From the observation deck of a skyscraper, Isabella measures a 67
angle of depression to a ship in the harbor below. If the observation deck is 824 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.

You're looking for a number w such that the numbers

{1 + w, 7 + w, 15 + w}

form a geometric sequence, which in turn means there is a constant r for which

7 + w = r (1 + w)

15 + w = r (7 + w)

Solving for r, we get

r = (7 + w) / (1 + w) = (15 + w) / (7 + w)

Solve this for w :

(7 + w)² = (15 + w) (1 + w)

49 + 14w + w ² = 15 + 16w + w ²

2w = 34

w = 17

Then the three terms in the sequence are

{18, 24, 32}

and indeed we have 24/18 = 4/3 and 32/24 = 4/3.

The lub is 0.23[tex]\mathbf{\overline{43}}[/tex], while the glb is 0.2

The given set is presented as follows;

E = {0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,...}

The least upper bound, lub, of a set, E, is known as the supremum of the set which is the number B such that all x ∈ E are of the value x  ≤ B, while there all y ∈ E has a x ∈ E such that t < x

Therefore;

The supremum, lub of the given set is 0.23[tex]\overline{43}[/tex]

The greatest lower bound, glb, b, also known as the infimum, is defined as follows;

b is the greatest lower bound if for all x ∈ E then x ≥ b

Given that b < t, then where x ∈ E, there exist a x < t

The glb of the given set is 0.2

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Answer:

x = 1

y = 2

Step-by-step explanation:

5x + 2y = 9

-5x + 4y = 3

==> 6y = 12 ==> y = 12/6 ==> y = 2.

we replace y by its value in the first or the second equation, so will have:

5x + 2×2 = 9

5x + 4 = 9

5x = 5

x = 1

Answer:

77.5

Step-by-step explanation:

Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B

9514 1404 393

Answer:

  OBADR

Step-by-step explanation:

The first two letters are swapped, and the last two letters are swapped.

  BOARD . . . becomes

  OBADR

Answer:

y = 4

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1 : √3 : 2

The sides in this triangle are in the order:

y : 4√3 : x

y/1 = 4√3/√3

y = 4

9514 1404 393

Answer:

  64.1 ft²

Step-by-step explanation:

The area of the cone is given by ...

  A = πr(r +h) . . . . for radius r and slant height h

  A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²

Step-by-step explanation:

jlejej

are u using chrome os

Answer:

-18/x+3

Step-by-step explanation:

9514 1404 393

Answer:

  a) CP = SP/1.1

  b) CP = $59.50

  c) GST = $5.95

Step-by-step explanation:

a) Divide by the coefficient of CP.

  SP = 1.1×CP

  CP = SP/1.1

__

b) Use the formula with the given value.

  CP = $65.45/1.1 = $59.50

__

c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.

  GST = SP -CP = $65.45 -59.50 = $5.95

  GST = CP×0.10 = $59.50 × 0.10 = $5.95

Mean:

[tex]E(X) = \displaystyle \sum_{x\in\{1,2,3,4\}}x\,P(X=x) = 1\times0.4 + 2\times0.1 + 3\times0.3 + 4\times0.2 = \boxed{2.3}[/tex]

Variance:

[tex]\displaystyle V(X) = E\left((X-E(X))^2\right) = E(X^2) - E(X)^2 \\\\ E(X^2) = \sum_{x\in\{1,2,3,4\}}x^2\,P(X=x) = 1^2\times0.4 + 2^2\times0.1 + 3^2\times0.3 + 4^2\times0.2 = 6.7 \\\\ \implies V(X) = 6.7 - 2.3^2 = \boxed{1.41}[/tex]

Standard deviation:

[tex]\sigma_X = \sqrt{V(X)} = \sqrt{1.41} \approx \boxed{1.19}[/tex]

Answer:

N=18

Step-by-step explanation:

Hope it will help you

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Have a nice day

Answer:

18

Step-by-step explanation:

use the concept of similarity and enlargement.

[tex] \frac{15}{n} = \frac{5}{6 } [/tex]

[tex]n = \frac{15 \times 6}{5} [/tex]

[tex]n = 18[/tex]

Step-by-step explanation:

Hey there!

From the given figure;

Angle FVT = 43°

VT = 53

Taking Angle FVT as reference angle we get;

Perpendicular (p) = FT = ?

Base (b) = VT = 53

Taking the of tan;

[tex] \tan( \alpha ) = \frac{p}{b} [/tex]

Keep all values and simplify it;

[tex] \tan(43) = \frac{ft}{53} [/tex]

0.932515*53 = FT

Therefore, FT= 49.423.

Hope it helps!

Answer:

A. 49.42

Step-by-step explanation:

tan 43 = FT ÷ VT

0.932515086 = FT ÷ 53

49.42 = FT

Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.

g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]

Option C

Hope this helps!

Triangle DEF is scalene

Must click thanks and mark brainliest

The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.

A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.

Given that:-

it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.

Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.

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Answer:

Z = (42-20)/4 = 5.5

Z = X-μ / σ

Step-by-step explanation:

The z-score for the data value of 42 is 5.5.

A z-score is defined as the fractional representation of data point to the mean using standard deviations.

Formula of z-score = (X - μ) / σ

Given,

μ = 20

σ = 4

X = 42

z-score = (X - μ) / σ

Substitute the values,

z-score =  (42-20)/4

z-score = 22/4

z-score =  5.5

Hence, the z-score for the data value of 42 is 5.5.

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Answer:

brown

Step-by-step explanation:

it might be brown because it compelled

Answer:

18

Step-by-step explanation:

7-5=2

2x9=18

Answer:

In a bag of balls, 1/4th are green, 1/8th are blue, 1/12th are yellow and the remaining 26 are white. How many balls are blue?

There are 4 colours of balls - green, blue, yellow and white.

Add (1/4)+(1/8)+(1/12) = (6/24)+(3/24)+(2/24) = 11/24 so the balance or (24–11)/24 = 13/24 = 26 white. Hence the total number of balls are 2*24 = 48.

Of the 48 balls, green are (1/4)*48 = 12, blue are (1/8)*48 = 6, yellow are (1/12)*48 = 4 and the rest, white are 26.

Check: Total number of balls = 12+6+4+26 = 48

Answer: 6 balls are blue....

Answer:

1/5

Step-by-step explanation:

Answer:

c.

Step-by-step explanation:

Step-by-step explanation:

28000 ÷ 100

=280

280 × 5

=1400

Using the shell method, the volume integral would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]

That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].

The volume itself would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]

Using the disk method, the integral for volume would be

[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]

where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.

The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have a function:

[tex]\rm y = x^8[/tex]   or

[tex]x = \sqrt[8]{y}[/tex]

And  y = 256

By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.

[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]

Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]

[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]

After solving definite integration, we will get:

[tex]\rm V = \pi(\frac{4096}{5} )[/tex]  or

[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit

Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

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Answer:

Step-by-step explanation:

Let t = 2

h = 122.5 - 4.9·2² = 122.5-19.6 = 102.9

We have to figure out what the product of DA is,

[tex]\begin{bmatrix}-1&2&3\\8&-4&0\\6&7&1\\ \end{bmatrix}\begin{bmatrix}1\\3\\5\\ \end{bmatrix}=\begin{bmatrix}a\\b\\c\\ \end{bmatrix}[/tex]

We know that,

[tex]\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix}=\begin{bmatrix}ax+by+cz\\dx+ey+fz\\gx+hy+iz\\\end{bmatrix}[/tex]

So,

[tex]a=-1\cdot1+2\cdot3+3\cdot5=-1+6+15=20[/tex]

[tex]b=8\cdot1+(-4)\cdot3+0\cdot5=8-12=-4[/tex]

[tex]c=6\cdot1+7\cdot3+1\cdot5=6+21+5=32[/tex]

So the solution is,

[tex]a,b,c=\boxed{20,-4,32}[/tex]

Hope this helps :)

Answer:

First one: 2.5

Second: -6

8.5+69.5(5) = 147.5

150 - 147.5 = 2.5

8.5 + 69.5(5) = 356

350 - 356 = -6

ED2021

The residual for 2 phone lines is $2.5.

The residual for 5 phone lines is -$6.

The residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.

In the question, we are asked to find the residual for 2 and 5 lines using the least-squares regression equation y = 8.5 + 69.5x and the actual costs given to us.

We know that the residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.

Thus for 2 phone lines:-

Actual Cost = $150.

Predicted Cost, y = 8.5 + 69.5*2 = 147.5.

Residual = Actual Cost - Predicted Cost = 150 - 147.5 = $2.5.

Thus, the residual for 2 phone lines is $2.5.

Thus for 5 phone lines:-

Actual Cost = $350.

Predicted Cost, y = 8.5 + 69.5*2 = 356.

Residual = Actual Cost - Predicted Cost = 350 - 356 = -$6.

Thus, the residual for 2 phone lines is -$6.

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90/-10

= 9/-1

= -9

So, -9 is the quotient.