consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. the possible outcomes of the sample space s are listed as follows, where in each case the die on the left is blue and the one on the right is gray. s = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in roster notation. Enter EMPTY or o for the empty set.) The event that the sum of the numbers showing face up is at least 9. E Compute its probability.
The set of events that the sum of the numbers showing face up is at least 9 is E = {36, 45, 46, 54, 55, 56, 63, 64, 65, 66} and the probability is 5/18.
In the roster form, the elements (or members) of a set are listed in a row between curly brackets. For the event that the sum of the numbers showing face up is at least 9 and is written as a set, look at the sum of values of blue and gray dies that has values greater than equal to 9.
Here, the total outcome S = 36
By doing that, we get,
E = {36, 45, 46, 54, 55, 56, 63, 64, 65, 66} = 10
Then, the probability of getting a sum of at least 9 is calculated as,
[tex]\begin{aligned}P(X\geq 9)&=\frac{\text{Number of favorable outcomes}}{\text{total number of outcomes}}\\&=\frac{n}{S}\\&=\frac{10}{36}\\&=\frac{5}{18}\;\text{or}\;0.28\end{aligned}[/tex]
The answer is 5/18.
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Solve the equation x+5/4=20/16
Answer:
x = 0
Step-by-step explanation:
x + 5/4 = 20/16
x + 5/4 = 5/4
x = 0
Match each expression with an equivalent radical form. One of the radical form
options will not have a match.
7/1/2
7
13
3/7/7/
72
3/7/7
1. √72
2. √√37
3. √√3
4. 3/7
5. √7
Answer:
see the attachment
Step-by-step explanation:
You want to match several expressions with fractional exponents to their equivalent radical forms.
Fractional ExponentThe relationship between the two forms is ...
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]
If n=2, or m=1, these are omitted from the radical form.
The attachment shows the matching values.
Problem 2 (D.16 Exercise 5, p 511). Forty rats are placed at random in a house having 4 rooms. There is one door between rooms 1 and 2, one door between rooms 1 and 4, one door between rooms 2 and 4, one door between rooms 2 and 3, and two doors between rooms 3 and 4 see the book for a picture). There are no doors between rooms 1 and 3. After each minute, a rat may change rooms, or stay still. All possibilities are equally likely. So, here is the transition matrix: [1/3 1/4 0 1/5 ] 1/3 1/4 1/4 1/5 0 1/4 1/4 2/5 1/3 1/4 1/2 1/5 Predict the long-term distribution of rats. What is the long-term probability that a given marked rat is in room 4? You must use the method of eigenvalues and eigenvectors.
The long-term probability that a given marked rat is in room 4 is 1/3
What is meant by probability?
In statistics, probability is defined as the measure of the likelihood of an event to happen and it measures the certainty of the event.
Here we have given that Forty rats are placed at random in a house having 4 rooms. There is one door between rooms 1 and 2, one door between rooms 1 and 4, one door between rooms 2 and 4, one door between rooms 2 and 3, and two doors between rooms 3 and 4 see the book for a picture). There are no doors between rooms 1 and 3. After each minute, a rat may change rooms, or stay still.
And we need to find the the long-term probability that a given marked rat is in room 4.
By using the eigenvalues method, we know that
Room 4 has the 3 exits that is from Room 1, Room 2 and Room 3.
So, here we have 3 possibilities for the exit so, the rat can choose any one these three ways,
So, the probability can be written as,
=> 1/3
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Sunset Lake is stocked with 2800 rainbow trout and after 1 year the population has grown to 7000. Assuming logistic growth with a carrying capacity of 28000, find the growth constant kk, and determine when the population will increase to 14600.
The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.
How to find the increase of population?The increase of population can be found by using the logistic equation. It is
[tex]P(t) = \frac{K}{1 + Ae^{-kt} }[/tex]
Where
P(t) = population at time t (in years)K = carrying capacityA = (K- P₀)/P₀k = growth constant of proportionalityt = time (in years)Sunset Lake is stocked with the rainbow trout. We have
P₀ = 2800P(1) = 7000K = 28000Find the growth constant k and time t when P(t) = 14600!
A = (K - P₀)/P₀
A = (28000 - 2800)/2800
A = 25200/2800
A = 9
After 1 year, we have 7000 rainbow trout. The growth constant is
[tex]7000 = \frac{28000}{1 + 9e^{-k(1)} }[/tex]
[tex]1 + 9e^{-k} = 4[/tex]
[tex]9e^{-k} = 3[/tex]
[tex]e^{-k} = \frac{1}{3}[/tex]
k = - ln (1/3)
k = 1.0986
Use k value to find the time when the population will increase to 14600!
[tex]14600 = \frac{28000}{1 + 9e^{-1.0986t} }[/tex]
[tex]1.9178 = 1 + 9e^{-1.0986t}[/tex]
[tex]0.9178 = 9e^{-1.0986t}[/tex]
[tex]\frac{0.9178 }{9} = e^{-1.0986t}[/tex]
[tex]t = \frac{ln \: 0.10198}{-1.0986}[/tex]
t = 2.078
t ≈ 2.1 years
It is in another 1.1 years after t = 1.
Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.
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Find the composite function
Please help me! I'm so confused and awful at math
Step-by-step explanation:
it is really a simple concept : instead of the isolated variable x you grab the whole function of g(x) and put that into the place of any x appearance in f(x) : g(x) becomes the input argument for f(x).
so,
f(g(x)) = sqrt(36/(x + 3)) = 6×sqrt(1/(x + 3))
(2/15x - 5) - (-0.7x + 2)
The expression (2/15x - 5) - (-0.7x + 2) is simplified to 5/12x - 3
What is an algebraic expression?An algebraic expression can be defined as an expression made up of variables, terms, coefficients, factors and constants.
These expressions are also made up of arithmetic operations.
From the information given, we have;
2/15x - 5) - (-0.7x + 2)
expand the bracket
2/15x - 5 + 7/10x - 2
collect like terms
2/15x + 7/10x - 5 + 2
Add the like terms
4x + 21x /30 - 3
Add the numerators
25x/60 - 3
Divide the common terms, we have;
5/12x - 3
Hence, the expression is 5/12x - 3
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X 1 2 3 4 5 6 7 8
Y 0,5 0,8 1,2 1,9 3 4,8 7,5 11,9
regresi linear
The equation of the linear regression is y = 1.49x- 2.76
How to determine the linear regression equationFrom the question, we have the following parameters that can be used in our computation:
X 1 2 3 4 5 6 7 8
Y 0,5 0,8 1,2 1,9 3 4,8 7,5 11,9
Rewrite as
X 1 2 3 4 5 6 7 8
Y 0.5 0.8 1.2 1.9 3 4.8 7.5 11.9
When the points are entered in a graphing calculator, we have
Sum of X = 36Sum of Y = 31.6Mean X = 4.5Mean Y = 3.95Sum of squares (SSX) = 42Sum of products (SP) = 62.6The regression equation is represented as
Regression Equation
ŷ = bX + a
Substitute the known values in the above equation, so, we have the following representation
b = SP/SSX = 62.6/42 = 1.49048
a = MY - bMX = 3.95 - (1.49*4.5) = -2.75714
So, we have
y = 1.49048X - 2.75714
Approximate
y = 1.49x- 2.76
Hence, the regression equation is y = 1.49x- 2.76
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Complete question
Given that
X 1 2 3 4 5 6 7 8
Y 0,5 0,8 1,2 1,9 3 4,8 7,5 11,9
Calculate the regression linear equation
Problem 5: (8 marks) Find the Taylor series for the following function, centred at the given a.
(a) f(x) = 7 cos (−x), a = 0.
(b) f(x) = x^4 + x^2 + 1, a = −2.
(c) f(x) = 2^x, a = 1.
(d) f(x) = x tan^−1(x^2), a= 0.
Taylor Series for following parts,
a) f(x) = 7 - (7/2)x² + (7/24)x⁶ +......
b)f(x) = 21 - 18(x+2) + 25(x + 2)² - 8(x+3)³ +......
c)f(x) = 2 + 2log(2)(x -1) +(log2)²(x-1)² + (1/3 (log2)³(x-1)³ + --------
d)f(x) = x² + ----
What is Taylor Series ?The Taylor series giving the expansion of the function f(x) in the neighborhood of the point a. If the function is continuous in the neighborhood, all its derivatives exist, and the series converges, then The form f(x) = f(a)+f′(a)/1!(x−a)+(f′′(a)/2!)(x−a)²+⋯+(fⁿ(a)/n! )(x−a)ⁿ --(1) where fⁿ(a) is the nᵗʰ derivative of f(x) evaluated at a.
a) f ( x) = 7 cos(-x) = 7 cos(x) , a = 0
f(a ) = 7 cos(0°) = 7
f'(x) = - 7 sin(x) , f'(a) = 7 sin(0°) = 0
f"(x) = - 7cos(x) , f"(a) = -7 cos(0°) = -7
f"'(x) = 7 sin(x) , f"'(a) = 7 sin(0° ) = 0
....................................
put all the values in above equation (1) we get,
f(x) = 7 + 0/1! (x -0) - (7/2!)(x-0)² )+ 0 +(7/4!) (x-0)⁴-0 + ----------
f(x) = 7 - (7/2)x² + (7/24)x⁶ +......
b) f(x) = x⁴ + x² + 1, a = -2
f(a= -2) = (-2)⁴ +(-2)² +1 = 21
f'(x) = 4x³ + 2x
f'(a= -2) = 4(-2)³ + 2×(-2) = -36
f"(x) = 12x² + 2
f"( a = -2) = 12(-2)² + 2 = 50
.....
put all the values in above equation (1) we get,
f(x) = 21 - (36/2)(x+2) + (50/2!)(x + 2)² - ( 48/3!)(x+3)³ +......
f(x) = 21 - 18(x+2) + 25(x + 2)² - 8(x+3)³ +......
c) f(x) = 2ˣ ; a = 1
f( a= 1) = 2¹ = 2
f'(x) = 2ˣ log(2)
f'(a= 1) = 2 log(2)
f"(x) = 2ˣ ( log(2) )²
f"( a = 1) = 2 ( log(2) )²
................
put all the values in above formula we get,
f(x) = 2 + 2log(2) +( 2/2!)(log2)² + (2/3!)(log2)³
+--------
f(x) = 2 + 2log(2)(x -1) +(log2)²(x-1)² + (1/3(log2)³(x-1)³ + --------
d) f(x) = x tan⁻¹(x²) ; a= 0
f(a=0) = 0
f'(x) = x (1/(1+x⁴) + tan⁻¹(x²)
f'(a = 0) = 0
f"(x) = ((1+x⁴) - x 4x³)/(1+x⁴)² + (1/(1+x⁴)
= (2/(1+x⁴) - 4x⁴/(1+x⁴)²
f"( a = 0) = 2 - 0 = 2
f"'(x) = - 8x³/(1+x⁴)² - 12x³/ (1+x⁴)² + 16x⁷/(1+x⁴)⁴
f"'(a = 0) = 0
..............
f(x) = 0 +0 + 2/2! (x-0)² + 0 +-------
f(x) = x² + ----
Hence, we get all required Taylor Series for
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Consider the following partially completed two-way ANOVA table. Suppose there are 6 levels of Factor A and 4 levels of Factor B. The number of replications per cell is 6. Use the 0.05 significance level. (Hint: estimate the values from the F table.)1. Complete an ANOVA table. (Round MS and F to 2 decimal places.)
Source SS df MS F
Factor A 75 Factor B 25 Interaction 300 Error 600 Total 1,000Find the critical values to test for equal means. (Round your answer to 2 decimal places.)
Critical values to test for equal means are Factor A , Factor B
and Interaction respectively
The DF value we get after is 143 and the integration value we get is 1.76
What is a value ?
Value in ethics and social sciences refers to the degree of significance of something or an activity, with the goal of deciding the best courses of action to take or the best ways to live, or to define the significance of certain activities.
The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. Consider this: If we take 45 into consideration. The tens column is where the fourth digit is located in this instance.
The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important."
(a)
DF for Factor A = 6 - 1 = 5
DF for Factor B = 4 - 1 = 3
DF for Interaction of Factor A and B = 5*3 = 15
Number of replications per cell = 6
Total no of observations = 6*(N_Factor A)*(N_Factor B) = 6 * 6 * 4 = 144
DF Residuals = 144 - 5 - 3 - 15 - 1 = 120
Total DF = N - 1 = 143
(b) Critical F values
Factor A = F(5,120) = 2.30
Factor B = F(3,120) = 2.69
Interaction = F(15,120) = 1.76
(c) As F statistics for Factor A, Factor B as well as Interaction is >> Fc, Hence we can Reject the Null Hypothesis and warrant the rejection of the claim for equality of means
Hence there is a significant difference in Factor A and there is a significant difference in Factor B.
(d) As the F statistics for Interaction = 4.2 >> Fc (1.76), Hence we can conclude that there is a significant Interaction impact of Factor A and Factor B.
Hence there is a significant difference for Interaction term.
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Please help, confused which expression is equivalent???
Answer:
D
Step-by-step explanation:
m^ (-3 · -4) = m^12
n ^ (-2 · -4) = n^8
m^12 n^8
a complete description of simple harmonic motion must take into account several physical quantities and various mathematical relations among them. this information is needed to solve oscillation problems of this type. the position of a 60 gg oscillating mass is given by x(t)
a complete description of simple harmonic motion must take into account several physical quantities and various mathematical relations then the position of a 60 gg oscillating mass is given by x(t) -20 sin 10t
this information is needed to solve oscillation problems of this type
the position of a 60 gg oscillating mass is given by x(t)
x = 2 cos wt = 2 cos 10t ; w = 10
velocity = dx/dt = -2 x 10 sin 10 t.=- 20 sin 10t
t = .4
velocity = -20 sin 10 x .4 = -20 sin 4 = -20 x -0.7568 = 15.136 cm /s
w = √ k / m = 10 = √ k / .05
k = 15.136 N/m
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34) A company advertises on a website. A worker tracked the number of visits to the website and the number of clicks on the advertisement. The table shows the data for several days. A linear function can be used to model the data.
Based on the table, what is the best prediction of the number of clicks on the advertisement if 1,500 people visit the website?
A) 77 B) 137 C) 83 D) 105
The best prediction of the number of clicks on the advertisement if 1,500 people visit the website is; C: 83
How to interpret Function Tables?
We want to find the best prediction of the number of clicks on the advertisement if 1,500 people visit the website.
Now, we see the coordinates from the table;
(1045, 60)
(1106, 63)
(1500, y)
where y is the best prediction of the number of clicks on the advertisement if 1,500 people visit the website.
By interpolation, we can say that;
(y - 63)/(1500 - 1106) = (63 - 60)/(1106 - 1045)
(y - 63)/394 = 3/39
(y - 63)/394 = 1/13
Cross multiply to get;
y - 63 = 394/13
y = 93
Looking at the options, the closest option is option C.
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the base of a solid is a circular disk with radius 3. find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.
the base of a solid is a circular disk with radius 3. Therefore, the volume of the solid is 27π.
The volume of a solid is determined using the formula V = πr²h, where r is the radius of the base and h is the height of the solid. In this problem, the base is a circular disk with radius 3, and the cross-sections are isosceles right triangles with hypotenuse lying along the base. Since the cross-sections are isosceles right triangles, the height of each triangle is equal to the radius of the base, which is 3. Therefore, the height of the solid is also 3. Substituting these values into the formula gives V = π(3)²(3), which simplifies to V = 27π.
Therefore, the volume of the solid is:
V = πr²h
V = π(3)²(3)
V = 27π
Therefore, the volume of the solid is 27π.
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Omar has a classic car valued at $24275. It has been appreciating in value at the rate of 4.05% per
year. How much can he expect the car to be worth in 10 years?
The computation of the future value is $92,691.08
How to calculate the future value?As we know that
Future value = Present value × (1 + interest rate)^number of years
where, the Present value is $24275
The Interest rate is 4.05%
And, the number of the year is 10 years
Now placing these values to the above formula;
So, the future value is;
Future value = Present value × (1 + interest rate)^number of years
= $24275× (1 + 0.0405)^10
= $24275× 1.448298166
= $92,691.08
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If g(x) = 5x, what is the value of x when
g(x) = -60?
A) 12
C) -55
B) -300
D) -12
Answer:
-12
Step-by-step explanation:
If g(x) = 5x, then plugging in -60 for g(x) gives -60 = 5x. Dividing both sides of this equation by 5 gives -12 = x. Therefore, the correct answer is -12.
NEED HELP ASAP , THANKS! :)
I don’t quite understand , please fill the rest in
From the first two rows we can see that:
P = 435,n = 1,r = 0.039.Fill in the missing values.
Row 2[tex]435*1.039^3 = 487.91[/tex]Row 3[tex]435*1.039^t[/tex] and [tex]435*1.039^3 = 487.91[/tex]Row 4[tex]435*e^{0.039t}[/tex] and [tex]435*e^{0.039*3}=435*e^{0.117}=488.99[/tex]
A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the height, to the nearest foot, at a time of 3 seconds.
The height of the rocket in given time using regression equation is 586 feet.
The regression equation is, y = 7.70961x² + 176.30826x - 12.44515
Given,
A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet
That is,
x ; 0.6, 1.3, 1.8, 2.5, 3.1
y ; 108, 218, 285, 368, 436
We have to write a quadratic regression equation for the given set;
The quadratic regression equation is;
y = 7.70961x² + 176.30826x - 12.44515
Now,
We have to find the height at a time of 3 seconds using the equation;
So,
y = 7.70961 x 3² + 176.30826 x 3 - 12.44515
y = 69.38649 + 528.92478 - 12.44515
y = 585.86612
y = 586
Height of the rocket= 586 feet
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You are refilling your inventory of welcome packets for new customers. For each packet, it takes 5 minutes to print, 2 minutes to organize, and 5 minutes to proofread. The ink in the printer will need to be changed every 5 packets, which takes 3 minutes. You have 3 hours to dedicate to this task. Assume thathe ink in the printer was already changed before beginning and that you have to complete each packet before completing any steps for the next one. How many welcome packets will you be able to fully complete in the time allotted?
Answer:
5x + 2x + 5x + (3/5x) = 180
12x + 0.6x = 180
12.06x = 180
x = 14
14 packetsStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-How factorize this : ( + )( – ) + (– + )( – )
Answer:
this very easy to factorize this because (-+)is- (+-)-
(++)+ (--)+ but the sign which is bigger we have to keep that
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. TRUE or FALSE​
Answer:
True
Step-by-step explanation:
This is true by definition.
In a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.
How many were in math only?
How many were not majoring in computer science?
How many were not math or computer science?
a. The number of students who were in math only is 7 students.
b. The number of students who were not majoring in computer science is 15.
c. The number of students who were not math or computer science is 8
How to calculate the number of students?From the information given, in a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.
It should be noted that the number of math majors only will be:
= 13 - 6
= 7
The number of students not majoring in computer science will be:
= 25 - 10
= 15
Those not math or computer science majors will be:
= 25 - 6 - 7 - (10 - 6)
= 8
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4. Find the length of A B.
Using the Pythagorean triplet, the value of AB is 2.
In the given question we have to find the length of AB.
From the given diagram we can see that;
ED = 2, DC = 8 and BC = 6.
To solve this question we use the Pythagorean Triplet.
Pythagorean triples consist of the three positive numbers a, b, and c, where a^2+b^2 = c^2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.
Since we have to find the value of AB.
So we can write it as
EC^2 = AE^2+AC^2
(ED+DC)^2 = AE^2+(AB+BC)^2
Now putting the value
(2+8)^2 = AE^2+(6+AB)^2
10^2 = AE^2+(6+AB)^2
As we know that triplet (6,8,10).
The value of EC is 10, AE = 6, the value of AC can't be 6 because one part of value of AC is already given 6. So the value of AC is 8. AS BC=6, so AB=2.
Hence, the value of AB is 2.
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A rectangular prism made is 3 units high, 2 units wide, and 5 units long. What is its surface area in square units? Explain or show your reasoning.
Answer:
62 square units
Step-by-step explanation:
You want the surface area of a rectangular prism 3 units high, 2 units wide, and 5 units long.
AreaThe surface area of a rectangular prism is given by the formula ...
SA = 2(LW +H(L +W))
ApplicationUsing the given dimensions, L=5, W=2, H=3, the area is ...
SA = 2(5·2 +3(5 +2)) = 2(10 +3(7)) = 2(31)
SA = 62 . . . square units
The surface area of the prism is 62 square units.
Dec 09, 1:25:07 PM Given the following exponential function, identify whe growth or decay, and determine the percentage rate of Growth y = 2400(1.78)* % increase Submit Answer
The exponential function is y = 2400(1.78)x
Since 1.78 < 1, the function is an exponential decay function.
The function can also be written as 2400(1 - 0.04)x.
The rate of decrease is 4% (that's 0.04 expressed as a percent)
What is exponential function?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to opine that the exponential function is "the most important function in mathematics".To learn more about algebras refer to:
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In 2012, James Cameron descended to the bottom of Challenger Deep in the Marianas Trench; the deepest point in the ocean. The vessel he rode in was called DeepSea Challenger. Challenger Deep is 35,814 feet deep at its lowest point. The ascent can be modeled by a different proportional relationship y =kx. What is the value of k in this case?
What the value of k means in the proportional relationship y =kx is; the change in depth per second of the ascent.
How to Interpret Proportional Relationships?We are told that;
James Cameron descended to the bottom of Challenger Deep in the Marianas Trench; the deepest point in the ocean.
The vessel he rode in called DeepSea Challenger was 35,814 feet deep at its lowest point.
Now, if the time spent is denoted as x in seconds and the depth is denoted as y, the the relationship will be;
y = -kx
where -k is the constant of proportionality which is the change in depth per second of descent.
Now, if the ascent can be modeled by a different proportional relationship y = kx, then it means that k here will be the change in depth per second of the ascent.
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You have at most $23 to spend at a market. Apples cost $0.50 each, and pears cost $0.75 each. Let a be numbers of apples and p be numbers of pears. Write an inequality that represents the numbers of apples and pears you can afford
Do not include the dollar sign ($) in your inequality.
Answer:
0.5a + 0.75p ≤ 23
Step-by-step explanation:
Cost of a apples: 0.5a
Cost of p pears: 0.75p
The total cost must be $23 or less.
0.5a + 0.75p ≤ 23
you are dealt three cards without replacement from a standard 52-card deck. a) Find the probability of being dealt no hearts. b) Next, use complements to find the probability of being dealt at least one heart.
The the probability of being dealt no hearts is 0.75 and probability of being dealt at least one heart is 0.25 .
Total number of cards = 52
A : the probability of being dealt no hearts
B: the probability of being dealt with hearts
P( A ) = 1 - P( B)
= 1 - 13/52
= 1 -0.25
=0.75
C : probability of being dealt at least one heart
P(C) = 13C1 / 52C1
= 13 / 52
=0.25
Probability is a way to tell or calculate the possibility of an event to occur. Using it, we can make predictions about the likelihood of an event happening, or how likely it is , it helps to make predictions more clear .
The probability can be between 0 and 1 here , P being 0 means a failure and P being 1 means a success.
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A regular hexagon has a perimeter of 120 m. Find its area. Express your answer in the simplest radical form.
A) 1800√3m^2
B) 5√3m^2
C) 600√3m^2
D) 3600√3m^2
The area of the regular hexagon value calculated using given perimeter of the regular hexagon is equal to option C. 600√3 square meters.
As given in the question,
Perimeter of the regular hexagon is equal to 'P' = 120m
Relation between the area of the regular hexagon 'A' and the perimeter of the regular hexagon 'P is given by :
A = √3 × ( P²/24 )
= √3 × [(120)²/ 24]
= √3 × ( 14400 / 24 )
= √ 3 × 600
= 600√3 square meters
Therefore, the area of the regular hexagon using the perimeter of the regular hexagon is equal to Option C. 600√3 square meters.
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In each of 10 and 11, show that the given system has no periodic solutions other than constant solutions. dx dt = 2x 3y xy2, dy dt = y + x3 x2 y
The system does not have a periodic solution in each of 10 and 11.
A solution of the period depends on the independent variable t is called Periodic Solution. For a periodic solution x(t)( in the case of a system, x is a vector), there is a number T≠0 such that
x(t+T)=x(t) for t∈R.
The given equations are:
[tex]\frac{dx}{dt} =-2x-3y-xy^2\\\\\frac{dx}{dt} =y+x^3+x^2y[/tex]
F is the derivative of dx/dt and Gis the derivative of dy/dt:
[tex]F(x,y)=-2x-3y-xy^2\\G(x,y)=y+x^3+x^2y[/tex]
When Fx+Gx has the same sign on the entire domain D, then there are no periodic solutions on the domain D.
Fx+Gx=-2-y^2+1-x^2
=-1-y^2-x^2
<for all real numbers x,y[tex]\neq[/tex]0
Fx+Gx have the same sign for all pairs of real numbers with x[tex]\neq[/tex]0 and y[tex]\neq[/tex]0
Thus, there are no periodic solutions in the system(excluding contact solutions)
Hence proved.
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