The probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.
What is probability?Statistics and probability theory both make substantial use of probability, which is a measure of the possibility or chance of an event occurring. A number between 0 and 1, where 0 denotes an event that is impossible and 1 denotes an event that is certain, is used to indicate the likelihood of an occurrence.
We must count the number of favourable possibilities—those that match the event of interest—and divide that number by the total number of potential outcomes in order to calculate the probability of an occurrence.
There are 8 letters in the word, so the total number of arrangements is 8! = 40,320.
For O and E to be together we consider it as a sing letter, thus:
There are 7! ways to arrange the letters of new word.
Now, OE can be written as OE or EO thus:
2 x 7! = 10,080
Now, the probability of O and E together is:
Probability = 10,080 / 40,320
Probability = 0.25
Hence, the probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.
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9. Conrad aims to save money to travel to Puerto Rico in order to work on a team that studies ancient cities there. What is this an example of?
A. Quantitative value
OB. Priority
OC. Poverty
O D. Value
The answer is D. Value. A value is something that a person considers important or desirable in life. It can be a principle, a goal, a belief, or an attitude that guides one’s choices and actions. Conrad’s aim to save money to travel to Puerto Rico and work on a team that studies ancient cities there is an example of his value because it shows what he cares about and what motivates him.
A quantitative value is a value that can be measured or expressed numerically, such as income, height, weight, etc. A priority is something that is more important than other things and needs attention first. Poverty is the state of being extremely poor. None of these terms describe Conrad’s aim accurately.
Conrad’s aim to travel to Puerto Rico and work on a team that studies ancient cities there is not a priority because it is not something that he needs to do urgently or immediately. It is also not something that depends on external factors or demands. It is his value because it reflects his interest, passion, and motivation in life. It is something that he would pursue even if it was difficult or challenging.
Or maybe if it's priority then I'm sorry.
PLEASE PLEASE PLEASE HELP!
Answer:
w-4
Step-by-step explanation:
Suppose we going to find⊕
(4-w)÷(-w-9 ) =⊕÷(w+9 )
⇒(4-w) ÷ -(w+9) =⊕÷(w+9)
cross-multiply we will get
∴ ⊕={(4-w)×(w+9)}÷-(w+9)
= -(4-w) after cancelling ( w+9)
therefore our answer is ( w-4 )
whats the slope of y=-4
Answer: The slope of y = -4 is 0.
Step-by-step explanation:
write an equation of vertical line through the point (9,-10)
Answer:
x = 9
Step-by-step explanation:
An equation for a vertical line is in the form:
x = anumber
The given information is the point (9,-10) this is in the form (x,y). So this gives us the information that x is 9. That is the equation!
x = 9
The equation of the vertical line through (9,-10) is
x = 9
A basketball player has a 70% accuracy rate for making free throws. Mark thought that each attempt was independent and the probability stayed at 70% for this player.
During a game, this player was fouled and given the chance to take two free throws.
P left parenthesis X equals k right parenthesis equals left parenthesis 1 minus p right parenthesis to the power of k minus 1 end exponent p
Using the geometric distribution formula, what is the probability that this player misses his first free throw, but makes the second one? Answer choices are rounded to the hundredths place.
If a basketball player has a 70% accuracy rate for making free throws. The probability that this player misses his first free throw, but makes the second one is 0.21.
How to find the probability?The probability of making a free throw is 0.7, so the probability of missing a free throw is 0.3.
Let X be the number of trials (free throws) until the first success (a made free throw). Since we want to know the probability of missing the first free throw and making the second one, we want to find P(X = 2).
Using the geometric distribution formula, we have:
P(X = 2) = (1 - p)^(k-1) * p
where:
p is the probability of success (making a free throw)
k is the number of trials (2 in this case), and (1 - p)^(k-1) is the probability of having k-1 failures (missing the first free throw) followed by one success (making the second free throw).
Plugging in the values, we get:
P(X = 2) = (1 - 0.7)^(2-1) * 0.7
= 0.3 * 0.7
= 0.21
Therefore, the probability is 0.21 (rounded to the hundredths place).
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This is an algebraic equation.
-12x^2/2x^2
Step-by-step explanation:
solving equipment step:
*SIMPLIFY THE EXPRESSION
- 12x² ÷(2x²²)
Rewrite
simply the equation
=12x² ÷ 2x²²
=-6x²÷x²²
Now cancel common factors
=-6x÷x^20
#Brainac
|x-y|+4
X=-1 Y=3
Please help
Solve with steps
Step-by-step explanation:
it is 8 bcs -1 - 3 = -4 turn it to 4 and +4
The Singh family ordered a large pizza with a diameter of 20 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.
274.75 square inches
39.25 square inches
314 square inches
157 square inches
274.75 square inches of pizza are remaining. Option A is the correct option.
What is π in math?
The ratio of a circle's diameter to its circumference, or "pi," is a mathematical constant that is roughly equal to 3.14159 (/pa/; also written as "pi"). Numerous mathematical and physics formulas contain the number. It is an irrational number, meaning that although fractions like 22/7 are frequently used to approximate it, it cannot be expressed exactly as a ratio of two integers.
Given that, the diameter of large pizza is 20 inches.
The radius of a circular shape is half of the diameter.
The radius of the pizza is (20 inches)/2 = 10 inches.
Area of a circular shape is ∏r² .
The area of the pizza is 3.14×10² = 314 in²
The total part of the pizza is considered as 1.
One-eighth of the pizza is eaten, and the remaining portion is (1-1/8) = 7/8.
The area of remaining pizza is
314 in² × (7/8)
= 274.75 square inches
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Norma watched a beetle and a spider on the sidewalk. The beetle crawled 2/3 of a yard and the spider crawled 3/5 of a yard. How much farther did the beetle crawl than the spider?
The beetle crawled 1/15 of a yard farther than the spider.
What is the fraction?
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing a numerator(upper value) and denominator(lower value).
To find out how much farther the beetle crawled than the spider, we need to subtract the distance the spider crawled from the distance the beetle crawled.
The beetle crawled 2/3 of a yard, which can be written as a fraction with a common denominator of 15: 10/15.
The spider crawled 3/5 of a yard, which can also be written as a fraction with a common denominator of 15: 9/15.
Now we can subtract the distance the spider crawled from the distance the beetle crawled:
10/15 - 9/15 = 1/15
Hence, the beetle crawled 1/15 of a yard farther than the spider.
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Question
If the end behavior is decreasing to the left, what might be true about the function? Select all that apply.
Select all that apply:
The degree is even and the leading coefficient is positive.
The degree is even and the leading coefficient is negative.
The degree is odd and the leading coefficient is positive.
The degree is odd and the leading coefficient is negative.
FEEDBACK
MORE INSTRUCTI
If the function is increasing to the left and falls to the right,
Leading coefficient of the function will be negative and the degree of the function will be Odd.
What is a polynomial's leading coefficient?
The term in a polynomial that has the highest power of x is the leading term. For instance, the leading term in the equation 7+x3x2 is 3x2. The coefficient of the first term is referred to as a polynomial's leading coefficient. The leading coefficient in the aforementioned example is 3.
Leading coefficient of the function will be negative and the degree of the function will be Odd.
Similarly, if the function is increasing to the right and falls to the left,
Leading coefficient of the function will be positive and the degree of the function will be Odd.
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100 POINTS NEED HELP ASAP
Answer:
Step-by-step explanation:
we would cut it into small pieces and find their area,
Add three segments:
PH, HK and LNThis will give us the following shapes:
Semicircle with diameter PH,Triangle HKJ,Triangle LMN,Rectangle ONKH.You may find each area and add up to get the total area.
(PLEASE HURRY!) A table giving various values of linear functions f(x) and g(x) is shown below. What is the solution to the system?
Answer:
A. (2, 1)
Step-by-step explanation:
You want the solution to the system of equations represented by the given table and graph.
SolutionWhen we are given two functions and asked for "the solution to the system", we generally mean the value of x that satisfies f(x) = g(x). That will be represented on a graph as the point (x, f(x)), or (x, g(x)), where the function graphs intersect.
TableWhen you're looking for the solution in a table, you look for the row of the table where the value of f(x) is the same as the value of g(x). For the given table, we see that f(x) = g(x) = 1 on the last row of the table, where x=2. This means the solution is ...
(x, f(x)) = (2, 1)
Identify AB as a major arc, minor arc, or semicircle.
o Major arc
• Minor arc
O Semicircle
Find the measure of the arc.
AB=
AB can be identified to be, based on the circle, to be a A. Major arc.
The measure of the arc would be 226 degrees.
How to find the measure of the arc ?A major arc is an arc on a circle that is greater than 180 degrees, or half the circumference of the circle. A major arc is also known as a large arc. It extends from one endpoint of a minor arc to the other endpoint of the same arc, passing through the center of the circle.
AB is a major arc because it is larger than half of the circle which means it is greater than 180s degrees.
The measure of arc AB is:
= Half a circle angle + arc CB
= 180 + 46
= 226 degrees
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PLEASEEEE HURRY!!!!!!!
For the equation: 2(x - 7) = 3 - 7x + 5 + 8 + 7x + 11 , the right side of the equation can be simplified by combining like terms.
Simplify the right side of the equation:
The left side of the equation can be simplified using the Distributive Property.
Simplify the left side of the equation:
Answer:
2x-14=27
Step-by-step explanation:
Right Side) Combine like terms
Step 1) 3+5+8+11=27
Step 2) -7x+7x=0
Right side: 27
Left Side) Distribute
2*x=2x
2*(-7)=-14
Answer : 2x-14=27
CAN SOMEONE HELP WITH THIS QUESTION?✨
As a result, when the camera and the rocket are 4255 feet apart, the rate trigonometry of change in the angle of elevation after launch is roughly -0.15807 radians/foot.
what is trigonometry?Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. The issue first originated in the Hellenistic era, during the third century BC, as a result of the use of geometry in astronomical investigations. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.
Where is the camera's angle of elevation and c is the rocket's height above ground level.
We may express the angle of elevation using the given formula as:
r θ = tan⁻¹(c/2000)
c2 + x2 = d2, where d = 4255 ft 2c(dc/dx) + 2x = 0, and dc/dx = -x/c.
When we multiply c by 2000 tan() and x by (d2 - 20002) (since x is the horizontal distance between the camera and the rocket), we get: dc/dx = -(d2 - 20002) / (2000 tan())
tan1(0.02d/2000) = tan1(d/100000)
dc/dx = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -0.005(d2 - 20002) / d
dc/dx = -0.005(42552 - 20002) / 4255 -0.15807 radians per foot
As a result, when the camera and the rocket are 4255 feet apart, the rate of change in the angle of elevation after launch is roughly -0.15807 radians/foot.
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The area of a square is represented by the formula A = s². When that square is cut by a diagonal, two isosceles triangles are formed. the area of one of the returning triangles is A= 1/2s².Suppose the side of the original square is 10 cm. Find the area of one of the triangles.
Using the given formula [A = 1/2s²], we know that the area of one of the triangles is (C) 50 cm².
What is the area?A patch's area on a surface determines how big it is.
Whereas a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.
A plane figure's area is the space that its perimeter encompasses.
The area of a closed figure is the total number of unit squares covering its surface.
The area is measured in square units like cm² and m².
So, we know that the area of the triangle is now:
A = 1/2s²
The side of the square is: 10 cm
Then, the area of the one triangle is:
A = 1/2s²
A = 1/2*10²
A = 1/2*100
A = 50 cm²
Therefore, using the given formula [A = 1/2s²], we know that the area of one of the triangles is (C) 50 cm².
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FILL IN THE BLANKS PLEASE. 20 POINTS.
An inverse is the ___________ or reverse. In math operations, inverse operations were introduced when we learned about fact families, but no one told us the numbers were related because of inverse operations. The inverse operations we use most are: Subtraction and _______ and multiplication and _______. Did you know that exponents and radicals are also _________ operations?
Answer:
Opposite, addition, division, inverse
Step-by-step explanation:
Express the number 78.263 using ones, tenths, and thousandth so
Answer:
70 + 8 + 0.2 + 0.06 + 0.003
Step-by-step explanation:
Expressing the number means to be written based on the place values.
Therefore:
7 = tens place value (70)
8 = ones place value (8)
. = decimal point (.)
2 = tenths place value (0.2)
6 = hundredths place value (0.06)
3 = thousandths place value (0.003)
~
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Solve for x, using a
tangent and a secant line.
?]°
x = [?
X
15°
40°
Remember : a = b
I think that the answer is 40 degreee
The required measure of section x on the circle is 95°.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property.
Here,
From the given we have,
a = 40,
c = x
b = 15
Now, put this value in the given formula,
a = c-b / 2
So,
40 = x - 15/2
x -15 = 80
x = 95°
Thus, the required measure of section x on the circle is 95°.
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CONVERT 25 DEGREES CELECIOUS TO TO FERENHEIGHT SHOW THE CONVERSION STEPS.
Answer:
Step-by-step explanation:
The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32F = [ C × (9/5) + 32 ] Given that, C = 25F = 25 × (9/5) + 32F = 45 + 32F = 77Thus, 25° C is equivalent to 77° F.
If f(x) = 3x + 10 and g(x) = 2x - 4, find (f+ g)(x).
O A. (f+ g)(x) = 3x + 2x+6
OB. (f+ g)(x) = -3* - 2x - 14
O C. (f+ g)(x) = 5x + 6
D. (f+ g)(x) = 3x - 2x+14
S
Answer: C. (f+ g)(x) = 5x + 6
Step-by-step explanation:
C. (f+ g)(x) = 5x + 6
This is because when you add two functions together, you simply add their coefficients together and add the constants together. So, in this case, you add 3 and 2 to get 5 and add 10 and -4 to get 6. Therefore, the answer is 5x + 6.
Answer:
The correct answer is C. (f+ g)(x) = 5x + 6
CAN U HELP ME ASAP ????????
The solution to the system of equations is given as follows:
(1,9).
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
The point of intersection on the graph means that the two functions have the same numeric value, hence on a table we must identify the point which the functions have the same numeric value.
From the table, function f(x) and g(x) both contain the point (1,9), hence this is the point of intersection of the two lines, and the solution is given as follows:
(1,9).
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Mary Jo spends $2,300 to buy stock in two companies. She pays $19 a share to one of the companies and $24 a share to the other. If she ends up with a total of 100 shares, how many shares did she buy at $19 a share and how many did she buy at $24 a share?
She bought ____ shares at $19 and ___ shares at $24.
Answer:
Mary Jo bought 20 shares at $19 a share and 80 shares at $24 a share.
Step-by-step explanation:
Let's use algebra to solve the problem. Let x be the number of shares Mary Jo buys at $19 a share, and y be the number of shares she buys at $24 a share.
We know that Mary Jo spends a total of $2,300, so we can write the equation:
19x + 24y = 2300
We also know that she ends up with a total of 100 shares, so we can write the equation:
x + y = 100
Now we have two equations with two variables, which we can solve using substitution or elimination.
Let's use substitution. Solve the second equation for x:
x = 100 - y
Substitute this expression for x in the first equation:
19(100 - y) + 24y = 2300
Simplify and solve for y:
1900 - 19y + 24y = 2300
5y = 400
y = 80
So Mary Jo bought 80 shares at $24 a share.
To find the number of shares she bought at $19 a share, substitute y = 80 in the second equation:
x + 80 = 100
x = 20
Therefore, Mary Jo bought 20 shares at $19 a share.
In summary, Mary Jo bought 20 shares at $19 a share and 80 shares at $24 a share.
A mobile base station (BS) in an urban environment has a power measurement of 25 µW at 325 m. If the propagation follows an inverse 4th power law (Section 3.2.2), what is a reasonable power value, in µW, to assume 1.3 km from the BS?
Give your answer in scientific notation to two decimal places.
Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to equation two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
The received power at a distance d is determined by:
Pr is equal to Pt, Gt, Gr, and (/4d)2.
where:
The transmitted power is Pt.
The transmitter antenna gain is Gt.
the receiver antenna gain, or Gr.
is the signal's wavelength.
Pr2 = (d1/d2)4 * Pr1
where:
At a distance of 325 m, Pr1 is the received power, which is specified as 25 W.
d1 is 325 metros away, while d2 is 1.3 kilometres away (i.e., 1300 m)
Inputting the values provided yields:
Pr2 = 25 W * (325/1300 m)4 = 25 W * 0.0625 = 1.5625 W
Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.
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Find the measure of
The similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°
How to evaluate for variable x of the adjacent anglesThe triangles RDS and ADB area similar thus the lines AB and RS are parallel to each other and the adjacent angles of m∠SRA and m∠BAR are supplementary, so their sum is equal to 180°.
m∠SRA and m∠BAR are supplementary so;
(6x + 8)° + (9x + 7)° = 180°
15x + 15 = 180°
15x = 180° - 15 {subtract 15 from both sides}
15x = 165
x = 165/15 {divide through by 15}
x = 11
m∠A = 9(11) + 7 = 106°
m∠R = 6(11) + 8 = 74°
m∠S = 4(11) + 14 = 58°
Therefore, the similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°
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Possible question:
Find the measure of the angles with the variable x for the similar triangles ∆RDS and ∆ADB.
Tan^2a-cosec^2a+1=0 value of pie
the solutions for a are:
a = n×π, π/4, or 7π/4, where n is any integer.
define integerAn integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals.
tan²(a) - csc²(a) + 1 = 0
tan²(a) - (1/sin²(a)) + 1 = 0
(tan²(a)sin²(a) - 1 + sin²(a))/sin²(a) = 0
Simplifying the numerator:
(tan²(a) - 1)sin²(a) = 0
Using the identity tan^2(a) = sec²(a) - 1:
(sec²(a) - 2)sin²(a) = 0
Expanding and simplifying:
sec²(a)sin²(a) - 2sin²(a) = 0
sin²(a)(sec^2(a) - 2) = 0
So either sin²(a) = 0 or sec²(a) - 2 = 0.
If sin²(a) = 0, then a is an integer multiple of pi (i.e., a = n×π for some integer n).
If sec²(a) - 2 = 0, then sec²(a) = 2,
cos(a) = ±√(2)/2
So a can be π/4 or 7π/4.
Therefore, the solutions for a are:
a = n×π, π/4, or 7π/4, where n is any integer.
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4. Claire jogs around an oval track and is able to complete one lap in 5 minutes.
If she jogs at the same pace for 42 minutes, how many laps would she be able
to jog? Write an inequality and find the number of whole laps Claire completes.
The inequality that represent how many laps she can do is "number of laps < 8.4".
Claire can jog a maximum of 8 laps in 42 minutes.
What number of whole laps did Claire completes?Since Claire can jog one lap in 5 minutes, we can use division to find how many laps she can complete in 42 minutes:
= 42 minutes / 5 minutes per lap
= 8.4 laps
However, since Claire cannot jog a fractional number of laps, we need to round down to the nearest whole number of laps. This is because she will have only completed a fraction of a lap by the time she reaches the end of the 42 minutes, and we want to know how many whole laps she completes. Therefore, we can write the inequality as "number of laps < 8.4".
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A sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 k. The ballon begins to shrink and shrivel up. Use gas particle motion to explain why.
This causes the volume of the balloon to decrease, leading to an increase in the number of collisions between gas particles and the inside surface of the balloon, and causing the balloon to shrink and shrivel up.
What is temperature?Temperature is a measure of the average kinetic energy of the particles in a substance or system. In other words, it is a measure of how hot or cold something is relative to a standard reference point. The SI unit of temperature is the kelvin (K), but temperature is often measured in degrees Celsius (°C) or Fahrenheit (°F) in everyday life. Temperature plays a crucial role in many natural and man-made processes, and is a key factor in determining the behavior of matter at different states.
Here,
When a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy and slow down. As the temperature drops, the average kinetic energy of the gas particles decreases, causing them to move slower and collide less frequently. This results in a decrease in pressure inside the balloon.
According to the Ideal Gas Law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. As the pressure inside the balloon decreases, its volume also decreases, since the number of moles of gas and the gas constant remain constant.
Since the balloon is sealed, the gas particles cannot escape, so they continue to collide with each other and the inside surface of the balloon. As the volume of the balloon decreases, the gas particles become more crowded, increasing the number of collisions between them. This leads to a decrease in the distance between the gas particles and the inside surface of the balloon, causing the balloon to shrink and shrivel up.
In summary, when a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy, slow down, and collide less frequently, resulting in a decrease in pressure inside the balloon.
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1. Solve the triangles:
2. Solve for x and y.
3. The Mighty Drop ski slope has an angle of elevation of 75°. If the top of the slope has an elevation of 800
feet, what is the length of the run?
4. Little Judy let go of her red balloon. The balloon is now 2240 feet up in the air and 350 feet to the west.
What is the angle of elevation when little Judy looks at her red balloon?
The answer of the given question is (3) the length of the run of the Mighty Drop ski slope is approximately 181.8 feet. (4) the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.
What is Slope?A slope typically refers to the angle of an incline or ramp, or the ratio of vertical change to horizontal change of a straight line or curve on a graph. For an incline or ramp, the slope is the angle between the surface and the horizontal plane. It is defined as the ratio of the vertical rise to the horizontal run of the ramp.
In the context of a graph, slope refers to the steepness of a line or curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or curve. The slope of a line can be positive (if the line goes up from left to right), negative (if the line goes down from left to right), or zero (if the line is horizontal).
(3) . To solve for the length of the run of the Mighty Drop ski slope, we can use the trigonometric function tangent, which relates angle of elevation to ratio of opposite and adjacent sides of right triangle.
Let x be the length of the run. Then we have:
tangent(75°) = opposite/adjacent
tangent(75°) = 800/x
Solving for x, we get:
x = 800 / tangent(75°)
x ≈ 181.8 feet
Therefore, the length of the run of the Mighty Drop ski slope is approximately 181.8 feet.
(4) . To solve for the angle of elevation when little Judy looks at her red balloon, we can use the trigonometric function arctangent.
Let θ be the angle of elevation. Then we have:
tangent(θ) = opposite/adjacent
tangent(θ) = 2240/350
Taking the arctangent on both sides, we will get:
θ = arctangent(2240/350)
θ ≈ 82.7°
Therefore, the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.
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Part 1
The population of a small town can be modeled by Pt, where t is the number of years since 1975. Interpret the slope of the graph of this function as a rate of change.
The slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.
What is the slοpe?The slοpe οf a line is a measure οf its steepness. Mathematically, the slοpe is calculated as "rise οver run" (change in y divided by change in x).
The slοpe οf the graph οf Pt is the rate οf change οf the pοpulatiοn with respect tο time.
Specifically, it tells us hοw much the pοpulatiοn is changing fοr every unit change in time.
Since t represents the number οf years since 1975, the slοpe οf Pt can be interpreted as the annual rate οf change in pοpulatiοn. Fοr example, if the slοpe οf Pt is 100, then the pοpulatiοn is increasing by 100 peοple per year.
Therefοre, the slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.
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