The probability that the number of lost-time accidents occurring over a period of 8 days will be no more than 5 is 0.6695
This scenario can be modeled using the Poisson distribution, which is a probability distribution that describes the number of events that occur in a fixed time period when the events occur independently and at a constant rate.
The mean rate of lost-time accidents per day is given as 0.6. Therefore, the mean rate of lost-time accidents over 8 days is
Mean rate = (0.6 accidents/day) x (8 days) = 4.8 accidents
Let X be the number of lost-time accidents occurring over 8 days. Then, X follows a Poisson distribution with parameter λ = 4.8.
To find the probability that the number of lost-time accidents occurring over a period of 8 days will be no more than 5, we need to calculate
P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Using the Poisson probability mass function, we get
P(X = k) = (e^(-λ) × λ^k) / k!
where k is the number of lost-time accidents.
Substituting λ = 4.8 and k = 0, 1, 2, 3, 4, 5 in the above formula, we get
P(X = 0) = (e^(-4.8) × 4.8^0) / 0! = 0.0082
P(X = 1) = (e^(-4.8) × 4.8^1) / 1! = 0.0393
P(X = 2) = (e^(-4.8) × 4.8^2) / 2! = 0.0944
P(X = 3) = (e^(-4.8) × 4.8^3) / 3! = 0.1573
P(X = 4) = (e^(-4.8) × 4.8^4) / 4! = 0.1888
P(X = 5) = (e^(-4.8) × 4.8^5) / 5! = 0.1815
Therefore,
P(X ≤ 5) = 0.0082 + 0.0393 + 0.0944 + 0.1573 + 0.1888 + 0.1815 = 0.6695
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A fish tank, in a shape of rectangular prism, measures
100 cm × 60 cm X40 cm. The water level reached the blvoo eveD gror vIs midpoint of the base (the 50 cm mark), when the tank was tilted to rest on a 60 cm edge, as shown in the
100
diagram on the right. What would be the depth of the water, if the tank is returned to its horizontal position (resting on its 60 cm × 100 cm base)?
When the tank is tilted, the water level reaches the midpoint of the 60 cm side, which is 30 cm from the bottom of the tank. This means that the height of the water is 30 cm.
To find the depth of the water when the tank is returned to its horizontal position, we need to use the concept of similar triangles. The two triangles formed by the water level and the sides of the tank are similar, because they have the same angles.
Let x be the depth of the water in centimeters when the tank is returned to its horizontal position. Then we have:
(40 - x) / 60 = 30 / 50
Simplifying this equation, we get:
40 - x = 36
x = 4
Therefore, the depth of the water in the fish tank when it is returned to its horizontal position is 4 cm.
Can someone help I’ll give 10 points
Answer:
Hey Sweetheart!
z=4
4x4x4= 64
Hope this Helps!!!
a) use these data to estimate the mean wrist extension for people using this new mouse design using a 90% confidence interval. (round your answers to three decimal places.) , (b) what assumptions are required in order for it to be appropriate to generalize your estimate to the population of students at this university? yes, the assumption would have to be made that the 24 students in the study formed a random sample of people in the country. no, we can generalize the estimate to the population of students at this university. yes, the assumption that the 24 students in the study formed a random sample of students at all universities. yes, the assumption would have to be made that the 24 students in the study formed a random sample of students at this university. no, we cannot generalize the estimate to any population as we have less than 30 students. to the population of all university students? no, we cannot generalize the estimate to any population as we have less than 30 students. yes, the assumption would have to be made that the 24 students in the study formed a random sample of people in the country. yes, the assumption would have to be made that the 24 students in the study formed a random sample of students from this university. no, we can generalize the estimate to the population of all university students. yes, the assumption that the 24 students in the study formed a random sample of students at all universities. (c) based on your interval from part (a), do you think there is reason to believe that the mean wrist extension for people using the new mouse design is greater than 20 degrees? explain why or why not. no, the entire confidence interval is below 20, so the results of the study would be very likely if the population mean wrist extension were greater than 20. no, the confidence interval contains 20, so the results of the study would be very likely if the population mean wrist extension were greater than 20. yes, the confidence interval contains 20, so the results of the study would be very unlikely if the population mean wrist extension were as low as 20. yes, the entire confidence interval is above 20, so the results of the study would be very unlikely if the population mean wrist extension were as low as 20.
The random sample of [tex]24[/tex] students has a mean of [tex]1.9149[/tex], and the data suggests that the mean is [tex]20^{0}[/tex].
How to Use the Sample Mean Formula to Determine the Sample Mean?x = (xi) / n is the general solution for computing the sample mean. Thus, xi refers to all X sample values, xi represents the sampling distribution, and n is the total number of specimen terms inside the data collection.
What does sample in statistics mean?The statistic known as the sampling distribution is created by arithmetically averaging the values of the variables in a group. The sample mean is an estimate of the anticipated value if the sample is taken from probabilistic with a common expected value.
(a) Sample mean [tex]= (17 + 21 + 20 + 19 + 23 + 22 + 20 + 20 + 18 + 21 + 19 + 24 + 22 + 20 + 19 + 20 + 19 + 20 + 21 + 22 + 23 + 21 + 18 + 22)/24 = 20.5[/tex]Sample standard deviation [tex]= 1.9149[/tex]
Next, we can use a t-distribution with [tex]23[/tex] degrees of freedom
Confidence interval [tex]= (20.5 - 0.8277, 20.5 + 0.8277) = (19.6723, 21.3277)[/tex]
b) The assumption required in order to generalize the estimate to the population of students at this university is that the [tex]24[/tex] students in the study formed a random sample of students at this university.
(c) There is not enough evidence to suggest that the mean wrist extension for people using the new mouse design is greater than [tex]20^{0}[/tex].
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A 2-yard piece of rope costs $22. 86. What is the price per foot?
The price per foot of the 2-yard rope is $6.36.
To find the price per foot of the 2-yard rope, we need to first convert the length to feet. Since there are 3 feet in a yard, a 2-yard rope is equal to 6 feet.
Next, we divide the total cost of the rope ($22.86) by the length of the rope in feet (6 feet) to get the price per foot:
$22.86 ÷ 6 = $3.81 per yard
To convert this to the price per foot, we divide $3.81 by 3 (since there are 3 feet in a yard):
$3.81 ÷ 3 = $1.27 per foot
Therefore, the price per foot of the 2-yard rope is $1.27 x 5 = $6.36.
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Which of the following is a point of tangency on the circle below?
A. Point Y
B. Point Z
C. Point W
D. Point X
Based on the diagram, the point of tangency is Point Z. Therefore, the answer is B.
What is point of tangency?A point of tangency is a point at which a straight line, called a tangent line, touches a curve or a circle at only one point.
At the point of tangency, the tangent line is perpendicular to the radius of the circle that intersects the point of tangency.
The point of tangency is the point where a tangent line to the circle touches the circle at only one point.
In the given diagram, the line segment XZ appears to be a tangent to the circle.
Therefore, the point of tangency is the point where the line segment XZ touches the circle.
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A cylinder has radius 1.6 meters. Its volume is 95 cubic meters. Find its height to the nearest tenth of a meter. Use 3.14 as approximation for
The height of the given cylinder with radius 1.6 meters is 11.81 meters.
Explain about the volume of cylinder?A cylinder is a solid made up of two congruent circles in parallel planes, respective interiors, and all the parallel line segments with ends on the circular regions that are perpendicular to the took the shape the centers of both circles.
A three-dimensional solid's volume is the amount of room it occupies up. When calculating the volume, make sure that each of the quantities belong to the same unit.
Radius r = 1.6 meters.
Volume of cylinder V = 95 cubic meters
Formulae for volume of cylinder = πr²h
Height = ?
V = πr²h
95 = 3.14 * 1.6² * h
h = 95 /(3.14 * 1.6²)
h = 11.81
Thus, the height of the given cylinder with radius 1.6 meters is 11.81 meters.
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Line segment AB in the coordinate plane has endpoints with coordinates A (1,5) and B (9,17). Which of the following is true?
The correct option- The perpendicular bisector of AB has the slope -1/3.
Explain about the slope of line?The difference between the change in y-values and the change in x-values is known as the slope of a line. This figure represents the slope of a line.
A quantity called the slope of a line is used to quantify how steep a line is. This number may be zero, positive, or negative. Moreover, it may be unreasonable or rational.Any two lines with the same slope are said to be parallel. When a line is rotated 90 degrees, it becomes perpendicular and becomes parallel. Four 90 degree angles result from the intersection of two perpendicular lines.Formula for slope m = (y2 - y1)/(x2 - x1)
Line segment AB coordinates :
A (1,5) and B (9,17).
Slope m1 = (17 - 5)/(9 - 5)
m1 = 12/4
m1 = 3
The line perpendicular to AB.
Let the slope of m2.
The relation between the slopes of perpendicular lines:
m1 x m2 = -1
3 x m2 = -1
m2 = -1/3.
Thus, the slope of the line perpendicular to the given line AB is found as: -1/3.
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Complete question:
AB in the coordinate plane has endpoints with coordinates A (1,5) and B (9,17). Which of the following is true?
The perpendicular bisector of AB has slope 3/2.
The perpendicular bisector of AB has slope -2/3.
The perpendicular bisector of AB has slope -2/3.
The perpendicular bisector of AB has slope -1/3.
Question 5
During gym class, Kathryn did 5 times as many pushups as Grace. Together, they did a total of 42 pushups. How
many push-ups did each person do during the gym class?
Part A
Write a system of equations that represents the situation.
y=
x + y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
The number of pushups done by Grace and Kathryn is 7 and 35 respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data,
Let the equation be represented as A
Now , the value of A is
Let the number of pushups by Grace be x
Let the number of pushups by Kathryn be y
Now, Kathryn did 5 times as many pushups as Grace
[tex]y = 5x[/tex] be equation (1)
And, they did a total of 42 pushups together
[tex]x + y = 42[/tex] be equation (2)
Substituting the value of y in the equation, we get
[tex]x + 5x = 42[/tex]
[tex]6x = 42[/tex]
Divide by 6 on both sides, we get
[tex]x = 7[/tex] pushups
And, [tex]y = 35[/tex] pushups
So, the number of pushups by Grace is 7 and by Kathryn is 35 respectively
Lauren leans a 16-foot ladder against a wall so that it forms an angle of 78 ∘ ∘ with the ground. how high up the wall does the ladder reach? round your answer to the nearest hundredth of a foot if necessary.
The ladder reaches the height of approximately 16.03 feet up the wall. (Rounded to the nearest hundredth of a foot)
We can use trigonometry to solve this problem. Let h be the height up the wall that the ladder reaches, and let θ be the angle that the ladder makes with the ground. We know that the length of the ladder (hypotenuse) is 16 feet and the angle θ is 78 degrees.
We can use the trigonometric function tangent (tan) to find the height h:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height h, the adjacent side is the distance from the ladder to the wall (which is the same as the distance from the wall to Lauren), and the angle θ is 78 degrees. So we have:
tan(78°) = h/x
where x is the distance from the ladder to the wall. Solving for h, we get:
h = x * tan(78°)
We don't know the value of x, but we can use the fact that the ladder is 16 feet long to find it. Using the Pythagorean theorem, we have:
x^2 + h^2 = 16^2
Substituting h = x * tan(78°), we get:
x^2 + (x * tan(78°))^2 = 16^2
Simplifying, we get:
x = 16 / √(1 + tan^2(78°))
x ≈ 3.83 feet
Finally, we can substitute x into our equation for h:
h = x * tan(78°)
h ≈ 16.03 feet
Therefore, the ladder reaches approximately 16.03 feet up the wall. Rounded to the nearest hundredth of a foot, the answer is 16.03 feet.
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Frank organized a raffle. He sells 300 tickets for £5 each. The prizes cost £400. He gives 55% of the profit to Charity A and 45% of the profit to Charity B. Work out how much each charity receives.
Answer:
Step-by-step explanation:
The total revenue from selling 300 tickets for £5 each is:
300 x £5 = £1500
The profit will be the difference between the total revenue and the cost of prizes:
£1500 - £400 = £1100
The amount of profit that goes to Charity A is:
55% x £1100 = £605
The amount of profit that goes to Charity B is:
45% x £1100 = £495
Therefore, Charity A receives £605 and Charity B receives £495.
. In which step does a mistake first occur?
(24+3 + 10)-14 + 2
Step 1: (8 + 10) -14 + 2
Step 2: 18 -14+2
Step 3: 4 +2
Step 4: 2
NEED HELP ASAP !!
TY
Answer:
The first one...............
(57x -32< 72 respuesta son desigualdades
Answer:
x < 2
Step-by-step explanation:
57x - 32 < 72
57x < 104
x < 2
I need help pleasee!
Answer:
a. After 10 minutes of hiking, Kiran will have covered a distance of:
distance = rate × time
distance = 0.04 mile/min × 10 min
distance = 0.4 mile
So, his remaining distance on the trail will be:
remaining distance = total distance - covered distance
remaining distance = 1.8 mile - 0.4 mile
remaining distance = 1.4 miles
Therefore, Kiran's remaining distance on the trail after 10 minutes of hiking is 1.4 miles.
b. We can use the same formula to find out how far Kiran will have walked after a certain amount of time:
distance = rate × time
We know that Kiran walks at a rate of 0.04 mile a minute, and we want to find out how much time it will take him to cover the remaining distance of 0.2 mile. So we can rearrange the formula to solve for time:
time = distance / rate
time = 0.2 mile / 0.04 mile/min
time = 5 minutes
Therefore, Kiran will have 0.2 mile left on the trail after 5 minutes of walking.
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Acellus; Perimeter, Circumference, and Area II
Based on the information, the area of the figure would be: 86.13 units ²
How to find the area of the figure?To find the area of the figure we must perform the following procedure:
1. Find the area of the triangle with the following formula:
height * base / 2 = area of the triangle
6 * 6 / 2 = area of the triangle
18 = area of the triangle
2. Find the area of the rectangle with the following formula:
height * base = area of rectangle
6 * 9 = area of the rectangle
54 = area of rectangle
3. Find the area of the semicircle with the following formula:
[tex]\pi[/tex] * r² / 2 = area of the semicircle
[tex]\pi[/tex] * 3² / 2 = area of the semicircle
[tex]\pi[/tex] * 9 / 2 = area of the semicircle
28.27 / 2 = area of the semicircle
14.13 = area of the semicircle
4. We must add the area of all the figures to find the total area.
14.13 + 54 + 18 = 86.13 units ²
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You work part-time at a diner that pays you $6. 75/hr plus tips. Tips average $3. 50/hr. Your deductions are FICA (7. 56%), Federal tax withholding (9. 6%), and state tax withholding (6. 7%). You work 13 hours per week. What is you gross pay per month including tips? $533. 00 $351. 00 $507. 00 $520. 0
Your gross pay per month including tips is $533.00. The answer is A) $533.00.
First, let's calculate your hourly wage including tips:
Hourly wage including tips = $6.75 + $3.50 = $10.25
Next, let's calculate your total earnings per week:
Total earnings per week = hourly wage including tips x hours worked per week
= $10.25 x 13 hours
= $133.25
Now let's calculate the deductions from your earnings:
FICA deduction = 7.56% x $133.25 = $10.08
Federal tax withholding = 9.6% x $133.25 = $12.80
State tax withholding = 6.7% x $133.25 = $8.92
Total deductions = $10.08 + $12.80 + $8.92 = $31.80
Finally, let's calculate your gross pay per month:
Gross pay per month = total earnings per week x 4 weeks - total deductions
= ($133.25 x 4) - $31.80
= $533.00
Therefore, your gross pay per month including tips is $533.00. The answer is A) $533.00.
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in how many ways can you choose a committee of size 10 with at least 2 men if there are 30 women in the club and 20 men in the club lsing set difference?
Therefore, the number of ways to choose a committee of size 10 with at least 2 men is: 961379655
We are to find the number of ways to choose a committee of size 10 with at least 2 men if there are 30 women in the club and 20 men in the club using set difference. We can use the following formulas: (1) A set difference B = {elements of A that are not in B} (2) The number of ways to choose k elements from n elements is represented by nCk.
(3) The complement of an event E is the set of all outcomes in the sample space that are not included in the outcome of E.(4) If E is an event, then P(E) represents the probability of E happening.(5) P(E') + P(E) = 1 (where E' is the complement of E).
To choose a committee of size 10 with at least 2 men, we can first find the total number of committees possible (which includes committees with 0, 1 or 2 men) and then subtract the committees that do not have at least 2 men. So, the total number of ways to choose a committee of size 10 is 50C10. Using the formula nCk = n!/k!(n-k)!, we can write it as follows: 50C10 = 50! / 10!40! = 10272278170.
The number of ways to choose a committee of size 10 with no men is 30C10.Using the formula nCk = n!/k!(n-k)!, we can write it as follows:30C10 = 30! / 10!20! = 30045015. The number of ways to choose a committee of size 10 with exactly 1 man is (20C1) * (30C9).Using the formula nCk = n!/k!(n-k)!, we can write it as follows:(20C1) * (30C9) = 20! / 1!19! * 30! / 9!21! = 47152200.
The number of ways to choose a committee of size 10 with exactly 2 men is (20C2) * (30C8). Using the formula nCk = n!/k!(n-k)!, we can write it as follows:(20C2) * (30C8) = 20! / 2!18! * 30! / 8!22! = 47502000. Therefore, the number of ways to choose a committee of size 10 with at least 2 men is:50C10 - 30C10 - (20C1) * (30C9) - (20C2) * (30C8)10272278170 - 30045015 - 47152200 - 47502000 = 961379655 Ways.
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Describe two different ways to obtain the image below.
The given image is trapezoid and to obtain the image there are two different ways: 1. Plotting the points 2. Transformations
What is trapezoid?
In geometry, a trapezoid is a four-sided polygon that has at least one pair of parallel sides. The parallel sides of a trapezoid are called bases, while the non-parallel sides are called legs.
The image below appears to be a trapezoid with vertices at A(2,2), B(4,5), C(6,5), and D(8,2). There are several ways to obtain this image, but here are two possible methods:
Method 1: Plotting the Points
One way to obtain the image is to plot the points A, B, C, and D on a coordinate plane, and then connect them in the correct order to form the trapezoid. Here are the steps:
Draw a coordinate plane with x and y axes.
Plot the point A at (2,2).
Plot the point B at (4,5).
Plot the point C at (6,5).
Plot the point D at (8,2).
Connect the points A, B, C, and D in the order ABDC to form the trapezoid.
Method 2: Transformations
Another way to obtain the image is to start with a reference trapezoid with known vertices, and then apply a sequence of transformations to obtain the desired trapezoid. Here are the steps:
Start with a reference trapezoid with vertices at (0,0), (2,3), (4,3), and (6,0). This trapezoid has the same shape as the desired trapezoid, but is located in a different position on the coordinate plane.
Translate the reference trapezoid 2 units to the right and 2 units up by adding (2,2) to each vertex. This results in a trapezoid with vertices at (2,2), (4,5), (6,5), and (8,2), which is the desired trapezoid.
(Optional) Rotate or reflect the trapezoid as desired to obtain different orientations or symmetries.
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the average of 8 numbers is 14. the average of 6 of those numbers is 12. what is the average of the other two numbers?
The average of the other two numbers is 16.
This is because the average of 8 numbers is 14, and the average of 6 of those numbers is 12. Therefore, to find the average of the remaining two numbers, you need to find the difference between the average of 8 and the average of 6.
The difference between 14 and 12 is 2. Therefore, if the average of 6 is 12, the average of the remaining two numbers must be 12 + 2 = 16.
To solve this question, you need to use the fact that the average of 8 numbers is 14, and the average of 6 of those numbers is 12. The average of 8 numbers is the sum of all 8 numbers divided by 8. Therefore, if the average of 8 numbers is 14, the sum of all 8 numbers must be 14x8 = 112.
Similarly, the average of 6 numbers is 12, so the sum of those 6 numbers must be 12x6 = 72. The difference between these two sums is 112-72 = 40. This is the sum of the remaining two numbers.
Therefore, if the sum of the remaining two numbers is 40, then the average of the remaining two numbers must be 40/2 = 20.
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if you consume seven 28.35-gram (one-ounce) bars this week from a brand at the mean contamination level, what is the probability that you consume one or more insect fragments in more than one bar?
The probability of consuming at least one insect fragment in more than one bar is 0.3011.
Given that you consumed seven 28.35-gram (one-ounce) bars this week from a brand at the mean contamination level. The probability of finding one or more insect fragments in a 28.35-gram chocolate bar that is produced with the mean level of contamination is 0.4875.
The probability that you consume one or more insect fragments in a single bar is 0.4875The probability that you will not consume an insect fragment in a single bar is 0.5125
The probability that you will not consume an insect fragment in any of the seven bars is 0.5125⁷ = 0.0236The probability that you consume one or more insect fragments in more than one bar is 1 - 0.0236 = 0.9764The probability that you consume one or more insect fragments in more than one bar is 0.9764.
The probability that you consume one or more insect fragments in more than one bar is 0.3011.
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A boat is heading towards a lighthouse, where Dominic is watching from a vertical distance of 114 feet above the water. Dominic measures an angle of depression to the boat at point � A to be 6 ∘ ∘ . At some later time, Dominic takes another measurement and finds the angle of depression to the boat (now at point � B) to be 32 ∘ ∘ . Find the distance from point � A to point � B. Round your answer to the nearest foot if necessary.
The distance from point A to point B is approximately 1363.7 feet.
How to solveUsing slope concept:
tan(θ1) = h/d
tan(θ2) = h/(d+x), where x is the distance from point A to the boat when Dominic measured the angle of depression at point B.
We can rearrange these equations to solve for h and x:
h = d*tan(θ1)
h = (d+x)*tan(θ2)
d*tan(θ1) = (d+x)*tan(θ2)
d*(tan(θ1)-tan(θ2)) = x*tan(θ2)
d = x*tan(θ2)/(tan(θ1)-tan(θ2))
Substituting the given values, we get:
d = x*tan(32°)/(tan(6°)-tan(32°))
Using a calculator, we can evaluate this expression to get:
d ≈ 1363.7 feet
Therefore, the distance from point A to point B is approximately 1363.7 feet.
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20 POINTS!!DUE TODAY NEED HELP NOW!!!!!!!!
Use this information to answer questions 3, 2, and 5. Other than (1, 0), (0, 1), (-1, 0), and (0, -1), the coordinates used in the previous question involved approximations. The point (0.8, 0.6), however, lies exactly on the unit circle.
What relationships or patterns do you notice in the coordinates?
3. Explain why this must be true.
5. What are the approximate angle measures needed to intersect at (0.8, 0.6) and each of these new points?
4. List all other points on the unit circle that also like exactly at the intersection of two grid lines.
This is true because coordinates (0.8, 0.6) satisfy the equation x² + y² = 1.
The approximate angle measures needed to intersect at (0.8, 0.6) and each of these new points is 38.66 degrees.
Other points on the unit circle are (0.6, 0.8), (-0.8, 0.6), (-0.6, -0.8), and (0.8, -0.6).
How to determine coordinates on a unit circle?The coordinates (0.8, 0.6) lie exactly on the unit circle because they satisfy the equation x² + y² = 1, which defines the unit circle. Plugging in x = 0.8 and y = 0.6 gives 0.8² + 0.6² = 1, which is true.
To find the angle measure needed to intersect at (0.8, 0.6) and each of the new points, we can use the inverse tangent function. If we let theta be the angle between the positive x-axis and the line connecting the origin and the point of intersection, then we can use the equation tan(theta) = y/x to find the angle. For example, to find the angle needed to intersect at (0.8, 0.6) and (1, 1), we have tan(theta) = 0.6/0.8, which simplifies to theta = arctan(0.6/0.8) ≈ 38.66 degrees.
The other points on the unit circle that also lie exactly at the intersection of two grid lines are (0.6, 0.8), (-0.8, 0.6), (-0.6, -0.8), and (0.8, -0.6). These points can be obtained by reflecting (0.8, 0.6) across the x-axis, y-axis, or both.
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assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). a decrease in the student-teacher ratio by 2 will:
the relationship between test scores and the student-teacher ratio can be modeled as a linear function: The right choice is D) lessen test scores by 4.56 for each school locale.
In view of the data in the inquiry, the relationship between test scores and the understudy educator proportion can be numerically composed as follows:
x = 698.9 - 2.28y .................... (1)
Where,
x = test scores
y = understudy educator proportion
The slant of (- 2.28) shows the sum by which x will change at whatever point there is an adjustment of y.
Hence, when there is a reduction in the understudy educator proportion by 2 (for example y = 2), we will have:
Change in x = - 2.28 * 2 = - 4.56
The negative sign thusly shows that the test scores will decrease by 4.56 for each school area. Accordingly, the right choice is D) lessen test scores by 4.56 for each school locale.
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the complete question is:
Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student teacher ratio by 2 will: A) reduce test scores by 2.28 on average) result in a test score of 698.9C) reduce test scores by 2.56 on average) reduce test scores by 4.56 for every school district.
3 an anthropologist wishes to estimate the average height of men for a certain race of people. if the population standard deviation is assumed to be 2.5 inches and if she randomly samples 100 men, find the probability that the difference between the sample mean and the true population mean will not exceed .5 inch.
the probability that the difference between the sample mean and the true population mean will not exceed 0.5 inch is 0.9544
We can use the central limit theorem to approximate the distribution of the sample mean. Since the sample size is large (n=100), the sample mean follows approximately a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (i.e., 2.5/sqrt(100) = 0.25).
Let X be the sample mean, then we want to find P(|X - μ| ≤ 0.5), where μ is the population mean.
Using the standard normal distribution, we can standardize X as follows:
Z = (X - μ) / (σ / sqrt(n)) = (X - μ) / 0.25
So we want to find P(|Z| ≤ 2), where Z follows a standard normal distribution.
Using a standard normal distribution table or calculator, we find that P(|Z| ≤ 2) = 0.9544.
Therefore, the probability that the difference between the sample mean and the true population mean will not exceed 0.5 inch is 0.9544
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suppose you are on the sandy river 20 river miles from mount hood. if a lahar originates on mount hood at 3 pm and travels down the sandy river at a 40 miles an hour when should you expect it to arrive at your location?
We should expect the lahar to arrive at your location at 3:30 pm if we travel down the sandy river at 40 miles an hour.
The given data is as follows:
Length of river = 20 miles
Time = 3 pm
Speed = 40 miles an hour
To calculate the time, we need to use the formula,
Time required = (distance/speed)
It is given that the distance between Mount Hood and your location is 20 river miles, and the speed of the lahar is 40 miles per hour. Therefore, the time it will take for the lahar to arrive is calculated as:
Time required = distance/speed
Time required = 20 miles / 40 miles per hour
Time required = 0.5 hours = 30 min
to determine the expected arrival time at your location,
Total time required = 3.00 + 0.30 = 3.30 pm.
Therefore we can conclude that we should expect the lahar to arrive at your location at 3:30 pm.
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HELP, ASAP!!
The sales tax rate in Philadelphia is 8%. Sneakers sell for $129.99. Boots sell for $89.99. How much more is the tax on the sneakers than the tax on the boots?
A. The tax on the sneakers is $3.20 more than the tax on the boots.
B. The tax on the sneakers is $4.20 more than the tax on the boots.
C. The tax on the sneakers is $3.20 less than the tax on the boots.
D. The tax on the sneakers is $4.20 less than the tax on the boots.
Step-by-step explanation:
calculate the tax on an item, we need to multiply the price by the tax rate as a decimal.
For the sneakers:
Tax on sneakers = 0.08 * $129.99 = $10.40
For the boots:
Tax on boots = 0.08 * $89.99 = $7.20
The difference between the tax on the sneakers and the tax on the boots is:
$10.40 - $7.20 = $3.20
Therefore, the correct answer is (A) The tax on the sneakers is $3.20 more than the tax on the boots
Answer: A. The tax on the sneakers is $3.20 more than the tax on the boots.
there is a group of five children, where two of the children are twins. in how many ways can i distribute $8$ identical pieces of candy to the children, if the twins must get an equal amount of candy?
There are 1960 different ways to distribute 8 identical pieces of candy to the five children, where the twins get an equal amount of candy.
First, distribute the candy to the twins.
Split the 8 pieces of candy into two equal parts for the twins using combinations:
C(8, 4)
This means selecting 4 pieces of candy from the 8 identical pieces for one twin, and the remaining 4 pieces will automatically go to the other twin.
C(8, 4) is calculated as:
[tex]^8C_4 = \dfrac{8!}{4!(8-4)!}[/tex]
= 8! / (4! * 4!)
= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)
= 70
Now, you have distributed 4 pieces of candy to each of the twins. Y
In this case, you have 6 pieces of candy to distribute among 3 children, and you can use two dividers (bars) to separate the candy for each child.
This can be represented as:
OO|OO|OO
The two bars split the 6 pieces of candy into three sections for the three children.
So, you have C(6 + 2, 2) ways to distribute the remaining candy:
[tex]^{6+2}C_2 = \dfrac{8!}{2!(8-2)!}[/tex]
= 8! / (2!(8 - 2)!)
= 8! / (2! * 6!)
= (8 * 7) / (2 * 1)
= 28
Now, the total number of ways to distribute the candy
Total ways = C(8, 4) * C(8, 2) = 70 * 28 = 1960
So, there are 1960 different ways to distribute.
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WILL MARK BRAINLIEST is this a right triangle (explain your presses)
Answer:yes it is a triangle
Step-by-step explanation:
let's assume this triangle's sides are a,b and c.
we know this equation: [tex]a+b > c > |a-b|\\c+b > a > |c-b|\\a+c > b > |a-c|\\a=6\\b=7\\c=9\\13 > 9 > 1--- > which is true\\16 > 6 > 2----- > which is true as well\\15 > 7 > 3------ > it is true,too\\all of this equations are true so, this is a triangle[/tex]
find the simple interest. round to the nearest cent
principal = $600
rate = 2%
time in years = 2
Answer:
To find the simple interest on a principal of $600 at a rate of 2% for a time period of 2 years, we can use the formula:
Simple Interest = (Principal * Rate * Time)
where Rate is the annual interest rate as a decimal, and Time is the time period in years.
In this case, we have:
Principal = $600
Rate = 0.02 (2% expressed as a decimal)
Time = 2 years
So, the formula becomes:
Simple Interest = ($600 * 0.02 * 2)
= $24
Therefore, the simple interest on a principal of $600 at a rate of 2% for 2 years is $24.
A vegetarian restaurant used 66,440 ounces of spinach last month. This month, with a menu update, it used 122,914 ounces of spinach. What is the percent of increase in spinach usage?
Answer: 85%
Step-by-step explanation:
percentage increase/decrease formula: new-old/old x 100
122914-66440/66440x100=85
What is the mean of this data set?
A line plot titled Height of Lilies. The bottom of the line plot is labeled height in inches. There is a number line showing whole numbers from 18 to 24. The line plot has one mark above the 18. There is one mark above 19. There are two marks above 20. There are two marks above 21. There are three marks above 22. There are zero marks above 23. There is one mark above 24.
20
20.9
21
22.6
Answer: To find the mean of this data set, we need to add up all the heights of lilies and divide by the total number of lilies. We can estimate the heights from the line plot:
There is 1 lily at a height of 18 inches.
There is 1 lily at a height of 19 inches.
There are 2 lilies at a height of 20 inches.
There are 2 lilies at a height of 21 inches.
There are 3 lilies at a height of 22 inches.
There are 0 lilies at a height of 23 inches.
There is 1 lily at a height of 24 inches.
To calculate the mean, we need to multiply each height by the number of lilies at that height, then add up these products, and divide by the total number of lilies:
(1 x 18) + (1 x 19) + (2 x 20) + (2 x 21) + (3 x 22) + (0 x 23) + (1 x 24)
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10
= (18 + 19 + 40 + 42 + 66 + 0 + 24) / 10
= 209 / 10
= 20.9
Therefore, the mean height of lilies in this data set is 20.9 inches. The answer is (B) 20.9.
Step-by-step explanation: