Therefore, the observed value of the test statistic for testing the null hypothesis H0: p = 0.5 versus the alternative hypothesis H1: [tex]p > 0.5[/tex]is z= 1.8. The correct answer is (e) z=[tex]0.59— 0.5/√0.5(0.5)/100.[/tex]
In this particular question, the observed value of the test statistic for testing the null hypothesis H0: p = 0.5 versus the alternative hypothesis H1: p > 0.5 is to be determined. The question provides a random sample of 100 likely voters in a small city, which produced 59 voters in favor of Candidate A. The formula for calculating the test statistic is as follows:
z= (p- P) / sqrt[P(1-P) / n]
where p is the sample proportion, P is the hypothesized population proportion, and n is the sample size.
Substituting the given values into the formula, we get:
z= [tex](0.59- 0.5) / sqrt[0.5(0.5) / 100][/tex]
z= [tex]0.09 / 0.05[/tex]
z=[tex]1.8[/tex]
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the likelihood that the decision made based on the sample differs from the decision that would have been made if the entire population had been examined is
The likelihood that the decision made based on the sample differs from the decision that would have been made if the entire population had been examined is called sampling risk.
What is Sampling error?Sampling error refers to the disparity between a sample's characteristics and those of the population from which it was drawn. It arises from using a sample rather than the whole population to estimate statistics such as mean, variance, and proportions.
Since a sample only represents a portion of the population, it cannot be expected to have the same characteristics as the whole population. The study of sampling error is an essential part of statistical analysis, as it is a source of uncertainty in making inferences about the population from a sample.
To reduce the sampling error in your survey, you can utilize a larger sample size. It is also beneficial to ensure that the sample is chosen randomly and without bias.
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I Really want this pleaseeeeeeeeeeeeeeeeeee
Answer:no
Step-by-step explanation:
using the Pythagorean theorem:
a^2+b^2=c^2
42^2+26^2=50^2
1764+676=2500
2440=2500
2440<2500
So the answer is no
WHAT IS THE ANSWER
I NEED HELP ASAP
Answer: yes, yes, no
Explanation: In order for a figure to be a triangle, the two smallest sides must add up to be larger than the biggest side. The reason why the last one isn't a triangle is because 6+8 EQUALS 14 and is not greater than 14.
The closing stock prices for a particular social media company follows an unknown distribution with a mean of $150 and a standard deviation of $25. An investor is looking to find the likelihood of the closing stock price falling above the average. After randomly selecting n=52 closing stock prices from the social media company, use a calculator to find the probability that the sample mean is between $155 and $160.
Rounded to three decimal places.
Rounded to three decimal places, the probability that the sample mean is between $155 and $160 is 0.072.
To find the probability that the sample mean is between $155 and $160, we will use the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample mean (with a large enough sample size) will be approximately normally distributed with the same mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Mean of the sample distribution: μ = $150
Standard deviation of the sample distribution: [tex]σ/√n = $25/√52 ≈ $3.46[/tex]
Now, we'll calculate the z-scores for $155 and $160:
[tex]Z1 = (155 - 150) / 3.46 ≈ 1.445[/tex]
[tex]Z2 = (160 - 150) / 3.46 ≈ 2.890[/tex]
Using a z-table or calculator, we can find the probability for each z-score:
[tex]P(Z1) ≈ 0.9259[/tex]
[tex]P(Z2) ≈ 0.9981[/tex]
Now, we can find the probability between the two z-scores:
[tex]P(1.445 < Z < 2.890) = P(Z2) - P(Z1) = 0.9981 - 0.9259 = 0.0722[/tex]
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use half angle identity. help
pls
Required value of the given expression is (1+√2)
Given expression is [tex]tan \frac{11\pi}{8} [/tex]
We want to solve it.
Now,
[tex] \tan( \frac{11\pi}{8} ) = \tan( \frac{3\pi}{8} + \frac{8\pi}{8} ) \\ = \tan( \frac{3\pi}{8} + \pi ) \\ = \tan( \frac{3\pi}{8} ) [/tex]
Finding [tex] \tan( \frac{3\pi}{4} ) [/tex]
Let,
[tex] \tan(2t) = \tan( \frac{3\pi}{4} ) = - 1[/tex]
Use half angle identity,
[tex] \tan(2t) = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ - 1 = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ {tan}^{2} t - 2tant - 1 = 0[/tex]
Let,[tex]x = tant[/tex]
So,[tex] {x}^{2} - 2x - 1 = 0[/tex]
Now, [tex]x = 1 \pm \sqrt{2} [/tex]
So,
[tex]tant = tan \frac{3\pi}{8} = 1 \pm \sqrt{2} [/tex]
[tex]tan \frac{3\pi}{8} [/tex] is positive,then required value is 1+√2.
So, option D is the correct answer.
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x-2
A. 44 in
B. 48 in
C. 52 in
D. 64 in
X
X
x-2
The figure above consists of five congruent rectangles. If the total area of the figure is 75in¹, what
is its perimeter?
The perimeter of the figure, given the rectangles and the total area, can be found to be 48 inches
How to find the perimeter ?The total area is 75 in² which means that the areas of all 5 rectangles add up to 75 in². We can use this to solve for x to be:
5 × ( x × ( x - 2 )) = 75 in²
5 × ( x² - 2x ) = 75 in²
x² - 2x = 15 in²
(x - 5)(x + 3) = 0
x - 5 = 0 or x + 3 = 0
x = 5 or x = -3
Dimensions of a rectangle cannot be negative so x is equal to 5.
The perimeter is then:
= ( x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x -2 ) + x
= ( 5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5 -2 ) + 5
= 48 inches
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[tex] \frac{cos9 + \sin9 }{cos9 - sin9} = tan54[/tex]
Prove the above question
To Prove :
[tex] \sf \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} = \tan54\degree \\ \\ [/tex]
[tex] \sf LHS = \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} \\ \\ [/tex]
[tex] \sf RHS = \tan54\degree \\ \\ [/tex]
Solving for LHS :
Divide numerator and denominator by cos9°
[tex]\longrightarrow \: \: \sf\dfrac { \dfrac{ \cos9\degree}{ \cos9\degree} + { \dfrac{\sin9}{ \cos9} }}{ \dfrac{ \cos9\degree }{ \cos9\degree} - { \dfrac{ \sin9\degree}{ \cos9\degree}}} \\ \\ [/tex]
[tex] \longrightarrow \: \: \sf\dfrac{1 + { \dfrac {\sin9\degree}{ \cos9\degree}} }{1 - { \dfrac{ \sin9\degree}{ \cos9\degree} }} \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf \dfrac{1 + \tan9\degree}{1 - \tan9\degree} \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf{ \dfrac{ \tan45 \degree + \tan9\degree}{1 - \tan45 \degree \tan9 \degree}} \: \: \: \: \: \: \: \sf \red{\bigg( \tan(A + B) = \dfrac{ \tan A + \tan B}{1 - \tan A \tan B} \bigg)} \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf \tan(45\degree + 9\degree) \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf \tan54 \degree[/tex]
LHS = RHS
Hence, proved!!Alex used his grandmother’s recipe to make 11 3/7 pounds of granola. If he fills as many bags as he can with 2 2/3 pounds of granola in each bag, how many pounds will he have left over?
A 16/21 pound
B 2 20/21 pounds
C 4 2/7 pounds
D 8 16/21 pounds
The number of pounds that he will have left over from 11 3/7 pounds is 4 2/7
How many pounds will he have left over?To find out how many bags of granola Alex can fill, we need to divide the total amount of granola he made by the amount of granola in each bag.
We can convert 11 3/7 pounds to an improper fraction:
11 3/7 pounds = 80/7 pounds
Also, we have
2 2/3 pounds = 8/3 pounds
Now we can divide the total amount of granola by the amount in each bag:
(80/7) ÷ (8/3)
To divide fractions, we invert the second fraction (change it to its reciprocal) and multiply:
(80/7) × (3/8)
Simplifying, we get:
(80 x 3) / (7 x 8) = 30/7
Divide
(80 x 3) / (7 x 8) = 4 2/7
Hence, the bags is 4 2/7
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13xy^2 - 12x^2y + 5x^2y simplify
which would be the expected adult height for a toddler who is 34 inches tall at the 30-month checkup? use numbers only.
The expected adult height for a toddler who is 34 inches tall at the 30-month checkup is around 5 feet 7 inches.
To determine the expected adult height, one must multiply the current height by 1.08. Since 34 inches x 1.08 is equal to 36.72 inches, the expected adult height is 5 feet 7 inches.
The calculation for adult height is an approximation. Factors such as nutrition, genetics, and gender play a role in final height.
It is important to note that this calculation is just a guide and the actual adult height may differ from the predicted adult height.
To get a more accurate estimation of the expected adult height, it is recommended to have multiple height checks throughout childhood and take into account growth patterns.
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Please help 20 points I’ve been struggling :(
5x + 4y = -16
Complete the steps to convert the equation in standard form to Slope intercept form
Answer: I'm pretty bad at math, but I made it more simple for you :)
Step-by-step explanation:
The answer is y = 4 + 5x/4
I hope it helped a bit sorryy
6. complete the interpretation for the p-value: if delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of or any statistic (larger, smaller) is .
If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.
This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.
The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.
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The complete question is:
Complete the interpretation for the p-value:
If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .
g the sequence is decreasing and bounded below by 0. explain in clear english (briefly) why this means it must have a limit.
Since the sequence is always decreasing and cannot go below the lower bound, it becomes increasingly closer to the lower bound, and thus converges to a limit.
A sequence is said to be decreasing if each term is smaller than the previous one, and bounded below if there exists a lower bound such that no term in the sequence is smaller than this bound. In this case, the sequence is decreasing and bounded below by 0.
When a sequence is both decreasing and bounded below, it must have a limit because the terms cannot continue to decrease indefinitely, as they cannot go below the lower bound (in this case, 0). This means that as we progress through the terms of the sequence, the difference between consecutive terms will decrease and eventually approach a constant value.
The limit of a sequence is a value that the terms of the sequence approach as they get closer and closer to the end. In this situation, the limit is the smallest possible value that the sequence can approach, without going below the lower bound.
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A population of a town increases by 7% every year. If its population today is 40,000, what is its population in 3 years?
A = 40,000(1 + 0.07)^3
A = 40,000(1.07)^3
A = 47,676.08
Therefore, the population of the town in 3 years will be approximately 47,676.
find the next two terms 9.56,9.57,9.58,9,59
The next two terms in this arithmetic progression is 7.60 and 7.61.
What is arithmetic progression?An arithmetic prοgressiοn (AP) is a sequence where the differences between every twο cοnsecutive terms are the same. Fοr example, the sequence 2, 6, 10, 14, … is an arithmetic prοgressiοn (AP) because it fοllοws a pattern where each number is οbtained by adding 4 tο the previοus term. A real-life example οf an AP is the sequence fοrmed by the annual incοme οf an emplοyee whοse incοme increases by a fixed amοunt οf $5000 every year.
We know the Arithmetic progression formula:
[tex]\rm a_{n}=a_{1}+(n-1)d[/tex]
[tex]\rm a_n[/tex] = the nᵗʰ term in the sequence
[tex]\rm a_1[/tex] = the first term in the sequence
d = the common difference between terms
Here 4 terms are given
5th and 6th terms are to be found,
Thus,
a₁ = 9.56
d = (9.56 -9.57) = 0.01
n = 5
Then
5th term is :
aₙ = a₁ + (n - 1)d
aₙ = 9.56 + (5 - 1)0.01
aₙ = 9.56 + (4)0.01
aₙ = 9.56 + 0.04
aₙ = 7.60
6th term is :
aₙ = a₁ + (n - 1)d
aₙ = 9.56 + (6 - 1)0.01
aₙ = 9.56 + (6)0.01
aₙ = 9.56 + 0.05
aₙ = 7.61
Thus, The next two terms in this arithmetic progression is 7.60 and 7.61.
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You have a trust that when mature will be $250,000 that you will receive when you are 50 years old. You are 25 years old now. If the trust is growing at 8% per year what is the value of the trust now?
The present value of the trust which grows at the rate of interest 8% for 25 years is equal to $ 36504.477
The future value of the trust is equal to $250,000
Interest rate is equal to 8% per year
To calculate present value of the trust use the formula,
Present Value = Future Value / (1 + r)^n
r is the annual interest rate
n is the number of years.
Let us consider PV represents the present value of the trust.
Present age = 25 years
Maturity age of the trust = 50 years
Number of years used amount to mature is equal to,
= 50 - 25
= 25 years
Substitute the values into the present value formula we have,
PV = 250,000 / (1 + 0.08)^25
Simplify it we get,
⇒ PV = 250,000 / 6.848475
⇒ PV = 36504.477
Therefore, the present value of the trust mature for 25 years is equal to approximately $36504.477.
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Answer for x=
Please
Answer:
53°
Step-by-step explanation:
it’s vertical, verticals are always identical, I think
when player a played football, he weighed 204 pounds. how many standard deviations above or below the mean was he?
Player A's weight was 0.208 standard deviations below the mean weight of the football team.
To calculate the standard deviation, we first need to calculate the mean weight of the football team
Mean weight = (sum of all weights) / (number of team members)
(174+176+178+184+185+185+185+185+188+190+200+202+205+206+210+211+211+212+212+215+215+220+223+228+230+232+241+241+242+245+247+250+250+259+260+260+265+265+270+272+273+275+276+278+280+280+285+285+286+290+290+295+302) / 52
= 225.5 pounds
Now we can calculate the standard deviation using the following formula:
Standard deviation = sqrt((sum of (x - mean)^2) / N)
Where x is the weight of a team member, N is the total number of team members.
We can simplify this formula by calculating the variance first:
Variance = (sum of (x - mean)^2) / N
So we have
Variance = ((174-225.5)^2 + (176-225.5)^2 + ... + (302-225.5)^2) / 52
= 10764.35
Now we can calculate the standard deviation
Standard deviation = sqrt(Variance)
= sqrt(10764.35)
= 103.76
To find out how many standard deviations above or below the mean Player A's weight was, we can use the following formula
Z-score = (x - mean) / standard deviation
Where x is Player A's weight, mean is the mean weight of the team, and standard deviation is the standard deviation we just calculated.
So we have
Z-score = (204 - 225.5) / 103.76
= -0.208
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The given question is incomplete, the complete question is:
Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.
174, 176, 178, 184, 185, 185, 185, 185, 188, 190, 200, 202, 205, 206, 210, 211, 211, 212, 212, 215, 215, 220, 223, 228, 230, 232, 241, 241, 242, 245, 247, 250, 250, 259, 260, 260, 265, 265, 270, 272, 273, 275, 276, 278, 280, 280, 285, 285, 286, 290, 290, 295, 302
median = 241
the first quartile = 205.5
the third quartile = 272.5
Assume the population was Football Team A. When Player A played football, he weighed 204pounds. How many standard deviations above or below the mean was he?
In a sale, the normal price of a boat is reduced by 15%
The sale price of the boat is £272 000
Work out the normal price of the boat.
Answer:
£320 000
Step-by-step explanation:
Let x = original price of the boat.
When you reduce a price by 15%, what percent remains in the sale price?
100% - 15% = 85%
After reducing the price of the boat by 15%, the sale price is 85% of the original price.
85% of x = £272 000
0.85x = 272 000
Divide both sides by 0.85
x = 320 000
Answer: £320 000
this question pertains to a standard 52-card deck (52 total cards, 4 suits each with 13 possible values: ace, two, king, etc). you draw two cards at random with replacement. what is the probability that at least one card is a spade?
The probability of drawing at least one spade when drawing two cards with replacement from a standard deck of cards is approximately 0.26%.
When drawing two cards at random with replacement from a standard 52-card deck, there are 4 possible outcomes for the first card being a spade and 4 possible outcomes for the second card being a spade.
However, there is also 1 possible outcome where both cards are spades, which would be counted twice if we add the outcomes for the first and second cards separately. Therefore, the total number of outcomes where at least one card is a spade is 4 + 4 - 1 = 7.
The total number of possible outcomes when drawing two cards with replacement is 52 x 52 = 2,704.
Therefore, the probability that at least one card is a spade when drawing two cards with replacement is:
P(at least one spade) = 7 / 2,704 ≈ 0.0026
So, the probability that at least one card is a spade is approximately 0.0026 or 0.26%.
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If f(x) = 3x + 2, find f(2).
a. 2
b. 5
c. 8
d. 9
e. 12
Answer:
C
Step-by-step explanation:
Since the number in the parenthesis is treated as "x", for f(2), replace "x" with 2. So the equation will be f(2) = 3(2) + 2. Then multiply. f(2) = 6 + 2. Lastly add them up. f(2) = 8. The answer is 8.
How many hours after the chemical reaction starts are the concentrations of the two products equal?
Responses
0.6
1.0
1.5
2.0
Answer:0.6
Step-by-step explanation: because i got it correct
8) What is the lower quartile of the numbers
4, 6, 7, 8, 10, 12, 20?
(a) 4
(b) 6
(c) 7
(d) 8
The lower quartile of the given set of numbers 4, 6, 7, 8, 10, 12, 20 is 6. So, correct option is B.
To find the lower quartile of a set of numbers, we first need to arrange them in ascending order. The given numbers are: 4, 6, 7, 8, 10, 12, 20.
Next, we divide the data set into four equal parts. The lower quartile is the median of the lower half of the data set. In this case, the lower half is 4, 6, and 7.
To determine the median of the lower half, we need to find the middle value. Since we have an odd number of data points in the lower half, the middle value is the single value between the two extremes. In this case, the median is 6.
This corresponds to option (b) in the given choices: 6.
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A rental car company charges $74. 90 per day to rent a car and $0. 13 for every mile driven. Tyee wants to rent a car, knowing that:
He plans to drive 175 miles. He has at most $210 to spend. Write and solve an inequality which can be used to determine
�
x, the number of days Tyee can afford to rent while staying within his budget
Tyee can afford to rent the car for at most 2 days while staying within his budget.
Let x be the number of days Tyee can rent the car within his budget.
The total cost of renting the car will be the sum of the daily rental fee and the cost of miles driven:
Total cost = rental fee + (cost per mile x miles driven)
Using the given information, we can write the inequality:
74.90x + 0.13(175)x ≤ 210
Simplifying the expression, we get:
74.90x + 22.75x ≤ 210
97.65x ≤ 210
x ≤ 2.15
Therefore, Tyee can afford to rent the car for at most 2 days while staying within his budget.
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most people in the united states with a mental disorder in any given 12-month period receive treatment during the same time frame.
Explanation:
Most people with a mental illness in the United States receive care at some point in their lives, but most receive insufficient or inappropriate care. In any given year, fewer than one-third of people with a diagnosable mental illness obtain treatment.
However, according to a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame.
According to the National Survey on Drug Use and Health (NSDUH), about one in five adults (18.5%) had a mental illness in 2019. It is said that roughly 22.3 million people aged 18 and above received care for a mental health condition in the preceding year.
Treatment may involve medication, therapy, support groups, or a combination of these methods. The majority of people with mental illness may significantly benefit from these treatments.
As per a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame. This statement is true.
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Target is selling a speaker for $166.50. It is at Costco for $90. What percentage did
Target markup the speaker?
Answer:
45.6%
Step-by-step explanation:
166.50 minus 45.6% equals 90 dollars
A straw is placed inside a rectangular box that is 1 inches by 1 inches by 3 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
The length of the straw, which fits exactly along this diagonal, is also [tex]\sqrt{11}[/tex] inches.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The problem states that the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner. We can visualize this diagonal as a line that runs through the center of the box, from one corner to the opposite corner.
To find the length of this diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).
In this case, the bottom and back sides of the box form the legs of a right triangle, and the diagonal of the box forms the hypotenuse. So we can apply the Pythagorean theorem as follows:
Diagonal = [tex]\sqrt{bottom^2 + back ^2 + height ^2 }[/tex]
Therefore, the length of the straw, which fits exactly along this diagonal, is also [tex]\sqrt{11}[/tex] inches.
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PLEASE HELP ME
A pizza shop surveyed a random group of customers to determine their favorite pizza topping. Out of 400 people, how many would you expect to say their favorite topping is sausage?
The percent that reported mushroom as their favorite from the pizza shop survey would be 10 %.
The percent that instead reported cheese or pepperoni as their favorite is 62.5 %.
Out of 400 people, the number that would say their favorite was sausage is 50 people .
How to find the number of people in the survey ?The percent that prefer mushroom would be:
= Number of those who chose mushroom / Number surveyed
= 8 ( 35 + 8 + 15 + 12 + 10 )
= 8 / 80
= 10 %
The percentage that instead chose cheese or pepperoni:
= ( 15 + 35 ) / ( 35 + 8 + 15 + 12 + 10 )
= 50 / 80
= 62.5 %
The number out of 400 that would be expected to choose sausage :
= 10 / ( 35 + 8 + 15 + 12 + 10 ) x 400
= 50 people
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Números que multiplicados me den 24 y sumados me den -11
The two numbers that multiply to give 24 and add to give -11 are -3 and -8.
How do we get these numbers?To find these numbers, you can use a system of equations. Let x and y be the two numbers. Then we have:
xy = 24 (because the two numbers multiply to give 24)x + y = -11 (because the two numbers add to give -11)We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for x:
x + y = -11
x = -11 - y
We can then substitute this expression for x into the first equation:
xy = 24
(-11 - y)y = 24
Expanding and rearranging, we get:
y^2 + 11y + 24 = 0
This is a quadratic equation that we can solve using factoring or the quadratic formula. Factoring, we get:
(y + 3)(y + 8) = 0
So either y + 3 = 0 or y + 8 = 0. This means that y can be -3 or -8. Substituting each of these values into x = -11 - y, we get:
If y is -3, then x is -11 - (-3) = -8
If y is -8, then x is -11 - (-8) = -3.
Translated question "Numbers that multiply to give me 24 and add to give me -11"
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An airplane is 5,000 ft above ground and has to land on a runway that is 7,000 ft away as shown above. Let x be the angle the pilot takes to land the airplane at the beginning of the runway. Which equation is a correct way to calculate x?
The fourth equation which is tan x = [tex]\frac{7000}{5000}[/tex] is the correct way to calculate x. This has been obtained by using trigonometry.
What is trigonometry?
Trigonometry is the study of right-angled triangles, which includes the sides, angles, and connections of each triangle.
We are given that the airplane is 5,000 ft above ground and has to land on a runway that is 7,000 ft away with an angle x.
Since, we are not given the hypotenuse so, we will use tan θ.
We know that in trigonometry, tan θ is calculated as the ratio of the opposite side to the adjacent side.
So,
tan x = [tex]\frac{7000}{5000}[/tex]
Hence, the fourth equation is the correct answer.
Learn more about trigonometry from the given link
https://brainly.com/question/13729598
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