The diagram shows the locations of John and Mark in relationship to the top of a tall building labeled A.
A) Describe < 4 as it relates to the situation
B) Describe < 3 as it relates to the situation
Answers
a]
∠4 is the angle of elevation as seen by Mark from his location. It is the angle between the horizontal and the line from the object to the observer's eyes.
b]
∠3 is the angle of depression and it is congruent to the angle 5, which is the angle of elevation as seen by John from his location.
Related Questions
A box contains 16 transistors, 5 of which are defective. if 5 are selected at random, find the probability that
a. all are defective. and. none are defective.
Answers
Only one way of selecting the 5 defective transistors:
Number of ways of selections available = 6C5 = 16!/[5!*(15-5)!] = 4368
Probability they are all defective = Number of ways of selecting 5 defectives/Total number of ways possible = 1/4368 ≈ 0.000229
Part (b): None are defective
Total number of non defectives = 16 -5 = 11
Number of ways of selecting 5 non defective = 11C5 = 462 ways
Total number of ways possible = 16C5 = 4368
Probability of selecting 5 non defectives = 462/4368 = 11/104 ≈ 0.1058
A - all defective
B - none defective
[tex] \displaystyle
|\Omega|=\binom{16}{5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{2\cdot3\cdot4\cdot5}=4368\\
|A|=1\\
|B|=\binom{11}{5}=\dfrac{11!}{5!6!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\\\
P(A)=\dfrac{1}{4368}\approx0.02\%\\
P(B)=\dfrac{462}{480480}=\dfrac{1}{1040}\approx0.1\% [/tex]
What did the prince do whenever he found a girl who might be cinderella
Answers
Final answer:
When a prince in fairy tales finds a potential Cinderella, he typically engages in a quest to determine if she is the one, reflecting the theme of male heroism and romantic pursuit found in traditional literature and films.
Explanation:
The passage raises the theme of romantic endeavors and the traditional role of women in classical literature and film, typically anchored within the context of royalty and fairy tales. When the prince in such stories finds a girl that could potentially be Cinderella, typically he would engage in a quest to discover if she truly is the one - often symbolized by a glass slipper fitting or other identifying item. This quest underscores the narrative of countless romantic tales where the male lead seeks to find and often rescue his female counterpart, a concept reflected in various Disney princess movies.
In the greater realm of literature and films, the prince often represents the chivalrous savior. This tradition is evident in the series of princess-centric stories produced by Disney, where a common girl becomes royalty by marriage or starts as a princess whose ultimate happiness is achieved through romance. Although contemporary stories may showcase more agency in their female protagonists, the motif of the male hero remains prevalent.
What is the value of y in the equation 2(3y + 6 + 3) = 196 − 16?
Answers
2(3y + 9) = 196
6y + 18 = 196
6y + 18 - 18 = 196 - 18
6y = 178
Divide both sides by 6
y = 178 / 6
y ≈ 29.667
What is the value, after 7 years...
Answers
Answer:
13946
Step-by-step explanation:
A 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours. Assuming the variables are directly related, how many hours would a 9-ounce candle be expected to burn?
18
27
33
45
Answers
to find the rate it burns:
20 ounce / 60 hours = 1/3 ounce per hour
divide 9 ounces by 1/3 ounce per hour to find total time:
9 / 1/3 = 27 hours
Answer:
B. 27.
Step-by-step explanation:
We have been given that a 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours.
We know that a direct proportional equation is in form [tex]y=kx[/tex], where k represents constant of proportionality.
Let is find value of k by substituting [tex]x=20[/tex] and [tex]y=60[/tex] in above equation as:
[tex]60=k*20[/tex]
[tex]\frac{60}{20}=\frac{k*20}{20}[/tex]
[tex]3=k[/tex]
The equation [tex]y=3x[/tex] represents our given direct proportional relation.
Now, we will substitute [tex]x=9[/tex] to solve for y as:
[tex]y=3*9[/tex]
[tex]y=27[/tex]
Therefore, a 9-ounce candle would be expected to burn for 27 hours and option B is the correct choice.
To the nearest hundredth, what is the area of a circle with a radius of 3 units
Answers
28.27 square units (APEX)
Answer:
28.27
Step-by-step explanation:
gl on test
The spoke of a wheel reaches from the center of the wheel to its room if the circumference of the rim of the wheel is 42 inches how long is each spoke
Answers
so to find the (d) you divide 48÷3.14=15.29 inches. As the spoke goes from the center to its rim, it it is the radius, which is half of the diameter.15.29/2 is
B) 7.64 inches.
Which sequence is modeled by the graph below? coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8)
a. an = 1(2)n − 1
b. an = 2(1)n − 1
c. an = 1 + (2)n − 1
d. an = (2)(n − 1)
Answers
Answer: The correct option is d.
Explanation:
From the given information it is noticed that the coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8).
The coordinates are in the form of (x,y), it means the value of xth term of the sequence is y.
The point (1,1) represents that the first term is 1. Similarly from (2, 2) (3, 4) and (4, 8) points we can say that the second term is 2, third term is 4 and fourth term is 8.
The sequence is 1,2,4,8.
It can be written as,
[tex]2^0,2^1,2^2,2^3[/tex]
Since the base is common that is 2 and the power is one less than the position of term. So the sequence is in the form of,
[tex]a_n=2^{n-1}[/tex]
Therefore, the correct option is d.
If the person can't accommodate and the glasses is + 2.50d, at which distance will the person see clearly
Answers
At a + diopter measurement is a nearsighted person take the value of 2.5 and make it the denominator with 1 as the numerator to find the distance in meters that they can see clearly past their face.
1/2.5 = 2/5 of a meter.
Answer:
40 cm or 2/5 of a meter.
Step-by-step explanation:
A short-sighted person, at a positive diopter, will take an estimation of about 2.5 and make it the denominator by 1 as the numerator to find out the distance (in meters) that they can see clearly.
We can find the value of f, given the value for P:
P = +2.50
f = 1 / p = 1 / 2.50
(changing the units, it will be) ---> 100 / 2.50 which is equal to 40 cm.
Therefore, 40 cm which is 2/5 of a meter is the distance a person with glasses +2.5d can see clearly.
can someone please explain the steps to solve these questions.
Answers
A class had 30 pupils at the beginning of this school term, but now has 5 more pupils. What is the percent of increase?
The question is basically asking how much 5 is in ratio to 30. So just divide 5 (the given amount) by 30 (the total amount). The answer is 0.16, or 16%
Any answers please??
Answers
X-axis= (x,y) --->(x,-y)
Y-axis= (x,y) --->(-x,y)
X-axis= (-4,4) --->(-4,-4)
Y-axis= (-4,-4) --->(4,-4)
X-axis= (4,-4) --->(4,4)
Hope this Helps! :)
Find the area of the surface of the part of y=4x+z^2 that lies between the planes
Answers
[tex]y=z^2+4x[/tex]
X)Solve for [tex]x[/tex] by simplifying both sides of the equation, then isolate the variable
[tex]x=- \frac{ z^{2} }{4}+ \frac{y}{4} [/tex]
Z)Take the root of both sides and solve.
[tex]z= \sqrt{-4x+y}, - \sqrt{-4x+y} [/tex]
Slips of paper numbered 1 through 14 are placed in a hat. in how many ways can two numbers be drawn so that the sum of numbers is 12
Answers
1 and 11
2-10
3-9
4-8
5-6
6-6
so there are 6 ways
20 PTS AND I'LL MARK BRAINLIEST
∠1 and ∠2 are a linear pair, and ∠2 and ∠3 are vertical angles. m∠2=(5+4y)∘ and m∠3=(6y−25)∘ . What is m∠1 ?
Answers
5+4y=6y-25 (We'll add the degrees symbol later)
5 = 2y - 25
30 = 2y
y = 15°
We can plug the y-value into the value for m∠2.
5 + 4(15) = 65°
Now, we can easily find m∠1, since they are a linear pair.
m∠1 + m∠2 = 180
m∠1 + 65 = 180
m∠1 = 115°.
m∠1 equals 115°.
Hope this helps!
Find all solutions to the equation sin2x+sinx-2cosx-1=0 in the interval [0, 2pi)
Answers
_____
Replacing sin(2x) with 2sin(x)cos(x), you have
2sin(x)cos(x) +sin(x) -2cos(x) -1 = 0
sin(x)(2cos(x) +1) -(2cos(x) +1) = 0 . . . . factor by grouping
(sin(x) -1)(2cos(x) +1) = 0
This has solutions
sin(x) = 1
x = π/2
and
2cos(x) = -1
cos(x) = -1/2
x = {2π/3, 4π/3}
WILL MARK BRAINLIEST
There are 50 red beans and 50 white beans in a bag. The first bean selected is red. The red bean is returned to the bag. What are the chances of the second bean selected being red?
Answers
Hope this helps :)
Norma stopped to get gas for her car before beginning a trip. her odometer read 2587 miles, and she filled up her tank with 26 gallons. at the end of her trip, her odometer read 3295 miles. what is her car's miles per gallon?(round to the closest gallon)
Answers
Assuming that at the end of the trip all the gas had been consumed, a total of 26 gallons was consumed.
Therefore,
Car consumption = 708/26 = 27.23 miles/gallon
Express the complex number in trigonometric form. -2 + 2square root of three i
Answers
Answer:
The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]
Step-by-step explanation:
Given : Complex number [tex]-2+2\sqrt{3}i[/tex]
To find : Express the complex number in trigonometric form?
Solution :
The complex number [tex]a+ib[/tex] trigonometric form is [tex]r(\cos\theta+i\sin\theta)[/tex]
Where, [tex]r=\sqrt{a^2+b^2}[/tex]
and [tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]
On comparing with given complex number [tex]-2+2\sqrt{3}i[/tex]
a=-2 and [tex]b=2\sqrt{3}[/tex]
Substitute the value,
[tex]r=\sqrt{a^2+b^2}[/tex]
[tex]r=\sqrt{(-2)^2+(2\sqrt{3})^2}[/tex]
[tex]r=\sqrt{4+12}[/tex]
[tex]r=\sqrt{16}[/tex]
[tex]r=4[/tex]
[tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]
[tex]\theta=\tan^{-1}(\frac{2\sqrt3}{-2})[/tex]
[tex]\theta=\tan^{-1}(-sqrt3)[/tex]
[tex]\theta=\tan^{-1}(\tan(-60))[/tex]
[tex]\theta=-60[/tex]
Substituting all values in the formula,
[tex]r(\cos\theta+i\sin\theta)[/tex]
[tex]4(\cos(-60)+i\sin(-60))[/tex]
[tex]4(\cos(60)-i\sin(60))[/tex]
Therefore, The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]
Look at the figure rectangle PQRS, find m angel P
Answers
Answer: [tex]144^{\circ}[/tex]
Step-by-step explanation:
In the given figure , we have given a parallelogram .
We know that the opposite sides and angles of a parallelogram are equal.
Thus from the given parallelogram PORS we have
[tex]\angle {Q}=\angle {S}\\\\\Rightarrow\ (4\alpha-12)^{\circ}=3\alpha^{\circ}\\\\\Rightarrow\ 4\alpha-12=3\alpha\\\\\Rightarrow 4\alpha-3\alpha=12\\\\\Rightarrow\ \alpha=12[/tex]
Also, the value of angle p is given by :-
[tex]\angle {P}=12\alpha^{\circ}\\\\\Riightarrow\ \angle {P}=12(12)^{\circ}\\\\\Riightarrow\ \angle {P}=144^{\circ}[/tex]
How many questions can i miss on a 28 question test to get a 70%?
Answers
0.7(28) = 19.6
You need to get 19.6 points for a 70%. To calculate the points missed, subtract this from the total points on the test:
28 - 19.6 = 8.4
You can only miss 8.4 points on the test, or no more than 8 questions, to get a grade of 70%.
please help...
The radius of the planet is 4100 miles. Find the distance d to the horizon that a person can see on a clear day from a height of 1298 feet above the planet. (hint: use the conversion 1 mile = 5280 ft) Round your answer to the nearest 10th, and don't forget to convert feet to miles.
Answers
[tex]1298ft*\frac{1mi}{5280ft}= \frac{59}{240} mi[/tex]
Next, we are going to set up a right triangle using the radius of the Earth and the distance above the planet.
The hypotenuse of our triangle will be the radius of the Earth + the distance above the planet. One of the legs of our triangle will be the radius of the Earth, and the other leg, [tex]d[/tex], will be the distance that a person will see on a clear day.
Using the Pythagorean theorem:
[tex]d^2= (\frac{984059}{240} )^2-4100^2[/tex]
[tex]d= \sqrt{(\frac{984059}{240} )^2-4100^2} [/tex]
[tex]d=44.9[/tex] miles
We can conclude that the distance, [tex]d[/tex], to the horizon that a person can see on a clear day from a height of 1298 feet above the planet is 44.9 miles.
A multiple choice test has 9 questions each of which has 5 possible answers
Answers
What is the radian measure of a 150° angle?
Answers
[tex]\bf \begin{array}{ccll} radians&de grees\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \pi &180\\ x&150 \end{array}\implies \cfrac{\pi }{x}=\cfrac{180}{150}\implies \cfrac{\pi \cdot 150}{180}\implies \stackrel{simplified}{\cfrac{5\pi }{6}}[/tex]
The radian measure of a 150° angle is (5/6) π rad, found by multiplying 150° by the conversion factor π/180.
To find the radian measure of a 150° angle, we use the relationship between degrees and radians. Recall that a full circle in degrees is 360° and in radians is 2π rad. Therefore, we can say that 360° equals 2π radians. To convert degrees to radians, we multiply the degree measure by the fraction π/180.
For a 150° angle, the calculation would be:
150° multiplied by the conversion factor π/180
150° * (π/180) = (150/180) * π = (5/6) * π rad
Thus, the radian measure of a 150° angle is (5/6) π rad.
Recently, the texas junior college teachers association annual conference was held in austin. at the time a taxi ride in austin was $ 1.75 $1.75 for the first 1 5 15 of a mile and $ 0.25 $0.25 for each additional 1 5 15 of a mile. if the distance from one of the convention hotels to the airport is 5.8 5.8 miles, how much will it cost to take a taxi from that hotel to the airport?
Answers
Recently, the texas junior college teachers association annual conference was held in austin. at the time a taxi ride in austin was $ 1.75 for the first 1/5 of a mile and $ 0.25 for each additional 1/5 of a mile. if the distance from one of the convention hotels to the airport is 5.8 miles, how much will it cost to take a taxi from that hotel to the airport?
we know that
(1/5) miles is equal to 0.20 miles
so
for the first 0.20 miles----------> $1.75
Remaining Distance = 5.8 - 0.2 miles = 5.6 miles
5.6/(0.2) =28 (this is the number of (1/5)th of a mile after the 1st (1/5)th
Each of these costs 0.25 dollars
28*0.25 = 7 dollars
total cost=$1.75+$7------> $8.75
the answer is
$8.75
To calculate the total taxi fare in Austin, first calculate the initial fee for the first 1/15 mile and then the cost for each additional 1/15 mile. For 5.8 miles, the total cost amounts to $23.25, comprising a $1.75 initial fare and $21.50 for the subsequent distance.
Let's break down the cost of a taxi ride based on the given pricing structure. To find the total cost of a taxi ride for a given distance, we need to calculate the cost for the first 1/5 mile and the additional cost for the remaining distance.
The initial cost for the first 1/5 mile is given as $1.75.
We know the total distance is 5.8 miles. Since the first 1/5 mile is included in the initial cost, the distance to be charged in increments of 1/5 mile is:
[tex]\[ 5.8 - \frac{1}{5} = 5.8 - 0.2 = 5.6 \, \text{miles} \][/tex]
To find the number of 1/5 mile increments in 5.6 miles, divide by 0.2:
[tex]\[ \frac{5.6}{0.2} = 28 \][/tex]
Thus, there are 28 additional 1/5 mile increments.
Each additional 1/5 mile increment costs $0.25. Thus, the total cost for the additional distance is:
[tex]\[ 28 \times 0.25 = 7.00 \][/tex]
The total cost is the initial cost plus the cost for the additional distance:
[tex]\[ 1.75 + 7.00 = 8.75 \][/tex]
Thus, the total cost to take a taxi from the hotel to the airport, given a distance of 5.8 miles, is $8.75.
Center c of the circle above has coordinates of (4, 3). what is the circumference of the circle?
Answers
C = 2 * pi * r = (2)(3.14)(3) = 18.8 or so
A pretzel maker was interested in knowing the number of pretzels in each bag it sold. The results of their research are shown in the box-and-whisker plot. What is the median number of pretzels?
Answers
The median number of pretzels is 54.
What is Box and whisker plot?The lower and upper quartiles are represented by the left and right sides of the box in a box and whisker plot. The box encompasses the interquartile interval, which contains 50% of the data. The median is the vertical line that divides the box in half. On the box plot, the mean is sometimes shown by a dot or a cross.
From the given box plot we can have the following information:
Minimum = 45
Lower Quartile = 47
Median= 54
Upper Quartile= 61
Maximum = 68
Thus, the Required median is 54.
Learn more about Box- whisker plot here:
https://brainly.com/question/22812839
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HELP ! I've been stuck on this for over 15 mins. :(
What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5?
an = 8 − 5(n − 1); all integers where n ≥ 1
an = 8 − 5(n − 1); all integers where n ≥ 0
an = 8 − 3(n − 1); all integers where n ≥ 1
an = 8 − 3(n − 1); all integers where n ≥ 0
Answers
Plug in a1 = 8:
an = 8 + (n - 1)d
FInd d:
Given that a2 = 5
5 = 8 + (2-1)d
5 = 8 + d
d = -3
Plug in d = -3:
an = 8 -3(n - 1)
Answer: an = 8 -3(n - 1) ; n ≥ 1
In a poll of students at basketball champoin 82% of the students say that basketball is better than fottball.
Answers
What is log base 5(4*7 )+log base 5 of 2 written as a single log?
A.log base 5 of 21
B.log base 5 of 26
C.log base 5 of 30
D.log base 5 of 56
Answers
D. log base 5 of 56
The explanation is show below:
1. You have the following logarithm expresssion:
log5(4*7 )+log5(2)
2. By the logarithms properties, you can rewrite the logarithm expression as following:
log5(28)(2)
log5(56)
3. Therefore, as you can see, the answer is the option mention before.
Answer:
D. log base 5 of 56
Step-by-step explanation:
Since, by the multiplication law of logarithm,
[tex]log_a(m)+log_a(n) = log_a(mn)[/tex]
Given expression is,
log base 5(4*7 )+log base 5 of 2
[tex]=log_5(4\times 7)+log_5(2)[/tex]
[tex]=log_5(28)+log_5(2)[/tex]
By the above property,
[tex]=log_5(28\times 2)[/tex]
[tex]=log_5(56)[/tex]
= log base 5 of 56
Hence, Option D is correct.
given function f(x)=x^2-x+8, find each of the following. f(9) f(-6) f(0)
Answers
f(9) - substract x = 9 to the equation of the function:
[tex]f(9)=9^2-9+8=81-9+8=80\\\\f(-6)=(-6)^2-(-6)+8=36+6+8=50\\\\f(0)=0^2-0+8=8[/tex]