The probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket is 2.37.
Given Probability of giving tickets to cars that are stopped = 0.23
Probability of not giving tickets to cars that are stopped = 1 - 0.23 = 0.77
the probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket
Here n = 100, p = 0.77, q = 0.23
mean = np = 100*0.77 = 77
standard deviation = [tex](sigma = \sqrt{(100)*(0.77)*(0.23) } = 4.208[/tex]
[tex]P(X\geq 67) = \frac{67 - 77}{4.208}[/tex] = 2.37
P-VALUE is 0.99126 from z-table
Probability is a fundamental concept in mathematics that helps us quantify the likelihood of events occurring and is applicable to a wide range of fields. It is a measure of the uncertainty of an event, expressed as a number between 0 and 1. An event with probability 0 is impossible, while an event with probability 1 is certain.For example, the probability of rolling a six on a fair six-sided die is 1/6, since there is only one favorable outcome out of six possible outcomes.
Probability theory has wide applications in fields such as statistics, finance, engineering, and physics, among others. It is used to model and analyze various phenomena, including weather patterns, stock prices, quantum mechanics, and more.
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Annabelle works in a deli and has been tracking the daily sales of different items over several months. Annabelle found that when there was an increase in the number of cups of hot chocolate sold, the number of cups of coffee sold also increased. Similarly, when there was a decrease in the number of cups of hot chocolate sold, the number of cups of coffee also decreased.
Which of the following is a valid conclusion?
A.
There is no correlation between the sale of hot chocolate and the sale of coffee.
B.
The increase in the sale of hot chocolate caused an increase in the sale of coffee.
C.
The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee.
D.
No conclusion can be drawn about the correlation or causation of the sale of hot chocolate and the sale of coffee.
Option C is the correct answer. The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee.
What is correlation?
Correlation is a statistical measure that shows how closely two or more variables are linked to one another. It is a measurement of the strength and direction of the linear connection between two variables, in other words.
Based on the information provided, it can be concluded that there is a correlation between the sale of hot chocolate and the sale of coffee.
Option A can't be considered because it conflicts with the material provided.
Option B indicates a causal relationship that cannot be proven merely on the basis of the observed correlation between the sales of hot chocolate and coffee.
Option D is untrue as well because a correlation has been found.
Therefore, option C is the valid conclusion that can be drawn from the given information, stating that the increase in the sale of hot chocolate is correlated to, but not necessarily caused by, the sale of coffee.
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Compute the interest on 250000 at a 7. 5% interest rates for half a year
the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.
To calculate the interest on 250000 at a 7.5% interest rate for half a year, we first need to determine the annual interest rate, as most interest rates are quoted on an annual basis. To do this, we can divide the annual interest rate of 7.5% by 2 to get the half-yearly interest rate, which is 3.75%.
Next, we can use the formula for simple interest to calculate the interest earned over half a year. Simple interest is calculated by multiplying the principal amount (in this case, 250000) by the interest rate (3.75%) and the time period (0.5 years).
So, the interest earned would be:
Interest = Principal x Rate x Time
= 250000 x 0.0375 x 0.5
= 4687.50
Therefore, the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.
It's worth noting that this calculation assumes that the interest is simple interest, which means that the interest earned is not reinvested. If the interest is compounded (i.e., the interest earned is reinvested), then the interest earned would be higher.
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What are the values of x and y? *
The values of sides x and y of the triangle are 6.75 and 11.25 units respectively.
The Pythagorean TheoremThe square of the hypotenuse side of the right-angled triangle equals the sum of the squares of the other two sides, according to Pythagoras' Theorem. The three sides of this triangle are referred to as the perpendicular, base, and hypotenuse.
by using the Pythagorean theorem:
Equation1: y ² =x ² + 9²
Equation2: (12 + x) ² =1 5 ² + y ²
Putting values of equation1 in 2 we get
(12 + x) ² =1 5 ² +x ² + 9²
144 + x²+ 2×12x = 225 + x²+ 81
x=6.75
Putting value of x in equation1
y ² =6.75 ² + 9²
y=11.25
Hence, the values of x and y are
x = 6.75 unit
y =11.25 unit
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For the following indefinite integral, find the full power series centered at
x=0 and then give the first 5 nonzero terms of the power series. [infinity]
Σ∫(e^9x - 1) / 6x dx
n=0
From the given information provided, the first 5 nonzero terms of the power series are 1.5 + 13.5x + 60.75x² + 183.375x³ + 1018.1595x⁴.
To find the power series for the given indefinite integral, we can first find the antiderivative of the integrand using substitution. Let u = 9x, du = 9dx, then:
∫(e⁹ˣ - 1) / 6x dx = (1/6) ∫([tex]e^u[/tex] - 1) / u du
We can then expand the integrand into a power series using the Maclaurin series for [tex]e^u[/tex] and ln(1+u):
(1/6) ∫([tex]e^u[/tex] - 1) / u du = (1/6) ∫[Σ(uⁿ/n!) - Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1))] du
= (1/6) [Σ(uⁿ/n! × du) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × du)]
= (1/6) [Σ(uⁿ/n! × 9dx) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × 9dx)]
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺⁾ xⁿ / (n+1))
We can now simplify and group terms to obtain the power series centered at x=0:
(3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺¹⁾ xⁿ / (n+1))
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) + (1/6) Σ((-1)ⁿ × (-9)⁽ⁿ⁺¹⁾ × xⁿ / (n+1))
To find the first 5 nonzero terms, we can plug in n=0 through n=4 and evaluate each term:
n=0: (3/2) × 1 = 1.5
n=1: (3/2) × 9x = 13.5x
n=2: (3/2) × 81x² / 2 - (1/6) × 81x² / 3 = 60.75x²
n=3: (3/2) × 729x³ / 6 + (1/6) × 729x³ / 4 = 183.375x³
n=4: (3/2) * 6561x⁴ / 24 - (1/6) * 6561x⁴ / 5 = 1018.1595x⁴
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the probability of class failure is 7%. if 56 students take a class, what number of students is expected to fail the class?
The probability of class failure is 7%. If 56 students take a class, the expected number of students who will fail the class is 4.
We will use the above formula to find the expected value of class failure. Let x be the number of students expected to fail the class.
Expected value = Probability x Total number of trials
The probability of class failure is 7%, so the probability of passing the class is 100% - 7% = 93%. The total number of trials is the total number of students taking the class, which is 56. Putting these values into the formula gives us:
Expected value = 7% x 56
Expected value = 0.07 x 56
Expected value = 3.92
We cannot have a fraction of a student, so we can round this number up to get the expected number of students who will fail the class.
Therefore, the expected number of students who will fail the class is 4.
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Which system of inequalities has the solution shown in the graph?
If the dartboard has a diameter of 14 inches and each number occupies 1/20 of the board, how much space does a single number occupy in square inches?
Each number occupies 7.7 inches² of the dartboard.
What is area?In geοmetry, area is the amοunt οf space a flat shape, like a pοlygοn, circle οr ellipse, takes up οn a plane. The area οf a shape is always measured in square units. Tο find the area οf simple shapes like a square οr the area οf a rectangle, yοu οnly need its width, w, and length, l (οr base, b). The area is length times width:
First we need the area of the dartboard
Area = πr²
here r = d/2 = 14/2 = 7
Area of dartboard = πr²
[tex]$ \rm = \frac{22}{7 } \times 7 \times 7[/tex]
= 22 × 7
= 154 inches²
Now, its is said that each number occupies 1/20 of the board,
Then area of each number = 154 × 1/20
= 7.7 inches²
Thus, Each number occupies 7.7 inches² of the dartboard.
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5. the number of people arriving for treatment at an emergency room can be modeled by a poisson process with a mean of 5 people per hour. how many people do you expect to arrive during a 45-min period?
If the number of people arriving for treatment at an emergency room is modeled by a Poisson process with a mean of 5 people per hour, we can use this information to estimate the expected number of people who will arrive during a 45-minute period.
The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time, given the average rate at which the events occur. In this case, the Poisson distribution can be used to estimate the number of people who will arrive during a 45-minute period, given that the mean arrival rate is 5 people per hour.
To calculate the expected number of arrivals, we first need to convert the 45-minute time period into hours. There are 60 minutes in an hour, so 45 minutes is equivalent to 0.75 hours.
Next, we can use the Poisson distribution formula, which is:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the mean arrival rate (in this case, 5 people per hour), k is the number of arrivals we are interested in, and e is Euler's number (approximately 2.71828).
Expected number of arrivals = λ * t = 5 * 0.75 = 3.75
Therefore, we can expect approximately 3.75 people to arrive for treatment during a 45-minute period, assuming that the number of arrivals follows a Poisson distribution with a mean of 5 people per hour.
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9. There are 8 black socks, 6 blue socks, and 14 white socks in a drawer. If one sock is randomly chosen from the
drawer, then what is the probability that the sock will not be blue?
The probability that the socks will not be blue would be =11/14.
How to calculate the probability of socks that are not blue in colour?Probability can be defined as the expression that shows the possibility of the occurrence of an event.
The formula that is used to calculate probability = the chosen events/total number of outcomes.
The total number of black socks = 8
The total number of blue socks = 6
The total number of white socks = 14
The total number of socks (outcomes) = 8+6+14 = 28
The socks that are not blue = 8+14 = 2
Therefore the probability that they socks won't be blue = 22/28 = 11/14.
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you have an srs of 23 observations from a large population. the distribution of sample values is roughly symmetric with no outliers. what critical value would you use to obtain a 98% confidence interval for the mean of the population?
The Critical value to be used to gain the 98 confidence interval for the population mean is2.508 and can be determined using the t- distribution table.
critical value is the value of a test statistic that defines the upper and lower bounds of the confidence interval or determines the position of statistical significance in a statistical test.
Given
You have an SRS of 23 compliances from a large population.The distribution of the sample values is roughly symmetric, with no outliers.98% confidence interval.The following way can be carried out to determine the critical value
Step 1-First determine the degrees of freedom using the following formula
degrees of freedom = n- 1
where n is the sample size.
Step 2- Replace" n" in the below formula.
degrees of freedom = 23- 1
= 22
Step 3- Now you can use the t- distribution table to determine the critical value to get a 98 confidence interval.
critical value = 2.508
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Help, please!
The answer is presented on the image, thank you!
Answer:
PQ = 3QR = 5EF = 10Step-by-step explanation:
You want to know the side lengths of the triangles shown if DE = 8.
Value of xSide DE is marked as x+6. If its length is 8, then we have ...
x +6 = 8
x = 2 . . . . . subtract 6
Side lengthsThe unknown side lengths are then ...
PQ = x+1 = 3
QR = x+3 = 5
EF = x+8 = 10
__
Additional comment
These are both 3:4:5 right triangles. The larger is twice the size of the smaller. You can guess this because a 3:4:5 right triangle is the only one with a side length of 4 and integer lengths for the other sides.
fatima is 1.27m tall. charlotte is 0.89m tall lila is taller than charlotte by half the difference betweem fatimas height and charlottes height. how tall in meters is lila?
Lila's height is 0.89 + 0.19 = 1.08m.
What is height ?
Height typically refers to the measurement of an object or person from the base to the top, usually measured vertically. It is often used in reference to the physical dimension of a person or object, such as the height of a building, tree, or individual.
According to the question:
In the context of the given problem, height refers to the height of Fatima, Charlotte, and Lila.
Fatima is 1.27 meters tall, Charlotte is 0.89 meters tall, and Lila is taller than Charlotte by half the difference between Fatima's height and Charlotte's height.
The difference between Fatima's height and Charlotte's height is 1.27 - 0.89 = 0.38m.
Half of that difference is 0.38/2 = 0.19m.
So, Lila is taller than Charlotte by 0.19m.
Therefore, Lila's height is 0.89 + 0.19 = 1.08m.
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3 2/5 -1 3/5!!
Please i need help!
Answer:
Step-by-step explanation:
3 2/5 -1 3/5 = 1.8
nineteen students are eligible to play doubles tennis. what is the maximum number of different 2-person teams possible?
By permutation and combination, Maximum 171 number of different 2 - person teams are possible.
Provide an example of permutation and combination?
An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are organized in a linear or sequential order.
As an illustration, set A=1,6 has the permutation 2, which is 1,6,1. Permutations include the arrangement of individuals, digits, numbers, alphabets, letters, and colors. Combinations include things like choosing a menu, cuisine, clothing, a subject, and a team.
Total number of ways to choose different 2 person out of 19 person.
= ¹⁹C₂
= 19!/2! (19 - 2)!
= 19!/2! 17!
= 19 * 18 * 17!/2 * 1 * 17!
= 19 * 7
= 171
Hence, maximum 171 number of different 2 - person teams are possible.
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four times the sum of a number and four is 136. translate into an equation and then solve for the number?
Answer: y-98
Step-by-step explanation:
the gallup poll surveyed a representative sample of american adults and offered a list of seven personal economic problems that many people face. what are the top financial concerns that people have?
According to a histogram that displays the percentage of replies over time, an April Gallup poll indicated that 55% of Americans think autonomous cars would be widely used in the next ten years.
Whether completely automated "driverless automobiles" would be widely deployed in the United States was the subject of a Gallup Poll conducted in April, which polled Americans ages 18 and older.
How soon, in your opinion, do you believe autonomous cars will be widely used in the US? According to the survey, 55% of Americans think autonomous cars will become commonplace over the next ten years.
The survey's results were displayed as a histogram, displaying the proportion of replies at various time intervals. This indicates how many respondents indicated that driverless cars will be widely utilised within a particular time period (e.g., within 5 years, within 10 years, etc.).
This survey reveals how people feel about autonomous cars in the future and how soon they believe they will be a common sight on the roads.
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The question is -
A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.
How much fencing is required to enclose a circular garden whose radius is 26 m? Use 3. 14 for PI
to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.
To determine the amount of fencing required to enclose a circular garden with a radius of 26 meters, we need to calculate the circumference of the circle. The circumference is the distance around the perimeter of the circle, which can be calculated using the formula:
Circumference = 2 x π x radius
where π is the mathematical constant approximately equal to 3.14, and the radius is the distance from the center of the circle to any point on its perimeter.
So, in this case, the circumference of the circular garden can be calculated as follows:
Circumference = 2 x 3.14 x 26 m
= 163.64 m
Therefore, to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.
It's worth noting that the formula for calculating the circumference of a circle can be used to find the amount of fencing required for any circular enclosure, such as a circular pond or a circular pool.
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Define The Fundamental Counting Principle: Unit 2: Probability Lesson 2: Counting Our Way to Probabilities Describe what it means to count with replacement and without replacement: You need a new password for an email account. The requirements are that the password needs to be 8 characters long considering of 5 lowercase letters followed by 3 numbers. If you are allowed to use characters more than once (with replacement), how many different possibilities are there for a password? (Use an image to help you understand). Let's use the same example as above, only this time you may only use each letter or number one time. That is without replacement or repetition.
Similarly, there are 10 choices for the first number, 9 choices for the second number, and 8 choices for the third number. Therefore, the total number of possibilities is[tex]26 × 25 × 24 × 23 × 22 × 10 × 9 × 8 = 14,776,320[/tex] possibilities.
Fundamental Counting Principle and how to count with and without replacement.The Fundamental Counting Principle (FCP) states that if there are m ways to perform an event and n ways to perform a second event, then there are m × n ways to perform both events. For example, suppose there are 2 shirts, 3 pants, and 4 pairs of shoes in your closet. Using the FCP, you can calculate the number of outfit combinations: 2 × 3 × 4 = 24.If you are allowed to use characters more than once (with replacement), the number of different possibilities for a password can be calculated by multiplying the number of choices for each character type. There are 26 lowercase letters, so there are 26 choices for the first letter, 26 choices for the second letter, and so on. Similarly, there are 10 digits, so there are 10 choices for each number.
Therefore, the total number of possibilities is [tex]26 × 26 × 26 × 26 × 26 × 10 × 10 × 10 = 26^5 × 10^3 = 11,881,376,000[/tex] possibilities.If you may only use each letter or number one time, then you cannot repeat any choices. Therefore, the number of possibilities is reduced. There are 26 choices for the first letter, 25 choices for the second letter (since one has already been used), and so on.
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job elimination in the past year, of businesses have eliminated jobs. if businesses are selected at random, find the probability that at least have eliminated jobs during the last year. round your answer to at least three decimal places. do not round your intermediate calculations.
The probability that at least 5 have eliminated jobs during the last year is 0.002965.
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
n = 9
p = probability of businesses have eliminated jobs = 0.13
X = Number of businesses have eliminated jobs ~
Binomial( n= 9 , p = 0.13)
[tex]P(X \geq 5)[/tex]
[tex]P(X \geq 5) = 1-P( X < 5)[/tex]
[tex]P(X \geq 5) = 1-P( X \leq 4)[/tex]
Use following Excel command:
=1-BINOM.DIST(x, n, p, cumulative)
=1-BINOM.DIST(4,9,0.13,TRUE)
=0.0029649
=0.002965
Thus
[tex]\mathbf{{P(X \geq 5) =0.002965}}[/tex].
Therefore, probability that at least 5 have eliminated jobs during the last year is 0.002965.
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Complete question';
Job Elimination in the past year, 13% of businesses have eliminated jobs. If 9 businesses are selected at random, find the probability that at least 5 have eliminated jobs during the last year. Round the answer to at least four decimal places P(at least 5 have eliminated jobs during the last year) X
at an airport restaurant, two sodas and four hamburgers cost $12.00. an order of four sodas and two hamburgers costs $9.00. how much does one hamburger cost?
At an airport restaurant, the cost of one hamburger is $2.50.
How to get the cost of one hamburger?Two sodas and four hamburgers cost $12.00, and an order of four sodas and two hamburgers costs $9.00.
To know the cost of each soda and hamburger, we need to use the equation (x and y)
Use x for soda, and use y for hamburger
Two sodas and four hamburgers cost $12.00
Then, (2 x x) + (4 x y) = 12
2x + 4y = 12
We need to divide the numbers by 2, as follows:
x + 2y = 6
four sodas and two hamburgers cost $9.00
(4 x x) + (2 x y) = 9
4x + 2y = 9
We have to substitute the "x", as follows:
4 (6-2y) + 2y = 9
24 - 8y + 2y = 9
24 - 6y = 9
24 - 9 = 6y
15 = 6y
y = 2.5
Therefore, the cost of one hamburger is $2.50.
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please help!! I need this by the end of tonight..!
Answer:
y=2.05x
Step-by-step explanation:
Figure out what the total cost is for 1 of them then you put that in as your M value, then X stands for number of sheets so 2.05 multiplied by the number of sheets sold you get your Y which is the total cost in dollars for x sheets.
Jarvis and his family are at the dine-in movies and wish to purchase some popcom. A large popcom costs $18 and a small popcom costs $12. Jarvis offered to pay for the popcom with $50 in his wallet.
Create an inequality in standard form that describes this situation.
Use the given numbers and the following variables.
• x = the number of large popcoms
• y = the number of small popcorn
Answer:
18x + 12y ≤ 50
Step-by-step explanation:
Let x be the number of large popcoms and y be the number of small popcoms.
The cost of a large popcom is $18, and the cost of a small popcom is $12. The total cost of purchasing x large popcoms and y small popcoms is given by:
Total cost = 18x + 12y
The problem states that Jarvis has $50 in his wallet to pay for the popcoms. Therefore, we can write the following inequality:
18x + 12y ≤ 50
This inequality represents the situation where Jarvis and his family want to purchase popcoms, and Jarvis has $50 to spend. The inequality ensures that the total cost of the popcoms does not exceed $50.
assuming a constant growth factor, by what percent did the population of gotham city grow each year? give at least 3 decimal places.
Assuming a constant growth factor, the population of Gotham City grew by approximately 4.287% each year.
This can be calculated using the formula for exponential growth, which is:
y = a * (1 + r)^t
Where: y = final value of the population
a = initial value of the population
r = annual growth rate expressed as a decimal
t = number of years
For this problem, let's assume that the initial population of Gotham City was 100,000 and that the population grew for 10 years.
Using these values, we can calculate the annual growth rate as follows:
100,000 * (1 + r)^10 = final population
r = (final population / 100,000)^(1/10) - 1
Plugging in a final population of 148,644 (which is a 48.644% increase from the initial population),
r = (148,644 / 100,000)^(1/10) - 1r = 0.04287 (rounded to 5 decimal places)
Therefore, the annual growth rate (or percentage increase) is approximately 4.287% (rounded to 3 decimal places).
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where is the water table in a swamp? group of answer choices well below the surface. at the surface. well above the surface. generally, 2 miles below the surface.
Generally, the water table in a swamp is located 2 miles below the surface.
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the slant height of a cone measures 26 centimeters. The height of the cone measures 24 centimeters.
What is the exact surface area of the cone?
help!!
Enter your answer in the box.
The value of the exact surface area of the cone is 360π
What is the exact surface area of the cone?To find the surface area of a cone, we need to calculate the area of the circular base and the curved lateral surface.
The radius of the circular base can be found using the Pythagorean theorem:
r = √(s^2 - h^2)
where s is the slant height and h is the height.
In this case, we have:
r = √(26^2 - 24^2)
r = 10
So, the surface area is
S = πr² + πrl
This gives
S = π * 10² + π * 10 * 26
S = 360π
Hence, the exact surface area of the cone is 360π
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Brooke played her flute for 3/4 hour each day for 5 days and for 1/2 hour each day for 2 days how many hours did she play it in all
⇒To be able to answer this question to find how many hours Brooke played his flute for 5 days we ought to first convert the 5 days to hours.
⇒There are 24 hours in a day this means that in 5 days we have =24×5
=120 hours.
⇒We have 120 hours in 5 days , it is said that Brooke played her flute [tex]\frac{3}{4}[/tex],
Meaning she played the flute [tex]\frac{3}{4}[/tex] hours of 120 hours which is equal
[tex]\frac{3}{4} *\frac{120}{1}\\=90[/tex]
For 5 days Brooke played her flute 90 hours
⇒The next step is to convert the 2 days to hours which is equivalent to 24×2
=48 hours are in 2 days, it is said Brooke played the flute [tex]\frac{1}{2}[/tex] hours of 2 days. This simply is equivalent to
[tex]\frac{1}{2} *\frac{48}{1} \\=24[/tex]
⇒For 2 days Brooke played the flute 24 hours,
The total number of hours she played it all is =Number of hours she played it in 5 days+ Number of hours she played it in 2 days.
=90+24
=114
⇒In total of these 7 days she played the flute for 114 hours
Two ships are near a buoy in the open ocean. One ship is 20 km due north of the buoy, and the other ship is 13.5 km due east of the buoy.
Enter a number in the box to correctly complete the statement. Round the answer to the nearest tenth.
In this instance, the buoy forms the right corner of a triangle made up of the two ships and the buoy. To the closest tenth, the distance between the two ships is roughly [tex]24.1[/tex] km.
What is the distance between two object?To find the distance between the two ships, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs
(the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In this case, the two ships and the buoy form a right triangle, with the buoy at the right angle.
Let d be the distance between the two ships, x be the distance of the northern ship to the buoy and y be the distance of the eastern ship to the buoy. Then we have:
[tex]d^2 = x^2 + y^2[/tex]
Substituting the given values, we get:
[tex]d^2 = (20 km)^2 + (13.5 km)^2[/tex]
[tex]d^2 = 400 km^2 + 182.25 km^2[/tex]
[tex]d^2 = 582.25 km^2[/tex]
[tex]d ≈ 24.1 km[/tex]
Therefore, the distance between the two ships is approximately 24.1 km, rounded to the nearest tenth.
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help please i dont get this
● < P=R " angles opp =sides"
●PQ =QR " Angles opposite = sides"
therefore PQR is an isosceles " 2 opp angles and sides are equal "
Tell whether the angles are complementary, supplementary, or neither.
A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by
X raysUV radiationGlycosylaseDepurination
Explanation:
A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by X-rays.
Nonhomologous end joining is a DNA repair mechanism that can join two DNA fragments with little or no homology between them. X-rays, which are high-energy electromagnetic waves, can cause damage to DNA by breaking the strands of the double helix.
This damage can be repaired by mechanisms like nonhomologous end joining, so a strain of Mycobacterium tuberculosis that is deficient in this repair mechanism would be more sensitive to damage by X-rays.
UV radiation, glycosylase, and depurination are not directly related to nonhomologous end joining repair and would not have the same effect.
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