The intensity of the beam 17 feet below the surface is 0.440265 times the initial intensity i0 of the incident beam is I(17) ≈ 0.002678.
It can be calculated as:
Let I(t) be the intensity of the beam at a depth of t feet below the surface, and
let k be a constant of proportionality.
Then we have:
[tex]dI/dt = -kI[/tex]
This equation says that the rate of change of intensity with respect to depth is proportional to the intensity itself, and the negative sign indicates that intensity decreases as depth increases.
We can solve this differential equation using separation of variables:
[tex]dI/I = -k dt[/tex]
[tex]\int\ dI/I = \int\ -k dt[/tex]
[tex]ln(I) = -kt + C[/tex]
[tex]I = e^{(C - kt)}[/tex]
where C is the constant of integration.
Now we can use the given information to find the value of k and the constant of integration C.
We know that at a depth of 3 feet below the surface, the intensity is 25% of the initial intensity i0:
[tex]I(3) = 0.25 i0[/tex]
[tex]e^{(C - 3k)} = 0.25 i0[/tex]
We also know that the depth at which we want to find the intensity is 17 feet below the surface:
t = 17
Now we can use the equation we derived earlier to find the intensity at a depth of 17 feet:
[tex]I(17) = e^{(C - 17k)}[/tex]
To find the constant of integration C and the constant of proportionality k, we can use the fact that we have two equations with two unknowns. First, we can solve the equation for C:
[tex]e^{(C - 3k)} = 0.25 i0[/tex]
[tex]C - 3k = ln{(0.25 i0)}[/tex]
[tex]C = ln{(0.25 i0)} + 3k[/tex]
Now we can substitute this expression for C into the equation for I(17):
[tex]I(17) = e^{(C - 17k)}[/tex]
[tex]I(17) = e^{(ln(0.25 i0) + 3k - 17k)}[/tex]
[tex]I(17) = e^{(ln(0.25 i0) - 14k)}[/tex]
Finally, we can solve for k using the fact that we know the intensity decreases by a factor of 0.25 when the depth increases from 0 to 3 feet:
[tex]dI/dt = -kI[/tex]
[tex]ln(I) = -kt + C[/tex]
[tex]I(3) = 0.25 i0[/tex]
[tex]e^{(C - 3k)} = 0.25 i0[/tex]
Taking the natural logarithm of both sides, we have:
[tex]C - 3k = ln{(0.25 i0)}[/tex]
Substituting the expression for C we derived earlier, we have:
[tex]ln{(0.25 i0)} + 3k - 3k = ln{(0.25 i0)}[/tex]
[tex]ln{(0.25 i0)} = ln{(0.25 i0)}[/tex]
This equation is true for all values of k, so we can choose any value for k that satisfies the differential equation.
For simplicity, we can choose[tex]k = ln(4)/3[/tex], which makes the constant of proportionality equal to[tex]-ln(4)/3.[/tex]
Now we can substitute this value of k into our expression for I(17) and simplify:
[tex]I(17) = e^{(ln(0.25 i0) - 14k)}[/tex]
[tex]I(17) = e^{(ln(0.25 i0) - 14ln(4)/3)}[/tex]
[tex]I(17) = 0.25 i0 e^{(-14ln(4)/3)}[/tex]
[tex]I(17) \approx 0.002678[/tex]
The intensity of the beam 17 feet below the surface is approximately 0.002678.
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Question 1 0.5 pts A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept focused on the man. Place the steps below in the correct order that they should be performed in order to the determine the rate at which the searchlight is rotating when the man is 15 ft from the point on the path closest to the searchlight. 1. Step 1 Draw a picture 2. Step 2 Write down the numerical info 3. Step 3 Determine what you are asket 4. Step 4 Write an equation relating the 5. Step 5 Plug in your known informatic 6. Step 6 Differentiate both sides of the h at a speed of 4 ft/s. A searchlight is located on the ground 20 ft d on th [Choose ] ey the de Differentiate both sides of the equation with respect to t on the 1 Determine what you are asked to find Write down the numerical information that you know Write an equation relating the variables Draw a picture Plug in your known information to solve the problem Write down the numerical info v V Determine what you are asker
In order to determine the rate at which the searchlight is rotating when the man is 15 ft from the point on the path closest to the searchlight, the following steps should be performed in this order
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Solve: 3√x-√9x-17 =1
The solution to the equation (3√x) - √(9x-17) = 1 is x = 9.
What is the solution to the given equation?Given the equation in the question (3√x) - √(9x-17) = 1.
To solve for x in the given equation:
(3√x) - √(9x-17) = 1
We can start by isolating the square root term on one side of the equation. Adding √(9x - 17) to both sides, we get:
(3√x) = √(9x - 17) + 1
Squaring both sides of the equation, we get:
(3√x)² = (√(9x - 17) + 1)²
9x = -16 + 2√(9x - 17) + 9x
Solve for 2√(9x - 17)
2√(9x - 17) = 16
36x - 68 = 256
Add 68 to both sides
36x - 68 + 68 = 256 + 68
36x = 324
x = 324/36
x = 9
Therefore, the solution is x = 9.
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I need help please
Answer:
136
Step-by-step explanation:
35x2+7x6+12x2
Which fractions are the equivalent to 4 10 + 40 100 ? A. 80 100 B. 4 5 C. 20 100 D. 8 10
4 10 + 40 100 is equivalent to 2/5 + 2/5, which simplifies to 4/5.
To find fractions that are equivalent to 4 10 + 40 100, we need to simplify the given fraction to its lowest terms.
First, we can simplify 4 10 by dividing both the numerator and denominator by the greatest common factor, which is 2. This gives us 2/5.
Next, we can simplify 40 100 by dividing both the numerator and denominator by the greatest common factor, which is 20. This gives us 2/5 as well.
Therefore, 4 10 + 40 100 is equivalent to 2/5 + 2/5, which simplifies to 4/5.
Now, to find fractions that are equivalent to 4/5, we can multiply the numerator and denominator by the same non-zero number.
For option A, 80/100 can be simplified to 4/5 by dividing both the numerator and denominator by 20. Therefore, A is equivalent to 4/5.
For option B, 4/5 is already in its simplest form, so B is equivalent to 4/5.
For option C, 20/100 can be simplified to 1/5 by dividing both the numerator and denominator by 20. Therefore, C is not equivalent to 4/5.
For option D, 8/10 can be simplified to 4/5 by dividing both the numerator and denominator by 2. Therefore, D is equivalent to 4/5.
In summary, options A, B, and D are equivalent to 4 10 + 40 100, while option C is not.
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a company purchased a new computer system for $28,000. one year later, the resale value of the system was $15,700. assume that the value of the computer system declines according to an exponential model. At what rate was the value of the computer system changing 4 years after it was purchased?
A. Declining at the rate of $2,767.74 per year.
B. Declining at the rate of $1,601.26 per year.
C. Declining at the rate of $3,6214.88 per year.
D. Declining at the rate of $8,803.21 per year.
E. Declining at the rate of $2,546.52 per year.
F. None of the above.
The rate at which the value of the computer system is changing 4 years after it was purchased is "Declining at the rate of $8,803.21 per year". The correct option is D.
We can use the exponential decay formula [tex]V(t) = V0 * e^{-kt}[/tex], where V(t) is the value of the computer system after t years, V0 is the initial value, and k is the decay rate.
We know that V(1) = $15,700 and V(0) = $28,000, so we can solve for k:
[tex]$15,700 = $28,000 * e^{-k*1}[/tex]
[tex]e^{-k} = 0.5607[/tex]
-k = ln(0.5607) ≈ -0.5797
k ≈ 0.5797
Therefore, the decay rate is approximately 0.5797 per year.
To find the rate of change of the value of the computer system 4 years after it was purchased, we can take the derivative of V(t) with respect to t:
dV/dt = -k * V0 * [tex]e^{-kt}[/tex]
Substituting t = 4, V0 = $28,000, and k ≈ 0.5797, we get:
dV/dt = -0.5797 * $28,000 * [tex]e^{-0.5797*4}[/tex] ≈ -$8,803.21 per year
Therefore, the value of the computer system is declining at the rate of approximately $8,803.21 per year 4 years after it was purchased.
The correct answer is (D) Declining at the rate of $8,803.21 per year.
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I NEED ANSWERS ASAP….
Answer:
Step-by-step explanation:
It is set up
7x+5x+2y=20
7x+5x=12x
12x+2y=20
x=0
y=10
12(0)+2(10)=20
Ok so maybe this was not the same type of equation i thought it was it is not that easy!
-. If f(x) = x² + 3x-2, find f(x) when x = -2
Answer:
-4
Step-by-step explanation:
substitute -2 into the formula and solve
[tex]f(x)=(-2)^2+3(-2)-2\\f(x)=4+(-6)-2\\\boxed{f(x)=-4}[/tex]
what is the value of y in the solution to the system of equations below.
y=-x+6
2x-y=-9
Answer:
I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.
for the first equation y=-x+6, y intercept is (0,6)
for equation two 2x-y=-9, y intercept is (0,9)
In both of the equations the x value is 1.
Solving for y without graphing. Y=9+2x
and x=-1
Step-by-step explanation:substitute i
HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5
It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.
Calculator Q15. y is directly proportional to x.
When x = 500, y = 50
b) Calcualte the value of y when x = 60.
If y is directly proportional to x, when x = 60, y = 6.
What is proportional?Proportional refers to a relationship between two quantities in which one quantity is a constant multiple of the other. In other words, if one quantity increases or decreases by a certain factor, the other quantity will also increase or decrease by the same factor.
What is directly proportional?Directly proportional is a specific type of proportionality where two quantities increase or decrease by the same factor. In other words, if one quantity doubles, the other quantity also doubles. If one quantity triples, the other quantity also triples, and so on.
In the given question,
If y is directly proportional to x, we can use the formula:
y = kx
where k is the constant of proportionality.
To find the value of k, we can use the given values:
y = kx
50 = k(500)
Solving for k:
k = 50/500
k = 0.1
Now that we know the value of k, we can use the formula to find the value of y when x = 60:
y = kxy = 0.1(60)
y = 6
Therefore, when x = 60, y = 6.
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Use the following function to find d(0)
d(x)=-x+-3
d(0)=
Answer:
d(0) = -3
Step-by-step explanation:
d(x) = -x + -3 d(0)
d(0) = 0 - 3
d(0) = -3
So, the answer is d(0) = -3
What is the answer I keep getting 32
Answer:
2 9/14
Step-by-step explanation:
What are the integer solutions to the inequality below?
−
4
<
x
≤
0
Step-by-step explanation:
x = +1
x = -2
x = -3
x = -4
Use number line to find the value and fit equation
a data set consists of the data given below plus one more data point. when the additional point is included in the data set the sample mean of the resulting data set is 32.083. what is the value of the additional data point?
The value of the additional data point is [tex]$19.17$[/tex].
What is the value of the additional data point?Let us first find the mean of the given data:
[tex]Mean = \frac{\sum_{i=1}^{n} x_i}{n}=\frac{39 + 45 + 43 + 42 + 44}{5}= 42.6[/tex]
Now let's find the value of the additional data point. Let the value of the additional data point be x. Therefore, the new sum of data is
[tex]$(39+45+43+42+44+x)$[/tex].
Total numbers of data are 6 (five given in the set and one additional data point).So, the mean of the resulting data set is given by:
[tex]32.083 = \frac{(39+45+43+42+44+x)}{6}[/tex]
Multiplying both sides of the equation by 6 we get:
[tex]6 \times 32.083 = (39+45+43+42+44+x)[/tex]
We have the value of [tex]$39+45+43+42+44$[/tex] which is [tex]$213$[/tex].
Therefore, substituting all the values, we get:
[tex]193.83 + x = 213[/tex]
On subtracting [tex]$193.83$[/tex] from both sides, we get the value of
[tex]x. x = 213 - 193.83 = 19.17[/tex]
Therefore, the value of the additional data point is [tex]$19.17$[/tex]
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Find the distance between each pair of points.
a. M= (0,-11) and P=(0,2)
b. A= (0,0) and B= (-3,-4)
c. C= (8,0) and D=(0,-6)
Answer:
To calculate the distance between each pair of points given, we can use the distance formula which is derived from the Pythagorean theorem. The formula is:
distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]
Using this formula, we can calculate the following distances:
a. Distance between M and P = 13 units
b. Distance between A and B = 5 units
c. Distance between C and D = 10 units
f(x)=3x^2+12+11 in vertex form
Answer:
y = -3(x - 2)^2 + 1. Explanation: x-coordinate of vertex: x = -b/(2a) = -12/-6 = 2 y-coordintae of vertex: y(2) = -12 + 24 - 11 = 1
Step-by-step explanation:
Answer:x-coordinate of vertex:
x = -b/(2a) = -12/-6 = 2
y-coordinate of vertex:
y(2) = -12 + 24 - 11 = 1
Vertex form:
y = -3(x - 2)^2 + 1
Check.
Develop y to get back to standard form:
y = -3(x^2 - 4x + 4) + 1 = -3x^2 + 12x - 11.
Step-by-step explanation:
Will make you brainlist!
Answer:
x = -2 , y = 2
Step-by-step explanation:
label your equations (1) and (2) the question mention to use elimination method and make x the same for both. To do that multiply equation (1) by 2. than label it (3)so 3x becomes 6x adding the equation (2)+(3) cancels out -6x and 6x so you can find value of yuse value of y to find xhope this helps :)
If a can of paint can cover 600 square inches, how many cans of paint are needed to cover 1,880 square inches
Answer:
1,880 sq in ÷ 600 sq in/can ≈ 3.13 cans
If you want you can round that to 4 cans.
Find the particular solution of the first-order linear differential equation for x > 0 that satisfies the initial condition. Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) = 9 y = sin x + 9x cos x +9
Previous question
Answer: Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) ... linear differential equation for x > 0 that satisfies the initial condition.
Step-by-step explanation:
A straw that is 15cm long leans against the inside of a glass. The diameter of a glass is
5cm, and has a height of 8cm. How far past the edge of the glass would the straw extend?
Round your answer to the nearest tenth.
The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.
Guidance Missile System A missile guidance system has seven fail-safe components. The probability of each failing is 0.2. Assume the variable is binomial. Find the following probabilities. Do not round intermediate values. Round the final answer to three decimal places, Part: 0 / 4 Part 1 of 4 (a) Exactly two will fail. Plexactly two will fail) = Part: 1/4 Part 2 of 4 (b) More than two will fail. P(more than two will fail) = Part: 214 Part: 2/4 Part 3 of 4 (c) All will fail. P(all will fail) = Part: 3/4 Part 4 of 4 (d) Compare the answers for parts a, b, and c, and explain why these results are reasonable. Since the probability of each event becomes less likely, the probabilities become (Choose one smaller larger Х 5
The probability of all will fail is the lowest.
The given problem states that a missile guidance system has seven fail-safe components, and the probability of each failing is 0.2. The given variable is binomial. We need to find the following probabilities:
(a) Exactly two will fail.
(b) More than two will fail.
(c) All will fail.
(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.
(a) Exactly two will fail.
The probability of exactly two will fail is given by;
P(exactly two will fail) = (7C2) × (0.2)2 × (0.8)5
= 21 × 0.04 × 0.32768
= 0.2713
Therefore, the probability of exactly two will fail is 0.2713.
(b) More than two will fail.
The probability of more than two will fail is given by;
P(more than two will fail) = P(X > 2)
= 1 - P(X ≤ 2)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2))
= 1 - [(7C0) × (0.2)0 × (0.8)7 + (7C1) × (0.2)1 × (0.8)6 + (7C2) × (0.2)2 × (0.8)5]
= 1 - (0.8)7 × [1 + 7 × 0.2 + 21 × (0.2)2]
= 1 - 0.2097152 × 3.848
= 0.1967
Therefore, the probability of more than two will fail is 0.1967.
(c) All will fail.
The probability of all will fail is given by;
P(all will fail) = P(X = 7) = (7C7) × (0.2)7 × (0.8)0
= 0.00002
Therefore, the probability of all will fail is 0.00002.
(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.
The probability of exactly two will fail is the highest probability, followed by the probability of more than two will fail. And, the probability of all will fail is the lowest probability. These results are reasonable since the more the number of components that fail, the less likely it is to happen. Therefore, it is reasonable that the probability of exactly two will fail is higher than the probability of more than two will fail, and the probability of all will fail is the lowest.
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g a random sample of 100 automobile owners in the state of alabama shows that an automobile is driven on average 23,500 miles per year with a standard deviation of 3900 miles. assume the distribution of measurements to be approximately normal. a) construct a 99% confidence interval for the average number of miles an automobile is driven annually in alabama.
We can be 99% confident that the average number of miles an automobile is driven annually in Alabama is between 21,342.6 and 24,637.4 miles
To answer this question, we need to use the following formula for a confidence interval for the mean: CI = (μ - z*(σ/√n), μ + z*(σ/√n)), Where μ is the population mean, z is the z-score for the given confidence level, σ is the population standard deviation, and n is the sample size. Using the given information, we can calculate the confidence interval for the mean:CI = (23500 - 2.575*(3900/√100), 23500 + 2.575*(3900/√100)), CI = (21342.6, 24637.4)
To summarize, we used the formula for a confidence interval for the mean and the given information to calculate the confidence interval for the average number of miles an automobile is driven annually in Alabama. This confidence interval is (21342.6, 24637.4), which means we can be 99% confident that the average number of miles an automobile is driven annually in Alabama is between 21,342.6 and 24,637.4 miles.
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suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward a distance of 6 units. what are the coordinates of your position? (x, y, z)
The coordinates of your position If we start at the origin, we are moving only along the x-axis of a distance of 7 units in positive direction and then only in the negative y-axis direction and z-coordinate is zero are (7,-6,0).
The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.
The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).
The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).
Therefore, the coordinates of our position are (7, -6, 0)
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One number is 13 less than another number. Let x represent the greater number. What is the sum of these two numbers?
Answer:
2x - 13
Step-by-step explanation:
If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:
x + (x - 13) = 2x - 13
Smores, a Taste of Multivariate Normal Distribution Smores Company store makes chocolate (Xi), marshmallow (X2), and graham cracker (Xs). Assume that the profit (in millions) for selling these smores materials follow a multivariate uormal ditributim with parameters 1 0.3 0.3 and Σ= 0.31 0 0.3 01 What is the probability that 1. the profit for selling chocolate is greater than 6 millions? 2. the profit for selling chocolate is greater than 6 millions, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 mllion? 3. P(3X1-1X2 + 3X3 > 20)?
The probability of [tex]3X1-1X2 + 3X3[/tex] being greater than 20 is given by[tex]P(3X1-1X2 + 3X3 > 20) = 1- Φ((20-3μ1+μ2-3μ3)/(√3σ11+σ22+3σ33))[/tex].
In this case, [tex]μ1=10, μ2=10, μ3=10, σ11=0.3, σ22=0.3, σ33=0.3,[/tex] so the probability of [tex]3X1-1X2 + 3X3[/tex] being greater than 20 is 1-Φ(-1.0).
1. To answer this question, we can use the formula for a multivariate normal distribution.
The probability of the profit for selling chocolate being greater than 6 million is given by P(X1 > 6) = 1- Φ(6-μ1)/(√σ11). In this case, μ1=10, σ11=0.3, so the probability of the profit being greater than 6 million is 1-Φ(2.667).
2. To answer this question, we need to use the formula for the conditional probability of a multivariate normal distribution.
The probability of the profit for selling chocolate being greater than 6 million, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 million, is given by
[tex]P(X1>6 | X2=5, X3=5) = 1- Φ((6-μ1-Σ12*5-Σ13*5)/(√σ11-Σ12²-Σ13²))[/tex]. In this case,
[tex]μ1=10, σ11=0.3, Σ12=0.3, Σ13=0.3,[/tex]so the probability of the profit being greater than 6 million is 1-Φ(-0.1).
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LetR=[0, 4]×[−1, 2]R=[0, 4]×[−1, 2]. Create a Riemann sum by subdividing [0, 4][0, 4] into m=2m=2 intervals, and [−1, 2][−1, 2] into n=3n=3 subintervals then use it to estimate the value of ∬R (3−xy2) dA∬R (3−xy2) dA.Take the sample points to be the upper left corner of each rectangle
The Riemann sum is:Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.
We can create a Riemann sum to estimate the value of the double integral ∬R (3-xy²) dA over the rectangular region R=[0, 4]×[-1, 2] by subdividing [0, 4] into m=2 intervals and [-1, 2] into n=3 intervals. Then we can evaluate the function at the upper left corner of each subrectangle, multiply by the area of the rectangle, and sum all the results.
The width of each subinterval in the x-direction is Δx=(4-0)/2=2, and the width of each subinterval in the y-direction is Δy=(2-(-1))/3=1. The area of each subrectangle is ΔA=ΔxΔy=2*1=2.
Therefore, the Riemann sum is:
Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.
Evaluating the function at the upper left corner of each subrectangle, we get:
(3-0*(-1)²)2 + (3-20²)2 + (3-21²)2 + (3-41²)*2 = 2 + 6 + 2 + (-22) = -12.
Thus, the estimate for the double integral is -12.
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Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Hence, 28 toy soldiers are the correct answer.
In mathematics, how is a group defined?A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.
Let's refer to the quantity of toy soldiers as "x".
We are aware that x is within the range of 27 and 54 thanks to the problem.
x can be divided by 4 without any remainders.
The residual is 6 when x is divided by 7.
The leftover after dividing x by five is three.
These criteria allow us to construct an equation system and find x.
Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:
x = 4k, where k is some integer.
Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:
x ≡ 6 (mod 7)
This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:
4k ≡ 6 (mod 7)
We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:
4(1) ≡ 6 (mod 7)
4 ≡ 6 (mod 7)
It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.
k = 2:
4(2) ≡ 6 (mod 7)
1 ≡ 6 (mod 7)
k = 3:
4(3) ≡ 6 (mod 7)
5 ≡ 6 (mod 7)
k = 4:
4(4) ≡ 6 (mod 7)
2 ≡ 6 (mod 7)
k = 5:
4(5) ≡ 6 (mod 7)
6 ≡ 6 (mod 7)
k = 6:
4(6) ≡ 6 (mod 7)
3 ≡ 6 (mod 7)
k = 7:
4(7) ≡ 6 (mod 7)
0 ≡ 6 (mod 7)
We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:
x = 4(7) = 28
This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.
28 toy soldiers are the correct response.
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in new york city at rush hour, the chance that a taxicab passes someone and is available is 15%. what is the probability that at least 10 cabs pass you before you find one that is free (before: success on 11th attempt or later).
The probability that at least 10 cabs pass you before you find one that is free is 0.00528665 or approximately 0.53%.
How to determine the probabilityThe solution to the problem is explained below:
Let, P(passes someone) = 0.15 or 15%
P(available taxi cab) = 0.85 or 85%
Let X be the number of cabs that pass before you find an available taxi cab. In order to find the probability that you see at least 10 cabs pass before you find a free one, we have to use the cumulative distribution function (CDF).
The probability that X is greater than or equal to 10 is equivalent to 1 - (the probability that X is less than 10). That is,P(X >= 10) = 1 - P(X < 10)
The probability that X is less than 10 is the probability of seeing 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 taxis pass you by.
Hence,P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)P(X = 0) = P(find an available taxi cab on the 1st attempt) = P(available taxi cab) = 0.85
P(X = 1) = P(find an available taxi cab on the 2nd attempt) = P(passed by the 1st taxi cab) x P(available taxi cab on the 2nd attempt) = (1 - P(available taxi cab)) x P(available taxi cab) = 0.15 x 0.85 = 0.1275
P(X = 2) = P(passed by the 1st taxi cab) x P(passed by the 2nd taxi cab) x P(available taxi cab on the 3rd attempt) = (1 - P(available taxi cab))² x P(available taxi cab) = 0.15² x 0.85 = 0.01817
P(X = 3) = (1 - P(available taxi cab))³ x P(available taxi cab) = 0.15³ x 0.85 = 0.002585
P(X = 4) = (1 - P(available taxi cab))⁴ x P(available taxi cab) = 0.15⁴ x 0.85 = 0.0003704
P(X = 5) = (1 - P(available taxi cab))⁵ x P(available taxi cab) = 0.15⁵ x 0.85 = 0.00005287
P(X = 6) = (1 - P(available taxi cab))⁶ x P(available taxi cab) = 0.15⁶ x 0.85 = 0.000007550
P(X = 7) = (1 - P(available taxi cab))⁷ x P(available taxi cab) = 0.15⁷ x 0.85 = 0.0000010825
P(X = 8) = (1 - P(available taxi cab))⁸ x P(available taxi cab) = 0.15⁸ x 0.85 = 0.000000154
P(X = 9) = (1 - P(available taxi cab))⁹ x P(available taxi cab) = 0.15⁹ x 0.85 = 0.0000000221
Hence,P(X < 10) = 0.85 + 0.1275 + 0.01817 + 0.002585 + 0.0003704 + 0.00005287 + 0.000007550 + 0.0000010825 + 0.000000154 + 0.0000000221 = 0.99471335
P(X >= 10) = 1 - P(X < 10) = 1 - 0.99471335 = 0.00528665
Therefore, the probability that at least 10 cabs pass you before you find one that is free is 0.00528665 or approximately 0.53%.
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Write an equation of the line that is parallel to y = 12
x + 3 and passes through the point (10, -5).
Answer:
y = 12x - 125
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 12x + 3 ← is in slope- intercept form
with slope m = 12
• Parallel lines have equal slopes , then
y = 12x + c ← is the partial equation
to fond c substitute (10, - 5 ) into the partial equation
- 5 = 12(10) + c = 120 + c ( subtract 120 from both sides )
- 125 = c
y = 12x - 125 ← equation of parallel line
What’s -9.1 times 3.75
The probability of drawing a black ball from a bag containing 5 black and 3 red ball is
Answer:
The probability of drawing a black ball can be calculated using the following formula:
Probability of drawing a black ball = Number of black balls / Total number of balls
In this case, there are 5 black balls and 3 red balls, so the total number of balls in the bag is:
Total number of balls = 5 + 3 = 8
Therefore, the probability of drawing a black ball is:
Probability of drawing a black ball = 5/8
So, the answer is the probability of drawing a black ball from a bag containing 5 black and 3 red balls is 5/8.
Step-by-step explanation:
