more often used with computing Riemann sums. So either partitioning has a special meaning for you, or you have to approximate the area with a Riemann sum.

I'm going to assume you just want the exact area of the given region. Notice that the two curves y = 4e ˣ and y = -x + 4 intersect when x = 0 at the point (0, 4). Both curves then meet the vertical line x = 4. The exponential function is increasing while the linear one is decreasing, so 4e ˣ ≥ -x + 4.

The region is then the set of points,

R = {(x, y) | 0 ≤ x ≤ 4 and -x + 4 ≤ y ≤ 4e ˣ}

so the area is given by the integral,

[tex]\displaystyle\int_0^4 (4e^x-(-x+4))\,\mathrm dx=\int_0^4(4e^x+x-4)\,\mathrm dx=\left(4e^x+\frac{x^2}2-4x\right)\bigg|_0^4=\boxed{4e^4-12}[/tex]

Answer:

The results from both game A and game C align closely with the theoretical probability of winning those games, while the results from game B do not.

Step-by-step explanation:

Given the data:

Game Number of Wins Number of Losses

Get-It-Rolling (A) 26 173

Bag-of-Tokens (B) 54 141

Pick-Your-Tile (C) 17 175

EXPERIMENTAL PROBABILITY:

Game A :

Number of games played = 26 + 173 = 199

Experimental probability :

Probability of winning = number of wins / number of games played = 26 / 199 = 0.1306

Theoretical probability :

1 / 8 = 0.125

Game B :

Number of games played = 54 + 141 = 195

Experimental Probability of winning = number of wins / number of games played = 54 / 195 = 0.2769

Theoretical probability = 1 / 7 = 0.1429

Game C :

Number of games played = 17 + 175 = 192

Experimental Probability of winning = number of wins / number of games played = 17 / 192 = 0.0885

Theoretical probability = 1 / 12 = 0.08333

From the results, we can see that the results from both game A and game C align closely with the theoretical probability of winning those games.

Answer:

supplementary angle = angle 2 and angle 3

vertical angle = angle 2 and angle 4

hope it helps

Answer:

1. AC=EC=120 ft

2. Given as perpendicular

3. BC=CD

4. Perpendicular means 90° from the bridge

5. Area of Triangle same

Solution :

Let [tex]$x_i$[/tex] represents the prices for the digital camera.

              [tex]$x_i$[/tex]                   [tex]$x_i^2$[/tex]

           225              50625

           236              55696

            217               47089

           202              40804

           231               53361

           185               35225

           193               37249

           185               34225

           217               47089

[tex]$\sum x_i = 2136$[/tex]       [tex]$\sum x_i^2 = 460388$[/tex]

Mean, [tex]$(\overline X) = \frac{\sum x_i}{n}$[/tex]

                 [tex]$=\frac{2136}{10}$[/tex]

                 = 213.6

Variance, [tex]$\sigma^2 = \frac{\sum x_i^2}{n}-(\overline X)^2$[/tex]

                     [tex]$ = \frac{460388}{10}-(213.6)^2$[/tex]

                    = 46038.8 - 45624.96

                    = 413.84

Therefore, standard deviation,

[tex]$\sigma = \sqrt{Var}$[/tex]

   [tex]$=\sqrt{413.84}$[/tex]

   = 20.343

Now to find the 93% confidence interval, the formula us

[tex]$(\overline X)\pm (z) \times \frac{\sigma}{\sqrt{n}}$[/tex]

For 93%, the value of z is 1.81

∴ Confidence interval = [tex]$(\overline X)\pm (z) \times \frac{\sigma}{\sqrt{n}}$[/tex]

C.I. = [tex]$213.6\pm 1.81 \times \frac{20.343}{\sqrt{10}}$[/tex]

      [tex]$=213.6 \pm 11.6438$[/tex]

Therefore, lower bound = 213.6 - 11.6438

                                        = 201.9562

                  Upper bound = 213.6 + 11.6438

                                         = 225.2438

∴ [tex]$201.9562 < \mu < 225.2438$[/tex]

or [tex]$202< \mu < 225.2$[/tex]

The scale factor is the bigger over the smaller, so [tex]\frac{4}{3}[/tex] is the scale factor.

To find x, we just use a proportion Biggest to Smallest:

[tex]\frac{4}{3}=\frac{16}{x}[/tex]

4x = 48

x = 12

Answer:

b = 3.5 cm

Step-by-step explanation:

Given that,

The area of a rectangle, A = 14. sq cm

The length of one side, l = 4 cm

We need to find the length of another side. The formula for the area of a rectangle is given by :

A = lb

So,

[tex]14=4b\\\\b=\dfrac{14}{4}\\\\b=3.5\ cm[/tex]

So, the length of the other side is equal to 3.5 cm.

Answer:

c i think ???

Step-by-step explanation:

Answer:

i think the answer is 5x+1 that how i was taught srry if its wrong

Answer:

Soup B

Step-by-step explanation:

Given :

Soup A:

Sodium(mg) 720

Ounces 6 1

Soup B :

Sodium(mg) 600

Ounces 4 1

To Obtian the amount of sodium per ounce in each of soup A and B

Soup A :

Sodium per ounce = 720 mg / 61 = 11.803 mg / ounce

Soup B:

Sodium per ounce = 600 mg / 41 = 14.634mg / ounce

Hence. SOUP B contains more soudiun per ounce

Answer:

One third or 1/3

Step-by-step explanation:

Answer:

the distance between-5 to 120 on a number line is 124

Answer:

2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(9-7)/(4-3)

m=2/1

m=2

Answer:

D

Step-by-step explanation:

9514 1404 393

Answer:

  x = 4.9 cm

Step-by-step explanation:

The product of segment lengths is the same for each chord:

  (7 cm)(7 cm) = x(10 cm)

  x = (49 cm^2)/(10 cm)

  x = 4.9 cm

Answer:

B. 37 + 7 = 44

Step-by-step explanation:

If she jumps 4 more after jumping 3 to 40, means it's 4 + 3 = 7 and it reaches 44.