Answer:
The correct answer option is 48.
Step-by-step explanation:
In the given experiment, three events take place which include rolling a die, flipping a coin and spinning a spinner.
The possible outcomes of each of these events are as follows:
Rolling a die - 6
Flipping a coin - 2
Spinning a spinner - 4
Therefore, by multiplying their possible outcomes, we can find the number of elements in the sample space of this environment.
Number of elements = 6 × 2 × 4 = 48
A chef used 1/9 of a bag of potatoes for a meal. If the potatoes fed 5 people. What fraction of the bag did each person get
1/9 has to be divided by 5 if it is shared by others.
1/9 divided by 5 is 1/45 and each person would have 1/45
Answer is 1/45
Determine if the function f is an exponential function. If so, identify the base. If not, why not? F(x)= x^ -3
Answer:
Not an exponential function. The exponent is a constant.
Step-by-step explanation:
An exponential function has the variable in the exponent. This function raises the variable to a fixed power, so it is not an exponential function.
A box of 6 golf balls cost 7.32. At the rate,how much will a box of 15 golf balls cost
Answer:
$18.30
Step-by-step explanation:
First, you can figure out the cost per golf ball by dividing the price by the number of golf balls. If 6 balls = 7.32, then 1 ball = 7.32/6, or 1.22. Now you can multiply this by the number of balls in the box to find out the price: 1.22 * 15 = 18.30.
Another way to solve this is to set up a ratio of balls / price:
(x is the unknown price)
[tex]\frac{6}{7.32} =\frac{15}{x}[/tex]
Now, cross-multiplying, you find that 6x = 7.32 * 15, or 6x = 109.8. Dividing both sides by 6, you get x=18.30.
let g(x)=3x+2 and f(x)= x-2/3
find the value
1.) f(g(0))
2.) g(f(2))
3.) g(g((0))
To find the values of f(g(0)), g(f(2)), and g(g(0)), substitute the given values into the functions step-by-step.
Explanation:1.) To find the value of f(g(0)), we first substitute 0 into the function g(x): g(0) = 3(0) + 2 = 2. Then, substitute the value obtained into the function f(x): f(2) = rac{2-2}{3} = 0.
2.) To find the value of g(f(2)), we first substitute 2 into the function f(x): f(2) = rac{2-2}{3} = 0. Then, substitute the value obtained into the function g(x): g(0) = 3(0) + 2 = 2.
3.) To find the value of g(g(0)), we first substitute 0 into the function g(x): g(0) = 3(0) + 2 = 2. Then, substitute the value obtained into the function g(x) again: g(2) = 3(2) + 2 = 8.
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To find the value of f(g(0)), substitute 0 into g(x) to get g(0) = 2 and then substitute this value into f(x) to get f(g(0)) = 4/3. To find the value of g(f(2)), substitute 2 into f(x) to get f(2) = 4/3 and then substitute this value into g(x) to get g(f(2)) = 8. To find the value of g(g(0)), calculate g(0) = 2 and then substitute this value into g(x) to get g(g(0)) = 8.
Explanation:To find the value of f(g(0)), we need to substitute the value of 0 into the function g(x) to get g(0) = 3(0) + 2 = 2. Then, we substitute this value into the function f(x) to get f(2) = 2 - 2/3 = 4/3.
To find the value of g(f(2)), we need to substitute the value of 2 into the function f(x) to get f(2) = 2 - 2/3 = 4/3. Then, we substitute this value into the function g(x) to get g(4/3) = 3(4/3) + 2 = 6 + 2 = 8.
To find the value of g(g(0)), we need to calculate g(0) = 3(0) + 2 = 2. Then, we substitute this value into the function g(x) again to get g(2) = 3(2) + 2 = 8.
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What is the sum of the first 19 terms of the arithmetic series?
3+8+13+18+…
Enter your answer in the box.
_______
Answer:
i think its 912
Step-by-step explanation:
i am not sure though
The sum of the first 19 terms of the given arithmetic series is equal to 912.
Given the following sequence:
3 + 8 + 13 + 18 + …What is an arithmetic series?A arithmetic series can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
Mathematically, an arithmetic series is given by the expression:
[tex]S_n = \frac{n}{2}(2a +(n-1)d)[/tex]
Where:
d is the common difference.a is the first term of an arithmetic series.n is the total number of terms.Substituting the given parameters into the formula, we have;
[tex]S_{19} = \frac{19}{2}(2(3) +(19-1)5)\\\\S_{19} = 9.5(6+18(5))\\\\S_{19} = 9.5(6+90)\\\\S_{19} = 9.5 \times 96[/tex]
19 term = 912.
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At what value of x does the graph of the following function f(x) have a vertical asymptote?
F(x)= [tex]\frac{1}{x-6}[/tex]
A. -3
B. 0
C. 6
D. -6
Answer:maybe A.
but I'm not sure
Answer:
C.) 6
Step-by-step explanation:
x-6 = -6
Inververse Operation
-6=+6
(Honestly don't know if that is the right reasons but that is what I have been doing and I have got those answers right so maybe I'm doing it right...)
If an object is propelled upward from a height of s feet at an initial velocity of v feet per second, then its height h after t seconds is given by the equation h = -16t^2+vt+s, where h is in feet. If the object is propelled from a height of 12 feet with an initial velocity of 64 feet per second, it's height h is given by the equation h = -16t^2+64t+12. After how many seconds is the height 72 feet?
Answer:
The object first reaches 72 feet after 1.5 seconds; it is this height again after 2.5 seconds.
Step-by-step explanation:
To find the amount of time it takes to reach 72 feet, we solve the equation
72 = -16t² + 64t + 12
To solve this, we will set it equal to 0 by subtracting 72 from each side:
72-72 = -16t² + 64t + 12 - 72
0 = -16t² + 64t - 60
Next we will use the quadratic formula to solve this:
By setting up and solving the required quadratic equation, it is determined that an object propelled from a height of 12 feet with an initial velocity of 64 feet per second will take 3.75 seconds to reach a height of 72 feet.
Explanation:The height h of the object is given by the equation h = -16t^2 + 64t + 12. We need to solve for time t, where the height h is 72 feet. By setting the equation equal to 72, we get 72 = -16t^2 + 64t + 12.
Moving -16t^2 and 64t to the other side, we get 16t^2 - 64t + (72 - 12) = 0. This simplifies to 16t^2 - 64t + 60 = 0. Divide every term in the equation by four to get: 4t^2 - 16t + 15 = 0. This equation must now be solved using the quadratic formula: t = [-b +/- sqrt(b^2 - 4ac)] / (2a).
Plugging in the values a=4, b=-16, and c=15, we get two possible solutions: t = 1 and t = 3.75 seconds. As the object is propelled up and comes down, we take the larger value, t=3.75 seconds, because that's the actual duration for the object to reach the height of 72 feet.
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Find the following measure for this figure.
Lateral area =
55 square units
5√(47) square units
5√(146) square units
Answer: last option (5π√146 units²)
Step-by-step explanation:
To solve the exercise you must apply the formula for calculate the lateral area of a cone, which is shown below:
[tex]LA=r*L*\pi[/tex]
where r is the radius but L is the slant height.
As you can see in the figure attached:
[tex]r=5[/tex]
But you need to find the slant height with the Pythagorean Theorem (L would be the hypotenuse):
[tex]L=\sqrt{11^2+5^2}=\sqrt{146}[/tex]
Substitute into the formula, then:
[tex]LA=(5)(\sqrt{146})\pi=5\pi\ \sqrt{146[/tex]units²
Answer:
The correct answer is 5√146π square units
Step-by-step explanation:
From the figure we can see a cone
Points to remember
Lateral surface area of cone = πrl
r - Radius of cone
l - Slant height of cone
To find the slant height
From figure we get,
r = 5 units and height = 11 units
Slant height² = radius² + height² = 5² + 11² = 25 + 121 = 146
Slant height = √146 units
To find the lateral area
lateral area = πrl = π * 5 * √146 = 5√146π square units
The correct answer is 5√146π square units
Which expression is equivalent to 27 cubed ?
9^3
9
3^3
3
Answer:
your 3rd option because 3^3 is 27
I agree because when you do prime factorization you get 27 by doing it
Complete the tables of values
The equations are shown in the top of the tables,
Replace x in the equations with the values of x given:
a = 4^-0 = 1
b = 4^-2 = 1/16
c = 4^-4 = 1/256
d = (2/3)^0 = 1
e = (2/3)^2 = 4/9
f = (2/3)^4 = 16/81
The value of a, b, c, d, e, and f are 1, 1/16, 1/256, 1, 4/9, and 16/81 after plugging the values of x.
What is an exponential function?
It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×
where a is a constant and a>1
We have:
y = 4⁻ˣ
x = 0
a = 4⁻⁰ = 1
x = 2
b = 4⁻² = 1/16
x = 4
c = 4⁻⁴ = 1/256
y = (2/3)ˣ
x = 0
d = (2/3)⁰ = 1
x = 2
e = (2/3)² = 4/9
x = 4
f = (2/3)⁴ = 16/81
Thus, the value of a, b, c, d, e, and f are 1, 1/16, 1/256, 1, 4/9, and 16/81 after plugging the values of x.
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Which statement is true? A. A triangle can be congruent to a square. B. A rectangle can be congruent to a square. C. All circles are congruent. D. None of the above is true.
➷ Congruent means it is the same shape and size. Therefore, A is incorrect as a triangle and a square aren't the same shape. The same applies to B. C is also incorrect as not all circles are the same size.
In short, the correct answer is option D. None of the above is true.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
The answer is B
Step-by-step explanation:
Congruent means In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Meaning a square and an rectangle are congruent because they both have four sides
Plus: I just took the test and got it right
Fill in the blanks to complete the following statements. Bold left parenthesis a right parenthesis For the shape of the distribution of the sample proportion to be approximately normal, it is required that np(1minusp)greater than or equals______. Bold left parenthesis b right parenthesis Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals______. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.)
Answer:
For the shape of the distribution of the sample proportion to be approximately normal, it is required that np (1 -p ) greater than or equals 10.
Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals0.35.
Step-by-step explanation:
Normal distribution is the shape data takes as a symmetrical bell shaped curve. Normal approximation can only be taken when np or np(1-p) greater than 10.
Fill in the blanks to complete the following statements:
For the shape of the distribution of the sample proportion to be approximately normal, it is required that np(1 - p)greater than or equals__10____. Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals__0.35____.The first blank should be filled with '5' as per the npq rule for approximation using normal distribution and the second statement's blank is filled with '0.35', which is the population proportion.
Explanation:To complete your statements:
np(1-p) greater than or equals 5 - This is a common guideline when checking if we can use a normal distribution to approximate a binomial distribution, also referred to as the 'npq rule'. The mean of the sampling distribution with a population proportion of 0.35 (p) is 0.35. This is true based on the formula for the mean of a sampling distribution for proportions, which equals the population proportion (p).
It's essential to remember that in hypothesis testing of a single population proportion, the binomial distribution's shape needs to be similar to a normal distribution. The terms 'np' and 'nq' refer to the conditions for this binomial distribution. Here 'n' is the number of trials, 'p' is the probability of success, and 'q=1-p' is the probability of failure, both must be more significant than five for the approximation to be acceptable.
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What is the value after 7 years of a 2014 ford mustang that originally costs $25,000.00 if it depreciates at a rate of 8% per year round your answer to the nearest dollar
Answer:
After 7 years it will have a value of $13.946 to the nearest dollar.
Step-by-step explanation:
As it depreciates by 8% (0.08) a year the value of the car after each year is
1 - 0.08 = 0.92 of the previous year's value.
So we have the formula:
Value = 25,000(0.92)^7
= $13,946.17 (answer).
Answer:
The rounded answer is equal to 14000
Step-by-step explanation:
Pentagon ABCDE Pentagon FGHIJ. Find BC for GH = 12, IJ = 15, and DE = 10.
NEED URGENTLY!!!
Answer:
BC = 8
Step-by-step explanation:
These are similar shapes, so they multiply out to the same ratio.
Seeing that 10 * 1.5 = 15, BC * 1.5 should equal 12.
All we do is divide 1.5 from both sides to get 8.
Then, plug it back into the equation to check and it works.
Answer: x = 8
Step-by-step explanation:
You can solve by setting up the proportions of the corresponding sides of the pentagon and then solve for x (the value of BC).
So, IJ/DE values are 15/10 and are set equal to GH/x (x represents the value of BC; the value you are solving for). Hint: It may be helpful for you to draw a diagram of the two pentagons and label them with the letters and values provided in the problem. This will help you to set up your proportion problem accurately.
To solve you can cross multiply to find the value of x.
15/10 = 12/x
15x = 12 * 10
15x = 120
x = 120/15
x = 8
A potter works 4 days a week, makes 14 pots per day on average, and charges $24 a pot. Money per 4-day workweek?
WILL GIVE BRAINLIEST
Identify the factors of x2 + 16y2.
(x + 4y)(x + 4y)
(x + 4y)(x − 4y)
Prime
(x − 4y)(x − 4y)
Answer:
Prime
Step-by-step explanation:
Since none of the other answers work. Your answer is Prime.
Answer:
Prime
Step-by-step explanation:
(x + 4y)(x + 4y)
Appy FOIL method to multiply it
x^2 +4xy + 4xy +16y^2
x^2 + 8xy +16y^2
(x + 4y)(x − 4y)
Appy FOIL method to multiply it
x^2 -4xy + 4xy -16y^2
x^2 - 16y^2
(x − 4y)(x − 4y)
Appy FOIL method to multiply it
x^2 -4xy - 4xy +16y^2
x^2 - 8xy +16y^2
the options does not gives us x^2 +16y^2
So it is not factorable , It is prime
Ummm Hey,I don't know the answer for this question,when I solve the problem my answer always 6 but the real answer is 2 so I need help right now.
umm ok then its 2...
Given that the measure of ?x is 30°, and the measure of ?y is 35 °, find the measure of ?z.
To find the measure of angle z, subtract the measures of angles x and y from 180°. Therefore, angle z = 180° - 30° - 35° = 115°.
Explanation:The subject of the question is geometry, specifically dealing with the measures of angles. Without more context, it's difficult to provide an exact answer. However, if angles x, y, and z form a triangle, then the measure of angle z can be found using the property that the sum of all angles in a triangle is 180°.
To find the measure of angle z, you need to recall that the sum of the angles in a triangle is always 180°. So, you can start by finding the measure of angle z by subtracting the measures of angles x and y from 180°.
Therefore, angle z = 180° - 30° - 35° = 115°.
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Chuck's starting balance on his credit card was $268.23, and he made purchases of $125 and $98 during the month. He also made a payment of $100. If the finance charge is 1.4% per month on the unpaid balance, find the new balance at the end of the month.
Answer:
25.95
Step-by-step explanation:
Answer:
Roughly $396.71
Step-by-step explanation:
Chuck starts the month with $268.23 balance on his card
He makes a $125 and $98 purchase, add those two together to get $223, and then add that to the total starting balance of $268.23 to get $491.23.
At the end of the month, he made a $100 payment, subtracting $100 from the balance to get $391.23. $391.23 times 1.014 (Adding 1.4% converted into decimal form, to convert a percent into decimal form move the decimal left two places) equals $396.71
If 4 dice are rolled, what is the number of ways in which at least 1 die shows 3?
I think the number of ways is 671?
Can someone please help me with this?
Answer:
23
Step-by-step explanation:
angles in a triangle add up to 180 so
124+33=157
180-157=23
x=23
y is 23 as well and z is 124
The value of y varies directly with x, when x=1/4, y=25. What is the value of y when x= 2 1/3
The value of y, when x = 2 1/3 in a direct variation scenario where y = kx (k being the constant of variation), is approximately 233.3.
Explanation:In the given problem, the value of y varies directly with x. This means there's a constant of variation, k, such that y = kx. We can find k by plugging in the initial given values, x=1/4 and y=25, into this equation, which gives us k = y/x = 25/(1/4) = 100.
Now that we know k, we can calculate the value of y when x = 2 1/3 using the same equation. Here, y = kx = 100 * 2 1/3 = 100 * 7/3 = 700/3 = 233.3 recurring.
So, when x = 2 1/3, y is approximately 233.3.
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When [tex]\(x = \frac{1}{4}\), \(y = 25\)[/tex] in a direct variation relationship. The constant of variation[tex](\(k\))[/tex] is found to be 100. Thus, when[tex]\(x = 2 \frac{1}{3}\), \(y = \frac{700}{3}\).[/tex]
If the value of [tex]\(y\)[/tex] varies directly with[tex]\(x\),[/tex] we can express this relationship using the formula [tex]\(y = kx\),[/tex] where [tex]\(k\)[/tex] is the constant of variation.
Given that when [tex]\(x = \frac{1}{4}\), \(y = 25\),[/tex] we can use this information to find [tex]\(k\)[/tex]:
[tex]\[25 = k \times \frac{1}{4}\][/tex]
Solving for [tex]\(k\):[/tex]
[tex]\[k = 25 \times 4 = 100\][/tex]
Now that we know [tex]\(k = 100\),[/tex] we can find the value of[tex]\(y\)[/tex] when[tex]\(x = 2 \frac{1}{3}\)\\[/tex]
[tex]\[y = 100 \times 2 \frac{1}{3} = 100 \times \frac{7}{3} = \frac{700}{3}\][/tex]
Therefore, when [tex]\(x = 2 \frac{1}{3}\), \(y = \frac{700}{3}\).[/tex]
The owner of a bike shop sells unicycles and bicycles and keeps inventory by counting seats and wheels . one day , she counts 15 seats and 22 wheels. The equation repesenting the total number of seats is u + b = 15 where u is the number of unicycles and b is the number of bicycles
Answer:
Step-by-step explanation:
U+b=15
7+8=15
To construct a confidence interval using the given confidence level, do whichever of the following is appropriate. (a) Find the critical value z Subscript alpha divided by zα/2, (b) find the critical value t Subscript alpha divided by tα/2, or (c) state that neither the normal nor the t distribution applies.?
95 % ; n=100; σ = unknown; population appears to be skewed
Choose the correct answer below.
A. tα/2 =2.626
B. zα/2 = 1.96
C. tα/2 =1.984
D. zα/2 = 2.575
E. Neither the normal nor the t distribution applies
To construct a confidence interval using the given confidence level, do whichever of the following is appropriate. (a) Find the critical value z Subscript alpha divided by zα/2, (b) find the critical value t Subscript alpha divided by tα/2, or (c) state that neither the normal nor the t distribution applies.?
98 % ; n= 19; σ = 21.4; population appears to be normally distributed
A. zα/2 = 2.33
B. tα/2 = 2.214
C. zα/2 = 2.552
D. zα/2 = 2.055
E. Neither normal nor t distribution applies
Answer:
1: z = 1.96
2: t = 2.552
Step-by-step explanation:
1: When you don't know the population standard deviation and the sample size is large, you can still use a z test because many large samples are relatively normally distributed. A 95% confidence interval uses a z-score of 1.96
2. We are told that n < 30, so we use t distribution. Use the degrees of freedom, which is one less than the population, and the column that has 0.02 in the area of 2 tails.
In constructing a confidence interval, if the standard deviation is unknown and the population appears skewed, we typically use the t-distribution. However, without enough information given, the answer to the first problem tends towards 'Neither normal nor t distribution applies'. For the second problem, the standard deviation is given and the population appears normally distributed, hence answer is 'zα/2 = 2.33' from the z-table.
Explanation:The relevant subject matter here is Statistics, specifically, confidence intervals. The construction of a confidence interval depends on the knowledge of the standard deviation and whether the population is normally distributed or not.
For the first problem, since the standard deviation (σ) is unknown and the population appears to be skewed, student's t-distribution applies here. This would involve using tα/2 with degree of freedom (n-1) in place of the unavailable standard deviation. However, without enough data provided in the question, it is difficult to correctly compute tα/2. The answer therefore likely tends towards option E: 'Neither the normal nor the t distribution applies'.
For the second problem, the standard deviation (σ) is given and the population appears to be normally distributed. This suggests the normal distribution applies, hence you would compute zα/2, the critical value for the z-score at a 98% confidence level. Referring to a standard z-table at a 98% confidence level gives a z-score of approximately 2.33. So, the answer for this scenario is A: zα/2 = 2.33.
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Which system of linear inequalities is graphed?
Answer:
Should be the first one again
The dotted line is a vertical line at x -2, so we know the first equation is X<-2
The solid line means the equation has to be less than or equal to and since it crosses the dotted line at -2
the second equation would be y <=-x-2
The first choice is correct.
The school principal spent $2,000 to buy some new computer equipment.Of this money $120 was used to buy some new keyboards.What percent of the money was spent on keyboard
Answer:
6%
Step-by-step explanation:
120/2000= 60/1000= 6/100= 6%
6% of the money was spent on keyboard
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that school principal spent $2,000 to buy some new computer equipment.
Out of $2000 , $120 was used to buy some new keyboards
We need to find what percent of the money was spent on keyboard.
We need to find what is $120 of $2000
Let x/100 is the percent of amount spent for keyboard
x/100×2000=120
20x=120
Divide both sides by 20
x=6
Hence, 6% of the money was spent on keyboard
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If the heights of 4 family members is 153, 150, 151 and 152, find the mean height of the family.
Answer: 151.1
Step-by-step explanation:
First, you would add all the heights together (153+150+151+152=606)
Then you would divide 606 by the number of numbers in the data set in this case the number of family members which is (606 divided by 4= 151.1)
Answer:
151.5
Step-by-step explanation:
First of all, what is the mean in a set of numbers?
The mean is the average of all the numbers in the set. We can find this by finding the total value of all the terms and then dividing it by the number of terms. Let's just do a short example so we can make sure you understand.Let's look at this set of numbers:5, 3, 7, 4.To find the average of these numbers, we'll add all of the numbers and divide it by 4, the number of actual terms, in the set.
(5 + 3 + 7 + 4) / 4 = 19/4 which is also 4.75.Back to the actual problem.(153 + 150 + 151 + 152) / 4 = 151.5
Which is the equation of a parabola with vertex (0, 0), that opens to the right and has a focal width of 8? a.y^2=8x b.y^2=-8x c. x^2=8y d. x^2=-8yWhich is the equation of a parabola with vertex (0, 0), that opens to the right and has a focal width of 8? a.y^2=8x b.y^2=-8x c. x^2=8y d. x^2=-8y
Answer:
the first answer is A y^2=8x
Step-by-step explanation:
The equation of a parabola that opens to the right with vertex at the origin (0,0) and has a focal width of 8 is y^2 = 8x. This follows from the equation of a parabola in standard form, y^2 = 4ax, where 4a equals the focal width.
Explanation:The equation of a parabola in standard form is either y^2=4ax or x^2=4ay, depending on its orientation. The vertex is at the origin (0,0). A parabola that opens to the right or left has the form y^2 = 4ax, and one that opens upward or downward has the form x^2 = 4ay. Given that your parabola opens to the right and has a focal width of 8, it would utilize the first form. The focal width is the absolute value of 4a. Thus, for your parabola, 4a is equal to the focal width, which is 8. Therefore, a = 8/4 = 2. Hence, the equation of the parabola with vertex at the origin that opens to the right and has a focal width of 8 is y^2 = 8x.
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A helicopter flying 1600 feet above ground spots an airplane flying above. If the horizontal distance between the helicopter and airplane is 3,055 feet and angle of elevation is 71 degrees, find the airplane’s altitude.
Answer: 10,472.36 feet
Step-by-step explanation:
- Observe the diagram attached (It is not drawn to scale).
- Calculate the height between helicopter and airplane (h), as following:
[tex]tan\alpha=\frac{opposite}{adjacent}\\\\tan(71\°)=\frac{h}{3,055}[/tex]
Solve for h:
[tex]h=(3,055)(tan(71\°))\\h=8,872.36ft[/tex]
- Therefore, the altitude of the plane is:
[tex]altitude=1,600ft+8,872.36ft\\altitude=10,472.36ft[/tex]
You can use the tangent ratio to find the airplane's altitude.
The altitude of the airplane in the given condition is 10,471.72 ft
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
What is tangent ratio?In a right angled triangle(triangle with one of the angles as right angle which is 90 degrees), seeing from perspective of an angle, the tangent ratio is the ratio of the side opposite to that angle and the side which is perpendicular to that opposite side.
How to find the airplane's altitude if angle of elevation is given?Refer to the attached figure.
The altitude of the plane is the length of the line segment CE.
We have the rectangle ABDE, thus, AD = BE in terms of length.
(remember that |AB| means length of line segment AB).
Thus,
|CE| = |CB| + |BE| = |CB| + 1600 ft
Using the tangent ratio for triangle ABC from angle A, we get:
[tex]tan(A) = \dfrac{|CB|}{|AB|} = \dfrac{|CB|}{3055}\\\\tan(71) \approx 2.904 = \dfrac{|CB|}{3055}\\\\|CB| = 3055 \times 2.904 = 8.871.72 \: \rm ft[/tex]
Thus,
|CE| = |CB| + 1600 = 8871.72 + 1600 = 10,471.72 ft.
Thus,
The altitude of the airplane in the given condition is 10,471.72 ft
Learn more here about trigonometric ratios here:
https://brainly.com/question/22599614
Question for Math.
What is 3x-1?
the answer is -3 because i searched it and that’s what came up
The answer is -3 hope this helps