the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues. we first need to calculate the slope (m) and the y-intercept (b)
what do you mean by approximate ?
Approximate means "close to but not exactly" or "an estimate". In other words, an approximate value is a value that is not exact but is close enough to the actual value to be useful or meaningful in a given context.
In the given question,
To find the equation of the line of fit in slope-intercept form, we first need to calculate the slope (m) and the y-intercept (b) using the two given points (8, 12,800) and (14, 14,420).
m = (y₂ - y₁) / (x₂ - x₁)
m = (14,420 - 12,800) / (14 - 8)
m = 1,620 / 6
m = 270
b = y - mx
b = 12,800 - 270(8)
b = 10,940
Therefore, the equation of the line of fit in slope-intercept form is:
y = mx + b
y = 270x + 10,940
To use this equation to estimate the cost of raising a child born in 2013 at age 17, we can plug in x = 17 and solve for y:
y = 270x + 10,940
y = 270(17) + 10,940
y = 15,050
Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues.
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I need this answer please
Answer:
the y intercept is 1 so put a point there then move up 1 and to the right 3 and put a point then draw a line through the 2 points
Complete the proof that the point (3, 7) does or does not lie on the circle with center (-1, 4) and containing the point (-1, 9).
The point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).
Describe Distance Formula?The distance formula is a mathematical formula used to calculate the distance between two points in a two or three-dimensional space. It is derived from the Pythagorean theorem and is given by:
d = √((x2 - x1)² + (y2 - y1)²)
Where d represents the distance between the two points, (x1, y1) and (x2, y2) represent the coordinates of the two points in a two-dimensional space.
To determine if the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9), we need to calculate the distance between the center of the circle and the point (3, 7), and compare it to the radius of the circle.
Let's first find the radius of the circle. Since the circle contains the point (-1, 9), the distance between the center of the circle and (-1, 9) is equal to the radius. Using the distance formula, we get:
radius = √[(9 - 4)² + (-1 - (-1))²] = √[25] = 5
Now let's find the distance between the center of the circle (-1, 4) and the point (3, 7):
distance = √[(7 - 4)² + (3 - (-1))²] = √[3² + 4²] = 5
We see that the distance between the center of the circle and the point (3, 7) is equal to the radius of the circle. Therefore, the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).
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A line with a slope of 1/3 passes through (-1,-2). Write the equation of the line in general form.
Answer:
I think it will be
y=1/3x+0
A contestant draws a sequence of three cards, one question per card, and tries to answer the three questions. There are five cards with history questions, six cards with literature questions, and seven cards with science questions. Find the probability of each of the following. (Round your answers to four decimal places.) (a) the questions are history, literature, and science, in that order (b) all three are literature questions (c) the first is science, the second is history, and the third is science
(a) The probability of the questions being history, literature, and science, in that order, is 4.28%.
(b) The probability of all three cards being literature questions is 2.4%.
(c) 5%.
What is probability in cards?Probability can be used to estimate the chances of drawing a certain card and can help players to decide which moves to make when playing card games.
(a) The probability of the questions being history, literature, and science, in that order, is 5/18 x 6/17 x 7/16 = 0.0428 or 4.28%.
To calculate this probability, we use the formula
P(A and B and C) = P(A) x P(B|A) x P(C|B and A).
The probability of the first card being a history card is 5/18, since there are five history cards out of 18 total cards.
The probability of the second card being a literature card, given that the first card is a history card, is 6/17, since there are six literature cards out of the remaining 17 cards.
The probability of the third card being a science card, given that the first two cards are history and literature, is 7/16, since there are seven science cards out of the remaining 16 cards.
(b) The probability of all three cards being literature questions is 6/18 x 5/17 x 4/16 = 0.024 or 2.4%.
To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).
The probability of the first card being a literature card is 6/18, since there are six literature cards out of 18 total cards.
The probability of the second card being a literature card, given that the first card is a literature card, is 5/17, since there are five literature cards out of the remaining 17 cards.
The probability of the third card being a literature card, given that the first two cards are literature cards, is 4/16, since there are four literature cards out of the remaining 16 cards.
(c) The probability of the first card being a science card, the second being a history card, and the third being a science card is 7/18 x 5/17 x 7/16 = 0.05 or 5%.
To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).
The probability of the first card being a science card is 7/18, since there are seven science cards out of 18 total cards.
The probability of the second card being a history card, given that the first card is a science card, is 5/17, since there are five history cards out of the remaining 17 cards.
The probability of the third card being a science card, given that the first two cards are science and history, is 7/16, since there are seven science cards out of the remaining 16 cards.
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How to solve for x?????
The value of x using Pythagoras theorem to solve the diagram is 1.25 m.
What is pythagoras theorem?Pythagoras theorem states that the square of the hypotenus in a right angled triangle is equal to the sum of the of the two other sides.
To solve for x we use pythagoras theorem in the diagram below.
Formula:
a² = b²+c².......................... Equation 1From the diagram,
c = 3 mb = x ma = (x+2) mSubstitute these values into equation 1 and solve for x
(x+2)² = x²+3²x²+4x+4 = x²+94x = 9-44x = 5x = 5/4x = 1.25 mHence, x is 1.25 m.
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How are the points
(4, 5) and (-4, 5) related?
Answer:
The two points (4, 5) and (-4, 5) have the same y-coordinate, which means they lie on a horizontal line. This horizontal line is the x-axis. So, the points are related in that they both lie on the x-axis, with a distance of 8 units between them.
A conservation district in Ohio found that their land has a density of 95 rabbits per square mile. The area of the entire state of Ohio is about 44,825 square miles. If the population density of the state is the same as that conservation district, what is the rabbit population in Ohio?
Answer: 4,258,375
Step-by-step explanation:
Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.
Which equation can Sharon use to find c, the average amount the cable company charges per channel?
The equation that Sharon can use to find c is
300(c-0.20)= 180
The average amount the cable company charges per channel was $0.8.
What is equation?An equation is a mathematical statement which can be constructed by two expressions connected by an sign which is called equal '=' sign to find out the value of unknown variable.
For example, 3x – 11 = 16 is an equation. Solving this equation, we get the value of x as x = 9.
Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.
Let us take in previous case the bill was $c for one channel.
so for 300 channels it will be $300c.
If Sharon has for $0.20 less per channel
Then price per channel will be $(c-0.20)
For 300 channels it will be $300(c-0.20)
It equals to $180
so equating both values we get the equation and the equation will be,
300(c-0.20)= 180
The equation that Sharon can use to find c is
300(c-0.20)= 180
To find the average amount we will solve c from the equation.
300(c-0.20)= 180
⇒ c-0.20 = 180/300 [ dividing both sides by 300 we get]
⇒ c- 0.20 =0.6
⇒ c= 0.8 [ Adding both sides 0.20 we get]
Hence, The average amount the cable company charges per channel was $0.8.
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Find the slope of a line parallel to the line whose equation is 5x - 2y = 2. Fully
simplify your answer.
Answer:
To find the slope of a line parallel to 5x - 2y = 2, we need to first rearrange the equation in slope-intercept form, y = mx + b, where m is the slope of the line. 5x - 2y = 2 -2y = -5x + 2 y = (5/2)x - 1 The slope of the line is 5/2. Since we are looking for a line parallel to this line, the slope of the parallel line will be the same as the slope of the original line, which is 5/2. Therefore, the slope of a line parallel to 5x - 2y = 2 is 5/2.
Need some help
100 points!!
Answer:
145°
Step-by-step explanation:
∠1 + ∠2 = ∠3
5x + (4x + 10) = 10x - 5
9x + 10 = 10x - 5
10x - 9x = 10 + 5
x = 15
∠3 = 10x - 5 = 10(15) - 5 = 150 - 5 = 145
On a 8 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
On an 8-question multiple-choice test, where each question has 2 answers, the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]
Probability is a way to gauge how likely something is to happen1. It is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the event.
In an 8-item multiple-choice test with 2 possible answers for each, the likelihood of getting at least one question wrong can be computed as follows:
P(at least one mistake) = 1 - P (none wrong)
P(at least one wrong) [tex]=1-(\frac{1}{2})^{10[/tex]
P(at least one wrong) [tex]=1-\frac{1}{1024}\\\\=\frac{1023}{1024}[/tex]
On an 8-question multiple-choice test, where each question has 2 answers, the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]
The complete question is-
On an 8-question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
Give your answer as a fraction
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I need the answer pls help
Answer:
The function is shifted 1 unit to the right and then flipped over the x-axis. So the correct result is:
[tex]y = - f(x - 1)[/tex]
NEED BY 15 mins !!!! Identify the leading coefficient of the polynomial!!!!
A dog ate 6 cupcakes. that was 3/8 of all of them. How many cupcakes did you start?
what is the equation---------------
what is the answer---------------
Answer:
16
Step-by-step explanation:
Find an equivalent fraction which is 6/16.
2x = 7, 2Y = 5, then 2 x - y
The calculated value of the expression 2x - y for the given values of x and y is 9/2.
Evaluating the expression for x and yWe are given that 2x = 7 and 2y = 5, and we are asked to find the value of 2x - y.
This means that
x = 7/2 and y = 5/2
We can start by substituting the given values into the expression:
2x - y = 2(7/2) - (5/2)
Notice that since 2x = 7, then x = 7/2.
Similarly, since 2y = 5, then y = 5/2. Substituting these values into the expression, we get:
2x - y = 2(7/2) - (5/2) = 7 - 5/2 = 9/2
Therefore, the value of 2x - y is 9/2.
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HELP PLSSSSSSSSSSSSSSS
Answer:
E
Step-by-step explanation:
[tex]3(p - 4) = 2(p + 1)[/tex]
Multiply every term inside the bracket by the term on the outside:
[tex]3p - 12 = 2p + 2[/tex]
Collect like-terms (also, moving the term to the other side changes its sign to the opposite of the previous one):
[tex]p = 14[/tex]
EXPLANATION
step 1. 3×p - 3×4 = 2×p + 2×1 ( brackets means × or multiplication )
step 2. 3p - 12 = 2p + 2 ( collect like terms )
step 3. -2p - 3p = 2 + 12 ( calculate the like terms and when we calculate them it would not be multiplication or division )
step 4. -1p = 14 ( answering look like this )
step 5. -1p/ 1 = 14/1 ( divided it by the number to get the variable )
step 6. p = 14 ( finally answer the question and check it all your calculate )
If you think you are brilant do not run for only the answer, but check up and understand it how it come.
ANSWER
(E) 14
ind the x-intercept and y-intercept of the line.
=+−6x4y21
Write your answers as exact values. Do not write your answers as ordered pairs.
x-intercept:
y-intercept:
The x-intercept is 21/5 and the y-intercept is -7/2 of the given line.
What is the x and y-intercept of a line?
In a two-dimensional Cartesian coordinate system, the x-intercept of a line is the point where the line crosses the x-axis, which means the value of y is zero at that point. The x-intercept can be found by setting y = 0 in the equation of the line and solving for x.
Given that we have to find the y-intercept and x-intercept
The given equation is:
5x - 6y = 21
The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.
The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero
Finding x-intercept:
To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.
Substitute y = 0 in a given equation
5x - 6(0) = 21
x = 21/5
Thus x-intercept is 21/5.
Finding y-intercept:
To find the y-intercept, plug 0 in for 'x' and solve for 'y'
Substitute x = 0 in a given equation
5(0) - 6y = 21
-6y = 21
-2y = 7
y = -7/2
Thus y-intercept is -7/2
hence, the x-intercept is 21/5 and the y-intercept is -7/2 of the given line.
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Complete question:
Find the y-intercept and x-intercept of the line. 5x-6y=21
A warehouse worker uses a forklift to move boxes that weigh either 45 pounds or 70 pounds each. Let x be the number of 45-pound boxes and y be the number of 70-pound boxes. The forklift can carry up to either 60 boxes or a weight of 3000 pounds.
The total number of boxes that a forklift can carry is???
The total weight that the forklift can carry is ______ 3000 pounds.
Greater than, Less than, or Equal to
Write an inequality that models the number of boxes the forklift can carry. The inequality should contain x, y, and an inequality sign.
Write an inequality that models the amount of weight the forklift can carry. The inequality should contain x, y, and an inequality sign.
The inequality that models the amount of weight the forklift can carry is: 45x + 70y ≤ 3000
Define inequalityAn inequality is a mathematical statement that indicates a relationship between two expressions that are not equal. It uses comparison symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to show the relationship between the two expressions.
The total number of boxes that a forklift can carry is x + y.
The total weight that the forklift can carry is equal to 45x + 70y pounds, which is less than or equal to 3000 pounds.
Therefore, the inequality that models the number of boxes the forklift can carry is:
x + y ≤ 60
The inequality that models the amount of weight the forklift can carry is:
45x + 70y ≤ 3000.
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Equation in vertex form
Answer:
f(x) = -(x-3)+7
Step-by-step explanation:
Consider the equation and the following ordered pairs: (−4,y) and (x,2) . y=−3x−4 Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
To satisfy the equation y = -3x - 4, we need to substitute the given values of x and y in the equation and check if it holds true.
For the ordered pair (-4, y):
y = -3(-4) - 4
y = 12 - 4
y = 8
So, the ordered pair (-4, 8) satisfies the equation y = -3x - 4.
For the ordered pair (x, 2):
2 = -3x - 4
6 = -3x
x = -2
So, the ordered pair (-2, 2) satisfies the equation y = -3x - 4.
Given in Quadrilateral WXYZ, WY and XZ bisect each other at point a
Prove Quadrilateral WXYZ is a parallelogram
What is the missing statement in this proof?
Proof of Quadrilateral WXYZ as a Parallelogram using SSS Criterion for Congruence.
What is the proof that Quadrilateral WXYZ is a parallelogram using SSS criterion for congruence?
Since WY and XZ bisect each other at point A, we have AW = AY and AZ = AX.
Now, consider the triangles AWX and AYZ. By the Side-Side-Side (SSS) criterion for congruence, we have:
AW = AY (given)
AZ = AX (given)
WY = XZ (as WY and XZ bisect each other)
Therefore, by the SSS criterion for congruence, we have AWX ≅ AYZ.
By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, we have WX = YZ.
Since opposite sides are congruent, we have WX || YZ.
Similarly, we can show that WZ || XY.
Therefore, since both pairs of opposite sides are parallel, we can conclude that quadrilateral WXYZ is a parallelogram.
Missing statement: "By the SSS criterion for congruence, we have AWX ≅ AYZ."
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A rectangular paperboard measuring 20in long and 12in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for pi , and do not round your answer. Be sure to include the correct unit in your answer.)
Answer:
the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.
Step-by-step explanation:
The perimeter of the paperboard that remains after the semicircle is removed is equal to the sum of the four sides of the rectangular portion of the paperboard plus half the circumference of the semicircle.
The rectangle has dimensions of length = 20 inches and width = 12 inches. Therefore, the sum of the four sides of the rectangular portion of the paperboard is:
2(20) + 2(12) = 64 inches
The semicircle has a diameter equal to the width of the rectangle, which is 12 inches. Therefore, the radius of the semicircle is half the diameter, or 6 inches. The circumference of a full circle with a radius of 6 inches is:
2 * 3.14 * 6 = 37.68 inches
Half of the circumference of the semicircle is:
(1/2) * 37.68 = 18.84 inches
Therefore, the perimeter of the paperboard that remains after the semicircle is removed is:
64 + 18.84 = 82.84 inches
Thus, the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.
1. The product of th roots of the quadratic 6x + cx + 4 is 2 greater than the sum of the roots, and c is a constant. What is the c?
The prοduct οf th rοοts οf the quadratic 6x + cx + 4 is 2 greater than the sum οf the rοοts, and c is a cοnstant the value οf c = 4
What is quadratic equatiοn in math?ax² + bx + c = 0 is a quadratic equatiοn, which is a secοnd-οrder pοlynοmial equatiοn in a single variable. a 0.
By Vieta's fοrmulas, we knοw that the sum οf the rοοts is given by:
α + β = -c/6
And the prοduct οf the rοοts is given by:
αβ = 4/6 = 2/3
We are given that the prοduct οf the rοοts is 2 greater than the sum οf the rοοts:
αβ = α + β + 2
Substituting the values we knοw, we get:
2/3 = -c/6 + 2 + α + β
Simplifying this expressiοn, we get:
2/3 = -c/6 + 2 - c/6
Multiplying bοth sides by 6, we get:
4 = -c + 12 - c
Simplifying, we get:
2c = 8
c = 4
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|4x-4(x+1)|=4 Show solution on numberline
The equatiοn has nο sοlutiοn.
What is the equatiοn?An equatiοn is defined as a mathematical statement in algebra that prοves the equality οf twο mathematical expressiοns. Fοr example, the fοrmula 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the wοrd "equal."
Here the given equatiοn is ,
=> |4x-4(x+1)|=4
Nοw simplifying the equatiοn then,
=> 4x-4(x+1)=± 4
=> 4x-4x-4=±4
=>-4=±4
Hence the given equatiοn has nο sοlutiοn.
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Two students are selected at random from a class of 13 males and 6 females. Find the probability that both students are males. (See Example 4. Round your answer to two decimal places.)
The probability that both students selected are males is 0.46.
Multiplication rule of probability:The multiplication rule of probability for independent events states that the probability of two or more independent events occurring together is the product of their individual probabilities.
If event A has probability P(A) and event B has probability P(B), and A and B are independent events, then the probability of both A and B occurring
P(A and B) = P(A) x P(B)
Here we have
There are 13 males and 6 females in the class, for a total of 19 students.
The probability of selecting a male on the first draw is 13/19.
After one male has been selected,
There are 12 males and 6 females left in the class.
The probability of selecting another male on the second draw = 12/18
[ Since there is one less student in the class and one less male]
The probability of selecting two males in a row is the product of the probabilities of each individual event:
P(male and male) = P(male on the first draw) x P(male on the second draw | male on the first draw)
= (13/19) x (12/18)
= 0.456 or approximately 0.46 (rounded to two decimal places).
Therefore,
The probability that both students selected are males is 0.46.
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A fair die is rolled 5 times. What is the probability of having no 1 and no 5 among the rolls? Round your answer to three decimal places.
The probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.
What is the probability first law?According to the First Principle of Probability, the outcomes of one chance occurrence have no bearing on those of succeeding chances occurrences. Thus, the chance of getting heads the second or third time you flip it stays at 1 in 2. The chances of getting heads on the sixth flip, even if you got five consecutive heads, stay at 12.
The Bayes rules of probability are what?The Bayes Theorem asserts that the likelihood of a second tournament given the first occurrence multiplied by the odds of the first event equals the conditional event's likelihood depending on the presence of another event.
The probability of rolling a number other than 1 or 5 on a fair die is 4/6 or 2/3, since there are four favorable outcomes (2, 3, 4, 6) out of six possible outcomes.
To find the probability of rolling no 1 and no 5 in five rolls, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.
So, for each roll, the probability of rolling a number other than 1 or 5 is 2/3. Therefore, the probability of rolling no 1 and no 5 in five rolls is:
(2/3) * (2/3) * (2/3) * (2/3) * (2/3) = (2/3)⁵ ≈ 0.131
Rounding to three decimal places, the probability is approximately 0.131.
Therefore, the probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.
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A blueprint used a scale of 1.5 cm = 2 m to
represent a grain silo. If the height of the silo in
the drawing was 33 cm, how tall is the actual grain
silo?
Answer: The Silo is 44 meters tall
Step-by-step explanation:
To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)
As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commission on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $292. If she sells $800 of merchandise in one month, she is paid $384.
Here is the salary function used to represent this situation in terms of the amount of merchandise sold:
s(x) = 0.23x + 200
Find Alysse's salary when she sells $2,200 worth of merchandise.
Step-by-step explanation:
As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commission on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $292. If she sells $800 of merchandise in one month, she is paid $384.
Here is the salary function used to represent this situation in terms of the amount of merchandise sold:
s(x) = 0.23x + 200
Find Alysse's salary when she sells $2,200 worth of merchandise.
A boat is heading towards a lighthouse, whose beacon-light is 119 feet above the
water. From point A, the boat's crew measures the angle of elevation to the beacon,
5°, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 18°. Find the distance from point A to point B.
Round your answer to the nearest foot if necessary.
Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
Let's assume that the distance from point A to the lighthouse is x feet and the distance from point B to the lighthouse is y feet. Also, let's assume that the height of the boat's crew's eye level is h feet above the water.
From point A, we can use tangent function to find x:
tan(5°) = (119 + h) / x
From point B, we can use tangent function again to find y:
tan(18°) = (119 + h) / y
We want to find the distance between point A and point B, which is the difference between x and y:
distance AB = y - x
We need to eliminate h from these equations to solve for x and y. We can do this by solving for h in one equation and substituting it into the other equation:
h = x tan(5°) - 119
tan(18°) = (119 + x tan(5°) - 119) / y
tan(18°) = x tan(5°) / y
y = x tan(5°) / tan(18°)
distance AB = y - x = x (tan(5°) / tan(18°) - 1)
Now we can plug in the values and use a calculator to find the distance:
distance AB = x (tan(5°) / tan(18°) - 1)
distance AB = x (0.107 - 1)
distance AB = -0.893 x
Since the distance cannot be negative, we know that x must be greater than zero. Therefore, we can ignore the negative sign and solve for x:
x = distance AB / -0.893
Using a calculator, we get:
x ≈ 181.74 feet
Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.
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What is the smallest possible average of 200 distinct positive and odd integers?
201.5 is the smallest average of 200 different positive and odd integers.
Let's first consider the set of the first 200 odd positive integers: {1, 3, 5, ..., 397, 399, 401}.
The average of this set is (1+3+5+...+397+399+401)/200 = 201.
Now, we want to find a set of 200 distinct positive and odd integers that has a smaller average than 201.
One way to do this is to remove the largest element from the first set (401) and replace it with the smallest odd positive integer that is greater than 401, which is 403.
The new set is {1, 3, 5, ..., 397, 399, 403}.
The average of this set is (1+3+5+...+397+399+403)/200 = 201.5.
Hence, 201.5 is the smallest average that can be calculated from 200 different positive and odd integers.
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