The sides and the angle of the right triangle are a = 10√2, b = 10√2 and B = π / 4.
How to find the missing information of a right triangle
In this problem we need to determine the values of two sides and an angle of the right triangle. This can be done by means of the following properties:
A + B + C = π
sin A = a / c
cos A = b / c
tan A = a / b
Where:
A, B, C - Angles of the right triangle, in radians.a, b, c - Sides of the right triangle.If we know that A = π / 4, C = π / 2 and c = 20, then the missing angle and missing sides are, respectively:
B = π - π / 4 - π / 2
B = π / 4
cos (π / 4) = b / 20
b = 20 · cos (π / 4)
b = 10√2
sin (π / 4) = a / 20
a = 20 · sin (π / 4)
a = 10√2
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Lin plans to swim 12 laps in the pool. She has swum 9.75 laps so far.
How many laps does she have left to swim? Use y
for the number of laps that Lin has left to swim.
Lin plans to swim 12 laps and has already swum 9.75 laps, so the number of laps she has left to swim can be found by subtracting 9.75 from 12:
y = 12 - 9.75
Simplifying the right side:
y = 2.25
Therefore, Lin has 2.25 laps left to swim.
In circle S with � ∠ � � � = 60 m∠RST=60 and � � = 4 RS=4 units find area of sector RST. Round to the nearest hundredth
If the measure of angle RST is 60°, and RS=4 units, then the area of sector RST is 8.374 square units.
In geometry, a "Sector" of a circle is defined as the portion of circle enclosed by two radii and the arc between them. It can be thought of as a slice or a wedge cut out of a circle.
To find the area of the "sector-RST" in circle centered at "S", we use the formula for area of a sector of a circle, which is :
⇒ Area of sector = (θ/360) × π × r²,
where θ = central angle of sector in degrees, π = 3.14159, and r = radius of circle,
In this case, we are given that m∠RST = 60 degrees and RS = 4 units. Since RS is the radius of the circle centered at "S", we use RS = r,
Substituting the values, θ = 60 degrees, r = RS = 4 units,
We get,
⇒ Area of sector RST = (60/360) × 3.14 × (4)²,
= (1/6) × 3.14 × 16,
= 8.374 square units,
Therefore, the required area of sector is 8.374 square units.
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The given question is incomplete, the complete question is
In circle centered at "S", R and T are the points on the circumference with m∠RST = 60 and RS=4 units .Find area of sector RST.
in how many ways can you divide 5 people into two groups, where the first group has 2 people and the second has 3?
There are 10 ways to divide 5 people into two groups where the first group has 2 people, and the second group has 3 people.
There are two ways to divide 5 people into two groups where the first group has 2 people and the second has 3. The first way is to choose 2 people out of the 5 for the first group, which can be done in 5C2 ways, and then the remaining 3 people form the second group. The second way is to choose 3 people out of the 5 for the second group, which can be done in 5C3 ways, and then the remaining 2 people form the first group. Therefore, the total number of ways to divide 5 people into two groups with a group of 2 people and a group of 3 people is 5C2 + 5C3, which equals 10 + 10, or 20.
The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
where C(n, r) is the number of ways to choose r items from a set of n items, n! represents the factorial of n, and r! represents the factorial of r.
In this case, you want to choose 2 people from a set of 5. So, n = 5 and r = 2. Plug the values into the formula:
C(5, 2) = 5! / (2!(5-2)!)
C(5, 2) = 5! / (2!3!)
C(5, 2) = 120 / (2*6)
C(5, 2) = 120 / 12
So, there are 10 ways to divide 5 people into two groups where the first group has 2 people, and the second group has 3 people.
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Which of the following phrases can be used to represent -11?
the opposite of -11
eleven greater than zero
eleven below zero
positive eleven
Thx
Answer:
Eleven below Zero
Step-by-step explanation:
Every number below zero (less than zero) is a negative number.
The Hack family is planning a trip to a theme park next fall for nights. After much research, they have found several deals for lodging at the theme park. They have narrowed it down to three hotels: the Contemporary Resort, the Fun Times Resort, and The Princess Resort. Based on the rates in the table below, which is the best deal?
the Princess Resort is the best deal with a total cost of $657 for a four-night stay.
What is Total fixed cost?
Total fixed cost refers to the cost of all fixed assets which incur a fixed cost irrespective of the level of production in a company.
The Contemporary Resort costs $239 per night, so the total cost for four nights would be:
$239 × 4 = $956.
The Fun Times Resort costs $189 per night, so the total cost for four nights would be:
$189 × 4 = $756.
The regular cost is $219 per night, so the total cost for three nights would be:
$219 × 3 = $657. But since they get the fourth night free, the total cost for four nights would be:
$657 + $0 = $657.
Comparing the three options, the Princess Resort is the best deal with a total cost of $657 for a four-night stay.
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veterinary science: colts the body weight of a healthy 3-month-old colt should be about m 5 60 kg (source: the merck veterinary manual, a standard reference manual used in most veterinary colleges). (a) if you want to set up a statistical test to challenge the claim that m 5 60 kg, what would you use for the null hypothesis h0 ? (b) in nevada, there are many herds of wild horses. suppose you want to test the claim that the average weight of a wild nevada colt (3 months old) is less than 60 kg. what would you use for the alternate hypothesis h1 ? (c) suppose you want to test the claim that the average weight of such a wild colt is greater than 60 kg. what would you use for the alternate hypothesis? (d) suppose you want to test the claim that the average weight of such a wild colt is different from 60 kg. what would you use for the alternate hypothesis? (e) for each of the tests in parts (b), (c), and (d), would the area corresponding to the p-value be on the left, on the right, or on both sides of the mean? explain your answer in each case
(a) For the null hypothesis, we would use the claim that the average weight of a healthy 3-month-old colt is equal to 60 kg, that is,
H0 : μ = 60 kg.
(b) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg, that is,
H1: μ < 60 kg.
(c) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is greater than 60 kg, that is, H1: μ > 60 kg.
(d) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is different from 60 kg, that is, H1: μ ≠ 60 kg.
(e) For the test in part (b), the area corresponding to the p-value would be on the left of the mean because the alternate hypothesis is one-tailed and represents a left-tailed test.
For the test in part (c), the area corresponding to the p-value would be on the right of the mean because the alternate hypothesis is one-tailed and represents a right-tailed test.
For the test in part (d), the area corresponding to the p-value would be on both sides of the mean because the alternate hypothesis is two-tailed and represents a two-tailed test.
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what are the first four terms if a1=5 and an=3an-1?
Can someone help me ASAP? It’s due today
The only option that represents an independent event is: Option C: "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
How to Identify Independent Events?Independent events are defined as those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.
Looking at the given options, the only one that represents an independent event is "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
This is because each event does not depend on another one of the events being described.
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which vaule of y makes the equation true 13 - y = 17 true?
pls help
Answer:
y = -4
Step-by-step explanation:
13 - y = 17
y = 13 - 17 = -4
Answer:
y = -4
Step-by-step explanation:
Alright so you shift the y to the other side:
13 = 17 + y
Now you shift the 17 to the other side,
y = 13 - 17 = -4
Hence, y = -4
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Hello solve this, what is 9 x 5/7
Answer: 6 3/7
Step-by-step explanation:
9/1 x 5/7
If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.
Answer:
[tex]\frac{45}{7}[/tex] or 6.4285
Step-by-step explanation:
First, multiply 9 and 5, which gives you 45.
9(5)=45
Then, divide 45 by 7.
45/7=6.4285
That gives you [tex]\frac{45}{7}[/tex] or 6.4285
Hope this helps!
Determine whether the given set S is a subspace of the vector space V. Note: Pn(R) is the vector space of all real polynomials of degree at most n and Mn(R) is the vector space of all real n x n matrices = OA. V is the vector space of all real-valued functions defined on the interval [a, b], and S is the subset of V consisting of those functions satisfying f(a) = f(b). B. V = P5(R), and S is the subset of V P5(R) consisting of those polynomials satisfying p(1) > p(0). C. V = C3(1), and S is the subset of V consisting of those functions satisfying the differential equation y'" + 2y = x2. D. V = Mn(R), and S is the subset of all skew-symmetric matrices. VE. V = C2(I), and S is the subset of V consisting of those functions satisfying the differential equation y" – 4y' + 3y = 0. F. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed m X n matrix. OG. V = R", and S is the set of vectors (x1 , X2, X3 ) in V satisfying x1 – 4x2 + x3 = 3
S is a subspace of the vector space V.
For four conditions are satisfied,
The set S is a subspace of C3(1)
The set S is a subspace of Mn(R)
The set S is a subspace of C2(I)
The set S is a subspace of [tex]R^n[/tex]
The set S is not a subspace of P5(R) because it is not closed under scalar multiplication.
If p(x) is a polynomial in S, then 2p(x) may not satisfy the condition. [tex]p(1) > p(0).[/tex]
The set S is a subspace of C3(1).
The differential equation [tex]y\prime\prime\prime + 2y = x^2[/tex] is linear and homogeneous, so the sum of two solutions is also a solution, and a constant multiple of a solution is also a solution.
S is closed under linear combinations.
The set S is a subspace of Mn(R) because it is closed under addition and scalar multiplication.
If A and B are skew-symmetric matrices, then[tex](A + B)^T = A^T + B^T = -A - B = -(A + B), so A + B[/tex]is skew-symmetric. Similarly, if c is a scalar, then [tex](cA)^T = cA^T = -cA, so c A[/tex] is skew-symmetric.
S is a subspace of C2(I) because it is closed under addition and scalar multiplication.
If y1 and y2 are solutions to[tex]y\prime\prime - 4y\prime+ 3y = 0, then y1\prime\prime - 4y\prime + 3y1 = 0[/tex] and [tex]y2\prime\prime - 4y2\prime + 3y2 = 0[/tex].
Adding these equations gives [tex](y1 + y2)\prime\prime - 4(y1 + y2)\prime + 3(y1 + y2) = 0,[/tex] so [tex]y1 + y2[/tex]is also a solution.
Similarly, if c is a scalar, then [tex](cy)\prime\prime - 4(cy)\prime + 3(cy) = c(y\prime\prime - 4y\prime+ 3y) = 0[/tex], so cy is also a solution.
The set S is a subspace of [tex]R^n[/tex]because it is the null space of a fixed matrix A.
The null space of a matrix is always closed under addition and scalar multiplication.
The set S is not a subspace of [tex]R^n[/tex]because it is not closed under addition. If (1, 1, 0) and (0, 2, 1) are in S, then their sum (1, 3, 1) is not in S because. [tex]1 - 4(3) + 1 \neq 3.[/tex]
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Which of the numbers listed below are solutions to the equation? Check all
that apply.
x = 49
A. 9
B. 7
C. -7
D. -49
E. 49
F. None of these
The only solution for the equation is the one in option E, 49
Which numbers are solution for the equation?Here we have the equation:
x = 49
A value of x is a solution only if the equation is true, this means, we have the same number in both sides.
Here obviously there exist only one solution, and it is when x takes the value 49.
49 = 49
So the only correct option is E.
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Mr. Lewis and Ms. Yonkers are grading 87 papers for a math class. Mr. Lewis has already grade 32, but Ms. Yonkers has only graded 16. Write an equation with the variable (p) and show your work to determine how many papers they have left to grade.
The number of papers they have left to grade is 39.
What is Subtraction?
Subtraction is a mathematical operation that involves taking away or removing a certain number of items or quantity from a larger group. It is the inverse of addition and is denoted by the minus sign (-).
Let p be the number of papers they have left to grade.
The total number of papers is 87, and Mr. Lewis has already graded 32 and Ms. Yonkers has graded 16, so the number of papers they have left to grade is:
p = 87 - 32 - 16
p = 39
Therefore, they have 39 papers left to grade.
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Which situation can be represented by the equation 2x + 150 = 5x
Mary has 5 stamps and buys 150 stamps each week. Nick has no stamps and buys 2 stamps each week. When will Marty have
more stamps than Mary?
Mary has 2 stamps and buys 150 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have
the same number of stamps?
Mary has 150 stamps and buys 5 stamps each week. Nick has no stamps and buys 2 stamps each week. When will Marty have
more stamps than Mary?
Mary has 150 stamps and buys 2 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have
the same number of stamps?
The situation can be represented by the equation 2x + 150 = 5x is"Mary has 2 stamps and buys 150 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have the same number of stamps?" (option b)
The equation 2x + 150 = 5x means that two expressions, 2x + 150 and 5x, are equal. In other words, whatever value we substitute for x, these two expressions will always have the same value. We can use this equation to solve different situations by finding the value of x that satisfies the equation.
Mary starts with 2 stamps and buys 150 stamps each week, while Nick starts with no stamps and buys 5 stamps each week. To determine when they will have the same number of stamps, we need to use the equation 2x + 150 = 5x. We can rewrite the equation as 150 = 3x, and solve for x by dividing both sides by 3. This gives us x = 50, which means that it will take Mary 50 weeks to have the same number of stamps as Nick.
Hence the correct option is (b).
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PLEASE ANSWER DUE TODAY!!!!
Answer:
below
Step-by-step explanation:
26. yes because a straight line is formed
27. domain - -2 to 2
range -2 to 1
Answer:
Yes, the graph is a linear function.
Domain: x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]
Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]
Step-by-step explanation:
A linear function is an expression that will form a straight line when graphed (or a graph that forms a straight line). These points form a straight line, so the function is linear.
The domain of the function is everything that x can be equal to. We can see here that the ordered points are:
(-2, -1.5), (-1.5, -1), (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1), (1, 1.5), (1.5, 2)
So, the domain of the function is all of the x values of the ordered pairs, or:
x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]
(the symbol next to the x means "belongs to.")
As for the range, it is everything that y can be equal to. Let us look once again at the ordered pairs. The range of the function is equal to the y coordinates of these ordered pairs, or:
Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]
Keep in mind that if the function contains more than one value for x or y, it is listed ONLY ONCE in the domain/range.
Can someone help with this? Find the area of the shaded region. Anything helps, thank you
Thus, the Area of shaded region for the given sector of circle is found as:
1.14 sq. cm.
Explain about the sector of circle:Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle measurement and radius measurement are both crucial for solving circle-related difficulties.
Given:
radius r = 2 cminternal angle Ф = 90 degreesArea of shaded region = area of sector - area of triangle
Area of shaded region = Ф/360° * (πr²) - 1/2*base*height
Area of shaded region = 90/360° * (3.14*2²) - 1/2*2*2
Area of shaded region = 1/4*3.14*4 - 2
Area of shaded region = 3.14 - 2
Area of shaded region = 1.14 sq. cm
Thus, the Area of shaded region for the given sector of circle is found as:
1.14 sq. cm.
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An angle measures 3. 4° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
Let x be the measure of the angle we are trying to find, in degrees.
The complementary angle to x is 90° - x, since the sum of complementary angles is 90 degrees.
The problem tells us that x is 3.4 degrees less than its complementary angle, so we can set up the following equation:
x = (90 - x) - 3.4
Simplifying and solving for x, we get:
x = 86.6/2
x = 43.3
Therefore, the angle we are trying to find has a measure of 43.3 degrees, and its complementary angle has a measure of 90 - 43.3 = 46.7 degrees.
Topic 7: Tangents
For questions 19-20, determine if AB is tangent to circle C.
Based on the definition of the tangent of a circle and the Pythagorean triple of a right triangle, AB is not tangent to circle C in both question 19 and 20.
What is the Tangent of a Circle?In geometry, the tangent of a circle is a line that intersects the circle at exactly one point, which is called the point of tangency. This line is perpendicular to the radius of the circle at that point. This means that it forms a right angle at that point.
19. If AB is tangent to circle C, the lengths of the triangle ABC will form a Pythagorean triple. Let's check:
4.8² + 7.2² = 12²
74.88 = 144 [not true} Therefore, AB is not tangent to circle C.
20. Also, we will have the following:
15² + 11.2² = 6.8²
350.44 = 46.24 [not true].
AB is not tangent to circle C.
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Complex numbers [tex]z[/tex] and [tex]w[/tex] satisfy [tex]|z|=|w|=1, |z+w|=\sqrt{2}[/tex].
What is the minimum value of [tex]P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|[/tex]?
Okay, here are the steps to find the minimum value of P:
1) Given: |z|=|w|=1 (z and w are complex numbers with unit modulus)
|z+w|=sqrt(2)
Find z and w such that these conditions are satisfied.
Possible solutions:
z = 1, w = i (or vice versa)
z = i, w = 1 (or vice versa)
2) Substitute into P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|
For the cases:
z = 1, w = i: P = |-1-4+2(1+i)i| = |-5+2i| = sqrt(25+4) = 5
z = i, w = 1: P = |1-\frac{4}{i}+2(1+\frac{1}{i})i| = |-3+2i| = sqrt(9+4) = 5
3) The minimum value of P is 5.
So in summary, the minimum value of
P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|
is 5.
Let me know if you have any other questions!
please help me with this
The point (1,2) is the point of intersection of the two lines.
How to verify the pointIt should be noted that to verify if the point (1,2) is a solution to the system of linear equations, we need to substitute x=1 and y=2 into both equations and check if they are true.
The equation is true, so (1,2) is a solution to the first equation.
Substituting x=1 and y=2 into the second equation also makes the equation true.
Therefore, the point (1,2) is the point of intersection of the two lines.
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1. Find the height of the parabolic balloon arch for the prom when the position of the bottom anchors are at x = 3 feet and x = 7 feet.
The height of the parabolic balloon arch for the prom is 12.25 feet.
Using these assumptions, we can find the equation of the parabola that the arch follows as x = a(y-k)² + h, where (h,k) is the vertex and a is a constant that determines the shape of the parabola. We can find the value of a by using one of the points that the arch passes through, say (3,0):
3 = a(0-k)² + h h = 3 - a(k²)
Similarly, using the other point that the arch passes through, say (7,0):
7 = a(0-k)² + h h = 7 - a(k²)
Equating the expressions for h, we get:
3 - a(k²) = 7 - a(k²) a = -1/4
Substituting this value of a into one of the equations for h, say h = 7 - a(k²), we get:
h = 7 + 1/4(k²)
So the vertex of the parabola is at (h,k) = (7,0), and the equation of the parabola is x = -1/4(y² - 28y + 49).
To find the height of the arch, we need to find the y-coordinate of the vertex, which is k = 0. So the height of the arch is given by the distance between the vertex and the lowest point of the arch, which is the x-intercept of the parabola. To find the x-intercept, we set y = 0 in the equation of the parabola:
x = -1/4(0² - 28(0) + 49)
x = -1/4(49) = -12.25
However, since we are dealing with a physical object, the height cannot be negative. Therefore, we take the absolute value of the x-intercept, which gives us:
| -12.25 | = 12.25 feet
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sharon is a good student who enjoys statistics. she sets a goal for herself to do well enough compared to her peers so that her standardized score on her statistics final is equal to her percentile rank (written as a decimal) among her classmates. scores on the statistics final are normally distributed. what goal did she set for herself?
Sharon's desired percentile rank of 0.78.
To determine the goal Sharon set for herself, we need to understand the relationship between standardized scores and percentile ranks.
In a standardized test, such as Sharon's Statistics final, the standardized score represents how well a student performed relative to the average score of the test-takers.
The percentile rank, on the other hand, indicates the percentage of test-takers that scored below a particular student.
In Sharon's case, she wants her standardized score to be equal to her percentile rank.
Therefore, her goal is to achieve a standardized score of 0.78 (written as a decimal) on her Statistics final.
This means she aims to score better than approximately 78% of her classmates, as indicated by her desired percentile rank of 0.78.
Hence her desired percentile rank of 0.78.
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A triangle has two legs measuring 21 cm and 20 cm. Which of the following leg measurement will make a right triangle?
The leg measurement will make a right triangle is 21 cm.
What is hypotenous?The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.
Pythagorean theorem :
If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then
p² = q² + r²
The lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.
Now, p² = (20)² + (21)²
= 400 + 441 = 841
i.e. p = √(841) = 29
Therefore the length of the hypotenuse is 29 cm. The right angle traingle is 21 cm.
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Jane takes her turn on the vine to practice her swing. As she swings, she goes back and forth across the river bank alternately over land and water. She has spent some time thinking about her motion and tells Tarzan to set the stopwatch to take measurements. Assume that her distance varies sinusoidally with the time of her swing. Tarzan finds that when time is 2 seconds, she is -30 feet over land. At time equals 6 seconds, she has crossed 20 feet of water.
The equation for the sinusoidal function that represents Jane's motion would be d(t) = 25 x sin(π/4 x (t + 4)) - 5
How to find the sinusoidal function ?Let d(t) be the distance Jane is from the bank (in feet) at time t (in seconds). Since Jane's motion is sinusoidal, we can express it as:
d(t) = A x sin(B x (t - C)) + D
We need to find the values of A, B, C, and D that satisfy these conditions.
Since the amplitude is half the peak-to-peak amplitude, we have:
A = 50 / 2 = 25
The vertical shift (D) is the average of the maximum and minimum distances:
D = (20 + (-30)) / 2 = -10 / 2 = -5
Since the sine function is -1 at 3π/2 (270 degrees), we have:
π/4 x (2 - C) = 3π/2
2 - C = 6
C = -4
So, the equation of the sinusoidal function representing Jane's motion is:
d(t) = 25 x sin(π/4 x (t + 4)) - 5
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The question is:
Find the sinusoidal function that represents Jane's motion.
what is the surface are of a cylender when the radius is 6in and the height is 9 in
Answer:
565.486677646 inches squared
Step-by-step explanation:
Let's recall the formula for the surface area of a cylinder:
[tex]A=2\pi rh+2\pi r^2[/tex]
Where r is the radius and h is the height.
We are given that the radius is 6 inches and the height is 9 inches.
Substitute the values and solve the equation, like so:
[tex]A=2\pi (6)(9)+2\pi (6)^2=\\A=2\pi (54) +2\pi(36)=\\A=108\pi +72\pi =\\A=180\pi[/tex]
Thus, in terms of pi, the surface area is equal to [tex]180\pi[/tex].
180 times pi is equal to approximately 565.486677646 inches squared.
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In a race, 14 out of the 25 swimmers finished in less than 47 minutes. What percent of swimmers finished the race in less than 47 minutes? Write an equivalent fraction to find the percent.
We must first convert the given information into an equivalent fraction. The answer is 56%.
What is equivalent fraction?Equivalent fractions have the same value or represent the same portion of a whole even though they may have different numerators and denominators.
To do this, we must multiply both the numerator (14) and denominator (25) by the same number so that the denominator equals 100.
To do this, we must multiply both 14 and 25 by 4.
This gives us 14*4/25*4 = 56/100.
To convert this fraction to a percent, we can simply divide the numerator by the denominator and multiply the result by 100.
Therefore, 56/100 * 100 = 56%.
This result can also be found by setting up a proportion. We can set up the proportion as follows:
14/25 = x/100.
To solve for x, we must multiply both sides by 100. This gives us 14*100/25 = x.
Hence, x = 56. Therefore, 56% of swimmers finished the race in less than 47 minutes.
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The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to be poisson with a mean of 25 veh/hr. It takes an average of 1. 5 min for the necessary tickets to be bought for occupants of each car. (a)what is the expected length of queue at the ticket gate, not including the vehicle being served? (b)what is the probability that there are no more than 5 cars at the gate, including the vehicle being served? (c)what will be the average waiting time of a vehicle?
(a) The expected length of the queue, not including the vehicle being served, is 0.625 vehicles.
(b) The probability that there are no more than 5 cars at the gate, including the vehicle being served, is approximately 0.0176.
(c) The average waiting time of a vehicle at the ticket gate is 1.5 minutes or 0.025 hours.
(a) To find the expected length of the queue at the ticket gate, we need to calculate the expected number of vehicles waiting in the queue at any given time. This can be found by using the Little's Law, which states that the expected number of customers in a stable system is equal to the arrival rate multiplied by the average time spent in the system.
In this case, the arrival rate is 25 vehicles per hour, and the average time spent in the system is the time it takes to buy the tickets, which is 1.5 minutes or 0.025 hours. Therefore, the expected number of vehicles waiting in the queue is
E[N] = λW = 25 x 0.025 = 0.625 vehicles
So the expected length of the queue, not including the vehicle being served, is 0.625 vehicles.
(b) To find the probability that there are no more than 5 cars at the gate, including the vehicle being served, we need to use the Poisson distribution with a mean of 25 vehicles per hour. Let X be the number of vehicles arriving in an hour, then X Poisson(25).
P(X ≤ 5) = ∑ P(X = k) for k = 0 to 5
= ∑ (e^(-λ) × λ^k / k!) for k = 0 to 5
= e^(-25) × (25^0 / 0!) + e^(-25) × (25^1 / 1!) + ... + e^(-25) × (25^5 / 5!)
Using a calculator or software, this probability is found to be approximately 0.0176.
(c) The average waiting time of a vehicle can be found by dividing the expected number of vehicles waiting in the queue by the arrival rate. From part (a), we know that the expected number of vehicles waiting in the queue is 0.625 vehicles. The arrival rate is 25 vehicles per hour. Therefore, the average waiting time of a vehicle is
W = E[N] / λ = 0.625 / 25 = 0.025 hours or 1.5 minutes
So the average waiting time for a vehicle at the ticket gate is 1.5 minutes.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The two options that represent circles with diameter 12 units and center on the y-axis are:
x² + (y - 6)² = 36
x² + (y + 6)² = 36
What is circles diameter?The diameter of a circle is a straight line segment that passes through the center of the circle and connects two points on its circumference. It is twice the length of the circle's radius.
The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
x² + (y - 6)² = 36
x² + (y + 6)² = 36
Explanation:
For a circle with diameter 12 units, the radius is half of the diameter, which is 6 units.
Since the center of the circle lies on the y-axis, the x-coordinate of the center is 0.
The general equation for a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².
Using the given information, we substitute h = 0, k = ±6, and r = 6 to get the two equations:
(x - 0)² + (y - 6)² = 6² => x² + (y - 6)² = 36
(x - 0)² + (y + 6)² = 6² => x² + (y + 6)² = 36
Therefore, the two options that represent circles with diameter 12 units and center on the y-axis are:
x² + (y - 6)² = 36
x² + (y + 6)² = 36
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PLEASE ANSWER ASAP
1. How many atoms are present in 8.500 mole of chlorine atoms?
2. Determine the mass (g) of 15.50 mole of oxygen.
3. Determine the number of moles of helium in 1.953 x 108 g of helium.
4. Calculate the number of atoms in 147.82 g of sulfur.
5. Determine the molar mass of Co.
6. Determine the formula mass of Ca3(PO4)2.
IT WOULD BE HELPFUL
The number of atoms in 8.500 moles of chlorine atoms can be calculated using Avogadro's number, which is approximately 6.022 × 10²³ atoms/mole.
So, the number of atoms in 8.500 moles of chlorine atoms would be:
8.500 moles × 6.022 × 10²³ atoms/mole = 5.12 × 10²⁴ atoms of chlorine.
The molar mass of oxygen is approximately 16.00 g/mol. Therefore, the mass of 15.50 moles of oxygen would be:
15.50 moles × 16.00 g/mol = 248 g of oxygen.
The molar mass of helium is approximately 4.00 g/mol. Therefore, the number of moles of helium in 1.953 x 10^8 g of helium would be:
1.953 x 10^8 g / 4.00 g/mol = 4.88 x 10⁷ moles of helium.
The molar mass of sulfur is approximately 32.06 g/mol. Therefore, the number of moles of sulfur in 147.82 g of sulfur would be:
147.82 g / 32.06 g/mol ≈ 4.61 moles of sulfur.
The molar mass of cobalt (Co) is approximately 58.93 g/mol.
The formula mass of Ca₃(PO₄)₂ can be calculated by adding the molar masses of all the individual atoms in the formula.
The molar mass of calcium (Ca) is approximately 40.08 g/mol, the molar mass of phosphorus (P) is approximately 30.97 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol.
Therefore, the formula mass of Ca₃(PO₄)₂ would be:
3 × 40.08 g/mol (for Ca) + 2 × (2 × 30.97 g/mol + 4 × 16.00 g/mol) (for P and O) = 310.17 g/mol.
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