Sam says, "I am thinking of 3 consecutive numbers. The first is a multiple of 4, the second is a multiple of 5 and the third is a multiple of 6." What could the numbers be? Can you find 3 possible sets of numbers?

To match the third-order linear equations with their fundamental solution sets, we will analyze the characteristics of each equation and determine the corresponding solutions. The correct matches are as follows:

y'''−5y''+y'−5y=0 -> D. 1cos(t)sin(t)

y'''−y''−y'+y=0 -> C. 1e4te3t

y'''−7y''+12y'=0 -> B. 1tt3

y'''+3y''+3y'+y=0 -> F. e−tte−tt2e−t

ty'''−y''=0 -> E. e5tcos(t)sin(t)

y'''+y'=0 -> A. ettete−t

For the equation y'''−5y''+y'−5y=0, the characteristic equation has complex roots. The corresponding fundamental solution set is D. 1cos(t)sin(t).

The equation y'''−y''−y'+y=0 has distinct real roots. The fundamental solution set is C. 1e4te3t.

The equation y'''−7y''+12y'=0 has a repeated real root. The fundamental solution set is B. 1tt3.

In the equation y'''+3y''+3y'+y=0, the characteristic equation has a repeated complex root. The corresponding fundamental solution set is F. e−tte−tt2e−t.

For the equation ty'''−y''=0, we have a differential equation with a variable coefficient. The fundamental solution set is E. e5tcos(t)sin(t).

The equation y'''+y'=0 has distinct real roots. The fundamental solution set is A. ettete−t.

By matching the characteristics of each equation with the appropriate solution set, we can determine the correct matches for the given third-order linear equations.

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The absolute threshold is defined as the minimum detectable stimulus or intensity.

The absolute threshold refers to the minimum amount or level of a stimulus that is required for it to be detected or perceived by an individual. It is the point at which a stimulus becomes perceptible or noticeable to a person.

In sensory psychology, the absolute threshold is typically measured in terms of the lowest intensity or magnitude of a stimulus that can be detected accurately by a person at least 50% of the time. It represents the boundary between the absence of perception and the presence of perception.

The absolute threshold can vary depending on the sensory modality being tested. For example, in vision, it may refer to the minimum amount of light required for a person to see an object. In hearing, it may represent the minimum sound intensity needed for an individual to hear a tone.

Several factors can influence the absolute threshold, including individual differences, physiological factors, and the nature of the stimulus itself. Factors such as sensory acuity, attention, fatigue, and background noise can all affect an individual's ability to detect a stimulus.

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The required probabilities for the events in question are:

Based on the parameters given :

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Total number of slots = 18+18+2 = 38

A.)

Probability of green slots 2 or more times :

(2/38)² × (36/38)²³ = 0.00080

B.)

Probability of ball not entering the green slots

1 - P(green slots)

P(not entering green slot ) = 1 - 0.0008 = 0.9992

C.)

probability that ball falls into black slot 15 or more times :

(18/38)¹⁵ * (20/38)¹⁰ = \(2.21\times10^{-8}\)

D.)

Probability that ball falls into red slot 10 or less times :

(10/38)¹⁰ * (28/38)¹⁵ = \(1.63\times10^{-8}\)

Therefore, the required probabilities are :

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The relation displayed in the table is

The relation in the table is compared by identifying how a coordinate point are expressed as ordered pair and how they are expressed as a table

For instance, say (b, c) is represented in a table as

x    y

a    b

Using this instance and writing out the values in the table we have

(3, 3), (-1, 1), (2, -2), and (-3, 2)

This is similar to option B making option B the appropriate option

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Answer:

1)r=√V/πh

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

Hope it's helpful for you

pls mark above guy ans as brainliest

The general solution to the given differential equation is:

R = 4tan[arctan(R/8) + (C - 4ln2)/4]

To solve the given differential equation:

dR/dx = a(R^2 + 16)

We can separate the variables R and x by dividing both sides by (R^2 + 16):

1 / (R^2 + 16) dR/dx = a

Integrating both sides with respect to x, we get:

∫ 1 / (R^2 + 16) dR = ∫ a dx

We can evaluate the left integral using the substitution u = R/4:

1/4 ∫ 1 / (u^2 + 1) du = arctan(u/2) + C1

where C1 is a constant of integration.

Substituting back for u and simplifying, we have:

1/4 ∫ 1 / (R^2 / 16 + 1) dR = arctan(R/8) + C1

Multiplying both sides by 4, we get:

∫ 1 / (R^2 / 16 + 1) dR = 4arctan(R/8) + C

where C = 4C1 is a constant of integration.

To evaluate the integral on the left, we can use the substitution v = R/4:

∫ 1 / (v^2 + 1) dv = ln|v| + C2

where C2 is another constant of integration.

Substituting back for v and simplifying, we have:

∫ 1 / (R^2 / 16 + 1) dR = 4ln|R/4| + C

Combining this with our earlier result, we have:

4ln|R/4| + C = 4arctan(R/8) + C

Solving for R, we get:

R = 4tan[arctan(R/8) + (C - 4ln2)/4]

where C is the constant of integration.

Therefore, the general solution to the given differential equation is:

R = 4tan[arctan(R/8) + (C - 4ln2)/4]

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To solve this differential equation, we can separate the variables and integrate both sides: dR/(R^2+16) = a dx To integrate the left-hand side, we can use partial fractions: 1/(R^2+16) = (1/16) [1/(R+4) - 1/(R-4)] So the equation becomes:
(1/16) [1/(R+4) - 1/(R-4)] dR = a dx

Integrating both sides gives:

(1/16) ln(|R+4|) - (1/16) ln(|R-4|) = ax + C

where C is the constant of integration. We can simplify this expression by combining the logarithms and taking the exponential of both sides:

| (R+4)/(R-4) | = e^(16a x + C)

Since a is non-zero, we know that e^(16a x + C) is always positive. Therefore, we can remove the absolute value bars:

(R+4)/(R-4) = e^(16a x + C)

Multiplying both sides by (R-4) gives:

R+4 = e^(16a x + C) (R-4)

Expanding the right-hand side gives:

R+4 = e^(16a x + C) R - 4 e^(16a x + C)

Bringing all the R terms to one side gives:

R - e^(16a x + C) R = -4 - 4 e^(16a x + C)

Factorizing R gives:

R (1 - e^(16a x + C)) = -4 (1 + e^(16a x + C))

Dividing both sides by (1 - e^(16a x + C)) gives the solution:

R = 4 (e^(16a x + C) - 1) / (e^(16a x + C) + 1)

This is the general solution to the differential equation. The constant C can be determined by using an initial condition or boundary condition.
Hello! I'd be happy to help you solve the differential equation. We are given the differential equation:

dR/dx = a(R^2 + 16)

To solve this, we will follow these steps:

Step 1: Separate variables
We need to separate the variables R and x. We do this by dividing both sides by (R^2 + 16):

(1 / (R^2 + 16)) dR = a dx

Step 2: Integrate both sides
Now, we will integrate both sides with respect to their respective variables:

∫ (1 / (R^2 + 16)) dR = ∫ a dx

Step 3: Perform the integration
We will use the arctangent integration formula for the left side:

(1/4) * arctan(R/4) = ax + C

Step 4: Solve for R
To find R in terms of x, we first multiply both sides by 4:

arctan(R/4) = 4ax + 4C

Next, take the tangent of both sides:

tan(arctan(R/4)) = tan(4ax + 4C)

R/4 = tan(4ax + 4C)

Finally, multiply both sides by 4 to isolate R:

R = 4 * tan(4ax + 4C)

So, the solution to the differential equation is:

R = 4 * tan(4ax + 4C)

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Answer:

$15

Step-by-step explanation:

Answer

Use division, how many times will 14 go into 210?

210÷14=15

$15

Or you can also multiply 15x14=210

Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

Answer:

B one

Step-by-step explanation:

3y + 5 - 2y = 11

3y -2y + 5 = 11

Combine like terms

y + 5 = 11

Subtract  5 from both sides

y = 11 - 5

y = 6

So, Only one solution

Answer:

there is only 1 solution.

Step-by-step explanation:

We can solve the equation to find it's number of solutions, but we already know it only has 1 solution because it is a linear equation (y is raised to the first power).

3y + 5 − 2y = 11

y + 5 = 11

y = 6

This confirms that there is only 1 solution.-------

Answer:

x ≥ 5

Step-by-step explanation:

3x - 8 ≥ 7 ( add 8 to both sides )

3x ≥ 15 ( divide both sides by 3 )

x ≥ 5

There are 1144 hands of three cards dealt from a standard deck that contains cards from only one suit.

To calculate the number of hands of three cards dealt from a standard deck that contains cards from only one suit, we can use the following approach:

Choose one of the four suits - this can be done in 4 ways.

Choose three cards from the chosen suit - this can be done in (13 choose 3) ways.

As we have only one suit in our hand, we cannot choose any cards from the other three suits.

Therefore, the total number of hands of three cards that contain cards from only one suit is:

4 * (13 choose 3) = 4 * (286) = 1144

Hence, there are 1144 hands of three cards dealt from a standard deck that contains cards from only one suit.

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Answer:

125.84

Step-by-step explanation:

116.52(0.08)=9.32

116.52+9.32=125.84

Answer:

The total is $125.84.

Step-by-step explanation:

The total is equal to the original value (100%) + the tax amount (8%) which equals 108%. To multiply it, we move the decimal two to the left to get our figure (1.08) then multiply that times 116.52. So, 116.52x1.08=125.8416; for dollars I rounded to the nearest cent: $125.84.

The nearest whole number after rounding is, 14

Rounding a number to the nearest tenth means finding the nearest multiple of 0.1.

To do this, you need to look at the digit in the hundredths place (the second digit after the decimal point) of the number you want to round.

If that digit is 5 or greater, you round the number up by adding 0.1 to the nearest whole number.

If that digit is 4 or less, you round the number down by leaving the nearest whole number unchanged.

For example, rounding 3.456 to the nearest tenth gives 3.5, while rounding 3.444 to the nearest tenth gives 3.4.

Given that,

The decimal number  13.5,

after using rules of rounding,

it can be rounded as 14

Hence, the nearest whole number is 14

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Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

The range of the function is [400, ∞) because the interest rate is positive, so the amount of money in the savings account will always increase over time.

Here is a table of values for the function g(x) = 400(1.05)x:

x | g(x)

-------|--------

0 | 400

1 | 420

2 | 441

3 | 462.05

4 | 483.1625

... | ...

The function will never reach 0, because the interest rate is greater than 0.

Therefore, the amount of money in the savings account increases over time. It will never reach 0, because the interest rate is greater than 0.

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To determine if two quantities vary directly, we can check if their ratio remains constant when one quantity changes while the other is multiplied by a constant factor.

Wh

en two quantities vary directly, it means that they change in the same proportion. In other words, if one quantity increases, the other quantity also increases by a constant factor, and if one quantity decreases, the other quantity also decreases by the same constant factor.

To determine if two quantities vary directly, we can compare their ratios. Suppose we have two quantities, A and B. If their ratio, A/B, remains constant for different values of A and B, then the two quantities vary directly.

For example, let's consider the relationship between the distance traveled (D) and the time taken (T) for a moving object. If the ratio D/T remains constant for different distances and times, then we can say that the distance traveled and the time taken vary directly.

Mathematically, if

D/T = k,

where k is a constant, then D and T vary directly. This implies that if we double the distance traveled, the time taken will also double, or if we triple the distance, the time will also triple, and so on. The ratio D/T will always be the same constant value, indicating a direct

variation.

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Based οn the infοrmatiοn prοvided, we can see that the prοfit earned (p) is prοpοrtiοnal tο the number οf cοοkies sοld (c).

We can write the equatiοn as:

p = 0.25c

This equatiοn means that fοr every cοοkie sοld, the prοfit earned is $0.25. We can alsο write this equatiοn in slοpe-intercept fοrm as:

y = mx + b

where y represents prοfit earned (p), x represents the number οf cοοkies sοld (c), m represents the slοpe (0.25 in this case), and b represents the y-intercept (the value οf y when x is 0, which is 0 in this case).

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Answer:

x = 12

Step-by-step explanation:

12x = 146 - 2

x = 144 ÷ 12

x = 12

Answer:

(1/2)n

Step-by-step explanation:

I think this should be correct. A will be "1" and then for every scale (n) it will be scaled by 1/2.

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

The order of operations (PEMDAS) should be followed to solve mathematical expressions: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

So the solution for (7+3) x 4 ÷ 2 - 5 x 6

= (10) x 4 ÷ 2 - 5 x 6

= 40 ÷ 2 - 5 x 6

= 20 - 5 x 6

= 20 - 30

= -10

So the solution is -10

Answer:

7 + 3 = 10

10 * 4 = 40

40 / 2 = 20

20 - 5 = 15

15 * 6 = 90!

Step-by-step explanation:

Hope it helps ! =D

Answer: im having the same problem

Step-by-step explanation:

From the quadrilateral proof seen below we can prove that;

∠C + ∠D = 2∠AOB

The bisection of an angle simply means to divide an angle into two equal parts.

The sum of the interior angles of a quadrilateral is 360 degrees. Thus;

∠A + ∠B + ∠C + ∠D = 360°     ------(1)

In △AOB,

∠AOB + ∠A/2 + ∠B/2 = 180°

Multiply through by 2 to get;

2∠AOB + ∠A + ∠B = 360°

Thus;

∠A + ∠B = 360° - 2∠AOB

Put 360° - 2∠AOB for ∠A + ∠B in eq 1 to get;

360° - 2∠AOB + ∠C + ∠D = 360°

This simplifies to;

∠C + ∠D = 2∠AOB

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Complete question is;

Bisectors of two adjacent angles of angles A and B of quadrilateral ABCD intersect at a point O. Prove that 2∠AOB = ∠C + ∠D

The solution for equation is at (-2, 0).

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

Both linear equations with one variable and those with two variables exist.

Given equations,

y = x + 2

y = x² + 5x + 6

substitute value of y in second equation

x + 2 = x² + 5x + 6

x² + 4x + 4 = 0

x² + 2x + 2x +4 = 0

x(x +2) + 2(x + 2) = 0

(x + 2)(x + 2) = 0

x = -2

and y = x + 2

y = -2 + 2 = 0

Hence, the solution of equation is at x  = -2 and y = 0.

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Answer:

24

Step-by-step explanation:

Answer:

0.0416 the six repeats

Step-by-step explanation:

.15/3.6

0.0416

the six repeats

We have the function:

We must identify the function that:

0. reflects the function across the y-axis,

1. shift it 6 units up.

1) To reflect the function across the y-axis we replace x by -x:

2) To shift the result 6 units up, we sum +6 on the right side:

Plotting both functions, we get:

Answer

Second option

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, .

A random sample taken with replacement from the original sample, and having the same size as the original sample, is known as a "bootstrap sample" or "bootstrap replication."

Bootstrapping is a resampling technique used to estimate the sampling distribution of a statistic. When we have a limited sample size and want to draw inferences about the population, we can use bootstrapping to create multiple resamples by randomly selecting observations from the original sample with replacement.

Here's how it works:

The key idea behind bootstrapping is that the original sample serves as a proxy for the population, and by repeatedly resampling from it, we can approximate the sampling distribution of the statistic of interest. This approach is especially useful when the underlying population distribution is unknown or non-normal.

By using a bootstrap sample that is the same size as the original sample, we maintain the same sample size and capture the variability present in the original data.

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Answer:

it is d

Step-by-step explanation:

Answer:

(5x+3)(x-1)

Step-by-step explanation: