Solution :
Given :
There are five cities in a network and the cost of [tex]\text{building}[/tex] a road directly between [tex]i[/tex] and [tex]j[/tex] is the entry [tex]a_{i,j}[/tex]
[tex]a_{i,j}[/tex] refers to the matrix.
Road cannot be built because there is a mountain.
The given matrix :
[tex]\begin{bmatrix}0 & 3 & 5 & 11 & 9\\ 3 & 0 & 3 & 9 & 8\\ 5 & 3 & 0 & \infty & 10\\ 11 & 9 & \infty & 0 & 7\\ 9 & 8 & 10 & 7 & 0\end{bmatrix}[/tex]
The matrix on the left above corresponds to the weighted graph on the right.
Using the [tex]\text{Kruskal's algorithm}[/tex] we can select the cheapest edge that is not creating a cycle.
Starting with 2 edges of weight 3 and the edge of weight 5 is forbidden but the edge is 7 is available.
The edge of the weight 8 completes a minimum spanning tree and total weight 21.
If the edge of weight 8 had weight 10 then either of the edges of weight 9 could be chosen the complete the tree and in this case there could be 2 spanning trees with minimum value.
Evaluate −a2+c2 when c=−4.
Answer:
[tex]a = 4, -4[/tex]
Step-by-step explanation:
Step 1: Plug in -4 for c
[tex]-a^{2} + c^{2}[/tex]
[tex]-a^{2} + (-4)^{2}[/tex]
[tex]-a^{2} + 16[/tex]
Step 2: Solve for a
[tex]-a^{2}+16-16=0-16[/tex]
[tex]-a^{2}/-1 = -16/-1[/tex]
[tex]a^{2} = 16[/tex]
[tex]\sqrt{a^{2}} = \sqrt{16}[/tex]
[tex]a = 4, -4[/tex]
Answer: [tex]a = 4, -4[/tex]
A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events?
a. One out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
Answer:
a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.
b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.
Step-by-step explanation:
For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One out of four cars needs to have oil added.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
a. One out of the next four cars needs oil.
This is P(X = 1) when n = 4. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219[/tex]
0.4219 = 42.19% probability that one out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
This is P(X = 2) when n = 8. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115[/tex]
0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
This is P(X = 3) when n = 12. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581[/tex]
0.2581 = 25.81% probability that three out of the next 12 cars need oil.
Given C(4, 3) and D(-4, -3) are two points on a circle, centered at the origin. Given
that CD is a diameter of the circle,
a) Find the radius of the circle.
b) State the equation of the circle
Answer:000
Step-by-step explanation:000
A road crew must repave a road that is 2/3 miles long. They can repave 1/12 miles each hour. How long will it take the crew to repave the road?
Write your answer in simplest form.
You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x - 3y = 12
-x + 2y = 13
O A. Multiply the left side of equation 2 by 2. Then subtract the result from equation 1.
O B. Multiply equation 1 by 2 and equation 2 by 3. Then add the new equations.
C. Multiply equation 2 by-2. Then add the result to equation 1.
Answer:
A.
Step-by-step explanation:
The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.
If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.
If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.
When multiplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).
So, option B is not allowed (it is not allowed to multiply only one part of the equation)
Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 28. A pollster draws a sample of 92
people to interview.
Answer:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 41, standard deviation of 28:
This means that [tex]\mu = 41, \sigma = 28[/tex]
Sample of 92:
This means that [tex]n = 92, s = \frac{28}{\sqrt{92}} = 2.92[/tex]
Distribution of the sample means:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
1
Select the correct answer.
Simplify the following expression.
우
O A.
OB. 12
Oc. 1
OD.
64
Reset
Next
Answer:
1/64
Step-by-step explanation:
4^ (-11/3) ÷ 4 ^ (-2/3)
We know a^b ÷a^c = a^(b-c)
4 ^(-11/3 - - 2/3)
4^(-11/3 +2/3)
4^(-9/3)
4^ -3
We know a^-b = 1/a^b
1/4^3
1/64
The diameter of a circle is inches what is the area?
Answer:
Pie( r ^2)
Step-by-step explanation:
Here value of r is in inches
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=tcost, y=tsint, t=π
Step-by-step explanation:
the answer is in the image above
The firm has bonds with par value of 10,000,000 VND, coupon rate of 11%, annual interest payment, and the remaining maturity period is 07 years. If the bond's interest rate and current risk level have a return rate of 12%, what price should company C sell the bond in the present?
a.
10,000,000
b.
14,152,000
c.
12,053,000
d.
11,150,000
Didi invested a total of $16125 in two accounts paying 8.5% and 4% simple interest. If her total return at the end of 2 years was 1740 , how much did she invest in each account?
Answer:
5000 ;
11125
Step-by-step explanation:
Given :
Total principal = 16125
Rates = 8.5% and 4%
Period, t = 2 years
Total interest = 1740
Let :
Principal amount invested at 8.5% = x
Principal amount invested at 4% = 16125 - x
Interest formula :
Interest = principal * rate * time
Hence, mathematically ;
(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740
(0.17x + 1290 - 0.08x ) = 1740
0.09x + 1290 = 1740
0.09x = 1740 - 1290
0.09x = 450
x = 450 / 0.09
x = 5000
Amount invested at 4% :
16125 - 5000 = 11125
The value of the expression 23 +32–3x4–52-5+(7x4) is
Answer:
24
Explanation:
(23+32)-(3×4)-(52-5)+(7×4)
(55)-(12)-(47)+(28)
55-12=43-47+28= -1943-19=24How do u determine the equation of the line through each pair of points in slope-intercept form (y=mx+b). (3,0) and (2,4) (-6,3) and (2,-2)
Answer:
Y =-4X +12
Y =-0.625X -0.75
Step-by-step explanation:
(3,0) and (2,4)....
x1 y1 x2 y2
3 0 2 4
(Y2-Y1) (4)-(0)= 4 ΔY 4
(X2-X1) (2)-(3)= -1 ΔX -1
slope= -4
B= 12
Y =-4X +12
~~~~~~~~~~~~~~~~~
(-6,3) and (2,-2)
x1 y1 x2 y2
-6 3 2 -2
(Y2-Y1) (-2)-(3)= -5 ΔY -5
(X2-X1) (2)-(-6)= 8 ΔX 8
slope= - 5/8
B= - 3/4
Y =-0.625X -0.75
What is the squad root of 81
Answer:
[tex]9[/tex]
Step-by-step explanation:
Step 1: Find the square root of 81
[tex]\sqrt{81}[/tex]
[tex]\sqrt{9*9}[/tex]
[tex]\sqrt{9^{2}}[/tex]
[tex]9[/tex]
Answer: [tex]9[/tex]
Answer:
the square root of 81 is 9
Use the distributive property to remove the parentheses.
-5(6u - 4w-2)
Answer:
-30u+20w+10
Step-by-step explanation:
multiple each term inside the parenthesis by -5. remember negative times negative = positive
7/18 - 1/3 , 1/2 - 1/5 - 1/10 and 3 1/2 - 2 5/9 please help thank you
Answer:
Step-by-step explanation:
7/18=7/18
it cant be divided agian
1/3=1/3
it cant be divded agian
1/5=1/5
it cant be divded agian
1/10=1/10
it cant be divded agian
3 1/2=3/2
2 5/9 =10/9
i am not sure if this is what you wanted ...
PLEASE ANSWER I WILL GIVE BRAINLIEST FAST
Answer:
E &F
Step-by-step explanation:
The rules of a 30-60-90 Triangle is E, and F is just a different value of numbers (but the same ratio).
The longest leg is Select one:
a. 5√3
b. 10√3
c. 5
d. 20
Answer:
D:20
sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20
Step-by-step explanation:
find the exact value of tan -75
Which graph represents the function f (x) = StartFraction 5 minus 5 x squared Over x squared EndFraction? On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.
9514 1404 393
Answer:
2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3
Step-by-step explanation:
Technically, the curve is not a hyperbola. A hyperbola is of the form 1/x; this one is of the form 1/x².
The function can be simplified to ...
f(x) = 5/x² -5
which is a "hyperbola" with a vertical asymptote at x=0 and a vertical translation of -5 units to bring parts of it into the 3rd and 4th quadrants.
Select the correct answer. This table represents a quadratic function. x y 0 -3 1 -3.75 2 -4 3 -3.75 4 -3 5 -1.75
I really need one fast
I give all my points
Answer:
1/4
Step-by-step explanation:
that is the answer
I found the constant which was -3
a = 1/4
b=-1
Answer:
the value of a in the function's equation is 1/4
Step-by-step explanation:
Plato answer
What is the slope formula?
Answer:
D is your answer
Step-by-step explanation:
Answer:
Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx
Step-by-step explanation:
Find the perimeter and area of a square with sides 6 inches in length.
I need two examples of Solve a proportion with a mixed number in one of its numerators. SHOW ALL WORK!!!!!!!!!!!!
Answer:
A proportion equation is something like:
[tex]\frac{A}{B} = \frac{x}{C}[/tex]
Where A, B, and C are known numbers, and we want to find the value of x.
Now we want two cases where in one of the numerators we have a mixed number, where a mixed number is something like:
1 and 1/3
which actually should be written as:
1 + 1/3
1) a random problem can be:
[tex]\frac{1 + 1/3}{4} = \frac{x}{5}[/tex]
We can see that the numerator on the left is a mixed number.
First, let's rewrite the numerator then:
1 + 1/3
we need to have the same denominator in both numbers, so we can multiply and divide by 3 the number 1:
(3/3)*1 + 1/3
3/3 + 1/3 = 4/3
now we can rewrite our equation as:
[tex]\frac{4/3}{4} = \frac{x}{5}[/tex]
now we can solve this:
[tex]\frac{4/3}{4} = \frac{4}{3*4} = \frac{x}{5} \\\\\frac{1}{3} = \frac{x}{5}[/tex]
now we can multiply both sides by 5 to get:
[tex]\frac{5}{3} = x[/tex]
Now let's look at another example, this time we will have the variable x in the denominator:
[tex]\frac{7}{12} = \frac{3 + 4/7}{x}[/tex]
We can see that we have a mixed number in one numerator.
Let's rewrite that number as a fraction:
3 + 4/7
let's multiply and divide the 3 by 7.
(7/7)*3 + 4/7
21/7 + 4/7
25/7
Then we can rewrite our equation as
[tex]\frac{7}{12} = \frac{25/7}{x}[/tex]
Now we can multiply both sides by x to get:
[tex]\frac{7}{12}*x = \frac{25}{7}[/tex]
Now we need to multiply both sides by (12/7) to get:
[tex]x = \frac{25}{7}*\frac{12}{7} = 300/49[/tex]
At the beginning of an experiment, a scientist has 120 grams of radioactive goo. After 135 minutes, her sample has decayed to 3.75 grams. Find an exponential formula for G ( t ) G(t) , the amount of goo remaining at time t t .
Answer:
[tex]G(t) = 120e^{-0.0257t}[/tex]
Step-by-step explanation:
Amount of substance:
The amount of the substance after t minutes is given by:
[tex]G(t) = G(0)e^{-kt}[/tex]
In which G(0) is the initial amount and k is the decay rate.
At the beginning of an experiment, a scientist has 120 grams of radioactive goo.
This means that [tex]G(0) = 120[/tex], so:
[tex]G(t) = G(0)e^{-kt}[/tex]
[tex]G(t) = 120e^{-kt}[/tex]
After 135 minutes, her sample has decayed to 3.75 grams.
This means that [tex]G(135) = 3.75[/tex].
We use this to find k. So
[tex]G(t) = 120e^{-kt}[/tex]
[tex]3.75 = 120e^{-135k}[/tex]
[tex]e^{-135k} = \frac{3.75}{120}[/tex]
[tex]\ln{e^{-135k}} = \ln{\frac{3.75}{120}}[/tex]
[tex]-135k = \ln{\frac{3.75}{120}}[/tex]
[tex]k = -\frac{\ln{\frac{3.75}{120}}}{135}[/tex]
[tex]k = 0.0257[/tex]
So
[tex]G(t) = 120e^{-0.0257t}[/tex]
Write the sentence as an inequality. The cost of a ticket t will be no more than $52.
Answer:
t is less than or equal to $52, or t <= $52
Step-by-step explanation:
If you can't have more than $52, then use less than symbol (<). The sentence doesn't state that a ticket shouldn't cost $52, so it's safe to assume that you can have exactly $52.
The angles in a triangle are 89, 1, and 90 degrees. Classify the triangle by its angles and sides.
A. Right isosceles
B. Right Scalene
C. Obtuse scalene
D. Acute isosceles
E. Acute scalene
F. Obtuse isosceles
Answer: B. Right Scalene
Step-by-step explanation: Right because one of the degrees is 90 and scalene because no of the sides of the triangle are the same length.
Answer:
b
Step-by-step explanation:
(a). Find the value of log 216.
Answer:
2.334453751
Step-by-step explanation:
Press log on your Casio calculator (if you have one) and plug in 216, then close the parentheses!
Calculus 3 Problem
7. Determine if the field F(x, y, z) = ye^z i + xe^z j + xy e^z k is conservative. If it is, find a potential function.
Step-by-step explanation:
Given:
[tex]\vec{\textbf{F}}(x, y, z) = ye^z\hat{\textbf{i}} + xe^z\hat{\textbf{j}} + xye^z\hat{\textbf{k}}[/tex]
A vector field is conservative if
[tex]\vec{\nabla}\textbf{×}\vec{\text{F}} = 0[/tex]
Looking at the components,
[tex]\left(\vec{\nabla}\textbf{×}\vec{\text{F}}\right)_x = \left(\dfrac{\partial F_z}{\partial y} - \dfrac{\partial F_y}{\partial z}\right)_x[/tex]
[tex]= xe^z - ye^z \neq 0[/tex]
Since the x- component is not equal to zero, then the field is not conservative so there is no scalar potential [tex]\phi[/tex].
How do you know if a radical can be simplified? Explain.
Answer:
An expression is considered simplified only if there is no radical sign in the denominator. If we do have a radical sign, we have to rationalize the denominator . This is achieved by multiplying both the numerator and denominator by the radical in the denominator.
