Considering the Markov chain with transition matrix, the chain does have stationary distribution which exhibits State 1 is transient and the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729).
(a) Yes, the chain has a stationary distribution. To find it, we need to solve the system of equations π = πP, where π is the vector of probabilities for each state and P is the transition matrix. This gives us:
π_{1} = π(1/2)
π_{2} = π(1/3) + π(2/2)
π_{3}= π(2/4) + π(3/2)
π_{4} = π(3/5) + π(4/2)
π_{5}= π4/5
We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.
Solving this system of equations, we get:
π_{1} = 10/97
π_{2} = 30/97
π_{3}= 40/97
π_{4} = 14/97
π_{5}= 3/97
So the stationary distribution is (10/97, 30/97, 40/97, 14/97, 3/97).
(b) State 1 is transient, and all other states are recurrent.
(c) Yes, the chain still has a stationary distribution. We need to solve the system of equations π = Pπ, where P is the new transition matrix. This gives us:
π_{1} = π(1/2)
π_{2} = π(1/3) + π(2/2)
π_{3}= π(2/4) + π(3/2)
π_{4} = π(3/5) + π(4/2)
π_{5}= π4/5
We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.
Solving this system of equations, we get:
π_{1} = 2/9
π_{2} = 4/9
π_{3} = 8/27
π_{4} = 16/81
π_{5} = 32/729
So the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729)
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In a certain class of 40students, 90% passed ssce mathematics examinations and 75% passed English. If 2 students failed both mathematics and English, what percentage of students passed both examinations
30% percent of the students passed both Mathematics and English.
What is Percentage?A rate, number, or amount in each hundred is known as a percentage
Let's use a Venn diagram to represent the information given in the problem. Let M be the set of students who passed Mathematics, E be the set of students who passed English, and F be the set of students who failed both.
We know that there are 40 students in the class, and 90% passed Mathematics, so the number of students who passed Mathematics is 0.9 × 40 = 36. Similarly, 75% passed English, so the number of students who passed English is 0.75 × 40 = 30.
We also know that 2 students failed both Mathematics and English, so we can label the F section with 2.
where the number in each section represents the number of students who passed the respective exam.
To find the percentage of students who passed both examinations (i.e., the intersection of M and E), we need to add the number of students in the M and E intersection to the F section, then subtract that from the total number of students (40), and finally divide by 40 to get the percentage. That is:
percentage of students who passed both exams = (M ∩ E + F) / 40 × 100%
= (28 + 2) / 40 × 100%
= 30%
Therefore, 30% of the students passed both Mathematics and English.
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Need help with b, please show work
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with a, b, c being the sides, and A, B, C being the three corresponding opposite angles.
so, the angle at Q is
180 = 48 + 48 + angle Q = 96 + angle Q
84° = angle Q
5mm/sin(48) = PR/sin(84)
PR = 5×sin(84)/sin(48) = 6.691306064... mm
The length of PR is approximately 10.33 mm.
what is isosceles triangle ?
An isosceles triangle is a triangle with at least two sides that have equal length, and thus two corresponding angles that are also equal in measure. The third side and angle of an isosceles triangle may or may not be of different length or measure. The two sides that are equal in length are called the legs, and the third side is called the base. The angle opposite the base is called the vertex angle, while the angles adjacent to the legs are called the base angles. In an isosceles triangle, the two base angles are equal in measure.
Since the sum of the angles in a triangle is 180 degrees, we can find the measure of angle PQR as follows:
PQR = 180 - QPR - QRP
PQR = 180 - 48 - 48
PQR = 84 degrees
Since angles QRP and QPR have the same measure, we know that sides OP and OR have equal length (they are opposite those angles). Therefore, triangle POR is an isosceles triangle.
To find the length of PR, we can use the Law of Cosines:
PR^2 = OP^2 + OR^2 - 2(OP)(OR)cos(POR)
Since OP and OR are equal in length, we can simplify this equation to:
PR^2 = 2(OP^2) - 2(OP^2)cos(POR)
We know that POR is 180 - PQR = 96 degrees. We also know that OP = OR, and that QP = 5 mm. Using the Law of Cosines, we can find the length of OP:
OP^2 = QP^2 + OR^2 - 2(QP)(OR)cos(QPR)
OP^2 = 5^2 + OR^2 - 2(5)(OR)cos(48)
OP^2 = OR^2 - 5ORcos(48) + 25
Since OP = OR, we can substitute OP for OR in the above equation:
OP^2 = OP^2 - 5OPcos(48) + 25
5OPcos(48) = 25
OP = 25/(5cos(48))
OP ≈ 6.25 mm
Now we can substitute this value into the equation we derived earlier to find PR:
PR^2 = 2(OP^2) - 2(OP^2)cos(POR)
PR^2 = 2(6.25^2) - 2(6.25^2)cos(96)
PR ≈ 10.33 mm
Therefore, the length of PR is approximately 10.33 mm.
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Rina is climbing a mountain. She has not
yet reached base camp. Write an inequality
to show the remaining distance, d, in feet
she must climb to reach the peak.
The inequality that shows the remaining distance Rina must climb to reach the peak is 0 < d < P
Let's assume that the distance from Rina's current position to the peak of the mountain is "P" feet and the distance from her current position to the base camp is "B" feet.
Then, the remaining distance, "d", that she must climb to reach the peak can be calculated as follows
d = P - B
Since Rina has not yet reached the base camp, the distance she has traveled so far is less than the distance to the base camp, which means:
B > 0
Substituting this inequality in the equation for "d", we get
d = P - B < P
Therefore, the inequality that shows the remaining distance Rina must climb to reach the peak is:
0 < d < P
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1. how long is the hall which has a perimeter if 3480 cm and 300cm wide?
2. joe walks across the rotonda and travels 400meters, how many more meters will a car travel around it than the distance the pedestrian walk?
3.father will fence the rectangular yard with a length of 120m and a width of 100m,
how many meters of wire will her use for the fence?
Answer:
(3480 - 600)/2 = 1440cm
Step-by-step explanation:
Due today help pls!!!!
Answer:
32.1m
Step-by-step explanation:
[tex]2\pi r*(\frac{x}{360})=[/tex] arc length of sector of a circle
2 radii + arc length of a sector of a circle= perimeter of the sector
x=90 degrees
r=9
substitute values to find the arc length
[tex]2(9)*\pi *(\frac{90}{360} )= arc length\\arclength=14.1\\[/tex][tex]14.1+2(9)=32.1[/tex]
A bag contains 8 green cubes, 12 black cubes and 16 white cubes. What is the ratio of green to black to white cubes in its simplest form?
Answer:
Total number bags is 36
green cubes is 8white cubes is 16Black cubes is 121:2:3 the answer
Find the range of possible measures of X if the set of expressions represents measures of the sides of a triangle x, 4, 6
If the set of expressions represents measures of the sides of a triangle x, 4, 6 , the range of possible measures of x is 2 < x < 10.
To determine the range of possible measures of X if the set of expressions represents measures of the sides of a triangle x, 4, 6, we need to use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Mathematically, this can be expressed as:
x + 4 > 6
x + 6 > 4
4 + 6 > x
Simplifying these inequalities, we get:
x > 2
x > -2
x < 10
The first two inequalities indicate that x must be greater than 2, since the sum of any two sides of a triangle must be greater than the third side. The third inequality indicates that x must be less than 10, since the longest side of a triangle cannot be greater than the sum of the other two sides.
This means that x can take any value between 2 and 10, but not including 2 or 10, in order for the set of expressions to represent the measures of the sides of a triangle.
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A taxi service charges $2 for the first mile and then $1. 20 for every mile after that. The farthest the taxi will
travel is 25 miles.
If a represents the number of miles traveled, and y represents the total cost of the taxi ride, what is the most
appropriate domain for the situation?
The appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]
Explain about the linear equation?In a two-variable linear equation, x and y have a linear connection, meaning that the value of any one of the variables, y, relies upon that value of the other, x.
Cost for first mile of taxi service = $2.00
Additional cost = $1.20 per mile.
Peak distance = 25 miles.
a = number of miles traveled by taxi.
y = total cost of the taxi ride
The linear equation forms:
y = $1.20a + $2.00
When a = 0; y = $2.00
a = 25 ; y = $1.20*25 + $2.00 = 32
Thus, the appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]
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What is the solution to the equation 2.4m − 1.2 = −0.6m?
Answer:
0.4
Step-by-step explanation:
Subtract 2.4m on each side
-1.2 = -3.0m
divide by -3.0
you get 0.4
Find the surface area of the solid
The solid has a surface area of about 401.92 cm2.
How can you figure out surface area?A three-dimensional shape's surface area is the sum of all of its faces. The surface area of a shape can be calculated by finding the area of each face and combining them.
The surface areas of the cylinder and the hemisphere must be added to determine the solid's surface area.
The cylinder's surface area is equal to 2rh + 2r2, where r is the cylinder's radius and h is its height.
The hemisphere's surface area is equal to 2r2, where r is the hemisphere's radius.
As the cylinder's and hemisphere's radiuses are equal, we can sum their two surface areas as follows:
The solid's surface area is equal to 2rh plus 2r2 plus 2r2.
= 2πrh + 4πr²
Solid's surface area is equal to 2(4)(8) + 4(4)(2).
= 64π + 64π
= 128π
≈ 401.92 cm²
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1. Use algebraic methods to find where Yaseen's demand and supply functions intersect. What
does this point(s) represent in context of this problem? Show all your work.
2. Confirm your answer from question 7 by using Desmos to create a single graph that shows
both f(x) and g(x) with their domain restrictions. Provide a screenshot of your graph with the
intersection point(s) marked.
Therefore represented by the point of intersection, which is (10, 7). All products are sold at this price and quantity, clearing the market.
what is function ?A function is a mathematical concept that links an input (usually denoted by the variable x) to an output (usually denoted by the variable y or f(x)) in a well-defined way. A function can be compared to a computer that processes inputs and outputs in accordance with rules or guidelines. Each input value (also known as the domain) in a function is connected to precisely one output value (also known as the range). For instance, the linear function f(x) = 2x multiplies the input value x by two to create the output value.
given
f(x) = -0.5x + 12
The supply role is also provided by:
g(x) = 0.5x + 2
We must put these two functions equal to one another and then solve for x to determine where these two functions intersect:
-0.5x + 12 = 0.5x + 2
By multiplying both parts by 0.5, we get:
12 = x + 2
x = 10
The position at which the supply and demand functions intersect is therefore (10, f(10)) or (10, g(10)). We can enter the value x = 10 into either of the following functions to obtain the appropriate y-coordinate:
f(10) = -0.5(10) + 12 = 7
g(10) = 0.5(10) + 2 = 7
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What is the value of the expression?
1/2 ÷ 6
Answer:
0.25
Step-by-step explanation:
Answer:
1/12
Step-by-step explanation:
To solve this expression, we need to remember that division should be done before multiplication or addition/subtraction.
So we first simplify the expression by dividing 1/2 by 6:
1/2 ÷ 6 = 1/2 × 1/6
Next, we multiply the two fractions by multiplying their numerators and denominators:
1/2 × 1/6 = (1 × 1)/(2 × 6) = 1/12
Therefore, the value of the expression 1/2 ÷ 6 is equal to 1/12.
Amir and Brandon are sharing a cake they bought for 10 dollars. Half of
the cake is chocolate and half of the cake is vanilla. Amir likes chocolate
twice as much as vanilla. Brandon likes chocolate four times as much as
vanilla. They decide to use the divider-chooser method to share the cake. (a) Give a way Amir might split the cake if he’s the splitter. State which
piece Brandon would choose and how much it’s worth to him. (b) Give a way Brandon might split the cake if he’s the splitter. State
which piece Amir would choose and how much it’s worth to him
(a) If Amir is the splitter, he can divide the cake into two equal halves, offer Brandon the first choice, who will likely choose the chocolate half worth 6.67 dollars to him, and Amir will take the vanilla half worth 3.33 dollars to him.
(b) If Brandon is the splitter, he can divide the cake into two equal halves, offer Amir the first choice, who will likely choose the chocolate half worth 5 dollars to him, and Brandon will take the vanilla half worth 5 dollars to him.
(a) If Amir is the splitter, he can divide the cake into two equal halves, one chocolate and one vanilla. He can then offer Brandon the first choice of which half he wants. Since Brandon likes chocolate four times as much as vanilla, he will likely choose the chocolate half, which is worth 6.67 dollars to him (4/5 of the total value of the cake). Amir will then take the vanilla half, which is worth 3.33 dollars to him (1/5 of the total value of the cake).
(b) If Brandon is the splitter, he can divide the cake into two equal halves, one chocolate and one vanilla. He can then offer Amir the first choice of which half he wants. Since Amir likes chocolate twice as much as vanilla, he will likely choose the chocolate half, which is worth 5 dollars to him (1/2 of the total value of the cake). Brandon will then take the vanilla half, which is worth 5 dollars to him (1/2 of the total value of the cake)
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d)
1456 divided by 25
Answer:
58.24
Step-by-step explanation:
1456 ÷ 25 = 58.24
how can you make different trapezoids given two sides and one angle? draw trapezoids with side lengths of 8 yd and 5 yd and an angle of 45
A. you can make the parallel sides of each trapezoid different
B. you can make all four sides of each trapezoid different.
C. you can make all four angles of each trapezoid different.
D. all trapezoids will be the same given two sides and an angle
You can make all four sides of each trapezoid different. Since a trapezoid has four sides, we can change the length of each of the remaining two sides to create different trapezoids. option B is correct.
What is a trapezoid?A trapezoid is a four-sided polygon with two parallel sides and two non-parallel sides. It is sometimes called a trapezium outside of North America. The parallel sides of a trapezoid are called bases, while the non-parallel sides are called legs. The height of a trapezoid is the perpendicular distance between the bases. The area of a trapezoid is calculated by taking the average of the bases and multiplying it by the height. Trapezoids are commonly encountered in geometry and are used in many real-world applications, such as in construction and engineering.
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The exponential probability distribution is used with: A. A discrete random variable B. A continuous random variable C. Any probability distribution with an exponential term D. An approximation of the binomial probability distribution
The exponential probability distribution is employed with a random variable that is continuous in nature.
What do you mean by exponential probability distribution ?
In the field of probability, a probability distribution refers to a mathematical function that gives the probabilities of various possible outcomes of an experiment. The exponential probability distribution is a probability distribution that models the time between events in a Poisson process, where events occur continuously and independently at a constant average rate. It is a continuous probability distribution, meaning that the random variable takes on values within a continuous range, as opposed to a discrete probability distribution, where the random variable takes on only a finite or countable set of values.
Explanation of the correct answer :
The exponential probability distribution is defined by a single parameter, [tex]\lambda[/tex] which represents the average rate of occurrence of events in the Poisson process.
The probability density function (pdf) of the exponential distribution is given by [tex]f(x) = \lambda e^{(-\lambda x)}[/tex], where x is the time between events. The cumulative distribution function (cdf) is given by [tex]F(x) = 1 - e^{-\lambda x}[/tex].
The exponential probability distribution is used in many applications, such as queuing theory, reliability theory, and finance. For example, it can be used to model the time between customer arrivals in a queue, the time between machine failures in a manufacturing process, or the time until default on a bond.
In summary, the exponential probability distribution is a continuous probability distribution that is used with a continuous random variable, specifically to model the time between events in a Poisson process.
Hence, option B is correct.
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three fair, standard six-faced dice of different colors are rolled. in how many ways can the dice be rolled such that the sum of the numbers rolled is 10? (mathematics teacher calendar problem)
There are a total of 27 combinations that give a sum of 10 when rolling three dice.
We have,
The possible outcomes in the sample space for rolling three dice:
S = {(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 1, 5), (1, 1, 6),
(1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6),
(1, 3, 1), (1, 3, 2), (1, 3, 3), (1, 3, 4), (1, 3, 5), (1, 3, 6),
(1, 4, 1), (1, 4, 2), (1, 4, 3), (1, 4, 4), (1, 4, 5), (1, 4, 6),
(1, 5, 1), (1, 5, 2), (1, 5, 3), (1, 5, 4), (1, 5, 5), (1, 5, 6),
(1, 6, 1), (1, 6, 2), (1, 6, 3), (1, 6, 4), (1, 6, 5), (1, 6, 6),
(2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 1, 4), (2, 1, 5), (2, 1, 6),
(2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 2, 4), (2, 2, 5), (2, 2, 6),
(2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4), (2, 3, 5), (2, 3, 6),
(2, 4, 1), (2, 4, 2), (2, 4, 3), (2, 4, 4), (2, 4, 5), (2, 4, 6),
(2, 5, 1), (2, 5, 2), (2, 5, 3), (2, 5, 4), (2, 5, 5), (2, 5, 6),
(2, 6, 1), (2, 6, 2), (2, 6, 3), (2, 6, 4), (2, 6, 5), (2, 6, 6),
(3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 1, 4), (3, 1, 5), (3, 1, 6),
(3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 2, 4), (3, 2, 5), (3, 2, 6),
(3, 3, 1), (3, 3, 2), (3, 3, 3), (3, 3, 4), (3, 3, 5), (3, 3, 6),
(3, 4, 1), (3, 4, 2), (3, 4, 3), (3, 4, 4), (3, 4, 5), (3, 4, 6),
(3, 5, 1), (3, 5, 2), (3, 5, 3), (3, 5, 4), (3, 5, 5), (3, 5, 6),
(3, 6, 1), (3, 6, 2), (3, 6, 3), (3, 6, 4), (3, 6, 5), (3, 6, 6),
(4, 1, 1), (4, 1, 2), (4, 1, 3), (4, 1, 4), (4, 1, 5), (4, 1, 6),
(4, 2, 1), (4, 2, 2), (4, 2, 3), (4, 2, 4), (4, 2, 5), (4, 2, 6),
(4, 3, 1), (4, 3, 2), (4, 3, 3), (4, 3, 4), (4, 3, 5), (4, 3, 6),
(4, 4, 1), (4, 4, 2), (4, 4, 3), (4, 4, 4), (4, 4, 5), (4, 4, 6),
(4, 5, 1), (4, 5, 2), (4, 5, 3), (4, 5, 4), (4, 5, 5), (4, 5, 6),
(4, 6, 1), (4, 6, 2), (4, 6, 3), (4, 6, 4), (4, 6, 5), (4, 6, 6),
(5, 1, 1), (5, 1, 2), (5, 1, 3), (5, 1, 4), (5, 1, 5), (5, 1, 6),
(5, 2, 1), (5, 2, 2), (5, 2, 3), (5, 2, 4), (5, 2, 5), (5, 2, 6),
(5, 3, 1), (5, 3, 2), (5, 3, 3), (5, 3, 4), (5, 3, 5), (5, 3, 6),
(5, 4, 1), (5, 4, 2), (5, 4, 3), (5, 4, 4), (5, 4, 5), (5, 4, 6),
(5, 5, 1), (5, 5, 2), (5, 5, 3), (5, 5, 4), (5, 5, 5), (5, 5, 6),
(5, 6, 1), (5, 6, 2), (5, 6, 3), (5, 6, 4), (5, 6, 5), (5, 6, 6),
(6, 1, 1), (6, 1, 2), (6, 1, 3), (6, 1, 4), (6, 1, 5), (6, 1, 6),
(6, 2, 1), (6, 2, 2), (6, 2, 3), (6, 2, 4), (6, 2, 5), (6, 2, 6),
(6, 3, 1), (6, 3, 2), (6, 3, 3), (6, 3, 4), (6, 3, 5), (6, 3, 6),
(6, 4, 1), (6, 4, 2), (6, 4, 3), (6, 4, 4), (6, 4, 5), (6, 4, 6),
(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6),
(6, 6, 1), (6, 6, 2), (6, 6, 3), (6, 6, 4), (6, 6, 5), (6, 6, 6)}
Now,
The combination where the sum is 10 is 27.
ie.
{(1, 3, 6), (1, 4, 5), (1, 5, 4), (1, 6, 3), ........, (6, 1, 3), (6, 2, 2,), (6, 3, 1)}
Thus,
There are 27 ways of combination where the sum is 10.
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60°
d. Opposite C:
e. Adjacent C:
B
90°
1. Consider the triangle ABC. Which side is being described by the following labels?
a. Hypotenuse:
b. Opposite A:
c. Adjacent A:
30°
Side BC is the hypotenuse of the right triangle ABC. Against A: The side that is opposed to angle A is side BC. Adjacent A: Side AB is the side that faces angle A. The side that is in opposition to angle C is side AB.
What is the right triangle ABC's hypotenuse?The opposite side of any right-angled triangle, ABC, is referred to as the hypotenuse. Here, we adhere to the tradition that the side opposite angle A is designated with the letter a. Both sides opposing B and C are given the letters b and c, respectively.
If A and B make up the right triangle's legs, how do we solve for the hypotenuse, c?When a and b if the lengths of the legs of a right triangle are and the hypotenuse's length is c, then the sum of the squares of the legs' lengths equals the square of the hypotenuse's length.
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Estimating the within-group variance. Refer to the previous exercise. Here are the cell standard deviations and sample sizes for cooking enjoyment: Find the pooled estimate of the standard deviation for these data. Use the rule for examining standard deviations in ANOVA from Chapter 12 (page 560) to determine if it is reasonable to use a pooled standard deviation for the analysis of these data.
In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.
According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.
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is the bottled water you are drinking really purified water? a study of various brands of bottled water conducted by the natural resources defense council found that 25% of bottled water is just tap water packaged in a bottle (scientific american, july 2003).
Yes, there is a chance that the bottled water you are drinking is just tap water packaged in a bottle. According to a study by the Natural Resources Defense Council, 25% of bottled water is just tap water that has been packaged in a bottle. [Scientific American, July 2003]
What is bottled water?Bottled water is drinking water that has been packaged in bottles or containers for sale. Bottled water can come from a variety of sources, such as municipal supplies, springs, wells, and other sources. In some cases, bottled water is treated or purified to remove impurities and contaminants. However, not all bottled water is purified or treated, and some may be just tap water that has been packaged in a bottle.
What is purified water?Purified water is water that has been treated to remove impurities and contaminants. Purified water can come from any source, including municipal supplies, wells, and other sources. Purification methods may include filtration, reverse osmosis, distillation, or other methods. Purified water is commonly used in medical and industrial applications, as well as in homes for drinking and cooking.
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The function h(t) = –16t(t – 2) + 24 models the height h, in feet, of a ball t seconds after it is thrown straight up into the air. What is the initial velocity and the initial height of the ball?
Answer
Initial velocity = 32 ft/s
Initial height = 24 ft.
Explanation
The function gives us the function that models the height, h, in feet for the ball as a function of time, t, in seconds.
h(t) = -16t (t - 2) + 24
We are then asked to find the initial velocity and the initial height of the ball.
This means we find the velocity and the height of the ball at t = 0
Velocity is given as the first derivative of the height function
v = (dh/dt)
h(t) = -16t (t - 2) + 24
h(t) = -16t² + 32t + 24
v = (dh/dt) = -32t + 32
When t = 0
v = -32t + 32 = -32 (0) + 32 = 0 + 32 = 32 ft/s
Initial velocity = 32 ft/s
For the initial height, t = 0
h(t) = -16t (t - 2) + 24
h(t) = -16t² + 32t + 24
h(0) = -16(0²) + 32(0) + 24
h(0) = 0 + 0 + 24
h(0) = 24 ft
Initial height = 24 ft.
Answer:
The initial velocity of the ball is 32 feet per second.
The initial height of the ball is 24 feet.
Step-by-step explanation:
Velocity is the rate of change of distance with respect to time.
Therefore, to find the equation for velocity, differentiate the height function with respect to time.
[tex]\begin{aligned} h(t) &= -16t(t - 2) + 24\\&= -16t^2+32t+24\\\\\implies v=h'(t)&=-32t+32\end{aligned}[/tex]
The initial velocity of the ball is its velocity when t = 0.
Therefore, at time t = 0, the velocity is:
[tex]\begin{aligned}\implies v=h'(0)&=-32(0)+32\\&=32\sf\;ft\;s^{-1}\end{aligned}[/tex]
Therefore, the initial velocity of the ball is 32 feet per second.
The initial height of the ball is the height when t = 0.
Therefore, at time t = 0, the height of the ball is:
[tex]\begin{aligned} \implies h(0) &= -16(0)(0 - 2) + 24\\&= 0+24\\&=24\sf\;ft\end{aligned}[/tex]
Therefore, the initial height of the ball is 24 feet.
Does someone mind helping me with this problem? Thank you!
the answer to the problem that you need to is 1024
find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7.
The number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is 4680.
Step by step explanation:
The number of positive integers with exactly four decimal digits between 1000 and 9999 inclusive can be obtained as follows:
Total number of four decimal digits = 9999 − 1000 + 1 = 9000
Numbers that are multiples of 5 are obtained by starting with 1000 and adding 5, 10, 15, 20, ..., 1995, that is, 5k, where k = 1, 2, 3, ..., 399.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 5 is 399.
Numbers that are multiples of 7 are obtained by starting with 1001 and adding 7, 14, 21, 28, ..., 1428, that is, 7m, where m = 1, 2, 3, ..., 204.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 7 is 204.
Note that some numbers in the interval [1000, 9999] are divisible by both 5 and 7. Since 5 and 7 are relatively prime, the product of any number of the form 5k by a number of the form 7m is a multiple of 5 × 7 = 35.
The numbers of the form 35n in the interval [1000, 9999] are
1035, 1070, 1105, 1140, ..., 9945, 9980.
We can check that there are 285 numbers of this form.
To find the number of positive integers with exactly four decimal digits that are not divisible by either 5 or 7, we will subtract the number of multiples of 5 and 7 and add the number of multiples of 35.
Therefore, the number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is
9000 - 399 - 204 + 285 = 4680.
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Look at this series: 7, 10, 8, 11, 9, 12,. What number should come next?
Choose the correct answer.
When you get the sum of a data set and divide by the number of values collected, you get the
A)quantitative data
B)qualitative data
C)median
D)mean
Let V and W be vector spaces, and let T: V W be a linear transformation. Given a subspace U of V, let T(U) denote the set of all images of the form T(x), where x is in U. Show that T(U) is a subspace of W. To show that T(U) is a subspace of W, first show that the zero vector of wis n TU. Choose the correct answer below. a. Since V s a subspace of U the zero vector of u ou is in V. Since T s inear T Ou .w, where is the zero vector of w.?oms T(U) b. Since U is a subspace of W, the zero vector of w, ow, is in U. Since T is linear, T(0w) = 0v, where 0v is the zero vector of V So 0w is in T(U). c. Since V is a subspace of U, the zero vector of V, 0v is in U. Since T is linear, T(0v-0w where o,. is the zero vector of W Som s in T(U). d. Since U is a subspace of V, the zero vector of V, 0y, is in U.Since T is linear, Toy)-ow where Ow is the zero vector of W. So Ow is in T(U)
The T(U) is a subspace of W.
Since U is a subspace of V, the zero vector of V, 0v, is in U. Since T is linear, T(0v) = 0w, where 0w is the zero vector of W. So 0w is in T(U). Therefore, T(U) is a subspace of W.
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You ride your bicycle 40 meters. How many complete revolutions does the front wheel make?
What is the sum of the following equation? (2 points)
three tenths plus thirty-nine hundredths equal blank
A. thirty-six hundredths
B. forty-two hundredths
C. sixty-nine hundredths
D. ninety-six hundredths
Answer:
sixty nine hundredths
Step-by-step explanation:
three tenths can be expressed in decimal as 3/10
thirty nine hundredths can be expressed in decimal as 39/100
Therefore the sum of three tenths plus thirty nine hundredths equals
3/10 +39/100
We first find the l.c.m of the two fractions equals 100 so we have 100 as the denominator
then 100 divided by 10 multiplied by 3 +100 divided by 100 multiplied by 39 as illustrated below gives the answer
3/10 +39/100
=30+39/100
=69/100= sixty nine hundredths
I need to show my work please help
Answer:
x=15
Step-by-step explanation:
use the side splitter theorem
(x-6)/x = 3/5 (cross-multiply)
3x=5(x-6) distributive property
3x=5x-30
2x = 30
x = 15
a rectangular prism has a height of 1/5 m and a square base with an area of 7 1/2 m^2. What is the volume of the rectangular prism?
The volume of the rectangular prism is approximately 0.2996 cubic meters.
What is rectangular prism and its volume?Six rectangular faces that are congruent and parallel to one another make up the three-dimensional solid known as a rectangular prism. A rectangular cuboid is another name for it.
By multiplying the prism's length, width, and height, one may get the volume of a rectangular prism, which is the volume of the interior space of the prism.
Given that, area of the square base is 7 1/2 sq. m.
The side of the square base is thus,
√(7 1/2) ≈ 2.7386 m
The volume of the rectangular prism is given as:
Volume = length x width x height
Volume ≈ 2.7386 x 2.7386 x 1/5 m
Volume ≈ 0.2996 cubic meters.
Hence, the volume of the rectangular prism is approximately 0.2996 cubic meters.
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