Therefore, the probability that [tex]X + Y < 2900 is 0.98.[/tex]
P[tex](X + Y < 2900) = 0.98.[/tex]
To calculate the probability, we need to use the joint probability density function of X and Y, given as f(xy) = 6 × 10^(-6) exp(-0.001x-0002y) for x < y.
We can then use the integral equation to solve this equation:
[tex]P(X + Y < 2900) = ∫02900∫x2900-x 6×10-6exp(-0.001x - 0.0002y)dydx[/tex]
The integral yields:
P(X + Y < 2900) = 0.98.
for such more questions on density function
https://brainly.com/question/15714810
#SPJ11
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.
Learn more on unit circles here: https://brainly.com/question/23989157
#SPJ1
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.
To learn more about the time required
https://brainly.com/question/30697591
#SPJ4
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.
Know more about the volume of cylinder
https://brainly.com/question/23935577
#SPJ1
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
Learn more about area in: https://brainly.com/question/27683633
#SPJ1
a gallon of water weighs pounds. the rhoads family has a round, -foot diameter, above-ground pool. how much weight is added to the pool when it is filled with gallons of water?
When the Rhoads family fills their above-ground pool with approximately 3,205 gallons of water, they add a weight of approximately 503,432.61 pounds to the pool.
We can use the given weight of water per gallon to find the total weight of water added to the pool:
Weight of 1 gallon of water = 8.34 pounds
Number of gallons of water in the pool = 3,205 gallons
Radius of the pool = 6 feet (half of the diameter)
Volume of the pool = π × (Radius)^2 × Depth
The depth of the pool is not given, so let's assume it is 4 feet (a common depth for above-ground pools):
Volume of the pool = π × (6 feet)^2 × 4 feet
Volume of the pool ≈ 452.39 cubic feet
Number of gallons of water in the pool = Volume of the pool ÷ 7.48
Number of gallons of water in the pool ≈ 60,381.71 gallons
Total weight of water added to the pool = Weight of 1 gallon of water × Number of gallons of water in the pool
Total weight of water added to the pool ≈ 503,432.61 pounds
To know more about water weighs:
https://brainly.com/question/29258274
#SPJ4
_____The given question is incomplete, the complete question is given below:
A gallon of water weighs 8.34 pounds. The Rhoads family has a round, 12-foot diameter, above-ground pool. How much weight is added to the pool when it is filled with 3, 205 gallons of water?
studies have shown that bats can consume an average of 10 mosquitoes per minute. what is the probability that a bat does not consume any mosquitoes in a 30-second interval?
The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.
In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.
To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:
Average rate for 1 minute = 10 mosquitoes
Rate for 30 seconds = [tex]\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}[/tex]
= 5 mosquitoes
The Poisson distribution probability mass function is given by:
[tex]\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \][/tex]
Where:
[tex]\(\lambda\)[/tex] is the average rate of events.
In this case, to find the probability that k = 0.
So, let's plug in the values:
[tex]\(\lambda = 5\)[/tex]
[tex]\(k = 0\)[/tex], back to the formula as
[tex]\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \][/tex]
Calculating the probability as
[tex]\[ P(X = 0) = e^{-5}[/tex]
[tex]= 0.0067379[/tex]
Therefore, the probability is 0.0067379 or 0.67%.
Learn more about Probability here:
https://brainly.com/question/34689735
#SPJ12
5) The graph of the equation y = −3x - 5 is shown below. What would happen to the graph if the slope was changed to 1?
Answer:
The equation y = -3x - 5 represents a linear function with a slope of -3 and a y-intercept of -5.
To understand what would happen to the graph if the slope was changed to 1, we need to compare the graphs of y = -3x - 5 and y = x - b, where b is some constant.
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. So, when we change the slope of the equation y = -3x - 5 to 1, we get:
y = x - b
To find the value of b, we can substitute the coordinates of any point on the line. Let's use the y-intercept, which is -5:
-5 = 1(0) - b
b = -(-5)
b = 5
Therefore, the equation y = x - 5 represents the line with a slope of 1 and a y-intercept of 5.
To compare the graphs of y = -3x - 5 and y = x - 5, we can graph both equations on the same coordinate plane. Here's what the two graphs look like:
Graph of y = -3x - 5 (slope = -3, y-intercept = -5):
|
-5| x
| x
| x
| x
| x
| x
x---------------
-3 -2 -1 0 1 2 3
Graph of y = x - 5 (slope = 1, y-intercept = 5):
|
5| x
| x
| x
| x
| x
| x
x---------------
-5 -4 -3 -2 -1 0 1 2 3
As we can see, changing the slope of the equation from -3 to 1 rotates the line counterclockwise and makes it steeper. The y-intercept remains the same at -5.
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.
To learn more about trapezoid visit:
https://brainly.com/question/1410008
#SPJ1
the survey of 72 students about their favourite fruit apple banana guava grapes 12 18 6 36. draw a circle and divide it into 12 parts and represent the data given as a pie chart .
The slice for apple will have an angle of 60 degrees, the slice for banana will have an angle of 90 degrees, the slice for guava will have an angle of 30 degrees, and the slice for grapes will have an angle of 180 degrees.
What is pie chart?A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice is proportional to the quantity it represents. Pie charts are commonly used in business, media, and other fields to represent percentages, ratios, and proportions. They are useful for quickly understanding the relative sizes of different categories or groups in a dataset.
Here,
To create a pie chart from the given data, we first need to calculate the angle of each slice of the pie chart. To do this, we use the following formula:
Angle for a slice = (Frequency of the category ÷ Total frequency) × 360°
Using the given data, we can calculate the angle of each slice as follows:
Angle for apple = (12 ÷ 72) × 360° = 60°
Angle for banana = (18 ÷ 72) × 360° = 90°
Angle for guava = (6 ÷ 72) × 360° = 30°
Angle for grapes = (36 ÷ 72) × 360° = 180°
Now, we can draw a circle and divide it into 12 parts (each representing 30 degrees). Then, we can draw the slices of the pie chart using the angles we calculated above.
To know more about pie chart,
https://brainly.com/question/29148468
#SPJ1
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.
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.
To know more about Height:
https://brainly.com/question/25961201
#SPJ4
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
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.
To know more about probability refer here:
https://brainly.com/question/1596693#
#SPJ11
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.
To know more about average click on below link:
https://brainly.com/question/24057012#
#SPJ11
Each of the 17 guinea pigs needs its cage cleaned. If it takes 1 hour to clean 4 cages, how many hours will it take to clean all 17 cages?
It will take
hours to clean all the cages.
Answer:
Step-by-step explanation:
4 hours and 30 minutes
. 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...............
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]
Ms. Leon opened a savings
account with an initial deposit
of $750 and will not make any more
deposits or withdrawals. The account
earns 3% simple interest.
What is the total amount that
Ms. Leon will have in her account at
the end of 4 years?
Answer: $840
Step-by-step explanation:
The formula for calculating simple interest is:
I = P * r * t
where:
I is the interest earned
P is the principal (the initial deposit)
r is the interest rate (as a decimal)
t is the time (in years)
Using this formula, we can find the interest earned on Ms. Leon's account over 4 years:
I = 750 * 0.03 * 4
I = 90
So Ms. Leon will earn $90 in interest over 4 years. To find the total amount in her account at the end of 4 years, we need to add the interest earned to the initial deposit:
Total amount = Initial deposit + Interest earned
Total amount = 750 + 90
Total amount = $840
Therefore, Ms. Leon will have a total of $840 in her savings account at the end of 4 years.
Factorise p²q-pr²-pq+r²
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.
To know more about probability refer here:
https://brainly.com/question/30034780
#SPJ11
suppose there exists a hamming code of length 25 that corrects 2 errors. assuming that the probability of a correct transmission of an individual symbol is 0.75, find the probability that a message transmitted using this code will be correctly received.
The probability that a message transmitted using a Hamming code of length 25 and that corrects 2 errors will be correctly received is 0.6384.
Hamming codes use parity bits to detect and correct errors in the data. In this case, a code of length 25 with 2 error corrections can detect up to two errors and can correct up to one error.
Since the probability of a correct transmission of an individual symbol is 0.75, the probability of a correct transmission of the entire message is calculated by multiplying 0.75 by itself 25 times, giving a probability of 0.6384.
To know more about Hamming code click on below link:
https://brainly.com/question/9962581#
#SPJ11
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.
To know more about tangent line visit:
https://brainly.com/question/30162653
#SPJ9
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.
Know more about the slope of line
https://brainly.com/question/16949303
#SPJ1
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.
Can someone help I’ll give 10 points
Answer:
Hey Sweetheart!
z=4
4x4x4= 64
Hope this Helps!!!
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.
Learn more about Combination here:
https://brainly.com/question/29595163
#SPJ12
Suppose the central perk coffee shop sells a cup of espresso for two dollars in a cup of cappuccino for $2. 50 on Friday. Destiny sold 30 more cups of cappuccino then espresso for a total of $178. 50 worth of espresso and cappuccino how many cups of each month old
Destiny sold 23 cups of espresso and 53 cups of cappuccino on Friday, for a total sales amount of $178.50.
Let's start by defining our variables. Let x be the number of cups of espresso sold and y be the number of cups of cappuccino sold. We know that the price of espresso is $2 per cup and the price of cappuccino is $2.50 per cup. We also know that Destiny sold 30 more cups of cappuccino than espresso and the total sales amount was $178.50.
Using this information, we can create a system of equations to solve for x and y. The first equation comes from the fact that Destiny sold 30 more cups of cappuccino than espresso:
y = x + 30
The second equation comes from the total sales amount:
2x + 2.5y = 178.5
Now we can substitute the first equation into the second equation and solve for x:
2x + 2.5(x + 30) = 178.5
2x + 2.5x + 75 = 178.5
4.5x = 103.5
x = 23
So Destiny sold 23 cups of espresso. Using the first equation, we can find that she sold 53 cups of cappuccino:
y = x + 30
y = 23 + 30
y = 53
Therefore, Destiny sold 23 cups of espresso and 53 cups of cappuccino on Friday, for a total sales amount of $178.50.
To know more about total sales amount click here:
brainly.com/question/13571917
#SPJ4
Find the missing angle measure of the right triangle. Show all work. Round to the nearest tenth.
The missing angle measures 139 degrees.
what is triangle?
A triangle is a polygon that has three sides, three angles, and three vertices. It is a two-dimensional figure that is formed by connecting three non-collinear points. The three sides of a triangle can be of different lengths or the same length, and the angles can also vary in size. The sum of the three angles of a triangle always adds up to 180 degrees. Triangles can be classified based on their side lengths and angle measurements.
In a right triangle, the sum of the two acute angles is always equal to 90 degrees. Therefore, we can find the missing angle by subtracting the two given angles from 90 degrees.
Let's call the missing angle "x". Then we have:
x + 21 + 20 = 180 (the sum of angles in any triangle is 180 degrees)
x = 180 - 21 - 20
x = 139 degrees
Therefore, the missing angle measures 139 degrees.
To learn more about triangles from the given link: brainly.com/question/2773823
#SPJ1
Translate the figure 5 units left and 5 units up. -10-9 Plot all of the points of the translated figure. You may click a plotted point to delete it.
I hoped this helped!
: )
Step-by-step explanation:
originally - (6,-1) After translation - (1,4)
originally - (8,-1) After translation - (3,4)
originally - (4,-7) After translation - (-1,-2)
originally - (7,-9) After translation - (3,-4)
originally - (9,-9) After translation - (4,-4)
at 3:25 p.m., two trains left kalamazoo, michigan. one train traveled westward at a constant rate of
When they are 111 miles apart, the current time is 4:10 p.m.
If the time taken for two trains to be apart by 111 miles by "t" time.
Then at that time, t, the train which is at 82 mph, should have traveled a distance of 82T miles.
d1 = 82t
At the same time, t, the train which is at 66 mph, should have traveled a distance of 66T miles.
d2= 66t
The total distance traveled by both trains is d1 + d2 = D
D = 82t + 66t
D = 148t
From the given data, D = 111
Hence, 148t = 111
Solving the equation, the time t
t = 111÷148
t = 0.75
Converting it into minutes,
t = 0.75*60
t = 45 mins.
The current time ( T ) = the time at which both the trains left ( t1 ) + 45 mins.
T = t1+t
T = 3:25 + 45 min.
T =4:10 pm
Therefore, the current time is 4:10 p.m
To know about Time traveled problems:
https://brainly.com/question/2854969
The complete question is-
At 3:25 p.m., two trains left Kalamazoo, Michigan. one train traveled westward at a constant rate of 82 miles per hour, while the other traveled eastward at a constant rate of 66 miles per hour. if they are now 111 miles apart, what time is it now? show your work on how you solved this situation.
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.