Daniel sees a lighthouse in the harbor. He estimates the angle of elevation 70 . If the lighthouse is 120 feet tall, what is the approximate distance between Daniel and the top of the lighthouse?

Using subtraction, we get 2723237 in base 7 as the answer.

To convert 65210 to base 7 using subtraction, we can follow these steps:

1. Start with the largest power of 7 that is less than or equal to 65210. In this case, that is 7^4 = 2401.

2. Divide 65210 by 2401 to get the quotient and remainder:

  65210 ÷ 2401 = 27 with a remainder of 1363

3. Write down the quotient (27) and use the remainder (1363) to repeat steps 1-2 until the remainder is 0:

  1363 ÷ 343 = 3 with a remainder of 112

  112 ÷ 49 = 2 with a remainder of 14

  14 ÷ 7 = 2 with a remainder of 0

4. Write down the remainders in reverse order to get the base 7 equivalent of 65210:

  65210 = 2723237 in base 7.

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Answer:

1 and 3

Step-by-step explanation:

Answer:

The answer is

\( \frac{1}{2} \: and \: \frac{ \sqrt{2} }{2} \)

Step-by-step explanation:

Let The point (X, Y)

Since half of the diameter is equal to 1

Then

\( {x}^{2} + {y}^{2} = 1\)

Why is the measurement of angle is equal to 60, this triangle was equal

Then

\( {(x - 1)}^{2} + {y}^{2} = 1\)

By comparing the equals together

\( {x}^{2} = {(x - 1)}^{2} \\ {x}^{2} = {x}^{2} - 2x + 1 \\ 2x = 1 \\ x = \frac{1}{2} \\ Compensation \: in \: any \: equation \\ then \: y = \frac{ \sqrt{2} }{2} \)

A factorial anova includes only three or more independent variable(s). A factorial ANOVA involves analyzing the effects of two or more independent variables on a dependent variable. Therefore, it requires at least three independent variables to be included in the analysis. The correct answer is d.

Factorial ANOVA is a statistical analysis method used to examine the effects of multiple independent variables on a dependent variable. It involves examining the main effects of each independent variable, as well as the interactions between them.

A factorial ANOVA is typically used when researchers are interested in examining the combined effects of multiple variables on a single outcome. The method can be used in a wide range of fields, from psychology to biology to engineering, and is particularly useful in experimental research designs.

Overall, factorial ANOVA is a powerful tool for analysing complex data and uncovering the underlying relationships between variables. So, the correct answer is D).

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2p - 3q - 4r + 6r - 2q + p = 0

2p + p - 3q - 2q - 4r + 6r = 0

3q - 5q + 2r = 0

Answer:

the answer is 900 degrees

Step-by-step explanation:

The exterior angles of a polygon add up to 360º in measure. For a regular heptagon, each exterior angle has an equal measure xº, so that 7xº = 360º, or xº ≈ 51.43º. Interior angles supplement exterior angles, so they each have measure 180º - xº ≈ 128.57º. Multiply this by 7 to get a total of 900º.

Answer:

y = –5x/4 + 7

Step-by-step explanation:

x1 = 8 ,x2 = 4, y1 = –3 , y2 = 2

lets find the slope(m)

m = y2–y1/x2–x1

m = 2 – (–3)/ 4 – 8

m = 5/ –4

m= –5/4

to find the equation of a line using this as our guider y = mx + b

we will make use of one coordinate

(8,–3)

using the formula for one point

y – y1 = m(x – x1)

y – (–3) = –5/4(x – 8)

y + 3 = –5x/4 + 10

y = –5x/4 + 10 –3

y = –5x/4 + 7

i hope i helped pls rate the answer as brainliest if i deserve it

thanks

Answer:

Step-by-step explanation:

t = 158                         Corresponding angles

t + s = 180                   They are supplementary angles

158 + s = 180               Subtract 158 from both sides

s = 180 - 158

s = 22

As a note, all angles in this situation are either 158 or 22.

Answer:

-6x³ -1

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 is 630 in

they can all be turned into squares and multiplied.

Answer:

\(x\approx 24.0,\\y\approx 46.4\)

Step-by-step explanation:

Let the height of the largest triangle marked be \(h\). We can set up the following equation:

\(\sin 30^{\circ}=\frac{h}{34},\\h=34 \sin 30^{\circ}=17\) (if you're unfamiliar with trig, this is likely introduced to you as 30-60-90 triangle rules)

This height is also a leg of a 45-45-90 triangle, as marked in the diagram. From the isosceles-base-theorem, the other leg of this triangle must also be equal to \(h\). Therefore, we can use the Pythagorean theorem to solve for \(x\):

\(17^2+17^2=x^2\\x^2=\sqrt{17^2\cdot 2},\\x=17\sqrt{2}\approx \boxed{24.0}\) (you can also use trig or 45-45-90 triangle rules which are derived from the Pythagorean theorem)

Segment \(y\) consists of two shorter segments, a left segment and a right segment. We've already found that the left segment is equal to 17. To find the right segment we can use trig, the Pythagorean theorem, or 30-60-90 triangle rules (derived from the Pythagorean theorem):

Using Pythagorean Theorem:

\(y_{right}=\sqrt{34^2-17^2}\approx \boxed{29.4}\)

Therefore, we have:

\(y=17+29.4=\boxed{46.4}\)

Answer:

67 degrees for both of the other angles or 46 degrees and 88

Step-by-step explanation:

An isosceles triangle has two angle that are the same size so it could only be these.

The value of the expression x/y (x^2y^1) when x = 10 and y = 5 is 1000 based on the expression in the question

From the question, the expression is given as:

x/y (x^2y^1)

The values of the variables are given as:

x = 10

y = 5

Next, we substitute the values of x and y (i.e. x = 10 and y = 5) in the given expression x/y (x^2y^1)

So, we have:

x/y (x^2y^1) = 10/5 * (10^2 * 5^1)

Evaluate the exponents in the above expression

x/y (x^2y^1) = 10/5 * (100 * 5)

Evaluate the quotient in the above expression

x/y (x^2y^1) = 2 * (100 * 5)

Evaluate the product in the above expression

x/y (x^2y^1) = 1000

Based on the expression in the question, the value of the expression x/y (x^2y^1) when x = 10 and y = 5 is 1000

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Complete question

What is the value of x/y (x^2y^1) when y = 5 and x = 10?

Answer:

4188.79mi^3

Step-by-step explanation:

the formula for the volume of a sphere is 4/3*pi*r^3

since the radius is 10, 4/3*pi*10^3

Answer:

Step-by-step explanation:

Volume of sphere =  \(\frac{4}{3} \pi r ^{3}\)

Radiusof sphere = 10 mi

=4/3·π·10^3≈4188.7902mi³

Answer:

  20 km/hr

Step-by-step explanation:

The boat's still-water speed is the average of its speeds against and with the current:

  (15 +25)/2 = 20 . . . km/hr

__

If you want to write equations, you can let b and c represent the speeds of the boat and current in km/hr.

  b - c = 15 . . . . upstream speed

  b + c = 25 . . . . downstream speed

Add these two equations, and you get ...

  (b -c) +(b +c) = (15) +(25)

  2b = 40

  b = 20 . . . . divide by 2

The speed of the boat in still water is 20 km/hr.

Answer:

20 km/hr

Step-by-step explanation:

To solve this, you have to find the average speed it is going. To find this, you just add up all of the speeds mentioned and divide it by the number of speeds you added.

15 +25=40

40/2=20

20km/hr!!!

Good luck on what you are doing I hope you do well! Brainliest would be great :)

The height of the prism is 5x + 3 units.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

Given:

The volume of a rectangular prism is given by the expression

10x^3 + 46x^2 – 21x – 27. The area of the base of the prism is given by the expression 2x^2 + 8x – 9.

We have to find the height of prism.

Volume of the rectangular prism = Base × Height

The expression is in the Question be

10x ³ + 46 x² - 21x -27

And the  area of the base of the prism is given by the expression

2x² + 8x - 9 .

Put in the formula

10x ³ + 46 x² - 21x -27  = 2x² + 8x - 9  × Height

The factor of 10x ³ + 46 x² - 21x -27 are (5x +3 )(2x² + 8x - 9) .

put in the formula

(5x +3 )(2x² + 8x - 9) = (2x² + 8x - 9) × Height

Cancelled 2x² + 8x - 9 on both side.

(5x+3)unit = Height

Hence, the height of the prism is 5x + 3 units.

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It takes approximately 0.0533 seconds for the sound of the coin hitting the bottom of the well to reach Sara's ears.

If Sara hears the coin hit the bottom of the well, that means she is able to hear the sound produced by the coin reaching the bottom. The time it takes for sound to travel from the top of the well to the bottom is what we need to find.
To calculate the time it takes for sound to travel, we can use the formula:
Time = Distance / Speed
In this case, the distance is the depth of the well, which is 60 feet. The speed of sound is approximately 1,125 feet per second.
Plugging these values into the formula, we get:
Time = 60 feet / 1,125 feet per second
Simplifying this expression, we find:
Time ≈ 0.0533 seconds
Therefore, it takes approximately 0.0533 seconds for the sound of the coin hitting the bottom of the well to reach Sara's ears.

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Answer:

-38

Step-by-step explanation:

4-(3^4-6^2)+2(3)÷2

=>     4 - (81-36) + 2(3) ÷ 2      

=>     4 -  45 + 2(3)÷2

=>     4 -  45 + 6÷2

=>     4 -   45 + 3

=>     -41 + 3

=>     - 38

hope this helps :)

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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Answer:

The triangles are similar because angle N=angle E and angle F=angle H.

Angle-Angle (AA or AAA) Similarity theorem: If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

(4p-m)/4

m=-4 and p=2

Since you know what m and p represent, it shouldn't be hard to solve.

(4 [2] - [-4] )/4   The 4 would be positive since there are two negatives.

(8 + 4)/4 Do the work inside the parenthesis first...

(12)/4 now divide.

Answer:

I hope this helps

Step-by-step explanation:

plz mark brainliest

if we have n object, and as we know that arrangement given by = n!. (Permutation)

Hereafter taking each unique name, we will arrange it in raw, so we can say this problem is equivalently permutation problem, So we can say the way of drawing all names can be done in 10! Way.

So ANSWER IS 10!

A permutation is a mathematical technique for determining the number of possible arrangements in a sentence where the order of arrangements is important. A common math problem involves choosing some items in a particular order from a set of items.

A permutation also called an "order number" or "sequence", is the rearrangement of the elements of an ordered list so that they correspond one-to-one with themselves. (Faculty; Ouspensky 1937, p. 18). Permutations are said to be ordered combinations. The number of permutations r of n objects acquired simultaneously is determined by the following formula: P(n,r)=n!(n-r)!

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Let

y -----> number of quarters

x ----> number of dimes

we have that

the inequality that represents this situation is

Remember that

1 quarter =$0.25

1 dime=$0.10

so

rewrite the variables

see the attached figure to better understand the problem

Part 4b

The solution of the given inequality is the shaded area above the solid line 0.25q+0.10d=8.50

A solution to this inequality could be the point (50,50)

that means

the number of quarters is 50 and the number of dimes is 50

the ordered pair must satisfy the inequality

Verify

Part 4c

we have that

d=25 dimes

substitute in the inequality and solve for q

so

solve for q

the number of quarters must be greater than or equal to 24

Answer: -27a + 10

Step-by-step explanation:

1

Distribute

- 9a - 2 ( 9a - 5 )

- 9a - 18a + 10

2

Combine like terms

- 9a - 18a + 10

- 27a + 10

The profit per bag is approximately $2.50  and the total profit is approximately is $36 , the correct option is (c) .

In the question ,

a graph of relation of price and quantity is given .

Under the perfect competition , the profit maximization condition is where price is equal to the marginal cost

that means P = MC .

price is given as = $8 ,

Form the graph ATC = $5.5

per unit profit can be calculated using the formula ,

Per unit profit = Price - ATC

per unit profit = 8 - 5.5

= $2.5

From the graph , the quantity is Q = 14.4 (approximately)

Total profit is calculated using the formula

Total Profit = (profit per unit) × (quantity)

Total Profit = 2.5 × 14.4

= $36

Therefore , The profit per bag is approximately $2.50  and the total profit is approximately is $36 .

The given question is incomplete , the complete question is

This figure is the market for bags of coffee roaster . At a price of $8 per bag . Profit per bag is approximately is      and the total profit is       .

(a) $5.50 , $78

(b) $5.00 , $60

(c) $2.50 , $36

(d) $8.00 , $114

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The charity will make $367.50 if Greg's grandmother makes 15 bulky scarves with her yarn.

Two or more expressions with an Equal sign is called as Equation.

If Greg's grandmother has no more than 2,250 yards of yarn, and each bulky scarf requires 150 yards of yarn, then she can make at most 2,250/150 = 15 bulky scarves.

Each scarf will be sold for $24.50

If she makes 15 bulky scarves then the charity will make

15 x $24.50

= $367.50.

Therefore, the charity will make $367.50 if Greg's grandmother makes 15 bulky scarves with her yarn.

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Answer:

it's(-68) if you mean negative positive wise

Answer:

32

Step-by-step explanation:

V=\(\pi\)r^2

5120=\(\pi r^{2}\)x20

5120/20 = 256

\(\sqrt{256}\)=16

16+16 ( 16x2) = 32

32in.

Answer:

\( \boxed{x = - \frac{1}{6}} \)

Step-by-step explanation:

\( = > \frac{1}{2} x + \frac{3}{4} = \frac{2}{3} \\ \\ = > \frac{1}{2} x = \frac{2}{3} - \frac{3}{4} \\ \\ = > \frac{1}{2} x = ( \frac{2}{3} \times \frac{4}{4} ) - (\frac{3}{4} \times \frac{3}{3} ) \\ \\ = > \frac{1}{2} x = \frac{8}{12} - \frac{9}{12} \\ \\ = > \frac{1}{2} x = \frac{8 - 9}{12} \\ \\ = > \frac{1}{2} x = - \frac{1}{12} \\ \\ = > x = 2 \times ( - \frac{1}{12} ) \\ \\ = > x = - \frac{1}{6} \)