A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree. 23° 25° 65° 67°

Jacob worked for 1 hour in his first job and 2 hours in his second job. Jacob earned $30 in both jobs.

Let's suppose that Jacob worked for x hours in his first job.

According to the statement, he earned $10 per hour.

Also, he earned an extra $20 since there were 3 children.

Therefore, the total amount he earned in his first job can be calculated as $10x + $20.

Now let's suppose that Jacob worked for y hours in his second job.

According to the statement, he earned $15 per hour.

Therefore, the total amount he earned in his second job can be calculated as $15y.

It is given that Jacob earned the same amount of money in both jobs.

Therefore, we can set up the equation as: $10x + $20 = $15y

Simplifying the above equation:

10x + 20 = 15y10x = 15y - 20   (subtracting 20 from both sides)

2x = 3y - 4   (dividing both sides by 5)

Now we know that x and y are integers.

Therefore, 3y - 4 must be a multiple of 2.

The smallest such number is 2.

Therefore, we can set up the equation as:

3y - 4 = 2

Now solving the above equation:

3y = 6y = 2Since y = 2,

we can now find x as follows:

2x = 3y - 42x = 3(2) - 42x = 6 - 4x = 1

Therefore, Jacob worked for 1 hour in his first job and 2 hours in his second job.

Now, we can calculate the total amount he earned as:

$10(1) + $20 = $30$15(2) = $30

Therefore, Jacob earned $30 in both jobs.

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The trigonometric function is given as

Apply the half angle identity to find the value of tan 75 ,

Here,

Now rationalize the function.

Again simplify the trigonometric function,

Hence the answer is 3.732.

Greetings from Brasil...

Since Q is the central point of PR, then PQ = QR and PQ = PR/2 or QR = PR/2

QR = PR/2

PR = 2 · QR

9X - 31 = 2 · 43

The value of x is 13.

A line segment is basically a line which has two end points.

A line has always a linear equation which has highest degree of 1

According the given question

Line segment is PR and midpoint is Q

Given QR = 43 which one end to the midpoint

∴ Total length of the line segment is 2×43

= 86

Given PR = 9x - 31 which is the total length of the line segment.

∴ 9x - 31 = 86

  9x = 86 + 31

  9x = 117

    x = 117/9

    x = 13.

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Answer:

is 300 trust me

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

Convert both equations into y = mx + b form, where m is the slope and b is the y intercept.

8x + 4y = 12

4y = -8x + 12

y = -2x + 3

Rearrange the other equation:

3y = -6x - 15

y = -2x - 5

So, both equations have a slope of -2. But, one has a y intercept of 3 and the other has a y intercept of -5.

Because the lines have the same slope but different y intercepts, the lines are parallel.

Parallel lines have no solutions, because they will never intersect.

So, the system has no solutions.

Answer:

√28561

Step-by-step explanation:

√ = 169

Square root of 169 = 169²

√28561 = 169

[I apologize if I misunderstood the question.]

Answer:

sure when i have money

Step-by-step explanation:

i don't have money lol

∠T is congruent or equal to triangle TGA.

option D.

A right triangle is a type of triangle that has one angle measuring 90 degrees (a right angle) while the two remaining angles are known as complementary angles because they sum up to 90 degrees.

For the diagram given in this question, we can conclude that angle PAG is 45 degrees and angle TAG is also 45 degrees, since the line AG bisector angle PGT into two.

Angle TAG = 90⁰

angle TGA + angle GTA = 90 (complementary angles)

TGA = 45⁰ ≅ ∠T

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Answer:

4dfhhtxghgggytxxgg

Step-by-step explanation:

ez

The Surface area of the rectangular pyramid that is given in the image is: C. 471 cm².

The surface area is simply the space covered by the faces of the pyramid . Therefore:

Surface area = area of the rectangular face + the four triangular faces

Note that there are two pairs of identical triangular faces.

Area of the first pair of triangular faces = base * height = 10 * 16.2 = 162 cm²

Area of the second pair of triangular faces = base * height = 12 * 15.8 = 189.6 cm²

Area of the rectangular face = length * width = 12 * 10 = 120 cm².

Surface area of the rectangular pyramid = 120 + 189.6 + 162 = 471.6 cm².

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Usibg the distributive property to the algebraic expression 5(x - 7) will be 5x - 35.

The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands. Here, the number outside the brackets is multiplied with each term inside the brackets and then the products are added.

When you multiply a value by a sum, the distributive property of multiplication over addition is used. Say you want to multiply 5 by the product of 10 plus 3. When two terms are similar, we typically add the two numbers before multiplying by 5. However, the property states that you should first multiply each addend by 5.

Therefore, 5(x - 7) will be:

= 5(x) - 5(7)

= 5x - 35

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Answer:

N 62,875,000

Step-by-step explanation:

Cost of first meter is  1000

Each subsequent meter costs 500 more than the previous meter. So the costs per meter and sum can be expressed as

1st meter cost = 1000

2nd meter cost = 1500

3rd meter cost = 2000

4th meter cost = 2500

.....

Looking at the numbers above we see that they form an arithmetic sequence with 1000 as the first term, a common difference of 500 and with 500 terms

The total cost will the sum of the 500 terms in the series

The sum of an arithmetic sequence with n terms is given by
\(S_n = \dfrac{n}{2}\cdot (2a_1 + (n-1)\cdot d)\)

where
a₁ is the first term

d is the common difference

n is the number of terms

Sₙ is the sum of the first n terms

Substituting a₁=1000, d = 500, n =500 gives us:
\(S_{500} = \dfrac{500}{2}\cdot (2\cdot 1000 + (500-1)\cdot 500)\)

\(S_{500} = 250\cdot (2000 + 499\cdot 500)\\\\S_{500} = 250(2000 + 249500)\\\\\\S_{500} = 250\cdot 252500\\\\\\S_{500} = 250\cdot 251500\\\\S_{500} = 62,875,000\)

Total cost of constructing the bridge is N 62,875,000

Answer:

5 1/2

Step-by-step explanation:

a) r=d/t

   11/4x2/1= 22/4= 5 1/2

b) 1/2 hour x 2 equals one hour, so 2 3/4 x 2 equals rate per hr.

11/4x2=22/4= 5 1/2

Answer:

1 mph

Step-by-step explanation:

All you have to do is follow the formula. Distance/time=mph

The radial road is longer than the straight line by approximately 0.154 m. Therefore, the required answer is 0.154 m.

Given: AO = BO, ∠AOB = 60°,  and AB is joined by straight road ACB and radial road AB.

To Find: By how much radial road AB is longer than the straight line?

Let's construct the diagram below, In triangle AOB, using the sine rule:

AB / sin ∠ABO = BO / sin ∠BAO, AB / sin 60° = BO / sin 60° => AB = BO ...(i)

Let AC = BC = x m ∴ AB = 2x m (Since ∠AOC = ∠BOC = 60°)

In triangle ABC, using the cosine rule:AB² = AC² + BC² - 2ACBC cos ∠CAB(2x)² = x² + x² - 2(x)(x)(cos 120°)4x² = 2x² + x² + 2(x² )∴ x² = 2x² / 3 => x = (2 / √3)x

Let AD be the perpendicular distance of C from AB.

Then, AD = (x)sin 60° = (x√3 / 2) m And BD = (x)sin 30° = (x / 2) m

Thus, AB = AD + BD = (x√3 / 2) + (x / 2) = (2x + x√3) / 2From eq. (i), we have BO = 2x m

Therefore, radial road ACB is longer than straight line AB by = ACB - AB= (2x + x√3) / 2 - 2x= x(√3 - 2) / 2= [2 / √3]× [√3 - 2]≈ 0.154 m

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Answer:

1st option

Step-by-step explanation:

In right triangle BCD

cosC = \(\frac{adjacent}{hypotenuse}\) = \(\frac{b-x}{a}\) ( multiply both sides by a )

b - x = acosC ( subtract b from both sides )

- x = acosC - b ( multiply through by - 1 )

x = b - acosC

Answer:

x^2+2xy+y^2-x-y-12.

Answer:

\(12x^{2} -5x -2\)

Step-by-step explanation:

We multiply the first term 3x by 4x and then 3x multiplied by one. We proceed to multiply by -2 by 4x and multiplied by -2 +1. We finally add and get the result.

\(12x^{2} -5x -2\)

2 is 4 more than -2

I know this because there is no positive number -4 from 2 so you need to go to the negatives which means 2, 1 ,0, -1,-2.

Hope this helped<3

Have a wonderful day...

-Dignoris :)

Answer:

1:1.5

Step-by-step explanation:

Use algebra:

3.2 to 4.8 = 1 to x

\(\frac{3.2}{4.8} = \frac{1}{x}\)

Now cross-multiply:

3.2x=4.8×1

x=\(\frac{4.8}{3.6}\)

x=1.5

Possible outcomes are Head, Middle, and Tail.

Since all outcomes are equally likely, the probability of each event is same, therefore

P(Head) = P(Middle) = P(Tail)

= 1/3

P(B|A) is 1/3

P(C|A) is 2/3

A and B are independent

A and C are not independent

Part a

Finding the sample space, S

S = { (HH), (HM), (HT), (MH), (MM), (MT), (TH), (TM), (TT) }

Part b

Finding  P(B|A) and P(C|A):

n(B and A) = no. of outcomes in which the first toss is Middle and second toss is Tail = 1

n(A) = Total no. of events in which the first toss is Middle = 3

Therefore, P(B|A) = 1/3

n(C and A) = no. of outcomes in which the first toss is Middle and total no. of heads is zero = 2

n(A) = Total no. of events in which the first toss is Middle = 3

Therefore, P(C|A) = 2/3

Part c

Finding if A and B are independent, or if A and C are independent

Two events A and B are said to be independent when the occurrence of one event does not affect the occurrence of the other event and vice versa. In case of independent events,

P(A) = P(first toss is Middle) = 3/9 =1/3

P(B) = P(second toss is Tail) = 3/9 = 1/3

P(A and B) = P(first toss is Middle and second toss is Tail) = 1/9

P(A)*P(B) = (1/3)*(1/3)

= 1/9 = P(A and B)

Hence, we can say that events A and B are independent.

For A and C, we have,

P(A) = P(first toss is Middle) = 3/9

P(C) = P(total no. of Heads is 0) = 4/9

P(A and C) = P(first toss is Middle and total no. of heads is 0) = 2/9

P(A)*P(C) = (3/9)*(4/9)

= 4/27 P(A and C)

Hence, events A and C are not independent.

The question was incomplete, the complete question is:

(Extra Credit) Suppose you have a well-balanced "super coin" with three sides or outcomes equally likely: Head, Middle, and Tail. (the super coin is a die with opposite faces showing Head, Middle, and Tail) You tossed this super coin two times

a) Describe the sample space using the notation HM for example, if the results are Head first, and Middle second.

Let;

A = event the first toss is Middle,

B = event the second toss is Tail, and

C = event the total number of Heads is 0.

b) Find

P(B|A)

P(C|A)

c) Are A and B independent? YES, NO, Why?

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Answer:

\(-\frac{2}{5}\)

Step-by-step explanation:

The geometric progression given is:

-6250, 1250, -250...

The first term (a) is -6250, and the common ratio (r) can be gotten by dividing the second term by the first term:

r = 1250/-6250 = \(-\frac{1}{5}\)

A geometric progression is generally given as:

\(a_n = ar^{n - 1}\)

where \(a_n\) = nth term

The 7th term of the progression above is therefore:

\(a_7 = -6250 * (-\frac{1}{5} )^6\\\\a_7 = -\frac{2}{5}\)

The 7th term of the geometric progression is;

a_7 = -2/5

The formula for the nth term of a geometric progression is;

a_n = ar^(n - 1)

Where;

a is first term

r is common ratio

n is the position of the term in the series

We are given the series;

-6250, 1250, -250...

Thus;

First term; a = -6250

Common ratio; r = 1250/-6250

r = -1/5

Thus;

a_7 = -6250(-1/5)^(7 - 1)

a_7 = -2/5

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Answer:

Slope = (1/3)

Step-by-step explanation:

Point 1: (0, 2); Point 2: (3, 3)

             (x₁, y₁)              (x₂, y₂)

        y₂ - y₁        3 - 2           1

m = ----------- = ------------ = ---------

         x₂ - x₁        3 - 0          3

y - y₁ = m(x - x₁)

y - 2 = (1/3)(x - 0)

y - 2 = (1/3)x - 0

  +2              +2

--------------------------

y = (1/3)x + 2

I hope this helps!

The inequality on the graph is a linear inequality, and it can be written as:

y > 2x - 4

On the graph, we can see a linear inequality, we can see a dashed line with a positive slope, and the shaded area is above that line, so the inequality is of the form:

y > line.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

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

We can find two points on the graph, we can see that the line passes through (0, -4) and (2, 0), then the y-intercept is -4 and the slope is:

a = (0 + 4)/(2 - 0) = 2

y = 2x - 4

then the inequality is:

y > 2x - 4

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The number needed so that this probability is less than 1/2 is 23.

It should be noted that the first person can have any birthday. The second person's birthday has to be different. There are 364 different days to choose from, so the chance that two people have different birthdays is 364/365.

To find the probability that both the second person and the third person will have different birthdays:

(365/365) * (364/365) * (363/365) = 132

132/133 = 99.18%.

If we want to know the probability that four people will all have different birthdays, we multiply again:

(364/365) * (363/365) * (362/365)

= 98.36%.

We can keep on going the same way as long as we want. A formula for the probability that n people have different birthdays is

((365-1)/365) * ((365-2)/365) * ((365-3)/365) * . . . * ((365-n+1)/365).

365! / ((365-n)! * 365^n).

We know that the probability of finding at least two people with the same birthday is 1 minus the probability that everybody has a different birthday. It turns out that the smallest class where the chance of finding two people with the same birthday is more than 50% is... a class of 23 people. The probability is then about 50.73%.

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Complete question

If n people are present in a room, what is the probability that no two of them celebrate their birthday on the same day of the year? how large need be so that this probability is less than 1/2?

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = \(\int_a^b \delta\left|r^{\prime}(t)\right| d t\)

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

\(\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}\)

Further simplifying;

\(\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}\)

Now, use integration to find the mass of the wire;

       \(\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}\)

Therefore, the mass of the wire is estimated as 40π√2 units.

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The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

Answer:

1) See below for table.

2) Domain: \(\{1, 2, 3, 4\}\)

Range: \(\{160, 160, 205, 250\}\)

Yes, this is a function.

Step-by-step explanation:

We know that the electrician charges a base fee of $70 plus $45 for each hour of work.

We also know that the minimum the electrician charges is $160.

Let's write an equation. Let x denote the number of hours worked and y denote the total price. There's also a base fee of $70. So, we can write the following equation:

\(y=45x+75\)

Part 1)

Let's create our table for 1, 2, 3, and 4 hours. To do so, we simply need to substitute each value for x in our equation.

1 Hour:

We have:

\(y_1=45(1)+70\)

Multiply and add:

\(y_1=45+70=\$115\)

However, notice that the minimum the electrician charges is $160. Therefore, for one hour of work, the electrician will still charge $160. So:

\(y_1=\$160\)

2 Hours:

Substitute 2 for x:

\(y_2=45(2)+70=90+70=\$160\\\)

So:

\(y_2=\$160\)

3 Hours:

Substitute 3 for x:

\(y_3=45(3)+70=135+70=\$205\)

So:

\(y_3=\$205\)

4 Hours:

Substitute 4 for x:

\(y_4=45(4)+70=180+70=\$250\)

So:

\(y_4=\$ 250\)

Therefore, for 1, 2, 3, and 4 hours of work, the prices will be $160, $160, $205, and $250, respectively.

We can create the following table (please scroll down to see the table. Also, y is measured in dollars).

Part 2)

The domain of a relation are the input values.

In this context, our input values are the amount of hours worked, and we calculated for 1, 2, 3, and 4 hours of work.

Therefore, our domain in this context is:

\(\{1, 2, 3, 4\}\)

The range of a relation are the output values.

In this context, the output values are the price for x hours of work.

Therefore, our range in this context is:

\(\{160, 160, 205, 250\}\)

This relation does represent a function. Remember that a function cannot have repeating input values. In other words, no one input can be equal to two or more different outputs. However, one output can be mapped to two or more different inputs.

For our table, none of the inputs are repeating. So, our relation is a function.

And we're done!

(3) Add: Under applied overhead 34,000

(4) Adjusted cost of goods sold 364,000

1 and 2 RAW MATERIAL INVENTORY

Beginning balance 75,000

a 225,000 150,000 b, Ending Balance 150,000

WORK IN PROGRESS INVENTORY

Beginning balance 140,000

b 125,000 352,000 g

c 60,000

f 105,000

j Ending Balance 78,000

FINISHED GOODS INVENTORY

Beginning balance -

g 352,000 330,000 h

Ending Balance 22,000

FACTORY OVERHEAD

b 25,000

c 40,000 105,000 f

d 74,000

Ending Balance 34,000

COST OF GOODS SOLD

h 330,000

Ending Balance 330,000

Factory overhead applied on the basis of direct labor cost .

Hence applied overhead = 60,000 x 175% = $105,000Step: 2

3)

Computation of under /(over) applied OH

Actual OH($) Applied OH ($) Under /(over) applied OH ($)

139,000 105,000 34,000

Actual manufacturing overhead:

$

Indirect material 25,000

Indirect Labour 40,000

Other manufacturing overhead 74,000

139,000

4)

Cost of goods sold (Unadjusted) 330,000

Add: Under applied overhead 34,000

Adjusted cost of goods sold 364,000

Actal manufacturing overhead is more than applied overhead,it means factory overhead under applied and it will be added in unadjusted cost of goods sold to ascertain adjused cost of goods sold.

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Answer:

is there another number after the 7 if so if it is 5 or bigger it rounds up but 1-4 rounds down

Step-by-step explanation:

Answer:

0.23!! =D

hundredths (1/100)

Solution

Perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial.

To determine if the trinomials in the question is a perfect trinomial, we will factor each of the trinomials and then decide which is a perfect trinomial

The first trinomial above is a perfect trinomial

The second trinomial above is a perfect trinomial

The third trinomial above is not a perfect trinomial

The fourth trinomial above is a perfect trinomial

The summary of the solution is given below