The expected values are 60 blues, 30 reds and 30 greens
Which amount would you expect to pull?From the question, we have the following parameters that can be used in our computation:
6 blue cubes, 3 red cubes, and 3 green cubes
This means that we have the following proportions
Blue = 6/(6 + 3 + 3) = 1/2
Red = 3/(6 + 3 + 3) = 1/4
Green = 3/(6 + 3 + 3) = 1/4
If you draw a cube and replace it in the bag 120 times, we have
Blue = 1/2 * 120 = 60
Red = 1/4 * 120 = 30
Green = 1/4 * 120 = 30
Hence, the expected values are 60 blues, 30 reds and 30 greens
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Here is question 5 of 6. Thank you for the help
The critical value for a two-tailed test at the 0.05 significance level is 1.96.
The null hypothesis is that there is no difference in the proportion of men and women intending to vote for Donald Trump, and the alternative hypothesis is that there is a difference.
The test statistic is given by:
z = (p1 - p2) /√[(p×(1-p)×(1/n1 + 1/n2),
where p = (x1 + x2) / (n1 + n2) and x1 and x2 are the number of successes in samples 1 and 2 respectively, and n1 and n2 are the sample sizes of samples 1 and 2 respectively.
In this case, x1 = 120, x2 = 132, n1 = 250, and n2 = 240.
Plugging these values into the equation gives us z = 0.906.
Since the test statistic does not exceed the critical value, we fail to reject the null hypothesis. That is, there is not convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the 0.05 significance level.
Therefore, the critical value for a two-tailed test at the 0.05 significance level is 1.96.
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If all real numbers satisfy the inequality, select all real numbers. If no real numbers satisfies the inequality, select no solution.
how can you tell if it's all real numbers or if no real numbers.
The solution to the inequality is x >= -2 for inequality 3x-5≥-11
The given inequality is 3x-5≥-11
Three times of x greater than or equal to minus eleven
x is the variable
3x - 5≥ -11:
Adding 5 to both sides, we get:
3x ≥ -6
Dividing both sides by 3, we get:
solution is x≥-2
Therefore, the solution to the inequality is x >= -2.
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what two numbers multiply to 48 and add to -7?
Thus the numbers that we are looking for are 8 and -6.
What are the numbers?We would have to use a method in which we would call the numbers that we want to find x and y.
We know that we have to solve the problem as a simultaneous equation so that we can be able to obtain the numbers that we seek.
If
xy = -48 ---(1)
x + y =2 --- (2)
y = -48/x ---(3)
Substitute (3) into (2)
x - 48/x = 2
x^2 - 48 = 2x
x^2 -2x - 48 = 0
x = 8 and x = -6
Thus;
8 + y = 2
y = -6
Or
-6 + y = 2
y = 8
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Missing parts:
What numbers multiply to -48 and add to 2 at the same time
*Help time limit*
Tell me the domain and range
Tell me if the graph is a function or not.
A. Yes
B. No
C. x<=-3
D. All real numbers
E. x>=-3
F. y>=0
G. All real number
H. y<8
The graph is a function: A. yes
The domain of this function is: E. x ≥ -3.
The range of this function: G. all real numbers.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.
Range = {-∞, ∞} or all real numbers.
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If two angles are complementary then the sum of their measures is _______.
(Answer with a number ONLY)
If the two angles are complementary, then their sum is 90 degrees.
The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
If the two angles are complementary, then their sum is 90 degrees.
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Determine the relationship between the lengths of AB and BC. Please help
The relation between lengths of AB and BC are,
⇒ Lenght of AB and BC are different.
We have to given that;
Triangles ABD and BDC are given.
Here, All the angles of a triangle ABD are different from angles of BDC.
Hence, We get;
Both triangle ABD and BDC are congruent.
So, All the sides of ΔABD are different from the sides of different from ΔBDC.
Hence, Lenght of AB and BC are different.
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Sum of vectors a+b pick one of answer choices
Answer:
< - 1, 5 >
Step-by-step explanation:
a = < - 5, 2 >
b = < 4, 3 >
a + b
= < - 5, 2 > + < 4, 3 >
add corresponding elements
= < - 5 + 4, 2 + 3 >
= < - 1, 5 >
Question 4
A is at -6 and B is at 9. Find the point, T, so that T is three-fifths of the distance from A to B.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2 3 4 5 6 7 8 9 10
The location of point T on the number line is 3
Calculating the location of point TFrom the question, we have the following parameters that can be used in our computation:
A = -6
B = 9
T = three-fifths of the distance from A to B.
Using the above as a guide, we have the following:
T = A + 3/5 *(B - A)
Substitute the known values in the above equation, so, we have the following representation
T = -6 + 3/5 *(9 + 6)
Evaluate
T = 3
Hence, the location is 3
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Solve for circle theorem
The requried measure of the angles is given as:
(1) ∠OLQ = 32, (2) ∠NQP = 38°, (3) ∠NLP = 38°, and (4) ∠NPL = 52°.
As shown in the figure,
(1) Following the property of angle subtended by an arc on the center of the circle and at a point on the circumference of a circle,
∠OLQ = ∠OQL = 64/2 = 32°.
(2)
Following the figure,
∠NQP = ∠LQP - ∠LQN
= ∠LQP-[∠OQL+∠MQN]
= 90 - [32+20]
= 38°
Similarly,
∠NLP = 38°
∠NPL = 52°
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Calculator
What is the volume of this figure?
Enter your answer in the box.
ft³
4
3 ft
5 ft
6 ft
7 ft
2 ft
The volume of the solid figure is 75 ft³
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The volume of a figure is the amount of space it occupies in its three dimensional state.
To get the surface area:
Area of base = (6 ft * 2 ft) + (7 - 6)ft * 3 ft = 15 ft²
Volume of figure = area of base * height = 15 ft² * 5 ft = 75 ft³
The volume of the figure is 75 ft³
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Two stores are selling the same video game and both are having a sale. Store 1 is selling the game for $45.99 with a 15% discount. Store 2 is selling the game for $ 52.99 with a 20% discount. Which store should you purchase the game from to get the best deal?
well, presumably the best deal is the cheaper one, so let's check how much is it for each
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 45.99}}{\left( \cfrac{15}{100} \right)45.99} ~~ \approx ~~ 6.90\hspace{5em}\underset{ Store~1 }{\stackrel{ 45.99~~ - ~~6.90 }{\approx\text{\LARGE 39.09}}}\checkmark \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em} \stackrel{\textit{20\% of 52.99}}{\left( \cfrac{20}{100} \right)52.99} ~~ \approx ~~ 10.60\hspace{4em}\underset{ Store~2 }{\stackrel{ 52.99~~ - ~~10.60 }{\approx\text{\LARGE 42.39}}}[/tex]
Find the dot product for the pair of vectors
The result of -3u + 5v is the vector (12, -34).
Let's start by defining the two given vectors u and v:
u = (1, 3)
v = (3, -5)
To find the dot product of two vectors, we need to multiply their corresponding components and then add up the results. The formula for the dot product of two vectors can be written as:
u · v = u₁v₁ + u₂v₂ + ... + uₙvₙ
where u₁ and v₁ are the first components of vectors u and v, u₂ and v₂ are the second components, and so on up to un and vₙ, which are the nth components.
Using this formula, we can find the dot product of u and v as follows:
u · v = (1)(3) + (3)(-5)
= 3 - 15
= -12
So, the dot product of vectors u and v is -12.
Next, we need to calculate -3u + 5v. To do this, we need to multiply each component of vector u by -3 and add it to the corresponding component of vector v multiplied by 5. We can write this as follows:
-3u + 5v = (-3)(u₁, u₂) + (5)(v₁, v₂)
= (-3)(1, 3) + (5)(3, -5)
= (-3, -9) + (15, -25)
= (12, -34)
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A construction team maintains a 52 mile long sewage pipe. Each day the team can cover 4/5 of a mile. How many days will it take the team to complete the maintenance of the entire sewage pipe
It will take the team 65 days to complete the maintenance of the entire sewage pipe
How many days will it take the team to complete the maintenance of the entire sewage pipeFrom the question, we have the following parameters that can be used in our computation:
Sewage pipe = 52 miles
Distance covered each day = 4/5 miles
Using the above as a guide, we have the following:
Number of days = Sewage pipe /Distance covered each day
Substitute the known values in the above equation, so, we have the following representation
Number of days = 52/(4/5)
Evaluate the quotient
Number of days = 65
Hence, the number of days is 65
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Help plss will give brainliest and points
The new coordinates of dilated rectangle by scale factor of 1/4 are J(1, 2), K(3, 2), L(3, 1), and M(1, 1) we can draw figure.
We are given the coordinates of the vertices of a rectangle J(4,8), K(12,8), L(12,4), and M(4,4).
To dilate the rectangle by a scale factor of 1/4, we need to multiply each coordinate by 1/4.
Multiplying each x-coordinate by 1/4
x-coordinate of J: 4 * 1/4 = 1
x-coordinate of K: 12 * 1/4 = 3
x-coordinate of L: 12 * 1/4 = 3
x-coordinate of M: 4 * 1/4 = 1
Multiplying each y-coordinate by 1/4
y-coordinate of J: 8 * 1/4 = 2
y-coordinate of K: 8 * 1/4 = 2
y-coordinate of L: 4 * 1/4 = 1
y-coordinate of M: 4 * 1/4 = 1
Therefore, the coordinates of the dilated rectangle are: J(1,2), K(3,2), L(3,1), and M(1,1).
Using these new coordinates, we can draw the dilated rectangle by plotting the four vertices on a coordinate plane.
The dilated rectangle has the same shape and orientation as the original rectangle, but it has been reduced in size by a scale factor of 1/4.
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The sum of a certain infinite geometric series is $2.$ The sum of the squares of all the terms is ${}5.$ Find the common ratio.
The common ratio between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is, - 1/9
Now, We can formulate;
⇒ { a/ 1-r} = 2
And, a²/ (1 - r²) = 5
⇒ 2a/ ( 1+r ) = 5
⇒ 2(2 - 2r)/ 1 + r = 5
⇒ 4 - 4r = 5 + 5r
⇒ 9r = - 1
⇒ r = - 1/9
Thus, The common ratio between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is, - 1/9
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solve. y=2x^2+8 for the axis of symmetry and the vertex
The list represents the number of students who checked books out of the library in a 10-day period.
48, 63, 75, 40, 32, 52, 35, 68, 83, 40
Find the median and interpret its meaning as it relates to the number of students checking out books.
A. The median is 32, and it represents the difference in the lowest and highest number of students who checked books out.
B. The median is 83, and it represents the highest number of students who checked books out.
C. The median is 40, and it represents the most common number of books that students checked out.
D. The median is 50, and it represents the typical number of students who checked books out.
i need help please help its easy
The solutions for the inequality, in order from smallest to largest, are:
-7, -4, -2, 0, 0.9, 0.99, 0.999, 1
Which values make the inequality true?Here we have the inequality:
y ≤ 1
All the values that make the inequality true are the values equal or smaller than 1.
So we just need to list these in order from smaller to larger.
The correct order will be:
-7, -4, -2, 0, 0.9, 0.99, 0.999, 1
These are the solutions in order.
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Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0,2π). -2tan(-x)=5tan(x)-1
The value of solution of the equation is,
⇒ tan x = 1 / 3
We have to given that;
The expression is,
⇒ - 2 tan (-x) = 5 tan (x) - 1
Now,, We can simplify as;
⇒ - 2 tan (-x) = 5 tan (x) - 1
⇒ - 2 (- tan (x) ) = 5 tan (x) - 1
⇒ 2 tan (x) = 5 tan (x) - 1
⇒ 5 tan x - 2 tan x = 1
⇒ 3 tan x = 1
⇒ tan x = 1 / 3
Thus, The value of solution of the equation is,
⇒ tan x = 1 / 3
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A man is flying in a hot air balloon in a straight line at a constant rate of 5' per second while keeping it at a constant altitude. As he approaches the parking lot of a market. , he notices that the angle of depression from his balloon to a friend's car in the parking lot is 34ﾟ. A minute and a half later after flying directly over his friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 36ﾟ At that time what is the distance between him and his friend?
The distance is given as 272.98 feet.
What is Angle of Depression?The measurement of the angle of depression relates to the formation between a horizontal line and the observer's sightline to an object or point that exists beneath their level.
Therefore, it demonstrates the formed degree between the observer's line of vision towards a subject and the horizontal flatness visible when looking downwards at it from afar.
This notion is prevalent throughout trigonometry and play a vital role in areas including surveying, navigation and architecture. The degrees obtained from this practice are generally calculated via angles, with a complete 90-degree measure indicative of viewing straight downward over the designated target.
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Please help I need this asap
The inequality given that the function f is increasing over it s domain
f(x²-2)<f (7x-8), Df = (-∞,2) is: x ∈ (-∞,1) U (6,2).
What is the inequality?We know the values of x within the domain by setting the intersection points of the two functions f(x2-2) and f(7x-8).
f (x²-2) = f (7x-8)
So,
x²-2 = 7x-8
Simplify and find x
x² - 7x + 6 = 0
(x - 1)(x - 6) = 0
x = 1 or x = 6
The domain (-,2) is divided into the intervals (-,1), (1,6), and (6,2). Now let assess the interval endpoints because f is rising:
For x < 1:
x² - 2 < 7x - 8
x² - 7x + 6 < 0
(x - 1)(x - 6) < 0
For 1 < x < 6:
x² - 2 < 7x - 8
x² - 7x + 6 < 0
(x - 1)(x - 6) > 0
For x > 6:
x² - 2 < 7x - 8
x² - 7x + 6 < 0
(x - 1)(x - 6) < 0
Since f is rising across its domain the inequality f(x2-2) f(7x-8) has the following solution: x ∈ (-∞,1) U (6,2).
Therefore the inequality is x ∈ (-∞,1) U (6,2).
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What is the solid formed when rotated around the side length of 5?
O two cones with a radius of 2.4 units and a height of 1.8 units and 3.2 units
O two cones with a radius of 3.6 units and a height of 1.8 units and 3.2 units
O two cylinders with a radius of 2.4 units and a height of 2.6 units and 2.8 units
O two cylinders with a radius of 3.6 units and a height of 1.6 units and 2.8 units
Find the volumes and surface areas of the solids. Give your answers in terms of pi
The solid formed when the right triangle is rotated around the side length of 5 is two cones with a radius of 1.5 units and a height of 1.8 units and 3.2 units.
The volume of the smaller cone is approximately 3.82 cubic units, and the surface area is approximately 20.94 square units.
The volume of the larger cone is approximately 6.04 cubic units, and the surface area is approximately 20.94 square units.
We have,
When the right triangle is rotated around the side length of 5, it forms two cones with different heights and radii.
Now,
r = base / 2 = 3 / 2 = 1.5 units
h = height = 4 units
Using the Pythagorean theorem,
l = √(1.5² + 4²) = √(18.25) ≈ 4.27 units
The first cone has a radius of 1.5 units and a height of 1.8 units (5 - 4.27)
The second cone has a radius of 1.5 units and a height of 3.2 units (5 - 1.8).
Now,
The volume of a cone.
V = (1/3)πr^2h
The surface area of a cone.
A = πrl + πr^2
For the first cone:
V = (1/3)π(1.5)²(1.8) = 3.82 cubic units
A = π(1.5)(4.27) + π(1.5)² = 20.94 square units
For the second cone:
V = (1/3)π(1.5)²(3.2) = 6.04 cubic units
A = π(1.5)(4.27) + π(1.5)² = 20.94 square units
Thus,
The solid formed when the right triangle is rotated around the side length of 5 is two cones with a radius of 1.5 units and a height of 1.8 units and 3.2 units.
The volume of the smaller cone is approximately 3.82 cubic units, and the surface area is approximately 20.94 square units.
The volume of the larger cone is approximately 6.04 cubic units, and the surface area is approximately 20.94 square units.
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Calculate the value of x. Give your answer as an integer or as a fraction in its simplest form. 18 mm S 3 mm xmm T 10 mm8
The value of the missing length of the enlarged triangle in the simplest form would be = 60mm.
How to calculate the missing length of the triangle?To calculate the missing length, the formula for scale factor should be used such as follows;
Scale factor = Larger dimensions/smaller dimensions
length of ∆T = 10mm
length of ∆S = 3mm
scale factor = 10/3 = 3.33
If the width of ∆S = 18mm
width of ∆ T = 18×3.33
= 59.94 = 60mm
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6-Tel, Inc. is a telecommunication services provider looking to expand to a new territory Z; it is analyzing whether it should install its own telecom towers or lease them out from a prominent tower-sharing company T-share, Inc.
Leasing out 100 towers would involve payment of $5,000,000 per year for 5 years. Erecting 100 news towers would cost $18,000,000 including the cost of equipment and installation, etc. The company has to obtain a long-term secured loan of $18 million at 5% per annum. Owning a tower has some associated maintenance costs such as security, power and fueling, which amounts to $10,000 per annum per tower.
The company's tax rat is 40% while its long-term weighted average cost of debt is 6%. The tax laws allow straight-line depreciation for 5 years. Determine whether the company should erect its own towers or lease them out.
Answer:
The present value of leasing the towers is $19,576,000 while the present value of erecting new towers is $20,273,000. Therefore, the company should lease the towers.
Step-by-step explanation:
What is the range of the function f(x) = |x| + 5?
R: {f(x) ∈ ℝ | f(x) < 5}
R: {f(x) ∈ ℝ | f(x) ≥ 5}
R: {f(x) ∈ ℝ | f(x) > 5}
R: {f(x) ∈ ℝ | f(x) ≤ 5}
The range of the function f(x) = |x| + 5 include the following; B. R: {f(x) ∈ ℝ | f(x) ≥ 5}.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞} or -∞ ≤ x ≤ ∞.
Range = {5, ∞} or 5 ≤ f(x) ≤ ∞.
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I need help please to solving this problem
The height of the tower is given as follows:
h = 22.5 ft.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The reflection means that the two triangles are similar in this problem, hence the proportional relationship for the equivalent side lengths is given as follows:
3/13.5 = 5/h
Then the height is obtained as follows:
3h = 5 x 13.5
h = 5 x 13.5/3
h = 22.5 ft.
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Brenda's class took a field trip to the science museum. It took them 50 minutes to drive to the museum. They stayed at the museum for 3 hours and 45 minutes, and it took them 56 minutes to drive back to school. When the class arrived back at school, it was 3:47 P.M. What time did Brenda's class leave for the field trip?
Brenda's class left for the field trip at 10:16 A.M.
We have,
Let's break down the time of Brenda's class field trip:
50 minutes to drive to the museum
3 hours and 45 minutes (or 225 minutes) at the museum
56 minutes to drive back to school
Adding up all of these times, we get:
50 + 225 + 56 = 331 minutes
So the field trip took a total of 331 minutes.
If the class arrived back at school at 3:47 P.M., and we subtract 331 minutes from 3:47 P.M., we can determine the time they left for the field trip:
3:47 P.M. - 331 minutes
= 10:16 A.M.
Therefore,
Brenda's class left for the field trip at 10:16 A.M.
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Y= 4(x+ 3)^2 -100 I need the answerrrrr
Answer:A frequency table is a type of statistic used to organize and display data.
What is data set?
A data set is a collection of related data records or observations, usually containing information about a particular subject or area of study. Data sets can be used to analyze trends, make predictions, and provide insights into various phenomena. Data sets can be collected from a variety of sources, such as surveys, experiments, simulations, or other research methods. They are typically organized into tables and can include both quantitative and qualitative data.
It is a chart that shows how often something occurs within a given set of data. The categories in a frequency table are the different values or categories of data, and the frequencies are the number of times each category occurs.
Relative frequency is the ratio of the number of times a category occurs in the data set to the total number of values in the data set. It is usually expressed as a percentage or decimal. For example, if the data set contains 20 values and the category "A" occurs 5 times, the relative frequency of "A" is 25%.
Cumulative frequency is the sum of the frequencies up to a given point in the data set. It is used to show how many values are below or above a certain category. For example, if the data set contains 20 values and the category "A" occurs 5 times, the cumulative frequency of "A" is 5. This means that there are 5 values that are below or equal to "A" in the data set.
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A bag contains six yellow tickets numbered
one to six. The bag also contains three
green tickets numbered one to three . You
randomly pick a ticket. It is yellow or has
an odd number.
The probability of yellow or has an odd number is 8/9
Calculating the probability of yellow or has an odd number.From the question, we have the following parameters that can be used in our computation:
Green = 1 to 3
Yellow = 1 to 6
This means that
Odd = 2 + 3
Odd = 5
So, we have
P(Yellow) = 6/9
P(Odd) = 5/9
P(Yellow and Odd) = 3/9
The probability of yellow or has an odd number is
P = 6/9 + 5/9 - 3/9
Evaluate
P = 8/9
Hence, the probability is 8/9
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How do you find Exponential Decay Rate?
1+b
1-b
Answer:
Exponential decay is represented by the equation:
y = a * e^(-bx)
where:
y is the final value
a is the initial value
b is the decay rate
x is the time variable
The exponential decay rate, b, can be found by taking the natural logarithm (ln) of both sides of the equation, then rearranging to isolate the decay rate:
ln(y/a) = -bx
b = -ln(y/a)/x
So, to find the exponential decay rate, you would need to know the initial value (a), the final value (y), and the time elapsed (x). Then, you can use the formula above to calculate the decay rate, b.
The expressions "1+b" and "1-b" are not sufficient to find the exponential decay rate, as they do not contain enough information about the specific scenario or data set.
if this helps, can you please mark my answer brainliest?