The formula for Poisson distribution is:
P (x) = e^-k * k^x / x!
We know that:
3P(x = 1) = P(x = 2)
Therefore:
3 [e^-k * k^1 / 1!] = e^-k * k^2 / 2!
Simplifying by cancelling similar terms:
3 / 1! = k / 2!
k = 3 * 2! / 1!
k = 6
So at x = 4:
P (x = 4) = e^-6 * 6^4 / 4!
P (x = 4) = 0.1339 or 13.39%
starting from 105 feet away a person on a bicycle rides toward a checkpoint and then passes it.the rider is traveling at a constant rate of 35 feet per second.The distance between the bicycle and the checkpoint given by the equation is D=|105-35t|.at what times is the bike 60 feet away from the checkpoint?
A.1.3 sec and 2.6 sec
B.1.3 sec and 4.7 sec
c.1.1 sec and 2.6 sec
d.4.7 sec and 9.4 sec
WHO EVER ANSWERS IT FIRST AND RIGHT GETS BRAINIEST
Answer:
The correct option is B.
Step-by-step explanation:
It is given that starting from 105 feet away a person on a bicycle rides toward a checkpoint and then passes it.the rider is traveling at a constant rate of 35 feet per second.
The distance between the bicycle and the checkpoint given by the equation
[tex]D=|105-35t|[/tex]
We have to find the times at which the bike 60 feet away from the checkpoint.
Substitute D=60 i the given equation.
[tex]60=|105-35t|[/tex]
[tex]\pm 60=105-35t[/tex]
Case 1:
[tex]60=105-35t[/tex]
Subtract 105 from both the sides.
[tex]60-105=-35t[/tex]
[tex]-45=-35t[/tex]
Divide both sides by -35.
[tex]1.2857=t[/tex]
[tex]t\approx 1.3[/tex]
Case 2:
[tex]-60=105-35t[/tex]
Subtract 105 from both the sides.
[tex]-60-105=-35t[/tex]
[tex]-165=-35t[/tex]
Divide both sides by -35.
[tex]4.71428=t[/tex]
[tex]t\approx 4.7[/tex]
The bike is 60 feet away from the checkpoint at 1.3 sec and 4.7 sec. Therefore the correct option is B.fore the correct option is B.
What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ? Enter your answer in the box. ___units²
ALGEBRAAA
1. A square has the side measurement of s= 2 3/2,
Using the formula A=s^2, find the area of the square.
2 3/2 = 3 1/2 ( 3/2 = 1 1/2 + 2 = 3 1/2)
so area = 3 1/2 ^2
3 1/2 x 3 1/2 = 12 1/4
Area = 12 1/4
HELP PLEASE!!!
A wheel makes 20 revolutions per minute. Find the angular velocity.
10π rad/min
20π rad/min
40π rad/min
Answer:
Angular velocity of a wheel which makes 20 revolutions per minute is 40π rad/min
Step-by-step explanation:
Angular velocity, ω = 2πf , where f is the frequency.
Here frequency, f = 20 revolutions per minute
Substituting frequency value in angular velocity equation,
Angular velocity, ω = 2πf = 2 x π x 20 = 40π rad/min
So angular velocity of a wheel which makes 20 revolutions per minute is 40π rad/min
there are 6 grams of fat per serving of granola. each serving provides 180 calories. what percentage of these calories is from fat?
is it possible to have three points that would not fit on the same plane 2 dimensional surface? Why or why not
Cristina Suarez has insured her home for 80% of its replacement value of $155,000. Use the chart to determine the amount of coverage for her personal property, to the nearest dollar.
The final answer is 55,800
A car travels at an average speed of 64 miles per hour. how many miles does it travel in 4 hours and 45 minutes?
Final answer:
The car travels 304 miles in 4 hours and 45 minutes at an average speed of 64 miles per hour.
Explanation:
To find the distance the car travels in 4 hours and 45 minutes, we need to convert the time to hours and minutes. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours. Therefore, the total time is 4 + 0.75 = 4.75 hours.
To calculate the distance, we can use the formula:
Distance = Speed x Time
Given that the average speed is 64 miles per hour and the time is 4.75 hours, we can plug these values into the formula:
Distance = 64 mph x 4.75 hours = 304 miles.
A: What is the real part of the complex number? B: What is the imaginary part of the complex number? Select one answer for part A, and select one answer for part B. A: i B: 3 A: 3 A: 2i B: i B: 2i B: 2 A: 2
Xy has endpoints at x(2,-3) and y(-1,2). What is the length of xy
There are 2 4/5 pounds of bricks in a bag. each brick weighs 2/5 of a pound. how many bricks are in the bag?
1. What is the value of x in the triangle?
Enter your answer in the box. Round your final answer to the nearest hundredth.
x = cm
2. What are the values of the trigonometric ratios for this triangle?
Drag the answer into the box to match each ratio.
sinθ-----
cosθ-----
tanθ-----
OPTIONS YOU CAN DRAG
5/4
3/4
3/5
4/3
4/5
5/3
3. What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
x = °
4. What is the value of θ for the acute angle in a right triangle?
sin(θ)=cos(58°)
Enter your answer in the box.
θ= °
5. A party tent is used for an outdoor event. Ropes of equal length support each tent pole. The angle the rope makes with the floor is 55°.
What is the height of each pole?
Enter your answer in the box. Round only your final answer to the nearest tenth.
6. What is the exact value of sin 60° ?
Enter your answer, as a simplified fraction, in the box.
Answer: Took the test correct :)
Step-by-step explanation:Problem 1
cos(angle) = adjacent/hypotenuse
cos(18) = x/25
25*cos(18) = x
x = 25*cos(18)
x = 23.7764129073789
x = 23.78
Answer: x = 23.78
=====================================================
Problem 2
theta = greek letter that looks like a "zero" or the letter O with a horizontal line through it
With the reference angle of theta, the opposite side is 3. This side is the leg furthest from the angle theta. In contrast, the side 4 is the closest leg to theta. The longest side 5 is the hypotenuse. The hypotenuse is always the lonest side
sin(theta) = opposite/hypotenuse
sin(theta) = 3/5
cos(theta) = adjacent/hypotenuse
cos(theta) = 4/5
tan(theta) = opposite/adjacent
tan(theta) = 3/4
---------------------------
In summary:
sin(theta) = 3/5
cos(theta) = 4/5
tan(theta) = 3/4
=====================================================
Problem 3
cos(angle) = adjacent/hypotenuse
cos(x) = 15/29
x = arccos(15/29) .... inverse cosine or cos^(-1) also works
x = 58.852610078491
x = 58.85
Answer: x = 58.85
=====================================================
Problem 4
The rule we'll use is
sin(x) = cos(90-x)
sin(theta) = cos(90-theta)
cos(90-theta) = cos(58)
90 - theta = 58
90 - theta+theta = 58+theta
90 = 58+theta
90-58 = 58+theta-58
32 = theta
theta = 32
Answer: 32
=====================================================
Problem 5
x = height of pole
the vertical side is the side we want, which is the opposite side compared to the angle 55 degrees
sin(angle) = opposite/hypotenuse
sin(55) = x/25
25*sin(55) = x
x = 25*sin(55)
x = 20.4788011072248
x = 20.5
Each pole is roughly 20.5 feet tall.
=====================================================
Problem 6
The exact value is the fraction sqrt(3)/2 which can be written as \frac{\sqrt{3}}{2}
"sqrt" is shorhand for "square root"
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The price of a bracelet increase from $170 to $200 A Mother's Day what is the percent of increase in the price rounded to the nearest percent
if two angles are supplementary, then it adds up to 180 degrees True or false?
Cards numbered 1 through 30 are shuffled in a bin one card is randomly selected what is the probability of selecting a number that is a multiple of 11 ? please help
If y varies directly as x and y is 18 when x is 5 which expression can be used to find the value of y when x is 11?
Answer:
The value of y is [tex]\frac{198}{5}[/tex] or 39.6.
Step-by-step explanation:
It is given that y varies directly as x and y. It means y is directly proportional to x.
[tex]y\propto x[/tex]
[tex]y=kx[/tex] .... (1)
where, k is constant of proportionality.
It is given that y is 18 when x is 5.
Substitute y=18 and x=5 in equation (1).
[tex]18=k(5)[/tex]
Divide both sides by 5.
[tex]\frac{18}{5}=k[/tex]
The value of k is [tex]\frac{18}{5}[/tex]. So, the relation between x and y is
[tex]y=\frac{18}{5}x[/tex] .... (2)
We need to find the value of y when x=11.
[tex]y=\frac{18}{5}(11)[/tex]
[tex]y=\frac{198}{5}[/tex]
[tex]y=39.6[/tex]
Therefore the value of y is [tex]\frac{198}{5}[/tex] or 39.6.
An item is regularly priced at $65 . it is on sale for 80% off the regular price. how much (in dollars) is discounted from the regular price?
If PQ bisects CX at point J, and if JX = 4y and CJ = y+9 find y
By setting the given equations equal to each other (JX = CJ), we can create a new equation (4y = y +9). This equation simplifies to 3y = 9, giving a solution of y = 3.
Explanation:The problem you're facing deals with bisecting line segments, which is a topic under Geometry. Remember, if a segment bisects another, that means it divides the second segment into two equal parts. In this case, PQ bisects CX at point J, so JX = CJ.
We're also given that JX = 4y and CJ = y + 9. Because JX = CJ, we can set the two equations equal to each other and solve for y:
4y = y + 9
By subtracting y from both sides, we get
3y = 9
Finally, by dividing both sides by 3, we solve for y, which is 3
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John and Tim are looking at the equation the square root of the quantity of 3 times x minus 4 equals square root of x . John says that the solution is extraneous. Tim says the solution is non-extraneous. Is John correct? Is Tim correct? Are they both correct? Justify your response by solving this equation, explaining each step with complete sentences. (10 points)
A cookie factory uses 3/8 of a barrel of oatmeal in each batch of cookies with the factor uses 3/4 of a barrel of oatmeal yesterday how many batches of cookies did the factory make
The cookie factory made 2 batches of cookies yesterday. This is found by dividing the total amount of oatmeal used (3/4 of a barrel) by the amount used per batch (3/8 of a barrel).
Explanation:To find the number of batches of cookies the factory made, we would divide the total amount of oatmeal used by the amount used per batch.
The factory used 3/4 of a barrel of oatmeal yesterday, and each batch uses 3/8 of a barrel. So, we divide 3/4 by 3/8.
Before doing that, remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/8 is 8/3.
So, 3/4 divided by 3/8 is equivalent to 3/4 multiplied by 8/3, giving us a result of 2.
Therefore, the cookie factory made 2 batches of cookies yesterday using 3/4 of a barrel of oatmeal.
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Why, if two wrongs don't make a right, do two negatives make a positive in mathematics?
So, we can’t directly compare wrong with that of negative. Let me give an example. Let’s just think of Terrorism. Do you think there are positive and negative sides of terrorism? Mostly the answer would be no. There is no such things as positive and negative when we think of terrorism. But here we can directly say that Terrorism is always wrong whenever and wherever we talk about it.
I think now I have cleared your doubts about difference between wrong and negative. That’s why we can never say that two wrong can make a right. I hoped this helped!!
Final answer:
In mathematics, two negatives make a positive due to the rules of multiplication and addition. This rule is a fundamental property of mathematics and is consistent across various mathematical operations and contexts.
Explanation:
In mathematics, two negatives make a positive due to the rules of multiplication and addition. When two negatives are multiplied, the negative signs cancel each other out and result in a positive product. For example, (-4) x (-3) = 12, where both numbers are negative but the product is positive.
The same concept applies to addition as well. When two negative numbers are added, the negative signs combine and result in a negative sum. However, when two negative numbers are multiplied, the negative signs cancel out and produce a positive product.
It's important to note that this rule is a fundamental property of mathematics and is consistent across various mathematical operations and contexts.
Is this right? Domain and range of a function
How do u you a irrantional number from a rational number?
What is the reference angle for a 240° angle
The reference angle for a 240° angle is 60 degree.
What is a Reference Angle?Reference Angle is the acute angle between the terminal side and the x axis. The value of reference angle is always positive and less than 90 degree.
The angle is 240 degree, for which the reference angle has to be determined.
The angle 240 degree lies in the third quadrant between 180 and 270 degree.
To determine the reference angle, the given angle will be subtracted by 180 degree.
=> 240 - 180
=> 60 degree
To know more about Reference Angle
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Which of these statements about the two triangles is true?
There is not enough information to determine whether the triangles are congruent or not congruent.
The triangles are congruent by the SAS Congruence Postulate.
The triangles are not congruent.
Help me reduce this please!!!
The number of timeshare condos available at sunset beach is 3/5 the number of timeshare condos available at playa del mar. if the total number of timeshare condos available at the two beaches combined is 240, what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar?
To find the difference between the number of condos available at Sunset Beach and Playa Del Mar, we need to set up an equation and solve for the unknown. The number of timeshare condos available at Sunset Beach is 3/5 of the number available at Playa Del Mar. By solving the equation, we find that the difference is 60 condos.
Explanation:To solve this problem, we can set up an equation. Let's say the number of timeshare condos available at Playa Del Mar is x. According to the question, the number of condos available at Sunset Beach is 3/5 of x, or 3/5x.
So, the total number of condos available at both beaches is x + 3/5x = 240. We can combine the like terms to get 8/5x = 240.
To solve for x, we divide both sides of the equation by 8/5, which is the same as multiplying by its reciprocal, 5/8. Simplifying, we get x = 240 * 5/8 = 150.
Therefore, the number of condos available at Sunset Beach is 3/5 * 150 = 90, and the difference between the number of condos available at Sunset Beach and Playa Del Mar is 150 - 90 = 60.
Jan scored 539,178 points in a video game what is Jans score rounded to the nearest ten thousand?
a writer gets paid monthly at a rate of $300 for each article she completes last moth she wrote 11.8 articles how much money did she get paid last month? show your work
Answer:
She got paid last month $3540 .
Step-by-step explanation:
This problem can be solve by rule 3, knowing that she gets paid for each article a rate of $300.
1 article ------- $300
11.8 article----- x
Next you have to calculate the value of x as follows:
[tex]x=\frac{11.8*300}{1}[/tex]
x=3540
She got paid last month $3540.
Find three consecutive integers such that the sum of the first and twice the second is equal to the third plus four.