An observer (O) spots a plane flying at a 35° angle to his horizontal line of sight. If the plane is flying at an altitude of 17,000 ft., what is the distance (x) from the plane (P) to the observer (O)?
20,757 feet
24,251 feet
29,639 feet
31,262 feet
Answer:
here are numerous information's already given in the question. Based on those information's, the answer to the question can be easily deduced.
Angle at which the plane is flying in respect to the observer = 35 degree
Altitude at which the plane is flying = 17000 feet
The distance at which the plane is flying from the observer = x
Then
x = 17000/sin 35
= 17000/0.57357
= 29638.93 feet
= 29639 feet
From the above deduction, we can conclude that the correct option among all the options given in the question is the third option.
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The distance between the plane and the observer is 29,638 feet.
Data;
Angle = 35 degreesheight of the plane = 17,000ftdistance from the plane to the observer = xTrigonometric RatioThis is the use of SOHCAHTOA which is the relationship between sides of a right angle triangle and it's angle.
In this case, we have the value of opposite and angle and we need to find the hypothenuse.
Using sine of the angle,
[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 35 = \frac{17000}{x}\\ x = \frac{17000}{sin35}\\ x = 29,638 feet[/tex]
The distance between the plane and the observer is 29,638 feet.
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Marshall bought some pet supplies for $15. The sales tax was 6%. He wrote the expression 1.06(15) to find his total cost.
Which equivalent expression could he also use to find the total cost?
A. 15+0.6(15)
B. (1+0.06)15
C. 1+0.06(15)
D.15 + 0.06
if the raidus of mars(3,397 km) is about 13.7% of of neptunes radius, what is the radius of neptune?
A card is randomly selected from a deck of 52 cards. Find the probability that the card is between four and eight (inclusive) or is a club.
Answer:
20/52+13/52-5/52=.538
Step-by-step explanation:
The probability that the card is between four and eight (inclusive) or is a club is 4/13.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The number of cards can be written as,
The number of cards between 4 and 8 is 3 {4,5,6,7,8}.Number of club cards = 13Number of cards between 4 and 8 from heart, spades, and diamonds = 15Now, the probability that the card is between four and eight (inclusive) or is a club is,
Probability
= (Number of club cards+ Number of cards between 4 and 8)/(Total number of cards)
= (13+15)/(52)
= 28/52
= 4/13
Hence, the probability that the card is between four and eight (inclusive) or is a club is 4/13.
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There are three highways in the county. the number of daily accidents that occur on these highways are poisson random variables with respective parameters .3, .5, and .7. find the expected number of accidents that will happen on any of these highways today.
Final answer:
To find the expected number of accidents on three highways with Poisson distributions, sum the individual expectations: 0.3, 0.5, and 0.7, resulting in an expected 1.5 accidents per day.
Explanation:
The student asked how to find the expected number of accidents that will happen on any of the three highways in a day, given that the number of daily accidents on these highways are Poisson random variables with parameters 0.3, 0.5, and 0.7 respectively. To solve this, we shall sum the parameters of the Poisson distributions because the expectation of the sum of independent random variables is the sum of their expectations.
Therefore, we calculate the expected number of accidents as follows:
For the first highway with parameter 0.3, the expected number of accidents is 0.3.
For the second highway with parameter 0.5, the expected number of accidents is 0.5.
For the third highway with parameter 0.7, the expected number of accidents is 0.7.
Adding these together, we get:
Expected number = 0.3 + 0.5 + 0.7 = 1.5 accidents per day.
The square root of 150 is between
A.10 and 11
B.11 and 12
C.12 and 13
D.13 and 14
find the equation to the line that is perpendicular to y=2x-3 and goes through the point (-1,2)
A pooled proportion is calculated by giving each sample proportion an equal weight.
a. True
b. False
solve for first two positive solutions sin(3x)cos (4x)+cos(3x)sin(4x)=-0.9
The Lombardo family went out to dinner and their full mean costed $62. If they left a 20% tip, how much did they tip?
Tasha earns $400 per week plus a commission of 10% on her weekly sales. Each week she saves of her earnings. In the expression , what does the expression 400 + 0.1s represent in this situation?
In this situation, the expression 400 + 0.1s represents Tasha's total earnings for the week, including her base salary and commission.
Explanation:In this situation, the expression 400 + 0.1s represents Tasha's total earnings for the week. The $400 represents her base salary, and the 0.1s represents the commission she earns on her sales. The value of s represents Tasha's total sales for the week.
For example, if Tasha's total sales for the week are $2000, then her commission would be 0.1($2000) = $200. Adding this to her base salary of $400, her total earnings for the week would be $400 + $200 = $600.
Therefore, the expression 400 + 0.1s represents Tasha's total earnings for the week, including her base salary and commission.
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Raj eats 1/11 of a pound of grapes in 1/25 of a minute. How many minutes will it take him to eat a full pound of grapes?
What is the effect of decreasing the alpha level (for example, from a = .05 to a = .01)? it decreases the probability of a type i error. it decreases the size of the critical region. it decreases the probability that the sample will fall into the critical region. all of the other options are results of decreasing alpha?
Alyssa is building a brick mailbox. She is going to stack bricks that are each \dfrac23 \text{ft}
3
2
ftstart fraction, 2, divided by, 3, end fraction, f, t tall, and the finished stack of bricks needs to be 4\dfrac23 \text{ft}4
3
2
ft4, start fraction, 2, divided by, 3, end fraction, f, t tall.
How many bricks will go in the stack?
Which of the articles represent a proper fraction? A. 15/22 B. 8/8 C. 3/2 D. 12/9
If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. the cost to play the game is $5. what is the expectation of this game?
a. $3.06
b. -$2.78
c. -$3.06
d. $2.78
Final answer:
The expected value of the gambling game with a cost of $5, and potential winnings of $10 for a sum of 10 or $20 for a sum 3, is −$2.78. The calculation shows the player will lose $2.78 on average per game, indicating it is not a profitable game to play long term. So, option (b) is correct.
Explanation:
The student is interested in determining the expected value of a gambling game where rolling two dice can result in either winning money or losing the cost to play. To find the expected value, we must consider the probability of each outcome and its associated payoff.
First, we calculate the chances of rolling a sum of 10 with two dice. There are three combinations that give a sum of 10: (4,6), (5,5), and (6,4). Since there are 36 possible outcomes when rolling two dice, the probability of obtaining a sum of 10 is 3/36 or 1/12.
Similarly, the only combinations that result in a sum of 3 are (1,2) and (2,1). Thus, the probability of rolling a sum of 3 is 2/36 or 1/18.
The expected value (EV) can be calculated using the formula:
EV = (−cost to play) + [P(sum of 10) × winnings for 10] + [P(sum of 3) × winnings for 3]
Substituting the given values yields:
EV = (−5) + [(1/12) × 10] + [(1/18) × 20]
After calculating, we find tha-
EV = −$2.78.
Since the expected value is negative, this implies that, on average, the player will lose $2.78 per game. Therefore, playing this game would result in an average loss over time.
Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy. x3y2 − x4y + 4xy3 = 0
Through applying the techniques of implicit differentiation to the equation x³y² - x⁴y + 4xy³ = 0, the derivative dx/dy is found to be [x⁴ - 4y³ - 2x³y]/[3x²y² - 4x³y].
Explanation:The subject of your question is implicit differentiation in calculus, a branch of mathematics. You wish to know how to differentiate the equation
x³y² - x⁴y + 4xy³ = 0
with respect to y (y is independent and x is dependent).
The initial step in implicit differentiation is to derive every term of an equation. So, we end up with:
3x²y²(dx/dy) + 2x³y(dy/dx) - 4x³y(dx/dy) - x⁴ + 4y³ + 12x²y² = 0.
After grouping like terms together, the equation become:
dx/dy[3x²y² - 4x³y] = x⁴ - 2x³y - 4y³
Eventually, divide both sides by [3x²y² - 4x³y] to isolate dx/dy and get the final answer:
dx/dy = [x⁴ - 4y³ - 2x³y]/[3x²y² - 4x³y]
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Find the height of a door on a scale drawing if the door is 2 meters tall and the scale is 1 centimeter = 4 meters. Round to the nearest tenth.
The height of the door in the drawing will be 1/2 centimeters.
What is scale factor?Scale factor is used to compare the size of two objects. Mathematically, we can write -
{K} = S{O1}/S{O2}
13 mg
Given is that the height of a door on a scale drawing if the door is 2 meters tall and the scale is 1 centimeter = 4 meters.
Height of the door = 2 meters
Scale : 1 centimeter = 4 meters.
So, in one meters, there will be - 1/4 centimeters.
In 2 meters, there will be -
(1/4) x 2 = 1/2 centimeters
Therefore, the height of the door in the drawing will be 1/2 centimeters.
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Find the percent of tip: Cost of meal: $28.00 Tip: $3.36 The percent of the tip was ___%.
Answer:
12.00%
Step-by-step explanation:
[tex]$3.36\\[/tex] ÷ [tex]$28.00\\[/tex] = [tex]0.12\\[/tex]
[tex]100 *0.12=12%\\[/tex] %
248mph equals how many meters per second
You deposit $5000 each year into an account earning 8% interest compounded annually. How much will you have in the account in 20 years?
identify the type of of function represented by the equation y=2x^2
At what projection angle will the range of a projectile equal to 6 times its maximum height?
If an original conditional statement is represented by p → q, which represents the contrapositive?
~q → ~p that's the answer
You swim the 50-meter freestyle in 28.12 seconds.This is 0.14 second less than your previous fastest time. What was your previous fastest time?
If a person swim the 50-meter freestyle in 28.12 seconds. This is 0.14 second less than persons previous fastest time is 28.26.
What is Equation?
Two or more expressions with an equal sign is called as equation.
Given that,
One swim the 50-meter freestyle in 28.12 seconds..
The previous fastest time be x.
The new fastest time is 28.12 seconds.
New fastest time is 0.14 second less than your previous fastest time.
So, 28.12+0.14=x
28.26=x
Hence the previous fastest time is 28.26 seconds.
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Can someone please help?
The 2015 senior class from puma high school raised funds for an end of the year party at club sizzle. It costs $4,000 to rent out club sizzle plus $20 per student for food and drinks. If the senior class raised 11,000, how many students can attend the end of year party ? Write an equation for the situation and solve.
A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels, and nine (9) pennies. The customer buys a pair of shoes for $49.86. Based on the combination of bills and coins the customer has, what are the least number of bills and coins the customer can give the cashier in order to buy the shoes for the exact amount and not require any change back?
Which number is 100 times greater than 6 thousandths
Find the mean median mode and range of this date 49,49,54,55,52,49,55, if necessary round to the nearest tenth