Answer:
Part a) (a,b,c)=(10,19,9)
Part b) (a,b,c)=(9,3,1)
Please let be know if I have interpreted your question correctly. Thank you.
Step-by-step explanation:
Part a)
This is the way I interpret part a:
Find integers a,b,c such that a|(b-c) but a does not divide b and a does not divide c.
There are many triples satisfying part a.
One such triple is (a,b,c)=(3,10,7).
3 divides 10-7
But 3 does not divide 10 and 3 does not divide 7.
Another example is (a,b,c)=(2,7,5).
2 divides 7-5
But 2 doesn't divide 7 and 2 doesn't divide 5.
I will give another example.
(a,b,c)=(10,19,9)
10 divides 19-9
But 10 doesn't divide 19 and 10 doesn't divide 9
Part b)
This is the say I interpret part b:
a | (2b + 3c) but a does not divide b and a does not divide c
So lets let b=2 and c=5, then 2b+3c=19.
We just need to choose an a such that it divides 19 but not 2 and 5. That should be easy. 19 itself will do that.
So one (a,b,c) could be (19,2,5).
Let's try for another example.
Let b=3 and c=1.
Then 2b+3c=9.
So we just need to find an a that divides 9 but not 3 and not 1.
9 works.
So another example is (9, 3,1).
A man deposits $ 14,850 into a bank, which pays 4% interest that is compounded
semiannually. What will he have in his account at the end of three years?
Given:
Principal = $14850
Rate of interest = 4% compounded semiannually.
Time = 3 years
To find:
The amount after 3 years.
Solution:
Formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is principal, r is the rate of interest in decimal, n is the number of times interest compounded and t is the number of years.
The interest is compounded semiannually, so n=2.
Putting [tex]P=14850, r=4, n=2, t=3[/tex] in the above formula, we get
[tex]A=14850\left(1+\dfrac{0.04}{2}\right)^{2(3)}[/tex]
[tex]A=14850\left(1+0.02\right)^{6}[/tex]
[tex]A=14850\left(1.02\right)^{6}[/tex]
On further simplification, we get
[tex]A=14850(1.12616242)[/tex]
[tex]A=16723.511937[/tex]
[tex]A\approx 16723.51[/tex]
Therefore, the amount in the account after three years is $16723.51.
62x+2.63x = 1
Solve
EN
Step-by-step explanation:
answer is in photo above
Answer:
-2/5
Step-by-step explanation:
A home security system is designed to have a 90% reliability rate. Suppose that 6 home equipped with this system experience an attempted burglary. Find the probability that at least two of the alarms are triggered.
Answer:
0.999945 = 99.9945% probability that at least two of the alarms are triggered.
Step-by-step explanation:
For each alarm, there are only two possible outcomes. Either it is triggered, or it is not. The probability of an alarm being triggered is independent of any other alarm, 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.
A home security system is designed to have a 90% reliability rate.
This means that [tex]p = 0.9[/tex]
Suppose that 6 home equipped with this system experience an attempted burglary.
This means that [tex]n = 6[/tex]
Find the probability that at least two of the alarms are triggered.
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.9)^{0}.(0.1)^{6} = 0.000001[/tex]
[tex]P(X = 1) = C_{6,1}.(0.9)^{1}.(0.1)^{5} = 0.000054[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.000001 + 0.000054 = 0.000055[/tex]
Then
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.000055 = 0.999945[/tex]
0.999945 = 99.9945% probability that at least two of the alarms are triggered.
PLEASE HELP
A cube is a solid figure with six faces. Each face is a square. The surface area of a cube is the total area of all faces of the cube. When I increase the side length of a certain cube by 4, the surface area increases by 576. What is the volume of the original cube?
Step-by-step explanation:
the answer is in the image above
The volume of the original cube is 1000 cubic units.
What is volume of cube?The volume of a cube is equal to the product of length, width and height of a cube.
Let the length of side of the original cube = L
The surface area of the original cube A₁ = 6 L²
When increase the side length of a certain cube by 4
The surface area of the increased cube A₂ = 6 (L + 4)²
The surface area increases by 576
So, 6(L + 4)² - 6 L² = 576
6(L² + 16 + 8L) - 6 L² = 576
Divided by 6 both the sides,
L² + 16 + 8L - L² = 96
16 + 8L = 96
8L = 96 - 16
8L = 80
L = 80/8
L = 10
So, the length of side of the original cube = L = 10 units
The volume of the original cube = L³
The volume of the original cube = (10)³
The volume of the original cube = 1000 cubic units
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Plz help me solve this thanks
Answer:
y= -6/7
Step-by-step explanation:
.............. I did it, trust me
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with diameter 42 m. (Round your answer to two decimal places.) m3
Step-by-step explanation:
The volume of a hemisphere is given by :
[tex]V=\dfrac{2}{3}\pi r^3[/tex]
Taking differentiation,
[tex]\dfrac{dV}{dr}=2\pi r^2[/tex]
So,
[tex]dV=2\pi r^2\times dr[/tex]
Put r = 21 m and dr = 0.03 cm = 0.0003 m
[tex]dV=2\pi \times 21^2\times 0.0003\\\\dV=0.831\ m^3[/tex]
Hence, this is the required solution.
Find the area of the circle shown below if the radius is 13 inches. Use 3.14 for π. Use the formula π x R^2
A) None of these answers
B)2,122.64 inches
C)530.66 inches
D)20.41 inches
E)47.1 inches
Answer:
C
Step-by-step explanation:
that is the procedure above
The area of this circle with a radius of 13 inches is, C)530.66 inches
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
A circle with center A is given and the length of the line segment(radius),
AB = AD = AC = 13 inches.
We know, The area of a circle is,
= πr².
= π(13)² sq in.
= 530.66 sq in.
We can also find the perimeter or the circumference of the circle by the formula 2πr,
= 2π×13.
= 26π.
= 81.64 inches.
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[tex]\frac{y^2}{36} -1[/tex]
Answer:
that's my answer
Step-by-step explanation:
i hope it helps
write the equation to the axis of symmetry for this graph. help??
With the spot rate E_VND/USD = 21,000, the Forward Rate: F_VND/USD = 21,250; the Expected Rate after 3 months: Ee_VND/USD = 22,000, the hedging cost to an importer participating in the risk handling will be?
Answer:
Step-by-step explanation:
The importer needs to make the payment in the VND each time so the importer may enter into hedge to protect himself from the appreciation of the VND against the dollar, now if the importer enters into the forward contract of the hedge and he come across the reverse situation that means the VND is depriciating that means if the hedger would not have entered into a forward contract then they would have benefited more.
Lets convert above above rate in per VND rate to understand better.
E_USD/VND = 1/21000 = 0.000048
F_USD/VND = 0.000047
Ee_USD/VND = 0.000045
so as we can see above if we had enter into a hedge contract we have to pay the 0.000047 per VND and if we would not have enter into the contract we would have to pay the 0.000045 per VND hence cost of Hedging is 0.00002 USD per VND.
-7x is less than or equal to -21
What is the x value? Plz get back I need help with this soon.
On a coordinate plane, 3 lines are shown. Line m has points (negative 4, 3) and (0, negative 4). Line n has points (1, 2) and (3, negative 2). Line k has points (negative 3, negative 3) and (4, 1).
Use the diagram to answer the questions.
Is line m parallel to line n? Explain.
Is line m perpendicular to line k? Explain.
Answer:
actually, the answers are "No, the slopes are not equal"
and "Yes, the slopes are negative reciprocals".
Reason: just did it!!!!
Answer:
"No, the slopes are not equal"
and "Yes, the slopes are negative reciprocals".
Step-by-step explanation:
Yevgenia walks 8 x 2/3 miles every week which fraction represents the number of miles that Yevgenia walks each
Answer:
16/3
Step-by-step explanation:
When multiplyin fractions by whole numbers, you can make the whole number a fraction by simply making the denominator 1, than you will multiply numerators by numerators and denominators by denominators, therefore
8 x 2 = 16
1 x 3 = 3
16/3
A shopping attendant needs to price a large jigsaw puzzle returned by a customer. The customer paid a total of $33.04, including a convenience charge of $1.75 and 10% sales tax on the subtotal. Use the inverse to find the original price of the puzzle. If necessary, round your answer to the nearest cent.
Answer:
28.45
Step-by-step explanation:
33.04-1.75=31.29
31.29/1.10=28.45
What is the value of the expression below when z=3
6z^2 +2z+10
Answer:
6z^2 + 2z + 10
6 (3^2) + 2(3) + 10
6(9) + 6 + 10
54 + 16= 70
Janelle subtracts -4 from a number. The results is 2. What is the number?
Answer:
-2Step-by-step explanation:
Let the number is x, then we have:
x - (-4) = 2x = 2 + (-4)x = 2 - 4x = -2Can someone plz help..
Answer:
x = 40
3x=120
x+40 = 120
Step-by-step explanation:
The angles are vertical angles which means they are equal
3x= x+80
Subtract x from each side
3x-x =x+80-x
2x = 80
Divide by 2
2x/2 = 80/2
x = 40
3x = 3(40) =120
x+80 = 40+80 = 120
Help pleaseee (pre algebra)
Answer:
Robert had 78 coins or c=78
un tipo de bacteria se duplica cada 6 minutos.¿ cuántas bacterias habia en un comienzo si luego de una hora hay 2048?
Answer:
En un comienzo habia dos bacteria.
Step-by-step explanation:
find the volume of the rectangular prism in cubic feet
Answer:
1.632 ft^3
Step-by-step explanation:
3.4 times .8 times .6 = 1.632 ft.
therefore the volume of the rectangle is 1.632 ft^3
SEE ATTACHED IMAGE, THANK YOU!
Answer:
a)
X P[X]
0 5/14
1 15/28
2 3/28
b)
The expected value is 0.75
Step-by-step explanation:
Ok, we know that out of 8 cameras, 3 are defective.
So first let's find the probability for a camera randomly selected to be defective.
This is just the quotient between the number of defective cameras and the total number of cameras.
p = 3/8
then the probability that a camera is not defective is:
q = 5/8.
Ok, now we draw 2 cameras at random from the box.
We can define X as the number of defective cameras in these two drawn, we can have 3 possible values of X.
X = 0 (neither of the cameras is defective)
X = 1 (one of the cameras is defective)
X = 2 (both of the cameras is defective).
Let's find the probabilities for each case.
X = 0.
In this case, we first draw a non-defective camera, with a probability of:
P = 5/8.
The second camera drawn must be also non-defective, but now there are 4 non-defective cameras in the box and a total of 7 cameras (because one was already drawn).
Then the probability now is:
Q = 4/7
The joint probability is the product of the two individual probabilities:
P[0] = P*Q = (5/8)*(4/7) = (5/14)
X = 1
Here we have two cases:
the first is defective and the second is non-defective
the first is non-defective and the second is defective
So we just have a factor of 2, to consider both cases
Assuming the first case
Probability of drawing first a defective camera is equal to the quotient between the number of defective cameras and the total number of cameras:
P = 3/8
For the second draw we want to get a non-defective camera, here the probability is equal to the number of non-defective cameras remaining (5) and the total number of cameras (7, because we drawn one)
Q = 5/7
The joint probability, taking in account the permutation, is
P[1] = 2*P*Q = 2*(3/8)*(5/7) = (15/28)
finally, for X = 2
This is the case where we draw two defective cameras, we can use a similar approach as the one used in the first case:
For the first camera:
P = 3/8
For the second camera:
Q = 2/7
Joint probability:
P[2] = (3/8)*(2/7) = 3/28
then we have the table:
X P[X]
0 5/14
1 15/28
2 3/28
b)
The expected value for an event that has the outcomes:
{x₁, x₂, ..., xₙ}
Each one with the correspondent probability
{p₁, p₂, ..., pₙ}
is defined as:
EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ
Then in our case, the expected value is just:
EV = 0*P[0] + 1*P[1] + 2*P[2]
EV = 0 + 15/28 + 2*3/28
EV = (15 + 6)/28 = 21/28 = 0.75
An investment company advertised that last year its clients, on average, made a profit of 8% . Assuming that average refers to the mean, which of the following claims must be true based on this information?
a. This year some of their clients will make a profit of at least 8%.
b. Last year some of their clients made a profit of at least 8%.
c. Last year more than half of their clients made a profit of at least 8%.
d. Last year at least one of their clients made a profit of more than 11%.
e. Last year at least one of their clients made a profit of exactly 8%.
f. None of the above statements is true.
Answer:
The answer is "Option 2".
Step-by-step explanation:
Please find the complete question in the attached file.
When there is a mean value k in a set of data. Otherwise, we will assert with certainty that at least one of the values is k. They can't say anything at all about the maximum or even the minimum using knowledge only. Nevertheless, we know that certain numbers cannot be over and that all numbers cannot be below than mean. Mean also no value throughout the data set must be equal.
Which of the following is the net of a pyramid?
Answer:
The answer is A
Step-by-step explanation: a net of a pyramid will always have a square and 4 triangles around it.
What is the equation of the circle with center (−2, 5) that passes through
the point (4, −1)? Write the steps and instructions to find the equation.
Answer:
Step-by-step explanation:
the equation is 8 cause 10 equals 8
Simplify -|-7+4|
O 4
O -1/4
O -4
Answer:
Therefore, 7/4 simplified to lowest terms is 7/4.
A rectangular farm has an area of 1/2 square miles. If its length is 1/3 miles, what is its width?
Will give brain lest
Answer:
its 2/3 because if u divied the width u get that
Step-by-step explanation:
you welcome i tried
A farmer has a 40-acre farm in Georgia. The farmer is trying to determine how many acres of corn, peanuts, and cotton to plant. Each crop requires labor, fertilizer, and insecticide. The farmer has developed the following linear programming model to determine the number of acres of corn (X1), peanuts (X2), and cotton (X3) to plant in order to maximize profit. Max 550 X1 350 X2 450 X3 s.t. Constraint 1: 2 X1 3 X2 2 X3
Answer:
z (max) = 17461.54 $
x₁ = 29.23 acres
x₂ = 0
x₃ = 3.07
Step-by-step explanation: INCOMPLETE QUESTION.
As the problem statement establishes: "Each crop requires labor, fertilizer, and insecticide" and information about quantities and availability does not exist. To build a model and that such model would be feasible I copy from the internet the following data. We assume the problem is to maximize the number of acres to plant with a maximum of profit ( we will use as profit the numbers 550 ; 350 ; 450 for acres of corn, peanuts, and cotton)
Then z = 550*x₁ + 350*x₂ + 450*x₃ to maximize
labor (h) fertilizer ( tn) Insecticide (Tn)
acres of corn (x₁) 2 4 3
acres of peanut (x₂) 3 3 2
acres of cotton (x₃) 2 1 4
Availability acres 40 120 120 100
Constraints:
1) Size of the farm 120 acres
x₁ + x₂ + x₃ ≤ 40
2) labor 120 h
2*x₁ + 3*x₂ + 2*x₃ ≤ 120
3) Fertilizer 120 Tn
4*x₁ + 3*x₂ + 1*x₃ ≤ 120
4) Insecticide 100 Tn
3*x₁ + 2*x₂ + 4*x₃ ≤ 100
The Model is:
z = 550*x₁ + 350*x₂ + 450*x₃ to maximize
Subject to:
x₁ + x₂ + x₃ ≤ 40
2*x₁ + 3*x₂ + 2*x₃ ≤ 120
4*x₁ + 3*x₂ + 1*x₃ ≤ 120
3*x₁ + 2*x₂ + 4*x₃ ≤ 100
x₁ ≥ 0 ; x₂ ≥ 0 ; x₃ ≥ 0
After 3 iterations using an on-line solver optimal solution is:
z (max) = 17461.54 $
x₁ = 29.23 acres
x₂ = 0
x₃ = 3.07
exact value of cos 60° x sin 30°
Answer:
the exact value is 1/4
Step-by-step explanation:
Mark as brainllest if helps!!!
Answer:
0.25
Step-by-step explanation:
cos 60° = 0.5
sin 30° = 0.5
cos 60° x sin 30° = 0.5 x 0.5 = 0.25
Which equation can be used to find the measure of angle BAC?
Answer:
Step-by-step explanation:
tan x= opp./adj.
tan x = 12/5 so
x = tan^-1 (12/5)
second choice
Answer:
B
Step-by-step explanation:
If you horizontally stretch the quadratic parent function, f(x) = x^2, by a factor
of 5, what is the equation of the new function?
Answer:
New functinon is g(x) = (1/32)x^5
Step-by-step explanation:
If you horizontally stretch the quadratic parent function, f(x) = x^2, by a factor
of 5, the equation of the new function will be g(x) = (x/5)^2, or g(x) = (1/32)x^5
